Chemical Process Engineering Volume 2: Design, Analysis, Simulation, Integration, and Problem Solving with Microsoft Excel-UniSim Software for ... Process Safety, and Chemical Kinetics [2, 1 ed.] 1119853990, 9781119853992

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Volume 2 Chemical Process Engineering Design, Analysis, Simulation and Integration, and Problem Solving With Microsoft Excel – UniSim Design Software

Heat Transfer & Process Integration, Process Safety, Chemical Kinetics & Reactor Design, Engineering Economics, Optimization, Epilogue

Scrivener Publishing 100 Cummings Center, Suite 541J Beverly, MA 01915-6106

Publishers at Scrivener Martin Scrivener ([email protected]) Phillip Carmical ([email protected])

Volume 2 Chemical Process Engineering Design, Analysis, Simulation and Integration, and Problem Solving With Microsoft Excel – UniSim Design Software Heat Transfer & Process Integration, Process Safety, Chemical Kinetics & Reactor Design, Engineering Economics, Optimization, Epilogue

A. Kayode Coker and Rahmat Sotudeh-Gharebagh

This edition first published 2022 by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA and Scrivener Publishing LLC, 100 Cummings Center, Suite 541J, Beverly, MA 01915, USA © 2022 Scrivener Publishing LLC For more information about Scrivener publications please visit www.scrivenerpublishing.com. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http:// www.wiley.com/go/permissions. Wiley Global Headquarters 111 River Street, Hoboken, NJ 07030, USA For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com. Limit of Liability/Disclaimer of Warranty While the publisher and authors have used their best efforts in preparing this work, they make no rep­resentations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchant-­ability or fitness for a particular purpose. No warranty may be created or extended by sales representa­tives, written sales materials, or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further informa­tion does not mean that the publisher and authors endorse the information or services the organiza­tion, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Library of Congress Cataloging-in-Publication Data ISBN 9781119510185 Cover image: Chemical Plant - Industryviews | Dreamstime.com Cover background: Abstract Wave - Vitaliy Lesik | Dreamstime.com Cover design by Kris Hackerott Set in size of 11pt and Minion Pro by Manila Typesetting Company, Makati, Philippines Printed in the USA 10 9 8 7 6 5 4 3 2 1

Companion Web Page This 2-volume set includes access to its companion web page, from which can be downloaded useful software, spreadsheets, and other value-added products related to the books. To access it, follow the instructions below: 1. Go to https://scrivenerpublishing.com/coker_volume_two/ 2. Enter your email in the username field 3. Enter “Refining” in the password field

Gratitude To the Almighty father for providing us with the abundance of nature, so that human beings can further develop and make use of the many things in nature for our well-being and for the world. To all process/chemical engineers worldwide utilizing this abundance of nature for the good of mankind. Keep the heart of your thoughts pure, by so doing you will bring peace and be happy To honour God in all things and to perform everything solely to the glory of God Abd-ru-shin (In the Light of Truth) A. Kayode Coker

Dedication “I am always obliged to a person who has taught me a single word.” In memory of my late father and to my respected family for their endless support To engineers and scientists for their commitment to inclusion and sustainability R. Sotudeh-Gharebagh

Contents Preface xxi Acknowledgments xxiii About the Authors

xxv

8 Heat Transfer INTRODUCTION 8.1 TYPES OF HEAT TRANSFER EQUIPMENT TERMINOLOGY 8.2 DETAILS OF EXCHANGE EQUIPMENT Assembly and Arrangement CONSTRUCTION CODES THERMAL RATING STANDARDS DETAILS OF STATIONARY HEADS EXCHANGER SHELL TYPES 8.3 FACTORS AFFECTION SHELL SELECTION 8.4 COMMON COMBINATIONS OF SHELL AND TUBE HEAT EXCHANGERS AES BEM AEP CFU AKT AJW 8.5 THERMAL DESIGN 8.5.1 Temperature Difference: Two Fluid Transfer 8.5.2 Mean Temperature Difference or Log Mean Temperature Difference 8.5.3 Log Mean Temperature Difference Correction Factor, F 8.5.4 Correction for Multipass Flow through Heat Exchangers Example 8.1. Calculation of LMTD and Correction Example 8.2. Calculate the LMTD Solution Example 8.3. Heating of Glycerin in a Multipass Heat Exchanger Solution 8.6 THE EFFECTIVENESS – NTU METHOD Example 8.4. Heating Water in a Counter-Current Flow Heat Exchanger Solution Example 8.5. LMTD and ε-NTU Methods Solution Example 8.6 Solution 8.7 PRESSURE DROP, Δp 8.7.1 Frictional Pressure Drop

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x  Contents 8.7.2 Factors Affecting Pressure Drop (Δp) 630 TUBE-SIDE PRESSURE DROP, Δpf 631 SHELL-SIDE PRESSURE DROP Δpf 632 SHELL NOZZLE PRESSURE DROP (∆pnoz) 633 634 TOTAL SHELL-SIDE PRESSURE DROP, ∆ptotal 8.8 HEAT BALANCE 635 HEAT LOAD OR DUTY 636 8.9 TRANSFER AREA 636 OVER SURFACE AND OVER DESIGN 636 8.10 FOULING OF TUBE SURFACE 636 8.10.1 Prevention and Control of Gas-Side Fouling 643 8.11 EXCHANGER DESIGN 643 Overall Heat Transfer Coefficients for Plain or Bare Tubes 643 Example 8.7. Calculation of Overall Heat Transfer Coefficient from Individual Components 646 8.12 APPROXIMATE VALUES FOR OVERALL HEAT TRANSFER COEFFICIENTS 647 SIMPLIFIED EQUATIONS 662 8.12.1 Film Coefficients with Fluids Outside Tubes Forced Convection 668 0.14 VISCOSITY CORRECTION FACTOR (μ/μW) 670 HEAT TRANSFER COEFFICIENT FOR WATER, hi 670 SHELL-SIDE EQUIVALENT TUBE DIAMETER 672 SHELL-SIDE VELOCITIES 680 8.13 DESIGN AND RATING OF HEAT EXCHANGERS 681 RATING OF A SHELL AND TUBE HEAT EXCHANGER 681 8.13.1 Design of a Heat Exchanger 685 8.13.2 Design Procedure for Forced Convection Heat Transfer in Exchanger Design 686 8.13.3 Design Programs for a Shell and Tube Heat Exchanger 689 Example 8.8. Convention Heat Transfer Exchanger Design 691 8.14 SHELL AND TUBE HEAT EXCHANGER DESIGN PROCEDURE (SI UNITS) 702 TUBES 703 TUBE-SIDE PASS PARTITION PLATE 704 8.14.1 Calculations of Tube-Side Heat Transfer Coefficient 704 Example 8.9. Design of a Shell and Tube Heat Exchanger (SI Units) Kern’s Method 707 Solution 707 8.14.2 Pressure Drop for Plain Tube Exchangers 716 TOTAL TUBE-SIDE PRESSURE DROP 718 TUBE-SIDE CONDENSATION PRESSURE DROP 718 SHELL SIDE 718 718 A CASE STUDY USING UNISIM SHELL-TUBE EXCHANGER (STE) MODELER Solution 719 8.15 BELL-DELAWARE METHOD 734 OVERALL HEAT TRANSFER COEFFICIENT, U 736 SHELL-SIDE PRESSURE (Δp) 736 TUBE PATTERN 739 Accuracy of Correlations Between Kern’s Method and the Bell-Delaware Method 740 Specification Process Data Sheet, Design and Construction of Heat Exchangers 741 8.16 RAPID DESIGN ALGORITHMS FOR SHELL AND TUBE AND COMPACT HEAT EXCHANGERS: POLLEY et al. 742 8.17 FLUIDS IN THE ANNULUS OF TUBE-IN-PIPE OR DOUBLE PIPE HEAT EXCHANGER, FORCED CONVECTION 744 FINNED TUBE EXCHANGERS 745 ECONOMICS OF FINNED TUBES 745

Contents  xi

LOW-FINNED TUBES, 16 AND 19 FINS/IN. 750 FINNED SURFACE HEAT TRANSFER 751 8.17.1 Pressure Drop Across Finned Tubes 751 DESIGN FOR HEAT TRANSFER COEFFICIENTS BY FORCED CONVECTION USING RADIAL LOW-FIN TUBES IN HEAT EXCHANGER BUNDLES 751 8.17.2 Pressure Drop in Exchanger Shells Using Bundles of Low-Fin Tubes 753 TUBE-SIDE HEAT TRANSFER AND PRESSURE DROP 755 8.17.3 Double Pipe Finned Tube Heat Exchangers 755 FINNED SIDE HEAT TRANSFER 757 TUBE WALL RESISTANCE 763 TUBE-SIDE HEAT TRANSFER AND PRESSURE DROP 763 FOULING FACTOR 763 FINNED SIDE PRESSURE DROP 764 8.17.4 Design Equations for the Rating of a Double Pipe Heat Exchanger 765 Process Conditions Required 765 Inner Pipe 766 Annulus 767 Vapor Service 768 SHELL-SIDE BARE TUBE 768 SHELL SIDE (FINNED TUBE) 769 Annulus 771 8.17.5 CALCULATION OF THE PRESSURE DROP 771 EFFECT OF PRESSURE DROP (Δp) ON THE ORIGINAL DESIGN 772 NOMENCLATURE 773 Example 8.9 774 Solution 775 HEAT BALANCE 775 PRESSURE DROP CALCULATIONS 781 Tube Side 781 Tube-Side Δp 781 Shell-Side Δp 782 8.18 PLATE AND FRAME HEAT EXCHANGERS 784 Selection 788 8.19 AIR-COOLED HEAT EXCHANGERS 788 8.19.1 Induced Draft 790 8.19.2 Forced Draft 791 GENERAL APPLICATION 796 Advantages – Air-Cooled Heat Exchangers 798 Disadvantages 799 Mean Temperature Difference 801 8.19.3 Design Procedure for Approximation 801 8.19.4 Tube-Side Fluid Temperature Control 809 8.19.5 Rating Method for Air-Cooler Exchangers 811 THE AIR SIDE PRESSURE DROP, ∆pa (INCH H2O) 816 Example 8.10 817 Solution 817 8.19.6 Operations of Air-Cooled Heat Exchangers 818 8.19.7 Monitoring of Air-Cooled Heat Exchangers 819 8.20 SPIRAL HEAT EXCHANGERS 819 8.21 SPIRAL COILS IN VESSELS 821 8.22 HEAT-LOSS TRACING FOR PROCESS PIPING 821

xii  Contents Example 8.11 826 Solution 826 IN SI UNITS 827 8.23 BOILING AND VAPORIZATION 833 8.23.1 Boiling 833 8.23.2 Vaporization 837 8.23.3 Vaporization During Flow 837 8.24 HEATING MEDIA 837 Heat Fux Limit 840 8.25 BATCH HEATING AND COOLING OF FLUIDS 840 BATCH HEATING: INTERNAL COIL: ISOTHERMAL HEATING MEDIUM 840 Example 8.12. Batch Heating: Internal Coil Isothermal Heating Medium 842 Solution 842 BATCH REACTOR HEATING AND COOLING TEMPERATURE PREDICTION 842 Example 8.13: Batch Reactor Heating and Cooling Temperature Prediction 843 Solution 843 BATCH COOLING: INTERNAL COIL ISOTHERMAL COOLING MEDIUM 844 Example 8.14 Batch Cooling: Internal Coil, Isothermal Cooling Medium 845 Solution 845 BATCH HEATING: NON-ISOTHERMAL HEATING MEDIUM 846 Example 8.15: Batch Heating with Non-Isothermal Heating Medium 847 Solution 848 BATCH COOLING: NON-ISOTHERMAL COOLING MEDIUM 849 Example 8.16: Batch Cooling Non-Isothermal Cooling Medium 849 Solution 849 BATCH HEATING: EXTERNAL HEAT EXCHANGER, ISOTHERMAL HEATING MEDIUM 850 Example 8.17: Batch Heating: External Heat Exchanger Isothermal Heating Medium 853 Solution 853 BATCH COOLING: EXTERNAL HEAT EXCHANGER, ISOTHERMAL COOLING MEDIUM 854 Example 8.18: Batch Cooling: External Heat Exchanger, Isothermal Cooling Medium 854 Solution 855 BATCH COOLING: EXTERNAL HEAT EXCHANGER (COUNTER-CURRENT FLOW), NON-ISOTHERMAL COOLING MEDIUM 856 Example 8.19: Batch Cooling: External Heat Exchanger (Counter-Current Flow), Non-Isothermal Cooling Medium 856 Solution 856 BATCH HEATING: EXTERNAL HEAT EXCHANGER AND NON-ISOTHERMAL HEATING MEDIUM 857 Example 8.20: Batch Heating: External Heat Exchanger and Non-Isothermal Heating Medium 858 Solution 858 BATCH HEATING: EXTERNAL HEAT EXCHANGER (1-2 MULTIPASS HEAT EXCHANGERS), NON-ISOTHERMAL HEATING MEDIUM 859 Example 8.21: External Heat Exchanger (1-2 Multipass Heat Exchangers), Non-Isothermal Heating Medium 861 Solution 861 BATCH COOLING: EXTERNAL HEAT EXCHANGER (1-2 MULTIPASS), NON-ISOTHERMAL COOLING MEDIUM 863 Example 8.22: External Heat Exchanger (1-2 Multipass), Non-Isothermal Cooling Medium 863 Solution 864

Contents  xiii

BATCH HEATING AND COOLING: EXTERNAL HEAT EXCHANGER (2-4 MULTIPASS HEAT EXCHANGERS NON-ISOTHERMAL HEATING MEDIUM) BATCH HEATING AND COOLING: EXTERNAL HEAT EXCHANGER (2-4 MULTIPASS HEAT EXCHANGERS NON-ISOTHERMAL COOLING MEDIUM) Example 8.23: External Heat Exchanger (2-4 Multipass Exchanger), Non-Isothermal Heating Medium Example 8.24: External Heat Exchanger (2-4 Multipass Heat Exchangers), Non-Isothermal Cooling Medium HEAT EXCHANGER DESIGN WITH COMPUTERS FUNCTIONALITY PHYSICAL PROPERTIES UNISIM HEAT EXCHANGER MODEL FORMULATIONS A CASE STUDY: KETTLE REBOILER SIMULATION USING UNISIM STE NOZZLE DATA PROCESS DATA REFERENCES APPENDIX A HEAT TRANSFER 9 Process Integration and Heat Exchanger Network INTRODUCTION APPLICATION OF PROCESS INTEGRATION PINCH TECHNOLOGY HEAT EXCHANGER NETWORK DESIGN Energy and Capital Targeting and Optimization OPTIMIZATION VARIABLES OPTIMIZATION OF THE USE OF UTILITIES (UTILITY PLACEMENT) HEAT EXCHANGER NETWORK REVAMP HEAT RECOVERY PROBLEM IDENTIFICATION THE TEMPERATURE-ENTHALPY DIAGRAM (T-H) ENERGY TARGETS Construction of Composite Curves HEAT RECOVERY FOR MULTIPLE SYSTEMS Example 9.1. Setting Energy Targets and Heat Exchanger Network Solution THE HEAT RECOVERY PINCH AND ITS SIGNIFICANCE THE SIGNIFICANCE OF THE PINCH THE PLUS-MINUS PRINCIPLE FOR PROCESS MODIFICATIONS A TARGETING PROCEDURE: THE PROBLEM TABLE ALGORITHM THE GRAND COMPOSITE CURVE PLACING UTILITIES USING THE GRAND COMPOSITE CURVE STREAM MATCHING AT THE PINCH THE PINCH DESIGN APPROACH TO INVENTING A NETWORK HEAT EXCHANGER NETWORK DESIGN (HEN) The Design Grid NETWORK DESIGN ABOVE THE PINCH THE INTERMEDIATE TEMPERATURES IN THE STREAMS ARE: NETWORK DESIGN BELOW THE PINCH THE INTERMEDIATE TEMPERATURES IN THE STREAMS ARE: ABOVE THE PINCH BELOW THE PINCH

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xiv  Contents EXAMPLE 9.2 988 SOLUTION 989 DESIGN FOR THRESHOLD PROBLEMS 991 STREAM SPLITTING 993 ADVANTAGES AND DISADVANTAGES OF STREAM SPLITTING 994 EXAMPLE 9.3 994 SOLUTION 994 EXAMPLE 9.4 1002 STREAM DATA EXTRACTION 1003 SOLUTION 1003 HEAT EXCHANGER AREA TARGETS 1005 EXAMPLE 9.5 1010 SOLUTION 1010 EXAMPLE 9.6 1017 SOLUTION 1017 HEN SIMPLIFICATION 1018 HEAT LOAD LOOPS 1018 EXAMPLE 9.7. TEST CASE 3, TC3 LINNHOFF AND HINDMARCH 1019 SOLUTION 1019 HEAT LOAD PATHS 1024 NUMBER OF SHELLS TARGET 1025 IMPLICATIONS FOR HEN DESIGN 1027 CAPITAL COST TARGETS 1027 CAPITAL COST 1028 NETWORK CAPITAL COST (CC) 1028 TOTAL COST TARGETING 1028 ENERGY TARGETING 1029 1030 SUPERTARGETING OR ∆Tmin OPTIMIZATION EXAMPLE 9.8. HEN FOR MAXIMUM ENERGY RECOVERY 1030 SOLUTION 1030 SUMMARY: NEW HEAT EXCHANGER NETWORK DESIGN 1032 TARGETING AND DESIGN FOR CONSTRAINED MATCHES 1033 Process Constraints 1033 TARGETING FOR CONSTRAINTS 1033 HEAT ENGINES AND HEAT PUMPS FOR OPTIMUM INTEGRATION 1034 PRINCIPLE OF OPERATION 1034 HEAT PUMP EVALUATION 1036 APPLICATION OF A HEAT PUMP 1037 APPROPRIATE INTEGRATION OF HEAT ENGINES 1037 OPPORTUNITIES FOR PLACEMENT OF HEAT ENGINES 1038 APPROPRIATE INTEGRATION OF HEAT PUMPS 1038 OPPORTUNITIES FOR PLACEMENT OF HEAT PUMPS 1039 APPROPRIATE PLACEMENT OF COMPRESSION AND EXPANSION IN HEAT RECOVERY SYSTEMS 1040 PRESSURE DROP AND HEAT TRANSFER IN PROCESS INTEGRATION 1040 TOTAL SITE ANALYSIS 1040 APPLICATIONS OF PROCESS INTEGRATION 1045 Hydrogen Pinch Studies 1045 OXYGEN PINCH 1047 1047 CARBON DIOXIDE (CO2) MANAGEMENT MASS AND WATER PINCH 1048

Contents  xv SITE-WIDE INTEGRATION FLUE GAS EMISSIONS PITFALLS IN PROCESS INTEGRATION PINCH TO TARGET CO2 EMISSIONS PINCH TECHNOLOGY IN PETROLEUM AND CHEMICAL INDUSTRIES CONCLUSIONS INDUSTRIAL APPLICATIONS: CASE STUDIES Case Study-1: (From Gary Smith And Ajit Patel, The Chemical Engineer, P. 26, November 1987) SOLUTION Case Study-2: Crude Preheat Train Introduction Process Description Solution Above the Pinch Below the Pinch CASE STUDY-3: NETWORK FOR AROMATICS PLANT (G. T. POLLEY, AND M.H. PANJEH SHAHI, TRANS. INST. CHEME., VOL. 69, PART A, NOVEMBER 1991) Introduction Process Description STREAM DATA EXTRACTION SOLUTION GLOSSARY OF TERMS SUMMARY AND HEURISTICS HEURISTICS NOMENCLATURE REFERENCES BIBLIOGRAPHY 10 Process Safety and Pressure-Relieving Devices INTRODUCTION 10.1 TYPES OF POSITIVE PRESSURE-RELIEVING DEVICES (See Manufacturers’ Catalogs for Design Details) Pressure Relief Valve Pilot-Operated Safety Valves 10.2 TYPES OF VALVES/RELIEF DEVICES Conventional Safety Relief Valve Balanced Safety Relief Valve Special Valves 10.3 RUPTURE DISK EXAMPLE 10.1 Hypothetical Vessel Design, Carbon Steel Grade A-285, Gr C 10.4 DESIGN PRESSURE OF A VESSEL 10.5 MATERIALS OF CONSTRUCTION Safety and Relief Valves; Pressure-Vacuum Relief Values 10.6 RUPTURE DISKS GENERAL CODE REQUIREMENTS RELIEF MECHANISMS Reclosing Devices, Spring Loaded NON-RECLOSING PRESSURE-RELIEVING DEVICES PRESSURE SETTINGS AND DESIGN BASIS 10.7 UNFIRED PRESSURE VESSELS ONLY, BUT NOT FIRED OR UNFIRED STEAM BOILERS

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xvi  Contents EXTERNAL FIRE OR HEAT EXPOSURE ONLY AND PROCESS RELIEF 1112 10.8 RELIEVING CAPACITY OF COMBINATIONS OF SAFETY RELIEF VALVES AND RUPTURE DISKS OR NON-RECLOSURE DEVICES (REFERENCE ASME CODE, PAR. UG-127, U-132) 1113 Primary Relief 1113 Selected Portions of ASME Pressure Vessel Code, Quoted by Permission 1117 10.9 ESTABLISHING RELIEVING OR SET PRESSURES 1120 SAFETY AND SAFETY RELIEF VALVES FOR STEAM SERVICE 1120 10.10 SELECTION AND APPLICATION 1121 10.11 CAPACITY REQUIREMENTS EVALUATION FOR PROCESS OPERATION (NON-FIRE) 1121 INSTALLATION 1125 10.12 SELECTION FEATURES: SAFETY, SAFETY RELIEF VALVES, AND RUPTURE DISKS 1134 10.13 CALCULATIONS OF RELIEVING AREAS: SAFETY AND RELIEF VALVES 1136 10.14 STANDARD PRESSURE RELIEF VALVES RELIEF AREA DISCHARGE OPENINGS 1136 10.15 SIZING SAFETY RELIEF TYPE DEVICES FOR REQUIRED FLOW AREA AT TIME OF RELIEF 1137 10.16 EFFECTS OF TWO-PHASE VAPOR-LIQUID MIXTURE ON RELIEF VALVE CAPACITY 1137 10.17 SIZING FOR GASES OR VAPORS OR LIQUIDS FOR CONVENTIONAL VALVES WITH CONSTANT BACKPRESSURE ONLY 1137 PROCEDURE 1141 ESTABLISH CRITICAL FLOW FOR GASES AND VAPORS 1141 EXAMPLE 10.2 1144 Flow through Sharp Edged Vent Orifice 1144 10.18 ORIFICE AREA CALCULATIONS 1144 10.19 SIZING VALVES FOR LIQUID RELIEF: PRESSURE RELIEF VALVES REQUIRING CAPACITY CERTIFICATION [5d] 1148 10.20 SIZING VALVES FOR LIQUID RELIEF: PRESSURE RELIEF VALVES NOT REQUIRING CAPACITY CERTIFICATION [5d] 1149 10.21 REACTION FORCES 1152 EXAMPLE 10.3 1154 SOLUTION 1154 EXAMPLE 10.4 1156 SOLUTION 1156 10.22 CALCULATIONS OF ORIFICE FLOW AREA USING PRESSURE-RELIEVING BALANCED BELLOWS VALVES, WITH VARIABLE OR CONSTANT BACK PRESSURE 1158 10.23 SIZING VALVES FOR LIQUID EXPANSION (HYDRAULIC EXPANSION OF LIQUID-FILLED SYSTEMS/EQUIPMENT/PIPING) 1163 10.24 SIZING VALVES FOR SUBCRITICAL FLOW: GAS OR VAPOR BUT NOT STEAM [5D] 1168 10.25 EMERGENCY PRESSURE RELIEF: FIRES AND EXPLOSIONS RUPTURE DISKS 1171 10.26 EXTERNAL FIRES 1171 10.27 SET PRESSURES FOR EXTERNAL FIRES 1171 10.28 HEAT ABSORBED 1172 THE SEVERE CASE 1172 10.29 SURFACE AREA EXPOSED TO FIRE 1173 10.30 RELIEF CAPACITY FOR FIRE EXPOSURE 1175 10.31 CODE REQUIREMENTS FOR EXTERNAL FIRE CONDITIONS 1175 10.32 DESIGN PROCEDURE 1175 EXAMPLE 10.5 1176 SOLUTION 1176 10.33 RUNAWAY REACTIONS: DIERS 1179 10.34 HAZARD EVALUATION IN THE CHEMICAL PROCESS INDUSTRIES 1180 10.35 HAZARD ASSESSMENT PROCEDURES 1181 10.36 EXOTHERMS 1182

Contents  xvii 10.37 ACCUMULATION 1182 10.38 THERMAL RUNAWAY CHEMICAL REACTION HAZARDS 1183 10.39 HEAT CONSUMED HEATING THE VESSEL. THE Φ-FACTOR 1183 10.40 ONSET TEMPERATURE 1185 10.41 TIME-TO-MAXIMUM RATE 1185 10.42 MAXIMUM REACTION TEMPERATURE 1185 10.43 VENT SIZING PACKAGE (VSP) 1186 1189 10.44 VENT SIZING PACKAGE 2TM (VSP2TM) 10.45 ADVANCED REACTIVE SYSTEM SCREENING TOOL (ARSST) 1191 10.46 TWO-PHASE FLOW RELIEF SIZING FOR RUNAWAY REACTION 1191 10.47 RUNAWAY REACTIONS 1192 10.48 VAPOR PRESSURE SYSTEMS 1192 10.49 GASSY SYSTEMS 1192 10.50 HYBRID SYSTEMS 1193 10.51 SIMPLIFIED NOMOGRAPH METHOD 1193 10.52 VENT SIZING METHODS 1199 10.53 VAPOR PRESSURE SYSTEMS 1199 10.54 FAUSKE’S METHOD 1201 10.55 GASSY SYSTEMS 1202 10.56 HOMOGENEOUS TWO-PHASE VENTING UNTIL DISENGAGEMENT 1203 10.57 TWO-PHASE FLOW THROUGH AN ORIFICE 1204 10.58 CONDITIONS OF USE 1205 10.59 DISCHARGE SYSTEM 1206 Design of the Vent Pipe 1206 10.60 SAFE DISCHARGE 1206 10.61 DIRECT DISCHARGE TO THE ATMOSPHERE 1206 EXAMPLE 10.6 1207 Tempered Reaction 1207 SOLUTION 1207 EXAMPLE 10.7 1209 SOLUTION 1209 EXAMPLE 10.8 1210 SOLUTION 1210 EXAMPLE 10.9 1211 SOLUTION 1212 10.62 DIERS FINAL REPORTS 1215 10.63 SIZING FOR TWO-PHASE FLUIDS 1215 Step 1. Calculate the Saturated Omega Parameter, ωs 1215 Step 2. Determine the Subcooling Region 1216 Step 3. Determine if the Flow is Critical or Subcritical 1217 Step 4. Calculate the Mass Flux 1217 Step 5. Calculate the Required Area of the PRV 1218 SI UNITS 1218 EXAMPLE 10.10 1219 SOLUTION 1220 EXAMPLE 10.11 1222 SOLUTION 1222 TYPE 2. (OMEGA METHOD): SIZING FOR TWO-PHASE FLASHING FLOW WITH A NONCONDENSABLE GAS THROUGH A PRESSURE RELIEF VALVE 1226 EXAMPLE 10.12 1230

xviii  Contents SI UNITS EXAMPLE 10.13 SOLUTION TYPE 3 INTEGRAL METHOD EXAMPLE 10.14 SOLUTION GLOSSARY ACRONYMS AND ABBREVIATIONS NOMENCLATURE Subscripts Greek Symbols REFERENCES LISTING OF FINAL REPORTS FROM THE DIERS RESEARCH PROGRAM (DESIGN INSTITUTE FOR EMERGENCY RELIEF SYSTEMS) PROJECT MANUAL TECHNOLOGY SUMMARY SM 540 ALL/LARGE-SCALE EXPERIMENTAL DATA AND ANALYSIS BENCH-SCALE APPARATUS DESIGN AND TEST RESULTS 11 Chemical Kinetics and Reactor Design INTRODUCTION INDUSTRIAL REACTION PROCESSES Conventional Reactors Membrane Reactors Spherical Reactors Bioreactors CHEMICAL REACTIONS Conversion Type Equilibrium Type Kinetic Type IDEAL REACTORS Conversion Reactor Adiabatic Flame Temperature Heats of Reaction Equilibrium Reactor Gibbs Reactor CSTR Reactor PFR Reactor NON-IDEAL REACTORS Modular Analysis Multiscale Analysis BIOCHEMICAL REACTIONS Models of Enzyme Kinetics Constant Volume Batch Reactor CHEMICAL REACTION HAZARDS INCIDENTS Reactive Hazards Incidents Chemical Reactivity Worksheet (CRW) Protective Measures for Runaway Reactions PROBLEMS AND SOLUTIONS REFERENCES

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Contents  xix 12 Engineering Economics INTRODUCTION GROSS PROFIT ANALYSIS CAPITAL COST ESTIMATION Equipment/Plant Cost Estimations by Capacity Exponents Factored Cost Estimate Functional-Unit Estimate Percentage of Delivered Equipment Cost PROJECT EVALUATION Cash Flow Cumulated Cash Flow Return on Investment (ROI) Payback Period (PBP) Present Worth (or Present Value) Net Present Value (NPV) Discounted Cash Flow Rate of Return (DCFRR) Net Return Rate (NRR) Depreciation Double Declining Balance (DDB) Depreciation Capitalized Cost Average Rate of Return (ARR) Present Value Ratio (Present Worth Ratio) Profitability ECONOMIC ANALYSIS Inflation EXAMPLES AND SOLUTIONS Nomenclature CARBON TAX References

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13 Optimization in Chemical/Petroleum Engineering OPTIMAL OPERATING CONDITIONS OF A BOILER OPTIMUM DISTILLATION REFLUX FEATURES OF OPTIMIZATION PROBLEMS Objective Functions for Reactors LINEAR PROGRAMMING (LP) FOR BLENDING LP SOFTWARE THE EXCEL SOLVER PROBLEM SOLUTION Example 13.1 Solution Example 13.2 Solution Example 13.3 Solution A CASE STUDY: OPTIMUM REACTOR TEMPERATURE Solution Optimization of Product Blending Using Linear Programming INTRODUCTION BLENDING PROCESSES NON-LINEAR OCTANE BLENDING FORMULA

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xx  Contents

GASOLINE BLENDING Gasoline Blending Example – 3 Blend Stocks, 2 Specifications Non-Linear Programming Example 13.4 SOLUTION MATHEMATICAL FORMULATION Problem Solution Example 13.5 Solution Ethyl Corporation Model A CASE STUDY Solution NOTATION REFERENCES FURTHER REFERENCE

1388 1388 1389 1391 1391 1393 1394 1394 1394 1394 1396 1397 1402 1403 1403

Epilogue 1405 Index 1415

Preface An increased use of computational resources by engineers has greatly expedited the design of equipment and process plants in refining, and the chemical process industries. In addition, the availability of commercial and open source process simulation packages, and spreadsheets has drastically reduced the requirement of programming with high-level languages, such as BASIC, C, C++, COBOL, Java, FORTRAN and Pascal. Situations may arise where a simulation package is not readily available, too expensive or of a limited scope, in this case, hands-on tools; e.g. spreadsheets could be used to review other alternatives or develop specific programs. Furthermore, the simulation packages can be integrated with spreadsheets to enlarge their scope to equipment and process design due to the infrastructure they provide on component databases, physical property estimations and unit operations. A text-book, including the theory with equations, tables, and figures and the use of advanced tools is not readily available to the process designer. Our aim in preparing this text is to present theory, along with Excel spreadsheet and UniSim Design software programs for solving a wide range of design problems. The book will, therefore, benefit chemical/process engineers, students, technologists and practitioners in the petroleum, petrochemical, pharmaceutical, biochemical and fine chemical industries. The structured approaches are provided that can be used to solve a wide range of process engineering problems and thus analyze and simulate process equipment regularly. The process design concepts, guidelines; codes and standards are clearly important, and several excellent books and references are available to address these issues and will be cited in the book where applicable. However, these two volume-sets are unique in that to date no textbook on chemical process design and simulation has been published, which provides adequate information (theory, equations, figures, tables and programs) to enable the reader to perform robust calculations using Excel spreadsheet - UniSim Design software program. The better use of these tools in the special format shapes the core of the book as: –– Microsoft Excel® is part of the Microsoft Office. It is widely recognized as the most versatile spreadsheet for problem solving, which enables a chemical engineer to make computation and visualizations in an easiest way possible. Process engineers can use Excel spreadsheet for equipment and process design, ­modeling, simulation and optimization. Data bases and pivot tables can be easily designed with Excel spreadsheet to ease making calculations, understanding technical reports, and preparing charts and figures. –– The new improved UniSim R480 Design of Honeywell, is a smart and intuitive software; it creates thermodynamics and unit operation steady-state and dynamic models. Process simulation is a tool used to design a new process, an existing process or debottleneck, monitor process conditions, troubleshoot current operations to compare theoretical results, optimize process conditions for enhanced throughput, and to reduce energy yields, and emissions. The contents of this book have been formed over many years through the concentrated research and industrial efforts of the authors. Furthermore, to assist the user and to demonstrate the validity of the methods, worked examples and case studies of practical relevance using the Excel spreadsheet and UniSim Design software programs are provided throughout the text, and the source files are provided at the publisher website. In this way, the stu­ dents, and engineers can save time by using hands-on tools to ease the calculation and concentrate in understanding the fundamentals of the phenomena occurring in the process design sequences. These two volumes are fully extended version of the original title: Fortran Programs for Chemical Process Design, Analysis and Simulation by xxi

xxii  Preface A. Kayode Coker. In these volumes, we have provided examples in both Imperial and SI units, but we have intentionally kept most examples in Imperial units based on the following reasons: a) All problems solved in UniSim Design can be easily converted to any units of measurement and it makes no difference which unit is used. b) The use of both units is very useful from instructional viewpoint as students need to have some sort of practice with both units as the Imperial unit is still used in some countries. However, since all problems are carefully solved in Excel, the conversion is then easy, and we have also provided a conversion table to assist readers in their calculations. The book is primarily intended to serve senior students, early career engineers, university professors and practitioners, especially in the process, chemical, petrochemical, biochemical, mechanical, mining and metallurgical industries. However, other engineers, consultants, technicians and scientists concerned with various aspects of industrial design, and scale-up may also find it useful. It can be considered as a textbook to process design for senior and graduate students as well as a hands-on document for engineers at the entry level and practitioners. The content of this book can also be taught in intensive workshops in process industries.

Acknowledgments RSG wishes to express his profound gratitude to his students for reading the chapters and checking the programs. Further, he wishes to thank his current and former graduate students, Ms. Aghasi, Ms. Bakhshi and Messrs. Jabbari, Ahmadi, Moshiri, Khodabendehlou for checking the chapters and programs. Special credits are also extended to Professor Jamal Chaouki from Polytechnique de Montreal for hosting RSG for his sabbatical leave upon the completion of the book beside the main activity planned for sababtical. AKC expresses his gratitude to Ahmed Mutawa, formerly of SASREF for developing the conversion table software for the book. Thank you, Ahmed. Wherever it is required, permissions have been obtained to reproduce the works published by some organizations and companies. We acknowledge and thank the American Institute of Chemical Engineers, the Institution of Chemical Engineers (U.K.), Chemical Engineering (Mc-Graw Hill), Oil & Gas Journal, Tubular Exchanger Manufacturers’ Association, American Petroleum Institute, John Wiley & Sons, Nutter Engineering, and many other organizations that provided materials for this book. We express our gratitude to Honeywell Process Solutions for granting permission to incorporate the use of UniSim Design software simulation and many suites of software programs in the book. We wish to express our thanks to the Wiley-Scrivener team: Kris Hackerott- Graphics Designer, Bryan Aubrey – Copy editor, Myrna Ting – Typesetter and her colleagues. We are truly grateful for your professionalism, assistance and help in the production of this volume. Finally, very special thanks to Phil Carmical of Scrivener publishing company for his advice and helpful suggestions during the production of this volume. Finally, we should emphasize that process design is a creative, dynamic and challenging activity and for this reason, the design books like this one need continuous improvement with current digitalization outlook and abundant access to computation resources. We would appreciate and welcome any comments, suggestions, or feedback that you may have on this volume. A. Kayode Coker (www.akctechnology.com) A.K.C. TECHNOLOGY, U.K. Rahmat Sotudeh-Gharebagh ([email protected]) College of Engineering, University of Tehran, Iran

xxiii

About the Authors A. Kayode Coker PhD, is Engineering Consultant for AKC Technology, an Honorary Research Fellow at the University of Wolverhampton, U.K., a former Engineering Coordinator at Saudi Aramco Shell Refinery Company (SASREF) and Chairman of the Department of Chemical Engineering Technology at Jubail Industrial College, Saudi Arabia. He has been a chartered chemical engineer for more than 30 years. He is a Fellow of the Institution of Chemical Engineers, U.K., and a senior member of the American Institute of Chemical Engineers. He holds a B.Sc. honors degree in Chemical Engineering, a Master of Science degree in Process Analysis and Development and Ph.D. in Chemical Engineering, all from Aston University, Birmingham, U.K., and a Teacher’s Certificate in Education at the University of London, U.K., He has directed and conducted short courses throughout the world and has been a lecturer at the university level. His articles have been published in several international journals. He is an author of seven books in chemical engineering, a contributor to the Encylopedia of Chemical Processing and Design, Vol. 61, and a certified train – the mentor trainer. He is a Technical Report Assessor and Interviewer for chartered chemical engineers (IChemE) in the U.K. He is a member of the International Biographical Centre in Cambridge, U.K. (IBC) as Leading Engineers of the World for 2008. Also, he is a member of International Who’s Who for ProfessionalsTM and Marquis Who’s Who in the U.S. Rahmat Sotudeh-Gharebagh is currently a full Professor of Chemical Engineering at the University of Tehran (P.O. Box 11155–4563, Iran; email: [email protected]). He teaches process modeling and simulation, transport phenomena and fluidization, plant design and economics and soft skills. His research interests include computer-aided process design and simulation, fluidization, and engineering education. He holds a B.Eng. degree in chemical engineering from Iran’s Sharif University of Technology, plus a M.Sc. and a Ph.D. in Fluidization Engineering from Canada’s Polytechnique. He has been an invited Professor at Qatar University and Polytechnique de Montréal. Professor Sotudeh has more than 300 publications in major international journals and conferences, plus six books and four book chapters. He is the co-founder and Editor-in-Chief of Chemical Product and Process Modeling published by Walter de Gruyter GmbH, Germany, a Member of the Iranian Elite Foundation and an Expert Witness on the oil industry with the Iranian Expert Witness Organization and a winner of various awards and prizes.

xxv

8 Heat Transfer Introduction The escalating cost of energy in recent years has resulted in increased attention being given to conservation and efficient energy management. Other types of technology, for example, energy management and pinch technology (Chapter 9) have been employed in the energy integration of process plants and of heat exchangers, in particular. This has resulted in an improved performance of the plants at reduced operation costs. Heat transfer is perhaps the most important, as well as the most applied process, in refining, gas processing, chemical and petrochemical plants. The economics of plant operation is controlled by the effectiveness of the use and recovery of heat or cold (refrigeration). The service functions of steam, power, refrigeration supply, and the like are dictated by how these services or utilities are used within the process to produce an efficient conversion and recovery of heat. Shell and tube heat exchanger types are widely employed and generally, they are custom designed for any capacity and operating conditions, including from high vacuums to ultra-high pressures over 15,000 psig (100 MPa), from cryogenics to high temperatures ~ 2000oF (1100oC), and any temperature and pressure differences between the fluids, limited by the materials of construction. They can be designed for special operating conditions: heavy fouling, highly viscous fluids, erosion, corrosion, toxicity, multicomponent mixtures, vibration, etc. They are the most versatile exchanger types made from a variety of metals (e.g., Admiralty, copper, alloys, monel, nickel, aluminum, carbon/ stainless steel, etc.) and nonmetal materials (e.g., graphite, glass and Teflon) and in various sizes from 1ft2 (0.1m2) to 106 ft2 (105 m2). They are extensively employed as process heat exchangers in petroleum refining, petrochemicals and chemical industries; as boiler feed water heaters, phase change heat exchangers (e.g., reboilers and condensers), evaporators, steam generators, and oil coolers in power plants, in some air conditioning and refrigeration applications; in waste heat recovery applications with heat recovery from liquids and condensing fluids and in environmental control. The tube side is for corrosive, heavy fouling, scaling, hazardous, high temperature and pressure, and more expensive fluids, while the shell side is for cleaner, more viscous, lower flow rate, evaporating and condensing fluids. When a gas or vapor is used as an exchanger fluid, it is typically introduced through the shell side and viscous liquids, for which the pressure drop for flow through the tubes is high, are introduced on the shell side. Generally, shell and tube exchanger types are non-compact exchangers, and the heat-transfer area per unit volume ranges from 15 to 30 ft2/ft3 (50–100 m2/m3). Therefore, they require a considerable amount of space, support structure, capital and installation costs. As a result, they are often replaced with compact heat exchangers (e.g., plate exchangers, spiral plate heat exchangers) in those applications where the operating conditions permit it. For the equivalent cost of the shell and tube exchangers, compact heat exchangers provide high effectiveness and are more efficient in heat (energy) transfer. Although many excellent references [1–5] are available, and the technical literature contains important details of good heat transfer design principles and good approaches to equipment design, an unknown factor still enters into every design. This factor is the scale or fouling from the fluids being processed and is wholly dependent on the fluids, their temperature and velocity, and to a certain extent, the nature of the heat-transfer tube surface and its chemical composition. Due to the unknown nature of the assumptions, these fouling factors can markedly affect the design of heat transfer equipment. We shall review this aspect with others such as the pressure drop later in the chapter as these could have deleterious effects on the performance of heat exchangers resulting in high operating costs of millions of US dollars per annum. Conventional practice is presented here; however, Kern and Seaton [6] have proposed thermal concepts that may offer new approaches. A. Kayode Coker and Rahmat Sotudeh-Gharebagh. Chemical Process Engineering: Design, Analysis, Simulation and Integration, and Problem-Solving With Microsoft Excel – UniSim Design Software, Volume 2, (505–946) © 2022 Scrivener Publishing LLC

505

506  Chemical Process Engineering The most popular and reliable software packages for the design or rating of shell and tube heat exchangers are: • • • •

BJAC: U.S.-based company. HEI: Heat Exchange Institute, USA HTRI: Heat Transfer Research Institute (www.HTRI.net) USA HFTS: Heat Transfer Fluid Flow Services (HTFS programs are part of Aspen Technology’s Aspen Engineering Suite and Honeywell’s UniSim Design Suite).

Generally, the design methods and equations used by these companies and institutes are proprietary and therefore, are not provided in open literature. Tinker [7, 8] published the first detailed stream analysis method for predicting shell and tube heat transfer coefficients and pressure drop, and his model has been used as the basis for the proprietary computer methods developed by these institutes and companies. Tinker’s method is difficult and tedious to apply in manual calculations. However, it has been simplified by Devore [9, 10], using standard tolerances for commercial exchangers and only a limited number of baffle cuts. Devore presented nomographs that facilitate the application to the method in manual calculations. Mueller [11] has further simplified Devore’s method and provides an illustrative example. Bell [12, 13] provided a semi-analytical method based on research programs carried out on shell and tube exchangers at the University of Delaware, where his results accounted for the major bypass and leakage streams. This text provides the designer with a basis for manually checking the expected equations, coefficients, etc., enabling him/her to accept or reject the computed results. The text provides a basis for completely designing the process heat transfer equipment, and (except for specialized items such as fired heaters, steam boiler/generators, cryogenic equipment, and some other process requirements) and sizing (for mechanical dimensions/details, but not for pressure strength) the mechanical hardware that will accomplish this function. Additionally, the text presents research studies on fouling in shell and tube heat exchangers, and, in particular, to pre-heat trains in the refining of crude oil.

8.1 Types of Heat Transfer Equipment Terminology The chemical process industries (CPIs) require heat exchanger types to transfer heat from a hot stream to a cold stream. This heat transfer equipment must meet various codes/standards to deal with the thermal, mechanical, operational, installation and maintenance demands on the process. The optimal heat exchanger design should minimize operating costs and maximize product output. Shell and tube heat exchangers (Figures 8.1B–D) consist of a bundle of tube inside a cylindrical shell. One fluid (the tube side fluid) flows inside the tubes whilst the other fluid (the shell side fluid) flows through the shell and around the tubes. Heat is transferred across the tube wall separating the hot and cold streams. The shell type has a significant effect on the flow configuration and thermal performance of the heat exchangers. Shell and tube heat exchangers use baffles to transport heat to or from tube side process fluids by directing the shell side fluid flow. The increased structural support that baffles provide is essential to the tube stability, as they prevent the tube from sagging due to structural weight and and also minimize vibration due to cyclic flow forces. Baffles improve heat transfer at the expense of increased pressure drop. Tubesheets seal the ends of the tubes, ensuring separation between the two streams. The process engineer needs to understand the terminology of the heat-transfer equipment manufacturers in order to properly design, specify, evaluate bids, and check drawings for this equipment. The shell and tube exchanger consists of four major parts: • Front header – this is where the fluid enters the tube-side of the exchanger. It is sometimes referred to as the stationary header. • Rear header – this is where the tube-side fluid leaves the exchanger or where it is returned to the front header in exchangers with multiple tube-side passes. • Tube bundle – this comprises the tubes, tube sheets, baffles and tie rods etc., which hold the bundle together. • Shell – this contains the tube bundle.

Heat Transfer  507 The standards of the Tubular Exchanger Manufacturers Association (TEMA) [14] is the only assembly of unfired mechanical standards, including selected design details and Recommended Good Practice and is used by all reputable exchanger manufacturers in the U.S. and many manufacturers in other countries who supply U.S. plant equipment. These standards are developed, assembled, and updated by a technical committee of association members. The standards are updated and reissued every ten years. They do not designate or recommend thermal design methods or practices for specific process applications, but they do outline basic heat transfer fundamentals, and list suggested fouling factors for a wide variety of fluid or process services. The three classes of mechanical standards in TEMA are Classes R, C, and B, and they represent varying degrees of mechanical details for the designated process plant applications’ severity. The scope of standards/code designations [TEMA – 2007, 9th ed.] for mechanical design and fabrication are: RCB – Includes all classes of construction/design and are identical; shell diameter (inside) not exceeding 100 in. (2540 mm), product of nominal diameter, in. (mm) and design pressure of 100,000 psi (17.5 x 106 kPa) and maximum design pressure of 3,000 psi (20684 kPa). The intention of these parameters is to limit the maximum shell wall thickness to approximately 3 in. (76 mm), and the maximum stud diameter to approximately 4 in. (102 mm). R – Designates severe requirement of petroleum and other related processing applications. C – Indicates generally moderate requirements of commercial and general process applications. B – Specifies design and fabrication for chemical process service. RGP – Recommended Good Practice, includes topics outside the scope of the basic standards. Note: The petroleum, petrochemical, chemical, and other industrial plants must specify or select the design/fabrication code designation for their individual application as the standards do not dictate the code designation to use. Many chemical plants select the most severe designation of Class R rather than Class B primarily because they prefer a more rugged or husky piece of equipment. In accordance with the TEMA Standards, the individual vessels must comply with the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code, Section VIII, Div. 1, plus process or petroleum plant location state and area codes. The ASME Code Stamp is required by the TEMA Standards. Figures 8.1A–G and Table 8.1 from the Standards of Tubular Exchanger Manufacturers Association [14] give the nomenclature of the basic types of units. Note the nomenclature type designation code letters immediately below each illustration. These codes are assembled from Table 8.1 and Figures 8.1A–G. Many exchangers can be designed without all parts; specifically the performance design may not require (a) a floating head and its associated parts, or (b) an impingement baffle but may require a longitudinal shell side baffle (see Figures 8.1F and 8.1G). It is important to recognize that the components in Figures 8.1B–K are associated with the basic terminology regardless of the type of unit. Application and selection guides are shown in Table 8.2, Table 8.3 and Figure 8.2. Table 8.4 compares the attributes of these three classes of exchangers in order of decreasing cost and mechanical performance. Figures 8.1O and 8.1P show photographs of tube dundles with baffles, and Figure 8.1Q shows a typical shell of a shell and tube heat exchanger.

8.2 Details of Exchange Equipment Assembly and Arrangement The process design of heat exchange equipment depends to a certain extent upon the basic type of unit considered for the process and how it will be arranged together with certain details of assembly as they pertain to that particular unit. It is important to recognize that certain basic types of exchangers, as given in Table 8.2, are less expensive than others and inherently this is related to the fabrication of construction materials to resist the fluids, cleaning, future reassignment to other services, etc. The following presentation alerts the designer to the various features that should be considered. Furthermore, see Rubin [15].

508  Chemical Process Engineering FRONT END STATIONARY HEAD TYPES

REAR END HEAD TYPES

SHELL TYPES

E A

L FIXED TUBESHEET LIKE “A” STATIONARY HEAD

ONE PASS SHELL

CHANNEL AND REMOVABLE COVER

F

M FIXED TUBESHEET LIKE “B” STATIONARY HEAD

TWO PASS SHELL WITH LONGITUDINAL RAFFLE

B

N

G

FIXED TUBESHEET LIKE “N” STATIONARY HEAD

SPLIT FLOW

BONNET (INTEGRAL COVER)

P H C

OUTSIDE PACKED FLOATING HEAD

REMOVABLE TUBE BUNDLE ONLY CHANNEL INTEGRAL WITH TUBESHEET AND REMOVABLE COVER

DOUBLE SPLIT FLOW

S J

FLOATING HEAD WITH BACKING DEVICE DIVIDED FLOW

T

N

PULL THROUGH FLOATING HEAD CHANNEL INTEGRAL WITH TUBESHEET AND REMOVABLE COVER

K

KETTLE TYPE REBOILER

U U-TUBE BUNDLE

D

X W SPECIAL HIGH PRESSURE CLOSURE

CROSS FLOW

EXTERNALLY SEALED FLOATING TUBESHEET

Figure 8.1A  Nomenclature for Heat Exchanger Components. Figures 21.1A–G used by permission: Standards of Tubular Exchanger Manufacturers Association, 7th Ed., © 1988. Tubular Exchanger Manufacturers Association, Inc.

Construction Codes The American Society of Mechanical Engineers (ASME) Unfired Pressure Vessel Code [16] is accepted by almost all states as a requirement by law and by most industrial insurance underwriters as a basic guide or requirement for fabrication of pressure vessel equipment, which includes some components of heat exchangers. The code does not cover the rolling-in of tubes into tube-sheets. For steam generation or any equipment having a direct fire as the means of heating, the ASME Boiler Code [16] applies, and many states and insurance companies require compliance with this. These classes are explained in the TEMA Standards and in Rubin [17–19].

Heat Transfer  509 36

31

5

34

3

4

34

6

12

29

8

7

27

18

28

32

36

36

9

15

16 5

1

35

10

3

34

35

AES

12

11

34

13

33

17

Figure 8.1B  Floating head. (© 1988 by Tubular Exchanger Manufacturers Association, Inc.)

2

32

6

3

32

8

7

37

27

28

12

14

34

2

5

5

34

37

12

33

BEM

6

5

Figure 8.1C  Fixed tubesheet. (© 1988 by Tubular Exchanger Manufacturers Association, Inc.)

36

4

1

3

5

34

12

31

34

5

3

6

10

34

33

27

29

35

28

AEP

7

8

35

32

15

23

34

12

24

Figure 8.1D  Floating head – outside packed. (© 1988 by Tubular Exchanger Manufacturers Association, Inc.)

25

15

22

29

36

21

510  Chemical Process Engineering 3

4

36

34

1

5

34

34

31

5

6

10

12

12

8

30

35

34

27

28

7

32

35

CFU

9

33

Figure 8.1E  Removable U-bundle. (© 1988 by Tubular Exchanger Manufacturers Association, Inc.)

8

12

34

39 9

36 4

3 34 5

31

17

15

36

38

16

34 3

5

1

6 18

34 12

35

27

35

7

28

12

34

39

AKT

Figure 8.1F  Kettle reboiler. (© 1988 by Tubular Exchanger Manufacturers Association, Inc.)

34

36

4

3

5

1

8

10

3

6

34

12

28

7

12

34

35

27

35

23

34

24

26

24 23 15

12

AJW

Figure 8.1G  Divided flow – packed tubesheet. (© 1988 by Tubular Exchanger Manufacturers Association, Inc.)

34

5

1

3

36

4

Heat Transfer  511 Vapor Plus Liquid Out Top End

Liquid In

Figure 8.1H  Fixed tubesheet, single – tube pass vertical heater or reboiler (Used by permission: Engineers & Fabricators, Inc. Houston).

SEAL STRIP

CHANNEL

CHANNEL

BAFFLE CUT SECTION A-A

Figure 8.1I  Floating head, removable type. (Used by permission: Yuba Heat Transfer Division of Connell Limited Partnership.)

Figure 8.1J  Split – ring removable floating head, four – pass tube – side and two – pass shell side. (Used by permission: Engineers & Fabricators, Inc., Houston.)

512  Chemical Process Engineering

CHANNEL

CHANNEL

Figure 8.1K  U-tube exchanger. (Used by permission: Yuba Heat Transfer Division of Connell Limited Partnership.)

Figure 8.1L  A shell and tube heat exchanger showing an inlet nozzle on the shell – side in preparation for pressure testing.

Figure 8.1M  Reactor effluent vertical shell and tube heat exchangers in series of a hydrocracking unit.

Heat Transfer  513

Figure 8.1N  A shell and tube heat exchanger showing the nozzles on the shell and tube sides and nozzles at the rear end.

Figure 8.1O  Heat exchanger tube bundles with baffles.

Figure 8.1P  A tube bundle with segmental baffles.

Thermal Rating Standards The TEMA Code [14] does not recommend thermal design or rating of heat exchangers. This is left to the rating or design engineer, because many details are associated uniquely with individual applications. TEMA does offer some common practice rating charts and tables, along with some tabulations of selected petroleum and chemical physical property data in the sixth (1978), seventh (1988), eighth (1999) and ninth (2007) editions.

Details of Stationary Heads Many combinations of front header, shell and rear header can be made, although essentially there are three main combinations:

514  Chemical Process Engineering

Figure 8.1Q  Shell – side of a shell and tube heat exchanger.

Table 8.1  Standard TEMA heat exchanger terminology/nomenclature*. 1. Stationary Heat – Channel 2. Stationary Heat – Bonnet 3. Stationary Heat Flange – Channel Bonnet 4. Channel Cover 5. Stationary Head Nozzle 6. Stationary Tubesheet 7. Tubes 8. Shell 9. Shell Cover 10. Shell Flange – Stationary Head End 11. Shell Flange – Rear head End 12. Shell Nozzle 13. Shell Cover Flange 14. Expansion Joint 15. floating Tubesheet 16. Floating Head Cover 17. Floating head Cover Flange 18. Floating Head Backing Device 19. Split Shear Ring 20. Slip-on Backing Flange

21. Floating Heat Cover – External 22. Floating Tubesheet Skirt 23. Packing Box 24. Packing 25. Packing Gland 26. Lantern Ring 27. Tierods and Spacers 28. Transverse Baffles or Support Plates 29. Impingement Plate 30. Longitudinal Baffle 31. Pass Partition 32. Vent Connection 33. Drain Connection 34. Instrument Connection 35. Support Saddle 36. Lifting Lug 37. Support Bracket 38. Weir 39. Liquid Level Connection

*Key to Figures 10.1B-G. See Figure 10.1A for Nomenclature Code. Used by permission: Standards of Tubular Exchanger Manufacturers Association, 7th Ed., Table N-2, © 1988, Tubular Exchanger Manufacturers Association, Inc. All rights reserved.

• Fixed tubesheet exchangers. • U-tube exchangers. • Floating header exchangers. Fixed tubesheet exchangers: In a fixed tubesheet exchanger, the tubesheet is welded to the shell that results in a simple and economic construction in which the tube bores can be cleaned either mechanically or chemically. However, the outside surfaces of the tubes are inaccessible except to chemical cleaning. If large temperature differences occur between the shell and the tube materials, it may be necessary to incorporate expansion bellows in the shell to eliminate excessive stresses caused by the expansion. However, such bellows are often a source of weakness and may result in failure in operation. In circumstances where the consequences of failure are problematic, U-tube or floating header units are normally used. U-tube exchangers: In a U-tube exchanger, any of the front header types may be used and the rear header is normally an M-type. The U-tubes permit unlimited thermal expansion, the tube bundle can be removed for cleaning,

Figure no.

8.1C 8.1H

8.1B 8.1D 8.1G 8.1I 8.1J

8.1E 8.1K

8.1F

Type designation

Fixes Tube Sheet

Floating Heat or Tubesheet (removable and nonremovable bundles)

U-Tube; U-Bundle

Kettle

Tube bundle removable as U-type or floating head. Shell enlarged to allow boiling and vapor disengaging.

Only one tubesheet required. Tubes bent in U-shape. Bundle is removable.

One tubesheets “floats” in shell or with shell, tube bundle may or may not be removable from shell, but back cover can be removed to expose tube ends.

Both tubesheets Fixed to shell

Significant feature

Table 8.2  Selection guide heat exchangers types.

Boiling fluid on shell side, as refrigerant, or process fluid being vaporized. Chilling or cooling of tube-side fluid in refrigerant evaporation on shell side.

For horizontal installation. Physically large or other applications.

Bends must be carefully made, or mechanical damage and danger of rupture can result. Tube side velocities can cause erosion of inside of bends. Fluids should be free of suspended particles.

Internal gaskets offer danger of leaking. Corrosiveness of fluids on shellside floating parts. Usually confined to horizontal units.

High temperature differentials, above about 200°F extremes; dirty fluids requiring cleaning of inside as well as outside of shell, horizontal or vertical.

High temperature differentials, which might require provision for expansion in fixed tube units. Clean service or easily cleaned conditions on both tube side and shell side. Horizontal or vertical

Temperature difference at extremes of about 200°F due to differential expansion.

Limitations

Condensers; liquidliquid; Gas-gas; gas-liquid; cooling and heating, horizontal or vertical reboiling.

Applications best suited

1.2–1.4

0.9–1.1

1.28

1.0

(Continued)

Approximate relative cost in carbon steel construction

Heat Transfer  515

Figure no.

8.4A 8.4B 8.4C 8.4D

8.5A 8.5B

8.5A 8.5B

Type designation

Double Pipe

Pipe Coil

Open Tube Sections (water cooled)

Tubes require no shell, only end headers, usually long, water sprays over surface, sheds scales on outside tubes by expansion and contraction. Can also be used in water box.

Pipe Coil for submersion in coil-box of water or sprayed with water is simplest type of exchanger.

Each tube has own shell forming annular space for shell-side fluid. Usually use externally finned tube.

Significant feature

Table 8.2  Selection guide heat exchangers types. (Continued)

Condensing, relatively low heat loads on sensible transfer.

Condensing, or relatively low heat loads on sensible transfer.

Relatively small transfer area service, or in banks for larger applications. Especially suited for high pressures in tube (greater than 400 psig).

Applications best suited

Transfer coefficient is low, takes up less space than pipe coil.

Transfer coefficient is low, requires relatively large space if heat load Is high.

Services suitable for finned tube. Piping-up a large number often requires cost and space.

Limitations

0.8–1.1

0.5–0.7

0.8–1.4

(Continued)

Approximate relative cost in carbon steel construction

516  Chemical Process Engineering

Figure no.

8.6

8.7A 8.7B 8.7C

8.8

8.9A 8.9B 8.9C 8.9D

Type designation

Open Tube Sections (air cooled); Plain or finned Tubes

Plate and Frame

Small-tube Teflon

Spiral

Compact, concentric plates; no bypassing, high turbulence.

Chemical resistance of tubes; no tube fouling.

Composed of metalformed thin plates separated by gaskets. Compact, easy to clean.

No shell required, only end headers similar to water units.

Significant feature

Table 8.2  Selection guide heat exchangers types. (Continued)

Cross-flow, condensing, heating.

Clean fluids, condensing, cross-exchange.

Viscous fluids, corrosive fluids slurries, high heat transfer.

Condensing, high-level heat transfer.

Applications best suited

2.0–4.0

0.8–1.5

Process corrosion, suspended materials.

0.8–1.5

0.8–1.8

Approximate relative cost in carbon steel construction

Low heat transfer coefficient.

Not well suited for boiling or condensing; limit 350-500°F by gaskets. Used for liquid-liquid only; not gas-gas.

Transfer coefficient is low, if natural convection circulation, but is improved with forced air flow across tubes.

Limitations

Heat Transfer  517

Table 8.3  Characteristics of tubing.

12 13 14 15 16 17 18 19 20

⅝

Tube O.D. Inches

16 18 20 22

Thickness In.

½

0.109 0.095 0.083 0.072 0.065 0.058 0.049 0.042 0.035

0.065 0.049 0.035 0.028

Internal Area In2 0.1301 0.1486 0.1655 0.1817 0.1924 0.2035 0.2181 0.2299 0.2419

0.1075 0.1269 0.1452 0.1548

0.0603 0.0731 0.0799 0.0860

0.1636 0.1636 0.1636 0.1636 0.1636 0.1636 0.1636 0.1636 0.1636

0.1309 0.1309 0.1309 0.1309

0.0982 0.0982 0.0982 0.0982

0.1066 0.1139 0.1202 0.1259 0.1296 0.1333 0.1380 0.1416 0.1453

0.0969 0.1052 0.1126 0.1162

0.0725 0.0798 0.0835 0.0867

0.601 0.538 0.481 0.426 0.389 0.352 0.302 0.262 0.221

0.302 0.236 0.174 0.141

0.171 0.127 0.104 0.083

0.407 0.435 0.459 0.481 0.495 0.509 0.527 0.541 0.555

0.370 0.402 .0430 0.444

0.277 0.305 0.319 0.331

0.194 0.206 0.214 0.218

0.0061 0.0057 0.0053 0.0049 0.0045 0.0042 0.0037 0.0033 0.0028

0.0021 0.0018 0.0014 0.0012

0.00068 0.00055 0.00046 0.00038

0.00012 0.00010 0.00071 0.00065

0.0197 0.0183 0.0170 0.00156 0.0145 0.0134 0.0119 0.0105 0.0091

0.0086 0.0071 0.0056 0.0046

0.0036 0.0029 0.0025 0.0020

0.0791 0.0810 0.0823 0.0829

0.1865 0.1904 0.1939 0.1972 0.1993 0.2015 0.2044 0.2067 0.2090

0.1555 0.1604 0.1649 0.1672

0.1166 0.1208 0.1231 0.1250

0.0791 0.0810 0.0823 0.0829

203 232 258 283 300 317 340 359 377

168 198 227 241

94 114 125 134

46 52 56 58

Constant C**

0.049 0.035 0.028 0.022

Ft2 External Surface Per Ft Length

18 20 22 24

Ft2 Internal Surface Per Ft Length

⅜

Weight Per Ft Length Steel Lb* 0.066 0.054 0.045 0.040

Tube I.D. In.

0.0508 0.0539 0.0560 0.0571

Moment of Inertia In.4

0.0654 0.0654 0.0654 0.0654

Section Modulus In.3

0.0296 0.0333 0.0360 0.0373

Radius of Gyration In.

0.028 0.022 0.018 0.016

1.536 1.437 1.362 1.299 1.263 1.228 1.186 1.155 1.126

1.351 1.244 1.163 1.126

1.354 1.230 1.176 1.133

1.289 1.214 1.168 1.147

O.D. I.D.

22 24 26 27

B.W.G. Gage

(Continued)

0.177 0.158 0.141 0.125 0.114 0.103 0.089 0.077 0.065

0.0888 0.0694 0.0511 0.0415

0.0502 0.0374 0.0305 0.0244

0.0195 0.0158 0.0131 0.0118

Transverse Metal Area In.2

¼

518  Chemical Process Engineering

Table 8.3  Characteristics of tubing. (Continued)

Internal Area In2

Thickness In.

Tube O.D. Inches

0.134 0.120 0.109 0.095 0.083 0.072 0.065 0.058 0.049 0.035

0.2894 0.3167 0.3390 0.3685 0.3948 0.4197 0.4359 0.4525 0.4742 0.5090

Ft2 External Surface Per Ft Length

10 11 12 13 14 15 16 17 18 20

0.2291 0.2291 0.2291 0.2291 0.2291 0.2291 0.2291 0.2291 0.2291 0.2291

Ft2 Internal Surface Per Ft Length

⅞

0.1589 0.1662 0.1720 0.1793 0.1856 0.1914 0.1950 0.1987 0.2034 0.2107

Weight Per Ft Length Steel Lb* 1.062 0.969 0.893 0.792 0.703 0.618 0.563 0.507 0.433 0.314

0.607 0.635 0.657 0.685 0.709 0.731 0.745 0.759 0.777 0.805

0.482 0.510 0.532 0.560 0.584 0.606 0.620 0.634 0.652 0.680

Tube I.D. In.

0.833 0.808 .0747 0.665 0.592 0.522 0.476 0.429 0.367 0.268 0.0221 0.0208 0.0196 0.0180 0.0164 0.0148 0.137 0.0125 0.0109 0.0082

0.0129 0.0122 0.0116 0.0107 0.0098 0.0089 0.0083 0.0076 0.0067 0.0050

Moment of Inertia In.4

0.1262 0.1335 0.1393 0.1466 0.1529 0.1587 0.1623 0.1660 0.1707 0.1780 0.0505 0.0475 0.0449 0.0411 0.0374 0.0337 0.0312 0.0285 0.0249 0.0187

0.0344 0.0326 0.0309 0.0285 0.0262 0.0238 0.0221 0.0203 0.0178 0.0134

Section Modulus In.3

0.1963 0.1963 0.1963 0.1963 0.1963 0.1963 0.1963 0.1963 0.1963 0.1963

0.2662 0.2703 0.2736 0.2778 0.2815 0.2850 0.2873 0.289 0.2925 0.2972

0.2229 0.2267 0.2299 0.2340 0.2376 0.2411 0.2433 0.2455 0.2484 0.2531

Radius of Gyration In.

0.1825 0.2043 0.2223 0.2463 0.2679 0.2884 0.3019 0.3157 0.3339 0.3632

451 494 529 575 616 655 680 706 740 794

285 319 347 384 418 450 471 492 521 567

Constant C**

0.134 0.120 0.109 0.095 0.083 0.072 0.065 0.058 0.049 0.035

1.442 1.378 1.332 1.277 1.234 1.197 1.174 1.153 1.126 1.087

1.556 1.471 1.410 1.339 1.284 1.238 1.210 1.183 1.150 1.103

O.D. I.D.

10 11 12 13 14 15 16 17 18 20

B.W.G. Gage

(Continued)

0.312 0.285 0.262 0.233 0.207 0.182 0.165 0.149 0.127 0.092

0.259 0.238 0.219 0.195 0.174 0.153 0.140 0.126 0.108 0.079

Transverse Metal Area In.2

¾

Heat Transfer  519

Table 8.3  Characteristics of tubing. (Continued)

Internal Area In2

Thickness In.

Tube O.D. Inches

0.180 0.165 0.134 0.120 0.109 0.095 0.083 0.065 0.049 0.035

0.6221 0.6648 0.7574 0.8012 0.8365 0.8825 0.9229 0.9852 1.0423 1.0936

Ft2 External Surface Per Ft Length

7 8 10 11 12 13 14 16 18 20

0.3272 0.3272 0.3272 0.3272 0.3272 0.3272 0.3272 0.3272 0.3272 0.3272

Ft2 Internal Surface Per Ft Length

1¼

0.2330 0.2409 0.2571 0.2644 0.2702 0.2775 0.2838 0.2932 0.3016 0.3089

Weight Per Ft Length Steel Lb* 2.059 1.914 1.599 1.450 1.330 1.173 1.036 0.824 0.629 0.455

0.890 0.920 0.982 1.010 1.032 1.060 1.084 1.120 1.152 1.180

0.670 0.732 0.760 0.782 0.810 0.834 0.856 0.870 0.902 0.930

Tube I.D. In.

1.473 1.241 1.129 1.038 0.919 0.814 0.714 0.650 0.498 0.361 0.0890 0.0847 0.0742 0.0688 0.0642 0.0579 0.0521 0.0426 0.0334 0.0247

0.0392 0.0350 0.0327 0.0307 0.0280 0.0253 0.0227 0.0210 0.0166 0.0124

Moment of Inertia In.4

0.1754 0.1916 0.1990 0.2047 0.2121 0.2183 0.2241 0.2278 0.2361 0.2435 0.1425 0.1355 0.1187 0.110 0.1027 0.0926 0.0833 0.0682 0.0534 0.0395

0.0784 0.0700 0.0654 0.0615 0.0559 0.0507 0.0455 0.0419 0.0332 0.0247

Section Modulus In.3

0.2618 0.2618 0.2618 0.2618 0.2618 0.2618 0.2618 0.2618 0.2618 0.2618

0.3836 0.3880 0.3974 0.4018 0.4052 0.4097 0.4136 0.4196 0.4250 0.4297

0.3009 0.3098 0.3140 0.3174 0.3217 0.3255 0.3291 0.3314 0.3367 0.3414

Radius of Gyration In.

0.3526 0.4208 0.4536 0.4803 0.5153 0.5463 0.5755 0.5945 0.6390 0.6793

970 1037 1182 1250 1305 1377 1440 1537 1626 1706

550 656 708 749 804 852 898 927 997 1060

Constant C**

0.165 0.134 0.120 0.109 0.095 0.083 0.072 0.065 0.049 0.035

1.404 1.359 1.273 1.238 1.211 1.179 1.153 1.116 1.085 1.059

1.493 1.366 1.316 1.279 1.235 1.199 1.168 1.149 1.109 1.075

O.D. I.D.

8 10 11 12 13 14 15 16 18 20

B.W.G. Gage

(Continued)

0.605 0.562 0.470 0.426 0.391 0.345 0.304 0.242 0.185 0.134

.0433 0.365 0.332 0.305 0.270 0.239 0.210 0.191 0.146 0.106

Transverse Metal Area In.2

1

520  Chemical Process Engineering

Table 8.3  Characteristics of tubing. (Continued)

Internal Area In2

Thickness In.

Tube O.D. Inches

B.W.G. Gage 2.4328 2.4941 2.5730 2.6417

0.5236 0.5236 0.5236 0.5236

0.4608 0.4665 0.4739 0.4801

2.412 2.204 1.935 1.701

1.760 1.782 1.810 1.834

0.3144 0.2904 0.2586 0.2300

0.1354 0.1159 0.0931 0.0756 0.3144 0.2904 0.2586 0.2300

0.1806 0.1545 0.1241 0.1008

0.6660 0.6697 0.6744 0.6784

0.1853 0.4933 0.5018 0.5079

3795 3891 4014 4121

1860 2014 2180 2300

in. ft per see (sp. Gr. Of water at 60°F = 1.0)

1.136 1.122 1.105 1.091

1.218 1.170 1.124 1.095

0.709 0.648 0.569 0.500

0.575 0.476 0.369 0.293

Used by permission: Standards of the Tubular Exchanger Manufacturers Association, 7th Ed., Table D-7, © 1988. Tubular Exchanger Manufacturers Association, Inc. All rights reserved.

lb per tube hour **Liquid Velocity = C X sp. gr. of liquid

Aluminum 0.35 A.I.S.I. 300 Series S/Steels 1.02 Nickel-Chrome-Iron 1.07 Nickel-Copper 1.12 Titanium 0.58 Aluminum Bronze 1.04 Admiralty 1.09 Copper and Cupro-Nickels 1.14 A.I.S.I. 400 Series S/Steels 0.99 Aluminum Brass 1.06 Nickel 1.13

* Weights are based on low carbon steel with a density of 0.2836 lb/in.3 For other metals multiply by the following factors:

0.120 0.109 0.095 0.083

Ft2 External Surface Per Ft Length

11 12 13 14

Ft2 Internal Surface Per Ft Length

2

Weight Per Ft Length Steel Lb* 1.232 1.282 1.334 1.370

Tube I.D. In.

1.957 1.621 1.257 0.997

Moment of Inertia In.4

0.3225 0.3356 0.3492 0.3587

Section Modulus In.3

0.3927 0.3927 0.3927 0.3927

Radius of Gyration In.

1.1921 1.2908 1.3977 1.4741

Constant C**

0.134 0.109 0.083 0.065

O.D. I.D.

10 12 14 16

Transverse Metal Area In.2

1½

Heat Transfer  521

522  Chemical Process Engineering Shell and tube Exchangers Severe thermal expansion stresses

No

Yes Are bellows allowed?

Yes Is chemical cleaning possible?

No

Yes

High tube side fouling factor > 0.00035 W/m2.K

Removable bundle design

Is inter-stream leakage allowed?

No Are pressure and temp. within TEMA For the W?

Frequency of bundle removal

LOW

HIGH

Yes

Yes

High shell side fouling factor > 0.00035 W/m2.K

No Yes Fixed tubesheet

No No No

Is chemical cleaning possible?

Yes

Yes No

Number of passes > 2

Are ‘F’ shells or multi-allowed?

Yes

Is FT in unacceptable region?

No

Yes Is there a high tube side fouling factor (< 0.00035 W/m2.K) ? No

Yes

Yes No

AES

No No

BES

No

Yes

Yes

No

AET BET

No

Yes

No

Yes

Is tube access required without disturbing pipework? Yes Yes No No No No No AEW AEP BEW

No

Yes

Yes AEU AFU

No

Yes

No

Yes AEL AEM

No

BEM

BEU BFU

BED

No

Figure 8.2  Selection chart for choice of heat exchange configuration (see Figure 8.1 for definition of types) (Source: Linnhoff, B. et al., User guide on process integration for the efficient use of energy, IChemE., 1996).

Table 8.4  Comparison of TEMA class R, C and B heat exchangers (Cost decreases from left to right) [145]. Attribute

Class R

Class C

Class B

Application

Generally severe requirements such as petroleum and related processing applications

Generally moderate requirements such as commercial and general process applications

General process service

Corrosion allowance on carbon steel

0.125 in. (3.2 mm)

0.0625 in. (1.6mm)

0.0625 in. (1.6mm)

Tube diameters, OD

¾, 1, 1¼ ,1½, and 2 in.

R + ¼, 3/8, ½, and 5/8 in.

R +5/8 in.

Tube pitch and minimum cleaning lane

1.25 x tube OD ¼ inch lane

R + 3/8 tubes may be located 1.2 x tube OD

R + lane may be 3/16 inch in 12 inch and smaller shells for 5/8 and ¾ in tubes

Minimum shell diameter

8 inch, tabulated

6 inch, tabulated

6 inch tabulated

Longitudinal baffle thickness

¼ inch minimum

1/8 inch alloy, ¼ inch carbon steel

1/8 inch alloy, ¼ inch carbon steel (Continued)

Heat Transfer  523 Table 8.4  Comparison of TEMA class R, C and B heat exchangers (Cost decreases from left to right) [145]. (Continued) Attribute

Class R

Class C

Class B

Floating head cover crossover area

1.3 x tube flow area

Same as tube flow area

Same as tube flow area

Lantern ring construction

375oF maximum 300 psi up to 24 inch diameter shell 150 psi for 25 to 42 in. 75 psi for 43 to 60 in.

600 psi maximum

375oF maximum 300 psi up to 24 inch diameter shell 150 psi for 25 to 42 in. 75 psi for 43 to 60 in.

Gasket materials

Metal jacketed or solid metal for a) internal floating head cover, b) 300 psi and up, c) all hydrocarbons

Metal jacketed or solid metal for a) internal floating head b) 300 psi and up

Metal jacketed or solid metal for a) internal floating head b) 300 psi and up

Peripheral gasket contact surface

Flatness tolerance specified

No tolerance specified

No tolerance specified

Minimum tubesheet thickness with expanded tube joints

Outside diameter of the tube

0.75 x tube OD for 1 inch and smaller 1/8 inch for 1¼ OD 1 inch for 1½ OD 1.25 inch for 2 OD

0.75 x tube OD for 1 inch and smaller 1/8 inch for 1¼ OD 1 inch for 1½ OD 1.25 inch for 2 OD

Tube hole grooving

Two grooves

Above 300 psi design pressure or 350oF design temperature:2 grooves

Two grooves

Length of expansion

Smaller of 2 inch or tubesheet thickness

Small of 2 x tube OD or 2 inch

Smaller of 2 inch or tubesheet thickness

Tubesheet pass partition grooves

3/16 inch deep grooves required

Over 300 psi; 3/16 inch deep grooves required or other suitable means for retaining gaskets in place

Over 300 psi; 3/16 inch deep grooves required or other suitable means for retaining gaskets in place

Pipe tap connections

6000 psi coupling with bar stock plug

3000 psi coupling

3000 psi coupling with bar stock plug

Pressure gage connections

Required in nozzles 2 inch and up

Specified by purchaser

Required in nozzles 2 inch and up

Thermometer connections

Required in nozzles 4 inch and up

Specified by purchaser

Required in nozzles 4 inch and up

Nozzle construction

No reference to flanges

No reference to flanges

All nozzles larger than one inch must be flanged

Minimum bolt size

¾ inch

½ inch recommended; smaller bolting may be used

5/8 inch

524  Chemical Process Engineering and small bundle to shell clearances can be achieved. However, since internal cleaning of the tubes by mechanical means is difficult, it is normal only to use this type where the tube-side fluids are clean. Floating head exchanger: In this exchanger type, the tubesheet at the rear header end is not welded to the shell but allowed to move or float. The tubesheet at the front header (tube-side fluid inlet end) is of a larger diameter than the shell and is sealed in a similar manner to that used in the fixed tubesheet design. The tubesheet at the rear header end of the shell is of slightly smaller diameter than the shell, allowing the bundle to be pulled through the shell. The use of a floating head means that thermal expansion can be allowed for, and the tube bundle can be removed for cleaning. There are several rear header types that can be used, but the S-type rear header is the most popular. A floating head exchanger is suitable for the rigorous duties associated with high temperatures and pressures, but is more expensive (typically of order of 25% for carbon steel construction) than the equivalent fixed tubesheet exchanger. Figure 8.1A shows, the heat exchanger components and the front end shows the stationary head types as follows: The A type head has flanges on both ends. One attaches to a cover which may be removed for cleaning the tubes without disturbing the pipe work. The other attaches to the shell flange so that the head can be removed when it is necessary to remove the bundle. The B type is designated as the bonnet with only one flange. This attaches to the shell flange, and the pipe work must be detached for cleaning the tubes or withdrawing the bundle to clean the shell side. The C type has a channel which is integral with the tube sheet. Earlier editions of TEMA had no stationary N type head, and C was being used for fixed tube sheet exchangers. Type C is not often used other than for high pressures typically in excess of 1450 psi (100 bar). The N type has a channel, which is integral with both the tube sheet and the shell. The removable cover allows the tubes to be cleaned without disturbing the pipe work. The elimination of the shell flanges reduces the cost. Type N can sometimes be more economical than type A; however, there are often difficulties in manufacturing and maintenance. Type D is a special enclosure for high pressure tube-side fluids, typically in excess of 2175 psi (150 bar). Type Y (not in Figure 8.1A) is used when the exchanger is to be inserted in a pipeline and therefore, minimizes piping costs. It is sometimes referred to as a “cone-type” head. It is limited to a single pass on the tube-side or with suitable partitioning, any odd number of tube side passes.

Exchanger Shell Types The type of shell of an exchanger should often be established before thermal rating of the unit takes place. The shell is always a function of its relationship to the tube sheet and the internal baffles. Figures 8.1, 8.3 and 8.4 summarize the usual types of shells; however, remember that other arrangements may satisfy a particular situation. The heads attached to the shells may be welded or bolted as shown in Figure 8.4. Figure 8.1L shows a shell and tube heat exchanger of a refinery unit in preparation for pressure testing, and Figure 8.1M shows vertical shell and tube heat exchangers in series of a hydrocracking unit. Many other arrangements may be found in references [20–22]. The E type is the most common arrangement used in shell and tube heat exchangers. There are two shell-side nozzles, and each is positioned as close to its adjacent head as is mechanically possible. The shell-side fluid may enter from either end, and either nozzle may be at the top or bottom. Sometimes, a nozzle may be at the side, and both could be at the top or the bottom depending upon the process requirements. The E type is such that the shell side fluid enters from one end of the shell and leaves at the opposite end. The F type shell has both the shell nozzles at the stationary head end and a longitudinal baffle that divides the shell into two passes. The shell-side fluid enters from one end, traverses the entire length of the exchanger through onehalf of the shell cross-sectional area, turns around and flows through the second pass, then finally leaves at the end of the second pass. The two passes on the tube-side provide an arrangement for a counter-current flow with all the advantages. There are multiple possible even numbers of tube-side passes. However, for two or more passes, the thermal arrangement becomes the equivalent of having two shells in series. An F shell can often yield a comparable

Heat Transfer  525 Fixed Tube Sheet

Removable Tube Sheet

Shell with Expansion Joint Tube Sheets Fixed Both Ends Single Shell Pass

Two Shell Passes with or without Expansion Joint. (Expansion Joint Complicates)

Divided Shell Pass

U-Bundle Shell Single Shell Pass

Floating Tube Sheet Single Shell Pass

U-Bundle Two Shell Passes

Floating Tube Sheet Two Shell Passes

Vapor

Fixed or Removable Tube Sheets Vapor

Liquid Kettle Evaporator U-Bundle or Floating Tube Sheet Single Shell Pass

Liquid Evaporator or Chiller

Exchanger with Inlet Vapor Distributor

Floating Tube Sheet Single Shell Pass (can be Two Shell Pass)

Vapor

Liquid

Divided Flow Two Shell Passes Each Section

Kettle Reboiler U-Bundle or Floating Tube Sheet Single Shell Pass

Figure 8.3  Typical shell types.

shell side velocity and heat transfer area. By virtue of being a single shell, it can have lower operating costs than two E shells in series. There is also a reduction in piping cost, and the subordinate overall vertical height can be an advantage in many situations. Its limitation is the potential for leakage of the shell-side stream from the inlet pass to the outlet pass across the longitudinal baffle, and the consequent deterioration in performance due to the loss in shell-side performance and the loss in mean temperature difference (MTD). Thermal leakage is usually not appreciable unless the temperature difference between the shell-side inlet and outlet temperatures is high. With a high-temperature difference, thermal leakage can be avoided by providing a little extra heat transfer area. Another option is to employ an insulated longitudinal baffle if thermal leakage is prominent [23]. Employing eight to ten pairs of thin stainless steel strips pressing against the longitudinal baffle in the first inlet pass can minimize the leakage. The strips are prone to damage when such a tube bundle is removed from the shell; therefore, they should be replaced every time the tube bundle is taken out during turnaround. In order to minimize the physical leakage across the longitudinal baffle of an F shell, some licensors specify a maximum pressure drop of 4.978 lbf/in2 (0.35 kgf/cm2) on the shell-side. This is because the higher the shell-side pressure drop, the greater will be the tendency of the shell-side stream to leak across the longitudinal baffle. Therefore, limiting the permissible shell-side pressure drop is good engineering practice (GEP), although 4.978 lbf/in2 (0.35 kgf/cm2) might be somewhat conservative and 7.11 lbf/in2 (0.5 kgf/cm2) may be more realistic. Therefore, for services with a low allowable

526  Chemical Process Engineering Stationary Heads Bonnet Heads

Channel Heads Bolted Cover Plate

Single Pass

(Even Number Passes)

Double Pass

(Bolted to Shell Flange or Tube Sheet)

Welded to Tube Sheet

Bolted to Shell Flange or Tube Sheet

Return Heads and End Covers Bonnet Types If (a) to Shell, U-Bundle or Floating Tube Sheet Inside. (b) to Tube Sheet, Pass Partitions only as Needed.

Channel Types

Welded to Shell or to Stationary Tube Sheet

Tube Sheet Packed Against Shell

See Welded Example

Bolted to Shell Packing Gland at Tube Sheet

Bolted to Shell or to Stationary Tube Sheet

Welded or Bolted to Shell to Serve in Same Designs as Bonnet Types (except for Single Tube Pass with Expansion)

Floating Tube Sheet Shell Cover Bolted to Shell. Floating Head Cover Bolted to Tube Sheet or its Backing Ring.

Shell Cover Bolted to Shell. Floating Head Cover Bolted to Tube Sheet or its Backing Ring. Expansion of Tube Bundle Provided by External Packing Gland or by Internal Bellows on Outlet Nozzle (not shown). For Single Pass Tube Bundle.

Figure 8.4  Typical heads and closures.

shell-side pressure drop that conforms to either of the conditions described, (temperature cross and low shell-side flow rate), the use of an F shell is preferable, as reactor feed/bottom exchangers with condensation and/or vaporization provide good examples [23]. The F shell is used for temperature-cross situations where the cold stream leaves at a temperature higher than the outlet temperature of the hot streams. If a two-pass F shell has only two tube passes, this becomes a true counter-current arrangement in which a large temperature cross can be achieved. Rozenman and Taborek studied the effect of leakage through the longitudinal baffle on the performance of two-pass shell exchangers. However, if a U-tube exchanger is acceptable, a long baffle can be welded to the shell if four or eight tube passes are used, as this would eliminate the physical leakage problem and thus limit the shell-side pressure drop [24]. The G type shell has central nozzles at the top and the bottom of the exchanger. The shell-side is split by a horizontal baffle that is close to or on the center line of the shell. The main application of this shell arrangement is in horizontal thermosyphon reboilers with a short tube length where the inlet is at the bottom and the outlet at the top. The horizontal baffle may be quite short and may be perforated. Its prime function is to ensure that the shell-side fluid “sweeps” the ends and prevents the build-up of vapor adjacent to the turbulence, which would create areas that are not fully effective for heat transfer. Because TEMA specifies a maximum unsupported tube length of about 60 in. (1500mm) for 1 in. – OD tubes; TEMA unsupported span limit varies with tube OD, thickness and diameter. A G shell cannot be used for heat exchangers with tube lengths > 10ft. (3m), since this would exceed the limit on maximum unsupported tube length specified by TEMA – typically 5 ft. (1.5 m.), though it varies with tube OD, thickness and material.

Heat Transfer  527 The H shell is basically a double G shell. There are three full supports at the center of the tube length, the G, and H shells can be used where there is a temperature cross. This could be an attractive option to using two shells in series for non-reboiler applications. The TEMA H shell is used when a larger tube length is required. TEMA G and H shells are advantageous as the shell-side pressure drop is lower than that in an E shell, and there are no cross baffles. The J type shell is a divided-flow shell wherein the shell-side fluid enters the shell at the center and divides into two halves; one flowing into the left and the other to the right and leaving separately and further combined into a single stream. This is identified as a J 1-2 shell. Alternatively, the stream may be split into two halves, which enter the shell at the two ends, flow toward the center, and leave as a single stream. This is identified as a J 2-1 shell. The J type shell is normally used when the shell-side pressure drop is unacceptably high in an E shell. It is useful to compare an E shell and a J shell with the same baffle pitch. The mass flow rate has been halved, and the length along the flow path halved in the J shell. This configuration shows one nozzle on the top and two at the bottom, which may be reversed and the shell-side fluid may be heating or cooling. The K type shell is the kettle reboiler having a different configuration from the other shell types. The port where the bundle enters the shell is normally significantly smaller than the shell diameter. It has an intermediate vapor disengagement space in the shape of an enlarged shell, and full support plates can be used when required. The X type shell is a pure cross-flow, in which the shell-side fluid enters from the top or bottom of the shell, flows across the tubes, and exits from the opposite side of the shell. The flow may be introduced through multiple nozzles located throughout the length of the shell in order to achieve a better distribution of flow. The X type shell can be used with the cold fluid on the shell-side, but its main application is in cooling large volumes of gas (often accompanied by condensation) so that the inlet is normally at the top. The flow may be introduced through multiple nozzles located throughout the length of the shell. Cross-flow designs are used when there is a very small allowable pressure drop on the shell-side. The diagram shows an inlet and outlet nozzle. However, there are two or even four nozzles at the top and the bottom to give good distribution. Because of the low-pressure drop (i.e., there is negligible Δp in the shell, and the only Δp is accounted in the nozzles), the configuration is used for cooling and condensing vapors at a very low pressure, especially at vacuum. Full support plates can be located as required for structural equipment Table 8.5  Combination of flow pattern and design features for each shell type. Shell type

Description

E

One-pass shell Counter or co-current flow

F

Two-pass shell Longitudinal baffle

G

Split flow Longitudinal baffle Full support plate under nozzle

H

Double split flow Two longitudinal baffles Full support plate under nozzles and at shell midpoint

J

Divided flow Full support plate under center nozzle

K

Kettle reboiler or vaporizer Liquid disengages from vapor in dome Nozzle for liquid draw-off is not required for vaporizers

X

Crossflow Multiple nozzles typical for flow distribution

(Source: Thomas, G. Lestina, CEP, pp 34, June 2011).

528  Chemical Process Engineering integrity, as they do not interfere with the shell-side flow because they are parallel with the flow direction. Types G, H, J and X are often used in condensers, and where there is a requirement to minimize Δp, while type K is for kettle reboilers. Figure 8.1N shows a shell and tube heat exchanger with nozzles on the shell and tube sides, and the rear end. Table 8.5 summarizes the features of the different shell types as illustrated in TEMA notation of Figure 8.1A.

8.3 Factors Affection Shell Selection Several factors influence the selection of shell in a shell and tube heat exchanger. Among these are [25]: Plant piping layout constraints: These occur when existing exchangers are being replaced or during revamping. It is prohibitively expensive to rearrange nozzles and move pipes, and these constrain the designer to replace shells of the same type. For new construction, limits on bundle length and nozzle locations may influence shell types. For example, pipe racks facilitate the use of stacked E shells with an even number of tube passes. Temperature profile of the hot and cold fluid streams: When the terminal temperature approach (i.e., the difference between the outlet temperature of the hot stream and the outlet temperature of the cold stream) is greater than 3oC, any of the shell types can be used for the application. When the temperature approach is less than 3oC, some shell types have a clear advantage, e.g., multipass shells (such as F, G, and H shells) can handle a low-temperature approach and even some temperature cross. Of the single-pass shells, E shells with one tube pass and X shells are the best option to accommodate a temperature cross or low approach. Shell side pressure drop: shell type is one of the several factors that affects pressure drop together with the baffle design, tube pitch, bundle entry and exit design. The K shells generally provide a negligible pressure drop. Maintenance: When bundle removal is required, multipass shells have a disadvantage compared to single-pass shells, especially where the longitudinal baffle must be removed. Longitudinal baffle removal requires mechanical leaf seals, which can be damaged during removal and installation. Thermal performance is severely reduced due to flow bypassing that occurs resulting in damage to the seals. Due to this anomaly, some processing facilities do not permit the use of F shells. Specific application: There are applications where one shell type is preferable to another. For pure component boiling with 100% vaporization, K and X-shells are the most common. For tube-side thermosiphon reboilers, vertical E shells are typically selected. For viscous liquids, horizontal E shells with segmental horizontal baffles are suitable. For high pressure applications where special channel closures are employed (TEMA D type front heads), E shells are preferable. Table 8.6 summarizes the advantages and disadvantages of these shell types.

8.4 Common Combinations of Shell and Tube Heat Exchangers Yokell [26] lists various combinations of near head, shell and rear head used to specify different TEMA heat exchanger types. A description of the combinations shown in Figures 8.1B–8.1G are as follows:

AES The AES in Figure 8.1B is the most versatile of all the shell and tube exchanger types. The tubes can be mechanically cleaned is situ or the whole unit can be dismantled to clean the shell-side mechanically, renew the bundle or take the bundle for repair. A triangular pitch can be used for the design of an AES type; however, the vast majority of the units use a square or aligned rotated square tube pitch. Both the S and T type can only have an even number of tube passes, except for the special one pass type which has internal expansion bellows. The disassemble procedure is as follows: 1. 2. 3. 4. 5.

 e shell cover (Figure 8.1B (9)) is removed. Th The flanged joint is unbolted. The ring is split, and both halves are removed. The stationary head in the opposite end is removed. The tube bundle is pulled out, passing the tube sheet through the shell.

Heat Transfer  529 Table 8.6  Each shell type has advantages and disadvantages that make it suitable for specific applications. Shell type

Advantages

Disadvantages

E

Many baffle types are available to reduce pressure drop. Widely applicable in single-phase, boiling, and condensing services. Temperature cross is possible without reverse heat transfer with a single tube pass.

Reverse heat transfer is possible with an even number of tube passes and no fouling.

F

Temperature change for fluid streams can be higher than in an E-shell. Fewer shells in series are needed.

Longitudinal baffle can leak if it is not welded. Thermal conduction occurs across the longitudinal baffle. Removable bundles are more costly to maintain.

G

Split flow reduces entrance and exit velocities. Lower risk of vibration due to lower velocity and better tube support under nozzle. Suited for horizontal shell side reboilers.

Fewer tube –pass options with removable bundle. Thermal conduction occurs across the longitudinal baffle. Temperature profile is not as good as with counter-or co-current flow.

H

Double split flow lowers entrance and exit velocities and provides more support than in G-shells. Suitable for horizontal shell side reboilers.

More nozzle than G-shells. Thermal conduction occurs across the longitudinal baffle. Temperature profile is not as good as with counterand co-current flow.

J

Split flow lowers velocities. Many baffle types are available to reduce pressure drop.

More nozzles than an E-shell. Temperature profile is not as good as with counter and co-current flow.

K

Low pressure drop Circulation promotes wet-wall boiling.

Larger shell requires entrainment calculations Circulation is complicated, which could lead to the buildup of heavy components.

X

Low pressure drop due to single cross pass Temperature cross is possible without reverse heat transfer. Widely applicable to single-phase, boiling and condensing services.

Maldistribution is possible, often requiring the use of a distribution plate. Multiple nozzles are common. Removal of noncondensables is complicated for X-shell condensers.

(Source: Thomas G. Lestina, CEP, pp 34, 2011).

Ds

d1

Ds

d1

Figure 8.5  Comparison between TEMA T and TEMA S floating heads for the same tube – circle diameter. It can be appreciated that a smaller shell diameter is possible with the TEMA S type. (Source: Eduardo Cao, Heat Transfer in Process Engineering, Mc.Graw-Hill.)

530  Chemical Process Engineering Figure 8.5 shows a comparison between the pull through design and a split ring design, where the latter allows a smaller shell diameter.

BEM The BEM type in Figure 8.1C is a fixed tube sheet design with bonnet covers at both the stationary and the far ends. The stationary channel has to be removed to access the tubes, which involves disturbing the pipe work. The shellside can only be chemically cleaned. Its applications are therefore limited to exchangers with clean shell-side fluids or situations where chemical cleaning is available. It is normal to use a triangular or rotated triangular tube pitch to maximize the number of tubes in a fixed diameter shell. A BEM may be used for a counter-current flow design with one pass on the tube-side, where the channels at both ends would have a nozzle. The pressure drop on the tube-side Shell Cover Gasket

Vent or Drain

Shell Cover Gasket

Shell

G-Fin Pipe

Cone Plug Nut Union Nut

Shell Cover

Return Bend (Union-Fitted)

Return Bend (Welded)

Return Bend End of Section Element Fitted with Unions to Provide Access to the Interior of the Element at this End.

Twin Flange

Moveable Shell Supports

Shell End Piece Shell Nozzle Flange

Cone Plug Straight Adaptor (Threaded)

Welded Return Bend for the Section Element is Furnished when Access to the Interior of the Element at this End is not Required. Tools are Available that will Clean the Return Bend from the Opposite End.

Figure 8.6A(1)  Double – pipe longitudinal twin G-finned exchanger. (Used by permission: Griscom-Russel Co./Ecolaire Corp., Easton, PA. Bul. 7600.) Tube Bundles Available Longitudinal fintubes or bare tubes

Head Closures Available

Return End Bonnet Closure

The free-floating U-tube bundle compensates for the differential shell-tube expansion. Eliminates need for expansion joints or packed joints commonly used in shell and tube type heat exchangers. Large radius U-bends are easily cleaned with flexible shaft tube cleaners. Return End Bonnet Closure is a conservative through-bolted design.

Figure 8.6A(2)  Multitube hairpin fin tube heat exchangers. The individual shell modules can be arranged into several configurations to suit the process parallel and/or series flow arrangements. The shell size range is 31 – 6in. (Used by permission: Brown Fintube Co., A Koch® Engineering Co., Bul. B – 30-1.)

Heat Transfer  531

Figure 8.6A(3)  Longitudinal fins resistance welded to tubes. The welding of the fins integral to the parent tube ensures continuous high heat transfer efficiency and the absence of any stress concentrations within the tube wall. (Used by permission: Brown Fintube Co., A. Koch® Engineering Co., Bul. 80-1.)

Figure 8.6B  Cutaway view of finned double pipe exchanger. (Used by permission: ALCO Products Co., Div. of NITRAM Energy, Inc.)

FIXED-END CLOSURE

RETURN END CLOSURE

Figure 8.6C  High – pressure fixed – end closure and return- end closure. (Used by permission: ALCO Products Co., Div. of NITRAM Energy, Inc.)

Figure 8.6D  Vertical longitudinal finned – tube heater, which is used in multiple assembles when required. (Used by permission: Brown Fintube Co., A. Koch® Engineering Co., Bul. 4-5.)

532  Chemical Process Engineering

Figure 8.6E  Longitudinal finned – tube tank suction direct line heater. (Used by permission: Brown Fintube Co., A. Koch® Engineering Co., Bul. 4-5.)

Figure 8.6F(1)  Single concentric corrugated tube in single corrugated shell. (Used by permission: APV Heat Transfer Technologies.)

Figure 8.6F(2)  Multicorrugated tubes in single shell. (Used by permission: APV Heat Transfer Technologies.)

Twisted Tube bundle with all twisted tubes

Mixed tube bundle 1 out of 3 tubes twisted

Figure 8.6G  Twisted tubes with heat exchanger bundle arrangements. (Used by permission: Brown Fintube Co., A. Koch Engineering Co., Bul.100-2.)

can be reduced if the nozzles are in axial configuration. The nozzle at the inlet channel would be positioned on the shell axis, but it is normally desirable to have the outlet nozzle offset to make the tubes free draining. Where condensation is taking place inside the tubes would require offsetting the outlet nozzle. The construction sequence is as follows [27]: 1. Tube sheet and baffle holes are drilled. 2. The tubes are installed in one of the tube sheets. 3. The baffles and spacers are introduced through the tubes and tie rods. 4. The shell is placed in position.

Heat Transfer  533

Figure 8.7A  Typical one side of Plate for Plate and Frame Exchanger. (Used by permission: Graham Manufacturing Company, Inc., Bul. PHE 96-1.)

Distribution Area Located at the top and bottom of the plate, this area is responsible for ensuring fluid is distributed uniformly across the entire width of the plate, eliminating dead spots. This is more complex on modern units where inlet and outlet are aligned vertically for easier piping. Alfa Laval’s designs provide complete fluid distribution across even our widest plate.

Main Heat Transfer Zone Critical for creating the highest turbulance consistent with desired pressure drop Entrance Neck Designed for low pressure drop as well as low velocities for reliable erosion prevention

New designs provide improved uniform distribution and higher design pressure capabilities

Figure 8.7B  Typical flow patterns of fluid flow across one side of plate. The opposing fluid is on the reverse side flowing in the opposite direction. (Used by permission: Alfa Laval Thermal Inc. Bul. G-101.)

534  Chemical Process Engineering UPPER HEAD HEAT TRANSFER PLATE PACK

PANEL GASKET GIRDER

NAME PLATE BAFFLE

LOWER HEAD SUPPORT

SIDE B

SIDE A

Figure 8.7C  The patented COMPABLOC® welded plate heat exchanger is technologically advanced, compact and efficient. The fully welded (but totally accessible on both sides) design combines the best in performance, safety maintenance, and capital/maintenance costs. (Used by permission: Vicarb Inc., Canada publication VNT – 3110 © 1997.)

Figure 8.8  Single – pass shell and tube Teflon® tube heat exchanger, countercurrent flow. Tube bundles are flexible tube Teflon® joined in integral honeycomb tubesheets. Shell – side baffles are provided for cross- flow. Standard shell construction in carbon steel shell plain or Teflon (LT)® lined. Heads are lined with Teflon®. Tube diameters range from 0.125–0.375 in. O.D.; the temperature range is 80-400oF; pressure range from 40–150 psia. (Used by permission: AMETEK, Inc., Chemical Products Div., Product Bulletin “Heat Exchangers of Teflon®”.)

5. The second tube sheet is installed. 6. The shell is welded to the tube sheets. 7. The tubes are rolled into the tubesheets The main disadvantages of this type of exchanger are: 1. It cannot be disassembled for cleaning or inspection. 2. If the temperature difference between the fluids is high or the linear thermal expansion coefficients of the tube and shell materials are very different, when the exchanger is in operation, then the differential

Heat Transfer  535

Figure 8.9A  Spiral flow heat exchanger, cross – flow arrangement for liquids, gases or liquid/gaseous (condensable) fluids. (Used by permission: Alfa Laval Thermal Incc., Bul. 1205 © 1993.)

Figure 8.9B  Spiral flow heat exchanger; vaporizer. (Used by permission: Alfa Laval Thermal Inc., Bul. 1205 © 1993.)

Figure 8.9C  Coil assembly for bare tube Heliflow® exchanger. Tube sizes range from ¼ - ¾ in. O.D. Tube – side manifold connections are shown for inlet and outlet fluid. (Used by permission: Graham Manufacturing Company, Inc., Bul. HHE – 30 © 1992.)

536  Chemical Process Engineering

8 Coil* 1 Studs and nuts 2 Manifold nuts

9 Casing flange gasket

7 Manifold lower* 3 Manifold lock rings

5 4 Base plate Manifold gaskets

1 Studs and nuts

10 Casing

6 Manifold upper*

11 Vent and drain plugs

* Although they are numbered separately for clarity in explaining the Heliflow® heat exchanger, Items 6, 7, and 8 are not separate items. Coil and manifolds are a one-piece factory assembly.

Figure 8.9D  Assembly of components of Heliflow® spiral heat exchanger. (Used by permission: Graham Manufacturing Company, Bul. “Operating and Maintenance Instructions for Heliflow®.”).

Figure 8.10  Cast iron sections; open coil cooler – coil and distribution pan.

expansion between the shell and tubes creates forces acting on the tube to tubesheet joints that can damage the exchanger. The first of these problems cannot be solved with this type of heat exchanger as the design is unsuitable for cases in which both fluids may have a fouling tendency (if only one fluid is fouling, it can be located to the tube-side because the tube interiors can be cleaned mechanically). There are instances where mechanical cleaning of the tube exteriors is impossible and cleaning is only carried chemically by circulating a solvent or detergent. However, this alternative is infeasible in many applications where the fouling characteristics of the fluid require mechanical removal procedures.

Heat Transfer  537

Figure 8.11  Open tube sections. (Used by permission: Griscom-Russel Co./Ecolaire Corp., Easton, PA.)

Figure 8.12A  Circular – type finned tubing. (Used by permission Wolverine Tube, Inc.)

WALL THICKNESS AT FIN PORTION STANDARD GAGE INTEGRAL CONSTRUCTION (ONE PIECE)

WALL THICKNESS AT PLAIN END SECTION APPROX. TWO GAGES HEAVIER

Figure 8.12B  Low – finned integral tube details. (Used by permission Wolverine Tube, Inc.)

Figure 8.12C  Bimetallic high - finned tube. (Used by permission Wolverine Tube, Inc.)

538  Chemical Process Engineering

Figure 8.12D  Longitudinal fin tubes. (Used by permission: Brown Fintube Co., A Koch® Engineering Co.)

Figure 8.12E  A cutaway section of plate – type fins showing the continuous surface contact of the mechanically bonded tube and fins. (Used by permission: The Trane® Co., La Crosse, Wis.)

Figure 8.12F  Flat plate extended surface used in low – temperature gas separation plants; exploded view of brazed surfaces. (Used by permission: The Trane® Co., La Crosse, Wis.)

Fins

Tube Wall

Imbedded Fin Tension Wound Into Groove

Used above 400°F. (a)

Figure 8.12G  Tension wound fins.

Tension Wound Fin or Tube, Not Imbedded. Some Tubes have fins Soldered to Outer Tube Surface. Used to 250–300°F. (b)

Tension Wound Fin or Tube. Fin has Integral Foot which Presses against adjacent Fin. Used 300–400°F . & below (c)

Heat Transfer  539

Y

H

dr

di

do

Δx

do — DIAMETER OVER FINS. dr — ROOT DIAMETER OF FINNED SECTION. dl — INSIDE DIAMETER OF FINNED SECTION. Δx — WALL THICKNESS OF FINNED SECTION. Y — MEAN FIN THICKNESS. H — FIN HEIGHT.

Figure 8.12H  Geometrical dimensions for High- finned Wolverine Trufin® tubes. The fins are integral with the basic tube wall. (Used by permission: Wolverine Tube, Inc., Engineering Data Book, II. © 1984.)

Corrugation Pitch (P)

Prime Tube OD

Corrugated Section OD (do)

Prime Tube Wall

Wall at Corrugation Corrugation Depth

Figure 8.12I  Koro-Chil® corrugated tube, used primarily for D-X water – type chillers, water – cooled outside, refrigerant expanding / boiling inside. (Used by permission: Wolverine Tube, Inc.)

The second problem, where a differential expansion between the shell and tube bundle is encountered can be solved by installing a shell expansion joint (Figure 8.1C (14)). Such expansion joints act as elastic bellows absorbing the differential expansion without transmitting forces to the tubesheets. The need for such a joint is determined during mechanical design of the heat exchanger. The most feasible approach to solving these anomalies of the fixed tube sheet design is to adopt a removable bundle construction.

540  Chemical Process Engineering

Corrugation Pitch (P)

Corrugated Section OD (do)

Prime Tube OD

Wall at Corrugation

Prime Tube Wall

Corrugation Depth

Figure 8.12J  Korodense® corrugated tube. Used primarily in steam condensing service and other power plant applications. Efficiency is reported at up to 50% greater than plain tubes. (Used by permission: Wolverine Tube, Inc.)

DIMENSIONAL NOMENCLATURE USED FOR TYPE SET TURBO-CHIL

di

d

xp

dr

do

d - outside diameter of plain end do - diameter over lins dr - root diameter of tinned section di - inside diameter of linned section xp - wall thickness of plain section xf - wall thickness of finned section

xf

Figure 8.12K  Type S/T Turbo-Chil® finned tube with internal surface enhancement by integral ridging. (Used by permission: Wolverine Tube, Inc.)

AEP The only difference between the AEP as shown in Figure 8.1D and the BEM is that the AEP type has a channel and removable cover at the stationary end, and a packing floating head at the rear end. The floating head can be moved axially, and the shell-side is sealed by a packing (24) that is compressed by a packing gland (25). The floating tube sheet skirt (22) diameter is smaller than that of the shell. It can be removed to the left, passing through the shell, when the unit is disassembled. The split-on backing flange (20) is a loose flange that can be removed to the right after removal of the split shear ring (19). Any leakage at the floating-head joint can be easily detected, but this type of packed joint should not be used when toxic or flammable fluids are contained. Leakage through a stuffing box is more likely than is the failure of a gasketted joint. This unit is very limited in its design pressure and temperature ranges. Design pressure must be lower than 580 psi (40 bar) and design temperature must be lower than 602.6oF (317oC). API Standard 660, which is used in the petroleum industry, does not permit this type of construction.

Heat Transfer  541 Applied Fins manufactured on McElroy machines: Base Tube Diameter: From ½" min. to 2" max. (15.88mm–50.8mm) Fin height: From ¼" min. to ¾" max. (6.35mm–19.05mm) Fin pitch: From 5 fins/inch min. to 11.5 fins/inch max. (195–453 fins/metre) Fin thickness: From 0.012" min. to 0.028" max. (0.30mm–0.71mm)

‘G’ FIN (or Embedded fin) The strip is tension wound into a machined groove and securely locked in place by back-filling with base tube material. This ensures that maximum heat transfer is maintained at high tube metal temperatures. Maximum temperature: 450°C. Fin material: Aluminium, Copper or steel. Tube material: Carbon steel, Cr Mo steel, stainless steel, copper, copper alloys, incolloy, etc. ‘L’ FIN Controlled deformation of the strip under tension gives optimum contact pressure of the foot on the base tube to mximise heat transfer performance. The helical fin foot gives considerable corrosion protection to the base tube. Maximum temperature: 150°C. Fin material: Aluminium or copper. Tube material: Any metallic material.

Figure 8.12L  Various fin manufacturing techniques used by Profins, Ltd., “Finned and Plain Tubes” bulletin. (Used by permission: Profins, Ltd., Burdon Drive, North West Industrial Estate, Peterlee, Co. Durham SR82HX, England.)

CFU Figure 8.1E shows the CFU type geometry, which has a channel with tube sheet and removable cover at the front head stationary head, a two-pass shell with longitudinal baffle, and U-tube bundle on the rear end. The longitudinal baffles are used in the shell to control the overall flow direction of the shell fluids as in G and H shell types. The shellside-fluid enters at one end in either the upper or the lower half (first pass), traverses the entire length of the shell and through the half of the shell, turns around and flows through the other half of the shell, and finally leaves at the same end of the shell through which it entered. The longitudinal baffle does not extend to the tube sheet at the far end, but stops somewhat short of it so that the shell-side fluid can flow from the first pass into the second pass. This construction is used for temperature cross situation; i.e., where the cold fluid leaves at a temperature higher than the outlet temperature of the hot stream. If a two-pass F shell has only two tube passes, it becomes a true counter-current configuration, and it can handle a large temperature cross. The differential expansion problem can be solved with the U-tube construction as the design has the advantage of a lower cost because it eliminates one head. The principal limitations are [27]: 1. It is impossible to clean the interior of the tubes because it is not possible to pass a cleaning rod through them. 2. This construction cannot be used for single-pass exchangers. 3. Except for the outermost tubes, individual tubes cannot be replaced. Any leaking tube must be plugged.

542  Chemical Process Engineering 4. In very large diameters, support of the tubes is difficult (The U-tube bundle becomes susceptible to vibration hazards). However, the number of gaskets is minimal, and thus makes the design attractive in high-pressure service. ‘LL’ FIN Manufactured buy the same process as ‘L’ fin, the overlapped fin foot gives complete corrosion protection to the base tube. This is often used as an alternative to the more expensive extruded fin tube in hostile environments. Maximum temperature: 180°C. Fin material: Aluminium or copper. Tube material: Any metallic material.

Fins manufactured on Razmussen Machine Semi-crimped fin is a non taper fin wrapped under tension around the outside of the base tube.

Fin is tack welded to the base tube at each end of the finned section or wherever the finning is interrupted. Maximum temperature: 250°C. Base tube diameter: Fin height: Fin pitch:

5/8"–4½" max. (15.88mm–114mm)

¼" –1" (6.4mm–25.4mm) 3 fins/inch–10 fins/inch (118 fins/metre–394 fins/metre)

Generally tube and fin is in carbon steel or stainless steel.

Figure 8.12L (Continued)  Various fin manufacturing techniques used by Profins, Ltd., “Finned and Plain Tubes” bulletin. (Used by permission: Profins, Ltd., Burdon Drive, North West Industrial Estate, Peterlee, Co. Durham SR82HX, England.) DEFINITION OF “MICRORIB” I.D. - 272710 27 NUMBER OF RIBS 27 HELIX ANGLE OF RIBS 10 RIB HEIGHT (THOUSANDTHS OF AN INCH) Fm

W

D Di

Fh

di dr do Ha P Rh

Wf

D — Di — dr — do — di — W — Wf — Fh — Fm — P — Rh — Ha —

Outside Diameter of Plain End Inside Diameter of Plain End Root Diameter Diameter Over Fins Inside Diameter of Fin Section Wall Thickness of Plain End Wall Thickness Under Fin Height of Fin Mean Fin Thickness Mean Rib Pitch Height of Rib Rib Helix Angle

Figure 8.12M  Finned tube with internal ribs enhances heat transfer inside as well as outside the tubes. (Used by permission: High Performance Tube, Inc., “Finned Tube Data Book.”)

Heat Transfer  543

Inner Tube, 12, 14, 16, 18 or 20 Gage Outer Tube, 12, 14, 16, 18 or 20 Gage Combined Thickness of the Two Tubes Usually Equivalent to Overall Thickness of 9, 11, 12, 14 Gage.

Figure 8.13  Duplex tube. Note inside liner is resistant to tube-side fluid and outer finned tube is resistant to shell – side fluid. (Used by permission: Wolverine Tube, Inc.)

Front Head Pass Partition Plates

2 Pass

2 Pass

4 Pass

4 Pass

6 Pass

6 Pass

8 Pass

8 Pass Return Head Pass Partition Plates

(Pie or Segment Plates)

Front Head Pass Partition Plates

Return Head Pass Partition Plates

(Ribbon Plates)

Figure 8.14  Tube pass arrangements.

AKT Figure 8.1F shows a kettle reboiler and kettles having a channel and removable cover at the front end, stationary head type to access the tubes for cleaning without disturbing the pipe work. The shell is a kettle type reboiler and a pullthrough floating head in the rear end. The K shell is a special cross-flow shell used for kettle reboilers with an integral vapor disengagement space in the shape of an enlarged shell. A U tube bundle (AKU) can be used if the heating fluid

544  Chemical Process Engineering Baffles Channel Head Baffle Plate

Baffle Plate

Tube Sheet

Return End

Two Pass Tube Sheet

Baffle Four Pass

Nozzle Out

Return Head Tube Side Fluid in

Baffles Head Tube Sheet

Baffle Plate

Six Pass Tube Side (Not Acceptable Due to Poor Temperature Relationships)

Figure 8.15  Tube – side baffles.

standard segmental baffle designed for side to side flow

standard double split flow design

standard segmental two shell baffle design

standard segmental baffle designed for up and down flow

standard split flow design with horizontal baffle

standard segmental three shell pass baffle design

standard single flow design

standard double split flow design with horizontal baffles

P-K standard splash baffle and vapor liquid separator designs. Used for vapor generation.

Figure 8.16  Shell baffle arrangements. (Used by permission: Patterson – Kelley Div., a Harsco Company, “Manual No. 700A.”)

Heat Transfer  545

Figure 8.17  Horizontal cut segmental baffles. (Used by permission: B.G.A. Skrotzki, B.G.A., Power, © June 1954, McGraw-Hill, Inc., All rights reserved.)

Figure 8.18  Vertical cut segmental baffles. (Used by permission: B.G.A. Skrotzki, B.G.A., Power, © June 1954, McGraw-Hill, Inc., All rights reserved.)

is steam. However, if fouling stream is used as the heating medium a pull-through, TEMA T type floating head bundle would be appropriate. One of the advantages of the kettle type reboiler as compared to the stab-in bundle is that the heat transfer surface area is unlimited; therefore, it can be designed for any heat load to the tower. The surface area of an individual shell is limited by the maximum weight of the bundle normally 22046–26455 lb (10–12 tonnes). However, there is no theoretical limit to the number of shells in parallel, which could be used. In most cases, a single shell is adequate.

546  Chemical Process Engineering (a)

% Cut Based on Diameter Baffle Window: This Area Cut Out to Allow Vapor Passage. Size of Cut Set by Combinations of Heat Transfer Coefficient and Pressure Drop. Baffle

This Area Removed from Baffle to Allow for Liquid Drainage. Size Set to Suit Expected Flow. Vertical Cut Baffle (b) Baffle Window, Vapor Passage Area

% Cut Based on Diameter

Baffle nate Alter

I" Minimum V-Notch Accomodates Moderates Liquid Flow, or for Draining after Washout. Size to Suit Flow. This is Not Recommended for Horizontal Condensers.

Baffle

If Baffle Cut Must be Horizontal, Then Section (including Tubes) Should be Removed when Condensed Liquid Flow is High.

Horizontal Cut Baffle

Figure 8.19  Baffle details.

Advantages of the kettle type are that it can handle a wide range of percentage vaporization rates (10%–100% vaporization – propane chiller), and it is insensitive to process changes such as part load operation. Its disadvantages are that it is relatively expensive compared with alternative types of reboiler, and the type is more susceptible to fouling because of the recirculation around the bundle.

AJW Figure 8.1G shows the AJW type geometry, which has a channel and removable cover at the front head stationary head, a divided flow shell type and externally sealed floating tube sheet at the rear end. A TEMA J shell type is a divided flow shell used for minimizing shell-side pressure drop. The shell-side fluid enters at the center (i.e., along the length) and divides into two halves, one flowing to the left and the other to the right. The streams leave separately and are combined into a single stream by external piping (referred to as the J1-2 shell). Alternatively, the stream may be split into two halves and enter the shell at the two ends, flow toward the center and leave as a single stream; this is referred to as J2-1 shell. Watson [28] has provided illustrations of other TEMA configurations and Mukherjee [23] discusses the advantages of TEMA F shell as compared to other shell types. The most common combinations for an E type shell are shown in Table 8.5. Various configurations of heat exchanger types, baffles types, and assemblies are shown in Figures 8.8-8.33, and are further illustrated in sections on double pipe, spiral, and plate heat exchangers respectively.

Heat Transfer  547

Figure 8.20  Disc and doughnut baffles. (Used by trun – 1 permission: B.G.A. Skrotzki, B.G.A., Power, © June 1954, McGraw-Hill, Inc., All rights reserved.)

8.5 Thermal Design Engineering thermal design of heat transfer equipment is concerned with heat flow mechanisms of the following three types, simply or in combination: (1) conduction, (2) convection, and (3) radiation. Shell and tube exchangers are concerned primarily with convection and conduction; whereas heaters and furnaces involve convection and radiation. Radiation is not generally considered in conventional heat transfer equipment except for direct gas/oil-fired heaters and cracking units. Conduction is heat transfer through a solid nonporous barrier when a temperature difference exists across the barrier. The thermal transfer capability of the specific barrier or wall material, known as thermal conductivity, determines the temperature gradient that will exist through the material.



Q=−

ka k A(t 2 − t1 ) = − a A∆t Lc Lc

(8.1)

FLUID PATH

Figure 8.21  Baffles with annular orifices. (Used by permission: B.G.A. Skrotzki, B.G.A., Power, © June 1954, McGraw-Hill, Inc., All rights reserved.)

548  Chemical Process Engineering

Figure 8.22A  RODbaffles® exchanger cross-section showing assembly, using TEMA, E, F, H, J, K, and X shells. (Used by permission: © Phillips Petroleum Company. Licensing Div., Bul., 1114 – 94-A – 01.)

Figure 8.22B  RODbaffle® Intercooler in fabrication, 67 in., 40 ft, 2,232 – ¾ in. O.D. copper – nickel tubes, 1.00 in. pitch. TEMA AHL. (Used by permission: © Phillips Petroleum Company, Licensing Div., Bul. 1114 – 94 – A – 01.) RODbaffle

U, T

Dt

Dr

Pt

Figure 8.22C  RODbaffle® tube – baffle details. (Used by permission: © Phillips Petroleum Company, Licensing Div., Bul. 1114 – 94 – A – 01.)

Heat Transfer  549 Longitudinal Slide Bar

0°

Cross Strips Baffle Ring

Support Rod

W

Partition Blockage Plate

Y

270°

90°

Baffle Z X Baffle Y Z Baffle X

180°

Baffle W Tube Diameter (Dt)

Baffle Ring

Shell

Support Rod Tube Pitch Spacing (Pr) (Pt)

Support Rod Diameter (Dr) Tubesheet Ligament (lt)

Figure 8.22D  RODbaffle® layout details. Key elements are support rods, circumferential baffle rings, cross-support strips, and longitudinal tie bars. Four different RODbaffle® configurations are used to form a set: baffles W, X, Y and Z (Used by permission: © Phillips Petroleum Company, Licensing Div., Bul. 1114 – 94 – A – 01.)

TRANSVERSE SECTION NO PLATE BAFFLE

PLATE BAFFLE HORIZONTAL CUTS

PLATE BAFFLE VERTICAL CUTS

LONGITUDINAL SECTION

Figure 8.23A  Impingement baffles and fluid – flow patterns. (Used by permission: Brown & Root, Inc.)

Referring to Figure 8.34, conduction occurs through the tube wall and is represented by a temperature drop t4 – t5 and through the scale of fouling by the drops t3 – t4 and t5 – t6. Convection is heat transfer between portions of a fluid existing under a thermal gradient. The rate of convection heat transfer is often slow for natural or free convection to rapid for forced convection when artificial means are used to mix or agitate the fluid. The basic equation for designing heat exchangers is

550  Chemical Process Engineering

TRANSVERSE SECTION Fluid may be directed into the tubefield in any sector of any chosen dimensions.

LONGITUDINAL SECTION

Figure 8.23B  Impingement fluid – flow pattern with annular inlet distributor. (Used by permission: Brown & Root, Inc.) Vapor and Mist Inlet to Shell

Annular Area at Least 1.25 Times Nozzle Area

Impingement Baffle Exchanger Shell

Tubes Inside Shell

Figure 8.23C  Impingement baffle located in inlet nozzle neck.



Q = U A (t2 – t1) = U A Δt

(8.2)

where (t2 – t1) represents the temperature difference across a single fluid film. Referring to Figure 8.34, convection occurs through the fluid t1 – t3 and also t6 – t8. where A = net external surface areas of tubes exposed to fluid heat transfer (not just the length of the individual tubes), ft2 (m2). Q = heat load, Btu/h (kW). U = overall heat-transfer coefficient, Btu/(h-ft2-°F) (kW/m2.oC). t = mean temperature difference, °F, (oC) corrected. An important step in accurately establishing the required net surface area of an exchanger is to determine the true t.

Heat Transfer  551

PLAN VIEW OF BAFFLE CAM LOCKING BAR PACKING BAFFLE PLATE

SHELL

CAM BAR CAM IN CLOSED POSITION SECTIONAL VIEW OF BAFFLE

CAM IN OPEN POSITION

Figure 8.24A  Construction details of two-pass expanding shell – side baffle. (Used by permission: Struthers – Wells Corp., Bul. A – 22.)

Figure 8.24B  Assembly two-pass shell baffle for installation in shell of exchanger. (Used by permission: Struthers – Wells Corp., Bul. A – 22.)

For example, the simplest temperature difference involves constant temperature on each side of the tube, such as steam condensing on one side at about 410°F (210oC) and an organic hydrocarbon compound boiling at constant temperature of about 250°F (121oC). Use this simple temperature difference for Equation 8.9.



T = 410 – 250 = 160°F (89oC)

This applies regardless of the fluid flow pattern in the unit [29]. Such a unit could be like the one shown in Figure 8.1C; also see Figure 8.35B. For counter-current flow of the fluids through the unit with sensible heat transfer only, this is the most efficient temperature driving force with the largest temperature cross in the unit. The temperature of the outlet of the hot stream can be cooler than the outlet temperature of the cold stream; see Figure 8.35:



Hot : 200°F

100°F



Cold: 80°F

150°F

552  Chemical Process Engineering

1 2 Patent Number 2,482,355

3

Figure 8.24C  Longitudinal shell – pass baffle. (Used by permission: Henry Vogt Machine Co., Patent No. 2,482,355.) Minimum 1/4" for Ferrous and 1/8" for Non-Ferrous Exchanger Shell

Weld Longitudinal Baffle Guides Weld

Figure 8.24D  Longitudinal baffle, sliding slot detail.

Note that the Log Mean Temperature Difference (ΔTLMTD) is somewhat less than the arithmetic mean, represented by the following:

[(T1 – t2) + (T2 – t1)] ÷ 2,

or, (hot – cold terminal temperature difference) ÷ 2

(8.3)

The ΔTLMTD for this flow is given by reference 29, Equation 8.4, using end conditions of exchanger. Thus:

∆TLMTD =

(T2 − t1 ) − (T1 − t 2 ) (GTD − LTD) = T −t   GTD  In  2 1  In  LTD   T1 − t 2 

(8.4)

Heat Transfer  553

Figure 8.24E  A series of shell and tube heat exchangers. Spacer Bars Threaded in One Sheet and Welded to Other

Single Tube Sheet

Double Tube Sheet Spacer Bars Spaced Around Circumference as Needed for Strength. 1/2"

Tube Sheets

1/2" Diameter Rod Welded Continuously to Both Tube Sheets. Drill Bottom for Liquid Detection with 1/4" Diameter Hole, or Top for Gaseous Detection with 1/2" Diameter. Cover Top Hole to Prevent Water Entering.

Space

Double Tube Sheet Detail

Figure 8.25  Tube – to- double tube sheet assembly detail.

where GTD LTD

= Greater Terminal Temperature Difference, °F (oC) = Lesser Terminal Temperature Difference, °F (oC)

Figures 8.26, 8.27 and 8.28 show U tube bundle with tie rods attached to the baffles, tube - tube sheet joint details and seal strips respectively. Tube sheet layouts for U-tube exchangers with pitch and sizes are illustrated in Figures 8.29–8.33. Tables 8.7–8.11 provide the characteristics of the tubes, thermal conductivity of metals, and manufacturers’ suggested minimum radius of bends for tubes and maximum unsupported straight tube span dimensions respectively.

554  Chemical Process Engineering

Figure 8.26  A U – tube bundle with tie rods, spacers attached to the baffles.

Tube Sheet

Flush to 1/16" to 1/4"

Strength Weld

θ=15° Average θ=30° Maximum

Plain

Beaded or Belled

Ferrule, same Metal as Inner Tube Wall

Inner Tube Wall

θ Flared

Welded

Duplex Tube Beaded or Belled This Tube May also be Installed Plain End (No Ferrule) or Flared With of Without Ferrule.

1/8" Minimum

5/16" Minimum

1/8" 1/8" Minimum, Usually 1/4" 1/64"

Typical Grooved Detail

Figure 8.27  Tube to tube sheet joint details. Shell Baffles

Seal strips

Shell

Figure 8.28  Seal strips.

Seal strips

Clad Tube Sheet

Baffles

Heat Transfer  555 3¾"

I.D. of No. of Shell Holes 8 10 12 13¼ 14 15¼ 16 17¼ 18 19¼ 20 21¼ 22 23¼ 24

17/8"

R.O.B. = 2½ × Tube Dia.

“U” Type Tubes

8

10

12

14

16

18

20

22

24

26

28

30

32

34

36

38

12 38 68 98 110 140 152 186 210 240 276 310 346 404 416

I.D. of No. of Shell Holes 25 26 27 28 29 30 31 32 33 34 35 36 37 38

466 512 564 610 654 720 776 826 890 932 1,016 1,082 1,134 1,212

Note: Total Number of Holes in the Tube Sheet is Based on 3/8" Minimum Clearance Between Shell and Tubes. Actual Number of “U” Tubes is one-half the Above Figures. For 4 Tube Pass Layout “Count-out” Holes on Vertical Center Line. Omit Tubes as Required for Tie Rods and Impingement Plates. When Calculating Surface Area for Bundle, Reduce Tube Legnths to Allow for Shorter Tubes Near Center.

Tube Sheet Layout U-TUBE EXCHANGER Tube Passes: Two of Four Tube Size & Pitch: 3/4" on 5/16"

Shell Diameter, inches

Figure 8.29A  Tubesheet layout for U-tube exchanger. Tube passes: two or four. Tube sizes and pitch: ¾ in. on 15/16 in. Radius of bend: 2 ½ tube diameter.

2¼"

I.D. of No. of Shell Holes 8 10 12 13¼ 14 15¼ 16 17¼ 18 19¼ 20 21¼ 22 23¼ 24

11/8"

R.O.B. = 1½ × Tube Dia.

“U” Type Tubes

6

8

10

12

14

16

18

20

22

24

26

28

Shell Diameter, inches

30

32

34

36

38

26 52 90 108 132 166 186 220 240 282 314 348 392 434 470

I.D. of No. of Shell Holes 25 26 27 28 29 30 31 32 33 34 35 36 37 38

516 552 606 662 708 782 818 900 948 1,014 1,086 1,148 1,212 1,294

Note: Total Number of Holes in the Tube Sheet is Based on 3/8" Minimum Clearance Between Shell and Tubes. Actual Number of “U” Tubes is one-half the Above Figures. For 4 Tube Pass Layout “Count-out” Holes on Vertical Center Line. Omit Tubes as Required for Tie Rods and Impingement Plates. When Calculating Surface Area for Bundle, Reduce Tube Lengths to Allow for Shorter Tubes Near Center.

Tube Sheet Layout U-TUBE EXCHANGER Tube Passes: Two or Four Tube Size & Pitch: 3/4" on 15/16"

Figure 8.29B  Tubesheet layout for U-tube exchanger. Tube passes: two or four. Tube sizes and pitch: ¾ in. on 15/16 in. Radius of bend: 1 ½ tube diameter.

556  Chemical Process Engineering 3¾"

I.D. of Shell

17/8"

R.O.B. = 2½ × Tube Dia.

“U” Type Tubes

12

14

16

18

20

22

24

26

28

30

32

34

36

38

Shell Diameter, inches

No. of I.D. of Holes Shell

No. of Holes

12

64

26

458

14

98

28

540

16

140

30

634

18

186

32

728

20

240

34

834

22

306

36

952

24

380

38

1,078

Note: Total Number of Holes in the Tube Sheet is Based on 3/8" Minimum Clearance Between Shell and Tubes. Actual Number of “U” Tubes is one-half the Above Figures. For 4 Tube Pass Layout “Count-out” Holes on Vertical Center Line. Omit Tubes as Required for Tie Rods and Impingement Plates. When Calculating Surface Area for Bundle, Reduce Tube Lengths to Allow for Shorter Tubes Near Center.

Tube Sheet Layout U-TUBE EXCHANGER Tube Passes: Two or Four Tube Size & Pitch: 3/4" on 1"

Figure 8.29C  Tubesheet layout for U-tube exchanger. Tube passes: two or four. Tube sizes and pitch: ¾ in. on 1 in. Radius of bend: 2 ½ tube diameter.

3¾"

I.D. of Shell

R.O.B. = 2½ × Tube Dia. 17/8"

12

14

16

18

20

22

24

26

28

30

Shell Diameter, inches

32

34

36

38

No. of Holes

56

26

410

14

86

28

476

16

128

30

562

18

166

32

652

20

220

34

746

22

278

36

840

24

336

38

912

12

“U” Type Tubes

No. of I.D. of Holes Shell

Note: Total Number of Holes in the Tube Sheet is Based on 3/8" Minimum Clearance Between Shell and Tubes. Actual Number of “U” Tubes is one-half the Above Figures. For 4 Tube Pass Layout “Count-out” Holes on Vertical Center Line. Omit Tubes as Required for Tie Rods and Impingement Plates. When Calculating Surface Area for Bundle, Reduce Tube Lengths to Allow for Shorter Tubes Near Center.

Tube Sheet Layout U-TUBE EXCHANGER Tube Passes: Two or Four Tube Size & Pitch: 3/4" on 1"

Figure 8.29D  Tubesheet layout for U-tube exchanger. Tube passes: two or four. Tube sizes and pitch: ¾ in. on 1 in. Radius of bend: 2 ½ tube diameter.

Heat Transfer  557 5"

I.D. of Shell

12

14

16

18

20

22

24

26

28

30

32

34

36

No. of Holes

12

30

26

268

14

46

28

314

16

76

30

372

18

98

32

438

20

140

34

494

22

174

36

568

24

218

38

654

Note: Total Number of Holes in the Tube Sheet is Based on 3/8" Minimum Clearance Between Shell and Tubes. Actual Number of “U” Tubes is one-half the Above Figures. For 4 Tube Pass Layout “Count-out” Holes on Vertical Center Line. Omit Tubes as Required for Tie Rods and Impingement Plates. When Calculating Surface Area for Bundle, Reduce Tube Lengths to Allow for Shorter Tubes Near Center.

2½"

R.O.B. = 2½ × Tube Dia.

“U” Type Tubes

No. of I.D. of Holes Shell

38

Tube Sheet Layout U-TUBE EXCHANGER Tube Passes: Two or Four Tube Size & Pitch: 1" on 1 1/4" Δ

Shell Diameter, inches

Figure 8.29E  Tubesheet layout for U-tube exchanger. Tube passes: two or four. Tube sizes and pitch: 1 in. on 1 ¼ in. Radius of bend: 1 ½ tube diameter.

I.D. of Shell 8 10 12 13¼ 14 15¼ 16 17¼ 18 19¼ 20 21¼ 22 23¼ 24

No. of I.D. of Holes Shell 36 62 98 128 148 172 204 234 266 306 332 376 420 458 498

25 26 27 28 29 30 31 32 33 34 35 36 37 38

No. of Holes 534 596 632 696 740 810 854 934 972 1,056 1,096 1,198 1,250 1,326

15/16"

Note: Total Number of Holes in the Tube Sheet is Based on 3/8" Minimum Clearance Between Shell and Tubes. Make Allowances for Tie Rods and Impingement Plates.

10

12

14

16

18

20

22

24

26

28

Shell Diameter, inches

30

32

34

36

38

Tube Sheet Layout FIXED TUBE SHEET EXCHANGER (Also Non-Removable Floating Head) Tube Passes: Two Tube Size & Pitch: 3/4" on 15/16" Δ

Figure 8.29F  Tubesheet layout (also nonremovable floating head). Tube passes: two. Tube sizes and pitch: ¾ in. on 15/16 in.

558  Chemical Process Engineering I.D. of No. of Shell Holes

I.D. of Shell

No. of Holes

12

94

26

558

14

132

28

652

16

176

30

752

18

230

32

862

20

294

34

976

22

364

36

1092

24

438

38

1190

15/16"

Note: Total Number of Holes in the Tube Sheet is Based on 3/8" Minimum Clearance Between Shell and Tubes. Make Allowances for Tie Rods and Impingement Plates.

12

14

16

18

20

22

24

26

28

30

32

34

36

38

Tube Sheet Layout FIXED TUBE SHEET EXCHANGER (Also Non-Removable Floating Head) Tube Passes: Two Tube Size & Pitch: 3/4" on 1" Δ

Shell Diameter, inches

Figure 8.29G  Tubesheet layout (also nonremovable floating head). Tube passes: two. Tube sizes and pitch: ¾ in. on 1 in. Δ.

I.D. of No. of Shell Holes

I.D. of No. of Shell Holes

12

82

26

460

14

112

28

530

16

162

30

632

18

204

32

718

20

258

34

816

22

324

36

922

24

386

38

1,032

15/16"

Note: Total Number of Holes in the Tube Sheet is Based on 3/8" Minimum Clearance Between Shell and Tubes. Make Allowances for Tie Rods and Impingement Plates.

12

14

16

18

20

22

24

26

28

30

Shell Diameter, inches

32

34

36

38

Tube Sheet Layout FIXED TUBE SHEET EXCHANGER (Also Non-Removable Floating Head) Tube Passes: Two Tube Size & Pitch: 3/4" on 1"

Figure 8.29H  Tubesheet layout (also nonremovable floating head). Tube passes: two. Tube sizes and pitch: ¾ in. on 1 in.

Heat Transfer  559 I.D. of No. of Shell Holes

I.D. of No. of Shell Holes

12

52

26

280

14

70

28

336

16

90

30

394

18

124

32

452

20

158

34

514

22

196

36

570

24

234

38

640

15/16"

Note: Total Number of Holes in the Tube Sheet is Based on 3/8" Minimum Clearance Between Shell and Tubes. Make Allowances for Tie Rods and Impingement Plates.

12

14

16

18

20

22

24

26

28

30

32

34

36

38

Shell Diameter, inches

Tube Sheet Layout FIXED TUBE SHEET EXCHANGER (Also Non-Removable Floating Head) Tube Passes: Two Tube Size & Pitch: 1" on 1 1/4"

Figure 8.29I  Tubesheet layout (also nonremovable floating head). Tube passes: two. Tube sizes and pitch: 1 in. on 1 ¼ in. .

I.D. of No. of Shell Holes

I.D. of Shell

No. of Holes

56

26

328

14

82

28

384

16

110

30

454

18

144

32

518

20

180

34

584

22

222

36

660

24

274

38

744

12

15/16"

Note: Total Number of Holes in the Tube Sheet is Based on 3/8" Minimum Clearance Between Shell and Tubes. Make Allowances for Tie Rods and Impingement Plates.

12

14

16

18

20

22

24

26

28

30

Shell Diameter, inches

32

34

36

38

Tube Sheet Layout FIXED TUBE SHEET EXCHANGER (Also Non-Removable Floating Head) Tube Passes: Two Tube Size & Pitch: 1" on 1 1/4" ∆

Figure 8.29J  Tubesheet layout (also nonremovable floating head). Tube passes: one. Tube sizes and pitch: 1 in. on 1 ¼ in. Δ.

560  Chemical Process Engineering I.D. of No. of Shell Holes

I.D. of Shell

No. of Holes

12

37

26

241

14

61

28

271

16

85

30

313

18

109

32

363

20

123

34

421

22

163

36

463

24

199

38

517

Note: Total Number of Holes in the Tube Sheet is Based on 3/8" Minimum Clearance Between Shell and Tubes. Make Allowances for Tie Rods and Impingement Plates.

12

14

16

18

20

22

24

26

28

30

32

34

36

38

Shell Diameter, inches

Tube Sheet Layout FIXED TUBE SHEET EXCHANGER (Also Non-Removable Floating Head) Tube Passes: One Tube Size & Pitch: 1 1/4" on 1 1/2" ∆

Figure 8.29J  Fixed tubesheet layout (also nonremovable floating head). Tube passes: one. Tube sizes and pitch: 1 in. on 1 ¼ in. Δ.

I.D. of No. of Shell Holes

I.D. of Shell

No. of Holes

12

37

26

241

14

61

28

271

16

85

30

313

18

109

32

363

20

123

34

421

22

163

36

463

24

199

38

517

Note: Total Number of Holes in the Tube Sheet is Based on 3/8" Minimum Clearance Between Shell and Tubes. Make Allowances for Tie Rods and Impingement Plates.

12

14

16

18

20

22

24

26

28

30

Shell Diameter, inches

32

34

36

38

Tube Sheet Layout FIXED TUBE SHEET EXCHANGER (Also Non-Removable Floating Head) Tube Passes: One Tube Size & Pitch: 1 1/4" on 1 1/2" ∆

Figure 8.29K  Fixed tubesheet layout (also nonremovable floating head). Tube passes: one. Tube sizes and pitch: 1 ¼ in. Δ.

Heat Transfer  561 Flow

Tube O.D.

Flow

Tube O.D.

Pitch

90°

90°

tc Pi

h

h

tc Pi

Pitch In-Line Square Pitch

Diamond Square Pitch

Tube Flow O.D.

Flow

L

L

Tube O.D.

ch Pit 60°

60°

Pitch L

Pitch

h

c Pit

L L = Ligament In-Line Triangular Pitch (Apex Horizontal)

Triangular Pitch (Apex Vertical)

Figure 8.30  Tube spacing layouts for tubesheets.

Baffle cut

2

4

3

1

1

2

2 Passes

5

6

4

3

1

2

6 Passes

Figure 8.31  Pass partition arrangements for Tables 21.17A–21.17D.

4 Passes

Flow orientation in triangular pattern

562  Chemical Process Engineering TEMA Type L-1 Tube Pass 19-mm (3/4") Tubes Pitch = 25.4-mm (1") Triangle 42"

(1067 mm)

39" 37" 35"

(838 mm) (940 mm) (889 mm)

33"

(838 mm)

31"

(787 mm)

29"

(737 mm)

27"

(686 mm)

25"

(635 mm)

23.25"

(591 mm)

21.25"

(540 mm)

19.25"

(489 mm)

17.25"

(445 mm)

15.25" 13.25" 12" 10" 8"

(387 mm) (337 mm) (305 mm) (254 mm) (203 mm)

Outer tube limit for a 1067 mm shell Shell diameter 42" (1067 mm) Dashed lines represent the outer tube limits for the indicated shell diameters. Tubes must be removed for the installation of tie rods, impingement plates, and to satisfy entrance velocity requirements

Figure 8.32A  ¾ in. tube distribution in 1 in. triangular pattern, one – pass configuration. Rear head type L. TEMA Type L-2 Tube Passes 19-mm (3/4") Tubes Pitch = 25.4-mm (1") Triangle 42" (1067 mm) 39" 37" 35" 33" 31" 29" 27" 25" 23.25" 21.25" 19.25" 17.25" 15.25" 13.25" 12" 10" 8"

(838 mm) (940 mm) (889 mm) (838 mm) (787 mm) (737 mm) (686 mm) (635 mm) (591 mm) (540 mm) (489 mm) (445 mm) (387 mm) (337 mm) (305 mm) (254 mm) (203 mm)

9.5 mm Outer tube limit for a 1067 mm shell Shell diameter 42" (1067 mm) Dashed lines represent the outer tube limits for the indicated shell diameters. Tubes must be removed for the installation of tie rods, impingement plates, and to satisfy entrance velocity requirements

Figure 8.32B  ¾ in. tube distribution in 1 in. triangular pattern, two – pass configuration. Rear head type L.

Heat Transfer  563 TEMA Type L-4 Tube Passes 19-mm (3/4") Tubes Pitch = 25.4-mm (1") Triangle 42" (1067 mm) 39" 37" 35" 33" 31" 29" 27" 25" 23.25" 21.25" 19.25" 17.25" 15.25" 13.25" 12" 10" 8"

(838 mm) (940 mm) (889 mm) (838 mm) (787 mm) (737 mm) (686 mm) (635 mm) (591 mm) (540 mm) (489 mm) (445 mm) (387 mm) (337 mm) (305 mm) (254 mm) (203 mm)

9.5 mm 9.5 mm Outer tube limit for a 1067 mm shell Shell diameter 42" (1067 mm) Dashed lines represent the outer tube limits for the indicated shell diameters. Tubes must be removed for the installation of tie rods, impingement plates, and to satisfy entrance velocity requirements

Figure 8.32C  ¾ in. tube distribution in 1 in. triangular pattern, four – pass configuration. Rear head type L.

TEMA Type S-2 Tube Passes 19-mm (3/4") Tubes Pitch = 25.4-mm (1") Square

42" (1067 mm) 39" 37" 35" 33" 31" 29" 27" 25" 23.25" 21.25" 19.25" 17.25" 15.25" 13.25" 12" 10" 8"

(838 mm) (940 mm) (889 mm) (838 mm) (787 mm) (737 mm) (686 mm) (635 mm) (591 mm) (540 mm) (489 mm) (445 mm) (387 mm) (337 mm) (305 mm) (254 mm) (203 mm)

9.5 mm Outer tube limit for a 1067 mm shell Shell diameter 42" (1067 mm) Dashed lines represent the outer tube limits for the indicated shell diameters. Tubes must be removed for the installation of tie rods, impingement plates, and to satisfy entrance velocity requirements

Figure 8.32D  ¾ in. tube distribution in 1 in. square pattern, two – pass configuration. Rear head type S.

564  Chemical Process Engineering TEMA Type S-4 Tube Passes 19-mm (3/4") Tubes Pitch = 25.4-mm (1") Square

42" (1067 mm) 39" 37" 35" 33" 31" 29" 27" 25" 23.25" 21.25" 19.25" 17.25" 15.25" 13.25" 12" 10" 8"

(838 mm) (940 mm) (889 mm) (838 mm) (787 mm) (737 mm) (686 mm) (635 mm) (591 mm) (540 mm) (489 mm) (445 mm) (387 mm) (337 mm) (305 mm) (254 mm) (203 mm)

9.5 mm 9.5 mm

Outer tube limit for a 1067 mm shell Shell diameter 42" (1067 mm) Dashed lines represent the outer tube limits for the indicated shell diameters. Tubes must be removed for the installation of tie rods, impingement plates, and to satisfy entrance velocity requirements

Figure 8.32E  ¾ in. tube distribution in 1 in. square pattern, four – pass configuration. Rear head type S.

TEMA Type U-2 Tube Passes 19-mm (3/4") Tubes Pitch = 25.4-mm (1") Square 42" (1067 mm) 39" 37" 35" 33" 31" 29" 27" 25" 23.25" 21.25" 19.25" 17.25" 15.25" 13.25" 12" 10" 8"

(838 mm) (940 mm) (889 mm) (838 mm) (787 mm) (737 mm) (686 mm) (635 mm) (591 mm) (540 mm) (489 mm) (445 mm) (387 mm) (337 mm) (305 mm) (254 mm) (203 mm)

19 mm Outer tube limit for a 1067 mm shell Shell diameter 42" (1067 mm) Dashed lines represent the outer tube limits for the indicated shell diameters. Tubes must be removed for the installation of tie rods, impingement plates, and to satisfy entrance velocity requirements

Figure 8.32F  ¾ in. tube distribution in 1 in. square pattern, two – pass configuration. Rear head type U.

Heat Transfer  565 TEMA Type U-4 Tube Passes 19-mm (3/4") Tubes Pitch = 25.4-mm (1") Square 42" (1067 mm) 39" 37" 35" 33" 31" 29" 27" 25" 23.25" 21.25" 19.25" 17.25" 15.25" 13.25" 12" 10" 8"

(838 mm) (940 mm) (889 mm) (838 mm) (787 mm) (737 mm) (686 mm) (635 mm) (591 mm) (540 mm) (489 mm) (445 mm) (387 mm) (337 mm) (305 mm) (254 mm) (203 mm)

9.5 mm 19 mm Outer tube limit for a 1067 mm shell Shell diameter 42" (1067 mm) Dashed lines represent the outer tube limits for the indicated shell diameters. Tubes must be removed for the installation of tie rods, impingement plates, and to satisfy entrance velocity requirements

Figure 8.32G  ¾ in. tube distribution in 1 in. square pattern, four – pass configuration. Rear head type U. TEMA Type L-1 Tube Pass 25.4-mm (1") Tubes Pitch = 31.75-mm (1.25") Triangle 45" (1143 mm) 42" (1067 mm) 39" 37" 35" 33" 31" 29" 27" 25" 23.25" 21.25" 19.25" 17.25" 15.25" 13.25" 12" 10" 8"

(838 mm) (940 mm) (889 mm) (838 mm) (787 mm) (737 mm) (686 mm) (635 mm) (591 mm) (540 mm) (489 mm) (445 mm) (387 mm) (337 mm) (305 mm) (254 mm) (203 mm)

Outer tube limit for a 1143 mm shell Shell diameter 45" (1143 mm) Dashed lines represent the outer tube limits for the indicated shell diameters. Tubes must be removed for the installation of tie rods, impingement plates, and to satisfy entrance velocity requirements

Figure 8.32H  ¾ in. tube distribution in 1.25 in. triangular pattern, one – pass configuration. Rear head type L.

566  Chemical Process Engineering TEMA Type L-2 Tube Passes 25.4-mm (1") Tubes Pitch = 31.75-mm (1.25") Triangle 45" (1143 mm) 42" (1067 mm) 39" 37" 35" 33" 31" 29" 27" 25" 23.25" 21.25" 19.25" 17.25" 15.25" 13.25" 12" 10"

(838 mm) (940 mm) (889 mm) (838 mm) (787 mm) (737 mm) (686 mm) (635 mm) (591 mm) (540 mm) (489 mm) (445 mm) (387 mm) (337 mm) (305 mm) (254 mm)

Outer tube limit for a 1143 mm shell Shell diameter 45" (1143 mm) Dashed lines represent the outer tube limits for the indicated shell diameters. Tubes must be removed for the installation of tie rods, impingement plates, and to satisfy entrance velocity requirements

Figure 8.32I  1-in. tube distribution in 1.25 in. triangular pattern, two – pass configuration. Rear head type L. TEMA Type L-4 Tube Passes 25.4-mm (1") Tubes Pitch = 31.75-mm (1.25") Triangle

42" (1067 mm) 39" 37" 35" 33" 31" 29" 27" 25" 23.25" 21.25" 19.25" 17.25" 15.25" 13.25" 12" 10" 8"

(838 mm) (940 mm) (889 mm) (838 mm) (787 mm) (737 mm) (686 mm) (635 mm) (591 mm) (540 mm) (489 mm) (445 mm) (387 mm) (337 mm) (305 mm) (254 mm) (203 mm)

9 mm

9 mm Outer tube limit for a 1143 mm shell Shell diameter 45" (1143 mm) Dashed lines represent the outer tube limits for the indicated shell diameters. Tubes must be removed for the installation of tie rods, impingement plates, and to satisfy entrance velocity requirements

Figure 8.32J  1-in. tube distribution in 1.25 in. triangular pattern, four – pass configuration. Rear head type L.

Heat Transfer  567 TEMA Type S-2 Tube Passes 25.4-mm (1") Tubes Pitch = 31.75-mm (1.25") Square 45" (1143 mm) 42" (1067 mm) 39" (838 mm) 37" (940 mm) 35" (889 mm) 33" (838 mm) 31" (787 mm) 29" (737 mm) 27" (686 mm) 25" (635 mm) 23.25" (591 mm) 21.25" (540 mm) 19.25" (489 mm) 17.25" (445 mm) 15.25" (387 mm) 13.25" (337 mm) 12" (305 mm) 10" (254 mm) 8" (203 mm) 9 mm Outer tube limit for a 1067 mm shell Shell diameter 42" (1067 mm) Dashed lines represent the outer tube limits for the indicated shell diameters. Tubes must be removed for the installation of tie rods, impingement plates, and to satisfy entrance velocity requirements

Figure 8.32K  1-in. tube distribution in 1.25 in. square pattern, two – pass configuration. Rear head type S.

TEMA Type S-4 Tube Passes 25.4-mm (1") Tubes Pitch = 31.75-mm (1.25") Square

45" (1143 mm) 42" (1067 mm) 39" 37" 35" 33" 31" 29" 27" 25" 23.25" 21.25" 19.25" 17.25" 15.25" 13.25" 12" 10" 8"

(838 mm) (940 mm) (889 mm) (838 mm) (787 mm) (737 mm) (686 mm) (635 mm) (591 mm) (540 mm) (489 mm) (445 mm) (387 mm) (337 mm) (305 mm) (254 mm) (203 mm) 9 mm Outer tube limit for a 1067 mm shell Shell diameter 42" (1067 mm) Dashed lines represent the outer tube limits for the indicated shell diameters. Tubes must be removed for the installation of tie rods, impingement plates, and to satisfy entrance velocity requirements

Figure 8.32L  1-in. tube distribution in 1.25 in. square pattern, four – pass configuration. Rear head type S.

568  Chemical Process Engineering TEMA Type U-4 Tube Passes 25.4-mm (1") Tubes Pitch = 31.75-mm (1.25") Square 45"

(1143 mm)

42"

(1067 mm)

39" 37" 35" 33" 31" 29" 27" 25" 23.25" 21.25" 19.25" 17.25" 15.25" 13.25" 12" 10" 8"

(838 mm) (940 mm) (889 mm) (838 mm) (787 mm) (737 mm) (686 mm) (635 mm) (591 mm) (540 mm) (489 mm) (445 mm) (387 mm) (337 mm) (305 mm) (254 mm) (203 mm)

25.4 mm

9 mm Outer tube limit for a 1143 mm shell Shell diameter 45" (1143 mm) Dashed lines represent the outer tube limits for the indicated shell diameters. Tubes must be removed for the installation of tie rods, impingement plates, and to satisfy entrance velocity requirements

Figure 8.32M  1-in. tube distribution in 1.25 in. square pattern, two – pass configuration. Rear head type U.

TEMA Type U-2 Tube Passes 25.4-mm (1") Tubes Pitch = 31.75-mm (1.25") Square 45" (1143 mm) 42" (1067 mm) 39" 37" 35" 33" 31" 29" 27" 25" 23.25" 21.25" 19.25" 17.25" 15.25" 13.25" 12" 10" 8"

(838 mm) (940 mm) (889 mm) (838 mm) (787 mm) (737 mm) (686 mm) (635 mm) (591 mm) (540 mm) (489 mm) (445 mm) (387 mm) (337 mm) (305 mm) (254 mm) (203 mm)

25.4 mm Outer tube limit for a 1143 mm shell Shell diameter 45" (1143 mm) Dashed lines represent the outer tube limits for the indicated shell diameters. Tubes must be removed for the installation of tie rods, impingement plates, and to satisfy entrance velocity requirements

Figure 8.32N  1-in. tube distribution in 1.25 in. square pattern, four – pass configuration. Rear head type U.

Heat Transfer  569 Inside Tube

Effective Tube Length (Mean Tube Length)

R.O.B Radius of Bend

Outside Tube

Tube Sheet

Figure 8.33A  U – tube bundle. 32

32 ft. Tube Length (Max)

31 30

3/4" O.D.

29

1" O.D. 24 ft.

24 23 22

3/4" O.D.

21

1" O.D.

Effective Length, ft

20 16

16 ft.

15 14

3/4" O.D.

13 12

1" O.D.

12 ft.

11 10

3/4" O.D.

9

1" O.D.

8

8 ft.

Effective Tube Length Corrections for Calculating Ouside Surface Areas of U-Tube Bundles

7 3/4" O.D.

6 5

0

40

80

120

160

200

240

Basis For Chart Preparation: 1. Tube O.D. Minimum Radius Bend Pitch 3/4" 1.5 Tube Dia. 1" 1" 2.5 Tube Dia. 1.25" and 2. Tubes on Exchanger Center Line. 3. 3/8" Clearance Between U-Bundle and Inside of Shell. 4. Allowance of 1.5" for Thickness of Tube Sheet. Accuracy: All Other Counts 10 atm

0.1 times operating pressure

80

ax

=

/C m

0.25 0.50 0.75 1.00

in

Cm

60 40

(b) 100

0

Effectiveness ε, %

Effectiveness ε, %

(a) 100

Tube fluid

20 0

80 60 40 20

1

2

3

4

0

5

60

=0 ax m 0.25 /C in 0.50 Cm 0.75 1.00

40

Shell fluid

1 2 3 4 5 Number of transfer units NTU = AU/Cmin

(d) 100

Effectiveness ε, %

Effectiveness ε, %

(c) 100

20

80

ax

in

Cm

60

Shell fluid

Tube fluid

/C m

in

Cm

4 5 1 2 3 Number of transfer units NTU = AU/Cmin

(f) 100

=0

0.2550 0. 5 0.7 0 1.0

Cold fluid Hot fluid

Effectiveness ε, %

Effectiveness ε, %

40

0.250 0.5 5 0.7 1.00

40

0

1 2 3 4 5 Number of transfer units NTU = AU/Cmin

ax

60

0

20

(e) 100 80

=

/C m

Tube fluid 0

Shell fluid

Tube fluid

Shell fluid Number of transfer units NTU = AU/Cmin Parallel-flow

80

=0 ax m C 5 / in 0.2 Cm 5 1.00 7 . 0 0 5 . 0

80 60 40

20

20

0

0

.∞

ax

/C m

in

Cm

=0

0.25 4 0.5 2 0.75 1.33 1 Mixed fluid

Unmixed fluid 1 2 3 4 5 Number of transfer units NTU = AU/Cmin

1 2 3 4 5 Number of transfer units NTU = AU/Cmin

Figure 8.48  (A–F) Shows the ε – NTU charts for parallel, counter flow and some more commonly based configurations.

616  Chemical Process Engineering

Example 8.4. Heating Water in a Counter-Current Flow Heat Exchanger A counter-current double pipe heat exchanger as shown in Figure 8.49 is to heat water from 30oC to 90oC at a rate of 1.5 kg/s. The heating is to be accomplished by geothermal water available at 170oC at a mass flow rate of 2.5 kg/s. The inner tube is thin-walled and has a diameter of 15 mm. If the overall heat transfer coefficient of the heat exchanger is 650W/m2.oC, determine the length of the heat exchanger required to achieve the desired heating using the log mean temperature difference method, tLMTD and the effectiveness-NTU methods. Take: The specific heat of water and geothermal fluid to be 4.18 and 4.31 kJ/kg.oC respectively.

Solution Using the Log Mean Temperature Difference tLMTD From the heat balance involving the tube side and shell side of the exchanger, we have:



Q = Wh Cph (T1 – T2) = wc Cpc (t2 – t1)

2.5

4.31 (170 - T2) = 1.5



4.18

(90 – 30)

170 – T2 = 376.2 /10.775

T2 = 135.1oC The log mean temperature difference, TLMTD: 170°C

135.1°C Δt2 = 135.1°C − 30°C = 105.1°C

Δt1 = 170°C − 90°C = 80°C

30°C

90°C

∆TLMTD =

=

∆t 2 − ∆t1  ∆t  ln  2   ∆t1  105.1 − 80  105.1  ln  80 

= 91.97°C



Hot geothermal water 170°C 2.5 kg/s T1

Cold water t1

t2

30°C 1.5 kg/s D = 15mm T2

Figure 8.49  Schematic for Example 8.4.

80°C

Heat Transfer  617 The log mean temperature difference correction factor, F = 0.9571 The corrected mean temperature difference = 88.03oC The head load, Q = UAs F TLMTD



376200 = 650

As

88.03

As = 6.57 m2 The length of the tube is:

As= π D L

6.57 = π (0.015) L



L = 140 m

Effectiveness-NTU method In the effectiveness method, the heat capacity flow rates of the hot and cold fluids are determined and the smaller value is identified.

CPh = Wh Cph = (2.5kg/s) (4.31 kJ/kg.oC) = 10.775 kW/oC CPc = wc. Cpc = (1.5 kg/s) (4.18 kJ/kg.oC) = 6.27 kW/oC Therefore, CPmin = 6.27 kW/oC and the capacity ratio, c = CPmin/CPmax = 6.27/10.775 = 0.582 The maximum heat transfer rate is determined from Equation 8.38:

Q max = CPmin (T1 − t1 ) = (6.27 kW/°C)(170 − 30)°C = 877.8 kW





That is, the maximum possible heat transfer rate in this heat exchanger is 877.8 kW. The actual rate of heat transfer is:



Q = [wc Cpc (t2 – t1)]cold water = (1.5 kg/s)(4.18 kJ/kg.°C)(90 − 30) °C = 376.2kW

Therefore, the effectiveness of the heat exchanger is:

Actual heat transfer rate Q ε=  = Q max Maximum possible heat transfer rate =

376.2 kW = 0.429 877.8 kW

Knowing the effectiveness, the NTU of this counter current flow heat exchanger can be determined from Table 8.18 as:

618  Chemical Process Engineering

NTU = =



1  ε −1  ln (c − 1)  cε − 1  0.429 − 1 1   0.653 ln = (0.582 − 1)  0.582 × 0.429 − 1 

Then the heat transfer surface area becomes:



NTU =

NTU ⋅CPmin (0.653)( 6270 W °C ) UA s As = = 6.30m 2 = U CPmin 650 W m 2 .°C



To provide this much heat transfer surface area, the length of the tube is

A s = π DL and L =



6.3m 2 As = = 134 m π D π(0.015m)

Example 8.5. LMTD and ε-NTU Methods A double pipe counter-flow heat exchanger uses oil flowing at 0.1 kg/s with an initial temperature of 200oC to heat water also flowing at 0.1 kg/s from 35.0oC to 95oC. Determine the product of heat transfer coefficient and area using LMTD method and ε-NTU Method. The specific heat of oil = 2.1 kJ/kg.oC and water = 4.18 kJ/kg.oC

Solution From the heat balance



Q = Wh Cph (T1 – T2) = wcCpc (t2 – t1)



= 0.1 × 2.1 × (200 − T2) = 0.1 × 4.18 × (95 − 35)



(200 – T2) = 25.08/0.21 = 119.43

T2 = 80.53oC

Q = 25.08 kW

The log mean temperature difference, ΔTLMTD is determined as follows: 200°C

80.57°C Δt2 = 80.57°C − 35°C = 45.57°C

Δt1 = 200°C − 95°C = 105°C

35°C

95°C

∆TLMTD =



(105 − 45.57)  105  ln  45.57 

= 71.2°C

Heat Transfer  619 The product of heat transfer and area, UA is:

Q 25.08 = ∆TLMTD 71.2 = 0.352 kW/°C

UA = Using the ε-NTU Method

The heat capacity flow rates of the hot and cold fluids are:

CPh = 0.1 × 2.1 = 0.21 kW/oC CPc = 0.1 × 4.18 = 0.418 kW/oC Therefore, the minimum heat capacity flow rate, CPmin = 0.21 kW/oC. The maximum flow rate is:

Q max = CPmin (T1 − t1 ) = 0.21 × (200 − 35) = 34.65 kW



(8.38)

Therefore, the effectiveness of the heat exchanger is:

Actual heat transfer rate Q ε=  = Q max Maximum possible heat transfer rate

=

25.08 = 0.72 34.65



and the capacity ratio, c = CPmin/CPmax = 0.21/0.418 = 0.5024 The number of transfer units, NTU is:

NTU =

1  ε −1  ln (c − 1)  cε − 1 

0.72 − 1 1   ln  0.5024 × 0.72 − 1  (0.5024 − 1) = 1.655 =



The number of transfer units, NTU can be expressed by:



NTU =

UA (WC p )min



UA = 1.655 × 0.21 = 0.347 kW/oC



620  Chemical Process Engineering Percentage deviation % is:

(0.352 − 0.347) × 100 0.347 = 1.4%. =





Example 8.6 In a one-shell, two tube pass heat exchanger, water at 15oC enters at a rate of 5000 kg/h in the shell side. Engine oil flows at a rate of 2500 kg/h through the tubes. The surface area of the heat exchanger is 15m2. Overall heat transfer coefficient is 200 W/m2 oC. Determine the exit temperature of the two fluids, if oil enters at 150oC. Take Cp of oil = 2.6 kJ/kg.oC and Cp of water = 4.18 kJ/kg.oC.

Solution From the heat balance



Q = Wh Cph (T1 –T2) = wcCpc (t2 – t1)

CPh = 2500.0 × 2.6/3600 = 1.806 kW/oC CPc = 5000.0 × 4.18/3600 = 3.61 kW/oC Therefore, the minimum heat capacity flow rate, CPmin = 1.806 kW/oC. The maximum flow rate is:



Q max = CPmin (T1 − t1 ) = 1.806 × (150 − 15) = 243.81 kW

The capacity ratio, c = CPmin/CPmax = 1.806/3.61 = 0.5 Therefore, the effectiveness of the heat exchanger is:



Actual heat transfer rate Q ε=  = Q max Maximum possible heat transfer rate

For a one shell two tube passes, Table 8.18 gives the effectiveness ε:



 1 + exp  − NTU 1 + c 2   ε = 2 1 + c + 1 + c 2  1 − exp  − NTU 1 + c 2   

where

and

1 + c 2 = 1 + 0.52 = 1.118

−1

Heat Transfer  621 The number of transfer units:

NTU =

U ⋅A (CP)min

W 1  15 × 200  2 ⋅ m ⋅ 2  m .° C W  1.806 × 1000   ° C  = 1.66 =



 1 + exp  − NTU 1 + c 2   ε = 2 1 + c + 1 + c 2  1 − exp  − NTU 1 + c 2   



1 + exp[−1.66 × 1.118]   = 2 (1 + 0.5 + 1.118) 1 − exp[−1.66 × 1.118]   = 0.557

−1

−1

 The actual heat transfer rate, Q:

Q = ε Q max = ε(CP)min (T1 − t1 )

= (0.557)(1.806)(150 − 15) = 135.9 kW

The outlet temperatures of oil and water are:





(CP)oil (T1 − T2 ) = Q Q 135.9 T1 − T2 = = = 75.2°C (CP)oil 1.806 T2 = 150 − 75.2 = 74.8°C (CP)water (t 2 − t1 ) = Q Q 135.9 t 2 − t1 = = = 37.65 °C (CP)water 3.61 t 2 = t1 + 37.65 = 15 + 37.65 = 52.65°C

8.7 Pressure Drop, Δp When a fluid flows over a stationary or moving surface, the pressure of the fluid decreases along the length of the surface due to friction. This is commonly called the pressure drop of the system. See Figures 8.50 and 8.51.

622  Chemical Process Engineering dz R

r

T|r=R . 2πr

πR2p|z

z

πR2p|z + ∆z

Flow of fluid L

Figure 8.50  Forces acting on a segment of fluid. Direction of fluid flow through a pipe.

vz (r)

R r r+

dr

dA = 2 π r dr

Figure 8.51  Parabolic velocity distribution in laminar flow.

Consider the flow of fluid through the pipe, and owing to the friction at the tube wall, there is a pressure drop, which can be related to the shear stress at the wall. A force balance in a section of the pipe of length L is:



R2pz = R2pz+ z + 2 R Δzτr=R

(8.44)



 ∆p  2 − = ⋅τ  ∆z  R r =R

(8.45)

 ∂v  τ r =R = −µ  z   ∂r  r =R

(8.46)

and the shear stress at the tube wall is:



The minus sign signifies that the radial coordinate has its origin at the center of the pipe, so the derivative is negative. In laminar flow, the partial derivative in Equation 8.46 can be calculated from the velocity distribution



  r 2 v z = v z,max 1 −    R 

(8.47)

where vz,max is the velocity at the center of the tube. Since vz is a function of the radial coordinate, in all points of dA, the velocity is the same. The mass flow through dA is:



dA

dG = vz

(8.48)

Integrating in the entire section



∫

∫

G = dG = v z ρ dA



(8.49)

Heat Transfer  623 For the boundary layer to remain in laminar flow

Re =



ρv D < 2100 µ

(8.50)

G ρa t

(8.51)

where v is a mean velocity defined as

v=

where G = mass flow rate ρ = fluid density at = flow cross sectional area of the tube

Combining Equations 8.50 and 8.51 and rearranging gives

v=



R





=

∫ 0

∫ v ρdA = ∫ v dA z

z

ρa t

  r 2 v z,max 1 −  2πrdr  R  πR 2

2v = z,max R2

R



 r 

∫ 1 −  R   r dr



(8.53)

(8.54)

0

v=



(8.52)

at

v z,max 2

(8.55)



 ∆p  2 − = ⋅τ  ∆z  R r =R

(8.56)



=

2  dv z  −µ R dr  r =R

(8.57)

2 ⋅µ v z,max ∆z R 4v = µ 2 dz R 2

−∆p =



−dp = 32µ

v dz D2



(8.58)

(8.59)

624  Chemical Process Engineering or



−(p2 − p1 ) = 32µ

v dz D2

(8.60)

This expression relates the pressure drop in a pipe with the mean fluid velocity in laminar flow. When the flow regime is turbulent, the partial derivative of Equation 8.46 cannot be calculated and analytical solution is not possible, therefore the usual approach is to define the friction factor, f. From Equation 8.45,



−dp =

2 ⋅τ r =R dz R

(8.61)

The friction factor, f is defined as the ratio of the shear stress to the kinetic energy as:

f=





τ ρv 2 2

(8.62)

2  τ  ρv 2 dz −dp = ⋅ R  v2  2  ρ  2 −dp =

2 ρv 2 ⋅f dz R 2

(8.63)

(8.64)

Integrating Equation 8.64 between p = p1 and p2 and the pipe length z = 0 and L gives: p2



L

2 ρv 2 dz − dp = f R 2

∫

(8.65)

2 ρv 2 f L R 2

(8.66)

∫

0

p1

−(p2 − p1 ) = or



−(p2 − p1 ) = 4 f

2  L  ρv , N/m 2  D 2

(8.67)

In Imperial units:



−(p2 − p1 ) = 4 f

2  L  ρv  1  , lb /in 2  D  2g c  144  f

(8.68)

Heat Transfer  625 Pressure drop in an exchanger with number of tubes is:

−(p2 − p1 ) = 4 f

2  L  ρv  1   D  2g c  144 



(8.69)

or In terms of the mass flux, G and the specific gravity s of the fluid, by making the substitutions,



v = G/ρ and ρ = s ρ



∆pf =

f LG 2 2g c ρwater Di s

(8.70)

The specific gravity of liquids is usually referenced to water at 4oC, which has a density of 62.43 lbm/ft3. (The petroleum industry uses a reference temperature of 60oF, at which ρwater = 62.37 lbm/ft3, the difference in reference densities is significant.)

g c = 32.174



lbm ft 8 lbm ft 2 = 4.16975 × 10 lbf s lbf h 2

(8.71)

With these numerical values, Equation 8.70 becomes

∆pf =



f LG 2 lb , 2f 10 5.206 × 10 Di s ft

(8.72)

When L and Di are expressed in ft and G in lbm/h.ft2, the units of ΔPf are lbf/ft2. or

∆pf =

where

f LG 2 lb , f2 12 7.50 × 10 Di s φ in

(8.73)

= ( / w)0.14 for turbulent flow = ( / w)0.25 for laminar flow.

The viscosity correction factor accounts for the effect of variable fluid properties on the friction factor in non-isothermal flow, while the factor of 144 converts the pressure drop from lbf/ft2 to lbf/in2 (psi). where L = Pipe length, ft, m D = Pipe diameter, ft, m  lb ft  gc = 32.174  m 2   lbf s  f = friction factor (dimensionless) v = fluid velocity, ft/s2, m/s2 = fluid density, lbm/ft3, kg/m3

626  Chemical Process Engineering p1 = inlet pressure, lbf/in2, N/m2 p2 = outlet pressure, lbf/in2, N/m2 s, = dimensionless The friction factor f is a function of the Reynolds number and the roughness of the tube surface ( /D). A well-known graph representing the friction factor as a function of the Reynolds number is due to Moody [35]. The curves parameter is the relative roughness, defined as the quotient between the tube surface roughness and the pipe diameter ( /D). For laminar flow, the friction factor is defined by

f=



16 Re

(8.74)

At high Reynolds number, the dependence of the friction factor on the Reynolds number is weak, and it mainly depends on the surface roughness of the tube. i.e.

f = f (Re, /D) f≅



(8.75)

0.079 3 × 103 ≤ Re ≤ 105 14 Re

(8.76)

0.046 Re ≥ 2 × 104 Re1 5

(8.77)

and

f≅



Of particular interest are the pressure drops in pipes (tubes) and in heat exchanger shells. The Sieder and Tate equation for the pressure drop in tubes is:

∆p t =



f G 2Ln' , psi 5.22(10)10 (Di )(s)(µ / µ w )0.14

(8.78)

Figure 8.52 shows the tube friction factor f as a function of the tube Reynolds number. The Sieder and Tate equation for the pressure drop in shell is:



∆ps =

fG 2 Di (N + 1) , psi 5.22(10)10 (De )(s)(µ / µ w )0.14

(8.79)

Figure 8.53 shows the shell-side friction factors for bundles with 25 percent cut segmental baffles.

8.7.1 Frictional Pressure Drop The frictional pressure drop for fluids circulating in the tube-side of a heat exchanger can be considered as the sum of two effects: 1. Th  e pressure drop along the tubes 2. The pressure drop due to the change in direction in the exchanger heads

Heat Transfer  627 20

30 40 50 60 80 100

200

3

4 500 6 7 8 1000

2

DGt µ 3 4 5 6 7 8 10,000

2

3

0.006 0.005 0.004 0.003 0.002

0.001 0.0008

f, sq ft/sq m.

4 5 6 7 8 100,000

2

3

4 5 6 7 8 1,000,000 0.01 0.008

2 f × Gt2 × L × n f × Gt × L × n , psi = ΔPt = 2 × g × p × D × ϕt 5.22 × 1010 × D × s × ϕt D ID of tubes or pipe, ft f Friction factor, sq ft/sq in Gt Mass velocity, lb/hr (ft2) g Acceleration of gravity, ft/hr2 L Length of tube path or Ln in multipass exchangers, ft n Number of tube passes ΔPL Pressure drop in tubes or pipes, psi s Specific gravity p Density, lb/ft3 μ Viscosity at the caloric temperature, lb/ft × hr ϕw Viscosity at the tube wall temperature, lb/ft × hr ϕt (µ/µw)0.14 above Rct = 2100 ϕt (µ/µw)0.15 below Rct = 2100 Note Friction factors are dimensional, sq ft/sq m. to give ΔPt in psi directly. To obtain dimensionless friction factors multiply the ordinate by 144

0.0006 0.0005 0.0004 0.0003 0.0002

0.003 0.002

0.001 0.0008 0.0006 0.0005 0.0004 0.0003 0.0002

COMMERCIAL PIPES

EXCHANGER TUBES

0.006 0.005 0.004

f, sq ft/sq m.

Rct =

10 0.01 0.008

0.0001 0.00008

0.0001 0.00008

0.00006 0.00005 0.00004

0.00006 0.00005 0.00004

0.00003

0.00003

0.00002

0.00002

0.00001 10

20

30 40 50 60 80 100

200

3

4 500 6 7 8 1000

2

3 Rct =

4 5 6 7 8 10,000 DGt µ

2

3

4 5 6 7 8 100,000

2

3

0.00001 4 5 6 7 8 1,000,000

Figure 8.52  Tube – side friction factors by Kern.

The pressure drop along the tubes can be determined with the Fanning equation: 2  L  Gt  µ  ∆p = 4f N t    Di  2ρ  µ w 



0.01



(8.80)

f × G2 × Ds(N+1) f × G2 × Ds(N+1) , psi = 5.22 × 1010 × De × s × φs 2 × g × p × De × φs at = Flow area cross bundle, sq ft B = Baffle spacing, in. C' = Clearance between adjucent tubes, in. De = Equivalent diameter, ft. de = Equivalent diameter, in. See Fig. 28 for numerical values Ds = Inside diameter of shell, ft Gs = Mass velocity, lb/hr × sq ft a = Acceleration of gravity, 4.11 × 108 ft/hr2 ID = Inside diameter of shell, in. L = Tube length, ft N = Number of baffles N11 = Number of times fluid crosses bundle from inlet to outlet, 12L/ft Pr = Tube pitch, in. ∆Ps = Shell side pressure drop, psi p = Density, lb/ft3 µ = Viscosity at the caloric temperature, lb/ft × hr µw = Viscosity at the tube wall temperature, lb/ft × hr ϕs = (µ/µw)0.14 Note: Friction factors are dimensional, sq ft/sq in. to give ∆Ps in psi directly. To obtain consistent friction factors multiply the ordinate by 144

0.08

∆Ps =

0.06 0.05 0.04 0.03 0.02

0.01 0.008

f, sq ft/sq m.

−m

0.006 0.005 0.004 0.003 0.002

0.002

0.001 0.0008

0.001 0.0008

0.0006 0.0005 0.0004

0.0006 0.0005 0.0004

0.0003

0.0003

0.0002

0.0002

0.0001 10

20

30

50

100

200 300

500

1000

2000 3000 5000 DeGs Res = µ

10,000

Figure 8.53  Shell -side friction factors for bundles with 25% cut segmental baffles.

20,000 3

5

100,000

2

3

5

0.0001 1,000,000

628  Chemical Process Engineering where m = 0.25 for laminar flow, Re < 2100 = 0.14 for turbulent flow, Re > 2100 where Nt L is the total fluid path length corresponding to Nt tube passes. The friction factor in laminar flow is



f=

16 Re

(8.74)

For heat exchanger tubes, the friction factor in turbulent region (Re > 2,100), the friction factor depends on the roughness of the tube material. For ¾ or 1 in. smooth tubes, a recommended expression by Drew, Koo and McAdams within



f = 0.0014 +

0.125 Re0.32

5% is [36]: (8.81)

Some authors suggest increasing them by 20% for commercial steel heat exchanger tubes. Additionally, for clean commercial iron and steel heat exchanger tubes, an equation given by Wilson, McAdams and Seltzer within 10% is [37]



f = 0.0035 +

0.264 Re0.42

For turbulent flow in commercial heat exchanger tubes for Re



f=

(8.81A)

3000 [38]:

0.4137 Re0.2585

(8.81B)

Equation 8.81B is analogous to the friction factor equation given for the pipe and annulus by



f=

0.3673 Re0.2314

(8.81C)

However, the surface roughness tends to be lower for heat exchanger tubes than for pipes, thus resulting in lower friction factors for tubing. The pressure drop corresponding in the change in direction at the exchanger heads in multipass heat exchangers can be determined by:

∆pr = 4N t



=

G 2t 2ρ

4N t v 2  62.5  , psi s 2g c  144 

where lb ft gc = conversion factor, 32.174 m 2 Nt = number of tube passes. lbf s s = specific gravity v = fluid velocity, ft/s. Figure 8.54 shows the tube-side return pressure drop for varying mass velocity.

(8.82)

Heat Transfer  629 1.0 0.8 0.6 0.5 0.4

One velocity head for s = I.D (water),

( )

V2 625 psi 2g´ 144

0.3 0.2

Return pressure loss/pass = 4 velocity heads Total return pressure loss = (4 velocity heads) × passes 4n V2 62.5 or, ΔPr = s 2g´ 144 g´ = Acceleration of gravity, ft/sec2 n = Number of tube passes ΔPr = Return pressure drop, psi s = Specific gravity V = Velocity, fps

( )

0.1 0.08 0.06 0.05 0.04 0.03 0.02

0.01 0.008 0.006 0.005 0.004 0.003 0.002

0.001 10,000

2

3

4 5 6 7 8 100,000

2

3

4 5 6 7 8 1,000,000

Mass velocity, lb/hr (ft2)

2

3

4 5 6 7 891

Figure 8.54  Tube – side return pressure loss.

The pressure losses due to contraction at the tube inlets, expansion at the exits and flow reversal in the headers, can be a significant part of the total tube-side pressure drop. There is no satisfactory method for estimating these losses. Kern [39] suggested adding four velocity heads per pass. Butterworth [40] suggests 1.8. The loss in terms of velocity heads can be estimated by counting the number of flow contractions, expansions and reversals and using the factors for pipe fittings to estimate the number of velocity heads lost. For two tube passes, there will be two contractions, two expansions and one flow reversal. The head loss for each of these effects is: contraction 0.5, expansion 1.0, 180o bend 1.5; so for two passes the maximum loss is [41]:



2 × 0.5 + 2. × 1.0 + 1.5 = 4.5 velocity heads



= 2.25 per pass

Frank’s recommended value of 2.5 velocity heads per pass is the most value to use [42]:



  L   µ  −m  ρu 2t ∆p t = N t 8J f    , N/m 2 (Pa) + 2.5     Di   µ w   2

where Di = Inside diameter of the tube, m jf = Tube side friction factor (Figure 21.55) L = length of one tube, m m = 0.25 for Re ≤ 2,100 and m = 0.14 for Re ≥ 2100

(8.83)

630  Chemical Process Engineering Nt = number of tube-side passes ut = tube side fluid velocity, m/s ρ = density of tube side fluid, kg/m3 pt = tube side pressure drop, N/m2 (Pa) pt calculated by Equation 8.83 is an actually permanent pressure loss. The calculated pressure drop should be less than the maximum allowable pressure drop. In some applications, maximum allowable pressure drop is decided by process conditions, whilst in other applications, maximum allowable pressure drop is the optimum pressure drop. Heat exchanger design means achieving a balance between heat transfer coefficients relating to the fixed cost and the pressure drop, which is dependent on the operating cost. Increasing the heat transfer coefficient by modifying the heat exchanger design also increases the pressure drop. Therefore, the actual pressure drop should be equal to the optimum pressure drop that minimizes the total cost of heat exchanger (i.e., fixed cost + operating cost). Table 8.19 shows the optimum pressure drop based on economic considerations. Kern [39] gives the optimum pressure drop for gases as 2 psi (13.8 kPa) and for liquids as 10 psi (69 kPa). When condensation occurs inside the tube, it is difficult to predict the pressure drop as vapor mass velocity is changing throughout the condenser. A common practice is to calculate ∆p′t using Equation 8.84 for inlet vapor flow rate and conditions and multiply it by factor 0.5.



∆p t = 0.5∆p′t

(8.84)

pT = pt + pr

(8.85)

The total pressure drop is:



Pressure drops from Dowtherm A heat transfer media flowing in pipes may be calculated from Figure 8.52. The effective lengths of fittings, etc., are shown in Chapter 3. The vapor flow can be determined from the latent heat data and the condensate flow. With a liquid system, the liquid flow can be determined using the specific heat data. In the design of all parts of a system, special consideration should be given to the large amount of flash vapor liberated on the reduction of pressure. Because of the high ratio of specific heat to latent heat, much more flash vapor is liberated with Dowtherm A than with steam. Consequently, all constrictions that would cause high pressure drops should be avoided. In addition to steam and controlled-temperature water, a number of different heat transfer fluids of a wide range of temperatures from 100-700°F (37.8–371.1oC) are supplied by (a) the Dow Chemical Co., (b) Monsanto Chemical Co., (c) Multitherm Corp., (d) Union Carbide Corp., (e) Exxon Chemical Co., (f) Mobil Chemical Co., (g) Calfo division of Petro Canada, and (h) others with qualified products. Gulley [43] recently provided an improved equation for the pressure drop on the shell side of a shell and tube heat exchanger with an accuracy of -6% to + 9% when compared with available literature. He defined the total shell-side pressure drop as the sum of the cross flow Δpc, total cross-flow pressure drop in baffle end zones Δpends, total nozzle zone pressure drops Δpnoz, and the total baffle window pressure drops Δpw. He inferred that the improved accuracy of Δpw is due to taking into account the various tube layout patterns and using the friction factor. His method results in cost savings in heat exchanger surface area, pumping cost and avoiding under capacity.

8.7.2 Factors Affecting Pressure Drop (Δp) When increasing the heat transfer coefficients in a shell and tube heat exchanger, it is necessary to increase the fluid velocities. This can be carried out from heat transfer view point by the use of a small diameter, longer tube length rather than a shorter one with a high diameter; both having the same heat transfer area. The increase in velocity implies higher pressure drops in the shell and tube-sides. Where the heat exchanger requires to be installed in an existing process, the designer must adhere to the maximum allowable pressure drop. Alternatively, if the exchanger is to go in a new process, the designer can define the heat exchanger pressure drop (Δp), and then the required pumps can be specified to overcome this pressure drop. Where these cases occur, the designer decides by balancing the higher heat exchanger cost against a higher pumping power, and thus adopt the most cost-effective solution.

Heat Transfer  631

Tube-Side Pressure Drop, Δpf The frictional pressure drop Δpf loss on the tube side is given by

f n p LG2 Dp f  Di



(8.86)

 n p n t ) divided by the flow area per tube ( πDi2 4 ) . Further, the mass flux G is the mass flow rate per tube ( m Substituting yields: Dp f 



f Ln3p n2t Di5



(8.87)

The friction factor is inversely proportional to Reynolds number in laminar flow (Equation 8.74) and proportional to the -0.2585 power of Reynolds number in turbulent flow (Equation 8.81B). Since:

Re =



 per tube 4m np  n t Di π Di µ

(8.88)

Proportionality, Equation 8.87 becomes:





Dp f 

L n2p.74 n1t .74 Di4.74

Dp f 

L n2p n t Di4

(turbulent flow)

(laminar flow)

(8.89)

(8.90)

For a given amount of heat transfer surface and a specified tube Birmingham Wire Gauge (BWG),

Ai = nt

Di L = constant

(8.91)

If the tube diameter is also specified, then nt is inversely proportional to the tube length and the proportionalities of Equations (8.89) and (8.90) become:



Dp f  n2p.74 L2.74 (turbulent flow)

(8.92)



Dp f  n2p L2 (laminar flow )

(8.93)

Therefore, independent of the flow regime, pf is a strong function of both the tube length and the number of tube passes.

632  Chemical Process Engineering

Shell-Side Pressure Drop Δpf The shell-side pressure drop is:

f G2 d s (n b 1) Dp f  de



(8.94)

The number of baffles is approximately equal to the tube length divided by the baffle spacing in consistent units, i.e.

n b + 1  L Bs



(8.95)

Also,

G=

  m m pT pT = = = a s  d s C′ Bs  d s C′ Bs d s Bs (pT − Do )  144 pT   

(8.96)

The equivalent diameter, de depends on the tube-side and pitch. For a square pitch,

d e = 4 ( p2t − π Do2 4 ) πDo



(8.97)

Combining Equations 8.94 to 8.97 gives:



∆pf 

f L p2t Do2 π Do2  3 2 2 2 Bs d s (p t − Do )  p t −   4 

(8.98)

For a given tube and shell diameter, the relation simplifies to:





∆pf 

f LPt2 2   π D o B3s (Pt − Do )2  Pt2 −   4 

2  D   L  ρu  µ  ∆ps = 8jf  s    s   d e   Bs  2  µ w 

where Bs = baffles spacing, m de = equivalent diameter, m. ds = internal diameter of shell, m jf = shell-side friction factor (Figure 8.56) L = length of one tube, m us = shell side fluid velocity, m/s. ρ = density of shell-side fluid, kg/m3 ps = shell-side pressure drop, N/m2 (Pa)

−0.14

,N/m 2 (Pa)

(8.99)

(8.100)

Heat Transfer  633 Therefore, the shell-side pressure drop is strongly influenced by the baffle spacing, Bs. Increasing Bs, increases the flow area across the tube bundle, which lowers Δpf. However, the dependence is not as strong as might be inferred from the above relationship because the friction factor increases with baffle spacing. The dependence of f on Bs is rather complex since f increases directly with the ratio Bs/ds and indirectly through the Reynolds number. However, the baffle spacing is the main design parameter for controlling the shell-side pressure drop. Other parameters in reducing the shell-side pressure drop are using double and triple segmental baffles, and using J type and X type shells [44]. Figures 8.55 and 8.56 show plots of friction factor vs. Re for tube and shell-sides of shell and tube heat exchangers. The shell-side pressure drop can be improved by using better equations for the baffle window and the nozzle pressure drops. The baffle window pressure drop in the open literature is a function only of the number of tubes crossed and the velocity of the window. It does not account for the friction factor, type of tube pattern or fluid eddies. When there are no tubes removed under the shell nozzle and the nozzles are large, using the nozzle flow area can result in wrong pressure drop being calculated. Increasing the tube pitch pt, subsequently increases the flow rate through the tube bundle and thus lowers the pressure drop. However, this has the disadvantage of increasing the required shell size and hence the cost of the heat exchanger. Generally, the tube pitch is not used to control the pressure drop except in situations where there is no alternative. Shell-side Δpf also varies directly with the tube length. For a specified tube diameter and a given amount of heat transfer surface, reducing the tube length increases the number of tubes in the bundle, which may require a larger shell. This could affect the tube-side pressure drop. Another means of reducing the shell-side pressure drop is by increasing the baffle cut which reduces the length of the cross-flow path through the bundle. In practice, this parameter is highly correlated with the baffle spacing because an appropriate ratio of these parameters is necessary for good flow distribution in the shell [38].

Shell Nozzle Pressure Drop (∆pnoz) Shell nozzle pressure drop calculation methods are difficult to find in the literature as the nozzle pressure drop is difficult to predict accurately. There is a complex flow pattern of a tube matrix, bundle bypassing and recirculation. 10–1 9 8 7 6 5 4 3

Friction Factor, Jf

2 10–1 9 8 7 6 5 4 3 2 10–1

9 8 7 6 5 4 3 2

10–1

2 101

3

4 5 6 78 9 102

2

3

4 5 6 78 9 103

2

3

4 5 6 78 9 104

Reynolds Number, Re

Figure 8.55  Tube-side friction factors by Sinnott and Towler.

2

3

4 5 6 78 9 105

2

3

4 5 6 78 9 106

634  Chemical Process Engineering

Friction Factor, Jf

101 1 9 8 7 6 5 4 3

1

2

3

4 5 6 78 9 1

2

3

4 5 6 78 9 1

2

3

4 5 6 78 9 1

2

3

4 5 6 78 9 1

2

3

4 5 6 7 891 1 9 8 7 6 5 4 3

2

2

100 1 9 8 7 6 5 4 3

1 9 8 7 6 5 4 3

Baffle cuts, percent Δ and 15 25 35 45

2

10–1 1 9 8 7 6 5 4 3

2

1 9 8 7 6 5 4 3 2

2

10–2 1 1 101

2

3

4 5 6 78 9 1 102

2

3

4 5 6 78 9 1 103

2

3

4 5 6 78 9 1 104

2

3

4 5 6 78 9 1 105

2

3

4 5 6 78 9 1 106

1

Reynolds Number, Re

Figure 8.56  Shell – side friction factor by Sinnott and Towler.

Because of this, it is possible to have pressure loss coefficients greater than the customary 1.5 velocity heads for sharp edge expansion/contraction edges. If the bundle entrance area is equal to or greater than the inlet nozzle flow area, a pressure loss coefficient of 1.0 is used. If the bundle exit area is equal to or greater than the exit nozzle area, a pressure loss coefficient of 0.58 is appropriate. There are indications that it should be larger (minimum Kn = 0.8, maximum = 1.8). If the two shell-side nozzles are not the same size, calculate the inlet pressure drop and take 2/3 of it, and make a separate calculated pressure drop for the outlet and take 1/3 of it.



∆Pnoz = 0.000108K n ( v 2s )(ρ)

(8.100A)

where ∆Pnoz = Total nozzle pressure drop, lbf/in2 Kn = Pressure loss coefficient for total shell nozzle pressure drop, dimensionless. = (0.7 < Kn < 1.8) = Velocity in the shell nozzle entrance and exit areas, ft/s. vs ρ = shell fluid density, lb/ft3

Total Shell-Side Pressure Drop, ∆ptotal The total pressure drop on the shell side is expressed by:

Δptotal = Δpc + Δpends + Δpw + Δpnoz

(8.100B)

The terms ∆pc for the interior cross-flow sections and ∆pends for the end nozzles are determined by Taborek [45]. ∆pw is the baffle window pressure drop and ∆pnoz is the pressure drop for the nozzles and entrance effects. The baffle window pressure drop ∆pw is expressed by [43]:



∆p w =

K p (0.000108)( G 2w )(N b ) ρ

(8.100C)

Heat Transfer  635 and Kp is 2   Sl   K p = fi (C l Ncw D) − 2     Sw   



(8.100D)

Equations for the distortion factor, D are [43]:



Below a baffle cut of 24%:  D = 1.0 + 2.35 (0.24 – Bc)

(8.100E)



Above 29% baffle cut:  D = 1.0 + 1.9 (Bc – 0.29)

(8.100F)

where Bc = Baffle cut as a fraction of the shell I.D. Cl = Constant in Kp Equation (8.100D) D = Distortion factor of the shell fluid profile, dimensionless Kp = pressure loss coefficient for baffle window pressure drop, dimensionless fi = friction factor for an ideal tube bank gc = gravitational conversion factor, 32.174 lbm/lbf (ft/s2) Gw = mass velocity in baffle window, lb/(s) (ft2) Nb = number of baffles Ncw = number of effective tube rows crossed in baffle window. Sl = total of leakage areas, in2 Sw = net flow area in baffle window, in2. ρ = density of shell fluid, lbm/ft3 The constant Cl depends on the tube layout pattern. The values are: 30o triangular 2.2 3.64 90o square o 45 square rotated 2.29 1.79 estimate 60o triangular There are no published charts for 60o triangular tube pattern friction factors. The above constant was derived from using 0.78 of the square rotated friction factor. The 45o square rotated tube layout gives higher pressure drops than the 30o triangular tube pattern when the Reynolds number is below approximately 100,000. Above 100,000, the pressure drops are nearly the same. The Kp in Equation 8.100D is good above a Reynolds number of 800. Below 800, it calculates low pressure drops. Gulley [43] reported that the minimum number of tube rows effective in the baffle window investigated was 4.

8.8 Heat Balance In heat exchanger design, the exchange of the heat between fluids is considered to be complete (i.e., 100%) except in those cases when heat losses to the atmosphere or other outside medium are either known or planned. Plant [46] presented a technique for comparative heat exchange performance evaluation that is based on his efficiency method and can include almost any style and application of exchanger. In condensers where heat loss is desired, insulation often is omitted from piping carrying hot fluids to take advantage of the heat loss to the atmosphere. In any heat exchange equipment the heat released or lost by one fluid must be accounted for in an equivalent gain by a second fluid, provided that heat losses are negligible for otherwise considered.

636  Chemical Process Engineering

Heat Load or Duty The heat load on an exchanger is usually determined by the process service conditions. For example, the load on a condenser for vapors from a distillation column is determined by the quality and latent heat of vaporization at the condensing conditions, or for gas coolers, by the flow of gas and the temperature range required for the cooling.



q = W cp (t2 – t1)

(8.101)

q = W 1v

(8.102)

for latent heat changes:



For cooling (or heating) and latent heat change (condense or boil):



Q = q′ = Wcp (t2 – t1) + W1v

(8.103)

An item of heat exchange equipment can be used for any of these heat changes, or any combination of them, provided the loads are established to correspond with the physical and thermal changes actually occurring or expected to occur in the unit. Thus, the heat load must be known for the design of an exchanger, although it may be determined on existing equipment from operating data. This latter is termed performance evaluation.

8.9 Transfer Area The heat transfer area. A ft2, in an exchanger is usually established as the outside surface of all the plain or bare tubes or the total finned surface on the outside of all the finned tubes in the tube bundle. As will be illustrated later, factors that inherently are a part of the inside of the tube (such as the inside scale, transfer film coefficient, etc.) are often corrected for convenience to equivalent outside conditions to be consistent. When not stated, transfer area in conventional shell and tube heat exchangers is considered as outside tube area.

Over Surface and Over Design Over surface is a measure of the safety factor used in the design of a heat exchanger through fouling factors and the use of standard equipment sizes. This is easier to visualize as it refers directly with exchanger surface area than fouling factors and calculated versus required heat transfer coefficients. The percentage over surface is defined as [27]:



% over − surface =

A − Ac × 100 Ac

(8.104)

where A = actual heat transfer surface area in the exchanger Ac = calculated heat transfer surface area based on UC Over surface depends on the relative magnitude of the total fouling allowance and the film and wall resistances. While values of 20-40% are considered typical, higher values are not unusual. Equation 8.104 is often applied with the surface area calculated using the design coefficient, UD, rather than the clean coefficient, UC. In this instance, the calculated value is referred to as the over-design, as it represents the extra surface area beyond that required to compensate for fouling. Some over-design (typically about 10% or less) is considered acceptable and often desirable, since it provides an additional safety margin in the final design.

8.10 Fouling of Tube Surface One of the major causes of unreliable heat exchanger operations is fouling. It results in exchanger shutdowns, which create throughput losses and maintenance expense. Fouling also reduces the effectiveness of crude oil and other

Heat Transfer  637 pre-heat exchangers, thereby increasing energy consumption. Therefore reliable operation of heat exchangers is essential to minimize downtimes and increase profitability. Fouling is defined as a conductive resistance resulting in an accumulation of undesirable material (deposits) on the heat transfer surfaces, which results in an unacceptable pressure drop ( p). The undesirable material may be sediments, polymers, coking products, inorganic salts, biological growth, corrosion products, etc. This process influences heat transfer and flow conditions in a heat exchanger because of transient mass, momentum and heat transfer phenomena involved with exchanger fluids and surfaces, and depends significantly on heat exchanger operation conditions. Corrosion is mechanical deterioration of construction materials of heat exchanger surfaces under the aggressive influence of flowing fluids and environment that they are in contact with. Fouling and corrosion represent heat exchanger operation induced effects, and require consideration for both the design of a new heat exchanger and operation of an existing one. In general, fouling causes a reduction in thermal performance, it can accelerate corrosion or may result in eventual failures of some heat exchangers and an increase in p. For example, in refinery of crude oil, the impact of fouling is the additional fuel required for the furnace due to the reduced heat recovery in the pre-heat train as exchangers become fouled. The use of more fuel results in additional production of carbon dioxide (CO2) emission with associated environmental impact. Figures 8.57 and 8.58A–C shows the effect of corrosion-­erosion on the shell side of a shell-and-tube exchanger, corroded tubes and sediments of the shell-tube heat exchanger. The percentage effect of the fouling factor on the effective overall heat transfer coefficient is considerably more on units with the normally high value of a clean unfouled coefficient than for one of low value. For example, a unit with a clean overall coefficient of 400 when corrected for 0.003 total fouling ends up with an effective coefficient of 180, but a unit with a clean coefficient of 60, when corrected for a 0.003 fouling allowance shows an effective coefficient of 50.5 (see Figure 8.59). Most process applications involve fluids that form some type of adhering film or scale onto the surfaces of the inside and outside of the tube wall separating the two systems (Figure 8.28). These deposits may vary in nature (brittle, gummy), texture, thickness, thermal conductivity, ease of removal, etc. Although no deposits are on a clean tube or bundle, the design practice is to attempt to compensate for the reduction in heat transfer through these deposits by considering them as resistances to the heat flow. These resistances or fouling factors have not been accurately determined for very many fluids and metal combinations, yet general practice is to “throw in a fouling factor.” This can be

Figure 8.57  Corrosion and erosion on the shell – side of a shell and tube heat exchanger.

Figure 8.58A  Rusty flakes and corroded tubes of a tube bundle of a shell and tube heat exchanger.

638  Chemical Process Engineering

Figure 8.58B  Fouled and corroded tubes and segmental baffle of a shell and tube heat exchanger.

Figure 8.58C  A shell and tube heat exchanger with fouling of sediments at the rear end showing the floating head.

disastrous to an otherwise good technical evaluation of the expected performance of a unit. Actually, considerable attention must be given to such values as the temperature range, which affects the deposit, the metal surface (steel, copper, nickel, etc.) as it affects the adherence of the deposit, and the fluid velocity as it flows over the deposit or else moves the materials at such a velocity as to reduce the scaling or fouling. Figure 8.59A shows the relationship between fouling factor, temperature and velocity, and Figure 8.59B illustrates fouling resistance for various conditions of surface fouling on heat exchanger surfaces. Fouling in oil and refinery plants consumes an extra 0.2 quad (0.2 1015 Btu) of energy annually. The annual loss attributable to heat exchanger fouling in the U.S. and U.K. together is $16.5 billion. Heat exchanger fouling has a direct impact on plant profitability and is one of the costliest problems facing the refining and chemical industries and accounts for 0.2% of the gross national products (GNP) since it [47]: 1. 2. 3. 4. 5. 6. 7.

I ncreases capital costs due to the need to over surface the heat exchanger and for cleaning. Increases maintenance costs resulting from cleaning, chemical additives, or troubleshooting. Results in loss of production due to shut down or reduced capacity. Increases energy losses due to reduced heat transfer. Increases p and dumping of dirty streams present. Enhances heating costs with the associated increase in greenhouse-gas emissions (e.g. CO2, SO2, NOx, H2S). Increases capital expenditure for over-designed units.

Unless manufacturers/fabricators guarantee the performance of an exchanger in a specific process service, they cannot and most likely will not accept responsibility for the fouling effects on the heat transfer surface. Therefore, the owner must expect to specify a value to use in the thermal design of the equipment. This value must be determined with considerable examination of the fouling range, both inside and outside of the tubes, and by determining the effects these have on the surface area requirements. Just a large unit may not be the proper answer. Fouling of the tube surfaces is usually expressed [14] as follows:

Heat Transfer  639

EFFECT OF FOULING RESISTANCE ON TRANSFER RATES 500 400

FOULING RESISTANCE

.0006

300

.001 .002

200

.004

DESIGN COEFFICIENT

100 90 80 70

.003

.005 .006 .007 .008 .009 .01 .012 .014 .016 .018 .020

60 50 40 30

20

10

CLEAN COEFFICIENT

10

20

30

40

50 60 70 80 90100

200

300

400 500

1000

Figure 8.59  Chart for determining U-dirty from values of U – clean and the sum of tube – side and shell-side fouling resistances. Note: Factors refer to outside surface. Fouling resistance is sum of (ri + ro) as h-ft2 oF/Btu. (Used by permission: Standards of Tubular Exchanger Manufacturers Association © 1959 and 1968. Tubular Exchanger Manufacturers Association, Inc., All rights reserved.) 2 ro = fouling resistance on outside of tube, (h)(°F)(ft outside surface) (Btu) 2 ri = fouling resistance on inside of tube, (h)(°F)(ft inside surface) (Btu)

Fouling of the tube surfaces (inside and/or outside) can be an important consideration in the economic and thermal design of a heat exchanger. Most fouling can be categorized by the following characteristics [14]. Note that biological fouling is not included. • Linear • Falling-rate • Asymptotic Essential all three of these types are time-dependent regarding the buildup or increase in the thickness and/or density of the fouling material. Some authors [48] suggest the need for specific time-dependent data to better define fouling, and they propose calculation techniques but no actual physical data. If the time required to reach a certain

640  Chemical Process Engineering 0.008 0.007

Fouling Factor

0.005

Crude Oils

500°F and Up

0.004

300–500°F 200–300°F

0.003

500°F and Up

0.002

300–500°F Up to 300°F

0.001 0.030

Natural Convection Below 1 1/2 ft. per sec.

0.020 Fouling Factor, hr-ft2-°F/Btu

Highly Corrosive

400°F and Up

0.006

0.010

Wet Crude Oils Desalted Crude Oils

Note: If Water Temperature Exceeds 125°F, Multiply by 1.25

Scale Changes

If Other Fluid is Very Hot Multiply by: 200–400°F, 1.2–1.5 400 and Up, 1.5–2.0

0.009 0.008 0.007 0.006

Urban Canal (Chicago Sani. Canal)

0.005

Boiler Blowdown

0.004

Spray Pond

0.003

Hard (Over 15 grains per gal.)

0.002

River (Minimum)

0.001

Clean (Soft or Treated) Boiler or Spray Pond Feed, City or Well, Great Lakes, Engine Jacket Distilled

River (Average)

Coil in Box

3 2 5 4 Velocity, ft./sec.

6

Figure 8.59A  Fouling factors as a function of temperature and velocity. (Used by permission: W. L. Nelson, No. 94 in series, Oil and Gas Journal. © PennWell Publishing Company.)

level of fouling is measured or observed operationally, then cleaning maintenance schedules can be better coordinated by considering production downtime, rather than the need to improve the heat transfer being a surprise or “crater” situation. Epstein [49, 50] lists six types of fouling: • Precipitation or scaling fouling: is solids deposition at the heat transfer surface from a supersaturated fluid. A common example is salt crystallization from an aqueous solution. Precipitation can also occur via sublimation, e.g., ammonium chloride in overheads and effluent vapors. • Particulate fouling: results from sedimentation of dust, fine or other entrained solids that settle on heat transfer surface. • Chemical reaction fouling: is the breakdown and bonding of unstable compounds at the heat transfer surface. Oil sludge and polymerization are examples of chemical reaction fouling. • Coking: is a subset of chemical reaction fouling. It is one of the most problematic types of fouling. The term coking is used to describe many forms of organic fouling; typical occuring at high temperatures

Heat Transfer  641

ES

IN T. C

RA

.P. -

GEN ENS

°F. TO

M

MI NE

THERMAL RESISTANCE OF TYPICAL UNIFORM DEPOSITS

RIT . TA BL

ELF RE

IL GO ATI N

ALT

32

AL T-

RIC LUB

R

PA RA FF

IN

0.01

8

O .-P 6°F

SPH DA OA

WA X-

AS PH

JA CO B

AD AM S Mc

- McA DAMS BLACK

0.02

LAMP

Fouling Resistance–r, or r (hr-ft2-°F/Btu)

0.03

ER SCAL CaSO4 - BOIL

E & WHITE

E - PARTRIDG

ADAMS CRACKING COIL COKE - Mc

0

0

0.02

0.04

0.06 THICKNESS OF LAYER – INCHES

0.08

0.10

0.12

Figure 8.59B  Fouling resistance for various conditions of surface fouling on heat exchanger surfaces. Thermal resistance of typical uniform deposits. Note that the abscissa reads for either the inside, ri, or outside ro., fouling resistance of the buildup of the resistance layer or film on / in the tube surface. (Used by permission: Standards of Tubular Exchanger Manufacturers Association, 6th Ed., p. 138, © 1978. Tubular Exchanger Manufacturers Association, Inc., All rights reserved.)

400oF < T < 450oF bulk [204oC < T < 232oC] in the crude and middle distillate service. The foulant materials are characterized by high organic content and appear as black oily deposits. In severe coking situations, the effect is usually a 50 – 80% loss in heat transfer effectiveness. The rate of coking and the loss in effectiveness are a function of the tube wall temperature and the amount of fouling precursors like asphaltenes present in the fluid. In the extreme, the coke deposit is a very hard layer of carbon, salts and other compounds. • Corrosion fouling: accumulation of corrosion products produced by a reaction between fluid and heat transfer surface, and tube surface becomes fouled, e.g., iron oxide on the heat transfer surface. • Solidification fouling: liquid and/or its components in liquid solution solidify on the tube surface. • Biological fouling: biological organisms attach to heat transfer surface and build a surface to prevent good fluid contact with the tube surface, e.g., algae and mussels on the heat-transfer surface. Bott [51] proposed that good fouling management such as the use of continuous and reliable monitoring based upon historical performance data or real-time data can ensure improvement in the design procedures of heat exchangers and Waters et al. [52] have employed such monitoring technique using KBC proprietary software at the Irving Oil refinery in Canada. Figure 8.60 shows a typical fouling trend for a refinery shell and tube exchanger. This figure helps to understand the fouling pattern of each individual exchanger and the engineer can thus identify any change in behavior. One theory on fouling uses the asymptotic fouling expressed by:

Rt = R∞(1- eβt) where Rt = fouling resistance at time t, m2.K/W R∞ = asymptotic fouling resistance, m2.K/W

(8.105)

642  Chemical Process Engineering

Min Shutdown

Fouling Resistance (1/(Btu/hr.(ft2.F)))

0.05

Steam Cleaning

Exchanger Fouling Factor

0.06

0.04 0.03 0.02

02 Jul 04

01 Jan 04

02 Jul 03

01 Jan 03

02 Jul 02

01 Dec 01

02 Jul 01

01 Dec 00

01 Jul 00

01 Jan 00

02 Jul 99

01 Jan 99

0.01

Figure 8.60  Typical fouling trend chart for a refinery shell and tube exchanger.

β = undetermined constants t = time, s. Considerable interest in fouling crude oil preheat trains (PHT) has resulted in the setting up of a consortium of researchers from institutions, oil companies and industrial partnership via Engineering Science Data Unit (HIS, ESDU) with the sole aim at providing a platform to investigate fundamental parameters leading to deposition, to provide a framework for predicting deposition and avoiding it by design and to formulate methods of mitigation [53]. Fouling in service is often a combination of two or more mechanisms. Also, one mechanism may be an initiator for another mechanism. Fluids can be categorized into three groups according to their potential for fouling [54]: Nonfouling fluids do not require regular cleaning. Examples are non-polymerizing light hydrocarbons, steam and subcooled boiler feed water. Linear fouling fluids have a fouling layer that is too persistent to prevent with economic design velocities. The fouling layer continues to build as a roughly linear function of time. The fouling rate depends on velocity. At a low velocity, fouling is controlled by mass diffusion to the surface. An increase in velocity in this range invariably increases mass diffusion and promotes fouling. At a high velocity, fouling is controlled by deposit shearing and residence time, and decreases with increasing in velocity. Additionally, linear fouling mechanisms are strongly dependent on surface temperature. Examples are crude oils and polymerizing hydrocarbons. Asymptotic fouling fluids attain a maximum constant fouling resistance after a short-run time. The fluid velocity impacts a shear stress at the fouling layer that removes some of the deposit. As the fouling layer thickness increases, flow area is reduced and velocity increases, thus increasing the removal rate. When the removal rate equals the deposition rate, fouling reaches an asymptotic limit. The thickness of the final asymptotic fouling layer is inversely proportional to the original velocity. Cooling tower water is an example of an asymptotic fouling fluid. Description of crude oil fouling, mitigation and monitoring is provided elsewhere [55].

Heat Transfer  643

8.10.1 Prevention and Control of Gas-Side Fouling The standard methods for control or prevention of fouling on the gas side include: removal of potential residues from the gas; additives for the gas-side fluid; surface cleaning techniques and possibly by adjusting design to minimize fouling. Control of gas or liquid-side fouling is attempted before any cleaning method is tried. The control procedure is generally preceded by verification of the existence of fouling; identification of the feature that dominates the foulant accumulation and characterization of the deposit. Some of the methods for mitigating gas-side fouling are: Particulate fouling: Can be minimized by increasing the velocity of the gas stream if it flows parallel to the surface, or decreasing the velocity if the gas flow impinges on the surface; by increasing the outlet temperature of the exhaust gases from the exchanger above the melting point of the particulates; by minimizing the lead content in gasoline or unburned hydrocarbons in diesel fuel; by reducing the fuel–air ratio for a given combustion efficiency and by minimizing flow impact or ensuring the narrowest dimension in the flow cross-section, three to four times the largest particle size. Chemical reaction fouling: Is minimized by maintaining the right temperature range in the exhaust gas within the exchanger; by increasing or decreasing the velocity of the gaseous stream; by reducing the oxygen concentration in the gaseous stream; by replacing the coal with fuel oil and natural gas (in that order) and by decreasing the fuel–air ratio. Corrosion fouling: This is strongly dependent on the temperature of the exhaust stream in the exchanger. The outlet temperature of the exhaust gas stream from the exchanger should be maintained in a very narrow range: above the acid dew point above 300oF (150oC) for sulfuric acid or hydrochloric acid condensation or below 400oF (200oC) for attack by sulfur, chlorine and hydrogen in the exhaust gas stream. Since sulfur is present in all fossil fuels and some natural gas, the dew point of sulfur must be avoided in the exchanger, which is dependent on the sulfur content in the fuel [56]. pH value has been shown to affect the corrosion fouling rate, and the corrosion rate is minimized at a pH of 11 to 12 for steel surfaces. Low oxygen concentrations in the flue gases promote the fire-side corrosion of mild steel tubes in coal-fired boilers. Stainless steel, glass, plastic and silicon are highly resistant to low-temperature corrosion [Tgas< 500oF (260oC)], stainless steel and super alloys to medium-temperature corrosion [500oF (260oC) < Tgas< 1500oF (815oC)], and super alloys and ceramic materials to high-temperature corrosion [Tgas> 1500oF (815oC)]. Chrome alloys are suitable for high-temperature sulfur and chlorine corrosion and molybdenum and chrome alloys protect against hydrogen corrosion. Crystallization fouling: Can be minimized if the surface temperature is kept above the freezing of vapors from the gaseous stream; the solidification can be minimized by keeping a “high” velocity of freezable species, having some impurities in the gas stream, possibly decreasing the foulant concentration. Figure 8.65d shows an atmospheric residue shell-side before and after fouling, and Table 8.20 shows devices for fouling measurements. Appendix A (Tables 8.21–8.24, 8.25, 8.26A-B) shows fouling resistances and factors in the petrochemical processes. Tables 8.27A-B show the thermal conductivity of materials. Coker [83] discussed the effect of fouling on exchanger heat transfer performance, fouling mitigation and monitoring and Figure 8.61 shows the solution work flow using UniSim Design Software HEX network digital twin model in determining the optimum clening cycle.

8.11 Exchanger Design Overall Heat Transfer Coefficients for Plain or Bare Tubes The overall heat transfer coefficient as used in the relationship Q = UA t is the sum of the individual coefficient of heat transfer for the (a) fluid film inside the tube, (b) scale or fouling film inside the tube, (c) tube wall, (d) scale or fouling film outside the tube, and (e) fluid film outside the tube. These must each be established individually when

644  Chemical Process Engineering PFD P & ID datasheet

Quantified Fouling effect

UniSim HEX Network Digital twin model

Performance Monitoring and prediction

Total cost comparison

Quantified Cleaning benefit

Economic factors

Optimum Cleaning cycle

Efficiency

Figure 8.61  Solution workflow.

making a new design, or they may be grouped together as U when obtaining data on an existing unit (see Appendix A (Tables 8.28A and B)). Najjar, Bell, and Maddow [57] studied the influence of physical property data on calculated heat transfer film coefficients and concluded that accurate fluid property data is extremely important when calculating heat transfer coefficient using the relationships offered by Dittus-Boelter, Sieder-Tate, and Petukhov. Therefore, the designer must strive to arrive at good consistent physical/thermal property data for these calculations. Figure 8.34 illustrates the factors affecting the overall heat transfer expressed in equation form:



Uo =

1

1  A  A  1 A  ro + rw  o  + ri  o  +  o   Ai  h i  Ai  ho  A avg 



(8.106)

or



d  d o ln  o   di  1  do  1  do  1 1 1 = + + +  + Uo h o h od 2k w h i  d i  h id  d i 

(8.106A)

where Uo = Overall heat transfer coefficient corrected for fouling conditions, Btu/h (ft2) (°F), (W/m2.oC), and referenced to outside tube surface area ho = Film coefficient of fluid on outside of tube, Btu/h (ft2) (°F), (W/m2.oC) hod = Fouling factor for shell-side fluid, (W/m2.oC) hi = Film coefficient of fluid on inside of tube, Btu/h (ft2) (°F), (W/m2.oC) hid = Fouling factor for tube-side fluid, (W/m2.oC) ro = Fouling resistance (factor) associated with fluid on outside of tube, h (ft2) (°F)/Btu [m2oC/W] ri = Fouling resistance (factor) associated with fluid on inside of tube, h (ft2) (°F)/Btu [m2oC/W]

Heat Transfer  645 *rw = Resistance of tube wall Lw/kw, h (ft2) (°F)/Btu [m2oC/W] t = Lw = Thickness of tube wall, in or ft, as consistent **kw = Thermal conductivity of material of tube wall, (Btu-ft)/[(h) (ft2) (°F)], (W/m. oC) Ao = Outside area of unit length of tube, ft2/ft, Table 8.3 Ai = Inside area of unit length of tube, ft2/ft, Table 8.3 Aavg = Average of inside and outside tube area for unit length, ft2/ft T = Corrected mean temperature difference, °F (oC) Ao = A = Total required net effective outside heat transfer surface referenced to tube length measured between inside dimensions between tubesheets. rw = Resistance of tube wall referred to outside surface of tube wall, including extended surface, if present [14] d  (d)  In reference, [14]: (h) (°F) (ft2 outside surface)/Btu *rw = Also for bare tubes  24k  (d − 2f )  d = O.D. bare tube (or, root diameter of fin tube), in. (mm) di = Tube inside diameter, in. (mm) do = tube outside diameter, in. (mm) t = Tube wall thickness, in. (mm) N = Number of fins/in. **K = k = Thermal conductivity, Btu ft/(h) (ft2) (°F), [W/m oC] (Note the difference in units.) for conversion, (see Table 8.27 in Appendix A) w = Fin height, in. ln = Natural logarithm ** = must be consistent units, also * Note: Btu/(h) (ft2) (°F/ft) = 12 Btu/(h) (ft2) (°F/in.) For integral circumferentially finned tubes [14].



rw =

t [d + 2Nw(d + w)] 12k (d − t)

(8.107)

In actual exchanger operational practice, the U values at the hot and cold terminals of the heat exchanger are not the same and can be significantly different if evaluated only at the spot conditions. In order to obtain an overall heat transfer coefficient U that represents the transfer of heat throughout the exchanger, values should be evaluated at the caloric temperature for physical properties and individual film coefficients of the fluids. Often, bulk average temperatures are used, but these may not be sufficiently accurate. Film coefficients should be more accurately evaluated at or close to the tube wall temperatures. The ratio multiplier, Ao/Ai, is usually omitted for general process design from the ri factor for inside fouling. For thin walled (18.12 ga) and highly conductive metal tubes, such as high copper alloys, the resistance of the tube wall can usually be omitted with little, if any, significant effect on U. Each of these omissions should be looked at in the light of the problem and not as a blind rule. It is important to appreciate that the tube wall resistance of such useful tube wall materials as Teflon® and other plastics, Karbate® and other impervious graphites, glass, plastic-lined steel, and even some exotic metals, etc., cannot be omitted as they are usually thick enough to have a significant impact. Refer to Appendix A (Tables 8.27A and B in Appendix A) for thermal conductivity, k, values for many common metal tubes and allow a calculation of rw, tube wall resistance. Note that the conversation for thermal conductivity is:



Btu Btu × 0.0833 = (h)(ft 2 )(°F / ft) (h)(ft )(°F / in.) 2

(8.108)

646  Chemical Process Engineering and Btu/(h) (ft) (°F) = Btu-ft/ (h) (ft2) (°F) Appendix A (Table 8.27B) tabulates some unusual and useful thermal conductivity data. Note that individual heat transfer coefficients are not additive, but their reciprocals, or resistances, are

1 1 1 A   A  = + ro + rw  o  + ri +  o  U ho h i  Ai   A avg 



(8.109)

1/ho = resistance of outside fluid film 1/hi = resistance of inside fluid film Sometimes one of the fluid side scale resistances can be neglected or assumed to be so small as to be of little value, in which case only the significant resistances and/or film coefficients need to be used in arriving at the overall coefficient U. Note that Ao, Ai, and Aavg can be substituted by do, dit, and davg respectively. Theoretically, davg, and Aavg should be the logarithmic average, but for most practical cases, the use of the arithmetic average is completely satisfactory. Recognize that only the heat that flows through the sum of all the resistances can flow through any one resistance considered individually, even though by itself, a resistance may be capable of conducting or transferring more heat. Film coefficients defined on an inside tube surface area basis when converted to the larger outside surface area become

d  A  h io = h i  i  = h i  it   Ao   do 



(8.110)

This value is the used to represent the film coefficient equivalent to the converted inside coefficient, as hio. Figure 8.76 is convenient for solving for a clean U using known or estimated film coefficients only.

Example 8.7. Calculation of Overall Heat Transfer Coefficient from Individual Components An exchanger has been examined, and the following individual coefficient and resistance determined. What is the overall coefficient of heat transfer referenced to outside coefficients? (Methods for determining these film coefficients are given later.) Film coefficient outside tube, ho = 175 Btu/h ft2oF Film coefficient inside tube, hi = 600 Btu/h ft2oF Table 8.20  Devices for fouling measurements. Fouling unit

Measurement principle

Typical reference

Jet fouling Test Oxidation Tester (JFTOT)

Mass collection of solid by a filter.

Hazlett et al. [66]

Thermal fouling test

Change in fluid temperature for given heat rate

Dickakian [67]

Closed-flow loop

Change in heat transfer coefficient measured by a fouling probe

Panchal and Watkinson [68], Crittenden [69]

Laboratory fouling test apparatus (LFTA)

Autoclave with rotating cylinder around a heating probe

Eaton and Lux [70]

Heat Transfer  647 Fouling factor outside tube, ro = 0.001 h ft2oF/Btu = 0.0025 h ft2oF/Btu Fouling factor inside tube, ri Tube wall 1 in. -16 ga, Admiralty, 0.065 –in. thick, kw = 768 Btu/(ft2) (h)/(°F)/(in.) Inside area/ft = Ai = 0.2278 ft2/ft Outside area/ft = Ao = 0.2618 ft2/ft





Uo =

Uo =

1

0.065 1  0.2618  1 + 0.001 + + 0.0025 + 175 768 600  0.2278  1 0.00571 + .001 + 0.0000846 + 0.0025 + 0.00192

Uo = 1/0.01121 = 89.17 Btu/h (ft2) (°F) Note the relative effects of the tube wall resistance when compared to the fouling factors in this case.

8.12 Approximate Values for Overall Heat Transfer Coefficients Various fluid heat transfer operations can be characterized in a general way by values of the overall coefficient, U. The values given in Perry [58, 59] cannot be all-inclusive for every situation. However, they are suitable for use in estimating exchanger performance and in checking (approximately) the calculated values and similar non-exact comparison. Appendix A (Tables 8.27A-B and 8.28A and B) lists fouling factors and a variety of applications and the corresponding overall heat transfer coefficient (U) values. In general, these units have performed without difficulty, although the questions that cannot be answered are whether they may have been too large or how too large they may have been. Tables 8.29A, B and Table 8.30 give general estimating overall coefficients; Table 8.31 gives the range of a few common film heat transfer coefficients. Table 8.32 illustrates the effect of tube-wall resistance for some special construction materials. Table 8.32A lists estimating coefficients for glass lined vessels. For steam jacketed, agitated closed reactor kettles, the overall U usually will range from 40-60 Btu/h (ft2) (°F). Of course, the significant variables are the degree or type of internal wall turbulence and the viscosity and thermal characteristics of the internal fluid. For water or other liquid cooling in the reactor jacket, the U value usually ranges from 20-30 Btu/h ft2oF. For DuPont’s Telfon® tube (¼ -in. diameter) heat exchangers (Figure 8.10) for condensing, heating, and cooling service, the U values range from 15-35 Btu/h ft2 oF. Little or no fouling occurs on the Teflon® surface. The tube-side heat transfer coefficient is a function of dimensionless parameters such as the Reynolds and Prandtl numbers and the tube diameter. These are broken down into the following fundamental parameters: physical properties (namely viscosity, μ; thermal conductivity, k; and specific heat capacity, c; tube diameter, di; and mass velocity G). The variation in liquid viscosity is quite noticeable and has a dramatic effect on the heat transfer coefficient. The fundamental equation for turbulent heat transfer inside tube is:



Nu = 0.027 Re0.8 Pr 0.33

(8.111)

or



hD  DG  = 0.027  k  µ 

0.8

 cµ   k

0.33



(8.112)

648  Chemical Process Engineering Table 8.29A  General Evaporator Overall Coefficient, U. U, Btu/hr (ft2) (°F) Long-tube vertical evaporator Natural circulation Forced circulation

200-600 400-2,000

Short-tube evaporators Horizontal Calandria (vertical, thermosiphon)

200-400 150-500

Coil evaporators

200-400

Agitated-film evaporators, Newtonian liquid 1 centipoise 100 centipoise 10,000 centipoise

400 300 120

Used by permission: Coates, J., and Pressburg, B.S. Chemical Engineering, Feb. 22, 1960, pp. 139. McGraw-Hill, Inc. All rights reserved.

Rearranging Equation 8.112 gives:



 DG  h = 0.027   µ 

0.8

 cµ   k

0.33

 k  D

(8.113)

In Equation 8.111, viscosity influences the heat transfer coefficient as parameters of both the Reynolds and Prandtl numbers. From Equation 8.113,

h

μ0.33 – 0.8

(8.114)

μ-0.47

(8.115)

or

h

In Equation 8.115, the heat transfer coefficient is inversely proportional to the viscosity raised to the power of 0.47



h∝

1

µ

0.47



(8.116)

Similarly, the heat transfer coefficient is directly proportional to the thermal conductivity raised to the power of 0.67.

h

k0.67

(8.117)

These two facts account for the heat transfer coefficient such that a high thermal conductivity promotes a high heat transfer coefficient. Table 8.33 shows the thermal conductivity and heat transfer coefficient for some components.

Heat Transfer  649 Table 8.29B  Approximate overall heat transfer coefficient, U*. Use as a guide to the order of magnitude and not as limits to any value. Coefficients of actual equipment may be smaller or larger than the values listed. Condensing Hot fluid

Cold fluid

U, Btu/hr (ft2) (°F)

Steam (pressure)

Water

350-750

Steam (vacuum)

Water

300-600

Saturated organic solvents near atmospheric

Water

100-200

Saturated organic solvents, vacuum with some noncondensable

Water, brine

50-120

Organic solvents, atmospheric and high noncondensable

Water, brine

20-80

Aromatic vapors, atmospheric with noncondensables

Water

5-30

Organic solvents, vacuum and high noncondensables

Water, brine

10-50

Low boiling atmospheric

Water

80-200

High boiling hydrocarbon, vacuum

Water

10-30

Steam

Water

250-750

Steam

Light oils

50-150

Steam

Heavy oils

10-80

Steam

Organic solvents

100-200

Steam

Gases

5-50

Dowtherm

Gases

4-40

Dowtherm

Heavy oils

8-60

Flue gas

Aromatic HC and steam

5-15

Heaters

Evaporators Steam

Water

350-750

Steam

Organic solvents

100-200

Steam

Light oils

80-180

Steam

Heavy oils (vacuum)

25-75

Water

Refrigerants

75-150

Organic solvents

Refrigerants

30-100 (Continued)

650  Chemical Process Engineering Table 8.29B  Approximate overall heat transfer coefficient, U*. (Continued) Use as a guide to the order of magnitude and not as limits to any value. Coefficients of actual equipment may be smaller or larger than the values listed. Heat Exchangers (No Change of Phase) Water

Water

150-300

Organic solvents

Water

50-150

Gases

Water

3-50

Light oils

Water

60-160

Heavy oils

Water

10-50

Organic solvents

Light oil

20-70

Water

Brine

100-200

Organic solvents

Brine

30-90

Gases

Brine

3-50

Organic solvents

Organic solvents

20-60

Heavy oils

Heavy oils

8-50

Used by permission: Pfaudler, Inc., Bul. SB 95-500-1, © 1984.

The range of heat transfer coefficients for hydrocarbon liquids is rather large due to the large variation in their viscosity from < 0.1 cP for ethylene and propylene to > 1,000 cP for bitumen. The large variation in the heat transfer coefficients of hydrocarbon gases is due to the large variation in operating pressure. As operating pressure rises, gas density increases and the pressure drop (Δp) is directly proportional to G2 and inversely proportional to the density ρ. Thus, for the same Δp, a higher mass velocity G can be maintained when the density is higher, and this larger mass velocity gives a greater heat transfer coefficient. Figure 8.62 presents the effect of total fouling on the overall heat transfer coefficient. For example, if a clean nonfouled coefficient is corrected to the fouled condition by one overall fouling factor, the effect of changing the expected amount of fouling to another value can be readily determined. Figure 8.62 can be used to solve the overall heat transfer coefficient, U, equation for the clean coefficient, composed of the tube-side and shell-side film coefficients only. Correction for the tube-side and shell-side scaling and the tube-wall resistance can be added by looking up the clean U in Figure 8.62 and reading the dirty or fouled U valued or by using Equation 8.118 developed by Hedrick [60], which is reported to produce smooth curves for all value of L/d from 2 to 50 and across the Reynolds number range of 2,000 to 10,000.

h io = (16.1 d o )[BI k(cµ / k)1/3 (µ / µ w )0.14 ]



(8.118)

where B = (-3.08 + 3.075X + 0.32567X2 – 0.02185X3) (10 di/L) [1 – (X/10)0.256]



X = Re/1,000 Re = Reynolds number di = inside tube diameter, in. do = outside tube diameter, in.

(8.119)

Heat Transfer  651 Table 8.29C  Approximate overall heat transfer coefficient, U (Btu/h.ft2 oF). Condensing Process Side (Hot)

Condensing Fluid (Cold)

U (Btu/h.ft2 oF)

Hydrocarbons (light)

Water

100-160

Hydrocarbons w/ inerts (traces)

Water

30-75

Organic vapors

Water

70-160

Water vapor

Water

150-340

Water vapor

Hydrocarbons

60-150

Exhaust steam

Water

280-450

Hydrocarbons (light)

Refrigerant

45-110

Organics (light)

Cooling brine

50-120

Gasoline

Water

65-130

Ammonia

Water

135-260

Hydrocarbons (heavy)

Water

40-75

Dowtherm vapor

Liquid organic

75-115

Vaporization Hydrocarbons, light

Steam

90-210

Hydrocarbons, C4-C8

Steam

75-150

Hydrocarbons, C3-C4 (vac)

Steam

45-175

Chlorinated HC

Steam

90-210

HCI solution (18-22%)

Steam

120-240

Chlorine

Steam

130-220

Coils in Tank Coil Fluid

Tank Fluid

U (Btu/h.ft2 oF)

Steam

Aqueous sol’n (agitation)

140-210

Steam

Aqueous sol’n (no agitation)

60-100

Steam

Oil-heavy (no agitation)

10-25

Steam

Oil-heavy (agitation)

25-55

Steam

Organics (agitation)

90-140

Hot Water

Water (no agitation)

35-65

Hot Water

Water (agitation)

90-150

Hot Water

Oil-heavy (no agitation)

6-25

Heat transfer oil

Organics (agitation)

25-50 (Continued)

652  Chemical Process Engineering Table 8.29C  Approximate overall heat transfer coefficient, U (Btu/h.ft2 oF). (Continued) Salt brine

Water (agitation)

50-110

Water (cooling)

Glycerine (agitation)

50-75

Film Coefficients with Fluid Inside Tubes, Forced Convection Useful dimensionless groups for heat transfer calculation are [70]. Symbol

Name

Function

Gz

Graetz number

wc/kL

Gr

Grashof number

D3ρ2gβΔt/μ2

Nu

Nusselt number

h D/k

Pe

Peclet number

DG c/k

Pr

Prandtl number

c μ/k

Re

Reynolds number

DG/μ, or, D u ρ/μ

Sc

Schmidt number

μ/ρkd

St

Stanton number

h/cG

k = thermal conductivity, Btu/h-ft-°F c = specific heat of fluid, Btu/lb-°F = viscosity of fluid, centipoise = viscosity at the wall, centipoise w L = tube length, ft hio = inside film coefficient based on the outside tube diameter, Btu/(h) (ft2) (°F) where C or c = specific heat of fluid, Btu/(lb) (°F) D = inside diameter of tube, ft G = mass velocity, lb/h (ft2) g = acceleration of gravity, ft/(h2), or ft/s2, depends on the system of units h = heat transfer film coefficient, Btu/(h) (ft2) (°F) = factor for heat transfer, dimensionless jH k = thermal conductivity, Btu/(h) (ft2) (°F/ft) L = length, ft t = temperature difference for heat transfer, °F v = velocity, ft/h = viscosity, absolute, lb/(h) (ft) = density, lb/ft3 kd = diffusivity (volumetric), ft2/h = thermal coefficient of expansion, 1/°F

Stream Solvent Propylene (vaporization) Propylene (vaporization) Chilled water Oil Condensate and vapor Chilled water Propylene (refrigerant) Transformer oil Chlorinated Ci Ethylene vapor Propane liquid Steam Steam Steam Air mixture

Solvent

Solvent

C4 unsaturates

Solvent

Oil

Ethylene-vapor

Ethylene vapor

Condensate

Chilled water

Calcium brine-25%

Ethylene liquid

Propane vapor

Lights and choir. HC

Unsat. Light HC, CO, CO2, HI2

Ethanolamine

Steam

Outside tubes

Butadiene mix. (super-heating

A. Heating

In tubes

U, Overall Heat Transfer Coefficient, Btu/(h) (ft2) (°F)

U

H

H

U

H

…

…

…

…

…

…

1-2

H K-U

…

…

…

…

…

…

20-40

1-2

…

25-35

Velocities tube

H

K-U

H

K

H

H

K

K

H

H

Type equipment

Table 8.30  Overall heat transfer coefficients in typical petrochemical applications.

…

…

…

…

…

…

0.5-1.0

…

…

…

…

…

…

…

…

1.0-1.8

…

ft/s. shell

10-20

15-25

10-2

12-30

6-15

10-20

40-60

40-75

60-135

50-80

90-125

60-85

35-75

13-18

30-40

35-40

12

Overall coefficient

-30-220

400-40

400-100

-30-260

-25-100

-170-(100)

-20-+20

75-50

60-30

270-100

600-200

150-100

115-40

100-35

40-0

110-30

400-100

Temp. range, °F

0.005

0.001

…

0.001

…

…

0.002

0.001

0.001

.001

0.002

0.0015

.003

…

…

…

…

Tube

0.0015

0.001

…

0.001

…

…

0.005

0.001

0.001

.001

.001

.0015

.001

…

…

…

…

Shell

Estimated fouling

(Continued)

…

…

0.3

…

0.002

0.002

…

…

…

…

…

…

…

.005

0.006

0.0065

0.04

Overall

Heat Transfer  653

Styrene and tars Freon-12 Lean copper solvent Treated water C2-chlor HC, lights Hydrogen chloride Heavy C2-chlor. Perchlorethylene Air and water vapor Engine jacket water Absorption oil Air-chlorine Treated water

Steam

Chilled Water

Water*

Water

Water

Water

Water

Water

Water

Water

Water

Water

Water

KU H

Propylene refrig. Propylene refrig. Propylene refrig. Propylene refirg. Propylene refrig. Water

HC unsat. lights

Butadiene

Hydrogen chloride

Lights and chlori-ethanes

Ethylene

Unsat. Chloro HG

KU

H

K

K

Propylene refrig.

K

H

U

H

H

H

H

H

H

H

H

H

H

U (in tank)

Type equipment

C4, unsat

B. Condensing

Outside tubes

In tubes

U, Overall Heat Transfer Coefficient, Btu/(h) (ft2) (°F)

7-8

…

…

…

v

v

v

5-7

4-7

…

…

…

…

…

…

2-3

3-5

4-5

4-7

…

Velocities tube

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

1-2

…

…

…

ft/s. shell

Table 8.30  Overall heat transfer coefficients in typical petrochemical applications. (Continued)

90-120

60-90

15-25

110-60

65-80

50-60

58-68

170-225

8-18

80-115

230-160

20-35

55-35

45-30

7-15

6-10

100-125

100-120

100-130

50-60

Overall coefficient

145-90

120-(-10)

130-(-20)

0-15

20-35

45-3

60-35

200-90

250-90

130-90

175-90

370-90

150-90

300-90

230-90

360-100

90-110

180-90

90-25

190-230

Temp. range, °F

0.002

0.001

0.002

0.012

…

…

…

0.001

…

0.0015

0.0015

0.0015

0.001

0.001

0.002

0.002

…

…

0.001

0.001

Tube

0.001

0.001

0.001

0.001

…

…

…

0.001

…

0.001

0.001

0.0015

0.001

0.001

0.001

0.001

…

…

0.001

0.002

Shell

Estimated fouling

(Continued)

…

…

…

…

0.004

0.0055

0.005

…

0.005

…

…

…

…

…

…

…

0.005

0.004

…

…

Overall

654  Chemical Process Engineering

U KU

Water Water Water Water Propylene vapor Propylene Steam Steam Steam (exhaust) Steam Propylene cooling and cond. Air-chlorine (part. cond.) Light HC, cool and cond. Ammonia Ammonia Freon

Unsat Chloro HG

Unsat Chloro HG

Chloro HG

Solvent and noncond.

Water

Water

Water

Water

Treated water

Oil

Water

Chilled water

Water

Water

Water

Air-Water vapor

H

H

U

H

H

H

H

H

H

H

H

KU

H

H

Outside tubes

Type equipment

In tubes

U, Overall Heat Transfer Coefficient, Btu/(h) (ft2) (°F)

…

…

…

…

…

…

…

…

…

…

…

2-3

…

…

6

3-8

Velocities tube

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

ft/s. shell

Table 8.30  Overall heat transfer coefficients in typical petrochemical applications. (Continued)

10-20

10-50

280-300

140-65

60-10

110-90

120-90

270-90

10-15 (Co)

20-30 35-90

8-15 (C)

15-20 (Co)

110-150 8-15

30-45 (C)

375-130

220-130

230-130

300-90

130-90

200-90

260-90

110-(-10)

130-(-20)

110-90

Temp. range, °F

25-50

70-110

20-30

190-235

225-110

60-100

130-150

25-15

20-30

15-25

180-140

Overall coefficient

…

0.001

0.001

0.0015

0.0015

0.0015

0.003

0.0001

0.0015

0.002

0.0015

…

0.0015

0.001

0.002

0.001

Tube

…

0.001

0.001

0.003

0.005

0.001

0.001

0.0001

0.001

0.0001

0.001

…

0.004

0.001

0.001

0.001

Shell

Estimated fouling

(Continued)

0.01

…

…

…

…

…

…

…

…

…

…

0.003

…

…

…

…

Overall

Heat Transfer  655

VT VT

Steam Steam Steam Steam Steam Steam Steam Steam Naphtha frac. C3 Butadiene, unsat.

Chloro HC

Chloro, unsat HC

Chloro ethane

Chloro ethane

Solvent (heavy)

Mono-di-ethanolamines

Organics, acid, water

Amines and water

Steam

Propylene

Propylene-butadiene

*Unless specified, all water is untreated, brackish, bay or sea. Notes: H = horizontal, fixes or floating tubesheet T = thermosyphon V = Vertical U = U-tube horizontal bundle v = variable r = reboiler (C) = cooling range ∆t K = kettle type HC = hydrocarbon (Co) = condensing range ∆t Data/results based on actual and specific industrial equipment.

H

KU

Annulus, long F.N.

VT

VT

VT

H

U

VT

H

Steam

C4 Unsat.

H

Steam

Outside tubes

Type equipment

Solvent, Copper-NH3

C. Reboiling

In tubes

U, Overall Heat Transfer Coefficient, Btu/(h) (ft2) (°F)

…

…

…

…

…

…

…

…

…

…

…

…

7-8

Velocities tube

25-35

…

…

…

…

…

…

…

…

…

…

…

…

ft/s. shell

Table 8.30  Overall heat transfer coefficients in typical petrochemical applications. (Continued)

15-18

120-140

15-20

120-140

60-100

210-155

70-115

50-70

90-135

100-140

35-25

95-115

130-150

Overall coefficient

400-100

-150-40

270-220

360-250

450-300

450-350

375-300

30-190

300-350

230-130

300-350

95-150

180-160

Temp. range, °F

…

0.001

0.0035

0.002

0.003

0.002

0.004

0.002

0.001

0.001

0.001

…

…

Tube

…

0.001

0.0005

0.0015

0.0005

0.001

0.0005

0.001

0.001

0.001

0.001

…

…

Shell

Estimated fouling

0.02

…

…

…

…

…

…

…

…

…

…

0.0065

0.005

Overall

656  Chemical Process Engineering

Heat Transfer  657 Table 8.31  Approximate film heat transfer coefficients, hi or ho. Film Coefficient, Btu/h. (ft2) (°F) No Change of Phase Water Gases Organic solvents Oils

300-2000 3-50 60-500 10-120

Condensing Steam Organic solvents Light oils Heavy oils (vacuum) Ammonia

1000-3000 150-500 200-400 20-50 500-1000

Evaporation Water Organic solvents Ammonia Light oils Heavy oils

800-2000 100-300 200-400 150-300 10-50

Used by permission: Pfaudler, Inc., Bul. SB 95-500-1 ©1984.

Table 8.32  Effect of tube wall material and film conditions on overall heat transfer coefficient. Overall Heat Transfer Coefficient, U, Btu/h. (ft2) (°F) Percentages in ( ) refer to graphite tube

Tube

Heating water with steam

Condensing organic vapor with water

Cooling organic liquid with water

Cooling viscous organic liquid with water

Stainless steel, 304-16BWG

184(92.5)

79(96.5)

43(100)

18.9(100)

Impervious graphite, 3/16 in. tk. wall

199(100)

82(100)

43(100)

18.9(100)

Glass, 0.0625 in. wall

89(44.7)

56(68.3)

36(82.5)

17.3(91.6)

*Stainless steel 304, reactor, 21/32 in. wall

83(41.)

54(65.2)

35(80.9)

17.0(89.9)

*Glassed-steel reactor pipe, 11/16 in. steel wall

71(35.7)

48(58.5)

35(80.9)

16.3(86.2)

Film coefficients only, hi + ho

300

100

50

20

*Thickness based on 1,000-gal reactors for service at same pressure. Used by permission: Ackley, E. J., Chemical Engineering, April 20, 1959, p. 181. © McGraw-Hill, Inc. All rights reserved.

Gas and liquid heat transfer inside tubes has been studied by Sieder and Tate [60] and is represented by Figure 8.63. Also see references [61–63]. The equations representing portions of the graph are as follows:

658  Chemical Process Engineering Table 8.32A  Estimating overall heat transfer coefficient, U, for special applications. Overall Heat Transfer Coefficient (Service U)* Btu/(h) (ft2) (°F)** Material of construction (barrier material)

Heating water with steam

Heating water with heat transfer oil

Cooling organic liquid with water

Cooling viscous organic liquid with water

Stainless steel reactor, 0.656 in. wallδ

90.2

62.2

35.1

16.7

Glasteel reactor, 0.05 in. glass 0.688 in. steelδ

77.0

55.6

32.6

16.5

Combined film

300

137

50

20

hi ho conductance, hi + ho

*Fouling factors typical to process fluids and materials of construction are included. **Multiply by 4.882 for conversion to kcal/(hr) (m2) (°C). δ Thickness based on 1,000 –gal. reactors for service at same pressures.

Table 8.33  Heat transfer coefficients of certain components. Component

Thermal conductivity k, W/ moC (Btu/h ft oF)

Heat transfer coefficient h, W/m2.oC (Btu/h ft oF)

Cooling water

~ 64 (111)

7000 (39746)

Hydrocarbon liquids

0.09 - 0.14 (0.16-0.20)

291 – 1512 (1652 – 8585)

Hydrocarbon gases

0.02 – 0.03 (0.03-0.05)

58 – 582 (329 – 3305)

A. For viscous streamline flow of organic liquids, water solutions (not water) and gases with DG/ < 2,100 in horizontal or vertical tubes: deviation 6%-12% [39]: 1/3



hi D  DG   cµ   D    µ  = 1.86       ka  µ   k a   L    µ w 



hiD  4Wc  = 1.86   πk a L  ka



hi  µ  = 1.86  DG  cG

2/3

1/3

 µ   µ  w

 ka   µc 

2/3

0.14

0.14



(8.120)



 D  L

(8.121) 1/3

 µ   µ  w

0.14



(8.122)

B. For turbulent flow of viscous fluids as organic liquids, water solutions (not water) and gases with DG/ >10,000 in horizontal or vertical tubes: deviation 115%-210% [39]:



hi D  DG  = 0.023  ka  µ 

0.8

 cµ   k  a

1/3

 µ   µ  w

0.14



C. For transition region between streamline and turbulent flow, use Figure 8.63.

(8.123)

Heat Transfer  659 500

400

300

200

50

40

30

20

10

30

100 90 80 70 60

U clean

40 50 60 70 80 90 100

ht 200

300

500 100

80

60

40

20

700 800 900 1000

140

600

0 00 = 1 8000 0 hs 6 5000 40 300 260 220 180

400

Figure 8.62  Chart for determining U – clean from tube – side and shell – side fluid film coefficients; no fouling included. Note: s = shell – side, t = tube – side. (Used by permission: Elements of Heat Transfer, © 1957, Brown and Root, Inc.)

1,000 500

H

j =

hi D cµ –1/3 µ –0.14 ( µ ) kα ( kα )

100

50 30

hi = Inside Film Coefficient, Btu/(hr.)(sq.ft.)(°F) hio = Inside Film Coefficient Referenced to the Outside Area, Btu/(hr.)(sq.ft.)(°F) I D = Tube Inside Diameter, inches OD = Tube Outside Diameter, inches G = Mass Velocity, W/at, lb./(hr.)(sq.ft.) C = Specific Heat, Btu/(lb.)(°F) ka = Thermal Conductivity, Btu/(hr.)(sq.ft.)(°F/ft.) at = Flow Area Through Tubes, sq. ft. L = Length of Flow Path, ft. D = Inside Diameter of Tubes, ft. µ = Viscosity at Caloric Temperature, lb./ft/(hr.) µw = Viscosity at Tube Wall Temperature, lb./ft/(hr.) w = Weight Flow of Liquid, lb./hr. Note: Correct hi to hio : hio = hi ( I D ) OD Viscosity in Centipoise × 2.42 = lb./ft.(hr.)

10 8 6 5 4 3

24 36 48 72 120 40 2 180 360 500

LD =

2 1 10

20

30 40

60

100

200

400

1,000

4,000

10,000

100,000

1,000,000

Re = DG µ

Figure 8.63  Tube – side heat transfer, heating and cooling. (Adapted and used by permission: Kern, D. Q., Process Heat Transfer, 1st ed., © 1950. McGraw-Hill Book Co. All rights reserved. Originally adapted by Kern from Sieder and Tate.)

660  Chemical Process Engineering where c D G hi ka L w

= specific heat of fluid at constant pressure, Btu/(lb) (°F) = inside diameter of tube, ft = fluid mass velocity, lb/(h) (ft2 tube cross-section flow area) = film heat transfer coefficient inside tube, Btu/(h) (ft2) (°F) = thermal conductivity of fluid at average bulk temperature of fluid, Btu/h (ft2)/(°F/ft) = total heated or cooled length of heat transfer path, ft = mass flow rate of fluid flow per tube, lb/h = viscosity of fluid, lb/(h) (ft) = viscosity of fluid at wall temperature, lb/(h) (ft) w

Figures 8.64, 8.65, and 8.66 are useful in solving the equivalent of Equation 8.148 for turbulent as well as streamline flow of gases and vapors inside tubes. To use the charts, proceed as follows: A. for turbulent flow: 1. Determine p using fluid properties (Figure 8.64). 2. Determine tube-side film coefficient, hi, based on inside tube surface (Figure 8.65). 3. Correct hi for the effect of tube size by multiplying by the accompanying factor shown in Figure 8.65. B. For streamline flow: 1. Determine p (Figure 8.64). 2. Determine hi (Figure 8.66). Viscosity µ, centipoise 10–3

10–2

10–1

1

10

1

10

Spe

cifi ch

eat

,C

1.0 0.6

0.8 0.4

0.2 0.1

α

k y, al it m ctiv r e u 02 Th nd 1 0.0 003 4 co .00 0. .00 6 0 0 .00 8 0 .00 0

01

0.

02 0. 03 0. .04 0 .06 8 0 .0 0 1

0.

10–3

10–2

2 0. .3 0 .4 0 .6 0 .8 0 0 1. –1 10

Physical property factor, ϕp

Figure 8.64  Flow inside tube for gas and vapors. Physical property factor depends on viscosity, specific heat and thermal conductivity. (Used by permission: Ning Hsing Chen, Chemical Engineering, V. 66, No. 1, © 1959. McGraw-Hill, Inc., All rights reserved.)

Heat Transfer  661 Tubeside heat transfer coefficient, corrected for viscosity, hi Btu/hr-ft2-°F

103 ty er op pr l ica p ys r, ϕ Ph cto 10 fa 8 6 4

102

3

2

1 8 0. 0.6

0.4 0.3

0.2 0 0.1 08 0. 6 0.0

10

4 0.0 3 0.0 2 0.0 1 0.0 .008 0 06 0.0

04 0.0 03 0.0 02 0.0

1 10–1

102

10

1

103

Mass velocity G”, lb/sec-ft2 Tube Size Correction Factors for Turbulent Flow ¾" × 14 BWG 1.011 1" × 14 BWG 0.942 16 1.000 1¼" × 10 0.912 1" × 10 0.967 12 0.903 12 0.955 14 0.894

Figure 8.65  Flow inside tubes for gases and vapors. Heat transfer coefficient for vapors and gases in turbulent flow. (Used by permission: Ning Hsing Chen, Chemical Engineering, V. 66, No. 1, © 1959. McGraw-Hill, Inc., All rights reserved.)

3. Correct hi by multiplying by the tube size and heated length factors accompanying Figure 8.66. C. For water, the inside film coefficient is represented by Figure 8.67A. Furman [64] presents charts that reduce the expected deviation of the film coefficient from the ±20% of Figure 8.67A, B, C, and D. D. For heating and cooling turbulent gases and other low viscosity fluids at DG/ > 8,000; the Dittus-Boelter relation in used. See Figures 8.63, 8.68, and 8.69.



hiD  DG  = 0.0243  ka  µ 

0.8

 cµ   k  a

0.4

 µ   µ  w

0.14



(8.124)

For cooling, DG/ > 8,000, the following is sometimes used in place of the preceding relation, Figure 8.69:



hiD  DG  = 0.023  ka  µ 

0.8

 cµ   k  a

0.4

 µ   µ  w

0.14



(8.125)

When the Prandtl number (c /ka) can be used at 0.74, as is the case for so many gases such as air, carbon monoxide, hydrogen, nitrogen, oxygen, a close group of ammonia (0.78), and hydrogen sulfide (0.77), this relation reduces to the following:



hiD  DGC  = 0.026   k a  ka

0.8



(8.126)

662  Chemical Process Engineering Tubeside heat transfer coefficient, corrected for viscosity, hi Btu/hr-ft2-°F 10–2

10–1

1

0

1 .00

2 0.0 .03 4 0 .0 6 0 .0 8 0 .0 0

0.2 .3 0 .4 0 .6 0 .8 0

1

1.

0

0.

1

0. 01

al er m Th

102

02 0.0 .00304 0 0.0 06 8 0.0.00 0

co

nd u

ct

ivi

ty ,k

0.1

α

C eat, ific h Spec 10 8 6 4 3 2 1 0.8 0.6 0.4 0.3 0.2

10

10

102 103 104 Mass velocity G", lb/sec-ft2 Heated Length Correction Factors, Streamline Flow Tube Size Correction Factors for Streamline Flow 8 ft 1.26 16 ft 1.00 ¾ in. × 14 BWG 1.060 1 in. × 14 BWG 0.744 10 1.17 18 0.96 16 1.000 0.631 1 ¼ in. × 10 12 1.10 20 0.96 1 in. × 10 0.846 12 0.600 14 1.05 12 0.793 14 0.571

Figure 8.66  Flow inside tubes for gases and vapors. Heat transfer coefficient for streamline flow. (Used by permission: Ning Hsing Chen, Chemical Engineering, V. 66, No. 1, © 1959. McGraw-Hill, Inc., All rights reserved.)

Note that the values of the initial coefficients on the right side of the preceding equations vary significantly among several respected references; therefore, the engineer should not be surprised to note these variations in the literature.

Simplified Equations For common gases, Equation 8.123 can be simplified to give the following approximate equations:



0.014C p G0.8 hi = D0.2

(8.127)

Similarly, for water at ordinary temperatures and pressures,

where Cp = heat capacity of fluid, Btu/lb.oF

150(1 + 0.011t b )(V′ )0.8 hi = (D′ )0.2

(8.128)

Correction Factor, Fw

Heat Transfer  663

1.1 1.0 0.9 0.8 0.4

0.5 0.6 0.7 0.8 1.0 1.5 Inside Diameter of Tube

2.0

3,000

Film Heat Transfer Coefficient, hi, Btu/(hr.)(sq.ft.)(°F)

2,000

1,000 900 800 700 600

0 18 °F 0 140 , re 16 tu 0 00 ra 12 1 pe 0 m 80 6 e T 0 er 4 t a nW

ea

M

500 400 300

Based on 3/4" OD (0.62" ID) × 16 BWG Tube. To Obtain:

200

100 1

(a) hi for Other Tube, Multiply Curve Value, hic by Correction Factor, Fw Tube ID (b) hio, Multiply Corrected hi by Tube OD

2

3 4 5 6 7 8 9 10 Tube Velocity, Ft./Sec.

20

Figure 8.67A  Tube-side film heat transfer coefficient for water. (Used by permission: Kern, D. Q., Process Heat Transfer, 1st ed., © 1950. McGraw-Hill, Inc., All rights reserved. Original adapted from Eagle and Ferguson, Proc. Royal Society A 127, 450, © 1930.)

D = diameter, ft. D = diameter, in. G = mass velocity inside tube, lb/h ft2 hi = heat transfer film coefficient, Btu/h.ft2oF tb = average (i.e. bulk) temperature of water, oF V = velocity of water, ft/s. Equations 8.127 and 8.128 are dimensional, and a value of hi is obtained only if the units are employed for the indicated variables. Pierce [65] proposes and illustrates good agreement between the test data and the correlation for a smooth continuous curve for the Colburn factor over the entire range of Reynolds numbers for the laminar; transition, and turbulent flow regimes inside smooth tubes:



1/12

1   1  J 4 =  9.36  3/2  8 N   1.969(106 )    N1.6  Re  Re     −14 +    7.831(10 )  NRe    

(4)

(8.129)

664  Chemical Process Engineering 10 9 8 7

ho = FILM RATE REFERRED TO O.D. TUBE SURFACE

6

HEAT TRANSFER WATER INSIDE I" 18 BWG TUBES

5 4 3

2

10 9 8

CORRECTION MULTIPER FOR TUBE O.D. BWG 1" 3/4" 5/8" 20 0.975 1.67 2.36 18 1.000 1.73 2.46 18 1.030 1.80 2.58 14 1.067 1.89 2.78 12 1.120 2.04 3.02 10 1.185 2.20 3.35 8 1.270

7 6 5 4 3

2

10 9 8 7 6 5 4 3

2

1

WESTERN SUPPLY COMPANY

1

2

3

4

5

6 7

8 9 10

2

3

4

5

6 7

8 9 10

2

3

4

5

6 7

8 9 1

Figure 8.67B  Heat transfer film coefficient for water flowing inside 1 in. x 18 BWG tubes referred to outside tube surface area for plain tubes. Note the correction for tubes of wall gauges other than 18 BWG. (Used by permission: J. B. Co., Inc., Western Supply Div., Tulsa, Okla.)

Colburn Factor, J:



J = J4( b/ w)0.14

(8.130)

2/3 h = J ( C pρv/NPr )

(8.131)

Then, convective heat transfer coefficient:



where Cp = specific heat, J/kg K = J/kg-Kelvin D = diameter, m, meter J = Colburn factor = Colburn factor given by equation proposed by Pierce J4 L = length of tube, m NPr (Pr) = Prandtl number NRe (Re) = Reynolds number v = velocity, m/sec = dynamic viscosity, Pa-s (pascal-sec)

Heat Transfer  665 10,000 8,000 6,000

WATER–200°F.

4,000

600°F.

700°F.

500°F. 400°F.

2,000 300°F. 1,000 800

– (hi) (di)

600 400

200

100 80 60 40

20

10

10

50

100

500 (d·) (G') = (di) (v) (ρ)

1000

5000

10,000

Figure 8.67C  Tube-side (inside tubes) liquid film heat transfer coefficient for Dowtherm®, A fluid inside pipes/tubes, tubulent flow only. Note: h = average film coefficient, Btu/h – ft2 oF; di = inside diameter, in.; G′ = mass velocity, lb/s ft2; v = fluid velocity, ft/s; k = thermal conductivity, Btu/h ft2(oF/ft); μ = viscosity, lb/h ft; Cp = specific heat, (Btu/lb oF). (Used by permission: Engineering Manual for Downtherm Heat Transfer Fluids, © 1991. The Dow Chemical Co.)

b w kg

= density, kg/m3 = evaluate at bulk temperature = evaluate at wall temperature = kilogram

Buthod [1] presents Figure 8.69 for gases flowing inside tubes. Note that the coefficient refers to the outside tube surface area. It is useful for gases other than those shown because the scale can be multiplied by 10 to obtain the proper order of magnitude for specific heat. Simplify the relation for heating and cooling gases, using: c /ka = 0.78 and



= 0.435 (Reference [65, 66])

cG0.8 h = 0.0144 0.2 D

(8.132)

666  Chemical Process Engineering 10,000 8,000

LIQUID FILM COEFFICIENT FOR DOWNTHERM INSIDE PIPES

6,000 4,000 3,000

W AT ER

20

0° F

2,000

1,000 800 600

DOWTHERM A 500°F., 600°F. & 700°F. 400°F. 300°F.

h D1

400 300 200

DOWTHERM E 400°F. 300°F. 200°F. 100°F.

100 80 60 40

D1 = DIAMETER, INCHES G1 = MASS VELOCITY LB./(sec.)(sq. ft) h = FILM COEFFICIENT, B.t.u./(hr.)(sq. ft.)(°F.)

30 20

4000

2000

6000 8000 10000

D1 G1

600 800 1000

400

200

60 80 100

40

20

10

10

Figure 8.67D  Tube-side (inside pipes or tubes) liquid film heat transfer coefficient for Dowtherm® A and E at various temperatures. (Used by permission: Engineering Manual for Downtherm Heat Transfer Fluids, © 1991. The Dow Chemical Co.)

Note that below G = 1,200P2/3, results may be too conservative. Gases in turbulent flow in circular helical coils [66, 67]. Multiply hi for straight tubes by [1 + 3.5dit/DH] where c = specific heat capacity of the gas, Btu/lboF dit = inside tube diameter, in. DH = diameter of helix of coil, in. P = absolute pressure, atm. (this equation only) Ganapathy [68] developed nomograms for solving for film heat transfer coefficients for superheated steam, gases, liquids, and vapor refrigerants flowing inside exchanger tubes. See Figures 8.70A, B, C and D. Also see Rubin, reference [69].

Heat Transfer  667 1,000 800 600 500 400

hi D kα

= 0.023

DG 0.8 µ

c µ 0.4 kα

(Maximum Deviation = 30%)

300

)

ion

at

s en

d

n Co no

200 m

hi D kα

ea

100 80

te

ea

rh

e up

t dS

(

hi = Inside Film Coefficient, Btu/(hr.)(sq.ft.)(°F) D = Inside Tube Diameter, ft. kα = Thermal Conductivity of Fluid, Btu/(hr.)(sq.ft.)(°F/ft.) G = Mass Velocity, lb./(hr.)(sq.ft Cross-Section) µ = Absolute Viscosity, lb./(hr.)(ft) c = Specific Heat, Btu/(lb.)(°F)

S

60 50 40 30 20 10 1,000

10,000

ds

i Flu

DG µ

100,000

1,000,000

Figure 8.68  Convection inside film coefficient for gases and low viscosity fluids inside tubes – heating and cooling. (Used by permission: McAdams, W. H. Heat Transmission, 2nd. Ed. © 1942. McGraw-Hill, Inc., All rights reserved.)

hiα = Film Rate Referred to Outside Tube Surface, Btu/(hr.)(sq.ft.)(°F)

1,000

100

ic

cif

s

Ga

10

1" O.D. 3/4" O.D. Lower Limit of 1 Turbulent Flow 10

e Sp

a He

.7 t .8 .5 .6 .4 .3 .2

Multipliers for Tube Size BWG 1" 3/4" 5/8" 20 0.976 1.67 2.34 18 1.00 1.73 2.34 16 1.03 1.80 2.58 14 1.06 1.89 2.76 12 1.12 2.03 3.02 100 Flow Rate, lb./Tube(hr.)

1,000

Figure 8.69  Heat transfer to gases inside tubes. (Used by permission: Buthod, A. P., Oil & Gas Journal, V. 58, No. 3, © 1960. PennWell Publishing Company, All rights reserved.)

668  Chemical Process Engineering

400

10 9 8 7

10

2000 1600

5

H

200

p

1.5

1

0.5

REFERENCE LINE 1

2000 2500

2

TUBE DIAMETER IN.

1000

600 400

3

REFERENCE LINE 2

MASS FLOW, LB/HR G

300 400 500

AM

200

5000

STE

4000

4

SIA

100

1000 800

PR E S SUR E, P

3000

HEAT TRANSFER COEFFICIENT, BTU/(HR) {SO FT) (DEG F)

2000

15,000

2400

6

1000

10,000

2800

12

D

15

200 500 800 STEAM TEMPERATURE, °F T

1000

1200

Figure 8.70A  Determine the inside heat transfer coefficient for superheated steam. (Used by permission: Ganapathy, V., Hydrocarbon Processing, Sept. 1977 © Gulf Publishing Company, Houston, Texas. All rights reserved.)

Liquids in turbulent flow in circular helical coils [66, 70] should be handled the same way as for gases or use 1.2 x h1 for straight tubes.

8.12.1 Film Coefficients with Fluids Outside Tubes Forced Convection Film coefficients for turbulent flow that exist on the outside or shell-side of the conventional baffled shell and tube exchanger are correlated for hydrocarbons, organic compounds, water, aqueous solution, and gases by [39, 71]:



h o De DG  = 0.36  e s  ka  µ 

0.55

 cµ   k  a

1/3

 µ   µ  w

0.14



(8.133)

and as represented in Figure 8.71, deviation: 0 to +20%. The Gs is correlated for both cross- and parallel-flow through the bundle by using the hydraulic radius along the tubes only [39]. Figure 8.72 is helpful in visualizing shell-side fluid flow. where ho = film heat transfer coefficient outside of tubes in bundle, Btu/h (ft2) (°F) ka = thermal conductivity, Btu/h (ft2) (°F/ft) Gs = mass flow rate, lb/h (ft2) De = equivalent tube diameter, ft de = equivalent tube diameter, in. as = flow area across the tube bundle, ft2 Bs = baffle spacing, in.

Heat Transfer  669 1

100

5 14

200

CURVE TYPE OF GAS 1 - CARBON DIOXIDE 2 - AIR NITROGEN, OXYGEN, CARBON MONOXIDE, FLUE GASES 3 - AMMONIA 4 - METHANE 5 - HYDROGEN

10

300

500

1000

100 2000

G

700

H

4

4

3

3

2

2 1 1

0.5

REFERENCE LINE 1 TUBE DIAMETER, IN.

5000

5

REFERENCE LINE 2

4000

MASS FLOW, LB/HR

3000

HEAT TRANSFER COEFFICIENT, BTU/(HR) (SO FT) (DEG F)

10

400

D

0 T

200 400 600 GAS TEMPERATURE, °F

800

1000

1200

1400

Figure 8.70B  Determine the inside heat transfer coefficient of common gases. (Used by permission: Ganapathy, V., Hydrocarbon Processing, Sept. 1977 © Gulf Publishing Company, Houston, Texas. All rights reserved.)

c = specific heat of fluid, Btu/lb (°F) = viscosity at the caloric temperature, lb/ft (h) = viscosity at the tube wall temperature, lb/ft (h) w Kern’s [39] correlation checks well with the data of Short [72]. Bowman [73], and Tinker [74] for a wide variety of baffle cuts and spacing for segmental baffles, with and without leakage as summarized by Donohue [2]. Short’s data for disc and doughnut baffles are better calculated by [2]:



hD D G  = 0.23(d e )0.6  o w  ka  µ 

0.6

 cµ   k  a

0.33



(8.134)

where de = equivalent tube diameter for the shell side = 4 (flow area/wetted perimeter), in. Do = outside diameter of tube, ft Gw = weighted mass velocity = w/Se = w/(GcGb)0.5 in lb/(h) (ft2) Se = weighted flow area = [(cross flow area) (baffle window area)]0.5, ft2 Gc = cross-flow mass velocity, lb/h (ft2) Gb = mass velocity through baffle window opening, based on the area of the opening less the area of tubes passing through it, lb/h (ft2) = viscosity, lb/h (ft)

670  Chemical Process Engineering CURVE TYPE OF LIQUID

20,000

10,000

3000

3.0

2000

2.5

1 - SAE 10 2 - FR-114 3 - FR-11 4 - NH3 5 - KEROSENE 6 - ETHYL GLYCOL 7 - GASOLINE 8 - METHYL ALCOHOL 9 - DOWNTHERM A 10 - WATER

1500 2.0

1000

5000 4000 3000

10

1.5

2000 7 1000

1.0

1

0.7 TUBE DIAMETER, IN. D

H

9

6

0.8

REFERENCE LINE

HEAT TRANSFER COEFFICIENT BTU/(HR) (SQ FT) (DEG F)

MASS FLOW, LB/HR G

10

8

0.9

100

100 90 80

8

4

0.6

3 2

0.5 0.4 0 100 200 300 LIQUID TEMPERATURE, °F T

400

500

Figure 8.70C  Determine the inside heat transfer coefficient of common liquids. (Used by permission: Ganapathy, V., Hydrocarbon Processing, Sept. 1977 © Gulf Publishing Company, Houston, Texas. All rights reserved.)

Viscosity Correction Factor ( µ

µw )

0.14

The viscosity correction factor is only significant for viscous liquids. To apply the correction factor in the heat transfer coefficient correlation, an estimate of the wall temperature is required. This is carried out by first calculating the coefficient without the correction and using the following relationship to determine the wall temperature:



hi (tw – t) = U (T – t)



(8.135)

where t = tube side bulk temperature (mean) tw = estimated wall temperature T = shell-side bulk temperature (mean)

Heat Transfer Coefficient for Water, hi Equations 8.119, 8.121 may be used to determine the heat transfer coefficient for water; however, a more accurate estimate can be made by using equations developed specifically for water. The physical properties are conveniently incorporated into the correlation. The equation is [41]:

Heat Transfer  671 70

40

0.5

10

100

30

8

1.0

20

300

2

10

5

H

3000

1

G

D

REFERENCE LINE 1

5

2000

2

MASS FLOW LB/HR

4

REFERENCE LINE 2

3

11 5 9

400 500 600 700 800 900 1000 TUBE DIAMETER, IN.

HEAT TRANSFER COEFFICIENT, BTU/(HR) (SQ FT) (DEG F)

12

200

7 3 CURVE 6

1 - R-11 VAPOR 2 - R-11 LIQUID 3 - R-113 VAPOR 4 - R-113 LIQUID 5 - R-114 VAPOR 6 - R-114 LIQUID 7 - R-12 VAPOR 8 - R-12 LIQUID 9 - R-22 VAPOR 10 - R-22 LIQUID 11 - R-502 VAPOR 12 - R-502 LIQUID

4

0

TYPE OF REFRIGERANT

40 80 120 160 REFRIGERANT TEMPERATURE, °F

Figure 8.70D  Determine the inside heat transfer coefficient of several common vapor/liquid refrigerants. (Used by permission: Ganapathy, V., Hydrocarbon Processing, Sept. 1977 © Gulf Publishing Company, Houston, Texas. All rights reserved.)

10

2

1,000

8

6

as B c C' De de Gs ho Ds k p W µ µw

3

4

6

1,000

2

3

4

6

Pitch 1" 1–1/4" 1–9/16" 1–7/8" 13/16" Δ 15/16" Δ 1" Δ 1–1/4" Δ 1–9/16" Δ 1–7/8" Δ

C' 0.250" 0.250" 0.3125" 0.375" 0.1875" 0.1875" 0.250" 0.250" 0.3125" 0.375"

de 0.95" 0.99" 1.23" 1.48" 0.535" 0.55" 0.73" 0.72" 0.91" 1.08"

10,000 8

2

19 Fins/Inch C' 0.34" 0.34" – – 0.278" 0.248" 0.34" 0.34"

de

3

6

100,000 8

2

3

4

6

8

1,000 8

de

6

1.21" 1.21" – – 0.78" 0.75" 0.95" 0.91"

4 3 2

6

BAFFLE CUT 15% 25 35 45

3

4 3

BAFFLE CUT 15% 25 35 45

10

106

16 Fins/Inch C' 0.325" 0.32" – – 0.2655" 0.2655" 0.325" 0.32"

1.27" 1.27" – – 0.82" 0.80" 1.00" 0.97"

4

100 8

4

cµ kα

8

Bare Tube Tube OD 3/4" 1" 1–1/4" 1–1/2" 5/8" 3/4" 3/4" 1" 1–1/4" 1–1/2"

Flow area across bundle, sq ft Baffle spacing, in Specific heat of fluid, Btu/lb × °F Clearance between adjacent tubes, in Equivalent diameter, ft Equivalent diameter, in Mass velocity, lb/hr × sq ft Film coefficient outside bundle, Btu/hr × sq ft ×°F Inside diameter of shell, in Thermal conductivity, Btu/hr × sq ft × °F/ft Tube pitch, in Weight flow of fluid, lb/hr Viscosity at the caloric temperature, lb/ft × hr Viscosity at the tube wall temperature, lb/ft × hr

2 ho De kα

2

6

100 8

jH =

100

Mass velocity, Gs = W/as, lb/hr × sq ft 4 × axial flow area, in wetted perimeter Equivalent diameter, de =

2

–0.14

6

Flow area across bundle, as = Ds × C' × B /144p. ft.2

3

µ µw

4

8

4

–1/3

3

2

8

10 8

6

6

4

4

3

3

2

2

1 10

2

3

4 5 6

8

100

2

3

4 5 6

8 1,000

2

3 Res =

4 5 6 De Gs µ

8 10,000

2

3

4 5 6

8 100,000

2

3

4 5 6

8

1 106

Figure 8.71  Shell – side heat transfer curve for segmental baffles. (Used by permission: Engineering Data Book Section II, © 1959. Wolverine Tube, Inc.)

672  Chemical Process Engineering B

B

2

1

Baffle Diameter

Fluid Leakage Areas for Any Type Baffle

Crossflow

Baffle “Window” or Opening to Flow Parallel to Tubes, as Shell Side Passes from One Baffle Area to the Next

Baffle Pitch or Spacing 4

Bulk Flow 3 Path of Fluid

Fluid Flows Parallel to Tubes as it Passes From One Baffled Area to Next

Inside Shell of Exchanger

Tubes Project Through Baffles, but not Shown

Baffle Cut Off Here

Baffle Cut Off Here

Tubes Project Through This Area of Baffle

“Window” or “Cut” Baffles 2 and 4

Baffle “Window” or “Cut” Expressed as % Cut, which is (%) (Shell I.D.) Net Flow Area of Window is Full Window Area minus Area Occupied by Tubes.

Baffles 1 and 3

Flow Direction

Flow Direction

Ligaments Between Tubes, for Fluid Flow

Note: Area Available for Cross Flow used Consistent with Reference 61, other References 35, 21 use other Arrangements to Obtain Essentially the Same Results.

Figure 8.72  Shell-side baffles and cross-flow area.

where di h i ut t

hi =

4200(1.35 + 0.02t)u 0.8 t 0.2 di

(8.136)

= tube inside diameter, mm = inside heat transfer coefficient for water, W/m2oC = water velocity, m/s = water temperature, oC.

Shell-Side Equivalent Tube Diameter [39] See Figure 8.73 and Table 8.34. Best results are obtained when baffle pitch or spacing between baffles is between one-fifth to one shell diameter.

Heat Transfer  673

do 2 1

3 4

Free Area

5

8 7

Tube Clearance, C'

2

1 Free Area

6

6

4

5

Wetted Perimeter: Length = 1 – 2 + 3 – 4 + 5 – 6 + 7– 8

3

e, nc ara Cle be C' Tu

Tube Outside Diameter

Tu be Pit P ch,

Tube Pitch, P

Wetted Perimeter: Length = 1 – 2 + 3 – 4 + 5 – 6

De = 4 (Free Area)/Wetted Perimeter, feet

Figure 8.73  Equivalent diameter for tubes on shell-side of exchanger taken along the tube axis. (a) Square pitch, (b) triangular pitch on 609 equilateral angles. (Used by permission: Kern, D. Q., Process Heat Transfer, 1st ed. (c) 1959. McGraw-Hill, Inc., All rights reserved.)

h

8

20

7

15

10 9 8

5 4.5 4 3.5 3 2.5

(a)

2 (b) 1.5

Shell-side Coefficient of Heat Transfer, Btu/hr./sq. ft.

Film Coefficient of Heat Transfer, Btu/hr./sq. ft.

6

(c)

7 6 5 4

hi

40 30

20 15

10 9 8 7 6 5 4

3

2

1.5

1.0 1.0

ho

3

25 20 15

fv

5 4.5 4 3.5

10 9 8 7 6

3 2.5

5 4

2

Velocity Factor

25

Pressure Factor (Multiplier)

9

Tube-side Coefficient of Heat Transfer, Btu/hr./sq. ft.

10

3 2

1.5

2 1.5 Example: If the shell-side 1.0

1.0

coefficient of a unit is 25 Btu/hr (ft2) (°F) and velocity in the shell is doubled, read 1.0 the new shell-side coefficient, ha, as 36 (line a). If the tubeside coefficient is 25 and velocity is doubled, read the new tube coefficient, hi, as 43.1 (line a). In other cases, pressure drop would increase by a factor of 4. Note: This may be used in reverse for reduced flow.

Figure 8.74  Effect of velocity on heat transfer rates and pressure drop: shell – side and tube – side. (Used by permission: Shroff, P. D. Chemical Processing, No. 4, © 1960. Putman Publishing Co., Itasca, Ill. All rights reserved.)

674  Chemical Process Engineering Table 8.34  Shell-side equivalent tube diameters for various tube arrangements. Tube O.D. In.

Pitch

Equivalent diameter, de´, In.

½

5

/8 triangular

0.36

½

¾ triangular

0.74

¾

15

¾

1 triangular

0.73

1

1 ¼ triangular

0.72

1¼

1 9/16 triangular

0.91

½

5

/8 square

0.48

½

¾ square

0.88

¾

15

¾

1 square

0.95

1

1 1/4 square

0.99

1¼

1 9/16 square

1.23

/16 triangular

/16 square

0.55

0.72

Used by permission: Engineering Data book Section, ©1960 and 1984. Wolverine Tube Inc.; and Kern, D.Q. Process Heat Transfer, ©1950. McGraw-Hill Inc. All rights reserved.

For square pitch tubes, the shell-side equivalent diameter is





de =

4 × cross sectional area wetted perimeter

4 ( p2t − πd 02 / 4 ) de = ,in πd o 1.273 2 = p t − 0.785d o2 ) ( do

(8.137)

(8.138)

For 60° triangular equilateral pitch tubes:

4×

π  1 p × p t sin60° − d o2 2 t 8  πd o 2



de =



4 (0.5 p t )(0.866p t ) − 0.5 π d o2 4  de =  ,in. πd o 2 1.094 2 p t − 0.913d o2 ) = ( do

where de = equivalent diameter, in., shell side for cross flow pt = tube pitch, in

(8.139)

(8.140)

Heat Transfer  675 do = outside diameter of tube, in. Cross-flow area for Figure 8.71 is based upon the maximum flow area at the nearest tube row to the centerline of the shell [39]. The length of the flow areas is the baffle spacing.



as =

Ds (c´Bs ) 2 ,ft p t (144)

(8.141)



Gs =

W ,lb / (h)(ft 2 ) as

(8.142)

where Ds = shell inside diameter, in. c = clearance between tubes measured along the tube pitch, in. Bs = baffle spacing, in. W = weight flow of fluid, lb/h pt = tube pitch, in. Baffling on the shell-side of an exchanger is usually most beneficial in convection transfer and must be considered from both the heat transfer and pressure drop viewpoints. Close baffle spacing increases heat transfer and pressure drop for a given throughput. The average segmental baffle will have an open “window” for fluid passage of 25% of the shell diameter, or 75% of the shell diameter will have a baffle covering it from flow. The smallest “baffle cut” is used to specify the dimensions of a segmental baffle. The baffle cut is the height of the segment removed to form the baffle, expressed as a percentage of the baffle disc diameter. Baffle cuts from 15% to 45% are often used. Generally, a baffle cut of 20% to 25% will be the optimum, providing good heat transfer rates without excessive pressure drop. However, there is some leakage of fluid around the baffle as a clearance must be allowed for assembly. The clearance required will depend on the shell diameter; typical values, and tolerances are shown in Table 8.35. Another leakage path occurs through the clearance between the tube holes in the baffle and the tubes. The maximum design clearance will normally be 1/32 in. (0.8 mm). Some design relations in other references use this as a percentage of the shell cross-section area, and the corresponding relations must be used. In exchanger design, this cut-out is varied to help to obtain good operating performance; however, the spacing between baffles (baffle pitch) is much more significant in its effect on the film coefficient for a given baffle cut. If twice the number of baffles is used for a fixed fluid flow, the velocity across the tube bundle is doubled, and the increase in film coefficient is about 44%. However, the pressure drop will approach four times its value before doubling the number of baffles (see Figure 8.73). Figure 8.75 illustrates a low pressure drop baffle arrangement. Each situation must be examined, as no generalities will solve all detailed designs. Baffles should be held to a minimum spacing of 1/5 the shell diameter or 2 in., whichever is larger. Baffles spaced equally to shell diameter are found to give good average performance, and this guide is often used in estimating the initial spacing for baffles. Where possible the baffle spacing and percent baffle cut should provide equal flow area. This is of particular importance in pressure drop calculations. Figure 8.76 is useful for this equalization. Shell-side film coefficients can be conveniently obtained from the charts of Chen [75], Figures 8.77–8.79. These are based on Donohue’s equation [21]:



h o Do D G  = 0.22  o w  ka  µ 

0.6

 c pµ   k  a

0.333

 µ   µ  w

0.14



(8.143)

Equivalent tube diameter for shell-side heat transfer calculations is used by permission from Kern and Kraus [76].

676  Chemical Process Engineering Table 8.35  Typical baffle clearances and tolerances. Shell diameter, Ds

Baffle diameter

Pipe shells 6 to 25 in. (152 to 635 mm)

Ds −

Plate shells 6 to 25 in. (152 to 635 mm)

1 Ds − in. (3.2mm) 8

27 to 42 in. (686 to 1067 mm)

Ds −

Tolerance

1 in. (1.6mm) 16

+

3 in. (4.8mm) 16

1 in. (0.8 mm) 32

+0, −

1 in. (0.8 mm) 32

+0, −

1 in. (1.6 mm) 16

Shell

b

Flow Path

a

b

a

b

a

Flow Path Tube Field Tube Field

Detail

(a)

(b)

Figure 8.75  Baffling for low pressure drop shell-side designs.

0.45

% Baffle Cut, Height of Cut/Dia. Shell

0.40 0.35 0.30 0.25 0.20 0.15

1

2

3

4

5

Dia. Shell/Baffle Pitch

Figure 8.76  Determination of equal flow areas in bundle cross – flow and baffle window shell-side performance. (Used by permission: Engineering Data Book Section II, © 1959, Wolverine Tube Inc.)

Heat Transfer  677 Shell Side

104

'= Gb

103

1, 0 00

Gb' lb./sec.-sq.ft.

Mass velocity through baffle opening Gb'

15

20 0

10

5 40 00 0 30 0 0

0

102 30

50 40

20 15

10

10

102 103 Cross flow mass velocity, Gc', lb./sec.-sq.ft.

104

Figure 8.77  Shell – side mass velocity through baffle opening Gb. (Used with permission: Ning Hsing Chen, Chemical Engineering, V. 65, © 1958. McGraw-Hill, Inc., All rights reserved.)

The volumetric equivalent diameter, de in., is again calculated on the basis of 4 times the hydraulic radius; see Figure 8.73.



de =

4 × free area ,in. wetted perimeter

(8.137)

Viscosity, µ centipoise 0.1 C 10

1.0

10

100

6 4 2

1 0.6 0.4 0.2 0.1

kα 0.01 0.02 0.04 Physical property factor ϕp’

0.1 0.2 0.4 1.0

0.01

0.1 1.0 Shell Side Physical Property Factor, ϕp’ ´

10

Figure 8.78  Shell – side physical property factor for φ p. (Used with permission: Ning Hsing Chen, Chemical Engineering, V. 65, © 1958. McGraw-Hill, Inc., All rights reserved.)

678  Chemical Process Engineering (a) Equivalent Diameter, De, for Annulus



De =

4 (flow area) D22 − D12 = 4rh = (wetted perimeter) D1

(8.137A)

where D1 = outside diameter of inner tube, ft D2 = inside diameter of outer pipe, ft rh = hydraulic radius, ft = (radius of a pipe equivalent to the annulus cross-section) (b) Square Pitch and Rotated Square Pitch



de =

4p2t − π ( d e ' ) / 4 πd e ' 2

(8.144)

where pt is the tube pitch, in. (c) Triangular Pitch 2 4 0.5p t (0.866p t ) − 0.5π ( d e ' ) / 4  de = 0.5πd e '



(8.145)

For plain tubing, the nominal OD replaced d e′ . The volumetric equivalent diameter does not distinguish between square pitch and square pitch rotated by 45°. where d e′ = equivalent diameter of plain tube (used to correlate heat transfer and pressure drop) corresponding to the metal volume of a finned tube, in. It is the volumetric equivalent diameter of the root tube plus the addition to the root-tube OD. if the volume of the fin metal were added to it to form a new root-tube OD [76]. See Figure 8.11H de = equivalent diameter, in. For use in the equivalent diameter equations, the following volumetric d e′ , in., values are taken from reference [76]. Plain Tube Second Tube OD, in.

19 fins/in. x 1/16 in. High Equivalent Diameter d e ′ , in.

16 fins/in. x 1/16 in. High Equivalent Diameter d e ′ , in.

0.625

0.535

0.540

0.750

0.660

0.665

0.875

0.785

0.790

1.000

0.910

0.917

Used by permission: Based on data from Kern and Kraus, pp. 512-513, ©1972. McGraw-Hill, Inc.

The charts are used as follows: 1. Determine geometric mean mass velocity, Ge′ using Figure 8.77. (a) Cross-flow area for this method [38] equals the horizontal shell diameter minus the space occupied by the tubes along this diameter, multiplied by the baffle spacing. Determine Ge′, lb/s (ft2) by dividing the shell-side flow rate by the cross-flow area.

Heat Transfer  679

Heat transfer coeff. (Corrected for viscosity)

104 6

Heat transfer coefficient × viscosity correction factor, ha, Btu./hr. – sq. ft. – deg. F.

10 1= fp 8

4

Fig. 3

2 1.0 0.8 0.6

103

0.4 0.2 0.18 0.0 6 0.0 4 0.0

102

2

0.0

1

0.0

10

Correction factor for tube sizes 5/8" O.D. 1.000 0.926 34/" 0.825 1" 0.756 1 1/4"

103

102

10 105

104

Weighted mass velocity, G'e, lb./sec. – sq. ft.

Figure 8.79  Shell – side film coefficient. (Used with permission: Ning Hsing Chen, Chemical Engineering, V. 65, © 1958. McGraw-Hill, Inc., All rights reserved.)

(b) The baffle window cut-out area minus the area occupied by the tubes passing through this area is the net baffle opening flow area. Determine G b′ , as lb/s (ft2) by dividing the flow rate of the shellside by this new baffle opening flow area. (c) Read Ge′ , lb/s (ft2), from Figure 8.77 at the intersection of Gc ′ and G b′. 2. Determine the physical property factor, p´, using Figure 8.78. 3. Read the outside film coefficient, ho, using Figure 8.79. Note: This has the viscosity correction (( / w)0.14, included. A correction multiplier must be used to correct the results of Figure 8.79 for tubes different than 5/8-in. OD. The charts of Rubin [77] are somewhat similar and also useful for solving the equation by graph rather than by calculator. 150 100 18 Velocity, ft./sec.

70

Molecular Weight

29 44

50

Note: Velocities Should be kept Low to Prevent Erosion when Moisture or Suspended Particles Present. The Values Suggested Here are Maximum for Reasonable Operation. In order to Reduce Pressure Drop Velocities Must be Well Below Maximum Values. For Nozzles, Velocities can be 1.2 to 1.4 times Values Given.

100 200 400

30 20

10

7

10

20

30

50

70

100 200 300 Pressure, lbs./sq. in. Abs.

500

Figure 8.80  Maximum velocity for gases and vapors through heat exchangers on shell – side.

700

1,000

2,000

4,000

680  Chemical Process Engineering

Shell-Side Velocities Figure 8.80 suggests reasonable maximum velocities for gases and vapors through heat exchangers. If entrained liquid or solids are present, these velocities should be reduced. Pressure drop must be checked to determine the acceptability of any selected velocity. Table 8.36 presents suggested maximum velocities for fluids flowing through exchanger Table 8.36  Maximum recommended velocities through nozzle connections, piping, etc. associated with shell and/or tube sides of heat exchanger. Liquids: Viscosity in centipoise

Maximum velocity, ft. /s.

Remarks

More than 1500

2

Very heavy oils

1000 – 500

2.5

Heavy oils

500 – 100

2.5

Medium oils

100 – 35

5

Light oils

35 – 1

6

Light oils

Less than 1

8

…

Vapors and Gasses: Use 1.2 to 1.4 of the value shown on Figure 8.80 for velocity through exchangers.

100

0.003

0.01 0.02

0.05

0.1

cu. ft./sec. 0.2 0.5

1.0

2

5

10

20

70 50 30

No m

in

al

10 7

/2

"

1"

5

11

3

2"

O. D.

3"

2

8"

0.7

10 12 " 14 " N " O om .D in al . 15 "O .D .

6"

1.0

16 "

4"

Velocity, ft./sec.

20

0.5 0.3 0.2 0.1 1.0

2

3

5 7 10

20 30

50 70 100 200 300 500 1,000 2,000 G. p. m.

5,000 10,000

Figure 8.81  Nozzle sizes for fluid flow. (Used by permission: ITT Technologies, ITT Standard. All rights reserved.)

Heat Transfer  681 nozzles. The effect of entrance and exit losses on pressure losses should be checked, as they become important in lowpressure systems. Figure 8.81 is convenient in selecting pipe or nozzle sizes.

8.13 Design and Rating of Heat Exchangers Two main types of problems can exist in relation with heat exchanger design or computation. 1. To determine the suitability of an existing or proposed unit (rating). 2. To design a new unit to perform a certain service.

Rating of a Shell and Tube Heat Exchanger A general algorithm for thermal rating of a shell and tube heat exchanger is illustrated in Figure 8.82. The decision regarding whether an exchanger is thermally suitable for a given service is based on a comparison of calculated versus required overall heat transfer coefficients. The heat exchanger is suitable, if the calculated value of the design coefficient, UDes is greater than or equal to the required value, Ureq, that is needed to provide the required rate of heat transfer. If Ureq> UDes, the exchanger is unsuitable. However, the final decision to accept or reject the exchanger is based upon economics and sound engineering judgment. For example, it may be more economical to utilize an existing exchanger that is slightly undersized thus may require frequent cleaning than to purchase a larger exchanger. In general, the rating decision can be based on a comparison of heat transfer areas, heat transfer rates, corrected log mean temperature differences as well as heat transfer coefficients. The fouling factors often present the greatest uncertainty and as such do not enter the calculation until the final step of the algorithm (see Figure 8.82). Therefore, an exchanger can be rejected in step 3 of the algorithm before the fouling factors enter the calculation. The rating procedure in Figure 8.82 involves only the thermal analysis of the exchanger. A complete rating procedure must include a hydraulic analysis that involves the calculation of the pressure drops of both fluid streams, and compared with the specified maximum allowable pressure drops as described earlier. The steps for the rating of an exchanger are as follows: 1. Write the heat balance for the cold and hot streams:



Q = WhCph(T1 – T2) = wcCpc(t2 – t1)



(8.146)

and then calculate Q and the remaining unknown, flow rate or temperature. 2. With the four temperatures known, determine TLMTD as

∆TLMTD =

(T1 − t 2 ) − (T2 − t1 ) T −t  ln  1 2   T2 − t1 

(8.20)

3. Calculate P and R parameters:



t 2 − t1 T1 − t1

(8.24)

T1 − T2 w c C pc = t 2 − t1 Wh C ph

(8.25)

P= R=

682  Chemical Process Engineering Calculate the required overall coefficient Q Ureq = ( A ⋅ F∆TLMTD ) Calculate the clean overall coefficient 1 1  Do  1 Do1n(Do /Di ) = + + Uc h i  Di  h o 2k or  1  D  1 Do h(Do /Di )  + Uc =   o  +  2k  h i  Di  h o 

−1

Is Uc > Ureq ? Yes

No

Continue

Exchanger is not suitable

Obtain required fouling factors, RDi and RDo from Tables 8.24, 8.25, and 8.26 then compute D  RD = RD1  o  + RD  Di  Calculate the design overall heat transfer coefficient, UDes 1 1 = + RD UDes Uc or  1  UDes =  + RD   Uc 

-1

Is UDes > Ureq ? Yes

No

Exchanger is suitable

Exchanger is not suitable

Figure 8.82  Thermal rating procedure for a shell and tube heat exchanger (Source: R. W. Serth, Process Heat Transfer – Principles and Applications, Elsevier Science & Technology Books, 2007).

4. For the exchanger configuration (i.e. 1-2, 2-4, etc.) obtain Ft from graphs or analytical expression. 5. Obtain the physical properties of the fluids at the mean temperatures. These will be (T1+T2)/2 and (t1+t2)/2 for the hot and cold fluids respectively. These mean temperatures are referred to as T and t. To determine the heat transfer coefficients, it is essential to calculate (µ/µw) for each fluid, where µ is the viscosity at the mean temperature, and µw is the viscosity at the tube wall temperature. The tube wall temperature is not known, thus it is necessary to assume a tube wall temperature that will be verified later. A guess is made by considering the tube wall temperature to be an intermediate value between T and t, but closer to the temperature of the fluid with the higher film coefficient, h. The exponent 0.14 for the ratio (µ/µw) is used, as this factor is not very high and the first guess is a reasonable value. 6. The flow area of the fluid flowing into the tubes is determined:



at =

N t a ′t n

(8.147)

Heat Transfer  683 Need to increase heat transfer

Increase heat Transfer coefficient

Increase surface area

Increase number of tubes, decrease tube outside diameter

Increase shell diameter with appropriate number of tubes

Increase tube length

Shell side

Tube side

Decrease the baffle spacing or baffle cut

Employ multiple shells in series or parallel

Increase F or ε Use counterflow configurations Use multiple shells configuration Need to reduce pressure drop

Shell side

Tube side

Decrease number of tube passes

Increase tube diameter

Increase the baffle cut

Decrease tube length and increase shell diameter and number of tubes

Increase the baffle spacing

Increase Use double or tube pitch triple segmental baffles

Figure 8.82A  Influence of various geometrical parameters of a shell and tube exchanger.

where



a ′t =

πDi2 4

(8.148)

Nt = number of tubes n = number of tube passes The mass velocity of the tube-side fluid is calculated:



Gt = ρ v t =

wt at

(8.149)

7. Calculate the Reynolds number for the tube side fluid:



Re t =

Dt G t µ

(8.150)

8. Calculate hi, Equations 8.151 through 8.156 based on the Reynolds number. 9. Correct the external diameter:



h io

hi

10. Calculate the shell-side heat transfer coefficient, ho.

Di Do

(8.151)

684  Chemical Process Engineering Step 1 Specification Define duty Make energy balance if needed to calculate unspecified flow rates or temperatures

Step 10 Decide baffle spacing and estimate shell-side heat transfer coefficient

Step 2

Step 11

Collect physical properties

Calculate overall heat transfer coefficient including fouling factors, Uo, calc

Step 3 Assume value of overall coefficient Uo, ass Step 4 No

Decide number of shell and tube passes. Calculate ΔTLMTD, correction factor, F and ΔTm.

0
A calc , the exchanger is suitable for use. The excess area is:

Percent excess =



A real − A calc × 100 A calc

(8.158)

The tube side pressure drop calculation is as follows: With Ret calculated in step 7, obtain the friction factor from Equations 8.81 and 8.81A (see Chapter 3) and determine the straight tube pressure drop from Equation 8.83. Then calculate the pressure drops in the headers from Equation 8.82. The total pressure drop will be the sum of both effects. 17. Shell side pressure drop is calculated: 18. The heat exchanger will be suitable for the required service if the two following conditions are satisfied: a. Areal > Acalc as explained in step 16. b. Both the tube-side and shell-side p values must be less than the allowable values.

8.13.1 Design of a Heat Exchanger If a new heat exchanger is being designed to perform a certain service, all the geometric characteristics must be defined by the designer. In general, the procedure is to propose the heat exchanger configuration and then apply the rating methodology detailed earlier. Here, the goal is to minimize the difference between the assumed and calculated areas because any excess area results in additional cost. In addition, the heat transfer coefficients must be as high as possible so that the heat transfer area will be at a minimum value. However, the limitation to the increase in heat transfer coefficients is the allowable p for both fluids. The design will be optimal when p values of both fluids are close to the maximum allowable values. The heat transfer coefficients will also be close to the maximum and the heat transfer area is sufficient. Where any of these conditions are not satisfied, then the geometry of the unit needs to be changed. The following steps are used for the design of a heat exchanger. 1. D  etermine the unknown process variable (e.g., flow rate or temperature) of one of the streams from the heat balance. Then calculate the ΔTLMTD.

686  Chemical Process Engineering 2. S elect the number of shell passes or shells configuration. If there is no limitation owing to Ft considerations, a heat exchanger with one shell pass will be selected. It must be remembered that the countercurrent configuration provides the highest ΔT because Ft = 1. On many occasions, a pure countercurrent configuration is avoided because it makes the removable bundle construction difficult or because it requires a very high tube length or installation of shells in series becomes necessary. Therefore as an alternative, start with one shell pass and 2n tube passes, with n being any integer number. Calculate Ft. 3. Choose as a first guess the overall heat transfer coefficient, U from Tables 8.28A-B (Appendix A). 4. With the assumed U, determine an approximate value of the heat transfer area:

A′ =



Q U Ft ∆TLMTD

(8.159)

5. C  hoose the tube diameter, pattern and pitch; decide the allocation of fluids on the shell and tube sides. 6. Select the number of tubes per pass. This is done so as to have a reasonable tube-side fluid velocity. e.g., a fluid velocity of 1 m/s, the number of tubes is

np =



Wt ρ a ′t (1 m / s)

(8.160)

7. S elect the number of tubes, tube length and the number of tube passes. It is essential to find a combination of number of tubes and tube length in order to satisfy the value of



A = Nt



Do L

(8.161)

At the same time, the number of tube passes must be selected in such a way that the quotient between Nt and np is an integer. The number of tube passes n is chosen as:

n = Nt np

(8.162)

Adjusting np to get an integer. At the same time, the heat exchanger length must be reasonable. 8. Select the shell diameter. Determine the number of tubes that can be allocated in a certain shell diameter for different exchanger types from Appendix A (Table 8.16A-E). Once the number of tubes has been selected, it is possible to determine the necessary shell diameter pass partition arrangement. This is usually different from the area calculated in step 7 because the number of tubes may have slightly changed. 9. Calculate the corrected heat transfer area with the number of tubes determined in step 8.



A = Nt

Do L

(8.163)

10. S elect the baffle separation Bs a first guess, determine the Reynolds number that gives a reasonably high shell side heat transfer coefficient. This may require a few trial calculations. Once the heat exchanger is completely defined, then the rating method can be carried out as described earlier.

8.13.2 Design Procedure for Forced Convection Heat Transfer in Exchanger Design 1. E  stablish physical properties of fluids at the caloric or arithmetic mean temperature, depending upon the temperature range and order of magnitude of the properties. 2. Establish the heat duty of the exchanger. 3. Estimate or assume a specific unit and define its size and characteristics, based upon reasonable values of overall U and ∆TLMTD.

Heat Transfer  687 4. D  etermine the ∆TLMTD with correction if needed from Figures 8.40 and 8.41. 5. Calculate the tube-side flow rate based upon the assumed number of tubes per pass and the heat balance. 6. Determine the tube-side film coefficient for water, using Figure 8.67A or 8.67B. For other liquids and gases, use Figure 8.63A. Correct hi to the outside tube surface by

h io = h i



 I.D.   O.D. 

(8.164)

7. Determine the shell-side film coefficient for an assumed baffle spacing. (a) Establish Gs from Equation 8.162. (b) Calculate the Reynolds number, Re, expressed as

Re =



De G s µ

(8.165)

(c) Read jH from Figure 8.71. Note that 25% is a good average value for many designs using segmental baffles. (d) Calculate ho from



jH =

h o De  cµ  k  k

−1/3

 µ   µ  w

−0.14



(8.166)

Let / w = 1.0 (e) If ho appears too low, assume closer baffle spacing, up to 1/5 of the shell diameter and recalculate Gs and ho. If this second trial is obviously too low, then a larger shell size may be indicated; therefore, return to step 3, re-evaluate the assumed U to be certain that is attainable. 8. If the ho appears to have possibilities of satisfying the design, continue to a conclusion by assuming the tube-side and shell-side fouling (Tables 8.22-24 in Appendix A; Figures 8.59, 8.59A). 9. Calculate the overall heat transfer coefficient using Equation 8.106/106A. Neglect the tube-wall resistance, unless special situations indicate that is should be included. 10. Calculate the area required using Equation 8.2. 11. Calculate the net available area in the assumed unit, using only the effective tube length. 12. Compare values calculated in steps 10 and 11. If the calculated unit is too small, reassume a new larger unit for step 3 or try closer baffle spacing in step 7 but do not get baffles closer than 1/5 the shell I.D. 13. Calculate the percent of excess area. A reasonable figure is 10-20%. 14. Calculate the shell-side pressure drop. (Refer to the later section on “Pressure Drop Relations” and Figure 8.86. If p is too high, reassume unit (step 3).) 15. Calculate the tube-side pressure drop. (Use Figure 8.84 for the end return losses. For water in tubes, use Figure 8.84 for tube losses. For other liquids and gases in tubes, use Figure 8.85.)

Total pressure drop = (end return + tube) losses, psi. If the tube-side pressure drop exceeds a critical allowable value for the process system, then recheck by either lowering the flow rate and changing the temperature levels or reassume a unit with fewer passes on tube-side or more tubes per pass. The unit must then be rechecked for the effect of changes on heat transfer performance. Figure 8.82A illustrates the influence of various geometrical parameters on heat exchanger heat transfer and pressure drop.

688  Chemical Process Engineering

Figure 8.83  Exchanger rating example.

Heat Transfer  689 .01 f(Gt)2(L)(n) f(Gt)2(L)(n) = 2(g)(p)(D)(ϕt) 5.22(10)10(D)(S)(ϕt) ΔPt = Pressure Drop, psi D = Inside Diameter of Tubes, ft. f = Friction Factor, sq. ft./sq. in. Gt = Mass Velocity, lb./(hr.) (sq. ft./Cross Section) = lb./hr./ on N g = Acceleration of Gravity, ft./(hr.)2 L = Tube Length, ft. N = Total Number of Tubes S = Specific Gravity of Gas or Liquid Referenced to Water

.007

ΔPt =

.005 .003 Friction Factor, t, sq. ft./sq. in.

.002 .001 .0007 .0005 .0003 .0002 .0001

.00007 .00005 .00003 .00002 .00001 10

Pipe Tube s

p = Density, lb./cu. ft. µ = Viscosity at Caloric Temperature = lb./(ft.)(hr) µw = Viscosity at Tube Wall Temperature = lb./(ft.)(hr.) ϕt = (µ/µw)0.14 above Ret = 2,100 ϕt = (µ/µw)0.25 below Ret = 2,100 n = Number of Tube Passes Note: (µ in Centipoise)(2.42)=(µ in lb./(ft.)(hr.)) For Dimension less Friction Factor Multiply Ordinate, f, by 144

20 30

50 70 100

200

500

1,000 2,000

5,000 10,000 20,000 50,000 100,000

500,000 1,000,000

D Gt Ret = µ

Figure 8.84  Heating and cooling in tube bundles – tube-side friction factor. (Used by permission: Kern, D. Q., Process Heat Transfer, 1st ed. P. 836, © 1950. McGraw-Hill, Inc., All rights reserved. Using nomenclature of Standards of Tubular Exchanger Manufacturers Association.)

8.13.3 Design Programs for a Shell and Tube Heat Exchanger The procedures used for developing the design of heat exchangers vary depending on the type of the problem and the preference of the designer. Some designers prefer to perform heat exchanger design by a method referred to as rating an exchanger as outlined earlier. Here, the designer assumes the existence of an exchanger and conducts a series of calculations to determine whether it can handle the process requirements under defined conditions. If this is not the case, a different exchanger is assumed, and the calculations are repeated until a suitable design is developed. For example, with a given set of process requirements, the designer could assume the existence of an exchanger with a known tube size, tube spacing, baffle type, baffle spacing and number of tubes and passes. He/she might then proceed through the process design calculations by computing an overall heat transfer coefficient and determining all flow rates, areas, lengths and pressure drops. Repeated trials may be required to obtain an accurate overall heat transfer coefficient. The exchanger is thought to be suitable if the results of the final design indicate that it has reasonable dimensions, sensible costs and acceptable pressure drops. An alternative approach is to base the design for the optimum exchanger that will meet the required process conditions, where the heat transfer area, exit temperature and flow rate of utility fluid, number, length, diameter, and arrangement of tubes; tube-side and shell-side ∆ps are determined. Heat exchanger rating or design is usually performed using commercial software programs, as illustrated in the beginning of this chapter. The structure of these programs is generally complex because of the various parameters that must be adopted such as TEMA type; number of shell and tube passes; diameter and number of tubes; clearances; sealing strips; tube pattern and pitch; tube length; type of baffles and baffle cut; baffles spacing; and shell diameter. Many of these variables depend on the user preference and layout restrictions. Project specifications are defined by the user in the program input. Table 8.37 shows the basic information that should be supplied to a fabricator in order to obtain a quotation or price estimate on a proposed heat exchanger and Figure 8.82B illustrates the design structure for a shell and tube heat exchanger. The general method of designing heat exchanger types for a given set of process conditions is as follows: 1. D  etermine the rates of flow and rate of heat transfer required to meet the given conditions. 2. Decide on the type of heat exchanger to be used, and indicate the basic equipment specifications. 3. Evaluate the overall heat transfer coefficient and also the film coefficients. If necessary, the fluid velocities must be determined in order to obtain accurate heat-transfer coefficients.

690  Chemical Process Engineering 100 70 50 30

15 10

1

5

4

2 3 3

9 10 12 11 14 13 15 17 16 18

8

6 7

5

Pressure Drop, psi/100 ft.

7

1.5 1.0 0.7 0.5

Dia. BWG Key 1/2 16 1 18 2 20 3 5/8 16 4 18 5 3/4 14 6 16 7 18 8 7/8 14 9 16 10 18 11 1

0.3 1 1/4 0.15 0.1

1 1/2 300

500 700 1,000 1,500

3,000

5,000 7,000 10,000

12 14 16 18 10 12 14 10

11 12 13 14 15 16 17 18 30,000

Water Flow Rate, lbs./hr./Tube (1) For Water Temperature of 120°F., ΔPt Decreases about 6%. For Most Applications Temperature Correction is not Significant. (2) Increase ΔPt by 20% to Allow for Effect of Usual Fouling.

Figure 8.85  Pressure drop for water in smooth tubes at 68°F. (Used by permission: Scovill Heat Transfer Tube Manual, 3rd. Ed. Scovill, Manufacturing Co.)

4. 5. 6. 7.

 valuate the log mean temperature difference driving force. E Determine the necessary area of heat transfer and the exchanger dimensions. Analyze the results to see if all dimensions, costs, pressure drops and other design details are satisfactory. If the results of step 6 show that the exchanger is unsatisfactory, the specifications given in step 2 are inadequate. Choose new specifications and repeat steps 3 through 7 until a satisfactory design is achieved.

In general, when the designer selects a heat transfer equipment, it is essential to consider the process design variables and other parameters such as internal and outside diameters of the tubes and shell, total number of tubes, tube-wall thickness (specified by the BWG), tube pitch, standard tube length and baffle types. Pressure, temperature, corrosion and allowances for expanding the individual tubes into the tube sheets must be taken into consideration when the thickness is determined. Tube pitch is defined as the shortest center-to-center distance between adjacent tubes, while the shortest distance between two tubes is defined as the clearance. Tubes are commonly laid out on a square pattern or triangular pattern. The square pitch has the advantage of easier external cleaning, but the triangular pitch is

Heat Transfer  691 4 3

1.5 1.0 0.7 0.5

0.15

S=

Δpr, Pressure Drop/Pass, psi

2.0

0.5 0.7 5 1.5 1.0

0.3

0.10 0.07 0.05 0.03 Δpr (n) = End Return Loss per Exchanger n = Number of Tube Passes Δpr = Pass End Return Pressure Drop, psi. Include Entrance Loss and Exit Loss for One Pass. S = Specific Gravity of Fluid

0.015 0.010 0.007 0.005

This Allows Four Velocity Heads per Pass as per TEMA (88).

0.003

0.0015 0.0010 0.1 0.15

0.3

0.5 0.7 1.0

1.5 3 5 7 10 Tube Velocity, ft./sec.

15

30

50 70 100

Figure 8.86  Tube – side end return pressure drop per tube pass; viscosity close to water.

sometimes preferred because it allows the use of more tubes in a given shell diameter. Furthermore, the mechanical design of the heat exchanger must be to good engineering practice and must meet the requirements of the ASME or API-ASME safety Codes or other standard Codes. The TEMA publishes standards on general design methods and fabrication materials for shell and tube heat exchanger types. Note: It is to the benefit of purchasers of shell and tube heat exchangers to not insist on applying their design. If the heat exchanger is to be built to TEMA requirements, it will void the guarantee. The last line of paragraph G5.2 states: “The thermal guarantee shall not be applicable to exchangers where the thermal performance was made by the purchaser”.

Example 8.8. Convention Heat Transfer Exchanger Design See Figure 8.83. The liquid bottoms from a distillation column must be cooled from 176°F to 105°F. The cooling water is untreated at 90°F. Operating data: Bottom flow, lb/h 6,350 Average Cp, Btu/lb.oF 0.333 0.055 Average ka, Btu/h (ft2) (°F/ft)

692  Chemical Process Engineering Table 8.37  Process and mechanical information for a quotation/price estimate on a proposed heat exchanger. Process information

Mechanical information

1. Fluids to be used. Include fluid properties if they are not readily available to the fabricator.

1. Size of tubes a. Diameter b. Length c. Wall thickness.

2. Flow rates or amounts of fluids.

2. Tube layout and pitch a. Horizontal tubes. b. Vertical tubes.

3. Entrance and exit temperatures

3. Maximum and minimum temperatures and pressures.

4. Amount of vaporization and condensation

4. Necessary corrosion allowances.

5. Operating pressures and allowable pressure drops.

5. Special codes involved.

6. Fouling factors.

6. Recommended materials of construction

7. Rate of heat transfer (Source: Max S. Peters and Klaus D. Timmerhaus, Plant Design and Economics For Chemical Engineers, 4th ed., McGraw-Hill Int. 1991).

Average , cP 0.404 Average sp.gr 0.78 Physical properties are based on values at 140°F average temperature. Caloric fluid temperature for property evaluation can be calculated from Equation 8.42. The caloric value of hot liquid on the shell side is

th = th2 + F(th1 – th2)



Rough estimate Uc at cold end = 150,000 = 262, (38.2)(15)

Uh at hot end = 150,000 = 48.5, Btu 2

h ft °F

38.2(81)



C=

U h − Uc 48.5 − 262 = = −0.815 Uc 262

(Note: disregard sign)

Reading Figure 8.46,

∆t c = 15°F ∆t h = 81°F ∆t c 15 = = 0.185 ∆t h 81



Btu h ft 2 °F

Heat Transfer  693



F = 0.32

Then: th = 105 + 0.32 (176 – 105) = 127.7°F Note that the arithmetic average [½ (176 – 105) + 105 = 140°F] would be quite satisfactory for this design, because the properties do not vary significantly with temperature. From the heat balance, the heat duty Q is:



Q = Wh Cp (T1 – T2) 1. Heat duty = (6350) (0.33) (176 – 105) = 150,000 Btu/h 2. Estimated unit



Assume: U = 100, Btu/h ft2oF 3. Log mean temperature difference (Figure 8.40), 176° F

cooling

105° F

95 oF

warming

90oF

81oF

15oF

∆TLMTD = (81 – 15) / ln (81/15) = 39.2 oF

Required area of the tube is:



A=

150,000 = 38.2 ft 2 (100)(39.2)

Tubes: 1-in. O.D. × 14 BWG × 8 ft. long Total area, ATotal = π Do Nt L



Number of tubes required =

38.2 (0.2618 ft / ft) (8 − 6in./12) 2

= 20 tubes

Trial: 10-inch. I.D. shell with 24 1-in. tubes on 1¼ -in. triangular pitch, 4 tube passes. 4. From the heat balance on the tube-side: Water rate is:

694  Chemical Process Engineering

Q = w c C pc (t 2 − t1 ) wc =

1  150,000  Btu 1 = 30,000 lb/h  ⋅ ⋅  Btu ° F  (1)(95 − 90)  h   lb ° F



The volumetric flow rate, Q from the mass flow rate G is:



G=Q·

or

G 30,000 7.48  lb 1 USgal h  = × ⋅ ⋅  ⋅  ft 3 60s  62.3 60  h lb ρ   ft 3 = 60 gpm

Q=





Number of tubes per pass



at

24 tubes =6 4 pass

0.546 = 0.00379 ft 2 / tube 144 Flow area/pass = (0.00379) (6 tubes) = 0.0227 ft2 flow area Cross-sectional area/tube =

Water velocity, v is:

G=ρv A  lb 1 1 h  G 30,000 = ⋅ 2⋅   ⋅ ρ A (62.3)(0.0227)(3600)  h lb ft 3600s    ft 3 = 5.88 ft/s

v=



5. Film coefficient, tube side, From Figure 8.67A and B, at 5.88 ft./s and 93°F, read:

hi = 1,340 Btu/h (ft2) (°F) Correction for tube I.D. of 0.834 in., Fw = 0.94 Correction to the outside of tube: hio = (1,340) (0.94) (0.834)/1.0 = 1,050 Btu/h (ft2) (°F) 6. Film coefficient, shell side,

From Figure 8.71, read:



Heat Transfer  695



Cross-flow area = a s =

I.D.(c'Bs ) p t (144)

Assume baffle spacing of Bs = 10 in Shell I.D. = 10 in. c = 1.25 - 1.0 = 0.25 in. W = 6,350 lb/h. pt = 1.25 in.

as =



Gs =

Reynolds number: Re =

Dc G s µ

(10)(0.25)(10) = 0.139 ft 2 (1.25)(144)

W 6,350 = = 45,700 lb/h(ft 2 ) a s 0.139

Dc = (0.72/12) = 0.06 ft (Table 8.41)

= (0.404)(2.42) = 0.978 lb/ft (h) Re =



(0.06)(45,700) = 2,800 0.978

Reading Figure 8.71,

jH = 28 (for 25% cut segmental baffles) From Figure 8.87,



f = 0.0027 (for 25% cut segmental baffles)

Note: “f ” from Figure 8.87 is divided by 1.2 for plain tubes (not finned).

jH =

h o De  cµ  k a  k a 

h o = 28



= 28

−1/3

 µ   µ  w

−0.14

= 28

 0.055   (0.333)(0.404)(2.42   0.06    0.055

1/3

(1)

 0.055  (1.81)(1)  0.06 

ho = 46.4 Btu/h (ft2) (°F) Note that ( / w) is taken as 1.0 for fluids of low viscosity where the change in temperature does not introduce a significant increase in viscosity.

696  Chemical Process Engineering 10 0.10 9 8 7

2

3

4

100 5 6 7 89

2

3

4

1,000 5 6 7 89

2

3

4

10,000 5 6 7 89

Δps =

2

3

4

100,000 5 6 7 89

fs × Gs2 × D's (Nc+1)

2

3

4

B C' De de

3 2

0.01 9 8 7 6 5 4

BAFFLE

3

CUT 15%

0.001 9 8 7 6 5 4

p Density, lb./cu. ft. µ Viscosity at the Caloric Temperature, lb./ft. × hr. µw Viscosity at the Tube Wall Temperature, lb./ft. × hr 3 ϕs (µ/µw)0.14 2 Note: Friction Factors are Dimensional, sq. ft./sq. in., to give Δp s in psi Directly. For Dimensionless Friction Factor, Multiply Ordinate f, by 144. 2

3

4

5 6 7 89 100

2

3

4

0.01 9 8 7 6 5 4

2

0.001 9 8 7 6 5 4

10

2

3

25 35 45

2

3

fs1 (sq. ft.)/(sq. in.)

= 2 × g × p × De × ϕs Baffle Spacing, in. Clearance between Adjacent Tube, in. Equivalent Diameter, ft. Equivalent Diameter, in. See jH Curve for Numerical Values. D's Inside Diameter of Shell, ft. Gs Mass Velocity, lb./hr. (sq. ft. Flow Area) g Acceleration of Gravity, 4.18 × 108 ft./hr.2 L Tube Length, ft. Nc Number of Baffles Nc+1 Number of Times Fluid Crosses Bundle from Inlet to Outlet, 12 L/B p Tube Pitch, in. Δps Shell Side Pressure Drop, psi

6 5 4

0.0001

106 5 6 7 89 0.10 9 8 7 6 5 4

fs × G2s × D's (Nc+1) , psi 5.22 × 1010 × De × s × ϕs

3 2

5 6 7 89 1,000

2

3

4

5 6 7 89 10,000

2

3

4

DG Res = e s µ

5 6 7 89 100,000

2

3

4

0.0001 5 6 7 89 106

Figure 8.87  Shell – side friction factors for low – finned and plain tubes. (Used by permission: Engineering Data Book, © 1960, Wolverine Tube, Inc.)

Try to obtain a better coefficient by closer baffling, check extreme of 2-in. baffle spacing. 7. Shell-side film coefficient based on 2 in. baffle spacing,

Gs =



(6,350)(144)(1.25) = 229,000 lb / h (ft 2 ) (10)(0.25)(2) Re =



(0.06)(229,000) = 14,050 0.978

From Figure 8.71,

jH = 66 ho



(66)(0.055)(1.81) = 109.5 Btu/h (ft 2 )(°F) 0.06

8. Assume fouling, therefore the fouling factors on the shell and tube sides are:



Shell side, = 0.002  ft2 h oF/Btu



Tube side = 0.001  ft2 h oF/Btu 9. Overall coefficient,

U=



1

1 1 + 0.001 + 0.002 + 109.5 1,050

= 76.4 Btu/h(ft 2 )(°F)

Heat Transfer  697

1

.1

1

.1 1

10 20 30 Spe 4 5 0 0 cifi cG .8 rav ity 1 1 2

2 3 4 5

1

.2 .3 .5 .4

.1

De

Pressure Drop per Baffle, psi

10

1,000

nsi ty .01 lb./cu . ft. .02 .03 .05 .04

100

Longitudinal Flow, G 100

10

10 Longitudinal Flow, G

100

.01

.001

Figure 8.88  Pressure drop in exchanger shell due to longitudinal flow. (Used by permission: Buthod, A. P., Oil & Gas Journal, V. 58, No. 3, © 1960. PennWell Publishing Company. All rights reserved.)

10. Area required,

A=



150,000 = 50 ft 2 (76.4)(39.2)

11. Area available in assumed unit,

A = π Do N t L =π

6in.    1 (24) 8 −  12   12 

= 47 ft 2

Therefore, the assumed unit is too small. 12. Second trial, Assume:

698  Chemical Process Engineering 1,000

G, Mass Velocity, lb./(sq. ft.)(sec.)

Δp(Cross-flow) = F(Ft)(Nc+1)(nc)/p in psi. F = Pressure Drop Factor Ft = Tube Size Factor Nc = Number of Baffles nc = Number of Rows of Tubes in Cross-flow p = Fluid Density, lb./cu. ft. 100

ise

po

nti

, Ce sity

co Vis

20

10

1 .01

.1 Values of Ft

10 .5 1 2 5 5 .1 .2 0 . 2 1 .0 5 .0 .00

1

50

0

10

10 F, Pressure Drop Factor

Tube Size (inches) 5/8 3/4 3/4 3/4 1 1

Pitch 13/16 in. Δ 15/16 in Δ 1 in. 15/16 in. 1 1/4 in. Δ 1 1/4 in.

0

0

20

50

100

Viscous Flow 0.008 0.01 0.0025 0.0044 0.0075 0.0033

1,000 Turbulent Flow 0.01 0.01 0.0042 0.0044 0.0095 0.0042

Figure 8.89  Pressure drop in fluid flowing across tube banks with segmental baffles. (Used by permission: Buthod, A. P., Oil & Gas Journal, V. 58, No. 3, © 1960. PennWell Publishing Company. All rights reserved.)



12-in. I.D shell 44 tubes, 1-in. OD x 14 BWG x 8 ft long on 1¼ -in. triangular pitch, 4 tube passes. For the revised water rate, allow only 3°F rise.

From the heat balance on the tube side: Water rate is:



Q = wc Cpc T

where T = 3oF, Cpc = 1 Btu/lb.oF

wc =

150,000 1   Btu 1 = 50,000 lb / h  ⋅ ⋅  Btu (1)(3) °F   h   lb ° F

The volumetric flow rate, Q from the mass flow rate G is:



G=Q·

or

G 30,000 7.48  lb 1 USgal h  = × ⋅ ⋅  ⋅  ft 3 60s  62.3 60  h lb ρ   ft 3 = 100 gpm

Q=





Heat Transfer  699 Number of tubes per pass = 11 Water flow area = (11) (0.00379) = 0.0417 ft2 Water velocity, v from the volumetric flow rate is:

 gal Q 100 ft 3 1 min  v= = ⋅ ⋅ 2⋅  A (0.0417)(7.48)(60)  min 7.48 gal ft 60s 

= 5.34 ft/s.

Heat transfer film coefficient, tube side, From Figure 8.67A and B, read:

hi = 1,220 Btu/h.ft2.oF hio = (1,220) (0.94) (0.834) = 956 Btu/h (ft2) (°F) Heat transfer film coefficient, shell side, ho is as follows: Select baffle spacing of 5.5 in., equal to 16 baffles. The mass velocity, Gs is:



Gs =

(6,350)(144)(1.25) = 69,300 lb / h (ft 2 ) (12)(0.25)(5.5)

The Reynolds number, Re:



Re =

(0.06)(69,300) = 4,250 0.978

Reading Figure 8.71, jH = 35 Reading Figure 8.87 The friction factor, f is:



f = 0.0025 (for plain tubes)

The film heat transfer coefficient on the outside tube is:



ho =

(35)(0.055)(1.81) Btu = 58.1 0.06 h ft 2 °F

Use same fouling factors as for first trial. Overall heat transfer coefficient, U is:

U=



1

1 1 + 0.002 + 0.001 + 956 58.1 2 = 47.2 Btu/h(ft )(°F)

700  Chemical Process Engineering LMTD, 176° F

Shell

105° F

93 oF

tube

90oF

83oF

15oF

∆TLMTD = (83 – 15) / ln (83/15) = 39.75oC



Correction to LMTD read Figure 8.41 or from the Excel spreadsheet program (Example 8.1.xlsx) is:

P=



93 − 90 = 0.0349 176 − 90

R=



176 − 105 = 23.6 93 − 90 F = 0.9734

Corrected LMTD = (0.9734) (39.75) = 38.6°F Area required,



A=

150,000 = 82.4 ft 2 (47.2)(38.6)

Area available in assumed unit, second trial,

A = π Do N t L =π

3in.    1 (44) 8 −  12   12 

= 89.3 ft 2

(For low pressure design, 3 in. is a sufficient allowance for two tubesheets.) Percent excess area,



%=

89.3 − 82.4 (100) = 8.3% 82.4

This is satisfactory. Pressure drop, shell side (see “Pressure Drop” section),

Heat Transfer  701

f (G)2 (Ds )(Nc + 1) ∆ps = , psi 5.22(10)10 (De )(s)(φs )



(8.79)

where f = 0.0025 G = 69,300 lb/h ft2 Ds = 12/12 = 1 ft Nc + 1 = 16 + 1 = 17 = 0.72/12 = 0.06 ft. De s = 0.78 = 1.0 s



∆ps =

(0.0025)(69,300)2 (1)(17) = 0.0835 psi 5.22(10)10 (0.06)(0.78)

Use ps = 1.0 to 1.5 x 0.0835 psi for any critical pressure drop consideration. This should be safe. Pressure drop, tube side, from Figure 8.86. End return loss, pr=(0.75) (4) = 3.00 psi, from Figure 8.86. lb water per tube/pass = 50,000/11 = 4,550 p = (7/100) (8 ft) (4 passes) = 2.24 psi Total pressure drop = 2.24 + 3.0 = 5.24 psi Used p = 6 psi Nozzle sizes: Inlet water rate = 100 gpm Velocity in 3-in. connection = 4.34 ft/s. Head loss = 0.0447 (6 in./12) = 0.022 ft water. Outlet nozzle to be same. Inlet shell-side (bottom flow):



Liquid rate =

6,350 = 16.2 gpm (60)(8.33)(0.78)

Kinematic viscosity = 0.404/0.78 = 0.52 centistokes From Cameron Miscellaneous Liquids Table (Fluid Flow Chapter 3), Velocity in 2-in. connection = 1.53 ft/s. Note that a 1½ in. connection is satisfactory; however many plants prefer minimums of 2 in. connections on process vessels for main stream flows. Pressure loss is negligible = 0.006 (6 in./12) = 0.003 ft fluid Outlet shell side: Use same size as inlet, 2 in. Figure 8.83 shows the exchanger process data sheet for Example 8.16.

702  Chemical Process Engineering

8.14 Shell and Tube Heat Exchanger Design Procedure (SI Units) The cost of the shell and tube heat exchanger varies with the diameter of its shell. In accordance with TEMA standard, the shell size ranges from 6 in. (152 mm) to 60 in. (1520 mm). Standard pipes are available up to 24 in. size (600 mm NB). If the shell size is greater than 24 in., then it is fabricated by rolling a plate. The shell diameter depends on the tube bundle diameter. For fixed tube sheet shell and tube heat exchanger, the gap between the shell and tube bundle is minimum, ranging from 10 to 20 mm. For pull through floating head type, it is maximum ranging from 90–100 mm. The required shell diameter is determined by one of the following methods: Use of Standard tables: Standard tables are prepared based on actual tube sheet layout,. These tables give the maximum number of tubes that can be accommodated in various standard sizes of shell ranging from 6 in. (150 mm NB) to 120 in. (3000 mm NB). For the different numbers of tube side passes, different values of tube pitch and size and for the different arrangements of tubes. Appendix A (Tables 8.16A-E) show the data on tube sheet layouts. Use of approximate equations: Approximate equations are available in the literature to determine the shell diameter or the tube bundle diameter. The tube bundle diameter depends not only on the number of tubes but also on the number of tube passes, as spaces must be left in the pattern of tubes on the tube sheet to accommodate the pass partition plates. An estimate of the tube bundle diameter, Db is obtained from the following equations [4]: n1

D  Nt = k1  b   do 



(8.167)

and 1

 N  n1 Db = d o  t   k1 



(8.168)

where Nt = number of tubes Db = tube bundle diameter, mm Do = tube outside diameter, mm. Tube pitch p t , arrangement of tubes and number of = tube OD do tube side passes. Table 8.38 is used to determine the constants. Table 8.39 gives the tube geometry as a function of tube pitch, pt.

K1 and n1 are constants, values of which depend on ratio

Table 8.38  Constants for use in Equations 8.168-8.169. do = 1.25 Triangular Pitch No of tube side passes

1

2

4

6

8

K1

0.319

0.249

0.175

0.0743

0.0365

n1

2.142

2.207

2.285

2.499

2.675

No of tube side passes

1

2

4

6

8

K1

0.215

0.156

0.158

0.0402

0.0331

n1

2.207

2.291

2.263

2.617

2.643

Pt/do = 1.25 Square Pitch

Heat Transfer  703 Table 8.39  Tube geometry as a function of tube pitch, pt. Tube layout

Pitch normal to flow, pn

Pitch parallel to flow, pp

30o Triangular Staggered Array

pt

 3  2  Pt

60o Rotated Triangular Staggered Array 90o Square Inline Array 45o Rotated Square Staggered Array

Pt 2

3 Pt pt

pt Pt 2

2 Pt

Equation (8.168) is used for fixed tube sheet type and floating head shell and tube type heat exchangers. For U-tube heat exchangers, the following equations are used. 1

 N′  n1 Db = d o  t   k1 



(8.168A)

and

N′t = N t +



Db pt

(8.169)

where N′t = number of tube holes on tube sheet. After determining the tube bundle diameter Db, the shell inside diameter, Di can be determined by the following equation:

where C C C C

Di = Db + C

(8.170)

= clearance between shell inside diameter and tube bundle diameter, Db. = 10 to 20 mm for fixed tube sheet and U –tube = 50 to 80 mm for split-ring floating head = 90 to 100 mm for pull through floating head.

Tubes The tube size ranges from ¼ in. (6.35 mm) to 2.5 in. (63.5 mm) in shell and tube heat exchanger. Data for standard tubes are provide in TEMA standard. The size of standard tubes is equal to outside diameter of tube. Thickness of standard tubes are expressed in BWG. An increase in the value of BWG means decrease in tube thickness. For no phase change heat exchangers and for condensers, ¾ in. (19.05 mm OD) tube is widely used in practice. For

704  Chemical Process Engineering reboilers, 1 in (25.4 mm OD) tube size is common. Tubes are available in standard lengths, e.g., 6 ft. (1.83 m), 8 ft. (2.44 m) and 12 ft (3.66 m), 16 ft. (4.88 m) and 6 m.

Tube-Side Pass Partition Plate Tube-side passes are provided to decrease the tube-side flow area and to increase the tube-side fluid velocity, thus enhancing the tube-side heat transfer coefficient but at the expense of the pressure drop. This is true where there is no phase change on the tube side. Therefore, a larger number of tube-side passes is recommended if there is no change in the phase of the tube-side fluid. An example at the design stage: If the number of tube-side passes is increased from one to two, then for the given volumetric flow rate, flow area is halved and velocity is doubled. Since (where ut is the tube-side fluid velocity), on increasing the number of the tube heat transfer coefficient, h i ∝ u 0.8 t tube passes from 1 to 8, hi nearly becomes 1 – 7 times. But ∆p t ∝ u 2.8 t , so the pressure drop increases by 6.96 times. The tube-side pressure drop rises steeply with an increase in the number of tube passes. Consequently, for a given number of tubes and two passes, Δpt is much lower than the allowable value. However, for four passes it exceeds the allowable pressure drop. In such instances, a standard tube can be used and the designer may decide to accept a low fluid velocity. If the tube diameter and length are varied, the allowable pressure drop is better utilized and a higher tube-side velocity realized. The total pressure drop must be achieved for a given stream and the distribution of pressure drop in the many heat exchanger types for a given stream can be varied to obtain good heat transfer. An increase in hi means a decrease in heat transfer area required and a decrease in the fixed cost. An increase in Δpt means an increase in power required for pumping the tube-side fluid, which invariably increases the operating cost. Thus, an optimum number of tube-side passes should be decided. Tube-side passes are very common and are advantageously used for improving tube side heat transfer coefficient. These passes can be achieved by locating partition plates in channel covers.

8.14.1 Calculations of Tube-Side Heat Transfer Coefficient For heating or cooling on the tube side (no phase change), the tube-side heat transfer coefficient is determined by Sieder – Tate equation. If Re < 2100,

hd d   Nu = i i = 1.86 Re.Pr . i  kf L



0.33

 µ   µ  w

0.14



(8.171)

where If Nu ≤ 3.5, then Nu is taken 3.5 If Re > 4000, then the tube-side heat transfer coefficient is determined by Dittus-Bolter equation



Nu =

hi di  µ  = CRe0.8 Pr 0.33  kf  µ w 

where Nu = Nusselt number (dimensionless) = h i d i kf ρ u t di di Gt = Re = Reynolds number (dimensionless) = µ µ Cp µ Pr = Prandtl number (dimensionless) = k hi = Tube-side heat transfer coefficient, W/m2oC di = Tube inside diameter, m. L = Length of tube, m

0.14



(8.172)

Heat Transfer  705 k = Thermal conductivity of fluid, W/m oC Cp = Specific heat of fluid, kJ/kg. oC µ = Viscosity of fluid at the bulk fluid temperature, (N.s)/m2, (Pa.s) µw = Viscosity of fluid at the tube wall temperature, (N.s)/m2, (Pa.s) C = Constant = 0.021 for gases = 0.023 for non-viscous liquid = 0.027 for viscous liquid Gt = Tube-side mass velocity, kg/(s.m2)  m Gt = at N π at = Tube-side flow area = t × d 2t N 4 p Nt = Number of tubes Np = Number of tube-side passes ut = Tube-side fluid velocity = Gt/ρ, m/s ρ = Density of fluid, kg/m3 To calculate the tube-side heat transfer coefficient, first determine the tube-side flow area, at, then the tube-side mass velocity, Gt followed by the Reynolds number Re and the tube-side Prandtl number, Pr. Depending on the value of Re, use the appropriate equations to calculate hi. The tube-side heat transfer coefficient, hi can be calculated from the value of heat transfer factor, Jh for the entire range of Reynolds number (from Re = 10 - 106) for different values of L/di from:



Nu = h i

di  µ  = Jh Re.Pr 0.33  k  µ w 

0.14



(8.173)

The procedure for calculating the shell-side heat transfer coefficient and pressure drop for a single-shell pass exchanger is as follows: 1. Calculate the area for cross-flow As for the hypothetical row of tubes at the shell equator, given by:

As =



(p t − d o )Ds Bs pt

(8.174)

where pt  = tube pitch. do  = tube outside diameter, m Ds = shell inside diameter, m Bs  = baffle spacing, m





The term (pt – do)/pt is the ratio of the clearance between tubes and the total distance between tube centers. 2. Calculate the shell-side mass velocity, Gs and the linear velocity us:

Gs =

Ws As

us =

Gs ρ

(8.175)

(8.176)

706  Chemical Process Engineering where Ws = fluid flow rate on the shell side, kg/s    = shell side fluid density, kg/m3 3. Calculate the shell-side equivalent diameter (hydraulic diameter) For a square pitch arrangement

 2 πd o2  4  pt −   4  = 1.273 p2 − 0.785d 2 de = ( t o) do πd o



(8.135)

For an equilateral triangular pitch arrangement:

p 1 d2  4  t × 0.86 p t − π o   2 2 4  = 1.094 p2 − 0.913d 2 de = ( t o) πd o do 2



(8.137)

where de = equivalent diameter, m 4. Calculate the shell side Reynolds number, Re and Prandtl number, Pr given by



Re =





G s d e ρu s d e = µ µ

(8.177)

Cp µ k

(8.178)

Pr =

where µ  = viscosity of shell-side fluid at average temperature, kg/m.s (Pa.s) Cp = specific heat capacity of shell-side fluid at average temperature, W/m oC k  = thermal conductivity of shell-side fluid at average temperature, kJ/kg. oC 5. For the calculated Reynolds number, read the value of jh from Figure 8.71A, for the selected baffle cut and tube arrangement, and calculate the shell-side heat transfer coefficient hs from:



Nu =

ho de  µ  = jh Re Pr 0.33  kf  µ w 

0.14



(8.179)

or



Alternatively, calculate the shell-side heat transfer coefficient by the following correlation

Nu =

ho de  µ  = 0.36Re0.55 Pr 0.33  k  µ w 

0.14



This correlation is valid for the range of 2000 ≤ Re ≤ 106 The tube wall temperature can be estimated using the method given for the tube side

(8.180)

Heat Transfer  707 6. For the calculated shell-side Reynolds number, read the friction factor from Figure 8.56 and calculate the shell-side pressure drop from: 2  D   L  ρv  µ  ∆ps = 8jf  s    s   d e   Bs  2  µ w 



−0.14

, N/m 2 (Pa)

(8.181)

where L  = tube length Bs = baffle spacing The term (L/Bs) is the number of times the flow crosses the tube bundle = (Nb + 1), where Nb is the number of baffles.

Example 8.9. Design of a Shell and Tube Heat Exchanger (SI Units) Kern’s Method Design a shell and tube exchanger for the following duty. Kerosene, 25,000 kg/h (42o API) leaves the base of a side-stripping column at 200oC and is to be cooled to 90oC by exchange with 85,000 kg/h light crude oil (34oAPI) coming from a storage at 40oC. The kerosene enters the exchanger at a pressure of 5.5 bar and the crude oil at 6.5 bar. A pressure drop of 0.90 bar is permissible on both streams. Allowance should be made for fouling by including a fouling factor of 0.00035 W/m2oC on the crude stream and 0.0002 W/m2oC on the kerosene stream. Shell: Type AES, 19.05 mm (3/4 in ) outside diameter, 14.83 mm inside diameter, 5 m long tube on a triangular 23.81 mm pitch (pitch /dia = 1.25). Baffles: 25% cut segmental type Materials: plain carbon steel throughout.

Solution: The solution to this example shows the iterative nature of heat exchanger design calculations, and algorithm for the design of shell and tube exchangers is shown in Figure 8.82B, where the procedure set out in this figure is followed in the solution. Step 1. Hot Fluid: Kerosene: 25,000 kg/h (42oAPI) at 200oC cooled to 90oC by exchange with 85,000 kg/h light crude oil (34oAPI) at 40oC. The kerosene pressure is 5 bar and the crude oil pressure is 6.5.bar. Allowable pressure drop of 0.9 bar on both streams. Fouling factors: Kerosene 0.0002 m2.oC/W, and light crude oil 0.00035 m2.oC/W The outlet temperature of the crude oil is determined from the energy balance:



Q = U A. ∆TLMTD = WhCph (T1 – T2 ) = wc Cpc (t2 – t1)

The mean temperature of kerosene = (200 + 90) / 2 = 145oC. At this temperature, the specific heat capacity of 42oAPI kerosene = 2.47 kJ/kg.oC The heat duty:



Q=

25,000 × 2.47(200 − 90) = 1886.8 kW 3600

708  Chemical Process Engineering As a first trial, take the mean temperature of the crude oil as equal to the inlet temperature, 40oC. The specific heat capacity at this temperature = 2.01 kJ/kg.oC. The energy balance between kerosene and the crude oil gives:

1886.8 =



85,000 × 2.01(t 2 − 40) 3600

t2 = 79.8oC and the crude oil stream mean temperature = (79.8 + 40) / 2 = 59.9oC The specific heat capacity at this temperature is 2.05 kJ/kg.oC. Using this value for the second trial to determine the outlet temperature of the crude oil stream.

1886.8 =



85,000 × 2.05(t 2 − 40) 3600

t2 = 78.98oC, and the new mean temperature = (78.98 + 40) / 2 = 59.49oC Since there is no significant change in the specific heat capacity at this mean temperature from the value used, therefore the crude oil outlet temperature t2 = 78.98 oC (say 79oC). Step 2: Physical Properties Kerosene

inlet

mean

outlet

Unit of measurement

temperature

200

145

90

o

specific heat

2.72

2.47

2.26

kJ/kg oC

thermal conductivity

0.130

0.132

0.135

W/m oC

density

690

730

770

kg/m3

viscosity

0.22

0.43

0.80

mNsm-2

Crude oil

outlet

mean

Inlet

temperature

79

59.5

40

o

specific heat

2.09

2.05

2.01

kJ/kg oC

thermal conductivity

0.133

0.134

0.135

W/m oC

density

800

820

840

kg/m3

viscosity

2.4

3.2

4.3

mNsm-2

C

C

Step 3: Overall heat transfer coefficient, U. The overall heat transfer coefficient is in the range 300 – 500 W/m2.oC. From Table 8.28 in Appendix A, choose U =350 W/m2.oC Step 4: Exchanger Type and Dimensions An even number of tube passes is usually the preferred arrangement, as this positions the inlet and outlet nozzles at the same end of the exchanger, thus simplifying the pipework. Applying a counter current flow between kerosene and the crude oil streams: Calculation of LMTD,

Heat Transfer  709 200 °C

Shell

90° C

79 oC

tube

40 oC

121 oC

50 oC

∆TLMTD =

(121 − 50) ln

 121   50 

= 80.34°C

Correction to LMTD read Figure 8.41A,

P=



79 − 40 = 0.2437 200 − 40

R=



200 − 90 = 2.82 79 − 40

Computed correction factor, F from Equations 8.27–8.30 gives



F = 0.8673

Corrected LMTD, ΔTCMTD = (0.8673) (80.34) = 69.43°C The Excel spreadsheet program (Example 8.1.xlsx) calculates the LMTD and ΔTCMTD respectively. Step 5: Heat transfer area, A is:

Q = UA o ∆TCMTD Ao =

Q 1886.8 × 103 = 77.64m 2 = U∆TCMTD 350 × 69.43

Step 6: Layout and Tube Size Select a split ring floating head exchanger for ease of cleaning, shell type: AES. Use 19.05 mm (3/4 in.) outside diameter, 14.83 mm inside diameter, 5 m- long tube on a triangular 23.81 mm pitch (pitch / dia = 1.25). Choose a plain carbon steel for the shell and tubes as neither fluid is corrosive and the operating pressure is not high. Step 7: Number of Tubes Total area of tubes is:

A Total = π Do L N t Nt =

Ao 77.64 = = 259.46 A Total (π )(0.01905)(5)

710  Chemical Process Engineering Say 260 tubes. For two passes, the number of tubes per pass = 260/2 = 130 Check the tube-side fluid velocity, ut.



Tube cross-sectional area =



π d i2 π × (0.01483)2 = = 0.0001727 m 2 4 4

Area per pass = 130 x 0.0001727 = 0.02246 m2

Volumetric flow rate, Q is:

Q=

Wh 85,000 1  kg 1   ×  = × kg  ρ 3600 820  s  m3 

= 0.02879 m3 /s

The tube-side velocity, ut is:

ut =



0.02879 m = 1.28 0.02246 s

This velocity is satisfactory, but may be a little low. Step 8: Bundle and Shell Diameter From Table 8.46, for two tube passes, Kl = 0.249 and nl = 2.207 1

 N  nl D b = Do  t   Kl  1

 260  2.207 = 19.05  0.249  = 444 mm



Clearance is between 50 to 80 mm for split-ring floating head Choose C = 56 mm, so the shell inside diameter, Ds is Ds = 444 + 56 = 500 mm. Step 9: Tube-Side Heat Transfer Coefficient, hi



Re =

ρu t d i 820 × 1.28 × 0.01483 = = 4864 3.2 × 10−3 µ

Heat Transfer  711

Pr =



C p µ 2.05 × 103 × 3.2 × 10−3 = = 48.96 k 0.134

Re = 4864 and L/di = (5000/14.84) = 337, From Figure 8.55, the friction factor Jh,

jh = 3.5 × 10-3 The heat transfer factor, jh correlation is:





Nu = jh RePr

0.33

 µ   µ  w

0.14

hi di  µ  = jh RePr 0.33  kf  µ w 

0.14

Assuming  µ  is negligible,  µ  w

h i = 3.5 × 10−3

 0.134  (4864)(48.96)0.33  0.01483 

= 555.48 W/m 2 .°C

The tube-side velocity is low, if Uo = 350 W/m2.oC. So, increase the number of tube passes to four. This will reduce the cross-sectional area by ½ and double the fluid velocity.



u t = 2 × 1.28 = 2.56m s



Re = 2

4864 = 9728

jh = 4.9 × 10-3



h i = 4.9 × 10−3

 0.134  (9728)(48.96)0.33  0.01483 

= 1555 W/m2oC

Step 10. Shell-Side Heat Transfer Coefficient, ho With four tube passes, the shell diameter will be larger, therefore from Table 8.38, Kl = 0.175, nl = 2.285

712  Chemical Process Engineering 1

 N  nl D b = Do  t   Kl  1

 260  2.285 = 19.05  0.175  = 465.6 mm

The bundle shell clearance is still 56 mm

Ds = 465.6 + 56 = 521.6 mm (522 mm) Ds 521.6 = = 104.32 mm 5 5

As a first trial, take the baffle spacing = The shell-side flow area is:

As =



As =

(p t − d o )Ds Bs pt

(23.81 − 19.05) × 522 × 104 = 10853.04mm 2 = 0.01853m 2 23.81

Equivalent shell-side diameter de for a triangular pitch arrangement is:

1.094 2 ( pt − 0.913d o2 ) do 1.094 (23.812 − 0.913 × 19.052 ) = 19.05 = 13.53 mm

de =



Volumetric flow rate is:

25,000 1 m3 Q= × = 0.00951 3600 730 s

The shell-side fluid velocity, us:

us =







Q 0.00951 m = = 0.51 A s 0.01853 s

Re =

ρu sd e 730 × 0.51 × 0.01353 = = 11,714 µ 0.43 × 10−3

Pr =

C p µ 2.47 × 103 × 0.43 × 10−3 = = 8.17 k 0.13

Heat Transfer  713 Use segmental baffle cut with 25% cut, from Figure 8.71A, the heat transfer factor, jh is:

jh = 5.8 × 10−3 Nu =

ho de  µ  = Jh RePr 0.33  k  µ w 

0.14

 µ  Assuming  is negligible,  µ w 

h o = 5.8 × 10−3

 0.132  (11,714)(8.17)0.33  0.01353 

= 1325.69 W/m 2 °C



Step 11. Overall heat transfer coefficient, Uocal

1 Uo,cal 1 Uo,cal

d  d o ln  o   di  1 1  d  1  do  =  o + + + + R di   2k w ho h i  d i  h io  d i  19.05  19.05 × 10−3 ln   14.83  1  1   19.05  + + 0.0002 = + 0.00035 +  1555   14.83  (2 × 55) 1325.69 = 440 W/m 2 .°C

This value is above the initial estimate for Uo = 350 W/m2.oC. Percentage difference between Uo and Uocal is:

0
2,100), the friction factor depends on the roughness of the tube material. From Figure 8.55, at Re = 9728, the tube-side friction factor, Jf is:

Jf = 4.8 × 10-3

714  Chemical Process Engineering

L 5 = = 337.15 d i 0.01483



Nt = 4, ρ = 820 kg/m3, ut = 2.56 m/s The pressure drop for the tube side is:

  L   µ  −m  ρv 2t , N/m 2 (Pa) + 2.5 ∆p t = N t 8J f        2 D  µ i w   = 4[8 × 4.8 × 10−3 × 337.15 + 2.5] × 820 × 2.562 /2



= 96443.9 N/m 2 (0.96 bar)

This pressure drop is slightly higher than the allowable ∆pt = 0.9 bar by 0.6 bar (7%), therefore return to step 6 and modify the design. Modified Design We can reduce the tube-side velocity as this will reduce the heat transfer coefficient so the number of tubes must be increased to compensate. There will also be a pressure drop across the inlet and outlet nozzles. Allow 0.1 bar for this, a typical figure (~ 15% of the total); which leaves 0.8 bar across the tubes. ∆Pt ∝ u 2t and ut is proportional to the number of tubes per pass. So the pressure drop calculated for 260 tubes can be used to estimate the number of tubes required. Shell-Side pressure drop, Δps With four tube passes, the shell diameter will be larger, therefore from Table 8.38, Kl = 0.175, nl = 2.285 1

 N  nl D b = Do  t   Kl  1

 260  2.285 = 19.05  0.175  = 465.6 mm

The bundle shell clearance is still 56 mm

Ds = 465.6 + 56 = 521.6 mm (522 mm) As a first trial, take the baffle spacing =

(23.81 − 19.05) × 522 × 104 = 10853.04mm 2 = 0.01853m 2 23.81 1.094 2 de = ( pt − 0.913d o2 ) do 1.094 (23.812 − 0.913 × 19.052 ) = 19.05 = 13.53 mm

As =



Ds 521.6 = = 104.32 mm 5 5

Heat Transfer  715 Volumetric flow rate is:

Q=



25,000 1 m3 × = 0.00951 3600 730 s

The shell-side fluid velocity, us:

us =





Re =

Q 0.00951 m = = 0.51 A s 0.01853 s

ρu sd e 730 × 0.51 × 0.01353 = = 11,714 µ 0.43 × 10−3

At Re = 11,714 and at 25% baffle cut, From Figure 8.56, the shell-side friction factor, Jf is:

Jf = 4.8

10-2

The pressure drop, Δps is: 2  D   L  ρu  µ  ∆ps = 8jf  s    s   d e   Bs  2  µ w 

−0.14

, N/m 2 (Pa)

2   522   5000  730 × 0.51  = 8  4.8 × 10−2   13.75   104  2  



= 66537.87 N/m 2 (0.7 bar)

The pressure drop in the shell-side is within the allowable pressure of 0.9 bar. Step 13. Estimate Cost The cost of this design can be estimated using the methods given in volume 1, chapter 2 of Ludwig’s Applied Process Design for Chemical and Petrochemical Plants by Coker [78]. Step 14. Optimization There is scope for optimizing the design by reducing the number of tubes, as the pressure drops are within specification and the overall heat transfer coefficient is well above the required. However, the Kern’s method is only an approximation and a detailed design will require the use of simulation software as described earlier. Viscosity Correction Factor ( µ µ w )

0.14

The viscosity correction factor ( µ µ w ) was neglected in the design calculations of heat transfer coefficients and pressure drops. This is reasonable for the kerosene as it has a relatively low viscosity, but it is not so obvious for the crude oil. Checking the effect of this factor on the tube-side coefficient and pressure drop. 0.14

The inside area of the tubes

13.75

10−3

5

260 = 56.2m2

716  Chemical Process Engineering



Heat flux = Q/A = 1886.8 × 103 / 56.2 = 33,599.2 W/m2

The heat balance on the tube wall is:

(tw – t) hi = 33,559.2 where hi = 1237 W/m2oC, t is the mean temperature and t is the wall temperature. W

tw – t = 33,559.2 / 1237 = 27.16 oC tw = 27.16 + 59.5 = 86.66 oC The crude oil viscosity at this temperature = 2.1 × 10-3 Ns/m2  3.2 × 10−3  0.14 = 1.06 The viscosity factor µ µ w =  2.1 × 10−3  This value shows the viscosity factor can be neglected.

(

)

8.14.2 Pressure Drop for Plain Tube Exchangers Tube side The pressure loss through the inside of the tubes during heating or cooling in heat exchangers is given for liquids and gases by [39]



fG 2t Ln fG 2t Ln , psi ∆p t = = 2gρDi φ t 5.22(10)10 Di sφ t

(8.182)

the friction factor, f, ft2/in.2, must be obtained from Figure 8.84. Because it is not a dimensional factor, the pt relations take this into account.





 µ  φt =   µ w 

0.14

 µ  φt =   µ w 

0.25

for Re > 2,100

(8.183)

for Re < 2,100

(8.184)

For noncondensing gases and vapors in Equation 8.182 use the average of inlet and outlet gas density referenced to water at 62.4 lb/ft3 for the value of s. A convenient chart for water pressure drop in tubes is given in Figure 8.85. SI units



a 2  L   Gt   µ  ∆p t = 4 f n       Di   2ρ   µ w 

(8.185)

Heat Transfer  717 where a = -0.25 for laminar flow and -0.14 for turbulent flow A convenient chart for all fluids [38] including a 20% increase in pressure drop over theoretical smooth tubes is given in the copyrighted figure of Reference [2]: For streamline flow, Re < 2,100:

ff =



16 (see note below regarding f ) Di G t /µ

(8.186)

and this can be used in Equation 8.248. The turbulent flow [21], Re > 2,100:

DG  f f = 0.048  i t   µ 



−0.2



(8.187)

Divide this f by 144 in order to use an pt Equation 8.215. Stoever [79, 80] presents convenient tables for pressure drop evaluation. Pressure drop through the return ends of exchangers for any fluid is given as four velocity heads per tube pass [39]

≅

4nv 2 2g′′c

62.5 lbm ft 2  1 4nv 2 s  62.5   ft 2 . . ∆pr =  .  144in 2  ft 3 ( 2g′c )  144   s2 lbm . ft   lbf s 2



(8.188)

This is given in Figure 8.86. where

pr = return end pressure loss, including entrance losses, psi n = number of tubes passes per exchanger g c′ = gravitational constant 32.174 lbm/lbf . ft/s2 ρH2O = density of water (62.5 lbm/ft3 ) s = specific gravity of fluid (vapor or liquid) referred to water v = tube velocity, ft/s



∆pr =

4n(G ˝ )2  1   2g’s  (62.5)(144) 

G″ = mass velocity for tube side flow, lb/(s) (ft2 cross-section of tube)

(8.189)

718  Chemical Process Engineering In SI units

∆pr = 4n



ρv 2 , N/m 2 2

(8.190)

G 2t 2ρ

(8.191)

or

∆pr = 4n

where G = mass fluid velocity, kg/m2 s n = number of tube passes ρ = fluid density, (kg/m3) v = fluid tube velocity, m/s

Total Tube-Side Pressure Drop

PTOTAL = pt + pr, psi

(8.192)

Tube-Side Condensation Pressure Drop Kern [39] recommends the following conservative relation:



Dp t

9.56(10)

12

f (G t )2 Ln , psi Di s

(8.193)

This is one-half the values calculated for straight fluid drop, based on inlet flows; f is from Figure 8.84.

Shell Side Pressure losses through the shell side of exchangers are subject to much more uncertainty in evaluation than for tube side. In many instances, they should be considered as approximations or orders of magnitude estimates. This is especially true for units operating under vacuum less than 7 psia. Very little data has been published to test the above-atmospheric pressure correlations at below-atmospheric pressures. The losses due to differences in construction, baffle clearances, tube clearances, etc., create indeterminate values for exact correlation. Also see the shortcut method of Reference [81].

A Case Study Using UniSim Shell-Tube Exchanger (STE) Modeler A kerosene stream with a flow rate of 45,000 lb/h is to be cooled from 390oF to 250oF by heat exchange with 150,000 lb/h of oil at 100oF. A maximum pressure drop of 15 psi has been specified for each stream. Prior experience with this particular oil indicates that it exhibits significant fouling tendencies, and a fouling factor of 0.003 h.ft2oF/Btu is recommended. Physical properties of the two streams are provided in the table below. Design a shell and tube heat exchanger for this service. Table 8.40 shows the various criteria of placing fluids in the order of priority.

Heat Transfer  719 Table 8.40  Criteria for fluid placement, in order of priority. Tube side fluid

Shell side fluid

Corrosive fluid

Condensing vapour (unless corrosion)

Cooling water

Fluid with large ΔT (> 100oF)

Fouling fluid Less viscous fluid Higher pressure stream Hotter fluid Fluid property

Kerosene

Gas oil

Cp, Btu/lbm.oF

0.59

0.49

k, Btu/h.ft.oF

0.079

0.077

µ, lbm/ft.h

0.97

8.7

Specific gravity

0.785

0.85

Pr

7.24

55.36

Solution Figure 8.90 shows the screenshot of the crude distillation unit with heat exchanger E-100 as the basis for rating/checking and Figures 8.91– 8.116 show the various screenshots of the input data and results using UniSim Design Software shell and tube exchanger modeler (UniSim STE) R460. The following steps in inputting the data and generating the results are as follows: 1. Fluid placement Kerosene is not corrosive, but gas oil may be as it depends on salt and sulfur contents and temperature. At the low temperature of the oil stream in this application, corrosion should not be a problem provided the oil has been

Atmos Cond

Waste Water

Diesel Steam AGO Steam

PreFlsh Vap Raw Crude

O Gas

Kerosene Crude Heater PreFlsh Liq

Cold stream, assumed 1 bar DP

Naphtha

PreFlash

VS-1

Kerosene Dummy 1 E-100

Diesel Hot Crude

Mixer

Atm Feed

AGO-1 AGO

Q-Trim Main Steam

Crude Duty VS-3

T-100

Residue

VS-2

Dummy Hot E-101 stream, assumed 1 bar DP

Q-100 1

Q-101

SET-1 2

Q-102 Crude Oil

E-100

3

Figure 8.90  Screen shot of the crude distillation unit with heat exchanger E-100 as the basis for rating/checking. (Source: UniSim Design R443, Courtesy of Honeywell, All rights reserved).

720  Chemical Process Engineering

Figure 8.91  UniSim STE windows. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

desalted (if necessary). However, the oil should be placed in the tubes due to its relatively high fouling tendency as indicated in Table 8.40. Also, the kerosene should be placed in the shell due to its large ΔT of 140oF. 2. Shell and head types The recommended fouling factor for kerosene is 0.001 – 0.003 h. ft2. oF/Btu indicating a significant fouling potential. Therefore, a floating head exchanger is selected to permit mechanical cleaning of the exterior tube surfaces. Also, the floating tubesheet will allow for differential thermal expansion due to the large temperature difference between the two streams. Therefore a type AES exchanger is specified. 3. Tubing Following the design guidelines for a fouling oil service, 1 in. 14 BWG tubes are selected with a length of 14ft. 4. Tube Layout Since cleaning of the tube exterior surfaces will be required, square pitch is specified to provide cleaning lanes through the tube bundle. Following the design guidelines, for 1in. tubes a tube pitch of 1.25 in. is specified. 5. Baffles Segmental baffles with a 20% cut are required by the Simplified Delaware method. A baffle spacing of 0.3 shell diameters is chosen i.e. Bs/Ds = 0.3. 6. Sealing strips One pair of sealing strips per 10 tube rows is specified in accordance with the requirements of the Simplified Delaware method and the design guidelines. 7. Construction materials Since neither fluid is corrosive, plain carbon steel is specified for tubes, shell and other components. UniSim Shell-Tube Exchanger Modeler (UniSim STE) can be employed to determine 1 - 4 calculation types, namely:

Heat Transfer  721 Calculation Types 1. Design

For cost or area optimized thermal design to the specified process conditions and geometrical constraints; for designing a heat exchanger to meet a heat load duty and pressure drop limits, which is specified.

2. Checking (Rating)

To check whether a given exchanger will achieve the required duty for the specified inlet and outlet conditions, giving the ratio of the actual to required surface area; it determines whether a specified exchanger has adequate surface area to meet a duty you specify. Also calculates the stream pressure drops.

3. Simulation

To calculate the outlet conditions and performance of a given exchanger from the specified inlet conditions; determines the heat load, pressure changes and stream outlet conditions that will occur with a specified exchanger, with given stream inlet conditions.

4. Thermosyphon

To calculate the performance of a vertical or horizontal thermosyphon reboiler, the circulation rate, and the pipework pressure drops; determines the flow rate and duty of a specified exchanger, operating as a thermosyphon. The liquid height in the column and the pipework connecting the exchanger to the column are specified.

5. Geometry

Allows specifying and refinement of the geometry of an exchanger, including a detailed tube layout, without any need to specify information on the streams in the exchanger.

In this case study, option 2 is used to determine the heat exchanger duty and the stream pressure drops. After installation of UniSim Design R460 software on the computer, a new case is begun by clicking the Windows icon at the left side on the computer. All programs appear and by scrolling, the Honeywell folder appears. A click on this folder shows a list of design suites folders, namely: 1. U  niSim Design Software Design Suite R460.2 2. UniSim Design Software Heat Exchangers R460 3. UniSim Design Software Tools Clicking item 2 from the above shows the following: 1. D  ocumentation 2. Installation and Licensing Guide 3. Release Notes Name

Model

1. UniSim Shell and Tube Exchanger Modeler

UniSim STE

Shell and Tube heat exchanger

2. UniSim Crossflow Exchanger Modeler

UniSim CFE

Air coolers and other crossflow exchanger

3. UniSim Plate – Fin Exchanger Modeler

UniSim PFE

Plate – fin heat exchanger

4. UniSim Fired Process Heater Modeler

UniSim FPH

Furnaces and fired heaters

5. UniSim Plate Heat Exchanger Modeler

UniSim PHE

Plate heat exchanger

6. UniSim Feedwater Heat Exchanger Modeler

UniSim FWH

Feedwater heat exchanger

7. UniSim Process Pipeline Heat Exchanger Modeler

UniSim PPL

Process Pipeline heat exchanger

722  Chemical Process Engineering Click item 4 of UniSim STE R460 icon loads the main UniSim STE window and over this is the Welcome view as shown in Figure 8.91. From this view one can select to create a New file or open an Existing file. To start a new case simulation, click the New button as shown in Figure 8.91 appears for the start of inputting the data. Click on Input menu shows Figures 8.91, 8.92, which give access to all of the input data. The menu itself is divided into the different types of data required to describe the heat exchanger and the conditions under which it will operate. These include the different aspects of geometry, process conditions and physical properties. Select the Exchanger Geometry input form (Figure 8.94) and one sees the inputs, which give the basic exchanger shell and head types using the TEMA designations. This screen is typical of most screens in that the data are entered either in a text box or via a drop down menu. The drop down menu shows a list of possible inputs where one selects the appropriate item.

Figure 8.92  Screen shot of UniSim Shell – Tube Exchanger Modeler (UniSim STE). (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Figure 8.93  Screen shot of Input Data. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Heat Transfer  723

Figure 8.94  Screen shot of Exchanger Geometry – Exchanger General. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Figure 8.95  Screen shot of Exchanger Geometry – Exchanger Details. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

724  Chemical Process Engineering

Figure 8.96  Screen shot of Exchanger Geometry – Design Details. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Figure 8.97  Screen shot of Exchanger Geometry – Material Properties. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Heat Transfer  725

Figure 8.98  Screen shot of Tubes and Baffles – Tube Details. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Figure 8.99  Screen shot of Tubes and Baffles – Transverse Baffles. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

726  Chemical Process Engineering

Figure 8.100  Screen shot of Tubes and Baffles – Special Baffles/Supports. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Figure 8.101  Screen shot of Input Bundle layout – Bundle Details. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Heat Transfer  727

Figure 8.102  Screen shot of Output Bundle layout – Bundle Details. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Figure 8.103  Screen shot of Bundle layout – Bundle Details. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

728  Chemical Process Engineering

Figure 8.104  Screen shot of Bundle layout – Bundle Size. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Figure 8.105  Screen shot of Nozzles – Shell side. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Heat Transfer  729

Figure 8.106  Screen shot of Nozzles – Tube side. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Note: If at any point you are not sure what input you want or something is not clear, press and get context sensitive help. If you select the rear heat type and press you can see a listing of all the available rear head types. Selecting Process from the Input menu or by clicking on the Process Data button shows Figure 8.107. This figure shows another form of input screen where the input items are arranged in a spreadsheet format. If the data do not fit on the screen, a scroll bar allows you to access the other input items. The spreadsheet view is used when data are required several times, in this case for the two streams in the exchanger. Note the left-hand column is for the hot stream and the right-hand column is for the cold stream. Finally, select Input from the Physical Property Data menu or by clicking on the Physical Property Data button. The initial screen (Figures 8.108 and 8.109) shows the top level information about each stream. Depending on the type of the physical property data you are working with, you can either enter the physical property data for the stream directly or enter data for components and allow UniSim STE to perform vapor – liquid equilibrium and mixture calculations. All the physical property data are managed through these screens. Run UniSim STE by carrying out one of the following: • Click on the Run button in the Toolbar. • Select the Run menu and then Calculate All • Press UniSim STE now displays a status window that reports progress of the run. Part way through the run, a tube bundle layout diagram will appear (Figure 8.110). This gives you the opportunity to modify the tube layout if you wish. Also, Figure 8.111 is displayed, which shows the Results Summary illustrating that it is a Checking case. When the run completes, there are three possible outcomes and corresponding outputs will be displayed: • Successful run with no fatal errors and no warnings – a screen showing the Results Summary is displayed. • Successful run with no fatal errors but with one or more warnings – the Results Summary is displayed together with a list of the warnings associated with the run • Failed run due to fatal errors - the Error Log is shown with a description of the errors that have occurred.

730  Chemical Process Engineering

Figure 8.107  Screen shot of Process – Process. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Figure 8.108  Screen shot of Physical Properties: Crude oil. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Heat Transfer  731

Figure 8.109  Screen shot of Physical Properties: Kerosene. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

There are many different outputs that can be viewed from the Output menu as illustrated in Figure 8.112. The results can be printed or viewed from Output menu and among the various results are the following (Figures 8.113):

179.33 mm

195.32 mm

Thermal Results Summary Full Results TEMA Spec. sheet Setting Plan Tube Layout Line Printer, etc.

AES: 123 tubes Shell id = 489 mm Filename: Case study-1- Crude Oil-akc-rev1.STEi Case Study - Heat Exchanger Rating by A. K. Coker

Figure 8.110  Bundle Tube Layout. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

732  Chemical Process Engineering

Figure 8.111  Screen shot of Results Summary. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Figure 8.112  Screen shot of Output menu. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Heat Transfer  733

Figure 8.113  Screen shot of the Results. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

Figure 8.114  Screen shot of Process Diagram. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

734  Chemical Process Engineering A

5340 Overall 360

640

3510

T2

S1

S2 1030

T1

2740

3580

Inlet Channel

570

580

570

570

570

Pulling Length

Shell

Baffle Orientation

Views on arrow A

All Measurements Are In mm Warnings - This Setting Plan is approximate only For accurate Setting Plan use a full mechanical design package.

Weight Bundle/Dry/Wet

T1 Inlet T2 Outlet S1 Shell In S2 Shell Out Design Pressure barg Temperature C Passes kg 1003

NPS 6 5 5 2.5 Shell 5.9 299 1 2297

Rating lb 150 150 150 150 Tube 5.9 164 4 3219

Case Study - Heat Exchanger Rating by A. K. Coker E-100

20-Jun-2016 18:32

AES 488 - 4267

Figure 8.115  STE Thermal Setting Plan. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

8.15 Bell-Delaware Method Accurate sizing of the shell and tube heat exchanger involves the Bell-Delaware method to determine the shell-side film heat transfer coefficient, as described by Bejan and Kraus [82] and others. The Bell-Delaware method determines the heat transfer coefficient for an ideal bank of tubes, and then applies correction factors to account for the baffle cut and spacing, baffle leakage effects, bundle bypass flow, variable baffle spacing in the inlet and outlet sections, and adverse temperature gradient build-up if laminar flow occurs. Further design details of the Bell-Delaware method are provided elsewhere [83].

Heat Transfer  735

Figure 8.116  Heat Exchanger Specification Sheet. (Source: UniSim Shell–Tube Exchanger Modeler, Courtesy of Honeywell, All rights reserved).

736  Chemical Process Engineering

Overall Heat Transfer Coefficient, U The overall heat transfer coefficient, U, can be determined with the known parameters such as the tube (inside) and shell (outside) film heat transfer coefficients, fouling factors and the tube wall thermal conductivity by:

Uo,clean =





1

(8.194)

  d  d o ln  o   do 1  di  1  + +    di hi 2k w ho 

For fouled condition, the overall heat transfer coefficient is:

Uo,clean =



1   d  d o ln  o   d o 1 d o R f ,i  di  1 + + + R f ,o +    di hi ho  2k w di



(8.195)

where = overall heat transfer coefficient based on the outside area of the tubes. Uo di, do = inside and outside tube diameters respectively. hi, ho = inside and outside film heat transfer coefficients. = thermal conductivity of the tube material kw Rf,i, Rf,o = fouling factors on the tube and shell sides, respectively. General design practice is to limit the reduction in heat transfer due to fouling to about 80% of the clean heat transfer coefficient. This is implemented by a cleaning schedule as described earlier that removes accumulations before they become too severe. The calculated overall heat transfer coefficient, U, is compared with the assumed and possible iteration until the values are in reasonable agreement.

Shell-Side Pressure (Δp) The Bell-Delaware method accounts for tube bundle bypass and baffle leakage effects. It calculates p that is 20% to 30% of that calculated without the bypass and leakage effects. 1. The Crossflow Section Between the Interior Baffles Use the b coefficients in Table 8.41 to determine the friction factor for an ideal tube bank, which depends on the tube layout and Reynolds number as:



b

 1.33  Re sb2 fideal = b1    PR d o 

(8.196)

where



b=

b3 1 + 0.14Re sb4

(8.197)

Heat Transfer  737 Table 8.41  Correlation coefficients for Jideal and fideal [139]. Pitch layout

Reynolds number

a1

a2

a3

a4

b1

b2

b3

b4

30

0-10

1.4

-0.667

1.45

0.519

48

-1

7

0.5

30

10-100

1.36

-0.657

1.45

0.519

45.1

-0.973

7

0.5

30

100-1000

0.593

-0.477

1.45

0.519

4.57

-0.476

7

0.5

30

1000-10000

0.321

-0.388

1.45

0.519

0.486

-0.152

7

0.5

30

10000+

0.321

-0.388

1.45

0.519

0.372

-0.123

7

0.5

45

0-10

1.55

-0.667

1.93

0.5

32

-1

6.59

0.52

45

10-100

0.498

-0.656

1.93

0.5

26.2

-0.913

6.59

0.52

45

100-1000

0.73

-0.5

1.93

0.5

3.5

-0.476

6.59

0.52

45

1000-10000

0.37

-0.396

1.93

0.5

0.333

-0.136

6.59

0.52

45

10000+

0.37

-0.396

1.93

0.5

0.303

-0.126

6.59

0.52

60

0-10

1.4

-0.667

1.45

0.519

48

-1

7

0.5

60

10-100

1.36

-0.657

1.45

0.519

45.1

-0.973

7

0.5

60

100-1000

0.593

-0.477

1.45

0.519

4.57

-0.476

7

0.5

60

1000-10000

0.321

-0.388

1.45

0.519

0.486

-0.152

7

0.5

60

10000+

0.321

-0.388

1.45

0.519

0.372

-0.123

7

0.5

90

0-10

0.97

-0.667

1.187

0.37

35

-1

6.3

0.378

90

10-100

0.9

-0.631

1.187

0.37

32.1

-0.0963

6.3

0.378

90

100-1000

0.408

-0.46

1.187

0.37

6.09

-0.602

6.3

0.378

90

1000-10000

0.107

-0.266

1.187

0.37

0.0815

-0.022

6.3

0.378

90

10000+

0.37

-0.395

1.187

0.37

0.391

-0.148

6.3

0.378

p for one ideal cross-flow section is:



∆p b,ideal =

0.14

4f ideal Ws2 nr ,cc  µ w  2 ρs g c A s  µ  s

(8.198)

The bundle bypass correction factor uses parameters determined for Jb, the film coefficient correction factor for the bundle and partition bypass effects; it ranges from 0.5 to 0.8 [83]. For a Reynolds number Res ≤ 100, Cbp = 4.5. For Res > 100, Cbp = 3.7. The limit of Rb is 1.0 for ≥ 0.5 where is the ratio of sealing strip pairs to tube rows in cross-flow section.



(

)

R b = exp  −C bp rc 1 − 3 2ς 

The baffle leakage correction factor is a function of ra and rb, and it typically ranges from 0.4 to 0.5.

(8.199)

738  Chemical Process Engineering



R l = exp[ −1.33(1 + ra )rbc ]

(8.200)



c = −0.15(1 + ra) + 0.8

(8.201)

2. The Baffle Windows For an ideal window, determine the p using the equation corresponding to the flow regime as: For Res ≥ 100:



∆p w ,ideal = (2 + 0.6n tw )

ρv z2 2

(8.202)

where vz is defined as the geometric mean between the cross-flow velocity and the window velocity and is determined by:

vz = vm v w



(8.203)

vm = cross-flow fluid velocity = Gm/ρ vw = fluid velocity through window = Gw/ρ or



∆p w ,ideal =

Ws2 (2 + 0.6n tw ) 2ρs g c A s A w

(8.204)

If Res < 100







µ s Ws  nr ,tw L  Ws + bc2  +  ρ A s A w  pt − d o Dw  ρ A s A w

∆p w ,ideal = 26

Dw =

nr ,tw =

4 Aw π d o n tw +

Ds θ2 2



0.8[l c − 0.5(Ds − Dotl + d o )] Pp

(8.205)

(8.206)

(8.207)

3. The Entrance and Exit Sections, from the Nozzle to the First Baffle Window Combined with the cross-flow and baffle windows, the total pressure drop through the exchanger (excluding the nozzles) is:



 n  ∆ps = [(n b − 1)(∆p b,ideal )R b + n b ∆p w ,ideal ]R l + 2∆p b,ideal R b  1 + r ,tw  nr ,cc  

(8.208)

Cao Eduardo [27] and Hall [85] have presented Excel spreadsheet programs for the design of a shell and tube heat exchanger using the Bell-Delaware method, and Serth [38] has employed HEXTRAN software from Invensys SIMSCI-ESSCOR using the Bell-Delaware method in his examples.

Heat Transfer  739

Tube Pattern Kern uses the equivalent diameter, de (De) for the shell-side flow, which depends on the tube pattern. For square and triangular tubes, Equations 8.168 and 8.169 are used to calculate de. However, this approach has been refuted by other authors for the following reasons [27]: 1. The equivalent diameter is defined for a flow direction parallel to the tubes, whereas the shell-side flow is normal to the tubes. Table 8.42  Comparison of Kern, Bell-Delaware and Tinker methods. Kern

Bell-Delaware

Tinker

1. Ease of use

Simple

More involved

More involved

2. Resultant design

Very conservative

Not conservative

Not conservative

3. Cost of equipment

Very high

Relatively low

Relatively low

a. By pass and leakage streams

No

Yes

Yes

b. Inlet and outlet baffle spacing being different than the central one

No

Yes

Yes

c. Number of tube rows being different in inlet and outlet zones than in the center.

No

Yes

No

d. Seal strips

No

Yes

Yes

e. Different tube layouts and baffle cuts

No

Yes

Yes

f. Effectiveness of tube rows in window by a separate calculation.

No

Yes

Yes

g. Laminar flow

Original plots extended. Method remains unchanged.

Δplam calculated differently.

Method remains unchanged.

h. Size of tube bundle

Assumes shell full of tubes

Accounts for it by number of tubes in cross flow

Accounts for it by mean bundle width.

i. Pressure drop in the nozzle.

Yes

No

No

j. Δp due to gradual fouling of heat exchanger

Yes (takes an average working unit)

No

Yes

5. Basis of Reynolds number calculation

Equivalent diameter

Tube O.D.

Tube O.D.

6. Which mass velocity used?

Cross flow over the tube bundle

Geometric mean of cross-flow and window flow.

Cross-flow mass velocity multiplied by a factor for tubes in baffle window.

7. Multi-pass exchangers

All three were initially formulated for E-type shell. However, they can all be modified for use with any shell, and any number of passes.

4. Does it account for

(Source: Gupta, J. P., Working with Heat Exchangers: Questions and Answers, Hemisphere Publishing Corporation, 1986. [146])

740  Chemical Process Engineering 2. It is not possible to have a correlation that is valid for every geometry if geometric similitude does not exist. This implies that there should be different correlation for each geometry and when geometric similitude exists, any characteristic length can be used to define the Reynolds number, which does not require the equivalent diameter. Therefore the concept of using de has been abandoned by most researchers, who prefer to use the tube diameter for the Reynolds number and obtain a different correlation for each tube pattern.

Accuracy of Correlations Between Kern’s Method and the Bell-Delaware Method Heat exchangers designs have been arrived at using the Kern, Tinker or Bell method. The suitability and accuracy of these have been reviewed in the literature. Kern’s method cannot be applied to a TEMA type T floating head heat exchanger without sealing strips or with unsealed pass partition lanes. Whitley [86] presented a study of the errors found in heat

Figure 8.117  Specification process data sheet of shell and tube heat exchanger.

(Continued)

Heat Transfer  741

Figure 8.117  (Continued) Specification process data sheet of shell and tube heat exchanger.

transfer coefficient and pressure drop predictions obtained with the Kern and Bell methods. Palen and Taborek [6] show that the Bell-Delaware method allows the prediction of shell-side film coefficients in the range from 50% lower to 100% higher than the real values. Table 8.42 shows a comparison of the Kern, Bell-Delaware and Tinker methods.

Specification Process Data Sheet, Design and Construction of Heat Exchangers The specification process data sheet is a standard template to specify the characteristics of a heat exchanger. It is used as a basic engineering document in the design, purchasing and construction stages of a heat exchanger. Figure 8.117 is an example of such a template (see also Figure 8.83). The terminology included in the specification process data sheet represents the following: Operating pressure: This is the pressure to which the unit is submitted in normal operation. Design pressure: This is the maximum pressure at which the unit needs to continue operating, resulting from unusual conditions, e.g., during operating procedure or as a consequence of process excursions that must be tolerated. This is the pressure used by the mechanical designer to calculate the thicknesses of plates, tubes, flanges, etc. Hydraulic test pressure: Any pressure vessel designed per ASME code can withstand at ambient temperature in the absence of dynamic loads and for a limited time, pressure higher than the design pressure. Therefore, if a hydraulic test is specified, the test pressure will be 1.3 times the design pressure. Design temperature: This is the maximum temperature that may coexist with the design pressure. Process Specification: The following data must be specified: flow rates, inlet and outlet temperatures, physical properties, fouling factors, allowable pressure drops, and design and operating pressures and temperatures. Also, this stage includes the geometric specifications that must be adopted during design, such as maximum tube length, shell and tube fluid allocation, TEMA type and class, and materials of construction. Here, the process engineer completes these parameters in the specification sheet, thus defining the basis of the design.

742  Chemical Process Engineering Thermal design: This employs any of the methods described earlier. The result of the thermal design is the definition of the heat exchanger geometry, including tube diameter, and length, tube pattern and pitch, number of tubes and shell passes, shell diameter, number and type of baffles and nozzle size. This aspect is normally a process engineering activity and further design activities relate to the field of mechanical engineering. At the end of the thermal design, the specification data sheet will be complete, and will be possible to sketch an outline drawing of the exchanger, indicating location of the nozzles, main dimensions, types of supports and other information required by the process engineer. Mechanical design: Here, the heat exchanger components are mechanically designed, and the material specification is completed; mechanical tests (e.g., pressure tests) are specified and detailed drawings are prepared. Construction: Construction and drawings are left to the manufacturer. All the necessary details for the construction and welding procedures and methods are specified.

8.16 Rapid Design Algorithms for Shell and Tube and Compact Heat Exchangers: Polley et al. [88] Polley et al. [88] have developed rapid design algorithms for the design of both shell and tube heat exchangers and compact heat exchangers. These algorithms are based on the full use of allowable pressure drops of both of the streams being contacted as the design objective and a set of simultaneous equations. In the case of a shell and tube heat exchanger, they assumed that the best shell-side performance can be gained by making baffle window flow velocities and bundle cross-flow velocities equal. This in turn results in a “similarity concept” that can be used for the derivation of simple performance equations from shell-side models. They determined the exchanger geometry from values as follows: 1. The tube-side film heat coefficient can be directly related to the tube-side velocity and thus to the exchanger tube count. 2. From the tube count and total surface area, the tube length can be determined. 3. The shell diameter can be calculated from the tube count. 4. Finally, with the shell diameter known, and the shell-side velocity being determined from the shellside film coefficient, the number of baffles and baffle spacing required within the exchanger can be determined. They inferred that the rapid design algorithm avoids the need to evaluate many potential geometries, while ensuring the full use of the allowable pressure drop. The only restrictions are: The pressure drop (∆p) referred to is that associated with flow through the exchanger bundle, as no account is taken of any nozzle or header pressure drops. Allowance for these drops must be made ahead of design and checked after design. However, this restriction is not considered as adversely affecting the design. Kern correlations are generally considered too inaccurate for use in modern exchanger design. Their methodology started with a consideration of the Bell-Delaware Method as described earlier and proceeded to consider current state-of-the-art commercial methodologies. The algorithms used in the design have been tested with data from literature, which show that in the case of the shell and tube heat exchanger algorithm, there appears to be the first one which makes full use of both allowable pressure drops and thereby identifies the smallest exchanger for a given duty. Alternatively, in the case of compact heat exchangers, a major use of such an algorithm would be the identification of the best surface combination for a specific duty. The research showed that the basic algorithm can be applied using the Bell-Delaware method for shell and tube exchangers, as the approach can be further extended to even more sophisticated methods through the use of geometrical similarity (e.g., 25% baffle cut, baffle spacing equal to shell diameter).

Heat Transfer  743 For compact heat exchangers, the approach can be extended to duties involving isothermal two-phase flows. Figure 8.118 shows the algorithm of the rapid design of the shell and tube heat exchanger, and the notations used in this figure are. A = area (m2) d = tube diameter (m) Ds = shell diameter (m) FT = ∆TLMTD correction factor (non-counter-current flow) h = film heat transfer coefficient (W/m2 K) K = dimensional constant, solely dependent on physical properties, volumetric flow rate, and a single characteristic dimension. R = fouling resistance (m2 K/W) ∆p = pressure drop (kPa) Subscripts i o s t

= inside surface = outside surface = shell side = tube side

A

Input data E Solve:

Initialise: Shell-side friction factor Heat transfer j -factor

A=

F

Q 1 1 + Rfs + + Rft ht ΔTLMTDFT hs

do di

Δpt = Kt A h3.5 t Δps = (Ks1 A + Ks2)h2s

Initialise: Baffle cut

Find: A, ht and hs

D

Calculate: Tube length Number of baffles Tube side Reynolds No. and velocity Tube count

Initialise: Shell diameter C Estimate: Tube count and baffle spacing

Calculate: Shell side correction factors

Estimate: Shell diameter

C

Update: Shell diameter

Yes

Estimate: Tube-side and shell side constants

Ds Changed?

No B

A

Figure 8.118  New algorithm for shell and tube exchanger design. (Source: G.T. Polley, et al. [88]).

(Continued)

744  Chemical Process Engineering E

B

D

Calculate Δps

Change: No. of tube pass

Search for: Baffle cut

Yes

Search fails?

F

Update: Friction factor J -factor

Yes

Yes

Δps changed?

No No Estimate: Friction factor Heat transfer j-factor Δps

Δps changed?

No Output: Performance specifications Geometrical specifications

Figure 8.118  (Continued) New algorithm for shell and tube exchanger design. (Source: G.T. Polley, et al. [88]).

1 = side 1 of compact exchanger 2 = side 2 of compact exchanger

8.17 Fluids in the Annulus of Tube-in-Pipe or Double Pipe Heat Exchanger, Forced Convection A double pipe exchanger consists of one or more pipes or tubes, the smaller centered inside the larger as shown in Figure 8.119. One fluid flows in the annulus between the tubes, the other flows inside the smaller tube. The heat transfer surface is considered as the outside surface of the inside pipe. Longitudinal fins may be used on the outside of the inner tube. The flow is true counter-current, which can be beneficial when very close temperature approaches or very long temperature ranges are required. The fluid film heat transfer coefficient for the fluid inside the inner tube is determined in the same way as for any straight tube using Figures 8.63–8.69, or by the applicable relations correcting to the OD of the inner tube. Such an exchanger is used in service when the heat duty is moderate (i.e., UA < 100,000 Btu/h.oF) or when one stream is a viscous liquid or when flow rates are small. This type of exchanger is suitable for high pressure applications because of its smaller diameter. Also, several hairpin sections provide for flexibility in matching heat exchanger requirements with changing process conditions. A double pipe exchanger is suited for “dirty” service because it is easy to dismantle and clean. In addition, a double pipe exchanger can be considered in the following situations: • When the shell-side coefficient is less than half of the tube-side; the annular side coefficient can be made comparable to the tube-side. A high pressure can be catered for more economically in the annulus than in a larger diameter shell.

Heat Transfer  745 Flow Fluid D2 Tube (A) Tube (B)

D1

e)

r Tub

(Inne

D1 = Outside diameter of the inner tube (B). D2 = Inside diameter of the outer tube (A). Annulus area for flow is between tubes (A) and (B). Heat transfer coefficients used are: hi at inside surface of tube (B) ho at outside surface of tube (B)

Figure 8.119  Double-pipe tube arrangement showing annulus area.

• At duties requiring 100 – 200 ft2 of the surface, which make it more economical when a true countercurrent flow can be obtained, thus eliminating temperature crosses that require multishell and tube units. For the fluid in the annulus, the same relations apply (Equation 8.193), except that the diameter D, must be the equivalent diameter De. The value of h obtained is applicable directly to the point desired – that is, the outer surface of the inner tube [70].

Finned Tube Exchangers The procedures for designing exchangers using the finned tubes are generally specific to the types of fins under consideration. The 16 and 19 fins-per-in. low fin tubes (Figure 8.11A and B) are uniquely adaptable to the conventional shell and tube exchanger [89, 90] (see Table 8.43) and are the type of tubes considered here. These low-fin tubes can be installed and handled in the same manner as plain tubes. The larger diameter fins (5 or more per in.) are usually used in services with very low outside coefficients of heat transfer and require a unit design to accommodate the tube’s installation. Other finned tube configurations are shown in Figures 8.11A, E, G, and H and represent increased external finning possibilities. Internal ribs, shown in Figures 8.11K and M, can certainly help the film transfer coefficient, provided fouling is not a prominent factor. Other finned designs (number of fins/ in.) are available from most manufacturers, and in order to use them in heat transfer designs, specific data need to be available from the manufacturer. The literature cannot adequately cover suitable design data for each style of tube. Pase and O’Donnell [91] present the use of finned titanium in corrosive services. One of the outstanding books by Kern and Kraus [76] covering the entire topic of Extended Surface Heat Transfer includes detailed theory and derivations of relations plus practical applied problems for finned and compact heat exchangers. The longitudinal finned tube usually is adapted to double pipe exchangers but is used in the conventional bundle design with special considerations. Other finned tube references of interest are Hashizume [92] and Webb [93].

Economics of Finned Tubes Figure 8.120 is useful for roughly predicting the relative economic picture for adapting low finned tubes to the heating or cooling of oil on the shell-side of conventional shell and tube units. This is not a design chart. Figures 8.121 and 8.122 also indicate the relative advantage regions for the finned unit, for the average water cooled exchanger of 150 psi design.

.625

.750

.875

1.000

/8

¾

/8

1

7

5

O.D.

O.D.

.083

.095

.065 .083

.082 .095

.049 .065 .083

.065 .082 .095

.042

.049

.065

.058

.042

.058

.875

.065

.082

.035

.049

.065

.750

.042

.058

.054

.035

.049

.028

.065

.072 .625

.049

.065

.049

.042

.058

.028

Wall thickness

.035

.500

Rood dia.

.709

.745

.777

.791

.584

.620

.652

.666

.680

.459

.495

.527

.541

.555

.569

.370

.402

.416

.430

.444

I.D.

Finned section dimensions

.049

.042

Wall thk.

Plain section dimensions

Nominal size

19 Fins Per In.

.910

.785

.660

.535

dc

.678

.588

.496

.405

Outside area ft2 per lin ft

Table 8.43  Approximate estimating physical data for low-finned tubing for use in design calculations.

3.65

3.48

3.33

3.27

3.85

3.62

3.44

3.37

3.30

4.13

3.84

3.60

3.50

3.41

3.33

4.18

3.85

3.72

3.60

3.48

Surface area ration ao/ai

.395

.436

.474

.492

.268

.302

.334

.349

.363

.166

.192

.218

.230

.242

.254

.108

.127

.136

.145

.155

I.D. cross sectional area, in.2

.965

.841

.680

.612

.829

.727

.589

.530

.483

.695

.612

.490

.449

.376

.344

.444

.408

.368

.316

.275

(Continued)

Approx. wt/ft lb (Copper)

746  Chemical Process Engineering

.625

.750

.875

1.00

¾

/8

1 .709

.745

.584

.620

.459

.495

.370

.917

.790

.665

.540

dc

.598

.520

.438

.368

Outside area ft2 per lin ft

3.22

3.07

3.40

3.20

3.63

3.38

3.80

Surface area ration ao/ai

.395

.436

.268

.302

.166

.192

.108

I.D. cross sectional area, in.2

.9531 .9531 .9780 .9319 .3032 .3065 1

Admiralty (types of B & D)

85/15 red brass

Aluminum brass (type B)

1100 aluminum

3003 aluminum

Nickel

wt/ft Conversion Factor (wt/ft of Copper x Conv. Factor wt/ft of Alloy)

.083

.065

.083

.065

.083

.065

.065

I.D.

Admiralty (type C)

.875

.750

.625

.500

Wall thickness

1

.095

.082

.095

.082

.095

.082

.082

Rood dia.

Finned section dimensions

Copper

ALLOY

7

5

/8

16 Fins per in.

O.D.

O.D.

Wall thk.

Plain section dimensions

Nominal size

19 Fins Per In.

Table 8.43  Approximate estimating physical data for low-finned tubing for use in design calculations. (Continued)

.965

.841

.829

.727

.695

.612

.497

(Continued)

Approx. wt/ft lb (Copper)

Heat Transfer  747

O.D.

O.D.

.8761 .8978

Low carbon steel

Stainless steel

Note: Units are in., except as noted. Used by permission: Engineering Data Book, Section 2, ©1959. Wolverine Tube, Inc.

1

Monel

dc 1

I.D.

90/10 cupo-nickel

Wall thickness 1

Rood dia.

Finned section dimensions

70/30 cupro-nickel

Wall thk.

Plain section dimensions

Nominal size

19 Fins Per In.

Outside area ft2 per lin ft

Surface area ration ao/ai

Table 8.43  Approximate estimating physical data for low-finned tubing for use in design calculations. (Continued)

I.D. cross sectional area, in.2

Approx. wt/ft lb (Copper)

748  Chemical Process Engineering

Heat Transfer  749

ed

tsi

0.00 5

1.0 0.8 0.6 0.5 0.4 0.3

f=

2

Ou

10 8 6 5 4 3

Fin n

Viscosity in Centipoise

20

Tu be sE co d eF no f= o mi 0 uli ca f= ng l 0 F ac f = .000 t o 5 0.0 r 01 f= 0.0 02 f= 0.0 f= 03 0.00 4

40 30

0.2 0.1

0.001 0.002 0.003 0.004 Inside Fouting Factor Plain Tubes Economical

Figure 8.120  Estimating relationship for selection of low-finned units in oil heaters or coolers; for reference only (1950 costs). (Used by permission: Williams, R. B. and Katz, D. L. Petroleum Refiner, V. 33, No. 3 © 1954. Gulf Publishing Company. All rights reserved).

500

Uo, Overall Coefficient, Fouled, Btu/(hr.)(°F.)(sq. ft. Outside)

400

300

r=0 r = .0005 r = .001 r = .002 Outside Fouling Factors Limit Curves

200

Plain Tube Economical Above These Lines

r = .003

r = .004

100 90 80 70

r = .005 Finned Tubes Economical Below These Lines

60 50

.001 .002 .003 .004 Inside Fouling Factor, ri

.005

Figure 8.121  Approximate relationship of the overall coefficient fouled, and the fouling factor of inside tubes for predicting the economical use of finned tubes in shell and tube units. (Used by permission: Williams, R. B. and Katz, D. L., ‘Performance of Finned Tubes and Shell and Tube Heat Exchangers,’ © 1951. University of Michigan. Note: For reference only, 1950 costs).

Reduction in Number of Tubes in Exchangers Using Finned Tubes, %

750  Chemical Process Engineering 50 40

This is a Generalized Curve Do Not USe for Design

30 20 10 0

9 10 1 2 3 4 5 6 7 8 Plain Tube, Modified Film Coefficient, Inside/Outside, l l l l +r + ro i hi ho

Figure 8.122  Generalized design evaluation of low-finned tubes and fluid heat exchangers. (Used by permission: “An Opportunity.” Wolverine Tube, Inc.).

For example, for a plain tube with an overall fouling coefficient of 125, inside fouling of 0.0015 ft2 h °F/Btu, and outside fouling of 0.002 ft2h °F/Btu, the finned tube unit would be more economical. The fouling lines, r on the charts are the limit border lines of the particular economics, which assumed equal costs for the finned and bare tube exchangers. These are not to be used for specific exchanger design, but merely in deciding the region of applicability.

Low-Finned Tubes, 16 and 19 Fins/In. This tube has a ratio of outside to inside surface of about 3.5 and is useful in exchangers when the outside coefficient is poorer than the inside tube coefficient. The fin efficiency factor, which is determined by fin shaped and size, is important to final exchanger sizing. Likewise, the effect of the inside tube fouling factor is important to evaluate carefully. Economically, the outside coefficient should be about 1/5 or less than the inside coefficient to make the finned unit look attractive; however, this break-even point varies with the market and designed-in features of the exchanger. Process applications are primarily limited to low-finned tubing, although the high-finned tubes fit many process gas designs that require special mechanical details. This test limits the presentation to the low-finned design. Figure 8.123 shows weighted efficiencies of low-finned tubing of 11, 16 and 19 fins per in. length, 1/16 in. high radial. 1.00 Copper Aluminum Red Brass Admiralty

ef, WEIGHTED FIN EFFICIENCY

0.95 0.90

Aluminum Brass

0.85

Nickel Steel, 90–10 Cu-Ni 70–30 Cu-Ni

0.80

Stainless Steel

0.75 0.70 0.65 1.0

10

100

1,000

10,000

Figure 8.123  Weighted efficiencies of low-finned tubing of 11, 16 and 19 fins per in. length, 1/16-in. high, radial. (Used by permission: Engineering Data Book, 2nd Ed., © 1960. Wolverine Tube, Inc.).

Heat Transfer  751

Finned Surface Heat Transfer Rohsenow and Hartnett [94] recommend the Briggs and Young [95] convection film coefficient relation for externally finned tubes.



(D G )0.681 (c pµ )1/3 (s)0.2 (s)0.113 h fo Dr = 0.134 r max (µ ) (k) l t k

(8.209)

where hfo = mean outside finned surface heat transfer (usually gas) coefficient, Btu/(h) (°F) (ft2 external) Dr = root diameter of tube (external), ft dn = root diameter of tube, external, in. k = thermal conductivity of gas, Btu/(h) (ft2) (°F/ft) Gmax = gas mass velocity at minimum cross-section, through a row or tubes normal to flow, lb/(h) (ft2) Gm = mass velocity at minimum cross-section through a row of tubes normal to flow, lb/(h) (ft2) g = acceleration of gravity, 4.18 108, ft/(h) (h) n = number of rows in direction of flow = gas/vapor viscosity at bulk temperature, lb/(h) (ft) cp = specific heat, Btu/(lb) (°F) s = distance between adjacent fins, in. l = fin height, in. t = fin thickness, in. Pt = transverse pitch between adjacent tubes in same row, in. Pl = longitudinal pitch between adjacent tubes in different rows measured on the diagonal, in P = static pressure drop, lbf/ft2 ρ = density of gas, lb/ft3 f = mean friction factor, this is the “small” or fanning friction factor. Note: f = Pg ρ/ ( nG m 2 )

8.17.1 Pressure Drop Across Finned Tubes [166]

∆p = 18.93

(G m Dr )−0.316 (Pt )−0.927 (Pt )0.515 ( G 2m n ) (µ ) (Dr ) (Pl ) (g ρ)

(8.210)

These equations provide reasonable estimates per Rohsenow [94], who suggests using with caution, only when performance on the system is not available. Ganapathy [96] offers simplified equations and nomographs to solve these relationships. Table 8.44 provides a suggested range of overall heat transfer coefficients, Uo, for actual finned heat exchangers.

Design for Heat Transfer Coefficients by Forced Convection Using Radial Low-Fin Tubes in Heat Exchanger Bundles Kern and Kraus [76] reference the ASME-University of Delaware Cooperative Research Program on Heat Exchangers by Bell [97] and later work by Bell and Tinker. The Kern [76] recommendation is based on the Delaware work and the TEMA details of construction.

752  Chemical Process Engineering Table 8.44  Comparison of calculated, designed, and operating Uo values; ¾-in., 19 fins/in. finned tubes. Service

Calc’d. Uo

Propane condenser (66°F H2O)

Designed Uo

Operating Uo

35

47.4

Comments

9.9

9.5

14.8

Ethylene compressor intercooler (67°F H2O)

21

18

28.7

Ethylene compressore aftercooler (67°F H2O)

21

18.3

16.3

Propane compressor intercooler (67°F H2O)

21.6

20

23.8

Propane cross exchanger (liquid to gas)

14.2

8.2

11.6 & 9.1

Lower flow rate than used in calculations.

Gas cooler (67°F H2O)

17.6

13.3

14.6

Lower heat duty & inlet gas temperature than used in calculations

Gas heater (400 lb sat’d. steam)

22.7

15

22.5

Ethylene compressor intercooler (68°F H2O)

21.0

11.5

13.9

Lower flow rate than used in calculations

Methane gas-Ethylene liquid cross exchanger

25

20

26.2

Uo drops to 10 after fouling with hydrate ice.

Methane gas-propane liquid cross exchanger

25

17.9

19.7

Uo drops to 13 after fouling with hydrate ice.

Possibly fouled by oil.

Flow area across bundle, as = ds (C')(B)/144 PT, ft2 Mass velocity Gs = W/as, lb/ft2-hr 4(axial flow area) , in. Equivalent diameter de = Wetted perimeter as Flow area across bundle, ft2. B Baffle spacing, in. c Specific heat of fluid, Btu/lb-°F C' Clearance between adjacent tubes, in. De Equivalent diameter, ft. de Equivalent diameter, in. Gs Mass velocity, lb/ft2-hr 2 100 ho Film coefficient outside bundle, Btu/ft -hr-°F ds Inside diameter of shell, in. k Thermal conductivity, Btu/ft-hr-°F PT Tube pitch, in. W Weight flow of fluid, lb/hr µ Viscosity at the caloric temperature, lb/ft-hr µw Viscosity at the tube wall temperature, lb/ft-hr

B=

cµ –1/3 µ µw k

–0.14

Ethylene cross exchanger (liquid to gas)

jH =

ho De k

B=

10

1 10

Low-fin limit

102

Tube OD 3/4" 1" 1–1/4" 1–1/2" 5/8" 3/4" 3/4" 1" 1–1/4" 1–1/2"

103 Res =

De Gs µ

Pitch 1" 1–1/4" 1–9/16" 1–7/8" 13/16" Δ 15/16" Δ 1" Δ 1–1/4" Δ 1–9/16" Δ 1–7/8" Δ

104

ds

0.2

ds

Plain tube C', in. de, in. 0.250 0.95 0.250 0.99 0.3125 1.23 0.375 1.48 0.1875 0.535 0.1875 0.55 0.250 0.73 0.250 0.72 0.3125 0.91 0.375 1.08

Low fin 19 fins/in. C', in. de, in. 0.34 1.27 0.34 1.27

Low fin 16 fins/in. C', in. de, in. 0.325 1.21 0.32 1.21

0.278 0.278 0.34 0.34

0.2655 0.2655 0.325 0.32

105

0.82 0.80 1.00 0.97

0.78 0.75 0.95 0.91

106

Figure 8.124  Shell-side jH factors for bundles. One sealing strip per 10 rows of tubes and TEMA clearances. (Source: Engineering Data Book, 2nd Ed. © 1960. Wolverine Tube, Inc., Used by permission: Kern, D. Q. and Kraus, A. D., Extended Surface Heat Transfer, p. 506, © 1972. McGraw-Hill, Inc., All rights reserved).

Heat Transfer  753 Heat Transfer Coefficient, Shell Side



 k  cp µ  h o = jH    De   k 

1/3

 µ   µ  w

0.14



(8.211)

See Figure 8.124. where De = shell-side equivalent diameter outside tubes, ft, see Figure 8.73 cp = specific heat of shell-side fluid, Btu/(lb-°F) k = thermal conductivity of fluid, Btu/(ft) (h) (°F) = viscosity of shell-side fluid (at bulk temperature) lb/(ft) (h) = viscosity of shell-side fluid at tube wall temperature, lb/(ft) (h) w jH = heat transfer factor, dimensionless ho = heat transfer coefficient for fluid outside tubes based on tube external surface, Btu/(h) (ft2) (°F) Res = Reynolds Number, shell side, dimensionless Gs = mass velocity (cross-flow), lb/(h) (ft2) The baffle used in the preceding equation has 20% segmental cuts. Shell-side cross-flow velocity [76].



Cross-flow area, a s =

d sC′B 144p

(8.212)

where as = cross-flow area in a tube bundle, ft2 ds = shell-side I.D., in. p = tube pitch, in., see Figures 8.73. Cʹ = clearance between low-fin tubes, ( p − d ′e ), or for plain tubes, (p – d), in., see Figure 8.125 B = baffle pitch, in. Figure 8.124 allows for the correction for the bypass area between the outer tube limit of the bundle and the shell ID, or as an alternative, see Figure 8.71. Referring to Figure 8.143, the marking “low-fin limit” at Re = 500 is explained by Kern [76]; because the low-fin tube is somewhat more inclined to insulate itself with liquids of high viscosity, when a low shell-side Re number is the result of a high mass velocity and high viscosity as compared to a low mass velocity at low viscosity, caution is suggested [76].

8.17.2 Pressure Drop in Exchanger Shells Using Bundles of Low-Fin Tubes The Delaware [97] work is considered [76] the most comprehensive (up to its date of preparation), taking into account the individual detailed components that make up the flow and pressure loss components of a total exchanger operation. Figure 8.125 presents a recommended pressure drop correlation [76] for low-fin tubes in the shells and is based on clean tube pressure drop with no dirt sealing the leakage clearances between the tubes and baffle holes or baffle-toshell clearances. A fouled condition pressure drop may be an indeterminate amount greater. The authors [76] state that this University of Delaware correlation has some factors built in that limit the deviations to a relatively small range. Figure 8.125 has allowances built in for entrance and exit losses to the shell and leakage at baffles [76]. The suggested pressure drop for shell-side heating or cooling, including entrance and exit losses is:

754  Chemical Process Engineering 0.10 ΔPs =

fs × Gs2× Ds (ns + 1)

=

B = ds

fs × Gs2 × Ds (ns + 1)

, psi

ds = 8.07 in. ds = 15 1 in. 41 ds = 23 4 in. ds = 42 in.

fs, sq ft/sq in.

0.01

0.001 B = 0.2 ds

0.0001

10

100

ds = 8.07 in. ds = 15 1 in. 4 1 ds = 23 in. 4 and larger

1,000

10,000

100,000

1,000,000

Res = Des Gs/µ B C' Des des

= baffle spacing, in. = number of baffles = clearance between adjacent tubes, in. = number of times fluid crosses bundle from inlet to = equivalent diameter, ft outlet = equivalent diamater, in. See jH curve for = shell side pressure drop, psi numerical values = density lb/ft3 Ds = shell diamater, ft = viscosity at the caloric temperature, lb/ft-hr ds = shell diameter, in. = viscosity at the tube-wall temperature, lb/ft-hr Gs = mass velocity, lb/ft2-hr = (µ/µw)0.14 q = acceleration of gravity, 4.18 × 108 ft/hr2 L = tube length, ft Note: Friction factors are dimensional, sq ft/sq in. to give ΔPs in psi directly

Figure 8.125  Shell-side friction factors for bundles with 20% cut segmental baffles, one seal strip per 10 rows of tubes and TEMA clearances. These factors can be used for plain or low-finned tubes with the appropriate values of Des or des. (Source: Engineering Data Book, 2nd Ed. © 1960. Wolverine Tube, Inc., Used by permission: Kern, D. Q. and Kraus, A. D., Extended Surface Heat Transfer, p. 511, © 1972. McGraw-Hill, Inc., All rights reserved).

f Gc2 Ds (n b + 1) , psi ∆ps = (5.22 × 1010 )(De s φs )

where f

= friction factor, dimensionless, ft2/in.2 ps = shell-side pressure drop, psi Gc = cross-flow mass velocity, lb/(h) (ft2) Ds = shell I.D., ft nb = number of baffles De = Des = equivalent O.D. of tubes, ft, see earlier discussion on this topic. de = des = equivalent O.D. of tubes, in., see Figure 8.124 for numerical values. s = specific gravity, dimensionless ps = pressure drop of fluid, heated or cooled, including entrance and exit losses, lbf/in.2 = viscosity correction = ( / w), dimensionless s = viscosity of fluid at wall of tube, lb/(ft-h) w = viscosity of fluid in bulk at caloric temperature, lb/(ft-h) ρ = fluid density, lb/ft3 ds = shell diameter, in.

(8.213)

Heat Transfer  755 Bs = baffle spacing, in. Res = shell-side Reynolds Number Note that this figure can be used for plain or low-fin tubes when the appropriate value of De is used [76].

Tube-Side Heat Transfer and Pressure Drop Because finned tubes of the low-fin design are standard tubes, the inside heat exchange and pressure drop performance will be the same as determined for “plain” or “bare” tubes. Use the appropriate information from earlier design sections.

8.17.3 Double Pipe Finned Tube Heat Exchangers The double pipe heat exchanger is one of the simplest pieces of equipment that performs heat exchange in a continuous mode between two fluids. Figure 8.126 shows a hairpin heat exchanger, formed by two sets of concentric tubes with the corresponding connection pieces. In cases where a higher heat transfer area is required, several hairpins can be added in a series configuration as shown in Figure 8.126A. The unit parts are made of standardized pipe fittings, such that the assembly of this exchanger type can be easily fabricated. In order to avoid fluid leaks, it is necessary to install packing elements at both ends with their corresponding glands. This is essential because the unit must be disassembled for cleaning, thus welded unions should not be used. In packed unions, some leakage can occur, so that glands must be adjusted periodically. Also, disassembling the unit can be complicated and time-consuming. This is the reason why this exchanger type is seldom used in industry. Also, the maximum tube length is 20 ft. (6 m). Longer tubes can present too high deflection and distortion of the annular space, which can result in poor flow distribution. The maximum heat transfer area of a hairpin is rather small, and it would be necessary to use a great number of Shell Cover Gasket

Shell inlet Shell

Shell Cover

G-Fin Pipe

Threaded Adapter

Tube Outlet Tube Inlet

Welded Return Bend

Shell Supports (Moveable) Twin Flange

Union Nut Non-Finned Tube Shell End Piece

Cone Plug

Shell Outlet

Cone Plug Nut

Figure 8.126  Hairpin heat exchanger. T1

t2

t1 T2

Figure 8.126A  Hairpin heat exchanger in series.

756  Chemical Process Engineering

Figure 8.127  Photograph of a double pipe heat exchanger for liquefied petroleum gas product rundown in a LPG unit.

hairpins for most industrial applications. The unit is not compact, and thus involves a high labor cost. Figure 8.127 shows photograph of a double pipe heat exchanger for liquefied petroleum gas product rundown in a LPG unit. To properly rate and design this type of unit, the process data should be submitted to the manufacturer, because adequate published correlation literature is not available. Figures 8.5A, B, C, and D illustrate the usual construction of finned tube heat exchangers with the fins running parallel to the length of the tube. These are usually, but not always, installed with a tube or pipe outer shell. Typical fins are shown in Figure 8.128. The tube may be fabricated with fins attached by resistance welding rather than imbedding in the tube as shown in Figure 8.128B. The ID of the internal finned pipe usually ranges from ¾ -1½ in., and the outside surrounding pipe shell can be 2 ½-in., 3 in., and 3 ½ in. nominal standard pipe size. The number of fins ranges from 18 for the ¾-in. pipe, 24 or 32 for the 1 ½ -in. pipe, and 16 or 32 for the 1 ½-in. pipe with ½-in. fin height, per manufacturer Griscom-Russell/Ecolaire Corp. The fins of Figure 8.128B are imbedded longitudinally in groves “plowed” into the tube’s outer surface. The displaced metal is squeezed back against the imbedded fin base to form a tight metal-metal bond. This bond is not affected by changes in temperature. Except for fluid conditions that could produce galvanic corrosion, the fins can be fabricated from any selected material, not necessarily the same as the tube. Some usable fin and/or tube materials are steel, aluminum, aluminum bronze, stainless steel, admiralty, copper, copper-nickel, monel, and chrome moly alloy. This longitudinal fin style unit can be used in cross-exchange, kettle-type reboilers, chillers, and condensers. The rating/design of longitudinal finned tubes is presented by Brown Fintube Co. in an unnumbered bulletin, Reference [98]. The double pipe finned tube, Figure 8.5A, is often applicable for gas, viscous liquids, or small volumes, and the economics favor high operating pressure due to the small diameter shell [98]. They operate well in dirty or somewhat fouling conditions due to the ease of cleaning. Units can be fabricated with more than one finned tube in a larger

Uninterrupted and interrupted G-Fin tubes

Figure 8.128A  Typical longitudinal finned tubes. Uninterrupted and Interrupted G – Fin Tubes. (Used by permission: Griscom-Russell, Ecolaire Corp.).

Heat Transfer  757

(b)

(a)

(c)

(d)

(e)

(f) Liquid flow

Gas

Air flow

(h)

(g)

Gas flow

(i)

Figure 8.128B  Examples of extended surfaces on one or both sides. (a) Radial fins. (b) Serrated radial fins. (c) Studded surface. (d) Joint between tubesheet and low fin tube with three times bare surface. (e) External axial fins. (f) internal axial fins. (g) Finned surface with internal spiral to promote turbulence. (h) Plate fins on both sides. (i) Tubes and plate fins. (Source: S. M. Walas, Chemical Process Equipment: Selection and Design, Butterworths Series in Chemical Engineering, 1988).

shell. The fins are more effective or beneficial when the fin-side film coefficient is lower than the inside tube coefficient; therefore, the poorest heat transfer fluid conditions are best used on the finned side of the tube.

Finned Side Heat Transfer For a double pipe exchanger (one finned tube in each of two shells), see Figure 8.5A, the heat flow resistances are [98]. a. b. c. d.

Film resistances on the outside of the tube, ho. Metal tube wall resistance, Rm Film resistance on the inside of tube, hi. Note that fouling resistance on the tube finned side and the inside tube must be added.

l/Uo = 1/ho + 1/hi + Rm

(8.214)

where Uo, ho, hi = Btu/(h) (ft2) (°F)

Rm = (h) (ft2) (°F)/BTU e. See Table 8.45 for suggested overall heat transfer coefficients (U) and Table 8.46 for mechanical data

758  Chemical Process Engineering 1000 LAMINAR FLOW RE < 2100 ANY LIQUID

hoK–.667 C–.333

500

100

50

10 1000

5000

10,000 50,000 100,000 G – MASS VELOCITY (LBS PER SQ FT, HR)

106

500,000

500

0.

000 TRANSITION FLOW 2100 < RE < 18,500

0. 2 0. 3 0. 4 05

1

Figure 8.129A  For determination of ho, shell – side (finned side) film coefficient hoK-0.667C-0.333 for longitudinal fins, flow laminar, ho must be corrected for fin efficiency using Figure 8.151 and mechanical data as Table 8.42. (Used by permission: Bul., “How to Design Double – Pipe Finned Tube Heat Exchangers,” © Brown Fintube Company, A Koch® Engineering Company, Houston, Texas).

ISE

IPO

ITY

OS ISC

IN

T EN

C

1.0 2.0 3.0 4.0 5.0 0 10. 0 20. 0 30. 0 40.

V

hoK–.667 C–.333

.0 100

100

50

10 1000

5000

10,000 50,000 100,000 G — MASS VELOCITY (LBS PER SQ FT. HR)

500,000

10

Figure 8.129B  Shell-side film coefficient for longitudinal fins, transition flow. See Figure 8.150A for applicable details. (Used by permission: Brown Fintube Company, A Koch® Engineering Company, Houston, Texas).

Heat Transfer  759 01

00

10,000

5000

02 03 04 05 01 0 00 00 00 00

2 3 4 5 00 00 00 00

01

02 03 04 05

SE

OI

P TI

IT OS C IS

Y

IN

10

20 30 40 50 .0

10

N CE

hoK–.667 C–.333

V

1000

500 FINSIDE FILM COEFFICIENT TURBULENT FLOW RE > 18,500 ANY LIQUID

100 10,000

50,000

100,000 500,000 1,000,000 G – MASS VELOCITY (LB PER SQ FT, HR)

5×106

10×106

Figure 8.129C  Shell-side film coefficient, ho for longitudinal fins, turbulent flow. (Used by permission: Brown Fintube Company, A Koch® Engineering Company, Houston, Texas).

Figure 8.46 gives the usual Sieder-Tate chart and equation for tube-side, bare tube heat transfer. For the finned shellside heat transfer, see Figures 8.129A, B, C [98] or the recommendation of Kern and Kraus [76], Figure 8.130. The needed equivalent diameter, De, is determined [99] from the following:



De =

4NFA π(Ds + Dt ) + 2N(l)

(8.215)

where NFA = net free, in.2 from typical manufacturer’s data as Table 8.46. The denominator is the wetted perimeter. Ds = shell ID in. Dt = tube OD, in. N = number of fins per tube l = fin height, in. After determining the ho from the preceding figures, the film coefficient must be corrected for fin efficiency using Figure 8.130. where E = 100 (Tanh X)/X X = L(HF/6KT)0.50 L = fin height, in. HF = fin film coefficient K = conductivity of fin material, Btu/(h) (ft2) (°F/ft) E = % fin efficiency T = fin thickness, in.

760  Chemical Process Engineering Table 8.45  Estimating overall heat transfer rates, Uo, for longitudinal finned heat exchangers. With water for cooling or steam for heating, these are estimated values for preliminary study only: Process

Estimated overall rates “Uo”

Heating viscous materials Double pipe – cut & twist fins

12

Multitube bare tubes

15

Medium HC viscosity 3-15 cP avg. Heating – double pipe w/fins

15

Multitube bare tube

25

Cooling – double pipe w/fins

12

Multitube bare tube

20

Light HC viscosity < 1 cP Double pipe w/fins

25

Multitube w/fins

40

Multitube bare tube

75

Condensing & vaporizing – bare tube

150

Very light HC – bare tubes

150

Gases 0 psig w/½ psi DP 100 psig w/1 psi DP

}

25

bare tube fin tube

15

Water to water – bare tubes

200

Glycol to glycol Double pipe w/fins

10

Multitube bare tube w/turbulators

30

Many factors affect heat transfer rates for example velocity, tube wall temperature and pressure drop. These rates listed do not represent the limit, but are suggested values for study and estimating. Used by permission: Bul. “Application and Design Estimating of Double Pipe and Hairpin Exchangers.” ©Brown Fintube Co., A Koch® Engineering Co., Huston, Texas.

Conductivity values* Material

K

Monel

15.0

18-8 st.stl

9.5**

C.steel

25.0

Low chrom stl

17.0

1

1

X51

X53

1.900 x .145

36

.145

36 24

1.900 x

24

No. fins

4 in.

3 in.

Shell size sch. 40 IPS

1

½

Fin height in.

8.60

9.03

3.89

4.11

Net free area in.2

.379

.542

.301

.415

De equiv. dia., in.

.923

.889

.858

.801

Af, Ao

15.42

10.67

8.3

5.93

Ao, Ai

66

45

35

25

5 ft

131

91

71

50

10 ft

197

136

106

76

15 ft

262

182

141

101

20 ft

328

227

177

126

25 ft

Nominal surface, Ft2 Ao nominal length of section

Notes: 1. Fin thickness equals 0.035 in. (narrow web). 2. At/Ao ratio of fin surface to teal external heated surface. 3. Ao/Ai ratio of total external heated surface to inside tube surface. Used by permission: “How to Design Double-Pipe Finned Tube Heat Exchangers.” ©Brown Fintube Co., A Koch® Engineering Co., Houston Texas.

No. tubes

BFT section type

Tube O.D. & wall thick (in.)

Table 8.46  Brown fintube’s typical mechanical design data for fintube sections as needed for design calculations.

Heat Transfer  761

762  Chemical Process Engineering 1

HF E = 100 (TANH X) / X X = L (HF/6 KT)0.50 L

2

1/8 99

3 4

3/16

5 6 7 8 9 10

1/4 98

5/16

97 20 30

3/8

95

7/16

90

1/2

80

40 50 60 70 80 90 100

70 60 50 40

5/8 3/4 7/8 1.00

30 (II)

20

E

L = FIN HEIGHT – INCHES HF = FIN FILM COEFFICIENT K = CONDUCTIVITY OF FIN MATERIAL BTU/HR. FT.2 °F/FT. E = % FIN EFFICIENCY T = FIN THICKNESS, INCHES CONDUCTIVITY VALUES* MAT’L K MONEL 15.0 18–8 ST’LS ST’L 9.5** LOW CHROME STEELS 17.0 CARBON ST’L 25.0 NICKEL 35.0 ADM & BRASS 65.2 AL. 100 CU. 200 *AVERAGE K VALUES FOR TEMPERATURES 100°–600°F. FOR TEMP’S BEYOND THIS RANGE, SEE LITERATURE.

KT 10 9 8 7 6 5 4 3

2

**USE E CHART = 0.70 FOR DESIGN EFFICIENCY FOR THIS MAT’L. INSTRUCTIONS: STEP POINTS 1 I–II 2 A–III

INTERSECTION A B

200 10 1.50

300 400 500 (III)

1.0 0.9 0.8 0.7

(A)

(B)

0.6

5

0.5

3

0.4

2.00 2.50 (I)

1000

0.3

3.00 REFERENCE LINE

Figure 8.130  Finned transfer efficiency is never as great per unit area as the bare pipe; therefore, fin efficiency must be calculated to arrive at correct ho, shell-side heat transfer coefficient. (Used by permission: Technical paper. © Brown Fintube Co., A Koch® Engineering Company, Houston, Texas).

Nickel

35.0

Adm.% brass

65.0

Al

100

Cu

200

*Average K values for temperatures 100-600°F. For temperatures beyond this range, see literature. **Use E chart = 0.70 for design efficiency for this material.

Heat Transfer  763 The total surface area, Ao, in the annulus is the sum of the extended surface area and the bare pipe surfaces not covered by fins. The fin efficiency, w, ef or E, from Figure 8.130 is corrected for the percent surface that is finned. The corrected value, w is the effective surface efficiency.



w

= (E / 100)(Af / Ao) + (1 – Af / Ao)



(8.216)

where Af/Ao = fraction finned area (l – Af/Ao) = fraction bare or unfinned tube area The net effective surface true film heat transfer rate is obtained by correcting the coefficient for the bare surface; thus [98], fouling is excluded:

h bare = ( h oK −0.667 c −p0.333 )( K −0.667 c 0.333 ) p



(8.217)

using Figure 8.129A, B, or C. with ro = shell-side fouling resistance



hof =

hf =

w

1 (1/ h bare ) + ro

,Btu / (h)(ft 2 )(°F)

(8.218)

(hf ), outside film coefficient with fouling, Btu/(h) (ft2) (°F)

Tube Wall Resistance The pipe wall resistance to heat transfer is [98]:



 O.D.tube    O.D.tube  ln Rm =   2K m    I.D.tube 

(8.219)

where Km = thermal conductivity of tube metal, Btu/(h) (ft2) (°F/ft) Rm = wall resistance, (h) (ft2) (°F)/Btu

Tube-Side Heat Transfer and Pressure Drop Refer to the earlier section in this chapter, because tube-side pressure drop and heat transfer are subject to the same conditions as other tubular exchangers.

Fouling Factor (See the earlier discussion in this chapter for more information on this topic.) Fouling factors require a lot of data, judgment, and experience. Ruining a design is easy to do by allowing for too large a fouling factor and actually creating a unit so large that the needed design velocities for heat transfer film coefficients cannot be attained.

764  Chemical Process Engineering The double pipe longitudinal finned exchanger is designed by adding the fouling factor to each respective film coefficient before calculating the overall Uo [98].

Finned Side Pressure Drop Brown [98] recommends:



∆P =

(0.000432)(fo )(G′ )2 L (De )(Z / Z w )0.14 (ρ)

(8.220)

De G (Z)(2.42)

(8.221)

Use Figure 8.131 to determine fo.

where De G G′ Z ρ L D

Re =

= equivalent annulus diameter, ft; (see earlier calculation) = mass velocity flow rate, lb/(h) (ft2) = 3,600 (G′) = mass velocity flow rate, lb/(s) (ft2) = average viscosity, centipoise = fluid density, lb/ft3 = equivalent length of travel, including bend factor, ft = tube I.D., ft.

Figure 8.132 shows the heat transfer profiles for annuli and longitudinal fins.

10 1

50

100

500

1000

5000

10,000

50,000 100,000

100,000

1,000,000

500,000 10

0.5

0.2

FRICTION FACTOR (fo)

0.1 0.05

FINTUBE

0.02 0.01 BARE TUBE

0.005

0.002 0.001 100

1,000

10,000 Re' =

De G (Z)(2.42)

Figure 8.131  Shell – side friction factor, fo for pressure drop calculation is determined from plot vs. Reynolds number, z = viscosity at average flowing temperature, centipoise. (Used by permission: Brown Fintube Company, A. Koch® Engineering Company, Houston, Texas).

Heat Transfer  765 100 70 50

20 10 7

h De k

5 3

jH =

1 cµ – 3 k

µ µw

–0.14

30

2 1

24

0.7

fins ns

36 fi

0.5 10

50

100

500 1,000 Re = De G/µ

5,000

10,000

40,000

Figure 8.132  Heat transfer curve for annuli with longitudinal fins. (Adapted from DeLorenzo, B., and Anderson, E. D., Trans. ASME, V. 67, No. 697, © 1945. The American Society of Mechanical Engineers.) (Used by permission: Kern, D. Q., and Krauss, A. D., Extended Surface Heat Transfer, p. 464, ©, 1972, McGraw-Hill, Inc., All rights reserved).

After designing an approximate unit area requirement, it is important to review the final design performance details with a qualified exchanger manufacturer. See Table 8.46.

8.17.4 Design Equations for the Rating of a Double Pipe Heat Exchanger The equations required for the rating of a double pipe heat exchanger are as follows:

Process Conditions Required

Hot fluid: T1, T2, W, Cph, µa, ka, Δpa, Rd, sa or ρa



Cold fluid: t1, t2, w, Cpc, µt, kt, Δpt, Rd, st or ρt

The diameter of the pipe must be given or assumed. The fluids’ velocities must be in the range of 3-10 ft/s (0.9 -3.05 m/s). First, determine which fluid should be placed in the annulus and which in the inner pipe. This is established from the relative sizes of the flow areas for both streams. For the standard arrangements of double pipes, the flow areas are shown in Table 8.47. The following assumes that the cold fluid is in the inner pipe. 1. The heat duty, Q, Btu/h is:



Q = WCph (T1 – T2) = w Cpc (t2 – t1) 2. The log mean temperature difference, ΔTLMTD is:

(8.222)

766  Chemical Process Engineering Table 8.47  Flow areas and equivalent diameters in double pipe exchangers [70]. Flow area, in2

Annulus, in.

Exchanger, iron pipe size (IPS)

Annulus

Pipe

de

d e′

2

1.19

1.50

0.915

0.40

2.63

1.50

2.02

0.81

1¼

2½

1¼

3

2

2.93

3.35

1.57

0.69

4

3

3.14

7.38

1.14

0.53

∆TLMTD =

(T1 − t 2 ) − (T2 − t1 ) T −t ln 1 2 T2 − t1

{ }

Inner Pipe 3. The flow area, ap is:



ap =

π D2 2 , ft 4

(8.223)

Gp =

w lb , a p h ft 2

(8.224)

Re t =

DG p µt

(8.225)

Prt =

C pc µ t kt

(8.226)

4. The mass velocity, Gp:

5. The Reynolds number, Ret:

6. The Prandtl number, Prt:



7. The heat transfer film coefficient, hi, Btu/h ft2 oF:



hi D  DG p  = C  µ t  kt

0.8

 C pc µ t   k  t

0.33

 µt   µ  w

0.14



(8.227)

Heat Transfer  767 hi can be expressed by:



hi = C

 k t  0.8 0.33 Re Prt  D t

(8.228)

where µ t µ w = 1.0 C = 0.021 for gases C = 0.023 for non-viscous fluids. C = 0.027 for viscous fluids. Converting hi to hio, the heat transfer film coefficient referred to the pipe outside diameter, Btu/h ft2 oF is:

 inside dia. of inner pipe  h io = h i   outside dia. of inner pipe 

h io = h i

ID OD



(8.229)

Annulus 8. The flow area of the annulus is:



aa =

π ( Do2 − Di2 ) 2 , ft 4

De =

4 × flow area wetted perimeter

(8.230)

9. The equivalent diameter, De:

=

Do2 − Di2 , ft. Di



(8.231)

10. The mass velocity, Ga:

Ga =



W lb , a a h ft 2

(8.232)

De G a µa

(8.233)

11. The Reynolds number, Rea:



Rea =

768  Chemical Process Engineering 12. The Prandtl number, Pra:

Pra =



C ph µ a ka

(8.234)

13. The heat transfer film coefficient, ho is:



If Rea < 2100



h o = 1.86



k a 0.33 0.33  De  Rea Pra  L  Do

0.33



(8.235)

If Rea > 2100



ho = C

k a 0.8 0.33 Rea Pra Do

(8.236)

14. The overall heat transfer coefficient, Uo. Btu/h ft2 oF:

1 1 1 = + + Rd + R w Uo h io h o



(8.237)

15. The heat transfer area, A ft2:

A=



Q Uo ∆TLMTD

(8.238)

Vapor Service 16. The heat transfer film coefficient, hi, Btu/h ft2 oF:



0.0144C ph G0.8 hi = D0.2 e

(8.239)

1 1 = + Fol (h i is corrected for fouling) h if h i

(8.240)

and



Shell-Side Bare Tube hi is calculated using Equations 8.227, 8.228 and hif is calculated using Equation 8.240

Heat Transfer  769 17. The equivalent diameter, De is:

De = Ds,i – Dt,o

(8.241)

18. The overall heat transfer coefficient, Uo, Btu/h ft2 oF:

1  w = + Uo  k t  tube wall

1 1 + (h if )shell  Ai  hi    A o  tube

(8.242)

where the tube wall thickness, w is:



w = Dt,o – Dt,i, ft.

(8.243)

A i D t,i = A o D t,o

(8.244)

and



Shell Side (Finned Tube) 19. The equivalent diameter, De, ft, is:



De =

4 NFA π(Ds,i + Di,o ) − Nθ + 2HN

(8.245)

20. The net free cross-sectional area, NFA, shell-side, ft2:



NFA = CSA – NHθ

(8.246)

21. The cross-sectional area without fins, CSA, ft2:

CSA =



π 2 ( Ds,i − Di,o2 ) 4

(8.247)

22. Finned surface area, ft2:

Af = 2HN

(8.248)

23. Outside heat transfer area of tube, ft2/ft (for finned tubes includes fin area):

Ao = Dt,o + Af

(8.249)

24. Parameter for fin efficiency, X: 0.5



 h  X = H  if   6K i θ 

(8.250)

770  Chemical Process Engineering 25. The fin efficiency, e:

e=



tanh X 1  exp(X) − exp(− X)  =  X X  exp(X) + exp(− X) 

(8.251)

26. The effective surface efficiency for fins, eff :

A   A  e ff = e  f  +  1 − f   Ao   Ao 



(8.252)

27. The corrected film heat transfer coefficient, hifd, Btu/h ft2 oF:

hifd = (hif )(eff )

(8.253)

28. The overall heat transfer coefficient, Uo, Btu/h ft2 oF:

1  ∆w  = + Uo  k t  tube wall

1 1 + (h ifd )shell  Ai  hi    Ao  tube

(8.254)

where

π D t,i Ai = A o πDt,o + 2HN



(8.255)

Tube-Side Pressure Drop, pt 29. The pressure drop in the tube side is, the frictional head, h, ft:

h=



4 f G2 L , ft 2g ρ2 D

(8.256)

where



f=

16 for Re < 2,100 Re

(8.257)

Using Wilson et al. [37] correlation for commercial pipe:

The pressure drop, pt is:

f = 0.0035 +

0.264 for Re > 2,100 Re0.42

(8.258)

Heat Transfer  771



∆p t =

 ∆h ρ  , psi  144 

(8.259)

∆p t , ft. SpGr

(8.260)

Or in terms of static height h, ft.:

∆h = 2.31

where Sp Gr = specific gravity of liquid.

Annulus For an annulus, the equivalent diameter, D′e is:

4 π ( Do2 − Di2 ) 4 π(Do + Di ) = Do − Di

D′e =

(8.261)

The Reynolds number, Rea is:



D′e Ga µa

(8.262)

4 f Ga2 L , ft. 2g ρ2 D′e

(8.263)

Rea =

Head loss, ha, ft:

∆h a =



The pressure drop due to the reversal of flow in the annulus for each hairpin is:



v2 ∆h r = , ft/hair pin 2g

(8.264)

 (∆h a + ∆h r )ρ  ∆pa =   , psi 144 

(8.265)

The total annulus pressure drop pa is:



8.17.5 Calculation of the Pressure Drop The friction factors for both streams can be determined and the pressure drop for each fluid will be:

772  Chemical Process Engineering −a

L ρv 2  µ  ∆p t = 4 f D 2  µ w 



(8.266)

or



∆p t = 4 f

L ρv 2  1   µ  D 2g c  144   µ w 

−a

 lbm ft ft 2  1 . 2  3 . 2.  ft s lbm ft in  .   lbf s 2

(8.267)

where a = 0.14 for Re > 2,100 and a = 0.25 for Re < 2100. In Equation 8.267, D must be replaced by Di or Deq as required. For heat exchangers with more than one tube, the annulus fluid suffers an additional pressure drop when passing from one tube to the next through the connecting tees. This pressure drop can be determined by:



n t ρv 2 2 2

(8.268)

n t ρv 2  1  , psi 2 2g c  144 

(8.269)

∆pr =

or

∆pr =



Kern’s equation for tube-side return pressure drop is shown in Figure 8.86 and is expressed by [39].

∆pr =

ft 2  1 4n t v 2  62.5   ft 2 lbm .  2. 3.  s 2g c  144   s ft lbm ft 144in 2  .   lbf s 2

(8.270)

where v = velocity, ft/s gc = conversion factor (32.174 lbm/lbf. ft/s2) s = specific gravity nt = number of tube passes The total pressure drop is:



p = pt + pr

(8.271)

Effect of Pressure Drop (Δp) on the Original Design When improving the heat transfer coefficients, it is necessary to increase the fluid velocities as it is better to use a small-diameter, high-length tube rather than a shorter one with a higher diameter, both having the same heat transfer area. However, the increase in velocity invariably increases the p. If the heat exchanger must be installed in an existing process, the designer must adhere to the maximum allowable p. If the heat exchanger is for a new process unit, the designer can define the heat exchanger pressure drop, and the required pumps can be specified to overcome

Heat Transfer  773 this p. In these cases, the problem requires balancing a higher heat exchanger cost against a higher pumping power, so that the most cost-effective solution is chosen. Where the calculated p is excessive, it will be necessary to increase the flow area either by increasing the tube diameters or installing more branches in parallel. If the calculated p is smaller than the allowable, then a reduction in the flow area can be used. However, in either case, the design procedure would require revisiting. Since it is not possible to modify the flow area of the internal tube without affecting the annulus, the design of this equipment type is difficult to optimize. Therefore, it is necessary to accept a poor utilization of the allowable p in one stream in order to satisfy the requirement in the other. This exchanger type is limited to low-area and low-cost applications. Once the thermal design of the double pipe exchanger is completed, the mechanical design must be performed by verifying tubes thickness, selecting materials, rating the nozzles, choosing gaskets, and reviewing the mechanical drawings. This work falls within the mechanical engineering discipline.

Nomenclature A = cross-sectional area, ft2. = inside heat transfer area-tube, ft2/ft. Ai = outside heat transfer area-tube, ft2/ft (for finned tubes includes fin area). Ao = finned transfer area, ft2. Ai = flow area, ft2. ap = specific heat capacity of hot fluid, Btu/lb oF. Cp = specific heat capacity of cold fluid, Btu/lb oF. cp CSA = cross-sectional area, shell-side without fins, ft2. D = inside diameter, ft. Di, Do = for annuli, Di is the outside diameter of inner pipe, Do is the inside diameter of the outer pipe, inch. Dt,i = tube inside diameter, inch. Dt,o = tube outside diameter, inch. Ds,i = shell inside diameter, inch. = equivalent diameter for heat transfer, ft. De = equivalent diameter for pressure drop, ft. D′e e = fin efficiency. e = effective surface efficiency for fins. FOL = fouling factor, ft2 h oF/Btu f = friction factor, dimensionless. Δh = pressure drop, ft. Δha = annulus pressure drop, ft. Δhr = pressure drop due to reversal of flow in the annulus, ft. G = mass velocity, lb/h-ft2 = mass velocity in annulus, lb/h-ft2 Ga Gp = mass velocity of inner pipe, lb/h-ft2. g = acceleration due to gravity, 32.2 ft/s2 (4.18 108 ft/h2). ft   gc = Conversion factor  32.174 lbm lbf . 2   s  H = fin height, inch. hi, ho = heat transfer film coefficient for inside fluid and outside fluid respectively, Btu/h ft2 oF. = value of hi, when referred to the pipe outside diameter, Btu/h ft2 oF. hio ID = inside diameter, inch or ft. = heat transfer factor, dimensionless. jH k = fluid thermal conductivity, Btu/h ft oF.

774  Chemical Process Engineering Kt = thermal conductivity of tube material, Btu/h ft oF. L = pipe length, ft. NFA = net free cross-sectional area, shell side, ft2. N = number of fins. OD = outside diameter, inch or ft. Pr = Prandtl number, dimensionless. Δp = pressure drop, psi. Q = exchanger duty, Btu/h. = fouling resistance, ft2 h oF/Btu. Rd Re = Reynolds number, dimensionless. = wall resistance, ft. Rw s = specific gravity. T1, T2 = temperature of hot fluid, inlet and outlet respectively, oF. t1, t2 = temperature of cold fluid, inlet and outlet respectively, oF. ΔTLMTD = log mean temperature difference, oF. U = overall heat transfer coefficient, Btu/h ft2 oF. v = fluid velocity, ft/s. W = mass flow rate of hot fluid, lb/h. w = mass flow rate of cold fluid, lb/h. X = parameter used in fin efficiency. ρ = fluid density, lb/ft3 µ, µw = fluid viscosity (flowing and at wall), cP. θ = fin thickness (normally 0.035 inch). π = 3.1415927 a = annulus p = pipe.

Example 8.9 Petroleum distillate oil of 18000 lb/h, 28oAPI is to be cooled from 250 oF to 150 oF in a double pipe finned tube heat exchanger consisting of 3 in. Internal Pipe Size (IPS) shells with 1 ½ in. IPS inner pipes on which are mounted 24 fins ½ in. high by 0.035 in. (20 BWG) wide. Water from 80 oF to 120 oF will be the cooling medium. Allowable pressure drops of 10 psi are allowable on both streams, and the following fouling factors of 0.002 for the distillate oil and 0.002 for the water are required. Calculate the overall heat transfer coefficient and the exchanger fin efficiency. The details and physical properties are shown below: Tube side inner pipe

Shell side annulus

Type of Fluid

Cooling-tower water

Petroleum distillate

Flow rate, lb/h

23,310

18,000

Inlet temperature, oF

80

250

Outlet temperature, oF

120

150

Thermal conductivity, Btu/h.ft oF

0.366

0.074

Viscosity, cP

0.72

2.45

Specific heat capacity, Btu/lb oF

1

0.518

Density, lb/ft3

62.3

45

Number of passes

5

1

Heat Transfer  775

Fouling factor, h ft F/Btu 2o

Tube side inner pipe

Shell side annulus

0.002

0.002

Exchanger size: Shell side: 3 in (3.068 in. I.D., 3.5 in. O.D.) Tube side: 1 ½ in. (1.61 in. I.D., 1.9 in. O.D.) Tube length: 12 ft. Fins: 24, 0.5 in. high × 0.035 in. wide. Thermal conductivity of the tube material: K = 25 Btu/h ft oF

Solution Exchanger Hot fluid (Oil)

Cold fluid (Water)

Shell side

Tube side

ID = 3.068 in., OD = 3.5 in.

ID = 1.61 in., OD = 1.91 in.

Passes = 1

Passes = 5

Physical Property data Physical property

Oil

Water

Viscosity, cP

2.45

0.72

Density, lb/ft3

45.0

62.3

Specific heat, Btu/lb oF

0.518

1.0

Thermal conductivity, Btu/h ft oF

0.074

0.366

Conversion: µ ( lb ft.h ) = cP × 2.42

Heat Balance Heat lost by oil = heat gained by water That is: 1.



Q = W Cp (T1 – T2) = w cp (t2 – t1) Q = (180,000) (0.518) (250 – 150) = w (1) (120 – 80) 932400 = 40w W = 23310 lb/h.

776  Chemical Process Engineering 2. Assuming counter-current flow, the Log Mean Temperature Difference TLMTD is:

∆TLMTD =

(T1 − t 2 ) − (T1 − t1 ) T −t  ln  1 2   T1 − t1 

(250 − 120) − (150 − 80)  250 − 120  ln  150 − 80  = 96.9°F

=



3. The flow area, ap is:



ID pipe in ft. = 1.610/12 = 0.13417 ft. π(0.13417)2 4 = 0.0141 ft 2

ap = 4. The mass fluid velocity, Gp is:



Gp =

w 23310 lb = = 1648514.85 a p 0.01414 h.ft 2

5. The fluid’s Reynolds number in the tube is Ret:

Re t =

DG p µ

(0.13417 × 1648514.85) (0.72 × 2.42) = 126941

= 6. The Prandtl number Prt

cµ k 2.42 × 1.0 × 0.72 = = 4.7607 0.366

Prt = 7. Heat transfer film coefficient, hi:

Heat Transfer  777

hiD 0.33  µ  = C Re0.8 t Prt  µ  k w



0.14

 µ  where for non-viscous fluid, C = 0.023 and  = 1.0  µ w 



h i = 0.023

 0.366  (126941)0.8 (4.7607)0.33  0.13417 

= 1270.3 Btu/h ft 2 °F



The heat transfer film coefficient corrected for fouling:

1 1 = + FOL h if h i 1 = + 0.002 = 358.78 Btu/h ft 2 °F 1270.3

8. Shell-side (Finned Tube)

The equivalent diameter, De is:



De =

4 NFA π(Ds,i + Di,o ) − Nθ + 2HN

Ds, i = 3.068/12 = 0.2556 ft Dt,o = 1.9/12 = 0.1583 ft

Nθ = 24

0.035/12 = 0.07 ft.

9. Finned transfer area, Af:

Af = 2HN

=2 NHθ = 24

0.5

24

0.5/12 = 2 (ft2/ft)

0.035/144 = 2.917

10-3 ft2

10. Cross-sectional area, shell side without fins, CSA, ft2:

π 2 ( Ds,i − D2t,o ) 4 π = (0.25562 − 0.15832 ) 4 = 0.03163 ft 2

CSA =



778  Chemical Process Engineering

Net free cross-sectional area, NFA, ft2:



NFA = CSA - NHθ



= 0.03163 – 0.002917



= 0.0287 ft2

Outside heat transfer area-tube including fin area, Ao, ft2/ft:

Ao = πDt,o + 2HN

= π(0.1583) + 2



= 2.497 (ft2/ft) 11. Equivalent diameter, De is:

4 × 0.0287 π(0.2556 + 0.1583) − 0.07 + 2 = 0.0355 ft.

De =

12. Mass fluid velocity in the annulus, Ga:

W 18000 = NFA 0.0287 = 627178 lb/h ft 2

Ga = 13. Fluid velocity, vF is:

vF =

Ga (3600ρ)

627178 (3600 × 45) = 3.87 ft/s. =





14. The Reynolds number, Rea is:

G a De µ 627178 × 0.0355 = (2.45 × 2.42) = 3755.0

Rea =



Heat Transfer  779 15. The Prandtl number, Pra:

cµ k 0.518 × 2.45 × 2.42 = 0.074 = 41.5

Pra =



16. The film heat transfer film coefficient on the shell side:

h if De 0.33  µ  = CRe0.8 t Prt  µ  ka w



0.14

µ  where for non-viscous fluid, C = 0.023 and  = 1.0  µ w 



h if = 0.023

 0.074  (3755)0.8 (41.5)0.33  0.0355 

= 118.68 Btu/h ft 2 °F



The heat transfer film coefficient corrected for fouling:

1 1 = + FOL h if h i 1 = + 0.002 = 95.91 Btu/h ft 2 °F 118.68



17. Parameter X for fin efficiency, e is:

 h shell  X = H  if  6K t θ 

0.5

95.91  0.5    =  12   0.035   6 × 25 ×  12  = 0.6169



0.5

18. Fin efficiency, e:

e=

1  e0.6169 − e −0.6169  0.6169  e0.6169 + e −0.6169  e = 0.8898(89%) =



tanh(X) 1  e X − e − X  =  X −X  X X e + e 

780  Chemical Process Engineering 19. Effective surface efficiency for fins, e :

A   A  e′ = e  f  +  1 − f   Ao   Ao  = 0.8898

2   2  1 + −  2.497   2.497 

= 0.9117 (91.2%)



Corrected film heat transfer rate, hifd:

hifd = (hif )(e )

= 95.91

0.9117



= 87.45 But/h ft2 oF 20. Tube wall thickness, ∆W:



∆W = Dt,o – Dt,i



= 1.90 – 1.61 = 0.29 in/12 = 0.02417 ft. π(D t,i ) Ai = A o π(D t,o ) + 2HN π × 0.13417 π(0.1583) + 2.0 = 0.1688 =



21. Overall heat transfer coefficient, Uo:

1  ∆W  1 1 = + +  A Uo  K t  tube wall  (h ifd )shell i   h if × A  o tube

=

0.02417 1 1 + + 25 (358.78 × 0.1688) 87.45

= 34.59 Btu/h ft 2 °F



Heat Transfer  781

Pressure Drop Calculations Tube Side Fluid velocity, v from the mass flow rate G is:

G = ρv A G ρA

v=



where A is the area of tube of inside diameter = 1.61 in. (0.134 ft) is



A=

πDi2 π(0.134)2 = = 0.01413ft 2 4 4



G = 23310 lb/h = 23310/3600 = 6.475 lb/s



ρ = 62.3lb ft 3



Fluid velocity, v =



G 6.475 = ρ A (62.3 × 0.01413)

= 7.36 ft/s.

The friction factor, f is:

0.264 Re0.42 0.264 = 0.0035 + (126941)0.42 = 0.005397

f = 0.0035 +



Tube-Side Δp The tube-side p is:



a ft 2  1 L ρv 2  1   µ   lbm ft . . . ∆p t = 4 f   D 2g c  144   µ w   ft 3 s 2 lbm ft in 2  .   lbf s 2

where ( µ µ w ) =1.0, L = 12 ft, D = 0.134ft,

(8.267)

782  Chemical Process Engineering

 lb ft  g c = 32.174  m ⋅ 2  , v = 7.36 ft/s., ρ = 62.3 lb/ft 3  lbf s  L ρv 2  1  ∆p t = 4 f D 2g c  144  = 4(0.005397)

2  12   62.3 × 7.36   0.134   2 × 32.174 × 144 

= 0.704 lbf /in 2 pr on the return side of the tube with the number of tubes nt = 5 using Kern’s equation (8.270) is:

∆pr = =

4n t v 2  62.5  , psi s 2g c  144  4×5 7.362  62.5  × 1.0 (2 × 32.174)  144 

= 7.30 lbf /in 2



The total pressure drop 8.271 is:



p = pt + pr



= 0.704 + 7.30



= 8.0 lbf/in2

(8.271)

Shell-Side Δp Fluid velocity, vF = 3.87 ft/s



The friction factor for longitudinal fin, f at Re = 3755 is:



f = 0.0495 from Figure 8.131

The shell-side p for the annulus is: Head loss, ha, ft:

∆h a =



4 f Ga2 L , ft. 2g ρ2 D′e

2    lb  ft 2 2    4 × 0.0495 × 627178 × 12   h .ft  =   2 2 2  2 × 32.2 × 45 × 0.0355 × 3600   ft  lb  2  2 .  3  .ft × 3600  s ft

= 15.58 ft



(8.263)

Heat Transfer  783 The pressure drop due to the reversal of flow in the annulus for each hairpin is:

∆h r =

v2 ,ft/hair pin 2g

3.867 2 2 × 32.2 = 0.232 ft. =





(8.264)

The total annulus pressure drop pa is:

 (∆h a + ∆h r )ρ  ∆pa =   , psi 144   (15.58 + 0.232) × 45  =  144  = 4.94 psi.



(8.265)

Or in terms of pressure drop pa, psi:

[(∆h a ) + (∆h r )] × Sp.Gr 2.31 [15.58 + 0.232] × 0.72 = 2.31 = 4.93 psi.

∆pa =

where Sp Gr = specific gravity of liquid.

The Excel spreadsheet program (Example 8.9.xlsx) rates double pipe heat exchanger for fin tubes and the results are shown below. The fin efficiency is 89%, the heat transfer surface is 278 ft2 and the computed overall heat transfer coefficient is 34.61 Btu/h ft2 oF. The pressure drops have not been exceeded, and the double pipe exchanger will be suitable for the service. RESULTS OF THE DOUBLE PIPE HEAT EXCHANGER RATING USING BARE-TUBE/LONGITUDINAL FINNED TUBES

 

 

FORCED CONVECTION WITH NO CHANGE OF PHASE    

Tube Side

Side Side

FLUID NAME

WATER

OIL

FLUID FLOW RATE

23310

18000

lb/h

SPECIFIC HEAT CAPACITY

1

0.518

Btu/lboF

FLUID DENSITY

62.3

45

lb/ft3

FLUID VISCOSITY

0.72

2.45

cP

FLUID THERMAL CONDUCTIVITY

0.366

2.45

Btu/h.ft.oF

784  Chemical Process Engineering FLUID INLET TEMPERATURE

80

250

o

FLUID OUTLET TEMPERATURE

120

150

o

F

INSIDE DIAMETER

1.61

3.068

in.

OUTSIDE DIAMETER

1.9

3.5

in.

FOULING FACTOR

0.002

0.002

TUBE LENGTH

12

NUMBER OF TUBE PASSES

5

F

ft.

NUMBER OF FINS

24

FIN HEIGHT

0.5

in.

FIN THICKNESS

0.035

in.

THERMAL CONDUCTIVITY OF THE TUBE MATERIAL

25

FLUID VELOCITY

7.35

3.87

REYNOLDS NUMBER

126958

3759

PRANDTL NUMBER

4.76

41.503

FRICTION FACTOR

0.0054

0.0495

PRESSURE DROP

7.264

4.92

FIN MODULUS

0.617

FIN EFFICIENCY

89

%

EFFECTIVE SURFACE EFFICIENCY

91.2

%

LOG MEAN TEMP. DIFFERENCE, LMTD

96.92

o

HEAT TRANSFER FILM COEFF. CORRECTED FOR FOULING

87.386

Btu/h.ft2.oF

OVERALL HEAT TRANSFER COEFFICIENT

34.61

Btu/h.ft2.oF

HEAT LOAD ON UNIT

932400

Btu/h

HEAT TRANSFER SURFACE

 

 

 

 

277.96

Btu/h. ft. oF ft/s

psi

F

 

 

 

ft2

8.18 Plate and Frame Heat Exchangers Figures 8.8, A, B, and C illustrate the general arrangements of most manufacturers, although several variations of plate flow pattern designs are available to accomplish specific heat transfer fluids’ temperature exchanges. Also, the gasket sealing varies, and some styles are seal welded (usually laser) to prevent cross-contamination. Note that a Plate Heat Exchanger (PHE) has no interplate gaskets and is totally accessible on both sides, yet easy to clean. The construction materials for the plates include most corrosion-resistant metals, usually 304SS, 316SS, titanium, Incoloy 825®, Hastelloy®, and others, plus non-metallic fused graphite, and fluoroplastic Diabon F®. Typical gaskets between the plates include nitrile rubber, butyl, and EPDM elastromers, Hypalon® and Viton®, based on the various manufacturers’ literature. A heat transfer comparison is made in Figure 8.133, Figures 8.134A – F illustrate the general description and operating principles of PHEs, and detailed descriptions of these figures are provided by Cao [27]. The plate and frame designs are used in convection, condensing, and some evaporation/boiling applications. Table 8.48 shows a variety of gasket materials for PHEs. This type of exchanger usually provides relatively high heat transfer coefficients and does allow good cleaning by mechanically separating the plates, if back-flushing does not provide the needed clean up. An excellent discussion on the performance and capabilities is presented by Carlson [99]. To obtain a proper design for a specific application, it is necessary to contact the several manufacturers to obtain their recommendations, because the surface area of these units is proprietary to the manufacturer.

Heat Transfer  785

Shell & Tube Versus Plate Heat Exchanger

Plate Heat Exchangers Shell and Tube Heat Exchanges

Curves based on 15% excess surface for P.H.E and overall fouling of .0015 for shell and tube.

te la

Et hy

Eth yle ne

le ne G

lyc ol

Gly co l

ll and T ube

l Glyco

r

ge

n ha

xc tE a He

P er

W at er to 50 %

10.0

70 %

12.5

Wa ter to

15.0

Water to Wate r She

hyle ne

17.5

Wate r to 7 0% E t

P Average Pressure Drop

20.0

Wate r to 5 0% E thyle ne

Glyc o

l

22.5

e at W

o rt

at W

7.5 50

150

250

350

450

550

650

750

850

950

1050

1150

1250

U Overall Transfer Rate These curves provide a comparison of heat transfer rates for plate heat exchangers and shell and tube equipment. Tha values given are typical for pressure drops shown and are based upon the thermal characteristics of the fluids.

At a 12.5 psi pressure drop in water to water applications, the surface heat transfer rate achieved in a Graham plate exchanger exceeds that of a shell and tube unit by a factor of 3.4. Similar or higher improvement factors are obtained with other fluids.

Figure 8.133  Convection heat transfer comparison for shell and tube and plate and frame heat exchangers. (Used by permission: Bul, PHE 96-1 6/96, © Graham Manufacturing Company, Inc.).

Planar plate Cold fluid

Hot fluid

Figure 8.134A  Heat transfer through a plate.

Hot fluid

Closure plates Heat exchange plate

Cold fluid

Gaskets

Figure 8.134B  Principle of the plate heat exchanger [287].

786  Chemical Process Engineering Heat exchange plate

Compression bolts

Closure plates

Compression frame

Figure 8.134C  Elemental plate heat exchanger [287].

9

8

7

6

5

4

3

2

1

Cold fluid

Hot fluid

Figure 8.134D  Fluids circulation in a plate heat exchanger [287].

2

4

4

6 1 6

5

2

5 1

7

3

3

1-Fixed frame plate 3-Tightening bolts 5-Lower guiding bar 7-Plates

2-Movable pressure plate 4-Upper carrying bar 6-Support column

Figure 8.134E  Component parts of a plate heat exchanger [287].

7

Heat Transfer  787 Headers

Cold fluid

9

8

7

6

5

4

3

2

1

Hot fluid Channels

Figure 8.134F  Expanded view of the heat exchanger of Figure 8.154C [287].

Table 8.48  Typical gasket materials for plated heat exchangers. Material

Approximate temperature limit, oC

Fluids

Styrene-butane rubber

85

Aqueous systems

Acrylonitrile-butane rubber

140

Aqueous system, fats, Aliphatic hydrocarbons

Ethylene-propylene rubber

150

Wide range of chemicals

Fluorocarbon rubber

175

Oils

Compressed asbestos

250

General resistance to organic chemicals

Table 8.49  Fouling coefficients for plate heat exchangers. Fluid

Coefficient (W/m2 oC)

Factor (m2 oC/W)

Process water

30,000

0.00003

Towns, water (soft)

15,000

0.00007

Towns, water (hard)

6000

0.00017

Cooling water (treated)

8000

0.00012

Sea water

6000

0.00017

Lubricating oil

6000

0.00017

Light organics

10,000

0.0001

Process fluids

5000-20,000

0.0002 – 0.00005

788  Chemical Process Engineering Plate heat exchangers have superior overall heat transfer coefficient (U) that are superior to those of the shell and tube exchangers. For example, in clean water to water service, a shell and tube heat exchanger has a U value of 350 Btu/h ft2 oF much lower than the 1,000 Btu/h ft2 oF of a plate design at the same pressure drop. However, the plate heat exchanger’s much higher U values also mean that fouling factors have a much greater effect on calculations of exchanger surface area. For example, a fouling resistance of 0.001 ft2 h oF/Btu will increase the surface area of a shell and tube unit by about 35%, but will increase that of a PHE by 100%. As discussed earlier, caution should be exercised in specifying excess area for heat exchangers as this could result in fouling beyond what is considered in the design. It is thus essential to both understand the concept of fouling factors for PHE and to know how the factors are categorized by different suppliers. PHEs are compact, cost effective and are able to handle fouling fluids, thus making them an ideal choice for many services. Table 8.49 shows fouling coefficients for PHEs. The design details of plate and frame heat exchanger are provided elsewhere [83].

Selection The advantages and disadvantages of gasketted plate heat exchangers as compared with conventional shell and tube heat exchangers are: Advantages [41] 1. P  lates are attractive when material costs are high. 2. Plate heat exchangers are easier to maintain. 3. Low approach temperatures can be used, as low as 1oC, compared with 5 to 10oC for shell and tube heat exchangers. 4. Plate heat exchangers are more flexible; it is easy to add extra plates. 5. Plate heat exchangers are more suitable for highly viscous materials. 6. The temperature correction factor, Ft, will normally be higher with plate heat exchangers, as the flow is closer to true counter current flow. 7. Fouling tends to be significantly less in plate heat exchangers (see Table 8.49). Disadvantages 1. A  plate is not a good shape to resist pressure, and plate heat exchangers are not suitable for pressure greater than about 30 bar, or for high differential pressures between the two streams transferring heat. 2. The selection of a suitable gasket is critical (see Table 8.48). 3. The maximum operating temperature is limited to about 250oC, due to the performance of the available gasket materials. PHE types are widely used in the food and beverage industries, as they can be readily taken apart for cleaning and inspection. Their use is somehow limited in the chemical industry, as this depends on the relative cost for the particular application compared with a conventional shell and tube heat exchanger.

8.19 Air-Cooled Heat Exchangers Air-cooled heat exchangers (ACHEs) are used extensively in the hydrocarbon industries where water is rather scarce and expensive and a large fluid flow must be cooled. The capital investment for an air-cooled exchanger is often many times that of an equivalent conventional shell and tube heat exchanger. Initial investment costs for ACHEs are very high, but they offer lower operating and maintenance expenses. Because of the high investment, due care is essential in its design. Air-cooled heat exchangers are very seldom, if ever, finally designed by the user company (or engineering design contractor), because the best final designs are prepared by the manufacturers specializing in this unique design and requiring special data. This topic is presented here to aid the engineer in understanding the equipment and

Heat Transfer  789 INDUCED DRAFT

Fan

HY-FIN Cooler Fan PULLS air through fin tube sections FORCED DRAFT

HY-FIN Cooler

Fan

Fan PUSHES air through fin tube sections

Figure 8.135  Two types of air-cooled heat exchangers. (Used by permission: © Hudson Products Corporation).

Typical Forced Draft Air Cooled Exchanged Showing Two Exchanger Sections and One Fan

Figure 8.136  Typical forced draft air-cooled exchanger showing two exchanger sections and one fan. (Used by permission: Yuba Heat Transfer Division of Connell Limited Partnership).

790  Chemical Process Engineering

Figure 8.137  Typical induced draft air-cooled exchanger showing two exchanger sections and two fans. (Used by permission: GriscomRussell/Ecolaire Corporation, Easton, PA).

applications, but not to provide methods for preparing final fabrication designs [100–114]. Standard 661, 3rd ed., American Petroleum Institute, “Air Cooled Heat Exchangers for General Refinery Services” is a good basic reference. Air-cooled exchangers use atmospheric air on the outside of high-finned tubes (except bare tubes are used in a few applications) to cool or condense fluids flowing through the inside of the tubes. This type of exchanger is used to reject heat from a fluid inside the tubes (and associated headers) directly to ambient air [100]. To be effective, the air must flow in forced convection to develop acceptable transfer coefficients. Figures 8.135 – 8.137 illustrate the two types, designated by the type of air movement, induced draft or forced draft. The advantages and disadvantages of forced and induced draft fan operation on the performance of the unit as presented by Hudson Products Corp [100] are used by permission in the following discussions.

8.19.1 Induced Draft Advantages 1. B  etter distribution of air across the bundle. 2. Smaller possibility of hot effluent air recirculating into the intake. The hot air is discharged upward at approximately 2.5 times the intake velocity, or about 1,500 ft. per min. 3. Better process control and stability because the plenum covers 60% of the bundle face area, reducing the effects of sun, rain, and hail. 4. Increase capacity in the fan-off or fan-failure condition, because the natural draft stack effect is much greater. Disadvantages and Limitations 1. P  ossibly higher horsepower requirements if the effluent air is very hot. 2. Effluent air temperatures should be limited to 220°F (104.4oC) to prevent damage to fan blades, bearing, or other mechanical equipment in the hot air stream. When the process inlet temperature exceeds 350°F (176.6oC), forced draft design should be considered because high effluent air temperatures may occur during fan-off or low air flow operations. 3. Fans are less accessible for maintenance, and maintenance may have to be carried out in the hot air generated by natural convection. 4. Plenums must be removed to replace bundles.

Heat Transfer  791

8.19.2 Forced Draft Advantages 1. P  ossibly lower horsepower requirements if the effluent air is very hot. (horsepower varies inversely with the absolute temperature.) 2. Better accessibility of fans and upper bearings for maintenance. 3. Better accessibility of bundles for replacement. 4. Accommodates higher process inlet temperatures. Disadvantages 1. L  ess uniform distribution of air over the bundle. 2. Increased possibility of hot air recirculation, resulting from low discharge velocity from the bundles, high intake velocity to the fan ring, and no stack. 3. Low natural draft capability on fan failure. 4. Complete exposure of the finned tubes to sun, rain, and hail, which results in poor process control and stability. Extruded Serrated Fins are an enhanced-surface extruded fin. The extruded-serrated type is a patented Hudson Hy-Fin that has been tested by HTRI and represents the state of the art in fin construction technology.

Hundson STAC-FLO® Schematic

Hot Air

Hot Air

HY-FIN®

Exhaust Steam

Hy-Fin Tubes Standard Extruded Fins were first put into commercial production by Hundson Products. The aluminum sleeve from which the fins are extruded is first put into position along the entire effective length of the process tube. The sleeve and tube are mechanically bonded during a high-pressure extruding process to form an integral finned tube, ensuring long-term thermal integrity.

Tube Bundle

Cool Air

Divided Rear Header To Atmosphere Condensate Drain Pot 1

2

3

4

Motive Steam

Vacuum System

Steam Turbine

Condensate Storage

Condensate Pumps

Figure 8.138  Air-cooled Stac-Flo® steam condensers illustrating process system. Representative types of tubes are illustrated. (Used by permission: Bul. M-390621 10/90. © Hudson Products Corporation).

792  Chemical Process Engineering FIN TUBE PASS

TUBES ARE EXPANDED INTO TUBE SHEET USING AUTOMATICALLY CONTROLLED EXPANSION.

TUBE SHEET

CAST IRON HEADERS ARE AVAILABLE IN STANDARD SIZES.

PLUG SHEET FLOATING END (FOR EXPANSION) FULL PENETRATION WELDS

FABRICATED STEEL HEADER BRACKET WITH STAINLESS STEEL NAME PLATE

SHOULDER TYPE PLUG WITH SOLID METAL GASKET OPPOSITE EACH TUBE END.

Figure 8.139  Typical tube bundle using fabricated or cast end headers. (Used by permission: Yuba Heat Transfer Division of Connell Limited Partnership).

FINTUBE BRACKET WITH STAINLESS STEEL NAME PLATE

FULL PENETRATION WELDS

FLOATING END FOR EXPANSION

TUBES ARE EXPANDED INTO TUBE SHEET USING AUTOMATICALLY CONTROLLED EXPANSION

Figure 8.140  Typical tube bundle using flanged end cover plates. (Used by permission: Yuba Heat Transfer Division of Connell Limited Partnership).

Heat Transfer  793 16

9

10 3

13

5

14

1

4

2

7

11

8 6

12 3

PLUG HEADER

16

18

16

9

15

10

17

18

13

3

14

17

1

11

12 6

3

COVER PLATE HEADER 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

4

15

10. Side Frame 11. Tube Spacer 12. Tube Support Cross-member 13. Tube Keeper 14. Vent 15. Drain 16. Instument Connection 17. Cover Plate 18. Gasket

Figure 8.141  Typical construction of tube bundles with plug and cover plate headers. (Used by permission: Bul. M92-3003MC 10/94. © Hudson Product Corporation).

Hudson [100] states that the advantages of the induced draft design out weight the disadvantages. Although most units are installed horizontally, inclined, Figure 8.138, and the vertical units are also in service. Figures 8.139 and 8.140 show typical assemblies for tube bundles with fabricated or cast end headers and also with flanged cover plates. The tube bundle is an assembly of tubes rolled into tube sheets and assembled into headers. See Figures 8.136, 8.137, 8.139–8.141. The usual headers are plug and cover plate, but U-bend types can accommodate if the design so dictates. The headers may be: 1. C  ast box type, with shoulder or other plugs opposite every tube. The shoulder plug is generally considered best for most services. The hole of the plug provides access to the individual tubes for (a) cleaning, (b) rerolling to tighten the tube joint, and (c) plugging the tube in case of singular tube leaks. 2. Welded box type, same features as (1).

794  Chemical Process Engineering 3. C  over plate type using flat or confined gasket. This type provides complete access to all tubes upon removal of bolted cover plate. This is used for fouling or plugging services where frequent cleaning is necessary. 4. Manifold type, which is used in high pressure and special applications [89, 114]. For optimum heat transfer performance, horizontal baffles to isolate tube-side passes in horizontal bundles are preferred over vertical baffles that isolate groups of tubes in vertical columns. The expansion of capacity by adding more tube bundles or sections in parallel is easier, and the Mean Temperataure Difference is better with the horizontal pass plates. The fan drive may be operated by any of the available means, including: 1. 2. 3. 4. 5.

 irect electric motor or with belts. D Two-speed electric motor with belts or gears, gear or fluid coupling. Steam turbine direct or with gear or fluid coupling. Gasoline engine with belt, gear, or fluid coupling. Hydraulic drive (see Figure 8.141).

Gears should be specified as American Gear Manufacturer’s Association (AGMA) requirements for cooling tower service in order to ensure an adequate minimum service factor rating of 2.0. The spiral bevel type is probably used a little more often than the word gear. It is also cheaper. When gears are used with induced draft applications, the maximum temperature of the exit air must either be limited by specification, or the gears must be rated at the expected air temperature surrounding the case [115]. Remote lubrication should be provided for gears, bearings, etc., to prevent shutdown of the unit. For a V-belt drive, the type of belt section and maximum number of belts may be specified, as well as the minimum number – usually three. B-sections are most common. V-belts are not considered for drives over about 50-60 hp, and a minimum service factor of 1.4 should be specified for continuous duty. Belts should not be used in any conditions where the surrounding temperature is greater than 160°F, with or without fans operating. This is of particular importance in induced draft conditions where belts might be in the exit air stream. For general service, the fans are axial flow, propeller type with 2-20 blades per fan, which force or induce the air across the bundle. Four blades are considered minimum, and an even number of blades (2-20) are preferable to an odd number (for emergency removal of blades to obtain balance for continued partial operation). Fan diameters range from 3-60 ft. The blades may be solid or hollow construction [100], with the hollow design being the most popular. The blades are usually fixed pitch up to 48 in. diameter with applications for adjustable pitch above this size. Fixed pitch is used up to 60 in. diameter with aluminum fan blades when directly connected to a motor shaft. Variable pitch is used with belts, gears, etc., between the fan shaft and the driver to allow for the possibilities of slight imbalance between blades due to pitch angle variation. Aluminum blades are used up to 300°F (148.9oC), and plastic is limited to about 160-180°F (71.1–82.2oC) air stream temperature. Air noise is usually less with multi-bladed fans (four or more) than with two or three blades. In general, noise is not a real problem when associated with other operating machinery and when the frequency level is low and non-penetrating. When these units are isolated, the associated noise would be immediately noticeable but not objectionable unless confined between buildings or structures where reverberation could take place. The noise level is usually limited to 75 decibels maximum at 50 ft from the fan, and the blade tip speed is limited to 11,000-12,000 ft. per min (= blade dia. ln ft rpm). This may run higher for units below 48-in. dia. Figure 8.135 illustrates the assembly of a typical forced draft unit with electric motor and gear drive. Note that walkways and access ladders are necessary to reach the exchanger connections where valves are usually installed. If the designs require a pipe inlet or outlet at each end of the tube bundle, walkways may be required at each end. Pipe layout studies are necessary when multiple sections (exchanger bundles) are placed in the same service. The structural parts can be galvanized or pickled and painted to prevent the steel rusting. The specifications will depend upon local requirements and experience. Hail guards of stiff hardware cloth mounted in a removable frame are used to prevent hail damage to the relatively soft fins in hail-susceptible areas. If damaged just slightly, the performance is not impaired. Figure 8.142 shows a photograph of a forced draft air-cooled exchanger in a refinery facility.

Heat Transfer  795

ELECTRIC MOTOR DRIVE THROUGH REDUCTION GEARS Pedestal Mounted

HYDRAULIC MOTOR-DRIVE ON CONCRETE PEDESTAL Direct Mounted

STEAM TURBINE OR GASOLINE ENGINE DRIVE Ground Mounted With Tripod Support

ELECTRIC GEAR HEAD MOTOR Suspended Drive

ELECTRIC MOTOR DRIVE THROUGH REDUCTION GEARS Suspended Drive

V-BELT DRIVE CONCRETE PEDESTAL Tripod Mounting

V-BELT DRIVE Suspended Mounting

ELECTRIC MOTOR DIRECT DRIVE FAN Suspended Drive

STEAM TURBINE OR GASOLINE ENGINE Concrete Pedestals, Remote Location

Figure 8.142  Typical drive arrangements for air-coolers. (Used by permission: Griscom-Russell/Ecolaire Corporation).

Figure 8.143  Fan blade guard mounted directly below blades. Note that drive shaft connects through the opening. (Used by permission: Bul. 107. SMITHCO Engineering, Inc.).

796  Chemical Process Engineering Fan guards of wire grating or hardware cloth are mounted below the fan to prevent accidental contact with the moving blades and to keep newspapers, leaves, and other light objects from being drawn into the fan. The use of a wire fence around the entire unit is good to keep unauthorized individuals away from all of the equipment; however, a close fan guard, Figure 8.143, will prevent blade contact by the operators. Figures 8.144 and B, are usually finned with copper, aluminum, steel, or a duplex combination of steel inside with copper or aluminum fins outside. Other combinations are used to suit the service with the ratio of finned to bare tube surface of 15:1-20:1. Common sizes are ¾ in. and 1in. OD with ½ in. to 5/8 in. high fins, although 1 ½ in. OD as well as small sizes are available for a specific design. The minimum number of the tube rows recommended to establish a proper air flow pattern is four, although three rows can be used. The typical unit has 4-6 rows of tubes, but more can be used. Although more heat can be transferred by increasing the number of tubes, the required fan horsepower will be increased; so this balance must be optimized for an effective economical design. Tubes are laid out on transverse or longitudinal patterns; however, the transverse arrangement is usually used due to the improved performance related to pressure drop and heat transfer. The tube pitch is quite important for best air side performance. A typical representative tube arrangement for design optimization is for bare-tube OD, and tube pitch [114].



1-in./2-in./2.375 in. 1-in./2.25 in./2.625 in

For 1 in./2 in. (bare tube OD/finned tube OD) the usual range for tube pitch is 2.125–2.5. for a 1 in./2.25 in. tube, the pitch range would be 2.375-2.75. Reference [114] presents an interesting comparison of the effects of tube pitch on the heat transfer coefficient and pressure drop. Tube lengths vary from 5 ft to more than 30 ft. Units for some heavy lube oils have been installed without fins due to the poor heat transfer inside the tube, i.e., the fins could not improve the overall heat transfer coefficient above plain tubes. Economical tube lengths usually run 14-24 ft and longer. The performance of the tubes varies for a fixed number of tubes and number of tube rows with the number of fins placed per lin in. on the bare tube. The usual number of fins/in. ranges from 7-11, with the lower number giving less total finned surface, ft2 per lin ft of tube. Available extended or finned surface may be increased by changing the height of the fins from the usual ½ in. to 5/8 in. When the fluid in the tubes yields a low film coefficient, the amount of finned surface area is adjusted, as suggested, to provide an economical and compatible area. A high ratio of outside finned surface to bare tube surface is of little value when the outside air and inside fluid coefficients are about the same. The tubes are usually on 2 in. or ½ in. triangular (60°) spacing. Fin thickness usually varies from 0.016-0.014 in. The effect of mechanical bond on heat transfer resistance is discussed by Gardner [117]. It is helpful to the manufacturer for the purchaser to specify any conditions that are peculiar to the plant’s warehouse stock of tubes or process controlled preferences: Preferred bare tube OD and gage, giving minimum average wall thickness. Seamless or resistance welded base tube. Fin material preferred from atmospheric corrosion standpoint.

General Application Air-cooled units have been successfully and economically used in liquid cooling for compressor engine and jacket water and other recirculating systems, petroleum fractions, oils, and so on, and also in condensing service for steam, high boiling organic vapors, petroleum still vapors, gasoline, ammonia, and so on. In general, the economics of application favors service allowing a 30-40°F difference between ambient air temperature and the exchange exit temperature for the fluid. These units are often used in conjunction with water-cooled “trim” coolers, i.e., units picking up the exit fluid from the air-cooled unit and cooling it down to the final desired temperature with water. In some situations, the air-cooled unit can be carried to within 20-25°F of the dry bulb air temperature if this is the desired end point rather than adding a small trim cooler. Kern [118] has studied optimum trim cooler conditions. As the

Heat Transfer  797 Fins

Tube

Tension Wrapped Fin Some Manufacturers Solder-Bond the Fin to the Tube Temperature 300°F

Tension Wrapped Foot Fin

Temperature 350–500°F Duplex (or solid) Continuous Integral Fin This Same Type of Tube-Fin Design may be Obtained in OnePiece Construction. 500–600°F 500–550°F Temperature Imbedded Fin Minimum 16 ga. Tube Wall Required. Fins Imbedded in Tube (1) By Grooving Tube (2) By Special Fin Winding and Tube Wall Forming Temperature 650°F Fins may be of Same or Different Material than Tube Wall. Aluminum Fins are Most Popular for Average Installation. For Aluminum Fins Maximum Operating Temperatures are Listed.

Figure 8.144A  Fin designs for use with air-cooled exchangers.

temperature approach to the ambient air decreases, the power consumption increases rapidly at constant exchanger surface. This balance of first cost vs. operating cost is one of the key comparisons in evaluating these units. Because surface area affects the first cost much more than the normally required horsepower (driver), the selection of the proper unit is a function of the relative change in these two items for a fixed heat duty. The optimum design gives the lowest total costs (first, operating, and maintenance) over the life of the unit, taken in many instances as 15 years or longer. Fan horsepower runs 2-5 hp per 106 Btu/h [63]. First cost range from 25-150% of cooling tower systems, with an average indicated at greater than 30% [119].

Figure 8.144B  Illustrations of actual fin construction. (Used by permission: Bul. B589-455, 6/89. © Hudson Products Corporation).

798  Chemical Process Engineering

Figure 8.145  Air-cooled heat exchangers require monitoring of the liquid flow and the condition of the fan motors. (Source: Dannangelo, M., Hydrocarbon Processing, pp. 33-38, Nov., 2018).

Although these units find initial application in areas of limited water, they have not been limited to this situation. In many instances, they are more economical than cooling tower systems and have been successfully applied in combination with cooling towers (see Figure 8.146). Economic comparisons should include such items as tower costs, basin, make-up facilities, water treatment, pumps for circulation, power supply, blow down, piping, and so on. For small installations of air-cooled units, they should be compared with the prorate share of such cooling facilities unless the specific plant account of costs dictates otherwise. The overall economics of an air-cooled application depends upon the following: Quantity and quality of available water. Ambient air and water temperature. Fluid inlet as well as exit temperatures. Operating pressure. Fixed costs. Maintenance and operating costs. Physical location and space requirements. Mukherjee [114] presents an interesting examination of factors that can influence operating problems with aircooled heat exchangers.

Advantages – Air-Cooled Heat Exchangers 1. Generally simple construction, even at relatively high pressure and/or high temperatures. Amount of special metals often is reduced. 2. No water problems, as associated with corrosion, algae, treating, scale, spray, and so on. 3. Excellent for removing high level temperatures, particularly greater than 200°F (93.3oC). 4. Maintenance generally claimed to be one-third or less than water coolers. Clean fins by compressed air and brushes, sometimes while operating. 5. Lower operating costs under many conditions, depending upon the type of water system used for comparison. 6. Ground space often ≤ cooling towers; can also serve dual purpose by mounting air-cooled units above other equipment or in pipe ways or roofs of buildings. Vibration is no problem.

Heat Transfer  799

Disadvantages 1. R  ather high limitation on outlet fluid temperature. 2. Generally most suitable only for liquids or condensing vapors in tubes, with limited application for gas cooling due to low inside coefficient. 3. First capital costs may range from only 25-125% above water-cooled equipment for same heat load. Each situation must be examined on a comparative basis. 4. Fire and toxic vapor and liquid hazard, if leaks occur to atmosphere. 5. Not very suitable for vacuum services due to pressure drop limitations but are used such in applications. Chase [140] lists these factors affecting the overall costs: 1. E  xchanger sections a. Tube material and thickness. b. Fin material size, shape. c. Fin bond efficiency. d. Header type and pressure. e. Type of piping connections. 2. Air moving equipment a. Power source (electricity, gas, etc.). b. Power transmission to fan (direct, gear, belt, etc.). c. Number of fans. d. Fan material and design. 3. Structure a. Slab or pier foundation. b. Forced or induced draft. c. Structural stability. d. Ladders, walkways, handrails. e. Type of construction. f. Belts, reducing gears, shaft and fan guards. 4. Controls a. Temperature control instruments. b. Power. c. Louvers, rolling doors. d. Mixing valves. Factors to consider in evaluating the selection between induced and forced draft include the following [140]. 1. Induced Draft a. Recirculation of air is less (exit air velocity 2-3 times forced draft). b. Air distribution over exchanger is better. c. Sections are closer to ground and easier to maintain, provided driver mounted below cooler. d. Maximum weather protection for finned tubes (rain, hail, freezing). e. Few walkways needed, mounting easier overhead. f. Connecting piping usually less. 2. Forced Draft a. Mechanical equipment more easily accessible. b. Isolated supports for mechanical equipment. c. Simpler structure. d. Easier to adapt to other than motor drives. e. Fan horsepower less for same performance (due to difference in air density). f. Exchangers are easier to remove for repairs. Table 8.50 provides some useful correlations for air-cooled heat exchanger design [141].

800  Chemical Process Engineering Table 8.50  Correlations for air-cooled heat exchanger design. Correlation

Where used

Ha = 0.295G

0.681 a

d

−0.319 o

S

0.313

h

−0.2

b

−0.113

β

Air-side heat transfer coefficient Tube-side heat transfer coefficient (for mass velocities between 15 and 1000 × 103 lb/h ft2

0.8 −0.2 −0.4 0.4 Hl = 0.276K 0.6 µ l c pl l Gl di

0.19 ( Pe d L )

Tube-side heat transfer coefficient for laminar flow.

0.8

Nu = 3.66 +

1 + 0.117 ( Pe d L )

0.46

Tube-side heat transfer coefficient in turbulent flow.

f   2  Re Dh Pr Nu = f 1.07 + 12.7 ( Pr 2 3 − 1) 2 Nu Dh

1.25   Re   = 5.172 1 + 5.484 × 10−3 Pr 0.7     y   

0.5m

Tube-side heat transfer coefficient with twisted tapes.

The correlations need to be augmented with fin efficiency and fouling factors.

where H G d S

= heat transfer coefficient, W/m2 K = mass velocity, kg/m2 s = diameter of tube, m = fin surface area, m2 Hot Fluid IN 300°

Drift Eliminators

Air 73°

Hot Fluid IN 300°

Drift Eliminators

Cold Fluid OUT 93°

Cold Fluid OUT 85° Shutters

NO WATER REQUIRED

Air 95°

Air 65°

Water 68°

ILLUSTRATION OF SUMMER AND WINTER OPERATION OF THE COMBIN-AIRE (R)

SUMMER 1. Relatively small quantity of water required, with no treatment necessary. Salt water may be used. 2. Cooled water may be used for other cooling purposes. 3. Because of elevated temperature, air leaving Combinaire is under-saturated with water vapor, thus preventing spray carryover or missing.

WINTER 1. No water required. 2. Shutters may be made automatically reponsive to air temperature, thus automatically controlling percentage of air pre-cooled. 3. No possibility of icing as encountered in winter operated cooling towers.

TRADEMARK, HUDSON ENGINEERING CORP.

Figure 8.146  Combined system using cooling tower and air cooler units. (Used by permission: Hudson Products Corporation).

Heat Transfer  801 h = fin height, m b = fin thickness, m = equivalence function = viscosity of fluid kg/m s cp = specific heat, J/kg K Nu = Nusselt number Re = Reynolds number Pe = Peclet number f = friction factor Pr = Prandtl number L = length, m k = thermal conductivity, W/m K y = twist ratio Subscripts a = air l = liquid i = inner o = outer Dh = hydraulic diameter Figure 8.145 shows a photo of air-cooled heat exchangers requiring monitoring of the liquid flow and the condition of the fan motors, and Figure 8.146 shows the combined system using cooling water tower and air cooler units respectively.

Mean Temperature Difference These units are pure cross-flow and require the use of specific data not found in the TEMA Standards [142], but are available in [143, 144]. See Figures 8.149A, B and C.

8.19.3 Design Procedure for Approximation Specific designs are best obtained from manufacturers offering this type of equipment or from specific curves applicable to the units under study. A suggested inquiry specification sheet is shown in Figures 8.147 and 8.148 respectively. This serves to define the known factor as the time of inquiry and then to summarize the exact specifications as proposed by a specific vendor. The method summarized is essentially that of Smith [120]. 1. Determine heat duty for the exchanger from process fluid temperatures. 2. Select design ambient air temperature, t1. 3. Select design pressure on the tube-side, tube material, and gage. 4. From Table 8.51 select overall U for exchanger service. Note that Table 8.52 gives transfer rates based on outside finned surface. 5. Calculate,



T1 − t1 U(bare tube)

(8.272)

and from Figure 8.150, read optimum bundle tube row depth. 6. From Table 8.53, select (a) typical standard air face velocity, (b) ratio of surface area to face area, and (c) ratio of weight to face area. 7. Determine surface requirements by trial and error:

802  Chemical Process Engineering

Figure 8.147  Specification sheet for air-cooled exchangers.

Heat Transfer  803 Table 8.51  Typical overall heat transfer coefficients for air-cooled exchangers based on bare tube surface. Condensing service

U

Amine reactivator

100-120

Ammonia

105-125

Refrigerant 12

75-90

Heavy naphtha

70-90

Light gasoline

95

Light hydrocarbons

95-105

Light naphtha

80-100

Reactor effluent Platformers, Hydroformers, Rexformers

80-100

Steam (0-20 psig)

135-200

Gas cooling service Air or flue gas @ 50 psig (ΔP = 1 psi)

10

Air or flue gas @ 100 psig (ΔP = 2 psi)

20

Air or flue gas @ 100 psig (ΔP = 5 psi)

30

Ammonia reactor stream

90-110

Hydrocarbon gasses @ 15-50 psig (ΔP = 1 psi)

30-40

Hydrocarbon gasses @ 50-250 psig (ΔP = 3 psi)

50-60

Hydrocarbon gasses @ 250-1500 psig (ΔP = 5 psi)

70-90

Light cooling service Engine jacket water

130-155

Fuel oil

20-30

Hydroformer and Platform liquids

85

Light gas oil

70-90

Light hydrocarbons

90-120

Light naphtha

90

Process water

120-145

Residuum

10-20

Tar

5-10

Coefficients are based on outside bare tube surface for 1-in. O.D. tubes with 10 plain extruded aluminum fins per in., 5/8 in. high 21.2:1 surface ratio. Used by permission: Bul M92-300-3MC 10/94. ©Hudson Products Corporation.

804  Chemical Process Engineering Table 8.52  Overall heat transfer rates for air-cooled heat exchangers. Service

*Stab transfer rate

**Suggested no. of tube layers

Engine jacket water

6-7

4

Light hydrocarbons

4-5

4 or 6

Light gas oil

3-4

4 or 6

Heavy gas oil

2.5-3

4 or 6

Lube oil

1-2

4 or 6

Bottoms

0.75-1.5

6 or more

Flue gas @ 100 psig & 5 psi DP

2-2.5

4

Steam

7-8

4

Light hydrocarbon

4-5

4 or 6

Reactor effluent

3-4

6

Still overhead

2.75-3.5

4 or 6

Cooling service

Condensing service

*Transfer rate, Btu/(hr) (ft2) (°F), based on outside fin tube surface for 1-in. O.D. tubes with 5/8 in. high aluminum fins spaced 11 per in. **The suggested number of tube layers cannot be accurately predicted for all services. In general coolers having a cooling range up to 80°F and condensers having a condensing range up to 50°F are selected with 4 tube layers. Cooling and condensing services with ranges exceeding these values are generally figures with 6 tube layers. Used by permission: Griscom-Russell/Ecolaire Corporation, Easton, PA.

(a). Assume a temperature rise, t2 – t1. (b). Solve for total face area required:

FA =



Q (t 2 − t1 )(FV)(1.08)

(8.273)

(c). Calculate LMTD using t1, t2, T1, T2 Neglect correction to LMTD unless outlet air temperature, t2, is considerably greater than the required outlet tube-side temperature T2. (d). Calculate bare or plain tube surface required:

A=



Q U(LMTD)

This can be converted to finned surface by ratio of finned/bare surface areas. (e). Calculate face area, FA2:

FA 2 =

A = FA1 , (Table 8.54) surface area    face area 

(8.274)

Heat Transfer  805

Figure 8.148  Air-cooled equipment specifications form. (Used by permission: Segel, K. D., Chemical Engineering Progress, V. 55, © 1959. American Institute of Chemical Engineers. All rights reserved).

Table 8.53  Estimating heat factors, 1-in. O.D. tube

2 3/8-in. D spacing.

Depth, tube rows

4

6

8

10

12

Typical standard FV, ft/min**

595

540

490

445

405

Ft2 surface/ft2 face area

5.04

7.60

10.08

12.64

15.20

Weight lb/ft2 face area

75

88

115

131

147

**FV = face velocity Used by permission: Smith, E. C. Chemical Engineering, V. 65, p. 145, ©1958. McGraw-Hill, Inc. All rights reserved.

806  Chemical Process Engineering Table 8.54  Design face velocities for air-cooled exchangers. Face Velocity, ft/min (m/s.) Number of tube rows

8 fins/in. (315 fins/m) 2.375 in (0.0603 m) pitch

10 fins/in. (394 fins/m) 2.375 in (0.0635 m) pitch

10 fins/in. (394 fins/m) 2.5 in (0.0635 m) pitch

3

650 (3.30)

625 (3.18)

700 (3.56)

4

615 (3.12)

600 (3.05)

600 (3.35)

5

585 (2.97)

575 (2.92)

625 (3.18)

6

560 (2.84)

550 (2.79)

600 (3.05)

(Source: Chopey and Hicks [149]). MTD Correction Factors/1 Pass-Cross Flow HUDSON PRODUCTS CORPORATION Houston, Texas, USA TYPICAL TUBE LAYOUTS NOMENCLATURE:

INLET

T1 = INLET TEMPERATURE TUBE SIDE T2 = OUTLET TEMPERATURE TUBE SIDE t1 = INLET TEMPERATURE AIR SIDE t2 = OUTLET TEMPERATURE AIR SIDE

INLET

OUTLET

OUTLET 1.0

.9

.9

.8

.8

0.6 0.8

.7

R 8.0 6.0 5.0

.6

.5 0 T 1 – T2 R= t2 – t1

.1

3.0

4.0

.2 t2 – t1 r= T1 – T1

.3

2.5

2.0

1.75

1.2

1.5

1.0

.7

CORRECTION FACTOR F

0.4

CORRECTION FACTOR F

0.2

1.0

.6

.4

.5 r

.6

.7

.8

.9

1.0

MTD CORRECTION FACTORS 1 PASS-CROSS FLOW BOTH FLUIDS UNMIXED

Figure 8.149A  MTD correction factors/1 pass, cross-flow. (Used by permission: Bul. M92-300-3M C (10/94). © Hudson Product Corporation).



where subscript 2 refers to second or check calculation, and 1 refers to original trial. (f). If FA2 = FA1, proceed with detailed design If FA2 FA1, reassume new air outlet temperature and repeat from (a) (g). For detailed check: Assume tube-side passes and calculate hi, hio in the usual manner. From air velocity, ft/min, calculate quantity and film coefficient considering fin efficiency.

Figure 8.151 may be used directly to obtain effective outside fin coefficient, ho, based on the bare tube surface. Recalculate overall U. If this value differs greatly, the unit should be calculated until balance is reached.

Heat Transfer  807 MTD Correction Factors/2 Pass-Cross Flow HUDSON PRODUCTS CORPORATION Houston, Texas, USA TYPICAL TUBE LAYOUTS

NOMENCLATURE: T1 = INLET TEMPERATURE TUBE SIDE T2 = OUTLET TEMPERATURE TUBE SIDE t1 = INLET TEMPERATURE AIR SIDE t2 = OUTLET TEMPERATURE AIR SIDE

INLET

INLET

OUTLET

OUTLET

1.0

1.0

.8 10

7

5

3

4

2.5

1.75

2

5

1.2

1.5

0.8

1.0

0.6

.9

.8

.7

.7

.6

.6

.5

0

.1

.2

T –T R= 1 2 t2 – t1

.3

.4

t –t r= 2 1 T1 – t1

.5 r

.6

.7

.8

.9

CORRECTION FACTOR F

CORRECTION FACTOR F

.9

0.2

0.4

1.0

MTD CORRECTION FACTORS 2 PASS-COUNTER CROSS FLOW BOTH FLUIDS UNMIXED

Figure 8.149B  MTD correction factors/2 pass, cross-flow. (Used by permission: Bul. M92-300-3M C (10/94). © Hudson Product Corporation).

MTD Correction Factors/3 Pass-Cross Flow HUDSON PRODUCTS CORPORATION Houston, Texas, USA TYPICAL TUBE LAYOUTS

NOMENCLATURE:

INLET

T1 = INLET TEMPERATURE TUBE SIDE T2 = OUTLET TEMPERATURE TUBE SIDE t1 = INLET TEMPERATURE AIR SIDE t2 = OUTLET TEMPERATURE AIR SIDE

INLET

OUTLET

OUTLET

1.0

1.0

CORRECTION FACTOR F

5

1.5

.8

.7

R

10

7

5

3

4

2.5

2

1.2

1.0

0.8

0.6

0.4

.9

.8

1.75

.7

.6

.5 0

CORRECTION FACTOR F

.9

0.2

.6

.1 T 1 – T2 R= t2 – t1

.2 t2 – t1 r= T1 – t1

.3

.4

.5 r

.6

.7

.8

.9

1.0

MTD CORRECTION FACTORS 3 PASS-COUNTER CROSS FLOW BOTH FLUIDS UNMIXED

Figure 8.149C  MTD correction factors/3 pass, cross-flow. (Used by permission: Bul. M92-300-3M C (10/94). © Hudson Product Corporation).

808  Chemical Process Engineering Optimum Bundle Depth in Tube Rows

12

10

8 Basis: 1 in O.D. × 24 ft. Tubes Extruded Aluminum Fins on 2 3/8" Triangular Spacing

6

4 3

0

2

4 6 8 10 12 14 Temperature Level/Over-all Transfer Rate, (T1 – t1)/U

16

18

Figure 8.150  Optimum bundle depth. (Used by permission: Smith, E. C., Chemical Engineering, V. 65, Nov. © 1958. McGraw-Hill, Inc., All rights reserved).

(h). Calculate tube-side pressure drop in usual manner, including loss in headers. (i). Determine unit plant size:

Width =



face area assumed tube length (usually 4 ft, 6 in. min. through 30 ft)

(8.275)



Balance these to obtain practical or standard size units. Bundle widths are usually 4 ft, 6 in. and 7 ft. 6 in. (j). Calculate hp requirements from Figure 8.152; read surface. area/hp or read Figure 8.151 for pressure. drop for certain tube arrangements.

total surface, A surface area/hp



HP =



Also: HP = pv = 0.1 in. H2O, usually ps = 0.2 to 0.25 in. H2O at pt = pv + ps, in. H2O er = 0.65 usually ed = 0.95 usually

(ACFM)(p t ) (6,356)(e f )(ed )

(8.276) (8.277)

500 ft/min FV for each 3 rows of tubes

(k). Approximate weight:

= (face area) (weight/face area)(8.278) pv = velocity pressure, in. H2O = static pressure, in. H2O ps = total pressure, in. H2O pt ACFM = actual CFM at fan intake FA = face area of air cooled exchanger tube bundle, length x width, ft2 t1, t2 = inlet and outlet air temperature of fin unit T1, T2 = inlet and outlet tube-side fluid temperature of fin unit FV = face velocity, ft/min, entering face area of air cooled unit U = overall heat transfer rate based on bare tube OD, Btu/h (ft2) (°F)

Heat Transfer  809 1,000

0.6 0.4 0.3 0.2

0.1 100

n aci Sp Δ ") /4" 2 1 .016 n. ( in (0 I / in m F 8F in, minu F 200 400 1,000 ed ) Alu dd be acing Face Velocity, Ft./Min m I Sp /8" r 5 . (2" Δ o n n Fi in/I ot F " Fo Fin, 8 8 / 5 ot " Fo 1/2

10

100 Bundle Face Velocity, Ft./Min. Aluminum Fins:

g)

100

Btu/Hr. (sq. ft.)(°F), I" O.D. Tube Outside Bare Coeff., ho (Good for 2–10 Rows Deep)

0.8

5/8 "I 8 F nteg in/ ral Fo 5/8" ot In. Fin & 1/ , 8 2" Fin /In .

ΔP for 4 Rows, Inches H2O

1.0

10 1,000

Wrapped Fins* Imbedded Fin Foot Fin Integral Duplex Fin* Integral Duplex Fin*

*Note: Use 90% of ho from Curve. Compiled from Manufacturers Quotation Data.

Figure 8.151  Outside fin film, coefficient for air-fin exchangers. (Used by permission: Hajek, J. D., Compiled from manufacturer’s data).

8.19.4 Tube-Side Fluid Temperature Control The tube-side fluid responds quickly to changes in inlet air temperature. In many applications this is of no great consequence as long as the unit has been designed to take the maximum. For condensing or other critical service, a sudden drop in air temperature can create pressure surges in distillation or other process equipment, and even cause flooding due to changes in vapor loading. Vacuum units must have a pressure control that can bleed air or other inert gas into the ejector or vacuum pump to maintain near constant conditions on the process equipment. For some units the resulting liquid subcooling is not of great concern. Depending upon the extent of control considered necessary, the following systems are used (Figures 8.153 and 8.154): 1. By-pass control of inlet fluid with downstream mixing to desired final temperature. 2. Manual (for seasonal changes only) or automatic pitch control operated by air-motor on fan blades. 3. Variable speed drive (motor, turbine, hydraulic).

810  Chemical Process Engineering

Bundle Depth in Tube Rows

12

10

8

6

4 3

0

20

40 60 80 100 120 140 Bare Tube Surface Area/Fan Horsepower, sq. ft./Hp.

160

180

Figure 8.152  Surface per fan hp. (Used by permission: Smith, E. C., Chemical Engineering, V. 65, Nov. 1958 © McGraw-Hill, Inc., All rights reserved). 110 100 er pow rse o H

rQ

ua

ni

ty

80

Design Point

70

Ai

Ambient Air Temperature, °F.

90

60 50

Above 40°F. Pitch of Fan Blades Assists Convection Flow

40

Below 40°F. Pitch of Fan Blades Retards Convection Flow

30 20 10 0

10

20

30

40

50 60 70 80 Design Horsepower, % Design Air Quanity, %

90

100

110

120

Figure 8.153  Temperature control and horsepower savings with automatic variable pitch fans. (Used by permission: Hudson Products Corporation).

4. Fixed two-speed drive (usually for day and night operation). 5. Louvers on air off exchanger. 6. Shut down of fans (one or more) when multiple fans are used in the same process service. When only one fan and/or exchanger exists per process service, it may be advisable to control with an automatic variable pitch fan, unless a single- or two-speed drive is considered adequate. If the process service consists of several exchanger sections or tube bundles per cell (groups of bundles) and multiple fans are used, see Figure 8.155. If single fans are used per cell, see Figure 8.156. If several cells are used per process service, some of the fans should be considered for automatic variable pitch control (if continuous variable speed not used); some for two-speed control with or without louvers, and the remainder set on constant speed. Various combinations can be developed to suit the process, taking into account the change in air flow with speed and its effect on film coefficients. The manufacturer can supply this after the type of control is established.

Heat Transfer  811

Adjustable Shutters Shutters mounted above the cooling sections serve to protect them from overhead wind, snow, ice, and hail. In addition, they are also used to regulate, either manually or automatically, the flow of air across the finned tubes; thus, they control the process fluid outlet temperature.

PNEUMATIC TEMPERATURE CONTROLLER PRESSURE REGULATOR AND FILTER PNEUMATIC SHUTTER OPERATOR WITH POSITIONER

PNEUMATIC TEMPERATURE CONTROLLER

Controllable Pitch Fan The controllable pitch fan provides an infinitely variable air delivery across the K-fin sections through automatic changes in the fan blade angle. The temperature can be closely controlled to meet the varying demands of operating conditions and fluctuating atmospheric temperature with appreciable saving under low load conditons. For certain control applications, the ability of this fan to pump air backwards with negative blade angles is used.

Combination Controls The combination of adjustable shutters with variable speed drive or with controllable pitch fan is frequently used for close fluid temperature control. This system is particularly useful during start-up and shut-down procedures in which fluids are subject to freezing in cold ambient temperatures. It is also well-adapted to fluid temperature control while operating under high wind and freezing conditions. This diagram shows a two-speed electric motor with automatically adjustables shutters. The arrangement lends itself to many cooling services while effecting a horsepower savings through the use of the two-speed motor.

PRESSURE REGULATOR AND FILTER PNEUMATIC BOOSTER RELAY

PNEUMATIC SHUTTER OPERATOR WITH POSITIONER PRESSURE REGULATOR AND FILTER

PNEUMATIC TEMPERATURE CONTROLLER PNEUMATIC-ELECTRIC RELAYS MOTOR CONTROLLER

Figure 8.154  Schemes for temperature control of air coolers. (Used by permission: Griscom-Russell/Ecolaire Corporation).

For winter operation, it is important to consider the effect of cold temperatures on process fluid (gelling, freezing, etc.), and this may dictate the controls. In addition, tarpaulins or other moveable barriers may be added to reduce air intake or discharge. This can be a serious control problem. When a two-speed motor is reduced to half-speed, the air capacity will be cut 50%, and the required horsepower consumption will drop to one-eighth of full speed power.

8.19.5 Rating Method for Air-Cooler Exchangers The rating methods for air-cooled exchangers are outlined by Cook [121] and Ganapathy [122]. Here, the preliminary design of air coolers is based upon correlations, tables and graphs presented by Smith [120] and Brown [123] and fitted to a series of equations developed by Blackwell [124].

The Equations 1. The number of tube rows, R is:

812  Chemical Process Engineering A Sections Per Cell

B Nom. Lg. Tubes

C Fan Dia.

D Length

E Width CL to CL Col’s. per Cell

2 2 2 2 2 1/2 2 1/2 2 1/2

240" 288" 288" 360" 240" 288" 360"

8'–0" 8'–0" 10'–0" 10'–0" 10'–0" 10'–0" 10'–0"

18'–3 1/2" 22'–3 1/2" 22'–3 1/2" 28'–3 1/2" 18'–3 1/2" 22'–3 1/2" 28'–3 1/2"

10'–8 1/4" 10'–8 1/4" 10'–8 1/4" 10'–8 1/4" 13'–4 5/16" 13'–4 5/16" 13'–4 5/16"

(A) No. Sections per Cell

No. Cells

Total Width

Fan Dia. (C) (B) Nominal Tube Length PLAN

6'–5"

Galv. Chain Link Fence & Gate (Optional)

(E) CL to CL Col’s per Cell

(E) Length CL to CL Col’s

END ELEVATION

LEFT ELEVATION

10'–0"

Fan Ring

13'–0"

6'–7"

Ladder and Walkway Optional

Figure 8.155  Typical dimensions for air coolers with two fans. (Used by permission: Griscom-Russell/Ecolaire Corporation).





T −t R = C1 + C 2 ln  2 2   U 

(8.279)

A = C 3 (R)C4 FA

(8.280)

where C1 = 3.1679 = 3.7948 C2

2. The area ratio is:



Heat Transfer  813 A Sections Per Cell

B Nom. Lg. Tubes

C Fan Dia.

D Length CL to CL Col’s.

E Width CLto CL Col’s. per Cell

2 2 2 2 1/2 2 1/2

120" 180" 240" 180" 240"

8'–0" 10'–0" 10'–0" 10'–0" 12'–0"

8'–3 1/2" 13'–3 1/2" 18'–3 1/2" 13'–3 1/2" 18'–3 1/2"

10'–8 1/4" 10'–8 1/4" 10'–8 1/4" 13'–4 5/16" 13'–4 5/16"

(A) No. Sections per Cell

No. Cells

Total Width

Fan Dia. (C)

(B) Nominal Tube Length

(E) CL to CL Col’s per Cell

Ladder and Walkway Optional

Fan Ring

This Column in 240 Length only

Galv. Chain Link Fence & Gate (Optional)

10'–0"

6'–5"

13'–0"

6'–7"

PLAN

(D) Length CL to CL Col’s

END ELEVATION

LEFT ELEVATION

Figure 8.156  Typical dimensions for air coolers with one fan. (Used by permission: Griscom-Russell/Ecolaire Corporation).







where C3 = 1.2557 = 1.0031 C4

3. The face velocity of air, FV, ft/min.

where = 720.8542 C5 = 0.9530 C6

FV = C5(C6)R



(8.281)

Typical face velocities (FVs) used for design are shown in Table 8.54. These values result in air-cooled heat exchangers that approach an optimum cost [125]. This takes into account the purchase cost, the cost of installation and the

814  Chemical Process Engineering Table 8.55  Estimated outlet air temperature for air-cooled exchangers. Outlet air temperature, oC Process inlet temperature, oC

U = 50

U = 100

U = 150

175

90

95

100

150

75

80

85

125

70

75

80

100

60

65

70

90

55

60

65

80

50

55

60

70

48

50

55

60

45

48

50

50

40

41

42

(Source: Chopey and Hicks [149]).

cost of power to drive the fans. Table 8.55 lists an estimate of the outlet air temperature, based on 90oF – 95oF design ambient air temperature. 4. Estimated air outlet temperature, t1, oF

 T + T   t1 = 0.005U  1 2 − t 2  + t 2  2  



(8.282)

5. The effective log mean temperature difference, ∆TLMTD oF



∆TLMTD =

(T1 − t 2 ) − (T2 − t1 ) T −t ln 1 2 T2 − t1

{ }

(8.283)

6. The heat duty Q, Btu/h.



Q = w c t

(8.284)

where w = fluid flow rate, lb/h c = specific heat capacity, Btu/lb oF t = temperature difference, oF 7. The bare tube surface area based on the tube, OD, ft2



A=

Q (U)(∆TLMTD )

(8.285)

A C (R)C 4

(8.286)

8. The face area of bundle FA, ft2



FA =

3

Heat Transfer  815 9. The calculated outlet air temperature, t1′ , oF



t1′ =

Q + t2 (1.08)(FA)(FV)

(8.287)

10. The air flow over tubes, F std. ft3/min



F = (FA)(FV)

(8.288)

11. The ratio of the bare tube surface area based on the tube OD to the fan horsepower

A = C 7 + C 8 (R) Bhp



(8.289)

where C7 = 7.4212 C8 = 12.5342 12. The ratio of air cooler weight to the face area of bundle

Wt = C 9 + C10 (R) FA



(8.290)

where C9 = 36.4 C10 = 9.35 13. The tube bundle width, W, ft



W=

FA L

(8.291)

14. The area available, Av, ft2

Av =

Nr Nt Do L

(8.292)

where Nr = number of rows Nt = number of tubes per row = (tube bundle width)/ (tube spacing) = W/s L = tube length, ft Do = tube outside diameter, ft. If the area available, Av is less than the area required, A, increase the bundle width, and calculate the new outlet air temperature. Recalculate ∆TLMTD, the new required area, and the new available area. 15. Th  e air side heat transfer coefficient, ha, Btu/h. ft2 oF. The air side coefficient is determined on the basis of the outside surface of a bare tube, ha is expressed as:

ha = 8 (FV)0.5 for 10 fins per inch.

(8.293)

816  Chemical Process Engineering

ha = 6.75 (FV)0.5 for 8 fins per inch.

(8.294)

16. The tube wall heat transfer coefficient, hw, Btu/h ft2 oF



hw =

2k Do − D i

(8.295)

where k = thermal conductivity, Btu/h ft oF Do = outside diameter of tube, ft. Di = inside diameter of tube, ft 17. The overall heat transfer coefficient, U, Btu/h ft2 oF

1 1 1 1 1 = + + + U h a h i ( D i Do ) h w h s



(8.296)

where hi = inside of tube heat transfer coefficient, Btu/h ft2 oF hs = fouling coefficient, Btu/h ft2 oF

The Air Side Pressure Drop, ∆pa (inch H2O) The following equations are used to calculate the pressure drop on the air side [124]



∆pa = 0.0047Nr ( FV 100 ) for 10 fins per inch, 2.375 inch spacing (8.297)



∆pa = 0.0044Nr ( FV 100 ) for 8 fins per inch, 2.375-inch spacing

(8.298)



∆pa = 0.0037Nr ( FV 100 ) for 10 fins per inch, 2.5 inch spacing

(8.299)

1.8

1.8

1.8

where Nr = the number of tube rows FV = face velocity, ft/min. ∆pa = inch H2O where A Av Bhp c C1, C2, C3 C4, C5, C6 C7, C8, C9 C10 Di Do

= bare-tube surface, area ft2 = available area, ft2 = fan horsepower = specific heat of fluid, Btu/lb oF = constants = constants = constants = constant = inside diameter of tube, ft. = outside diameter of tube, ft.

Heat Transfer  817 F FA FV ha hi hs hw k L ∆TLMTD Nr Nt ∆pa Q R T1 T2 t1 t1′ t2 ∆t U W w Wt

= air flow over tubes, std ft3/min = face area of bundle, ft2 = face velocity of air, ft/min. = air side heat transfer coefficient, Btu/h ft2 oF = inside of tube heat transfer coefficient, Btu/h ft2 oF = fouling coefficient, Btu/h ft2 oF = tube wall heat transfer coefficient, Btu/h ft2 oF = thermal conductivity, Btu/h ft oF = pipe length, ft. = log mean temperature difference, oF = number of rows = number of tubes per row = air-side pressure drop, inch (H2O) = exchanger duty, Btu/h = number of tube rows = outlet process fluid temperature, oF = inlet process fluid temperature, oF = estimated air outlet temperature, oF = calculated outlet air temperature, oF = inlet air temperature, oF = temperature difference, oF = overall heat transfer coefficient (based on bare-tube, OD), Btu/h ft2 oF = tube bundle width, ft. = Fluid flow rate, lb/h. = air cooler weight, lb

Example 8.10 Calculate a preliminary air-cooler design using the following data. A light hydrocarbon liquid is to be cooled from 170oF to 135 oF in an air cooler. The heat transfer rate is 5.0 MM Btu/h. and the estimated overall heat transfer coefficient is 60 Btu/h.ft2 oF. The design dry bulb air temperature is 85oF and the tube length is 40ft.

Solution The Excel spreadsheet (Example 8.10.xlsx) program has been developed for a preliminary air cooler exchanger rating. The preliminary design results show the exchanger area is 1605 ft2 and the LMTD is 52 oF. The face area of the bundle is 282 ft2 (40 ft 7.05 ft), and the fan horsepower is 25.5 bhp. The required air flow is 163534 std ft3/min and the outlet air temperature is 113.3oF. The results of the Excel spreadsheet calculations are shown below. RESULTS OF AN AIR-COOLED HEAT EXCHANGER RATING

     

 

  FLUID NAME

Light Hydrocarbon Liquid

INLET PROCESS FLUID TEMPERATURE

170

o

OUTLET PROCESS FLUID TEMPERATURE

135

o

INLET AIR TEMPERATURE

85

o

OVERALL HEAT TRANSFER COEFFICIENT

60

Btu/h.ft2.oF

HEAT LOAD ON UNIT

5000000

Btu/h

F F F

818  Chemical Process Engineering TUBE LENGTH

40

ft.

NUMBER OF TUBE ROWS

4.49

RATIO OF BARE-TUBE SURFACE TO FACE AREA OF BUNDLE

5.7

FACE VELOCITY OF AIR

580.73

ft./min.

ESTIMATED AIR OUTLET TEMPERATURE

105.25

o

EFFECTIVE LOG MEAN TEMPERATURE DIFFERENCE, LMTD

57.06

o

BARE-TUBE SURFACE AREA BASED ON TUBE OD

1460.5

ft2

FACE AREA OF BUNDLE

256.2

ft2

CALCULATED OUTLET AIR TEMPERATURE

116.12

o

F F

F

THE DIFFERENCE BETWEEN THE CALCULATED AIR OUTLET TEMPERATURE AND THE ESTIMATED AIR OUTLET TEMPERATURE IS GREATER THAN 0.5

(TAO-TAO1) >= 0.5

EFFECTIVE LOG MEAN TEMPERATURE DIFFERENCE, LMTD

51.92

o

BARE-TUBE SURFACE AREA BASED ON TUBE OD

1605

ft2

FACE AREA OF BUNDLE

281.6

ft2

CALCULATED OUTLET AIR TEMPERATURE

113.3

o

FACE AREA OF BUNDLE

281.6

ft2

AIR FLOW OVER TUBES

163534

std. ft3/min

FAN HORSEPOWER

25.2

bhp

AIR-COOLER WEIGHT

22072.2

lb

TUBE BUNDLE WIDTH  

 

      7

F

F

ft.

8.19.6 Operations of Air-Cooled Heat Exchangers Problems encountered during the operation of an ACHE may reduce its efficiency and increase operating costs. Commonly occurring problems are [114]: 1. Tube-side flow maldistribution particularly relevant when two-phase flow is encountered. At lower temperatures, the performance reduction for a fixed maldistribution is higher. 2. Inadequate cooling – this often results from other problem (such as fans not operating properly, tube blockage, property changes, etc.) 3. Excessive fouling – congealing is the main reason cited for fouling inside ACHE tubes. Streams that have high pour points (greater than 6 - 10 oC) should normally not be cooled in ACHEs. (Most crude oils have a pour point less than 0oC). Depending on location, significant fouling on the air side could occur as well. 4. High inlet air-temperature. 5. Insufficient air-side flow rate – generally, this is a problem if the existing ACHE is used for higher flowrates or different operating conditions.

Heat Transfer  819 Berryman [126] provides a report on the condition monitoring of air-cooled heat exchangers and Table 8.56 in Appendix A gives a useful troubleshooting chart for air-cooled heat exchangers. Studies have been focused on the air side of air-cooled heat exchangers and inserts have been used on the tube-side particularly when cooling highly viscous liquids. However, little information is available on whether inserts should be used, the types of inserts and how they affect heat transfer and pressure drop. Air-cooled heat exchangers often have little control; fan speed is often fixed and louvers are open at a fixed angle or on manual control. Existing aircooled heat exchangers installation has more than sufficient tube bundles and fans to achieve the desired cooling. Therefore, optimization is required to ascertain which bundles and fans should be used for optimal operation with constraints from pipework. Optimization studies are essential, especially in refineries and other hydrocarbon processing plants using air-cooled heat exchangers that have been in operation for several years. The operating plants should embark on improving the performance of ACHEs with minimal investment, which is possible through operational changes and additional controls. Reviews of two-phase flow patterns, condensation, subcooling, boiling and vaporization are provided elsewhere [55].

8.19.7 Monitoring of Air-Cooled Heat Exchangers Many of the same problems encountered with liquid-cooled condensers also apply to air-cooled heat exchangers as fouling of the liquid pipes reduces their ability to transmit heat to the outside and reduces overall liquid flow. The air flow can also become fouled if air-borne dust, leaves and other debris become lodged in the passages. Monitoring sensors are required and these include: • The process liquid inlet and outlet have temperature sensors. • Measuring differential pressure (DP) across the panels can help to detect internal fouling. • Cooling air flow may be measured and used to control the fan speed; or if the fan speed is fixed, reading the negative pressure inside the exchanger with a DP transmitter can determine the air flow. Fan motors are fitted with vibration monitors and bearing temperature sensors. Figure 8.183 shows air-cooled heat exchangers that dissipates heat from liquid by transferring it to the atmosphere in a facility.

8.20 Spiral Heat Exchangers 1. The spiral design heat exchangers, Figures 8.10A, 8.10B, 8.10C, and 8.10D are conveniently adaptable to many process applications. The true spiral units (Figure 8.10A and 8.10B) are usually large and Steam In

Cooling Water Out

Cooling Water In

Condensate Out

Figure 8.157  Spiral flow in one channel, axial in another.

Non-condensables

820  Chemical Process Engineering Fluid - II

Fluid - II Fluid - I

Fluid - I

Figure 8.158  Spiral flow in both channels. Cooling Water Out

Steam In

Cooling Water In Non-condensables Condensate Out

Figure 8.159  Combination flow.

suitable for higher flow rates, and the Heliflow -style, Figure 8.10C, can be fabricated into small sizes, suitable for many “medium” (but not limited) process and sample cooler applications.   The spiral units are used as cross-flow interchangers, condensers, and reboilers. These units can often be conveniently located to reduce space requirements. They are suitable for vacuum as low as 3mm Hg, because the pressure drops can be quite low. Bailey [214] identifies temperature limits of -30 to +1,00°F, pressure limits of 0 to 350 psia, maximum flow rate per shell of 3,000 gpm, and a heat transfer area of 4,000 ft2. Trom [213] discusses a wide variety of process-related applications. 2. The Heliflow is a tubular version of the spiral plate heat exchangers, Figures 8.10C and 8.15-10D, and has a high efficiency and counter-flow operation with a wide range of applications while occupying a limited space. Its applications include vent condensing, sample coolers, instantaneous water heating, process heating and cooling, reboilers and vaporizers, cryogenic coolers. Advantages and disadvantages of Spiral Flow Heat Exchangers over the shell and tube heat exchangers. Advantages

Disadvantages

Compactness

More expensive as it requires a higher fixed cost for the same heat transfer surface

Centrifugal force increases the heat transfer coefficient particularly of highly viscous liquid slurries or sludges

The design is not well established as compared with the shell and tube heat exchanger

Heat Transfer  821 Foul at lower rate because of the single flow passage and curved flow path, thus preventing easy settlement of solids

Pressured drop is higher than the same shell and tube heat exchanger

Relative ease of cleaning

Maximum design pressure is 10 barg as the spiral construction limits the design pressure

The configuration reduces stress associated with differential thermal expansion

Gasket is special and assembly requires skill

Low maintenance cost

Figures 8.157–8.159 show spiral heat exchangers with different configurations, and process design of a spiral plate heat exchanger is provide by Coker [83].

8.21 Spiral Coils in Vessels Spiral coils can be useful in transferring heating and cooling from the helical or non-helical coil to and from a volume of liquid in a process vessel or storage tank. These coils in a stagnant or non-circulating tank are almost useless; therefore, the best arrangement is to use the coil in an agitated/missing tank. Batch heating and cooling will be reviewed later in the text.

8.22 Heat-Loss Tracing for Process Piping Many industrial processes require the transfer and storage of process fluids through pipelines and equipment. These fluids such as liquids, gases, vapors, slurries, suspensions have temperature characteristics that allow them to freeze, become viscous or condense at normal ambient temperatures. In order to prevent these problems, which typically occur during non-processing periods, it is essential that additional heat as well as insulation be added to the pipelines and equipment. Pipelines conveying viscous fluids are maintained at an elevated temperature by means of heat tracing. Pipelines containing vapors may also be heat traced to prevent components from condensing out. The heat loss from pipes is often reduced by thermal insulation. The thickness of insulation depends on an economic analysis involving both capital cost and the cost of heat loss from the insulated line. Heat tracing will normally be required when [4]: 1. Th  e lowest ambient site temperature will be below the freezing point of the liquid carried in the pipes. An exception must be for underground water pipes installed below the ground frost-level. Examples of liquid lines requiring heat tracing are: phosphoric acid, molten sulfur, glacial acetic acid, benzoic acid, cresol, naphthalene, phthalic anhydride, sorbitol, p-xylene and water. Sometimes heat tracing may be avoided by means of a ring main that keeps the liquid circulating through the pipework. 2. The liquid becomes highly viscous at a temperature above the ambient. Examples are certain crudes oils, fuel oils, polymeric materials, waxes, bitumen and tar residues, and caustic soda liquor. 3. The gas carried in the line has a dew point above the ambient temperature, and condensation of liquid from the gas is undesirable. Examples are: fuel gas in oil refineries where the liquid causes trouble in the gas burners; natural gas containing moistures that may cause freeze up of control valves or even the whole system; compressor suction lines (liquid is harmful to compressors); and H2S/water vapor (causes corrosion on condensation). Water lines are commonly insulated to avoid freezing. However, heat is invariably lost from insulated lines, and if the cooling resulting from this heat loss cannot be tolerated, heat tracing the lines becomes necessary. There are cases where blockages occur in pipelines, which cannot be unblocked by flushing with a solvent or by blowing in steam or air, unless they are heat traced. A process pipe requiring heat may be routed through the plant pipework in a complex

822  Chemical Process Engineering configuration of turns as well as elevations and drops. A tube or small-diameter pipe attached to the process pipe and carrying a heating medium for the addition of heat along the process pipework is commonly referred to as “heat tracing”. Many types of fluid heating media are used for heat tracing, such as steam, hot oil, or Dowtherm. Electric heating tape may be used. Steam tracing is selected for about 60% of pipe footage in chemical process plants. The fluid heating systems are simple in operation as any part of the pipework may be isolated by shutting valves. However, there is a possibility of fluid leakage, resulting to insulation damage and product contamination. Additionally, the temperature control is rather poor due to the large heat capacity of the fluid-heated system. Still, steam tracing is commonly employed because there is surplus low-pressure steam available in most plants. Since steam has a high latent heat, only a small quantity is required for a given heating load, and as steam has a high film heat transfer coefficient, condenses at constant temperature, and flows to the point of use without pumps. Lam and Samberg [127] have provided a comprehensive checklist and criteria between steam and electric tracing, and Table 8.57 in Appendix A lists a typical checklist for a petroleum refinery plant. The following equations will allow the design engineer to determine the heat loss and tracing requirements for any given pipeline, using any hot fluid medium as the heat source. The equations will calculate: • • • • •

The surface temperature of insulated traced pipe. Total heat transferred per 100 ft of pipe. Total heat transferred for the entire pipeline. Flow rate of hot media. Total number of heat tracers required with and without transfer cement.

Kern [70] and others have shown that the heat transferred through an insulated pipe involves four resistances. 1. 2. 3. 4.

 e film resistance on the inside wall of the pipe. Th Heat resistance through the pipewall. Heat resistance through the insulation. Air film resistance on the outside of the insulation.

The Equations 1. The average temperature of the hot medium, oF

Tm,avg = 0.5(Tmi + Tmo)

(8.300)

2. The average temperature of pipe and tracer, oF

Tavg = 0.5(Tm,avg + Tp)

(8.301)

3. The inside diameter of insulation, inch.

Di = OD + TAL

(8.302)

4. The outside diameter of insulation, inch.

Do = Di + 2Tk 5. Heat lost per foot of pipe, Q, Btu/h.ft.

(8.303)

Heat Transfer  823



Q=

2πK i (Ta − Ts ) D  ln  o   Di 

(8.304)

The heat loss per foot of pipe can be expressed in terms of the film heat transfer coefficient to air corrected for wind, Btu/h.ft oF



Q=

h a π Do (Ta − Tair ) 12

(8.305)

Using Equations 8.304 and 8.305 and rearranging the terms gives



Q=

2πK i (Ta − Ts ) h a πDo (Ts − Tair ) = 12  Do  ln    Di 

(8.306)

That is,

Ta – Ts = C(Ts – Tair)

(8.307)

where



C = (h a )

 Do   1   Do  ln  12   2K i   Di 

(8.308)

Equation 8.307 can be expressed in terms of Ts as follows:

Ts(1 + C) = Ta + CTair

(8.309)

and

Table 8.58  Values of ha for pipes in still air (ts – ta) oF (for an unlagged pipe, ts = tw). Nominal pipe dia, inch.

50

100

150

200

250

300

400

500

1/2

2.12

2.48

2.76

3.10

3.41

3.75

4.47

5.30

1

2.03

2.38

2.65

2.98

3.29

3.62

4.33

5.16

2

1.93

2.27

2.52

2.85

3.14

3.47

4.18

4.99

4

1.84

2.16

2.41

2.75

3.01

3.33

4.02

4.83

8

1.76

2.06

2.29

2.60

2.89

3.20

3.83

4.68

12

1.71

2.01

2.24

2.54

2.82

3.12

3.83

4.61

24

1.64

1.93

2.15

2.45

2.72

3.03

3.70

4.48

(Source: McAdams [82]).

824  Chemical Process Engineering Table 8.59  Correction factor for ha at different wind velocities (ts – ta) oF. Wind velocity, m/h

100

200

300

400

500

2.5

1.46

1.43

1.40

1.36

1.32

5.0

1.76

1.69

1.64

1.59

1.53

10.0

2.16

2.10

2.02

1.93

1.84

15.0

2.50

2.42

2.33

2.27

2.08

20.0

2.76

2.69

2.58

2.45

2.30

25.0

2.98

2.89

2.78

2.64

2.49

30.0

3.15

3.06

2.94

2.81

2.66

35.0

3.30

3.21

3.10

2.97

2.81

(For an unlagged pipe, ts = tw). (Source: McAdam [82]).



Ts =

Ta + CTair 1+ C

(8.310)

Equations 8.467 and 8.469 involve two unknowns, ha and Ts. An initial value of ha is assumed and Ts is calculated. McAdams [65] indicates that ha usually varies from 1.64 to 5.30 for pipes in still air, depending upon pipe size, surface, and air temperature. Table 8.58 gives values of ha for pipes in still air, and Table 8.59 lists the correction factor for ha at different wind velocities. 6. The combined convective and radiative heat transfer coefficient (hc + hr) is given by:



hc + hr =

D

0.19 o

564 [273 − (Ts − Tair )]

(8.311)

7. The wind factor, WF:



WF = C0 + C1 (Ts – Tair) + C2 (Ts – Tair)2

(8.312)

where C0 = 2.814 C1 = -0.00038857 C2 = -0.0000012857 8. The new film heat transfer coefficient to air corrected for wind, ha (Btu/h.ft2 oF)

ha = (hc + hr)(WF)

(8.313)

9. The total heat lost from pipeline, Qt, Btu/h

Qt = (Q)(LTotal)

(8.314)

Heat Transfer  825

where LTotal = total length of pipe, ft. 10. The flow rate of hot medium, W, lb/h



W=

Qt C p (Tmi − Tmo )

(8.315)

11. The number of tracers required without heat transfer cement is;



N TWOC =



Q



a(Tm,avg − Tp )

(8.316)

where

a = thermal conductance tracer to pipe without cement, Btu/h oF (ft of pipe)

12. The number of tracers required with heat transfer cement



N TWC =

Q b(Tm,avg − Tp )



(8.316a)

where b = thermal conductance tracer to pipe with cement, Btu/h oF (ft of pipe)   Table 8.60 lists the values of a and b. where a b C0, C1, C2 Cp Di Do ha hc + hr Ki LTOTAL NTWC NTWOC Q Qt Ta

= thermal conductance, tracer to pipe without heat transfer cement, Btu/h oF (ft of pipe, Table 8.60) = thermal conductance, tracer to pipe with heat transfer cement, Btu/h oF (ft of pipe, Table 8.60) = constants for wind factor equation. = specific heat of hot medium, Btu/lb oF = inside diameter of insulation, inch. = outside diameter of insulation, inch. = film heat transfer coefficient to air (corrected for wind, Btu/h ft2 oF) = combined convective and radiative heat transfer coefficients, (Btu/h ft2 oF) = thermal conductivity of insulation, Btu/h ft2 (oF/ft) = total pipe line length, ft = number of tracers required with heat transfer cement. = number of tracers required without heat transfer cement. = heat lost per ft of pipe, Btu/h ft. = total heat lost from pipeline, Btu/h = average temperature of pipe and tracer, oF Table 8.60  Thermal conductance tracer to pipe. Tube size, inch

a

b

3/8

0.295

3.44

1/2

0.393

4.58

5/8

0.490

5.73

(Source: Kohli [150]).

826  Chemical Process Engineering Tair TAL Tm,avg Tmi Tmo Tp Ts W WF

= air temperature, oF = allowance for tracer diameter, inch. = average temperature of hot medium, oF. = inlet temperature of hot medium, oF = outlet temperature of hot medium, oF = temperature in pipe, oF = outside surface temperature of insulation, oF = flow rate of hot medium, lb/h = Wind factor.

Blackwell [124] recommends approximately 1 ¼ inch between pipe and insulation to accommodate a ½ inch tracer line and heat transfer cement. He further recommends twice this value for three or more tracers. A 3/8 inch to 1 inch of space may be required for smaller tracers. Tracers are normally spaced equidistantly around the pipe, and are run parallel to it. In the case of heat lost from an insulated pipeline without tracing, the hot medium inlet and outlet temperatures are set to equal the temperature of the pipe.

Example 8.11 Determine the number of tracers required to maintain 100 ft of 8-inch (Schedule 40) process line (ID = 7.981 inch) at 500oF. Hot tracing medium is available at 630oF and has a heat capacity of 0.53 Btu/lb oF. The process line is covered with 2.5 inch of insulation, and this insulation has a thermal conductivity of 0.033 Btu/h ft2 (oF/ft). Design for 0oF air temperature and 20 mph winds. Use ½ inch tracers, the hot medium outlet temperature is 550oF. Allow approximately 1 ¼ inch between pipe and insulation to accommodate a ½ inch in tracer line and heat transfer cement. Assuming the trial film heat transfer coefficient is 4.0 Btu/h ft2 oF, and the thermal conductances tracer to ½ inch pipe are a= 0.393 and b = 4.58 Btu/h oF (ft of pipe) respectively.

Solution The Excel spreadsheet (Example 8.11.xlsx) program calculates the heat tracer requirements and heat loss for an insulated pipe line either with tracing or without tracing. The approximate number of tracers without the heat transfer cement of an 8-inch (Schedule 40) process line is 8. The heat transfer cement reduces the number required to 1.0. The circulation rate of the tracing medium is 755.3 lb/h, and the heat lost from 100 ft of pipe line is 26,716 Btu/h. For the same pipe without tracing, the heat lost from 100 ft of pipe line is 202.4 Btu/h ft and the total heat lost is 20,240 Btu/h RESULTS OF HEAT TRACER REQUIREMENTS FOR PIPELINES AND HEAT LOSS FROM AN INSULATED PIPELINE WITH TRACING   TOTAL PIPELINE LENGTH

100

ft.

TEMPERATURE IN PIPE

500

o

HOT-MEDIUM INLET TEMPERATURE

630

o

HOT-MEDIUM OUTLET TEMPERATURE

550

o

AIR TEMPERATURE

0

Btu/h

OUTSIDE PIPE DIAMETER

8.625

in.

INSIDE PIPE DIAMETER

7.981

in.

ALLOWANCE FOR TRACER DIAMETER

1.25

in.

INSULATION THICKNESS

2.5

in.

F F F

Heat Transfer  827 SPECIFIC HEAT CAPACITY OF HOT MEDIUM

0.53

Btu/lb.oF

4

Btu/h.ft2.oF

WITH CEMENT

0.393

Btu/h.ftoF

OUTSIDE SURFACE TEMPERATURE OF INSULATION

17.15

o

HEAT TRANSFER COEFFICIENT

1.32

Btu/h.ft2.oF

WIND FACTOR

2.807

FILM HEAT TRANSFER COEFFICIENT TO AIR   CORRECTED FOR WIND THERMAL CONDUCTANCE TRACER TO PIPE F

THE COMBINED CONVECTIVE AND RADIATIVE

HEAT TRANSFER COEFFICIENT TO AIR   CORRECTED FOR THE WIND

3.705

HEAT LOSS PER FOOT OF PIPE

267.16 Btu/h.ft

TOTAL HEAT LOSS FROM PIPELINE

26716

Btu/h

FLOW RATE OF HOT MEDIUM

755.3

lb/h

THE NUMBER OF TRACERS WITHOUT HEAT TRANSFER CEMENT

7.55

THE NUMBER OF TRACERS WITH HEAT TRANSFER CEMENT  

 

 

 

0.65

      

HEAT LOSS FROM AN INSULATED PIPE WITHOUT TRACING

Btu/h.ft2.oF

 

 

 

12.99

o

HEAT TRANSFER COEFFICIENT

1.299

Btu/h.ft2.oF

WIND FACTOR

2.81

  OUTSIDE SURFACE TEMPERATURE OF INSULATION

F

THE COMBINED CONVECTIVE AND RADIATIVE

HEAT TRANSFER COEFFICIENT TO AIR   CORRECTED FOR THE WIND

3.65

Btu/h.ft2.oF

HEAT LOSS PER FOOT OF PIPELINE

202.4

Btu/h.ft

TOTAL HEAT LOSS FROM PIPELINE

        20240

Btu/h

In SI Units The following equations are used for designing bare and cement heat tracers respectively [128]:



Q = UA T

(8.317)

Equations in determining the different areas across which heat transfer occurs:

 r −r  α = cos −1  1 2   r1 + r2 

(8.318)

Lai = (r1 – r2)(tan )

(8.319)

For bare tracing:

828  Chemical Process Engineering

Qta = Qal + Qpl

(8.320)

Q ta = 1.98451554 nL(π − α )(Ts − Tann )1.25 r20.75

(8.322)

L(Tp − Tamb )(2 π − (1.25 + 0.75n)(tan α ))  ln ( r1 rpinn ) ln ( rins r1 ) 1  + +  k ins k ins h o rins  

(8.323)

Q pl =

(8.321)

2nL(Tann − Tamb )(r1 − r2 )(tan α )  t ins + 1   k ins h o 

Q al =





 Ts + Tp + Tins  Tann =    3



(8.324)

Tin = 0.5Tsurf + 0.45Tp + 0.05Ts

(8.325)

k1 = Qta − Qal

(8.326)



k2 =



(2 π − (1.25 + 0.75n) α )  ln ( r1 rpinn ) ln ( rins r1 )  1 + +  k ins k ins h o rins   Tp = Tamb +

(8.327)

k1 k2

(8.328)

Equation (8.330) determines the hottest surface temperature for bare tracing, where q is the overall heat transmittance from cemented tracer to process fluid pipe:



  T  4  Tamb  4  54 − q =  0.548ε  surf  + 1.957 ( Tsurf − Tamb )     55.55    55.55

((

Tsurf



  r2 + t ins    (rs + t ins )ln  r2   = Ts −   (q) k ins   ho =

(Tsurf

q − Tamb )

)(

 2.85Vm + 1 )  

)

(8.329)

(8.330)

(8.331)

Heat Transfer  829 For cemented tracing, the following equations are:



L act =

(tan α )(r1 − r2 )  −1  (tan α )(r1 − r2 )  sin  tan   c1  

(8.332)

Qca + Qcp = Qal + Qpl

(8.333)

 (T − T )1.25  Q ca = (0.992257866nL)(0.4714r2 − 2α(r1 + c t ))  s ann0.25   (r2 + c t ) 

(8.334)

Qcp = 4qt nLr2 (Ts – Tp)

(8.335)

2nL(Tann − Tamb )  t ins + 1   k ins h o 

(8.336)

L(Tp − Tamb )(2 π − (1.25 + 0.75n)α )  ln ( r1 rpinn ) ln ( rins r1 ) 1  + +   kw k ins ho  

(8.337)





Q al =

Q pl =

c1 = Qca − Qal

c2 =

(8.338)

[2π − (1.25 + 0.75n)α]  ln ( r1 rpinn ) ln ( rins r1 ) 1  + +   kw k ins ho  

(8.339)

c3 = 4nqt r2

(8.340)

 c +c T +c T  Tp =  1 3 s 2 amb    c2 + c3



(8.341)

Equation (8.342) determines the hottest surface temperature for cemented tracing:

Tsurf

  r2 + c t + t ins      (rs + c t + t ins )ln  r2 = Ts −   (q) k ins  

(8.342)

where



  T  4  Tamb  4  54 − + 1.957 ( Tsurf − Tamb ) q =  0.548ε  surf     55.55   55.55  

((

where Ata = effective area of tracer exposure to annulus, m2

)(

 2.85Vm + 1 )  

)

(8.343)

830  Chemical Process Engineering Aal = effective area of annulus exposed to air, m2 Aca = effective area of cement exposed to air, m2 Acp = effective area of cement exposed to process fluid pipe, m2 Atl = effective area of tracer exposed to air, m2 Acl = effective area of cement exposed to air, m2 Dt = diameter of tracer pipe, m Tins = insulation thickness, m ct = cement thickness, m hc = heat transfer coefficient in still air, W/m2 K ho = heat transfer coefficient at surface, W/m2 K kw = thermal conductivity of pipe wall, W/m K kins = thermal conductivity of insulation, W/mK L = length of tracer connected to pipe, m Lai = length of insulation between annulus and air for bare tracer, m Lact = length of insulation between annulus and air for cemented tracer, m m = mass flow rate of steam, kg/h n = amount of bare or cemented tracers, tracers Ps = saturated steam pressure, kPa q = overall heat transmittance from cemented tracer to process fluid pipe, W/m2K Qta = energy transfer between tracer and annulus, J Qal = energy transfer between annulus and air, J Qpl = energy transfer between process pipe and air, J Qca = energy transfer between cement and annulus, J Qcp = energy transfer between cement and process fluid pipe, J Qtl = energy transfer between cement and air, J Qcl = energy transfer between cement and air, J r1 = outer radius of steam tracer pipe, m r2 = inner radius of process fluid pipe, m rpinn = inner radius of process fluid pipe, m Ts = saturated steam temperature, K Tp = process fluid temperature, K Tann = annulus temperature, K To

fo

Tm Pipe Td

Dp

Do Dl

Fun

nT Dr

ko insulation

Tracer

Figure 8.160A  Cross-sectional view of pipe with bare single tracer. Requirements may dictate 2 or 3 tracer pipes/tubes strapped to pipe at generally equal spacing around circumferences, then insulated. (Used by permission: Foo, K. W., Hydrocarbon Processing, V. 73, No. 1, Part 1, © 1994, Gulf Publishing Company).

Heat Transfer  831 Ta

Thermal conducting cement fo

Am Td

Dr nT

Ar z = Dr

Do Dl

Dp

Tn Tr

ko insulation

Pipe

Figure 8.160B  Cross-sectional view of pipe and tracer with thermal conducting cement. (Used by permission: Foo, K. W., Hydrocarbon Processing, V. 73, No. 1, Part 1, © 1994, Gulf Publishing Company).

Tamb = ambient design temperature, K Tsurf = outer surface temperature, K Tins = average insulation temperature, K Vm = wind velocity, m/s α = angle used in determining area, radians = emissivity of insulation lagging Figures 8.160–8.162 show various configurations of tracer and lagging, fittings, tracer placement on pipe using heat transfer cement, installation of heat transfer cement with tracing on valves, pumps and pipe respectively. Figure 8.163 shows self-regulating heat tracer for pipe and vessels. de Lange [128] has developed an Excel spreadsheet program based upon the above equations for bare and cemented tracers; it can be accessed from www.cheresources.com. Lagging

Aluminum foil

Product

Tracer

Wire netting Lagging

Product

Tracer

Lagging

Product

Tracer

Figure 8.160C  Various configurations of tracer and lagging.

832  Chemical Process Engineering 3/8 in. O.D. or 1/4 in. I.D.

Steam

Steam trap

Steam Steam trap

Steam trap

Steam trap Steam 1/2 in. O.D.

3/8 in. O.D. or 1/4 in. I.D.

3/8 in. O.D.

Steam

Steam trap

Tracer lines around pump easing

Steam trap

Typical instrument tracing

Figure 8.160D  How various pipe fittings, pumps, instruments are treated with steam tracing.

HAND GUN TRACER PROCESS PIPE

20° MAXIMUM

2D Typical Cross Section FILLET OF T40 OR T65 HEAT TRANSFER CEMENT

Installation of Tracing on Straight Runs of Pipe: Tracers are to be run parallel and in direct contact with the process pipe where possible. Tracer location on pipe is to be where most

STAINLESS STEEL BANDING & SEALS

accessible. If more than two tracers are used, they should be equally spaced circumferentially around the pipe.

Figure 8.161  Tracer placement on pipe using heat transfer cement. (Used by permission: Bul T-109M © 1994. Thermon® Manufacturing Co./Cellex Div).

Heat Transfer  833

THERMON TYPE T-80 OR T-85 HEAT TRANSFER CEMENT

STAINLESS STEEL BANDING & SEALS

INSULATION APPROX. 0.3" 1/2 × .020 S.S BANDING

D 2 TO 3D

TUBULAR TRACER

D 2 TO 3D METAL SURFACE

CROSS SECTION OF HEAT TRANSFER CEMENT ON PUMPS, VALVES & OTHER IRREGULAR SURFACES

THERMON T-80 OR T-85 HEAT TRANFER CEMENT

THERMON T-80 OR T-85 HEAT TRANFER CEMENT

THERMON T-80 OR T-85 HEAT TRANFER CEMENT TUBING CONNECTION, COMPRESSION TYPE OR BRAZED

STAINLESS STEEL BANDING & SEALS

180° BEND ON TUBULAR TRACERS

OFFSET ON TUBULAR TRACERS

NOTE: LARGER PIPE ELLS MAY REQUIRE ADDITIONAL BANDS TO SECURE.

STANDARD TUBULAR TRACERS

THERMON T-80 OR T-85 HEAT TRANFER CEMENT

INSTALLATION OF TUBULAR TRACER & HEAT TRANSFER CEMENT ON PIPE ELBOW

STANDARD TUBULAR TRACERS

ALTERNATE

STAINLESS STEEL BANDING & SEALS

THERMON T-80 OR T-85 HEAT TRANFER CEMENT

ALTERNATE STAINLESS STEEL BANDING & SEALS

PIPE FLANGE

CONNECTION OF TUBULAR TRACERS ON PROCESS PIPING

(2) 360° COILS

INSTALLATION OF TUBULAR TRACER & HEAT TRANSFER CEMENT ON PIPE FLANGE

Figure 8.162  Installation of heat transfer cement with tracing on valves, pumps, and pipe. (Used by permission: Bul. T-109-M, © 1994., Thermon® Manufacturing Co./Cellex Div.).

Chemelex BTV and QTVR heating cables share a similar construction, as illustrated at right.

Braided tin-copper shield and outer jacket of Tefzel* (optional)

Self-regulating. conductive-core heating element Insulating jacket

Copper bus wire

Chemelex® heating systems consist of insulated, electric heating cables with voltage applied to two parallel bus wires. Because of this parallel construction, all Chemelex® heating cables can be cut to any length and spliced and “teed” in the field.

Figure 8.163  Self-regulating heat tracer for pipe and vessels. Some simpler designs have temperature monitoring and power control. (Used by permission: Bul. (P6909) H53398 4/94. © Raychem Corporation, Chemelex® Division).

8.23 Boiling and Vaporization 8.23.1 Boiling Boiling occurs when a liquid comes in contact with a solid surface that is maintained at a temperature higher than the saturation temperature of the liquid at the existing pressure. It may occur under various conditions as illustrated below. When the heated surface is submerged below the free surface of a quiescent fluid, the boiling characteristic is referred to as pool boiling. In this situation, heat is transferred from the solid surface to the liquid by free convection.

834  Chemical Process Engineering The formation of vapor bubbles takes place at the surface, and the bubbles grow while moving up and subsequently collapse near the free surface. Boiling can be divided into various categories depending on the mechanisms occurring and the geometric situation. The principal mechanisms of boiling are: 1. N  ucleate boiling: in which bubbles are formed by nucleation at the solid surface. In highly subcooled boiling these bubbles rapidly collapse, transferring their latent heat to the liquid phase and thus heating it up towards the saturation temperature. 2. Convective boiling: in which heat is transferred by conduction and convection through a thin liquid film. The liquid then evaporates at the vapor-liquid interface with no bubble formation. 3. Film boiling: where the heated surface is blanketed by a film of vapor and the heat is conducted through the vapor, the liquid vaporizes at the vapor-liquid interface. The two main geometric situations are: 1. P  ool boiling: where the boiling occurs at a heated solid surface in a pool of liquid which apart from any convection induced, by the boiling, is stagnant. 2. Flow boiling: where the liquid is pumped through a heated channel typically a tube. It is generally assumed that only one of the boiling types occurs at once, and that at some point the mechanism suddenly switches from one type of boiling to the other. In fact, the mechanisms can coexist and as the quality increases, convective boiling gradually supplants nucleate boiling. Figure 8.164 shows a schematic of boiling curve, showing the regions in the curve. Direct and visual photographic evidence shows that: 1. The nucleate boiling region BC in Figure 8.165 consists of two parts: (a) The isolated bubble region, where bubbles behave independently as illustrated in Figure 8.166A;   and

E The regions of the curve

D

F to D to E: film boiling

Heat flux, (W/m2)

106

A to B: natural- convection single-phase liquid – there is no boiling in this region B to C: nucleate boiling C

105

B

F

A 1

Figure 8.164  Boiling curve from a heat flux-controlled surface.

10

ΔTsat (K)

100

1000

Heat Transfer  835 (a)

(b)

(c)

Figure 8.165  Visualization results in nucleate and film boiling.

(b) Th  e slugs and column region, where the bubbles start to merge and to depart from the heated surface by means of jets which then form large bubbles, or slugs, above the surface (Figure 8.166B). 2. Th  e film boiling region (FDE in Figure 8.164) illustrates where the heated surface is covered with a layer of vapor (Figure 8.193C). The liquid is not in contact with the heated surface. The vapor surface is unstable and bubbles are released from it into the liquid. 3. The transition boiling region (FC in Figure 8.164) is a complex region where parts of the surface are in film boiling regime and parts in the nucleate boiling regime of the slugs and columns type. Figures 8.166A and B illustrate a typical flux curve for water and hydrocarbons. In the region 1-2, the liquid is being heated by natural convection; in 2-3 the nucleate pool boiling occurs, with bubbles forming at active sites on the heat transfer surface, natural convection currents being set up. Q/A varies at tn where n is 3-4, and the peak flux is at point 3, corresponding to the critical t for nucleate boiling; at point 3 film boiling begins; and at 4-5-6 106

6

Heat Flux, Q/A, Btu/(hr.)(sq. ft.)

Peak 4

3

5

105

104

2 1

103

1

10

100

1,000

10,000

Temperature Difference, Δt, °F. (Between Heating Source and 212°F.) Regions: 1–2 = Natural Convection 2–3 = Nucleate Boiling 3–4 = Partial Film Boiling 4–5–6 = Film Boiling

Figure 8.166A  Heat flux for boiling water at 212oF. (Used by permission: McAdams, W. H., Heat Transmission, 3rd. Ed. © 1954. McGrawHill Book Co., All rights reserved).

8 6 4 3 300 psia. 500 psia.

8.4

0.3

50 psia. rs ec . 300 psia. 500 psia.

44

0.4

pe

0.6

ft.

1.0 0.8

ft.

ft. pe pe r se 24 c rs .3 ec . 40 ft. 0, . pe 50 0p rs ec sia . .

2

88

HEAT FLUX q, Btu. per sq. in. sec.

836  Chemical Process Engineering

0.2 30 40 60 80 100 200 400 ΔT ( = Tw – Ta), °F.

600

1000

1500

.7 300 psia.

6

500 psia.

4

3 VIEW

44

ft.

pe

rs

ec .

HEAT FLUX q, Btu. per sq. in. sec.

400 psia. 5

2 400

500

600

700 800 900 1000 ΔT ( = Tw – Ta), °F.

1500

Heat-transfer behavior of a mixture of hydrocarbon fuels (ref. 1)

Figure 8.166B  Heat transfer behaviour of a mixture of hydrocarbon fuels. (Used by permission: Jens, W. H. Mechanical Engineering, V. 76, Dec. 1954, p. 981. © American Society of Mechanical Engineers. All rights reserved).

film boiling occurs. In film boiling, heat is transferred by conduction and radiation through a film on the heating surface. Note that the rate of effective heat transfer decreases beyond point 3, and it is for this reason that essentially all process heating/boiling equipment is designed to operate to the left of point 3. Various guidelines have been proposed to limit the heat flux, Q/A and U to avoid film boiling, such as those given by Kern [70]: Umax = 300 Btu/h ft2 oF (1,703 W/m2 K) for organics, Umax = 1,000 Btu/h ft2 oF (5,768 W/m2 K) for water and (Q/A)crit = 12,000 Btu/h ft2 oF (37,855 W/m2 K) for inorganics. The latter does not permit the use of large temperature differences for natural-circulation vaporizers and reboilers; for forced circulation, the flux limit is relaxed to 20,000 Btu/h ft2 oF (63,092 W/m2), allowing for a higher ∆T driving force [83]. These guidelines for limiting the heat flux are considered conservative. The maximum heat flux for nucleate boiling depends on the physical properties of the boiling fluid, and the geometry of the heat exchanger. For example, forced vs. natural circulation, boiling inside vs. outside the tubes; smooth vs. enhanced tubes surfaces, etc. The maximum heat flux is generally expressed

Heat Transfer  837

(c)

Heat flux, (Btu/ft2 h)

105 104

(d)

103 102

(e)

(b) (a)

101 1

10

100 ΔT = Tsurface – Tsat, (°F)

1000

Figure 8.167  Typical saturated pool boiling curve.

as a function of the reduced pressure, Pr = P/Pc, and Qmax decreases as the pressure approaches the critical pressure. Generally, the critical heat flux for a single tube is derived from the critical pressure correlation to which appropriate geometry factors – e.g., a bundle correction factor for boiling outside the tubes, factors for enhanced surfaces are applied.

8.23.2 Vaporization Mechanisms or processes occur during which a liquid at the saturation temperature may be converted to a vapor by the addition of heat. If the boiling or vaporization occurs on a hot surface in a container in which the liquid is confined, the process is referred to as pool boiling. There are several different mechanisms by which pool boiling occurs, and these depend upon the temperature difference between the surface and the liquid, and to a lesser extent upon the nature of the surface and the liquid. Figure 8.167 illustrates the classic curve of heat flux vs. temperature difference between surface and liquid saturation temperature for saturated pool boiling. Table 8.61 in Appendix A gives the descriptions of the regimes in Figure 8.167.

8.23.3 Vaporization During Flow Certain classes of equipment, e.g., pump-through reboilers and thermosyphon operate with a net liquid velocity past the transfer surface. Under these conditions, the boiling processes are modified by a shear stress operating on the layer of liquid immediately adjacent to the hot surface. Generally, natural convection boiling phenomena will be suppressed by forced convection, and the nucleation process will decline to some degree, and possibly completely. With complete suppression, the superheated liquid is transported from the tube wall by turbulent eddies to the vapor-liquid interface, where vaporization takes place. The heat transfer coefficient under these conditions is greater than that which would exist if nucleate boiling only occurs. Film boiling may also occur under forced convection vaporization if the wall temperature is high enough. However, in this case, a mist flow may happen, in which the liquid inventory is carried along in the vapor as tiny droplets, which are heated and vaporized by contact with the superheated vapor. This process has very low heat transfer coefficients and should be avoided when designing vaporization equipment.

8.24 Heating Media The heating media can be steam, hot oil or process stream and are the most common in the refinery and petrochemical industries. Steam: In most cases, medium or low pressure steam is introduced to the reboiler rather than superheated steam. Superheated steam will create a dry wall boiling zone close to the tubesheet (Figure 8.168A). The dry wall area can be

838  Chemical Process Engineering Riser

(a) Maxinum liquid level

Reboiler

Steam

Downcomer Condensate pot

Steam condensate

Bottom of reboiler should be elevated just above top of condensate pot. Distillation column

(b)

Controlled Liquid level

Start up bypass To pump

Reboiler

Condensate pot regulates liquid level in exchamger tubes. Physical relationship between liquid level in condensate pot and required liquid in exchanger tubes is important. Condensate

Figure 8.168A & B  Piping arrangement for horizontal thermosyphon reboilers. (Source: R. Kern, How to Design Reboilers Systems, Chemical Engineering, August 1975.)

quickly fouled and thus create a high tube wall temperature that may cause tube failure. Additionally, as the thermal design of the desuperheating zone is normally oversized due to variation of steam superheating, a desuperheater may be installed if the superheat temperature is too high; a steam flow control cascaded with tower bottom temperature or heat input is used. A condensate pot or steam trap as shown in Figure 8.168B could be installed downstream of the reboiler to improve energy efficiency. Coker has reviewed various steam traps employed in the chemical process industries [83]. Process streams: The process streams are used as a heat medium to improve energy efficiency in many reboiler services. However, many of these applications present problems of film boiling due to high temperature difference between the heat medium and boiling liquid. This results in increasing reboiler size and the tendency for fouling. To avoid film boiling, the heating medium temperature should not exceed 80oF (27oC) over boiling liquid bulk temperature. The hot process stream can be cooled in another heat exchanger before entering the reboiler. The boiler heat duty can be regulated by a temperature bypass control. Hot oil: Most hot oil reboilers in chemical or gas plants do not have steam available or the steam temperature is too low. The hot oil system may have equivalent capital investment and operating cost like a steam system. However, it does not require boiler water treatment and blowdown disposal. Boiling flow regimes: Figure 8.167 shows the four boiling flow regimes, namely: natural convection (subcooled), nucleate, transition and film. A good reboiler design shall meet the process requirement and provide stable and flexible tower operation. Optimizing reboiler design requires a team effort of various disciplines, namely: process, fluid system, piping and heat transfer specialist. The heat transfer specialist must ensure to design the reboiler in the nucleate flow regime, which is left of the peak heat flux at the end of the nucleate zone. If it is impossible to design

Heat Transfer  839

Process data

Yes

Is vaporization ratio over 30%?

No

Yes

Is vapor to be superheated?

Is boiling liquid high fouling?

Yes

No Yes

Is boiling liquid very viscous?

No Is isothermal or narrow range boiling?

No No

Yes

Is boiling side slurry flow? No

Yes

Huge heat duty and circulation rate?

Yes Is fraction of preheating duty to total duty < 10%?

No

No Is liquid viscosity > 0.5?

Yes Kettle

Is vaporization ratio < 40%? Yes

Is vaporization ratio < 25%?

No Is reboiler duty very small?

Is reboiler one theoretical stage?

Yes

No Yes

Yes Stab in reboiler

No

No

Forced circulation reboiler

No

Horizontal circulation Yes

Horizontal oncethrough

Vertical oncethrough

Wide boiling range?

Yes

Is reboiler one theoretical stage? No “H” shell

Figure 8.169  Flow chart for selecting reboilers [147].

Yes “J” shell

No Vertical recirculation

840  Chemical Process Engineering the reboiler in the nucleate regime due to heat medium temperature, then the design in the stable film boiling regime with extra heat transfer area is preferable. Never design a reboiler in the transition boiling regime. Enhanced heat transfer surface: This is considered when pinch point is less than 10oF. Low-fin tubes are good for clean boiling service applications with 6 – 10oF temperature difference, otherwise high-flux tubes are used. If enhanced heat transfer surfaces are used, then a removable bundle is designed for easy access for inspection and cleaning.

Heat Flux Limit Chen [148] has provided a rule of thumb for the maximum heat flux recommended for nucleate boiling design: Btu/ft2-h

W/m2 oC

Kettle reboiler

9,000

51102

Thermosyphon reboiler

15,000

85170

Stripper reboiler

25,000

141950

Figure 8.169 shows the flowchart for selecting reboiler types.

8.25 Batch Heating and Cooling of Fluids Heating and cooling of process fluids in a batch-operated vessel is common in the chemical process industries. The process is an unsteady state in nature, because the heat flow and/or the temperature vary with time at a fixed point. The time required for the heat transfer can be modified by increasing the agitation of the batch fluid, the rate of circulation of the heat transfer medium in a jacket and/or coil, or the heat transfer area. Bondy and Lippa [129] and Dream [130] have compiled a collection of correlations of heat transfer coefficients in agitated vessels. Batch processes are sometimes disadvantageous because: • • • •

Use of the heating or cooling medium is intermittent. The liquid being processed is not readily available. The requirements for treating time requires holdup. Cleaning or regenerations is an integral part of the total operating period.

The variables in batch heating or cooling processes are surface requirement, time and temperature. Heating a batch may be done by external means (e.g., a jacket or coil) or by withdrawing and recirculating process liquid through an external heat exchanger. In either case, assumptions are made to facilitate calculation, namely: 1. 2. 3. 4. 5. 6. 7.

 e overall heat transfer coefficient U is constant for the process and over the entire surface. Th Liquid flowrates are at steady state. Specific heats are constant for the process. The heating or cooling medium has a constant inlet temperature. Agitation gives a uniform batch fluid temperature. There is no phase change. Heat losses are negligible.

The following discusses various heating or cooling process conditions in a batch vessel and the processing time relationships.

Batch Heating: Internal Coil: Isothermal Heating Medium When an agitated batch containing M of fluid with specific heat c and initial temperature t is heated using an isothermal condensing heating medium T1, the batch temperature t2 at any time θ can be derived by the differential

Heat Transfer  841 T1

T2

M

t

Figure 8.170  Agitated batch vessel.

heat balance. For an unsteady state operation as shown in Figure 8.170, the total number of heat transferred is q , and per unit time θ is:



I dq =

II

III

IV

dq ′ dt = Mc dθ dθ

=

Accumulation



in the batch

UADt

(8.344)

Transfer rate

where



t = T1 − t

(8.345)

dt = UA∆t dθ

(8.346)

Equating III and IV gives



Mc

Rearranging Equation 8.346 gives

dt UA = ⋅ dθ ∆t Mc



(8.347)

Integrating Equation 8.347 between the limits gives t2



∫ t1

θ

dt UA dθ = T1 − t Mc

∫ 0

Integrating Equation 8.348 from t1 to t2 while the batch processing time passes from 0 to θ yields:



 T − t  UA ln  1 1  = ⋅θ  T1 − t 2  Mc

(8.348)

842  Chemical Process Engineering or



or θ =

Mc  T1 − t1  ln UA  T1 − t 2 

(8.349)

where A = heat transfer surface area. c = specific heat of batch liquid. M = weight of batch liquid. T1 = heating medium temperature. t1 = initial batch temperature. t2 = final batch temperature. U = overall heat transfer coefficient. θ = time

Example 8.12. Batch Heating: Internal Coil Isothermal Heating Medium A tank containing 50,000 lb (22,679.5 kg) material with a specific heat of 0.5 Btu/lb.oF (2.1 kJ/kg.K) is to be heated from 68oF (293K) to 257oF (398K). The tank contains a heating coil with a heat transfer surface of 100 ft2 (9.29 m2) and the overall heat transfer coefficient from the coil to the tank contents of 150 Btu/h.ft2 oF (850 W/m2 K). Calculate the time required to heat the tank contents with steam condensing at 320oF (433K).

Solution Select and apply the appropriate heat transfer formula. When heating a batch with an internal coil with an isothermal heating medium, the following equation applies:

 T − t  UA ⋅θ ln  1 1  =  T1 − t 2  Mc ln



 W m 2 kg ⋅ K  (850)(9.29)  433 − 293  = θ ⋅ ⋅   433 − 398  (22,679.5)(2.1)(103 )  m 2 .K kg J  

(1.386)(22,679.5)(2.1)(103 ) hr θ= (850)(9.29)(3600) = 2.32 h.

An Excel spreadsheet program (Batch Heating: Internal Coil Isothermal Heating Medium.xls) has been developed for Example 8.12.

Batch Reactor Heating and Cooling Temperature Prediction Startup of a jacketed batch reactor requires control of the heat-up and cool-down rates. This involves determining and setting the jacket heat transfer fluid temperatures. An alternative is to make a trial heat-up and incorporate the results into a time-dependent heat transfer equation:



θ=

Mc  T1 − t1  ln UA  T1 − t 2 

(8.350)

Heat Transfer  843 Equation 8.350 can also be used to calculate the heat-up time for non-isothermal heating (e.g. by hot-water jacketing), provided that the difference between the outlet and inlet jacket temperatures is not greater than 10% of the difference between the batch and average water temperature [149]. Assuming that M, c, U and A are constants, where

UA Mc

(8.351)

1  T1 − t1  ln K  T1 − t 2 

(8.352)

K=

Equation 8.350 becomes



θ=

Rearranging Equation 8.352 gives the jacket temperature as a function of times as:



T1 =

t1 − t 2 eKθ 1 − eKθ

(8.353)

Therefore, by taking a series of readings during a trial heat-up, K can be determined. The heat-up and cool-down times for varying jacket temperatures can be predicted.

Example 8.13: Batch Reactor Heating and Cooling Temperature Prediction Assume that in Example 8.12, the overall cycle time for a batch reaction is 8 h. The cycle time will include 2 h for heat-up and 3 h for cool-down. The batch will be heated from 20oC to reaction temperature of 60oC, and then cooled to 35oC. Using a hot water jacket temperature of 80oC, it took 15 min. to heat the batch from 20oC and 30oC. Calculate the jacket temperatures required to heat-up and cool-down.

Solution From Equation 8.351

K=

 J 1 kg ⋅ K  UA (850)(9.29) = ⋅ m2⋅ ⋅ 3   2 kg 10 J  Mc (22,679.5)(2.1)(1,000)  s ⋅ m K

K = 0.00017 s −1

The jacket temperature required for a 2 h heat-up can be obtained from Equation 8.353 as:

t1 − t 2 eKθ T1 = 1 − eKθ =

20 − 60e

1    0.00017 × 2 × 3600s s

1 − e = 77°C

The jacket temperature required for a 3h cool-down is:

1   0.00017 × 2 × 3600s   s

844  Chemical Process Engineering

T1 = =

t1 − t 2 eKθ 1 − eKθ 60 − 35e

1    0.00017 s × 3× 3600 s 

1    0.00017 s × 3× 3600 s 

1− e = 30.3°C

A Microsoft Excel spreadsheet (Batch Reactor Heating and Cooling Temperature Prediction.xls) was developed for predicting the jacket temperature required for either heating up or cooling down reactants in a batch reactor.

Batch Cooling: Internal Coil Isothermal Cooling Medium Consider the same arrangement as before containing M of liquid with specific heat c and initial temperature T1 cooled by an isothermal vaporizing medium of temperature t1. If T is the batch temperature at any time , then



dq ′ dT = − Mc = UA∆t dθ dθ

(8.354)

t = T – t1

(8.355)

dT = UA∆t dθ

(8.356)

where

Then



− Mc

Substituting Equation 8.355 into Equation 8.356 and rearranging gives: T2



dT − = T − t1

∫

T1

θ

∫ 0

UA ⋅ dθ Mc

(8.357)

Integrating from T1 to T2, while the time passes from 0 to θ gives:



 T − t  UA ln  1 1  = ⋅θ  T2 − t1  Mc

or

where A = heat transfer surface area.

or θ =

Mc  T1 − t1  ln UA  T2 − t 1 

(8.358)

Heat Transfer  845 c = specific heat of batch liquid. M = weight of batch liquid. T1 = initial batch temperature. T2 = Final batch batch temperature. t1 = cooling medium temperature. U = overall heat transfer coefficient. θ = time

Example 8.14 Batch Cooling: Internal Coil, Isothermal Cooling Medium A tank containing 50,000 lb (22,679.5 kg) material with a specific heat of 0.5 Btu/lboF (2.1kJ/kg.K) is to be cooled from 230oF (383K) to 140oF (333K). The tank contains a cooling coil with a heat transfer surface of 100 ft2 (9.29 m2) and the overall heat transfer coefficient from the coil to the tank contents of 150 Btu/h.ft2 oF (850 W/m2.K). Calculate the time required to cool the tank contents with a cooling medium at 90oF (305K).

Solution Applying Equation 8.358, the time required to cool the tank contents is:



θ=

Mc  T1 − t1  ln UA  T2 − t 1 

(8.358)

where M = 50,000 lb c = 0.5 Btu/lb.oF U = 150 Btu/h.ft2.oF A = 100 ft2 T1 = 230oF T2 = 140oF t1 = 90oF

(50,000)(0.5)  230 − 90  ln  140 − 90  (150)(100) = 1.72 hr.

θ= Calculations: SI units

where M = 22,679.5 kg c = 2.1kJ/kg.K U = 850 W/m2.K A = 9.29 m2 T1 = 383K T2 = 333K t1 = 305K

θ=

Mc  T1 − t1  ln UA  T2 − t 1 

(8.358)

846  Chemical Process Engineering

θ=



(22,679.5)(2.1)  1000   383 − 305  ln (850)(19.29)  3600   333 − 305 

1 1 1   1000 J ⋅ ⋅ 2⋅  kg.  J kg.K m 3600 s    hr  s m2 K

= 1.72 hr.



An Excel spreadsheet (Batch Cooling: Internal Coil Isothermal Cooling Medium.xls) has been developed for Example 8.14.

Batch Heating: Non-Isothermal Heating Medium The non-isothermal heating medium has a constant flow rate Wh, specific heat Ch, and inlet temperature T1, but a variable outlet temperature. For an unsteady state operation:

I



II

III

IV

dq ′ dt = Mc = Wh C h (T1 − T2 ) = UA∆t LMTD dθ dθ

(8.359)

The log mean temperature difference ΔtLMTD is:



∆t LMTD =

T1 − T2  T −t ln  1   T2 − t 

(8.360)

Equating III and IV in Equation 8.359 and rearranging gives:



Wh C h (T1 − T2 ) = UA

T1 − T2  T −t ln  1   T2 − t 

(8.361)

Equation 8.361 becomes:



UA  T −t ln  1  =  T2 − t  Wh C h



T1 − t = e Wh Ch T2 − t

Rearranging Equation 8.363 gives:

(8.362)

UA

(8.363)

Heat Transfer  847

T2 = t +



T1 − t e

UA Wh C h



(8.364)

where UA

where K1 = e Wh Ch



(8.365)

Equating II and III in Equation 8.359 and substituting Equation 8.364 into Equation 8.359 gives:

Mc

dt   T − t  = Wh C h T1 −  t + 1    K1   dθ   K − 1 = Wh C h  1  (T1 − t)  K1 





(8.366)

Rearranging Equation 8.366 and integrating from t1 to t2 while the processing time passes from 0 to θ gives: t2



∫ t1

dt = T1 − t

θ

∫ 0

Wh C h  K1 − 1  dθ Mc  K1 

(8.367)

Integrating Equation 8.367 gives:



 T − t   Wh C h   K1 − 1  ln  1 1  = θ  T1 − t 2   Mc   K1 

(8.368)

 K1   Mc   T1 − t1  ln or θ =   K1 − 1   Wh C h   T1 − t 2 

(8.369)

or



where A = heat transfer surface area c = specific heat of batch liquid Ch = heating medium specific heat M = weight of batch liquid T1 = heating medium temperature t1 = initial batch temperature t2 = final batch temperature U = overall heat transfer coefficient Wh = heating medium flowrate θ = time

Example 8.15: Batch Heating with Non-Isothermal Heating Medium A tank containing 50,000 lb (22,679.5 kg) material with a specific heat of 0.5 Btu/lboF (2.1 kJ/kg.K) is to be heated from 68oF (293K) to 257oF (398K). The tank contains a heating coil with a heat transfer surface of 100 ft2 (9.29 m2) and the overall heat transfer coefficient from the coil to the tank contents of 150 Btu/h.ft2.oF (850 W/m2.K). Calculate the time required to heat the tank contents with steam condensing at 320oF (433K) and the flow rate of 10,000 lb/h (4535.9 kg/h).

848  Chemical Process Engineering

Solution Select and apply the appropriate heat transfer formula. When heating a batch with internal coil and a non-isothermal heating medium, the following equation can be applied.

dq ′ dt = Mc = Wh C h (T1 − T2 ) = UA∆t LMTD dθ dθ



(8.359)

where UA

where K1 = e Wh Ch ft 2  150 × 100   Btu = exp  ⋅    10,000 × 1.043   h . ft 2 .o F lb Btu ⋅  h lb.° F = 4.2129



   

(8.365)

and

 K1   Mc   T1 − t1  θ= ln  K1 − 1   Wh C h   T1 − t 2  =

 4.2129   50,000 × 0.5  ln  320 − 68   4.2129 − 1   10,000 × 1.043   320 − 257 

= 4.36 h.



(8.369)

Calculations: SI Units

K1 = e

UA Wh C h



{

}

850 × 9.29 × 3600 1  J m2 × ⋅  h 4535.9 × 4.366 1000  sm 2 .K kg 1000 J ⋅ ⋅  h kgK 3600 s  = 4.20156

= exp

    

 K1   Mc   T1 − t1  ln θ=  K1 − 1   Wh C h   T1 − t 2  =

 22679.5 × 2.1   4.2016  ln  433 − 293   4535.9 × 4.366   4.2016 − 1   433 − 398 

= 4.38 h.

An Excel spreadsheet (Batch Heating and Cooling with non-isothermal Heating Medium.xls) has been developed for Example 8.15.

Heat Transfer  849

Batch Cooling: Non-Isothermal Cooling Medium When cooling a batch with internal coil and a non-isothermal cooling medium, the following equation can be applied.



dq ′ dT = − Mc = Wc C c (t 2 − t1 ) = UA∆t LMTD dθ dθ

(8.370)

where

K2 = e



UA Wc Cc



and



 T − t   Wc C c   K 2 − 1  ln  1 1  = θ  T2 − t1   Mc   K 2 

or



 K 2   Mc   T1 − t1  ln θ=  K 2 − 1   Wc C c   T2 − t1 

(8.371)

where A = heat transfer surface area c = specific heat of batch liquid Cc = coolant specific heat M = weight of batch liquid T1 = initial batch temperature T2 = final batch temperature t1 = initial coolant temperature U = overall heat transfer coefficient Wc = coolant flow rate θ = time

Example 8.16: Batch Cooling Non-Isothermal Cooling Medium A tank containing 6613.87 lb (3000 kg) material with a specific heat of 0.8 Btu/lboF (3.3489 kJ/kg.K) is to be cooled from 230oF (383K) to 140oF (333K). The tank contains a coil with a heat transfer surface are of 43.0 ft2 (3.994m2) and the overall heat transfer coefficient from coil to the tank contents is 122.9 Btu/h.ft2.oF (697.8 W/m2.K). Calculate the time required to cool the tank contents, if cooling water is available at 89.6oF (305K) and at a flowrate of 4409.26 lb/h (2000 kg/h).

Solution Select and apply the appropriate heat transfer formula. When cooling a batch with internal coil and a non-isothermal cooling medium, the following equation can be applied.



dq ′ dT = − Mc = Wc C c (t 2 − t1 ) = UA∆t LMTD dθ dθ

(8.370)

850  Chemical Process Engineering

where

K2 = e

UA Wc Cc



ft 2  122.9 × 43.06   Btu ⋅   4409.26 × 1.0   h . ft 2 .° F lb Btu ⋅  h lb.° F = 3.3208

K 2 = exp

   

 K 2   Mc   T1 − t1  ln θ=  K 2 − 1   Wc C c   T2 − t1  =

 6613.87 × 0.8   3.3208  ln  230 − 89.6   4409.26 × 1.0   3.3208 − 1   140 − 89.6 



= 1.76 h.

(8.371)

Calculations: SI units

kg .K  J m2  697.8 × 3.994 3600   × ⋅ ⋅ 3   2  2000 × 4.184 1000   s . m .K kg h 10 J  ⋅   h 3600 s = 3.3228

K 2 = exp

 K 2   Mc   T1 − t1  ln θ=  K 2 − 1   Wc C c   T2 − t1  =

 3000 × 3.3489   3.3228  ln  383 − 305   2000 × 4.184   3.3228 − 1   333 − 305 

= 1.76 h.



(8.371)

An Excel spreadsheet (Batch Heating and Cooling with non-isothermal Cooling Medium.xls) has been developed for Example 8.16.

Batch Heating: External Heat Exchanger, Isothermal Heating Medium Figure 8.171 illustrates the arrangement in which the fluid in the tank is heated by an external heat exchanger. The heating medium is isothermal; therefore any type of exchanger with steam in the shell or tube side can be used (i.e., no advantage in the magnitude of Δt can be observed by using a multi-pass design, such as a 2:4 type). The variable temperature from the exchanger t will differ from the variable tank temperature t. An energy balance around the tank and the heat exchanger gives:

Heat Transfer  851

M

t

Wh Ch T1

t

t'

Wh Ch T1

Figure 8.171  Batch heating through an external heat exchanger, isothermal heating medium.

I



II

III

IV

dq ′ dt = Mc = Wh C h (t ′ − t) = UA∆t LMTD dθ dθ Heat accumulation Heat entering in the batch the batch by recirculation

(8.372)

Transfer rate in in the external exchanger

The log mean temperature difference tLMTD is:

∆t LMTD =

=

(T1 − t) − (T1 − t′ )  T −t  ln  1  T1 − t ′  t′ − t  T −t  ln  1  T1 − t ′ 



(8.373)

Equating III and IV in Equation 8.372 gives:

Wh Ch (t − t) = UA tLMTD That is

(8.374)

852  Chemical Process Engineering



Wh C h (t ′ − t) = UA

(t ′ − t) T −t ln 1 T1 − t ′

(8.375)

{ }

Rearranging Equation (8.375) gives:

UA  T −t  ln  1 =   T1 − t ′  Wh C h



(8.376)

Equation 8.376 can be expressed as:

where K 3 = e

T1 − t = e

UA Wh C h

UA Wh C h

(T1 − t ′ )

(8.377)

T1 – t = K3 (T1 − t )

(8.378)

Therefore

 T − t t ′ = T1 −  1   K3 



(8.379)

Equating II and III in Equation 8.372 gives:



Mc

dt = Wh C h (t ′ − t) dθ

(8.380)

Substituting Equation 8.379 into Equation 8.380 and rearranging yields:

Mc dt   T − t  ⋅ = T1 −  1   − t  K3   Wh C h dθ  =

(K 3 − 1)(T1 − t) K3



(8.381)

Rearranging Equation 8.381 and integrating from t1 to t2 while the time passes from 0 to θ gives: t2



∫ t1

θ

dt  K − 1   Wh C h  dθ = 3  T1 − t  K 3   Mc 

∫

(8.382)

0

which yields



 T − t   K − 1   Wh C h  ln  1 1  =  3  θ  T1 − t 2   K 3   Mc 

or



 K 3   Mc   T1 − t1  ln or θ =   K 3 − 1   Wh C h   T1 − t 2 

(8.383)

Heat Transfer  853 where A = heat transfer surface area c = specific heat of batch liquid Ch = heating medium specific heat M = weight of batch liquid T1 = heating medium temperature t1 = initial batch temperature t2 = final batch temperature U = overall heat transfer coefficient. Wh = heating medium flowrate θ = time

Example 8.17: Batch Heating: External Heat Exchanger Isothermal Heating Medium A tank containing 50,000 lb (22,679.5 kg) material with a specific heat of 0.5 Btu/lboF (2.093 kJ/kg.K) is to be heated from 72oF (295K) to 260oF (400K). The tank contains a heating coil with a heat transfer surface of 100ft2 (9.29 m2) and the overall heat transfer coefficient from the coil to the tank contents of 150 Btu/h.ft2.oF (852 W/m2K). Calculate the time required to heat the tank contents with steam condensing at 350oF (450K) at a flowrate of 33,000 lb/h (14,969 kg/h) and a specific heat of 0.9 But/lb.oF (3.77 kJ/kg.K).

Solution where

where K 3 = e

UA Wh C h

ft 2  150 × 100   Btu = exp  ⋅   33,000 × 0.9   h . ft 2 .° F lb Btu ⋅  h lb.° F = 1.65707



   

and

 K 3   Mc   T1 − t1  θ= ln  K 3 − 1   Wh C h   T1 − t 2   1.65707   50,000 × 0.5  ln  350 − 72   1.65707 − 1   33,000 × 0.9   350 − 260 



= 2.39 h.



Calculations: SI units

K3 = e



UA Wh C h

kg .K  J 3600   m2  852 × 9.29 × ⋅ ⋅ 3  = exp    2  14,969 × 3.77 1000   s . m .K kg h 10 J  ⋅   h 3600 s = 1.6568

(8.383)

854  Chemical Process Engineering and or

 K 3   Mc   T1 − t1  ln or θ =   K 3 − 1   Wh C h   T1 − t 2  =

 1.6568   22,679.5 × 2.093  ln  450 − 295   1.6568 − 1   14,969 × 3.77   450 − 400 

= 2.40 h.



(8.383)

An Excel spreadsheet (Batch Heating: External Heat Exchanger Isothermal Heating Medium.xls) has been developed for Example 8.17.

Batch Cooling: External Heat Exchanger, Isothermal Cooling Medium When cooling a batch with an external heat exchanger and an isothermal cooling medium, the equation is:



 T − t   Wc C c   K 4 − 1  ln  1 1  = θ  T2 − t1   Mc   K 4 

(8.384)

 K 4   Mc   T1 − t1  ln or θ =   K 4 − 1   Wc C c   T2 − t1 

(8.385)

or

where

UA

K 4 = e W c Cc A = heat transfer surface area c = specific heat of batch liquid Cc = coolant specific heat M = weight of batch liquid T1 = initial batch temperature T2 = final batch temperature t1 = initial coolant temperature U = overall heat transfer coefficient. Wc = coolant flowrate θ = time

Example 8.18: Batch Cooling: External Heat Exchanger, Isothermal Cooling Medium A tank containing 50,000 lb (22,679.5 kg) material with a specific heat of 0.5 But/lboF (2.093 kJ/kg.K) is to be cooled from 257oF (398K) to 104oF (313K). The tank contains a coil with a heat transfer surface of 100ft2 (9.29 m2) and the overall heat transfer coefficient from the coil to the tank contents of 150 Btu/h.ft2.oF (852 W/m2.K). Calculate the time required to cool the tank contents, if cooling water is available at 86oF (303K) and at a flowrate of 10,000 lb/h (4535.9 kg/h) and the specific heat capacity of 1 Btu/lb.oF (4.186kJ/kg.K).

Heat Transfer  855

Solution K4 = e

UA W c Cc

ft 2  150 × 100   Btu = exp  ⋅   10,000 × 1.0   h . ft 2 .° F lb Btu ⋅  h lb.° F = 4.4817



   

and

 K 4   Mc   T1 − t1  θ= ln  K 4 − 1   Wc C c   T2 − t1  =

 4.4817   50,000 × 0.5  ln  257 − 86   4.4817 − 1   10,000 × 1.0   104 − 86 

= 7.24 h



(8.385)

Calculations: SI units

K4 = e

UA W c Cc

kg .K  J 3600   m2  852 × 9.29 × ⋅ ⋅ 3   2  4535.9 × 4.186 1000   s . m .K kg h 10 J  ⋅   h 3600 s = 4.4848 = exp





and

 K 4   Mc   T1 − t1  θ= ln  K 4 − 1   Wc C c   T2 − t1  =

 4.4848   22,679.5 × 2.093  ln  398 − 303   4.4848 − 1   4535.9 × 4.186   313 − 303 

= 7.24h



An Excel spreadsheet (Batch Cooling: External heat exchanger, isothermal cooling medium.xls) has been developed for Example 8.18.

856  Chemical Process Engineering

Batch Cooling: External Heat Exchanger (Counter-Current Flow), Non-Isothermal Cooling Medium When cooling a batch with an external heat exchanger and a non-isothermal cooling medium, the following equation can be used:



Wb Wc C c   T − t   K − 1  ln  1 1  = 5 θ   T2 − t1   M   K 5 Wc C c − Wb c 

(8.386)

 K W C − Wb c   M   T 1 − t1  θ= 5 c c    ln   Wb Wc C c   K 5 − 1   T2 − t1 

(8.387)

or

where K 5 = exp UA (1 Wb c − 1 Wc C c ) 

A = heat transfer surface area c = specific heat of batch liquid Cc = Coolant specific heat M = weight of batch liquid T1 = initial batch temperature T2 = final batch temperature t1 = initial coolant temperature U = overall heat transfer coefficient. Wb = batch flowrate Wc = coolant flowrate θ = time

Example 8.19: Batch Cooling: External Heat Exchanger (Counter-Current Flow), Non-Isothermal Cooling Medium A tank containing 50,000lb (22,679.5 kg) material with a specific heat of 0.5 Btu/lb.oF (2.093 kJ/kg.K) is to be cooled from 257oF (398K) to 104oF (313K). The tank contains an external heat exchanger with a heat transfer of 200 ft2 (18.58 m2). The batch material is circulated through an external exchanger at the rate of 25,000 lb/h (11,339.8 kg/h). The overall heat transfer coefficient is 200 Btu/h.ft2.oF (1134 W/m2.K). Calculate the time required to cool the tank contents if cooling water is available at 86oF (303K) and at a flow rate of 10,000 lb/h (4535.9 kg/h).

Solution K 5 = exp UA (1 Wb c − 1 Wc C c ) 



1 1 1     Btu ⋅ ft 2 ⋅ = exp (200 × 200)  −  2  lb Btu  (25,000)(0.5) (10,000)(1.0)    ft . hr.° F  ⋅  hr lb.° F = 0.44932

   

Heat Transfer  857 and

 1  K W C − Wb c   M   T1 − t1   lb Btu ln  θ= 5 c c ⋅ ⋅ lb   ⋅       Wb Wc C c   K 5 − 1   T2 − t1   hr lb.° F lb lb Btu ⋅ ⋅   hr. hr lb.° F  (0.44932)(10,000)(1.0) − (25,000)(0.5)   50,000  ln  257 − 86  θ=    0.44932 − 1   104 − 86  (25,000)(10,000)(1.0) 

= 6.55h

Calculations: SI units

K 5 = exp UA (1 Wb c − 1 Wc C c )  1 1  1134 × 18.58 × 3600    = exp  −   (11,339.8)(2.093) (4535.9)(4.186)   1000 



J  s kg.K  h ⋅ m 2 ⋅ ⋅ 3600 ⋅ 3   2 h 10 J  kg  s . m .K = 0.44978

and

 1  K W C − Wb c   M   T 1 − t1   kg kJ ln  θ= 5 c c ⋅ ⋅ kg   ⋅      Wb Wc C c   K 5 − 1   T2 − t1   hr kg.K kg kg kJ  ⋅ ⋅   hr. hr kg.K    (0.44978)(4535.9)(4.186) − (11,339.8)(2.093)   22,679.5   398 − 303  θ=    0.44978 − 1  ln  313 − 303  (11,339.8)(4535.9)(4.186) 

= 6.55h



An Excel spreadsheet (Batch Cooling: External Heat Exchanger (Counter-Current Flow), Non-isothermal Cooling. xls) has been developed for Example 8.19.

Batch Heating: External Heat Exchanger and Non-Isothermal Heating Medium When heating a batch reactor with an external heat exchanger and non-isothermal heating, the following equation applies:



Wb W h C h   T − t   K6 − 1  ln  1 1  = θ   T1 − t 2   M   K 6 Wh C h − Wb c 

(8.388)

 K W C − Wb c   M   T1 − t1  or θ =  6 h h    ln   Wb Wh C h   K 6 − 1   T1 − t 2 

(8.389)

or



858  Chemical Process Engineering where K 6 = exp UA (1 Wb c − 1 Wh C h )  A = heat transfer surface area c = specific heat of batch liquid Ch = heating medium specific heat M = weight of batch liquid T1 = heating medium temperature t1 = initial batch temperature t2 = final batch temperature U = overall heat transfer coefficient. Wb = batch flowrate Wh = heating medium flowrate θ = time

Example 8.20: Batch Heating: External Heat Exchanger and Non-Isothermal Heating Medium A tank containing 50,000 lb (22,679.5 kg) material with a specific heat of 0.5 Btu/lb.oF (2.093 kJ/kg.K) is to be heated from 68oF (293K) to 257oF (398K). The tank contains an external heat exchanger with a heat transfer of 200ft2 (18.58m2). The batch material is circulated through the exchanger at the rate of 25,000 lb/h (11339.8 kg/h). The overall heat transfer coefficient is 200 Btu/h.ft2.oF (1134 W/m2.K). Calculate the time required to heat the tank contents with condensing steam at 320oF (433K) and at a flowrate 10,000 lb/h (4535.9 kg/h) at a specific heat of 0.9 Btu/lb.oF (3.767 kJ/kg.K).

Solution K 6 = exp UA (1 Wb c − 1 Wh C h ) 



1 1 1     Btu ⋅ ft 2 ⋅ = exp (200 × 200)  −  2  lb Btu  (25,000)(0.5) (10,000)(0.9)    ft . hr.° F  ⋅  hr lb.° F = 0.2881

   

and

 1  K W C − Wb c   M   T1 − t1   lb Btu ln  θ= 6 h h ⋅ ⋅ lb   ⋅       Wb Wh C h   K 6 − 1   T1 − t 2   hr lb.° F lb lb Btu ⋅ ⋅   hr. hr lb.° F  (0.2881)(10,000)(0.9) − (25,000)(0.5)   50,000  ln  320 − 68  θ=    0.2881 − 1   320 − 257  (25,000)(10,000)(0.9) 

= 4.29h



Heat Transfer  859 Calculations: SI units

K 6 = exp UA (1 Wb c − 1 Wh C h )  1 1  1134 × 18.58 × 3600    = exp  −    (11,339.8)(2.093) (4535.9)(3.767)   1000 



J  s kg.K  h ⋅ m 2 ⋅ ⋅ 3600 ⋅ 3   2 h 10 J  kg  s . m .K = 0.2884



and

 1  K W C − Wb c   M   T1 − t1   kg kJ ln  θ= 6 h h ⋅ ⋅ kg   ⋅      Wb Wh C h   K 6 − 1   T1 − t 2   hr kg.K kg kg kJ  ⋅ ⋅   hr. hr kg.K    (0.2884)(4535.9)(3.767) − (11,339.8)(2.093)   22,679.5   433 − 293  θ=    0.2884 − 1  ln  433 − 398  (11,339.8)(4535.9)(3.767) 

= 4.29h

An Excel spreadsheet (Batch Heating: External Heat Exchanger and Non-Isothermal Heating Medium.xls) has been developed for Example 8.20.

Batch Heating: External Heat Exchanger (1-2 Multipass Heat Exchangers), Non-Isothermal Heating Medium The procedure used for batch heating with external 1-2 multipass heat exchangers with non-isothermal heating media involves using the same heat balance media as defined by the following equation:

          



I

II

III

IV

dq ′ dt = Mc = Wb c(t ′ − t) = Wh C h (T1 − T2 ) = UA∆t LMTD dθ dθ

(8.390)

Equating II and III in Equation 8.390 gives



Mc

dt = Wb c(t ′ − t) dθ

(8.391)

Rearranging Equation 8.391 gives:



t′ = t +

M dt ⋅ Wb dθ

(8.392)

860  Chemical Process Engineering The parameter S can be defined by



S=

t ′ − t  M   1  dt = T1 − t  Wb   T1 − t  dθ

(8.393)

The parameter R can be defined by equation III and IV in Equation 8.390

R=



Wb c T1 − T2 = t′ − t Wh C h

(8.394)

Rearranging Equation 8.393 gives: t2

∫



t1

S ⋅ Wb dt = T1 − t M

θ

∫ dθ

(8.395)

0

Integrating from t1 to t2 as the time passes from 0 to θ yields:



 T − t   S ⋅ Wb  ln  1 1  = θ  T1 − t 2   M 

(8.396)

 M   T1 − t1  ln  θ=   S Wb   T1 − t 2 

(8.397)

The time θ required for heating is:

and



S=

2(K 7 − 1) 2 0.5 0.5 K 7 {R + 1 + (R + 1) } − {R + 1 − (R + 1) } 2

where



Wb c T −T   UA  2 K 7 = exp  (R + 1)0.5  and R = 1 2 =  t′ − t Wh C h  Wb c   A = heat transfer surface area c = specific heat of batch liquid Ch = heating medium specific heat M = weight of batch liquid T1 = initial temperature of heating medium t1 = initial batch temperature t2 = final batch temperature U = overall heat transfer coefficient. Wb = batch flowrate Wh = heating medium flowrate θ = time

(8.398)

Heat Transfer  861

Example 8.21: External Heat Exchanger (1-2 Multipass Heat Exchangers), Non-Isothermal Heating Medium 7500 gal (28387.5 l) of liquid benzene under pressure at 300oF (422K) is required for a batch extraction process. The storage temperature of the benzene is 100oF (311K). Available as a heating medium is a 10000 lb/h (4535.9 kg/h), 28oAPI oil stream at a temperature of 400oF (478K). A pump connected to the tank is capable of circulating 40,000 lb/h (18143.7 kg/h) of benzene. Available for the service is 400ft2 (37.16 m2) of clean double pipe heat exchanger surface, which in counterflow streams yields Uc of 50 But/h.ft2.oF (238.9 W/m2.K) calculated for the above flowrates. Calculate the time required to heat the contents using a 1-2 exchanger with the same surface and coefficient.

Solution Specific gravity of benzene = 0.88 Specific heat of benzene = 0.48 Btu/lb.oF Mass of benzene = 7500 x 8.33 x 0.88 = 55,000 lb.

R= =

Wb c T1 − T2 = t′ − t Wh C h (40,000)(0.48) = 3.2 (10,000)(0.6)

(R 2 + 1)0.5 = (3.22 + 1)0.5 = 3.3526



 UA  2  (R + 1)0.5  K 7 = exp    Wb c    (50)(400)  (3.3526) = exp   (40,000)(0.48)  = 32.86

S=

2(K 7 − 1) K 7 {R + 1 + (R + 1)0.5 } − {R + 1 − (R 2 + 1)0.5 } 2

2(32.86 − 1) 32.86[3.2 + 1 + 3.3526] − [3.2 + 1 − 3.3526] = 0.2576 =



The time required heating the batch with external 1-2 multi-pass heat exchangers and non-isothermal heating media is:

 M   T1 − t1  ln  θ=   S Wb   T1 − t 2  55,000  400 − 100  ln (0.2576)(40,000)  400 − 300  = 5.86h =

862  Chemical Process Engineering Calculations: SI units

R= =

Wb c T1 − T2 = t′ − t Wh C h (18143.68)(2.009) = 3.199 (4535.9)(2.5116)

(R 2 + 1)0.5 = (3.1992 + 1)0.5 = 3.3522



 UA  2  (R + 1)0.5  K 7 = exp    Wb c  



J kJ  1 1 1  (238.9)(37.16)  3600    (3.3522) = exp  ⋅m2 ⋅ ⋅ 3   2    h kJ kg 10 J  1000   s . m .K  (18143.68)(2.0093)   h kg.K 3600 s   = 19.15 2(K 7 − 1) K 7 {R + 1 + (R + 1)0.5 } − {R + 1 − (R 2 + 1)0.5 } 2(19.15 − 1) = 19.15[3.199 + 1 + 3.3522] − [3.199 + 1 − 3.3522] = 0.2525

S=



2

The time required heating the batch with external 1-2 multipass heat exchangers and non-isothermal heating media is:

 M   T1 − t1  ln  θ=   S Wb   T1 − t 2  24947.56  478 − 311  ln (0.2525)(18143.68)  478 − 422  = 5.94h =

An Excel spreadsheet (External Heat Exchanger (1-2 Multipass Heat Exchangers), Non-Isothermal Heating Medium. xls) has been developed for Example 8.21.

Heat Transfer  863

Batch Cooling: External Heat Exchanger (1-2 Multipass), Non-Isothermal Cooling Medium When cooling a batch with an external 1-2 multipass heat exchanger and a non-isothermal cooling medium, the following equations apply:



 Wc C c   T −t  ln  1 1  = S θ  Mc   T2 − t1 

(8.399)

 Mc   T1 − t1  ln  θ=   SWc C c   T2 − t1 

(8.400)

The time θ required for cooling is:

where S is defined by Equation 8.398, and:

R=



Wc C c Wbc

(8.401)

where WC   UA  2 K 7 = exp  (R + 1)0.5  and R = c c  Wbc  Wc C c   A = heat transfer area c = specific heat of batch liquid Cc = Coolant specific heat M = weight of batch liquid T1 = initial batch temperature T2 = final batch temperature t1 = initial coolant temperature U = overall heat transfer coefficient. Wb = batch flowrate Wc = coolant flowrate U = overall heat transfer coefficient θ = time

Example 8.22: External Heat Exchanger (1-2 Multipass), Non-Isothermal Cooling Medium A tank containing 50,000 lb (22,679.5 kg) material with a specific heat of 0.5 Btu/lb.oF (2.093 kJ/kg.K) is to be cooled from 257oF (398K) to 104oF (313K). The tank contains an external heat exchanger with a heat transfer of 200ft2 (18.58m2). The batch material is circulated through the exchanger at the rate of 25,000 lb/h (11339.8 kg/h). The overall heat transfer coefficient is 200 Btu/h.ft2.oF (1134 W/m2.K). Calculate the time required to cool the tank contents with cooling water available at a temperature of 86oF (303K) and at a flowrate 10,000 lb/h (4535.9 kg/h) at a specific heat of 1.0 Btu/lb.oF (4.186 kJ/kg.K).

864  Chemical Process Engineering

Solution Wc C c Wbc (10,000)(1.0) = = 0.8 (25,000)(0.5)

R=



(R 2 + 1)0.5 = (0.82 + 1)0.5 = 1.2806

(8.401)



 UA  2  (R + 1)0.5  K 7 = exp    Wc C c    (200)(200)  1.2806  = exp   (10,000)(1.0) 



= 167.75

and

2(K 7 − 1) K 7 {R + 1 + (R + 1)0.5 } − {R + 1 − (R 2 + 1)0.5 } 2(167.75 − 1) = 167.75[0.8 + 1 + 1.2806] − [0.8 + 1 − 1.2806] = 0.6460

S=



2

The time required cooling the batch with external 1-2 multipass heat exchangers and non-isothermal heating media is:

 Mc   T1 − t1  θ= ln    SWc C c   T2 − t1  (50,000)(0.5)  257 − 86  ln (0.646 × 10,000 × 1.0)  104 − 86  = 8.71 h. = Calculations: SI units

Wc C c Wbc (4535.9)(4.186) = = 0.799 (11339.8)(2.093)

R=



(R 2 + 1)0.5 = (0.7992 + 1)0.5 = 1.2806



(8.401)

Heat Transfer  865

 UA  2  (R + 1)0.5  K 7 = exp    Wc C c   3600   (18.58)(1134) = exp  × 1.2806 ×  1000   (4535.9)(4.186) = 166.64

and

2(K 7 − 1) K 7 {R + 1 + (R + 1)0.5 } − {R + 1 − (R 2 + 1)0.5 } 2(166.64 − 1) = 166.64.75[0.799 + 1 + 1.2806] − [0.799 + 1 − 1.2806] = 0.6462

S=



2

The time required cooling the batch with external 1-2 multipass heat exchangers and non-isothermal heating media is:

 Mc   T1 − t1  θ= ln    SWc C c   T2 − t1  (22,679.5)(2.093)  398 − 303  ln (0.6462 × 4535.9 × 4.186)  313 − 303  = 8.709 h.

=

An Excel spreadsheet (External Heat Exchanger (1-2 Multipass Heat Exchangers), Non-Isothermal Cooling Medium. xls) has been developed for Example 8.22.

Batch Heating and Cooling: External Heat Exchanger (2-4 Multipass Heat Exchangers Non-Isothermal Heating Medium) When heating a batch with an external 2-4 multipass heat exchanger and a non-isothermal heating medium, the following equations apply:



 T − t   S ⋅ Wb  ln  1 1  = θ  T1 − t 2   M 

(8.402)

 M   T1 − t1  θ= ln    S Wb   T1 − t 2 

(8.403)

The time θ required for heating is:



866  Chemical Process Engineering and



S=

2(K 8 − 1)[1 + {(1 − S)(1 − RS)}0.5 ] (K 8 − 1)(R + 1) + (K 8 + 1)(R 2 + 1)0.5

(8.404)

where

K8

exp

UA (R 2 1)0.5 2Wb c



(8.405)

Batch Heating and Cooling: External Heat Exchanger (2-4 Multipass Heat Exchangers Non-Isothermal Cooling Medium) When cooling a batch with an external 2-4 multipass heat exchanger and a non-isothermal cooling medium, the following equations apply:



 Wc C c   T −t  ln  1 1  = S θ  Mc   T2 − t1 

(8.406)

 Mc   T1 − t1  θ= ln    SWc C c   T2 − t1 

(8.407)

The time θ required for cooling is:

where S is defined by Equation 8.404 and



and R =

Wc C c Wbc

(8.408)

Because S cannot be expressed explicitly, Equation 8.404 can only be solved by trial and error, assuming different values of S until equality is reached. An alternative in solving Equation 8.404 is employing an Excel spreadsheet with a Solver or Goal Seek.

Example 8.23: External Heat Exchanger (2-4 Multipass Exchanger), Non-Isothermal Heating Medium Using Example 8.48 for 2-4 multipass heat exchanger, non-isothermal heating medium.

 UA  2  (R + 1)0.5  K 8 = exp    2Wb c   (50)(400)   = exp  × 3.3526  (2 40,000 0.48) × ×  

= 5.73

Heat Transfer  867

S= =

2(K 8 − 1)[1 + {(1 − S)(1 − RS)}0.5 ] (K 8 − 1)(R + 1) + (K 8 + 1)(R 2 + 1)0.5 2(5.73 − 1) 1 + (1 − S)(1 − 3.2S)  (5.73 − 1)(3.2 + 1) + (5.73 + 1) 3.22 + 1

Solving for S by trial and error until the RHS equals the LHS,



S = 0.273

The time θ required for heating is:

 M   T1 − t1  ln  θ=   S Wb   T1 − t 2 



55,000   ln  400 − 100  =  0.273 × 40,000   400 − 300  = 5.53 h



(8.403)

An Excel spreadsheet (External Heat Exchanger (2-4 Multipass Heat Exchangers), Non-Isothermal Heating Medium. xls) has been developed for Example 8.23.

Example 8.24: External Heat Exchanger (2-4 Multipass Heat Exchangers), Non-Isothermal Cooling Medium Using Example 8.23: for 2-4 multipass heat exchanger, non-isothermal cooling medium and

R



(R 2 1)0.5

WcC c Wb c 10, 000 1.0 25, 000 0.5 0. 8 (0.82 1)0.5

1.2806

(8.408)



 UA  2  (R + 1)0.5  K 8 = exp    2Wb c    (200)(200)  = exp  × 1.2806  (2 25,000 0.5) × ×  

= 7.7601

868  Chemical Process Engineering

S= =

2(K 8 − 1)[1 + {(1 − S)(1 − RS)}0.5 ] (K 8 − 1)(R + 1) + (K 8 + 1)(R 2 + 1)0.5 2(7.7601 − 1) 1 + (1 − S)(1 − 0.8S)  (7.7601 − 1)(0.8 + 1) + (7.7601 + 1) 0.82 + 1

Solving for S by trial and error until the RHS equals the LHS,



S = 0.755

The time θ required for cooling is:

 Mc   T1 − t1  ln  θ=   SWc C c   T2 − t1 

55,000 × 0.5    257 − 86  ln =  0.755 × 10,000 × 1.0   104 − 86  = 7.45h.



(8.407)

An Excel spreadsheet (External Heat Exchanger (2-4 Multipass Heat Exchangers), Non-Isothermal Cooling Medium. xls) has been developed for Example 8.24.

Heat Exchanger Design with Computers Several descriptions have been presented [131–135] to illustrate the usefulness of computers in various phases of heat exchanger design. Although any medium-sized digital computer can handle the decision and storage capacity, a large investment must be made in programming time required to achieve a good flexible program. Often several months are required to polish the program, but when completed, it can save many hours of calculation time. It is usually better to create programs specific to the types of exchanger performance, such as convection, condensing, thermosyphon reboiling, condensing in the presence of noncondensable gases, etc., rather than creating an overall program to attempt to cover all types. Computer methods for the design and analysis of heat exchangers are provided by commercial software companies as HEXTRAN, HTRI Xchanger suite (Heat Transfer Research, Inc.), HTFS suite (Aspen Technology, Inc.), BJAC programs (HETRAN and AEROTRAN) and HEI. HEXTRAN provides the most complete coverage of topics as it handles all types of heat exchangers and also performs pinch calculations for the design of heat exchanger networks. However, it does not perform mechanical designs calculations for shell and tube exchangers nor does it generate detailed tube layouts or setting plans. The HTRI and HTFS software packages use proprietary methods developed by their respective research organizations and are similar in their level of refinement. HTRI Xchanger suite lacks a mechanical design feature and HTFS suite handles all types of heat exchangers as it also performs mechanical design calculations and develops detailed tube layouts and setting plans for shell and tube exchangers. Neither HTRI nor HTRS performs pinch calculations for heat exchanger networks. The Honeywell UniSim Design Software or Aspen Technology heat exchanger suite contains a set of validated programs designed for use by process designers for the thermal design and simulation of heat exchanger equipment. For example, UniSim Design Software heat exchangers have five main programs, each for a different type of equipment.

Heat Transfer  869 Name

Model

UniSim Shell and Tube Exchanger Modeler

UniSim ® STE

Shell and tube heat exchangers

UnSim ® Cross Flow Exchanger Modeler

UniSim ® CFE

Air coolers and other crossflow exchangers

UniSim ® Plate-Fin Exchanger Modeler

UniSim ® PFE

Plate-fin heat exchangers

UniSim ® Fired Process Heater Modeler

UniSim ® FPH

Furnaces and Fired heaters

UniSim ® Plate Heat Exchanger

UniSim ® PHE

Plate heat exchangers

UniSim ® Feedwater Heat Exchanger Modeler

UniSim ® FWH

Feedwater heat exchanger

UniSim ® Process Pipeline Heat Exchanger Modeler

UniSim ® PPL

Process Pipeline heat exchanger

®

Functionality The main UniSim Design Software heat exchanger programs offer some or all of the following basic functionality: • Design: for designing a heat exchanger to meet a heat load duty and pressure drop limits, which are being specified. For cost or area optimized thermal design to the specified process conditions and geometrical constraints. • Checking (Rating): determines whether a specified heat exchanger has sufficient surface area to meet a specified duty. Also calculates the stream pressure drops. • Simulation: determines the heat load, pressure changes and stream outlet conditions that will occur with a specified exchanger and given stream inlet conditions. • Thermosyphon: determines the flow rate and duty of a specified exchanger, operating as a thermosyphon with given liquid height in the column and the pipework connecting the exchanger to the column. • Geometry: Allows the designer to define the exchanger geometry (e.g., tube layout, setting plan) without going on to perform heat exchanger calculations. Typical exchanger geometries are: Shells/Channels

TEMA shell types E, F, G, H, J and I (inverted J). Kettle reboilers. X-Shells. Double-pipe exchangers. Multi-tube hairpin exchangers. TEMA front and rear head types A, B, C, L, M, N, P, S, T, U, V, W. Falling film evaporators. Reflux condensers. Shells in parallel. Shells in series (up to 12).

Nozzles

Plain. Axial. Vapor belts. Impingement plates.

870  Chemical Process Engineering Baffles

Single segmental. Double segmental. Unbaffled exchangers. Rod baffles. Intermediate support baffles. Blanking baffles on U-tubes.

Tube bundles

Single pass. Multipass (up to 16). Full bundle (no tubes removed under nozzles). Normal bundle. No-tubes –in window designs.

Tubes

Plain tubes. Low-fin tubes (database included). Longitudinal fins in double-pipe and Unbaffled exchangers. Twisted tape inserts.

Physical Properties All of the commercial heat exchanger design programs allow the user to upload process data and stream properties from a process simulation. Caution is required when uploading data for streams that undergo partial vaporization or have other effects that cause significant changes in fluid properties and heat capacities between the exchanger inlet and outlet. The designer should break the exchanger into several exchangers in series in the process simulation, in order to obtain several sets of property data at intermediate temperatures for input into the heat software. The heat exchanger programs have both rating and design options and can be configured to determine a least-cost design for given desired outlet temperatures and allowable pressure drops. Alternatively, they can be employed to calculate outlet stream temperatures and pressures, given details of the exchanger geometry and process fluid inlet conditions. All the programs enable the designer to make adjustments to exchanger geometry and thus recalculate to view the impact on the stream outlet temperatures and pressure drops. The author has developed heat exchanger design programs for various exchanger types (e.g., shell and tube, double pipe, air coolers) in this chapter. These programs form preliminary design calculations before detailed designs are explored by the designers.

UniSim Heat Exchanger Model Formulations End Point: This model assumes linear temperature profiles in both hot and cold side fluids. It is therefore an appropriate selection in cases where the fluid specific heats are approximately constant, and when no phase changes are expected. Weighted: This model calculates the temperature profiles in a step-wise manner, carrying out flash computations along the way. It is therefore an appropriate selection in cases where phase changes in the flowing fluids are anticipated. Steady State Rating: This forms an extension of the End Point model incorporating a rating calculation and uses the same assumptions as the End Point model. Dynamic Rating: Two models are provided: Basic, which uses the same assumptions as the End Point model, and Detailed, based on the Weighted model assumptions. Figure 8.172 shows the flowchart for selecting reboiler types. Troubleshooting of shell and tube heat exchanger is provided elsewhere [83].

Heat Transfer  871

A Case Study: Kettle Reboiler Simulation Using UniSim STE UniSimR® STE is used to simulate kettle reboiler (Figure 8.172) having steam to vaporize hexane with a single carbon steel exchanger with geometric and process data as follow: Geometric data

Value

TEMA Designation

CKU

Shell Internal Diameter (mm)

940

Nozzle Diameter – Shell Inlet (mm)

203

Nozzle Diameter – Shell Vapor Outlet (mm)

406

Nozzle Diameter – Shell liquid Outlet (mm)

203

Nozzle Diameter – Tube Inlet (mm)

154

Nozzle Diameter – Tube Outlet (mm)

154

Tube Length (mm)

3352

Tube Outside Diameter (mm)

25.4

Tube Pitch (mm)

31.75

Tube wall thickness (mm)

2.108

Tube Pattern (degrees)

90

Tube-side Passes

2

Process data (SI Units)

Water (hot stream)

Hexane (cold stream)

Total Mass Flow (kg/h)

99792

83989

Inlet Temperature (oC)

96

67.9

Estimated Outlet Temperature (oC)

77

Inlet Pressure (bar)

2.5

1.09

Estimated Pressure Drop (bar)

0.207

0.207

Inlet Mass Quality

0

0

Outlet Mass Quality

0

Fouling Resistance (m2K/W)

0.0001

Figure 8.172  Kettle reboiler.

0.0001

872  Chemical Process Engineering Start a New case by clicking on UniSim Design Software heat exchanger icon STE R460 and a window (Figure 8.173) appears. Double clicking on New button shows the next window (Figure 8.174). This window shows the Input Data, Exchanger Geometry, Tubes and Baffles, Bundle Layout, Nozzles, Process, Physical Properties for the Hot and Cold Streams. The procedure of inputting data is as follows: 1. F  igure 8.175 initially indicates a Design run using SI units. 2. From the Start up view select Simulation as the Calculation Mode. Check the Basic Input Mode check box. Enter AKC1 as the Equipment Item Number and Kettle Reboiler as a Job Title (Figure 8.176). 3. The Exchanger Geometry property view will then appear. Select it from the Input menu if it does not. Specify the following in Figure 8.177. Field

Input

Front End Heat Type

TEMA C

Shell Type

TEMA K

Rear End Head Type

TEMA U

Shell Inside Diameter (mm)

940

Side for Hot Stream

Tubeside Hot

For a kettle, this is the diameter in the port region, which appromixates to that of the bundle (940 mm), not the larger diameter of the main region of the shell, where there is a vapor space above the liquid (Figure 8.178). 4. Select Bundle Geometry from the Input menu. Specify the following (Figure 8.179):

Figure 8.173  A snapshot of UniSim STE R460 Window. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Heat Transfer  873

Figure 8.174  A snapshot of Start up view indicating Design as the Calculation Mode. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Figure 8.175  A snaphot of UniSim STE R460, Start Up Window with Simulation as the Calculation mode. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

874  Chemical Process Engineering

Figure 8.176  A snapshot of Exchanger Geometry property view. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Figure 8.177  A snapshot of Tubes and Baffles property view. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Heat Transfer  875

Figure 8.178  A snapshot of Bundle Layout property view. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Check box

Field

Input

Tube Details

Tube Length (mm)

3352

Tube Outside Diameter (mm)

25.4

Tube Wall Thickness (mm)

2.108

Tube Pitch (mm)

31.75

Tube Pattern (degrees)

90

Number of Tube-side Passes

2

Bundle Layout

If a Tube Count was given, this would be entered on the Bundle Size tab. UniSim ® STE will calculate a value from the Bundle Size. For a K shell, there is no need to provide any information on the Transverse Baffles form tab.

Nozzle Data 5. F  rom the Input menu, select Nozzles (Figures 8.180 and 8.181). 6. Remember that for a K shell, there are three shell-side nozzles. Specify the following. Check box

Field

Nozzle 1

Nozzle 2

Nozzle 3

Shell-side

Nozzle Function

Inlet

Liquid Outlet

Vapor Outlet

Nozzle Internal Diameter (mm)

203

203

406

Nozzle Function

Inlet

Outlet

Unset

Nozzle Internal Diameter (mm)

154

154

Tube-side

876  Chemical Process Engineering

Figure 8.179  A snapshot of Nozzles showing the Shell side property view. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Figure 8.180  A snapshot of Nozzles showing the Tube side property view. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Heat Transfer  877

Figure 8.181  A snapshot of Process Data view of STE R460 (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Process Data 7. O  pen the Process view. 8. Enter the process data for the Water in the Hot stream column and the Hexane data in the Cold stream column. Field

Water (hot stream)

Hexane (cold stream)

Total Mass Flow (kg/h)

99792

83989

Inlet Temperature (oC)

96

67.9

Outlet Temperature (oC)

77

Inlet Pressure (bar)

2.6

1.09

Estimated Pressure Drop (bar)

0.207

0.207

Inlet Mass Quality (0 to 1)

0

0

Outlet Mass Quality (0 to 1)

0

Fouling Resistance (m2K/W)

0.0001

0.0001

UniSim STE calculates the outlet conditions in the simulation calculation. However, it is useful to specify some basis for an initial estimate of the outlet conditions. In this case, it is provided by the Water outlet temperature (Figure 8.182). In a kettle reboiler, the flow within the bundle is probably much greater than the cold stream feed to the bundle, due to recirculation within the kettle. UniSim STE will automatically make allowance for this, determining the local flow from the head of liquid around the bundle. If the stream were a multicomponent mixture, UniSim STE would also make allowance for composition changes due to this recirculation.

878  Chemical Process Engineering

Figure 8.182  A snapshot of Physical Properties views for Water stream. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

9. Select Physical Properties from the Input menu. 10. The first form is for the Hot stream. This is Water, so under Stream Data Source click on Water. This will cause data for water to be obtained from the UniSim Design Software Thermo databank when the program is run (Figure 8.183). 11. Click on the Cold Stream tab. Enter the Stream Name as Hexane and set the Stream Type to Hydrocarbon. Under Stream Data Source, click on Add. You will see a component selection box. Double click on n-Hexane and it will move to the Selected Components box (Figure 8.184). 12. The box at the bottom right of the tabbed page should be green and show Ready to indicate the components and property methods have been set (Figure 8.185). If you click on the Property Package check box, you will notice that Peng-Robinson for both phases has been selected, as a consequence of defining the Stream Type as Hydrocarbon. 13. Close the Data Source screen, and on the main Properties screen, you will see that your new data source, named Hydrocarbon 1, has been selected for stream 2 (hexane). Since the stream is a pure component, the composition default (1.0) is correct (Figure 8.186). Set the Pressure Levels as 1 and 3 bars respectively (Figure 8.187). 14. Click on Options button on the Properties Window. Check that a temperature ragne for properties is set. If not, set two values, e.g., 67–96 will cover the range possible in the exchanger (Figure 8.188). Close the Options screen. 15. On the main Properties screen click on Get Properties. You will see the property values for hexane appear on the spreadsheet (Figure 8.189). 16. Close the Physical Properties screen. 17. Select File and then Save As from the main UniSim® STE screen. Enter Case Study-Reboiler-akc1. 18. You have now entered all the data that are required and can run UniSim STE calculations by clicking on the Run icon, or by selecting Calculate All, under the Run menu (Figure 8.190). 19. You will see the Tube Layout diagram appear. Click on Items in the drop-down box and you will see spreadsheets appear defining the various features in the diagram. Figure 8.191 shows the kettle reboiler diagram with dimensions.

Heat Transfer  879

Figure 8.183  A snapshot of Physical Properties views for Hexane stream. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Figure 8.184  A snapshot of Physical Properties views for Hexane stream using Component Selection view. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Appendix A (Table 8.62) shows the advantages and disadvantages of various reboiler types, and the troubleshooting of the shell and tube heat exchanger, heat exchanger operations and some considerations for the choice of heat exchanger design, respectively. Figures 8.192–8.195 show snapshots of Kettle Reboiler diagram with dimensions, Tube Layout of Kettle Reboiler, Kettle Reboiler diagram and Kettle Reboiler specification sheet respectively.

880  Chemical Process Engineering

Figure 8.185  A snapshot of Physical Properties Window for Hexane stream from UniSim Thermo 1.0 showing green color. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Figure 8.186  A snapshot of Physical Properties Window for Hexane stream showing the composition default (1.0) in yellow. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Heat Transfer  881

Figure 8.187  A snapshot of Physical Properties Window for Hexane stream showing the composition default (1.0) in yellow and the Pressure Levels 1.05 and 0.95 bar respectively. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Figure 8.188  A snapshot of Properties Options and set two values 67 – 96 to cover the range possible in the exchanger. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

882  Chemical Process Engineering

Figure 8.189  A snapshot of property values for hexane by clicking on Get Properties from the Properties view. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Figure 8.190  A snapshot of the Geometric details after simulation calculation. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Heat Transfer  883

Figure 8.191  A snapshot of the Tube Layout after simulation calculation. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Figure 8.192  A snapshot of the Kettle Reboiler diagram with dimensions. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

450.85 mm

450.85 mm

884  Chemical Process Engineering

CKU: 588 tubeholes Shell id =940/1699 mm Filename: Case Study-Reboiler-akc1.STEi Kettle Reboiler

Figure 8.193  Tube Layout of Kettle Reboiler. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

A

6180 Overall 430

1190

1760

1500 S2

T1

T2

S3

S1 840

3820

3940

Inlet Channel

1200 1200

1590

820 820

Pulling Length

Shell Views on arrow A

Weight Bundle/Dry/Wet All Measurements Are In mm Warnings - This Setting Plan is approximate only For accurate Setting Plan use a full mechanical design package.

T1 Inlet T2 Outlet S3 Liquid Out S1 Feed Inlet S2 Vapour Out Design Pressure barg Temperature C Passes kg 2545

NPS 6 6 8 8 18 Shell 3.5 168 1 6694

Rating lb 150 150 150 150 150 Tube 5.0 196 2 15699

Kettle Reboiler AKC1

31-Oct-2019 01:25

CKU 940/ 1699 - 3352

Figure 8.194  Kettle Reboiler diagram. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell and UniSim are trademarks of Honeywell International Inc.)

Heat Transfer  885

Figure 8.195  Kettle Reboiler specification sheet. (Courtesy of UniSim STE R460, Honeywell Process Solutions, Honeywell® and UniSim® are trademarks of Honeywell International Inc.)

/8 in.

1 1/4 in.

1 in.

3

/4 in.

5

.00907

.01063

.00429

.00579

.00754

.00875

.01019

.01289

.01647

.00425

.00571

.00741

.00857

.00995

.01251

.01584

12

18

16

14

13

12

10

8

18

16

14

13

12

10

8

.00593

16

13

.00437

18

.00778

.00798

14

14

.00605

.00443

Factor

16

18

OD tube Gauge

Thermal conductivity, K

.000634

.000500

.000398

.000343

.000296

.000228

.000170

.000659

.000516

.000408

.000350

.000302

.000232

.000172

.000425

.000363

.000311

.000237

.000175

.000319

.000424

.000177

Carbon steel

25

89

.000251

.000199

.000158

.000136

.000118

.000091

.000067

.000261

.000205

.000162

.000139

.000120

.000092

.000068

.000169

.000144

.000123

.000094

.000069

.000127

.000096

.000070

.000178

.000141

.000112

.000096

.000083

.000064

.000048

.000185

.000145

.000114

.000098

.000085

.000065

.000048

.000119

.000102

.000087

.000067

.000049

.000090

.000068

.000050

Red brass 45% Ars. Admiralty copper

63

Value of r w

Table 8.26B  Metal resistance of tubes and pipes.

Appendix

.000754

.000596

.000474

.000408

.000353

.000272

.000202

.000784

.000614

.000485

.000417

.000359

.000276

.000204

.000506

.000432

.000370

.000282

.000208

.000380

.000288

.000211

.000932

.000736

.000585

.000504

.000436

.000336

.000250

.000967

.000758

.000599

.000515

.000444

.000341

.000252

.000625

.000534

.000458

.000349

.000257

.000469

.000356

.000261

.001085

.000857

.000682

.000587

.000508

.000391

.000291

.001128

.000883

.000698

.000599

.000516

.000397

.000294

.000728

.000621

.000533

.000406

.000299

.000547

.000414

.000303

70-30 CU-NI Monel

4-6% chrome ½% moly steel 80-20 CU-NI

14.6

17

21

34.4

.000067

.000053

.00042

.000036

.000031

.000024

.000018

.000069

.000054

.000043

.000037

.000032

.000024

.000018

.000045

.000038

.000033

.000025

.000018

.000034

.000025

.000019

.000460

.000364

.000289

.000249

.000215

.000166

.000124

.000479

.000375

.000296

.000254

.000219

.000168

.000125

.000309

.000264

.000226

.000172

.000127

.000232

.000176

.000129

Copper 99.9+CU Nickel

238

10

.000186

.000147

.000117

.000101

.000087

.000067

.000050

.000194

.000152

.000120

.000103

.000089

.000068

.000050

.000125

.000107

.000092

.000070

.000051

.000094

.000071

.000052

.001584

.001251

.000995

.000857

.000741

.000571

.000425

.001647

.001289

.001019

.000875

.000754

.000579

.000429

.001063

.000907

.000778

.000593

.000437

.000798

.000605

.000443

Stainless AISI type 302 & Aluminum -304

85

(Continued)

.00275

.000217

.000172

.000149

.000128

.000099

.000074

.000285

.000223

.000177

.000152

.000100

.000100

.000074

.000184

.000157

.000135

.000103

.000076

.000138

.000105

.000077

Yarkalbro, alum, brass

57.7

886  Chemical Process Engineering

Pipe ¾ in. IPS

2 in.

1 1/2 in.

.01055

.01504

.0299

.0363

X Hvy

Sch. 160

XX Hvy

.00722

14

St’d

.00560

16

.01499

.00419

18

8

.01545

8

.01197

.01226

10

10

.00979

12

.00961

.00845

13

12

.00732

14

.00831

.00566

16

13

.00422

Factor

18

OD tube Gauge

Thermal conductivity, K

.00145

.000916

.000602

.000422

.000600

.000479

.000384

.000332

.000289

000224

.000168

.000618

.000490

.000392

.000338

.000293

.000226

.000169

Carbon steel

25

89

.000576

.000363

.000239

.000167

.000238

.000190

.000153

.000132

.000115

.000089

.000067

.000245

.000195

.000155

.00134

.000116

.000090

.000067

.000408

.000257

.000169

.000119

.000168

.000134

.000108

.000093

.000081

.000063

.000047

.000174

.000138

.000110

.000095

.000082

.000064

.000047

Red brass 45% Ars. Admiralty copper

63

Value of r w

Table 8.26B  Metal resistance of tubes and pipes. (Continued)

.00173

.001090

.000716

.000502

.000714

.000570

.000458

.000396

.000344

.000267

.000200

.000736

.000584

.000466

.000402

.000349

.000270

.000201

.00214

.001347

.000885

.000621

.000882

.000704

.000565

.000489

.000124

.000329

.00246

.000909

.000721

.000576

.000497

.000431

.000333

.000248

.00249

.00157

.001030

.000723

.001027

.000820

.000658

.000569

.000495

.000384

.000287

.001058

.000840

.000671

.000579

.000501

.000388

.000289

70-30 CU-NI Monel

4-6% chrome ½% moly steel 80-20 CU-NI

14.6

17

21

34.4

.000153

.000096

.000063

.000044

.000063

.000050

.000040

.000035

.000030

.000024

.000018

.000065

.000052

.000041

.000036

.000031

.000024

.000018

.001055

.000666

.000437

.000307

.000436

.000348

.000279

.000242

.000210

.000163

.000122

.000449

.000356

.000285

.000246

.000213

.000165

.000123

Copper 99.9+CU Nickel

238

10

.000427

.000269

.000177

.000124

.000176

.000141

.000113

.000098

.000085

.000066

.000049

.000182

.000144

.000115

.000099

.000086

.000067

.000050

.00363

.00229

.001504

.001055

.001499

.001197

.000961

.000832

.000722

.000560

.000419

.001545

.001226

.000979

.000845

.000732

.000566

.000422

Stainless AISI type 302 & Aluminum -304

85

(Continued)

.000629

.000397

.000261

.000183

.000260

.000207

.000167

.000144

.000125

.000097

.000073

.000268

.000212

.000170

.000146

.000127

.000098

.000073

Yarkalbro, alum, brass

57.7

Heat Transfer  887

.01308

.01863

.0275

.0422

in. St’d

X Hvy

Sch. 160

XX Hvy .00169

.00110

.000745

.000523

Carbon steel

25

89

.000670

.000437

.000296

.000208

.000474

.000309

.000209

.000147

Red brass 45% Ars. Admiralty copper

63

Value of r w

.00201

.00131

.000887

.000623

.00248

.00162

.001096

.000769

.00289

.00188

.001276

.000896

70-30 CU-NI Monel

4-6% chrome ½% moly steel 80-20 CU-NI

14.6

17

21

34.4

.000177

.000166

.000078

.000055

.001227

.000799

.000542

.000380

Copper 99.9+CU Nickel

238

10

.000496

.000324

.00029

.000154

.00422

.00275

.001863

.001308

Stainless AISI type 302 & Aluminum -304

85

rw for 1 in. O.D. 16 BWG steel tube with 18 BWG admiralty liner = .00031 For other materials, divide factor number by the thermal conductivity of various materials: 60-40 Brass…………….55        Chrome Vanadium Steel        Tin ……………….35       Everdur #50………….19 Zinc…………………….64        SAE 6120…………………23.2     Lead………...........20        Wrought Iron…… .…40 1 K in Btu/(hr)(ft2)(°F/ft)       Used by permission: Griscom-Russell/Ecolaire Corporation. rw in Btu / (hr)(ft 2 )(°F)

Pipe ¾ in. IPS

Factor

OD tube Gauge

Thermal conductivity, K

Table 8.26B  Metal resistance of tubes and pipes. (Continued)

.000731

.000477

.000323

.000227

Yarkalbro, alum, brass

57.7

888  Chemical Process Engineering

Stream

Solvent

Propylene (vaporization)

Propylene (vaporization)

Chilled water

Oil

Condensate and vapor

Chilled water

Propylene (refrigerant)

Transformer oil

Chlorinated Ci

Ethylene vapor

Propane liquid

Steam

Steam

Solvent

Solvent

C4 unsaturates

Solvent

Oil

Ethylene-vapor

Ethylene vapor

Condensate

Chilled water

Calcium brine-25%

Ethylene liquid

Propane vapor

Lights and choir. HC

Unsat. Light HC, CO, CO2, HI2

Outside tubes

Butadiene mix. (super-heating

A. Heating

In tubes

H

U

H

…

…

…

…

1-2

H K-U

…

…

…

…

…

…

20-40

1-2

…

25-35

Velocities tube

H

K-U

H

K

H

H

K

K

H

H

Type equipment

U, Overall heat transfer coefficient, Btu/(h) (ft2) (°F)

…

…

…

…

0.5-1.0

…

…

…

…

…

…

…

…

1.0-1.8

…

ft/s. shell

Table 8.28B  Overall heat transfer coefficients in typical petrochemical applications.

10-2

12-30

6-15

10-20

40-60

40-75

60-135

50-80

90-125

60-85

35-75

13-18

30-40

35-40

12

Overall coefficient

400-100

-30-260

-25-100

-170-(100)

-20-+20

75-50

60-30

270-100

600-200

150-100

115-40

100-35

40-0

110-30

400-100

Temp. range, °F

…

0.001

…

…

0.002

0.001

0.001

.001

0.002

0.0015

.003

…

…

…

…

Tube

…

0.001

…

…

0.005

0.001

0.001

.001

.001

.0015

.001

…

…

…

…

Shell

Estimated fouling

(Continued)

0.3

…

0.002

0.002

…

…

…

…

…

…

…

.005

0.006

0.0065

0.04

Overall

Heat Transfer  889

Steam

Air mixture

Styrene and tars

Freon-12

Lean copper solvent

Treated water

C2-chlor HC, lights

Hydrogen chloride

Heavy C2-chlor.

Perchlorethylene

Air and water vapor

Engine jacket water

Absorption oil

Air-chlorine

Treated water

Ethanolamine

Steam

Steam

Chilled Water

Water*

Water

Water

Water

Water

Water

Water

Water

Water

Water

Water

Propylene refrig.

Propylene refrig.

Propylene refrig.

C4, unsat

HC unsat. lights

Butadiene

B. Condensing

Outside tubes

In tubes

K

K

K

H

U

H

H

H

H

H

H

H

H

H

H

U (in tank)

U

H

Type equipment

U, Overall heat transfer coefficient, Btu/(h) (ft2) (°F)

v

v

v

5-7

4-7

…

…

…

…

…

…

2-3

3-5

4-5

4-7

…

…

…

Velocities tube

…

…

…

…

…

…

…

…

…

…

…

…

1-2

…

…

…

…

…

ft/s. shell

65-80

50-60

58-68

170-225

8-18

80-115

230-160

20-35

55-35

45-30

7-15

6-10

100-125

100-120

100-130

50-60

10-20

15-25

Overall coefficient

Table 8.28B  Overall heat transfer coefficients in typical petrochemical applications. (Continued)

20-35

45-3

60-35

200-90

250-90

130-90

175-90

370-90

150-90

300-90

230-90

360-100

90-110

180-90

90-25

190-230

-30-220

400-40

Temp. range, °F

…

…

…

0.001

…

0.0015

0.0015

0.0015

0.001

0.001

0.002

0.002

…

…

0.001

0.001

0.005

0.001

Tube

…

…

…

0.001

…

0.001

0.001

0.0015

0.001

0.001

0.001

0.001

…

…

0.001

0.002

0.0015

0.001

Shell

Estimated fouling

(Continued)

0.004

0.0055

0.005

…

0.005

…

…

…

…

…

…

…

0.005

0.004

…

…

…

…

Overall

890  Chemical Process Engineering

Outside tubes

Propylene refrig.

Propylene refirg.

Propylene refrig.

Water

Water

Water

Water

Water

Propylene vapor

Propylene

Steam

Steam

Steam (exhaust)

Steam

Propylene cooling and cond.

In tubes

Hydrogen chloride

Lights and chlori-ethanes

Ethylene

Unsat. Chloro HG

Unsat Chloro HG

Unsat Chloro HG

Chloro HG

Solvent and noncond.

Water

Water

Water

Water

Treated water

Oil

Water

H

H

H

H

H

H

H

H

KU

H

H

H

KU

KU

H

Type equipment

U, Overall heat transfer coefficient, Btu/(h) (ft2) (°F)

…

…

…

…

…

…

2-3

…

…

6

3-8

7-8

…

…

…

Velocities tube

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

ft/s. shell

30-45 (C) 15-20 (Co)

110-150

375-130

220-130

230-130

300-90

130-90

200-90

260-90

110-(-10)

130-(-20)

110-90

145-90

120-(-10)

130-(-20)

0-15

Temp. range, °F

25-50

70-110

20-30

190-235

225-110

60-100

130-150

25-15

20-30

15-25

180-140

90-120

60-90

15-25

110-60

Overall coefficient

Table 8.28B  Overall heat transfer coefficients in typical petrochemical applications. (Continued)

0.0015

0.003

0.0001

0.0015

0.002

0.0015

…

0.0015

0.001

0.002

0.001

0.002

0.001

0.002

0.012

Tube

0.001

0.001

0.0001

0.001

0.0001

0.001

…

0.004

0.001

0.001

0.001

0.001

0.001

0.001

0.001

Shell

Estimated fouling

(Continued)

…

…

…

…

…

…

0.003

…

…

…

…

…

…

…

…

Overall

Heat Transfer  891

Air-chlorine (part. cond.)

Light HC, cool and cond.

Ammonia

Ammonia

Freon

Chilled water

Water

Water

Water

Air-Water vapor

VT VT

Steam

Steam

Steam

Steam

Steam

Steam

Steam

Steam

C4 Unsat.

Chloro HC

Chloro, unsat HC

Chloro ethane

Chloro ethane

Solvent (heavy)

Mono-diethanolamines

Organics, acid, water

H

U

VT

VT

VT

H

Steam

H

KU

U

H

H

U

Type equipment

Solvent, Copper-NH3

C. Reboiling

Outside tubes

In tubes

U, Overall heat transfer coefficient, Btu/(h) (ft2) (°F)

…

…

…

…

…

…

…

…

7-8

…

…

…

…

…

Velocities tube

…

…

…

…

…

…

…

…

…

…

…

…

…

…

ft/s. shell

60-100

210-155

70-115

50-70

90-135

100-140

35-25

95-115

130-150

10-20

10-50

280-300

140-65

450-300

450-350

375-300

30-190

300-350

230-130

300-350

95-150

180-160

60-10

110-90

120-90

270-90

10-15 (Co)

20-30 35-90

8-15 (C)

Temp. range, °F

8-15

Overall coefficient

Table 8.28B  Overall heat transfer coefficients in typical petrochemical applications. (Continued)

0.003

0.002

0.004

0.002

0.001

0.001

0.001

…

…

…

0.001

0.001

0.0015

0.0015

Tube

0.0005

0.001

0.0005

0.001

0.001

0.001

0.001

…

…

…

0.001

0.001

0.003

0.005

Shell

Estimated fouling

(Continued)

…

…

…

…

…

…

…

0.0065

0.005

0.01

…

…

…

…

Overall

892  Chemical Process Engineering

Steam

Naphtha frac.

C3

Butadiene, unsat.

Amines and water

Steam

Propylene

Propylenebutadiene

H

KU

Annulus, long F.N.

VT

Type equipment

…

…

…

…

Velocities tube

*Unless specified, all water is untreated, brackish, bay or sea. Notes: H = horizontal, fixes or floating tubesheet T = thermosyphon V = Vertical U = U-tube horizontal bundle v = variable r = reboiler (C) = cooling range ∆t K = kettle type HC = hydrocarbon (Co) = condensing range ∆t Data/results based on actual and specific industrial equipment.

Outside tubes

In tubes

U, Overall heat transfer coefficient, Btu/(h) (ft2) (°F)

25-35

…

…

…

ft/s. shell

15-18

120-140

15-20

120-140

Overall coefficient

Table 8.28B  Overall heat transfer coefficients in typical petrochemical applications. (Continued)

400-100

-150-40

270-220

360-250

Temp. range, °F

…

0.001

0.0035

0.002

Tube

…

0.001

0.0005

0.0015

Shell

Estimated fouling

0.02

…

…

…

Overall

Heat Transfer  893

894  Chemical Process Engineering

References 1. Buthod, A. P., “How to Estimate Heat Exchangers,” Oil and Gas Jour., V. 58, No. 3, p. 67 (1960). 2. Donohue, D. A., “Heat Transfer and Pressure Drop in Heat Exchangers,” Ind. Eng. Chem., V. 41, p. 2499 (1949). 3. Eckert, E. R. G., “Introduction to the Transfer of Heat and Mass,” p. 115, McGraw-Hill Book Co., New York (1950). 4. “Heat Exchangers” Manual No. 700-A, The Patterson-Kelley Co., Inc., East Stroudsburg, PA. 5. Bergelin, O. P., Lafferty, Jr. W. L., Leighton M. D. and R. L. Pigford, Heat transfer and pressure drop during viscous and turbulent flow across baffled and unbaffled tube banks. University of Delaware, Eng. Exp. Sta., Newark, Del. Bul; No. 4, 1958. 6. Kern, D. Q. and R. E. Seaton, “A Theoretical Analysis of Thermal Surface Fouling,” British Chem. Eng., V. 4, p. 258, June 1959. See also, Chem. Eng., V. 66, p. 125, Aug. 10, (1959). 7. Tinker, Proceedings on the General Discussion on Heat Transfer, Inst. Mech. Eng. London, Shell-side characteristics of shell and tube heat exchangers, p. 89 (1951). 8. Tinker, T., Shell-side characteristics of shell and tube exchangers, Trans. Am. Soc., Mech. Eng., 80 (Jan) 36 (1958). 9. Devore, A., Try this simplified method for rating baffled exchangers, Pet. Ref. 40 (May), 221 (1961). 10. Devore, A., Use nomograms to speed exchanger design, Hyd. Proc. and Pet. Ref. 41 (Dec.) 103 (1962). 11. Mueller, A. C., Heat Exchangers, section 18 in Rosenow, M.W., and H. P. Hartnell, (eds.), Handbook on Heat Transfer, McGraw-Hill (1973). 12. Bell, K. J., Exchanger design based on the Delaware research program, Pet. Eng., 32, No. 11, C26, 1960. 13. Bell, K., J., Approximate sizing of shell-and-tube heat exchangers, in Heat Exchanger Design Handbook, Vol. 3, Hemisphere Publishing Corp., New York, 1988. 14. Standards of Tubular Exchanger Manufacturers Association, 6th Ed. (1978) and 7th Ed. (1988), The Tubular Exchanger Manufacturers Association, Inc., Tarrytown, NY (also see No. 266). 15. Rubin, F. L., “Reboilers and Sectional Exchangers,” Chem. Eng., p. 229, Sept. (1953). 16. Unfired Pressure Vessels, Section VIII, ASME Boilers and Pressure Vessel Code (Latest Edition), ASME, 345 E. 47th Street, New York, NY. 17. Rubin, F. L., “What’s the Difference between TEMA Exchanger Classes,” Hydrocarbon Processing, V. 59, p. 92, June (1980). 18. Rubin, F. L. and N. R. Gainsboro, “Latest TEMA Standards for Shell and Tube Exchangers,” Chem. Eng., V. 86, p. 11, Sept. 24 (1979) 19. Boyer, J. and G. Trumpfheller, “Specification Tips to Maximize Heat Transfer,” Chem. Eng., p. 90, May (1993). 20. Donohue, D. A., “Heat Exchangers,” Petroleum Processing, p. 102, March (1956). 21. Donohue, D. A., “Heat Exchanger Design,” Pet. Ref., V. 34, Part 1, No. 8, p. 94 (1955); Part 2, No. 10, p. 129 (1955); Part 3, No. 11, p. 75 (1955); Part 4, V. 35, No. 1, p. 155 (1956). 22. Heat Exchangers Manual No. 700-A. The Patterson-Kelley Co., Inc., East Stroudsburg, PA. 23. Mukherjee, R., Does Your Application call for an F-Shell Heat Exchanger, CEP, p. 40, April (2004). 24. Bergles, A. E., Collier, J. G., Delhaye, J. M., Hewitt, G. F., and Mayinger F., Two-phase flow and heat transfer in the power and process industries. Washington D.C: Hemisphere, 1981. 25. Lestina, T. G., Selecting a heat exchanger shell, CEP, 34, June 2011. 26. Yokell, S., A Working Guide to Shell and Tube Heat Exchangers, McGraw-Hill (1990). 27. Cao, Eduardo, Heat Transfer in Process Engineering, McGraw-Hill (2010). 28. Watson, B., Thermal Design of Shell & Tube Heat Exchangers, Printed in the U.K., by PrintOnDemand-Worldwide.com (www.satcap.co.uk) 29. Gulley, D. L., “How to Figure True Temperature Difference in Shell-and-Tube Exchangers,” Oil and Gas Jour., Sept. 14 (1964). 30. Murty, K. N., “Quickly Calculate Temperature Cross in 1-2 Parallel-Counterflow Heat Exchangers,” Chem. Eng., p. 99, Sept. 16 (1985). 31. Bowman, R. A., A. C. Mueller, and W. M. Nagle, “Mean Temperature Difference in Design,” Trans. ASME, V. 62, pp. 283294 (1940). 32. Blackwell, W. W. and L. Haydu, “Calculating the Corrected LMTD in Shell-and-Tube Heat Exchangers,” Chem. Eng., p. 101, Aug. 24 (1981). 33. Ratnam, R. and P. S. Patwardhan, “Analyze Single and Multi-Pass Heat Exchangers,” Chem.Eng. Prog., V. 88, No. 6, p. 85 (1993). 34. Turton, R., D. Ferguson, and O. Levenspiel, “Charts for the Performance and Design of Heat Exchangers,” Chem. Eng., p. 81, Aug. 18 (1986).

Heat Transfer  895 35. Moody, L., Friction factor for pipe flow. Trans ASME, 66:671-84, 1944. 36. Drew, T. B., Koo, E. C., and W. H., McAdams, Trans AIChE, 28: 56-72, 1932. 37. Wilson, R. E., Mc Adams, W. H., and M. Seltzer, Ind. Eng., Chem., 14: 105-19, 1922. 38. Serth, W., Process Heat Transfer, Principles and Applications, Elsevier Science & Technology Books (2007). 39. Kern, D. Q., Process Heat Transfer, 1st ed., McGraw-Hill Book Co., Inc., New York (1950). 40. Butterworth, D., Course on the design of shell and tube heat exchangers. East Kilbride, Glasgow, U.K.: National Engineering Laboratory; 1978. Condensation – 1. Heat Transfer across the condensed layer. 41. Sinnott, R., and G. Towler, Chemical Engineering Design, 5th ed., Butterworth-Heinemann, 2009. 42. Frank, O., Simplified design procedure for tubular exchangers, In practical aspects of heat transfer. Chem. Eng. Prog. Tech. Manual AIChE. 1978. 43. Gulley, D., More accurate exchanger shell-side pressure drop calculations – use this method to reduce equipment size and pumping power cost. Hydro Proc. July 2004. 44. Gulley, D., Private Communication. 2013. 45. Taborek, J., Shell and tube heat exchangers in heat exchanger design handbook, part 3, sections 3.3.3 to 3.3. 9. Begell House; 2002. 46. Plant, C. A., Evaluate Heat Exchanger Performance, Chem. Eng., V. 99, No. 6, Part 1 and No. 7, Part 2, pp. 100 and 104, respectively (1992). 47. Ishiyama, E. M., Wilson, D. J., Patterson, W. R., Heins, A. V., and L. Spinelli, In: H. Muller-Steinhagen, et al., eds. The Importance of Scheduling and Desalter Control of Preheat Trains of Crude Distillation Units: A Case Study, Proc., of Int. Conf., on Heat Exchanger Fouling and Cleaning VIII; June 14-19, 2009. 48. Sanatgar, H. and E. F. C. Somerscales, “Account for Fouling in Heat Exchanger Design,” Chem. Eng. Prog., V. 87, No. 2, p. 53 (1991). 49. Epstein, N., “Fouling in Heat Exchangers,” Proc. 6th International Heat Transfer Conference Keynote papers, v.6, p. 235, Toronto, Canada, Hemisphere Publishing Co., New York, NY (1978). 50. Mukherjee, R., “Conquer Heat Exchanger Fouling,” Hydro Proc., V. 71, No. 1, p. 121 (1996). 51. Bott, T. Reg., To foul or not to foul. CEP November, 30-1, 2001. 52. Waters, A. J., Akinradewo, C. G., and D. Lamb, Fouling: implementation of a crude preheat train performance monitoring application at the Irving oil refinery. Proc. Int. Conf. Heat Exchanger Fouling Cleaning VIII, 33-8, June 14-19, 2009. 53. Macchietto, S., et al., Fouling in crude oil preheat trains: a systematic solution to an old problem. Proc. Int. Conf. Heat Exchanger Fouling Cleaning VIII June 14, 2009. 54. Shah, Ramesh K., Dusan, P. Sekulic, Fundamentals of heat exchanger design, John Wiley & Sons Inc., 2003. 55. Bouhaire, S., Selecting baffles for shell and tube heat exchangers. CEP, 2: 27, Feb. 2012. 56. Polley, G. T., and G. Gonzales-Garcia, Procedure for applying fouling models to predict overall fouling rates in industrial heat exchangers in: Steinhagen, H. Muller, et al., editors. Proceedings of Int. Conf. on Heat Exchanger Fouling and Cleaning VII – June 11-19, Austria: Schladming; 2009. 57. Najjar, M. S. K. J. Bell, and R. N. Maddox, “The Influence of Improved Physical Property Dta on Calculated Heat Transfer Coefficients,” Heat Transfer Eng., V. 2, No. 3-4, p. 27 (1981). 58. Perry, John H. (Ed), Chemical Engineers Handbook, 3rd ed. McGraw-Hill Book Co, Inc. (1950). 59. 58A. Green, D. W. (Ed) and J. O. Maloney, Perry’s Chemical Engineers’ Handbook, 6th ed., McGraw-Hill, Inc. All rights reserved. (1984). 60. Hedrick, R. H., “Calculate Heat Transfer for Tubes in the Transition Region,” Chem. Eng., V. 97, No. 6, p. 147 (1989). 61. Seider, E. N. and G. E. Tate, “Heat Transfer and Pressure Drop of Liquids in Tubes,” Ind. Eng. Chem., V. 28, p. 1429 (1936). 62. Starczewski, J., “Graphs Cut Exchanger Design Time,” Hydro. Proc. & Pet. Refiner, V. 40, No. 6, p. 165 (1961). 63. “Heat Exchangers – Special Report,” Hydro. Proc., V. 65, No. 6, p. 115 (1966). 64. Furman, T., “Heating and Cooling Inside Tubes,” British Chem, Eng., p. 262, May (1958). 65. Pierce, B. L., “Heat Transfer Colburn-Factor Equation Spans All Fluid Flow Regimes,” Chem. Eng., p. 113, Dec. 17 (1979). 66. McAdams, W. H., Heat Transmission, 2nd ed., McGraw-Hill Book Co., Inc. New York. (1942). 67. McAdams, W. H., Heat Transmission, 3rd ed., McGraw-Hill Book Co., Inc. New York (1954). 68. Ganapathy, V., “Evaluate Extended Surface Exchangers Carefully,” Hydro. Proc., V. 69, p. 65, Oct. (1990). 69. Rubin, F. L., “Heat Transfer Rates for Gases,” Pet. Refiner, V. 36, No. 3, p. 226 (1957). 70. Mathews, R. R., “Air Cooling in Chemical Plants,” Chem. Eng. Prog., V. 55, No. 5, p. 68 (1959), and as presented at AIChE meeting, Cincinnati, OH, December (1958). 71. Bergelin, O. P., Lafferty, Jr. W. L., Leighton, M. D., and R. L. Pigford, Heat transfer and pressure drop during viscous and turbulent flow across baffled and unbaffled tube banks. University of Delaware, Eng., Exp. Sta, Newark, Del. Bul; No. 4, 1958.

896  Chemical Process Engineering 72. Short, B. E., “Heat Transfer and Pressure Drop in Heat Exchangers,” Engineering Research Series No. 37, University of Texas, Austin, TX, pub. No. 4324, pp. 1-55 (1943). 73. Bowman, R. A., Misc. Papers, No. 28, p. 75, ASME, New York, NY (1936). 74. Tinker, T., “Shell-Side Characteristics of Shell-And-Tube Heat Exchangers,” Paper No. 56A-123, presented at ASME Meeting, New York, Nov. (1956). 75. Chen, Ning Hsing, “Save Time in Heat Exchanger Design,” Chem. Eng. v. 65, p. 153, Oct. 20, (1958). 76. Kern, D. Q. and Kraus, A. D., Extended Surface Heat Transfer, McGraw-Hill Book Co., (1972). 77. Rubin, F. L., “Heat Transfer Rates for Gases,” Pet. Ref., V. 36, No. 3, p. 226 (1957). 78. Coker, A. K., Ludwig’s Applied Process Design for Chemical and Petrochemical Plants, Vol. 1, Elsevier, 2007. 79. Stoever, H. J., Applied Heat Transmission, 1st ed., McGraw-Hill Book Co., Inc., New York (1941). 80. Stoever, H. J., “Heat Transfer,” Chem. and Met. Eng., p. 98, May (1944). 81. Starczewski, J., “Short Cut Method to Exchanger Shell-Side Pressure Drop,” Hydro. Proc., V. 50, No. 6, p. 147 (1971). 82. Bejan, A., and A. Kraus, Heat transfer handbook, John Wiley and Sons, 2003. 83. Coker, A. K., Ludwig’s Applied Process Design for Chemical and Petrochemical Plants, Vol. 3, Elsevier, 2015. 84. Kakac, S., and H. Liu, Heat exchangers: selection, rating and thermal design, 2nd ed. Boca Raton: CRC Press, 2002. 85. Hall, S., Rules of Thumb for Chemical Engineers, 5th ed., Elsevier, 2012 86. Whitley, D. L., “Calculating Heat Exchangers Shell-Side Pressure Drop,” Chem. Eng. Prog., V. 57, No. 9, p. 59 (1961). 87. Palen, J. W. and J. J. Taborek, “Refinery Kettle Reboilers,” AIChE Nat’l. Heat Transfer Conference, Chem. Eng. Prog., V. 58, No. 7, p. 37 (1962). 88. Polley, G. T., Panjeh Shahi M. H., and Picon Nunez M., Rapid design algorithms for shell and tube and compact heat exchangers. Trans. IChemE., Part A, 69, November 1991. 89. Bul. An Opportunity, Wolverine Tube, Inc. 90. Young, E. H. and D. J. Ward, “How to Design Finned Tube Shell and Tube Heat Exchangers,” The Refining Engr., p. C-32, No. (1597). 91. Pase, G. K. and J. O’Donnell, “Use Titanium Tubes to Create Higher Capacity Corrosion Resistant Exchangers,” Hydro. Proc., Occ. (1995). 92. Hashizume, K., “Heat Transfer Pressure Drop Characteristics of Finned Tubes in Cross-Flow,” Heat Transfer Eng., V. 3, No. 2, p. 15 (1981). 93. Webb, R. L., “Air-Side Heat Transfer in Finned-Tube Heat Exchangers,” Heat Trans. Eng., V. 1, No. 3, p. 33 (1980). 94. Rohsenow, W. M. and J. P. Hartnett, Handbook of Heat Transfer, McGraw-Hill, In. (1973). 95. Briggs, D. E. and Young, E. H., Chem. Eng. Prog. Sym. Series No. 41, Heat Transfer, Houston, Texas, V. 59, No. 1 (1963). 96. Ganapathy, V. “Charts Simplify Spiral Finned Tube Calculations,” Chem., Eng., V. 84, No. 9, p. 117 (1977). 97. Bell, K. J., ASME – University of Delaware Cooperative Research Program on Heat Exchangers, ASME and University of Delaware (1960). 98. “How to Design Double Pipe Finned Tube Heat Exchangers,” Brown Fintube Co., A Koch Engineering Co. 99. Carlson, J. A. “Understand the Capabilities of Plate and Frame Heat Exchangers,” Chem. Eng. Prog., V. 88, No. 7, p. 26 (1992). 100. “The Basics of Air-Cooled Heat Exchangers,” Hudson Products Corp., Bul. M92-300 (1994). 101. Cook, E. M., “Rating Methods for Selection of Air-Cooled Heat Exchangers,” Chem. Eng., p. 97, Aug. 3 (1964). 102. Rubin, F. L., “Power Requirements Are Lower for Air-Cooled Heat Exchangers with Variable-Pitch Fan Blades,” Oil and Gas Jour., Oct. 11, (1982). 103. Lerner, J. E., “Simplified Air Cooler Estimating,” Hydro. Proc., p. 93, Feb. (1972). 104. Larinoff, M. W., W. E. Moles, and R. Reichhelm, “Designed Specifications of Air-Cooled Steam Condensers,” Chem. Eng., May, 22 (1978). 105. Murtha, J. W. and S. H. Friedman, “Estimating Air-Cooled Exchangers Made Easy,” Chem. Eng., p. 99, Feb. 6, (1961). 106. Maze, R. W., “Air-Cooled or Water Tower, Which for Heat Disposal,” Chem. Eng., p. 106, Jan 6 (1975). 107. Rubin, F. L., “Winterizing Air-Cooled Heat Exchangers,” Hydro. Proc., V. 59, No. 10, p. 147 (1980). 108. Stuhlbarg, D. and A. M. Szurgot, “Eliminating Height and Wind Effects on Air-Cooled Heat Exchangers,” Chem. Eng., V. 94, No. 7, p. 151 (1987). 109. Shipes, K. V., “Air Coolers in Cold Climates,” Hydro, Proc., V. 53, No. 5, p. 147 (1974). 110. Harris, L. S., “For Flexibility, the Air-Evaporative Cooler,” Chem. Eng., p. 77, Dec. 24 (1962). 111. Hutton, D., “Properly Apply Closed-Circuit Evaporative Cooling,” Chem. Eng. Prog., V. 92, No. 10, p. 50 (1996). 112. Ganapathy, V., “Evaluate Extended Surface Exchangers Carefully,” Hydro. Proc., V. 69, p. 65, Oct. (1990). 113. Maze, R. W., “Air vs. Water Cooling; How to Decide Which System to use,” Oil and Gas Jour., p. 74, Nov. 19 (1974). 114. Mukherjee, R., “Effective Design Air-Cooled Heat Exchangers,” Chem. Eng. Prog., p. 26, Feb. (1997).

Heat Transfer  897 1 15. Bul. 2401, Griscom-Russell Co., Massillon, OH (1960). 116. Nauss, V., private discussion, Griscom-Russell Co., Massillon, OH (1960). 117. Gardner, K. A. and T. C. Carnavas, “Thermal-Contact Resistance to Finned Tubing,” Trans. of ASME Jour. of Heat Transfer, Paper No. 59-A-135. 118. Kern, D. Q. and R. E. Seaton, “Optimum Trim Cooler Temperature,” Chem. Eng. Prog., V. 55, No. 7, p. 69 (1959). 119. Thronton, D. P., “Water Scarce – Natural Gasoline Plant Uses Air for 80% of Required Cooling,” Petroleum Processing, V. 2, p. 52, Jan (1947). 120. Smith, E. C., “Air Cooled Heat Exchangers,” Chem. Eng., V. 65, p. 145 (1958). 121. Cook, E. M., Rating methods or selection of air-cooled heat exchangers, Chem. Eng., 97-104, August 3, 1964. 122. Ganapathy, V., Process design criteria. Chem. Eng., 112-9, March 27, 1978. 123. Brown, R., A procedure for preliminary estimates., Chem. Eng., 108-11, March 27, 1978. 124. Blackwell, W. W., Chemical process design on a programmable calculator, McGraw-Hill Book Company, 1984. 125. Chopey, N. P., and T. G. Hicks, Handbook of chemical engineering calculations, New York: McGraw-Hill Book Company, 1984. 126. Berryman, R. J., Condition monitoring of air-cooled heat exchangers, design and operation of heat exchangers. In: Proceedings of the Eurotherm Seminar. Feb. 27-March 1, 1991, 1992, Hamburg. 127. Lam, V., and C. Samberg, Choose the right heat tracing system. Chem. Eng. Prog., 63-7, March 1992. 128. deLange, J. A. B., Steam Tracing with MS Excel, www.cheresource.com 129. Bondy, F., and S. Lippa., Heat transfer in agitated vessels. Chem. Eng., 62-71, 1983. 130. Dream, R. F., Heat transfer in agitated vessels, Chem. Eng., 90-6, Jan. 1999. 131. Fabregas, J. A., “Electronic Computer Rates Heat Exchangers, Alco Products Review,” Alco Products, Inc. 30 Church St., New York, NY, Fall (1956). 132. Frank, R. G. E. and N. G. O’Brien, “Application of a General Purpose Analog Computer in the Design of a CoolerCondenser,” Chem. Eng. Progr., Sym. Series 56, No. 31, pp. 37-41 (1960). 133. Peiser, A. M., “Design of Heat Exchangers on Automatic Computers,” The Refining Engr., P. C-12, Oct. (1957). 134. Taborek, J. J., “Organizing Heat Exchangers Programs on Digitial Computers,” Chem. Eng. Prog., V. 55, No. 10, p. 45 (1959). 135. Whitley, D. L. and E. E. Ludwig, “Heat Exchanger Design with a Digital Computer,” Pet. Ref., V. 40, No. 1, p. 147 (1961). 136. Gulley, D., Troubleshooting shell and tube heat exchangers, Hydrocarbon Proc., 91, September 1996. 137. Gulley, D., Private Communication. 2013. 138. Lord, R. C., Minton, P. E., and R. P. Shisser, Guide to trouble-free heat exchangers, Chem. Eng., 77 (11): 153-60., 1970. 139. Kakac, S., and H. Liu, Heat exchangers: selection, rating and thermal design, 2nd ed. Boca Raton: CRC Press, 2002. 140. Chase, J. C., and H. E. Degler, “Economics of the Air-Cooled Heat Exchanger,” Pet. Engr., p. C-42, Jan, (1953). 141. Karami, I. A., Shastri, S. S., and C. Yap., Enhanced air-cooled heat exchanger performance. Hydro. Proc. Dec. 200., In www. hydrocarbonprocessing.com 142. Standards of the Tubular Exchanger Manufacturers Association, 7th ed., Tubular Exchanger Manufacturers Association, Inc., (1988). 143. “The Basics of Air-Cooled Heat Exchangers,” Hudson Products Corp., Bul. M92-300, (1994). 144. Kern, D. Q., and A. D. Kraus, Extended Surface Heat Transfer, Mc.Graw-Hill Book Co., (1972). 145. Rubin, F., What’s the difference between TEMA exchanger classes?, Hydroc. Proc., 9:92, 1980. 146. Gupta, J. P., Working with heat exchangers - questions and answers. Hemisphere Publishing Corp., 1990. 147. Rohsenow, W. M., A method of correlating heat transfer data for surface boiling of liquids. Trans. ASME Later J Heat Trans. 74: 969-75, 1962. 148. Chen, E., Optimize reboiler design. Hydro. Proc. July 2001, in http://www.hydrocarbonprocessing.com/Article/2600382/ optimize-reboiler-design.html. 149. Chopey, Nicolas, P., Minton, P.E., and S. S. Edward Morrison, Handbook of Chemical Engineering Calculation, 3rd., ed., McGraw-Hill; Chapter 7, 2003. 150. Kohli, I.P., Steam tracing in pipelines, Chem. Eng. (NY) pp. 163, Mar. 26, 1979.

898  Chemical Process Engineering

Appendix A Heat Transfer Table 8.16A  Full circle tube layouts floating heat exchanger ¾–in. O.D. tubes on 15/16 –in. Triangular Pitch. Number of passes 8

Net free distance 2 passes

Rows across

32

24

3.75

13

56

54

52

4.63

17

106

88

86

80

4.00

21

130

124

110

108

104

4.50

25

16

187

176

162

152

144

5.00

29

18

241

232

214

216

204

5.88

33

20

308

302

282

274

264

6.50

37

22

384

372

352

348

336

7.13

41

24

472

458

432

420

406

7.75

45

26

555

538

510

510

502

8.63

48

28

649

636

610

606

580

8.13

53

30

764

744

716

708

700

8.75

57

32

868

850

822

812

796

9.38

63

34

994

970

930

928

912

9.75

65

36

1131

1108

1066

1058

1028

10.50

71

38

1268

1246

1204

1190

1172

11.25

75

40

1414

1390

1360

1338

1316

12.06

79

42

1558

1544

1502

1482

1464

11.50

83

Size (in.)

1

2

4

6

8

42

40

32

10

73

68

12

109

14

Heat Transfer  899 Table 8.16B  Full circle tube layouts floating heat exchanger ¾–in. O.D. Tubes on 1 –in. Square Pitch. Number of passes 8

Net free distance 2 passes

Rows across

24

24

3.50

6

48

48

48

4.13

8

82

78

72

72

4.50

11

104

96

92

88

88

6.00

11

16

140

136

128

120

120

6.50

14

18

185

180

172

168

164

6.88

16

20

241

236

224

212

212

7.38

17

22

300

280

280

268

268

7.75

20

24

360

350

336

332

332

8.25

21

26

424

412

402

392

392

8.75

23

28

402

488

480

472

472

9.25

25

30

580

566

566

548

548

9.75

27

32

665

648

644

628

628

10.00

29

34

756

758

730

728

728

10.19

31

36

853

848

832

816

816

11.69

33

38

973

950

938

932

932

12.19

35

40

1085

1064

1052

1036

1036

12.69

37

42

1201

1176

1162

1148

1148

13.19

39

Size (in.)

1

2

4

6

8

32

32

26

10

56

52

12

82

14

900  Chemical Process Engineering Table 8.16C  Full circle tube layouts floating heat exchanger ¾–in. O.D. Tubes on 1 –in. Triangular Pitch. Number of passes 8

Net free distance 2 passes

Rows across

26

24

4.13

11

52

46

44

4.88

17

90

86

78

72

4.38

21

121

110

102

98

92

5.50

21

16

163

152

146

140

132

6.25

25

18

212

202

194

188

184

5.88

29

20

269

260

250

240

236

6.63

35

22

337

330

314

300

296

7.33

39

24

421

404

380

378

364

8.00

43

26

499

476

460

450

440

8.88

47

28

579

562

542

538

520

9.63

51

30

668

648

636

624

612

10.33

53

32

766

744

732

714

712

11.00

57

34

870

850

834

828

808

10.50

61

36

986

978

942

932

920

11.38

67

38

1108

1100

1060

1060

1036

12.13

71

40

1236

1228

1200

1190

1164

12.75

75

42

1367

1350

1322

1306

1288

13.25

77

Size (in.)

1

2

4

6

8

37

30

26

10

61

56

12

92

14

Heat Transfer  901 Table 8.16D  Full circle tube layouts floating heat exchanger, 1 –in. O.D. Tubes on 1 ¼ -in. Square Pitch. Number of passes 8

Net free distance 2 passes

Rows across

….

….

4.13

5

32

32

….

4.25

6

52

48

48

48

4.25

8

61

60

60

52

52

5.50

10

16

89

84

80

76

76

5.50

11

18

113

112

112

108

108

5.38

13

20

148

148

140

136

136

5.38

14

22

184

178

172

168

164

7.38

16

24

221

220

212

208

208

7.38

17

26

266

266

258

252

252

7.38

19

28

316

308

304

292

292

7.38

20

30

368

360

352

344

340

9.38

21

32

421

410

402

392

392

9.38

23

34

481

472

464

452

452

9.69

24

36

545

540

532

524

524

9.69

26

38

608

608

588

588

588

9.69

28

40

680

680

656

664

660

9.69

29

42

750

738

728

728

728

11.69

31

Size (in.)

1

2

4

6

8

21

16

16

10

37

32

12

48

14

902  Chemical Process Engineering Table 8.16E  Full circle tube layouts floating heat exchanger, 1 –in. O.D. Tubes on 1 ¼ -in. Triangular Pitch. Number of passes 8

Net free distance 2 passes

Rows across

16

12

4.13

9

32

32

28

4.50

13

52

48

46

44

4.63

15

73

68

60

58

56

4.25

19

16

97

98

86

82

80

4.25

21

18

130

126

118

114

112

6.50

25

20

170

164

152

150

144

6.75

27

22

212

202

196

188

184

7.00

31

24

258

250

242

232

228

7.25

33

26

304

302

286

278

272

7.50

37

28

361

348

338

336

324

7.75

39

30

421

408

400

394

388

8.00

43

32

482

472

456

446

440

8.25

47

34

555

538

524

520

500

11.06

49

36

625

618

592

588

572

10.44

51

38

700

688

672

660

640

10.69

55

40

786

776

752

742

736

11.00

59

42

872

850

834

824

816

11.32

61

Size (in.)

1

2

4

6

8

22

20

18

10

38

36

12

60

14

Heat Transfer  903 Table 8.17A  Tube count ¾ -in. (19.05 mm) tubes on triangular (30 Degrees) array, pitch 1 in (25.4 mm) TEMA type L. Internal shell diameter

   Number of tube passes

in

mm

1

2

4

6

8

203.2

38

36

32

24

10

254

69

62

56

48

12

304.8

105

94

88

76

13 ¼

336.5

129

120

108

104

15 ¼

387.3

181

166

154

148

17 ¼

438.15

235

218

206

198

19 ¼

488.9

295

280

262

252

21 ¼

539.7

356

344

330

314

23 ¼

590.5

431

418

398

388

25

635

504

492

462

446

27

685.8

597

578

550

538

29

736.6

694

674

646

634

31

787.4

799

778

750

732

33

838.2

919

888

854

834

35

889

1031

1004

968

946

37

939.8

1149

1128

1084

1052

39

990.6

1284

1258

1216

1202

42

1066.8

1499

1452

1416

1382

45

1143

1727

1686

1640

1616

904  Chemical Process Engineering Table 8.17B  Tube count ¾ -in. (19.05 mm) tubes on square (90 Degrees) array, pitch 1 in (25.4 mm) TEMA type S. Internal shell diameter

Number of tube passes

in

mm

2

4

6

8

203.2

22

20

18

10

254

40

40

36

12

304.8

70

64

70

13 ¼

336.5

90

84

84

15 ¼

387.3

126

114

114

17 ¼

438.15

164

158

156

19 ¼

488.9

218

210

198

21 ¼

539.7

268

262

260

23 ¼

590.5

334

326

314

25

635

392

378

364

27

685.8

462

450

426

29

736.6

544

534

510

31

787.4

634

610

594

33

838.2

716

702

674

35

889

816

796

780

37

939.8

914

896

882

39

990.6

1028

1012

988

42

1066.8

1194

1168

1156

45

1143

1390

1364

1336

Heat Transfer  905 Table 8.17C  Tube count ¾ -in. (19.05 mm) tubes on square (90 Degrees) array, pitch 1 in (25.4 mm) TEMA type U. Internal shell diameter

Number of tube passes

in

mm

2

4

6

8

203.2

26

20

20

10

254

48

44

40

12

304.8

74

68

68

13 ¼

336.5

94

88

84

15 ¼

387.3

126

122

114

17 ¼

438.15

172

170

160

19 ¼

488.9

218

218

218

21 ¼

539.7

280

278

268

23 ¼

590.5

346

338

330

25

635

408

390

386

27

685.8

478

470

454

29

736.6

560

546

534

31

787.4

646

634

618

33

838.2

744

730

716

35

889

840

820

816

37

939.8

946

932

918

39

990.6

1060

1048

1032

42

1066.8

1240

1220

1192

45

1143

1430

1404

1388

906  Chemical Process Engineering Table 8.17D  Tube count 1 -in. (24.4 mm) tubes on triangular (30 Degrees) array, pitch 1.25 in (31.75 mm) TEMA type L. Internal shell diameter

Number of tube passes

in

mm

1

2

4

6

8

203.2

22

22

12

12

10

254

40

36

32

28

12

304.8

61

58

48

48

13 ¼

336.5

81

72

68

58

15 ¼

387.3

104

100

94

82

17 ¼

438.15

145

132

122

114

19 ¼

488.9

181

174

162

152

21 ¼

539.7

224

218

202

198

23 ¼

590.5

270

264

246

242

25

635

317

306

286

280

27

685.8

376

362

338

328

29

7366

431

414

398

388

31

787.4

500

492

462

458

33

838.2

571

556

530

510

35

889

641

630

604

582

37

939.8

737

708

680

664

39

990.6

813

796

764

748

42

1066.8

941

918

888

868

45

1143

1091

1068

1028

1008

Heat Transfer  907 Table 8.17E  Tube count 1-in. (25.4 mm) tubes on square (90 Degrees) array, pitch 1.25 in (31.75 mm) TEMA type U. Internal shell diameter

Number of tube passes

in

mm

2

4

6

8

203.2

12

8

10

254

26

20

20

12

304.8

40

36

28

13 ¼

336.5

56

48

48

15 ¼

387.3

76

70

66

17 ¼

438.15

102

98

94

19 ¼

488.9

126

130

118

21 ¼

539.7

164

166

156

23 ¼

590.5

206

202

198

25

635

248

242

232

27

685.8

294

282

274

29

736.6

346

334

322

31

787.4

400

390

382

33

838.2

458

446

438

35

889

522

508

496

37

939.8

584

576

548

39

990.6

648

648

628

42

1066.8

758

744

742

45

1143

898

880

854

908  Chemical Process Engineering Table 8.17F  Tube count 1-in. (25.4 mm) tubes on square (90 Degrees) array, pitch 1.25 in (31.75 mm) TEMA type S. Internal shell diameter

Number of tube passes

in

mm

2

4

6

8

203.2

12

8

10

254

26

24

22

12

304.8

40

40

36

13 ¼

336.5

56

48

48

15 ¼

387.3

76

70

66

17 ¼

438.15

102

98

94

19 ¼

488.9

126

130

118

21 ¼

539.7

164

166

156

23 ¼

590.5

206

202

198

25

635

248

242

232

27

685.8

294

282

274

29

736.6

346

334

322

31

787.4

400

390

382

33

838.2

458

446

438

35

889

522

508

496

37

939.8

584

576

548

39

990.6

648

648

628

42

1066.8

758

744

742

45

1143

898

880

854

Heat Transfer  909 Table 8.21  Fouling resistances for water (Values in m2.K/W). Temperature of the Heating Medium

Up to 115oC

115 – 205°C

52°C or less Velocity, m/s

More than 52°C Velocity, m/s

   Temperature of Water

1 or less

1 or less

>1

Sea water

0.00009

0.00009

0.0002

0.0002

Brackish water

0.0004

0.0002

0.0005

0.0004

   Treated make up

0.0002

0.0002

0.0004

0.0004

  Untreated

0.0005

0.0005

0.0009

0.0007

City or well water

0.0002

0.0002

0.0004

0.0004

  Minimum

0.0004

0.0002

0.0005

0.0004

  Average

0.0005

0.0004

0.0007

0.0005

   Muddy or silty

0.0005

0.0004

0.0007

0.0005

Hard (over 15 grains/gal)

0.0005

0.0005

0.0009

0.0009

Engine jacket

0.0002

0.0002

0.0002

0.0002

Condensate

0.00009

0.00009

0.00009

0.00009

Treated boiler feed water

0.0002

0.00009

0.0002

0.0002

Boilers purge

0.0004

0.0004

0.0004

0.0004

1

Cooling tower and artificial spray pond

River water

Distilled or closed cycle

From Standards of the Tubular Exchangers Manufacturers Association Note: If the heating medium temperature is over 400oF and the cooling medium is known to scale, these ratings should be modified accordingly.

910  Chemical Process Engineering Table 8.22  Guide to fouling resistance. RGP-T2.4 Design Fouling Resistance (hr-ft2-°F/Btu) The purchaser should attempt to select an optimal fouling resistance that will result in a minimum sum of fixed, shutdown and cleaning costs. The following tabulated values of fouling resistances allow for over sizing the heat exchanger so that it will meet performance with reasonable intervals between shutdowns and cleaning. These values do not recognize the time related behavior of fouling with regard to specific design and operational characteristics of particular heat exchangers. Fouling Resistances For Industrial Fluids

Fouling Resistance of Natural Gas-Gasoline Processing Steams

Oils:

Gases and Vapors

Fuel oil #2

0.002

Natural gas

0.001-0.002

Fuel oil #6

0.005

Overhead products

0.001-0.002

Transformer oil

0.001

Engine lube oil

0.001

Liquids:

Quench oil

0.004

Lean oil

0.002

Rich oil

0.001-0.002

Natural gasoline and liquefied petroleum gases

0.001-0.002

Gases and Vapors: Manufactured gas

0.010

Engine exhaust gas

0.010

Fouling Resistances for Oil Refinery Streams

Steam (nonoil-bearing)

0.0005

Crude and Vacuum Unit Gases and Vapors

Exhaust steam (oil-bearing)

0.0015-0.002

Atmospheric tower overhead vapor

0.001

Refrigerant vapors (oil-bearing)

0.002

Light Naphtha

0.001

Compressed air

0.001

Vacuum overhead vapors

0.002

Ammonia vapor

0.001

CO2 vapor

0.001

Crude and Vacuum Liquids:

Chlorine vapor

0.002

Crude oil

Coal flue gas

0.005

Natural gas flue gas

0.005

Liquids: Molten heat transfer salts

0.0005

DRY

0 to 250 °F

250 to 350 °F

velocity ft/s

velocity ft/s

4

4

0.003

0.002

0.002

0.003

0.002

0.002

(Continued)

Heat Transfer  911 Table 8.22  Guide to fouling resistance. (Continued) Refrigerant liquids

0.001

SALT*

Hydraulic fluid

0.001

Industrial organic heat transfer media

0.002

350 to 405 °F

450°F and more

Ammonia liquid

0.001

velocity ft/s

velocity ft/s

Ammonia liquid (oil-bearing)

0.003

4

4

Calcium chloride solutions

0.003

DRY

0.004

0.003

0.003

0.005

0.004

0.004

Sodium chloride solutions

0.003

SALT*

0.006

0.005

0.005

0.007

0.006

0.006

CO2 liquid

0.001

*Assumes desalting @ approx. 250°F

Chlorine liquid

0.002

Methanol solutions

0.002

Ethanol solutions

0.002

Gasoline

0.002

Ethylene glycol solutions

0.002

Naphtha and light distillates

0.002-0.003

Kerosene

0.002-0.003

Light gas oil

0.002-0.003

Heavy gas oil

0.003-0.005

Heavy fuel oils

0.005-0.007

Fouling Resistance for Chemical Processing Streams Gases and Vapors:

0.003

0.002

0.002

0.005

0.004

Acid gases

0.002-0.003

Solvent vapors

0.001

Asphalt and Residuum

Stable overhead products

0.001

Vacuum tower bottoms

0.010

Atmosphere tower bottoms

0.007

0.004

Liquids: MEA and DEA solutions

0.002

Cracking and Coking Unit Streams:

DEG and TEG solutions

0.002

Overhead vapors

0.002

Stable side draw and bottom product

0.001-0.002

Light cycle oil

0.002-0.003

Caustic solutions

0.002

Heavy cycle oil

0.003-0.004

Vegetable oils

0.003 (Continued)

912  Chemical Process Engineering Table 8.22  Guide to fouling resistance. (Continued) Fouling Resistances for Oil Refinery Streams (Continued). Fouling Resistances for Oil Refinery Streams (continue)

Catalytic Hydro Desulfurizer: Charge

0.0040.005

Cracking and Coking Unit Streams (Continued)

Effluent

0.002

Light coker gas oil

0.003-0.004

H.T. sep. Overhead

0.002

Heavy coker gas oil

0.004-0.005

Stripper charge

0.003

Bottoms slurry oil (4.5 ft/sec min.)

0.003

Liquid products

0.002

Light liquid products

0.002 HF Alky Unit:

Catalytic Reforming, Hydrocracking and Hydrodesulfurization Streams:

Alkylate, deprop. Bottoms, main fract, overhead, main fract. fee

0.003

All other process streams

0.002

Reformer charge

0.0015

Reformer effluent

0.0015

Hydrocracker charge and effluent*

0.002

Recycle gas

0.001

Fouling resistances for Water

Hydrodesulfurization charge and effluent*

0.002

Up to 240°F

Overhead vapors

0.001

Temperature of Heating medium

240 to 400°F

Liquid product greater than 50° A.P.I.

0.001

Temperature of Water

125°

More than 125°

Liquid product 30-50° A.P.I.

0.002

Sea Water Brackish Water Cooling tower and artificial

Water Velocity ft/s

Water Velocity ft/s

3 and Less

More Than 3

3 and Less

More Than 3

0.0005

0.0005

0.001

0.001

0.002

0.001

0.003

0.002

Heat Transfer  913 Fouling Resistances for Oil Refinery Streams (Continued). spray pond: Treated makeup

0.001

0.001

0.002

0.002

Untreated

0.003

0.003

0.005

0.004

0.001

0.001

0.002

0.002

Minimum

0.002

0.001

0.003

0.002

Average

0.003

0.002

0.004

0.003

Extract*

0.003

Muddy or silty

0.003

0.002

0.004

0.003

Raffinate

0.001

Hard (more than 15 grains/gal)

0.003

0.003

0.005

0.005

Asphalt

0.005

Engine jacket

Wax slurries*

0.003

Distilled or closed cycle

Refined lube oil

0.001

Condensate

City or well water River Water:

*Precautions must be taken to prevent wax deposition on could tube walls.

Treated boiler feedwater Boiler blowdown

Visbreaker: Overhead vapor

0.003

Visbreaker bottoms

0.010

If the heating medium temperature is more than 400°F and the cooling medium is known to scale, these ratings should be modified accordingly.

Naphtha Hydrotreater: Feed

0.003

Effluent

0.002

Naphtha

0.002

Overhead vapors

0.0015

(Used by permission: Standards of Tubular Exchanger Manufacturers Association, Inc., Section 10, RGP T-2-32 and T-2-4, © 1988. Tubular Exchanger Manufacturers Association, Inc.)

914  Chemical Process Engineering Table 8.23  Suggested fouling factors in petrochemical processes r = (h) (ft2) (°F)/Btu. Temperature range Fluid

Velocity, ft/s

100°F

7

0.0015

0.002

4

0.0005-0.0015

0.001-0.0025

4

0.001

0.0015

Waters: Sea (limited to 125°F)

River (settled)

River (treated and settled)

4 mils, baked phenolic coating 65

0.0005

15 mils vinyl-aluminum coating

0.001

Condensate (100°-300°F)

4

0.0005

0.001

Steam (saturated) oil free with traces oil Light hydrocarbon liquids (methane, ethane, propane, ethylene, propylene, butane-clean) Light hydrocarbon vapors: (clean)

0.0005-0.0015 0.001-0.002

}

0.001

Chlorinated hydrocarbons (carbon tetrachloride, chloroform, ethylene, dichloride, etc.) Liquid

0.001

0.002

Condensing

0.001

0.0015

Boiling

0.002

0.002

Refrigerants (vapor condensing and liquid cooling) Ammonia

0.001

Propylene

0.001

Chloro-fluoro-refrigerants

0.001

Caustic liquid, salt-free 20% (steel tube)

3-8

0.0005

50% (nickel tube)

6-9

0.001

73% (nickel tube)

6-9

0.001 (Continued)

Heat Transfer  915 Table 8.23  Suggested fouling factors in petrochemical processes r = (h) (ft2) (°F)/Btu. (Continued) Temperature range Fluid

Velocity, ft/s

100°F

Gases (industrial clean) Air (atmos.)

0.0005-0.001

Air (compressed)

0.001

Flue gases

0.001-0.003

Nitrogen

0.0005

Hydrogen

0.0005

Hydrogen (saturated with water)

0.002

Polymerizable vapors with inhibitor

0.003-0.03

High temperature cracking or coking, polymer buildup

0.02-0.06

Salt brines (125°F max.)

4

0.002

0.003

Carbon dioxide (sublimed at low temp.)

0.2-0.3

916  Chemical Process Engineering Table 8.24  Fouling resistances for industrial fluids (m2 K/W). Oils

Gases and vapors

Fuel oil no. 2

0.0004

Manufactured gas

0.002

Fuel oil no. 6

0.0009

Diesel engine exhaust gas

0.002

Transformer oil

0.0002

Steam (nonoil bearing)

0.00009

Engine lube oil

0.0002

Exhaust team (oil bearing)

0.004

Quench oil

0.0007

Compressed air

0.002

Refrigerant vapors in refrigerant cycle condensers

0.004

Liquids Refrigerant liquids

0.0002

Ammonia vapour

0.0002

Hydraulic fluids

0.0002

CO2 vapor

0.0002

Industrial organic heat transfer media

0.0002

Chlorine vapour

0.0004

Molten salts

0.00009

Coal fuel gas

0.002

Ammonia, liquid

0.0002

Natural gas flue gas.

0.0009

Ammonia, liquid (or bearing)

0.0005

Calcium chloride solutions

0.0005

Fouling Resistances for Chemical Processing Streams Liquids

Gases and vapors

MEA and DEA solutions

0.0004

Acid gases

0.0004

DEG and TEG solutions

0.0009

Solvent vapors

0.0002

Stable side draw and bottom products

0.0002

Stable overhead products

0.0002

Caustic solutions

0.0004

Vegetable oils

0.0005

Fouling Resistances for Oil Refinery Streams Liquids

Gases and vapors

Rich oil

0.0002

Natural gas

0.0002 – 0.0004

Lean oil

0.0004

Column overhead products

0.0002

Natural gasoline and LPG

0.0002 (Continued)

Heat Transfer  917 Table 8.24  Fouling resistances for industrial fluids (m2 K/W). (Continued) Fouling Resistances for Oil Refinery Streams Crude Oil Temp.0 – 120oC

120 – 180oC

180 – 230oC

> 230 oC

Velocity, m/s

Velocity, m/s

Velocity, m/s

Velocity (m/s)

0.60 -

0.60 -

0.60

0.60 -

< 0.60 1.20 > 1.20

< 0.60 1.20> 1.20

< 0.601.20> 1.20

< 0.601.20 > 1.20

Dry

0.0005

0.0004

0.0004

0.0005

0.0004

0.0004

0.0007

0.0005

0.0004

0.0009

0.0007

Salt

0.0005

0.0004

0.0004

0.0009

0.0007

0.0007

0.001

0.0009

0.0007

0.00012

0.001

0.0007

Fouling Resistances for Oil Refinery Streams (m2.K/W) (Cont.) Crude and vapour unit gases and vapors

0.0002

Catalytic re-forming, hydrocracking, and hydrodesulfurization streams

Atmospheric tower overhead vapors

0.0002

Re-former charge

Light naphtha

0.0004

Re-former effluent

Vacuum tower overhead vapors

Hydrocracker charge and effluent* Recycle gas

Crude and vapour unit liquids

Hydrodesulfurization charge and effluent

Gasoline

0.0004

Overhead vapors

Naphtha and light distillates

0.0005

Liquid products more than 50o API

Kerosene

0.0005

Liquid products from 30 – 50o API

Light gas oil

0.0005

Heavy gas oil

0.0005 – 0.0008

Heavy fuel oil

0.0008 – 0.0012 Light end processing streams

Asphalt and residuum

Overhead vapors and gases

Vacuum tower bottoms

0.0002

Liquid products

Atmospheric tower bottoms

0.0014

Absorption oils Reboiler streams (Continued)

918  Chemical Process Engineering Table 8.24  Fouling resistances for industrial fluids (m2 K/W). (Continued) Cracking and coking unit streams

Alkylation trace acid streams

Overhead vapors

0.0004

Light-cycle oil

0.0004

Heavy-cycle oil

0.0005 – 0.0007

Lube oil processing streams

Light coker gas oil

0.0005 – 0.0007

Feed stock

Heavy coker gas oil

0.0007 – 0.0009

Solvent feed mix

Bottom slurry oil (minimum 4.5 ft/s)

0.0005

Solvent

Light liquid products

0.0005

Extract Raffinate

Naphtha hydrotreater

Asphalt

Feed

0.0005

Refined lube oil

Effluent

0.0004

Wax slurries

Naphtha

0.0004

Overhead vapors

0.0003

Visbreaker Overhead vapour

0.0005

Visbreaker bottoms

0.0020

Heat Transfer  919 Table 8.25  Preliminary design resistances. Basis: Pressures used in Commercial Fractionations Heating Side, rp’

Clean

Service

Condensing steam

0.0005

0.0010

Cooling hot water

0.0025

0.0045

Cooling hot oil

0.0080

0.0100

Combustion gases

*

*

Boiling Side, rh’

Clean

Service

C2-C4 hydrocarbons

0.0030

0.0040

Gasoline and naphtha

0.0050

0.0060

Aromatics

0.0030

0.0040

C2-C7 alcohols

0.0040

0.0070

Water (atm. pressure)

0.0015

0.0025

*For direct-fired reboilers, estimate area on basis of heat flux: Radiant zone q/A = 10,000 Btu/(h)(ft2)(°F) Convection zone q/A = 3,5000 Btu/(h)(ft2)(°F) Used by permission: Fair, J.R., Petroleum Refiner. Feb. 1960, reference 45. © Gulf Publishing Company, Houston, Texas. All rights reserved.

Table 8.26A  Comparison of fouling resistance of No. 6 fuel oil. Copper

Stainless Steel

Thermal conductivity, k, Btu/h.ft. F

225.0

8.4

Heat transfer resistance, t/k, (h.ft2.oF)/Btu

0.000081

0.0004861

Fouling resistance per TEMA, Rf (h.ft2.oF)/Btu

0.005

0.005

Total

0.0050181

0.0054861

Actual fouling resistance

0.005

0.0025

Total

0.0050181

0.0029861

Percent fouling resistance

100%

60%

o

(Source: A. Corp, CEP, pp. 14, February 2006).

1

1 /4 in.

1 in.

3

/4 in.

5

/8 in.

OD tube

.00995

.01251

.01584

8

.00741

14

10

.00571

16

12

.00425

18

.00857

.01647

8

13

.01289

10

.00754

14

.01019

.00579

16

12

.00429

18

.00875

.01063

12

13

.00907

.00593

16

13

.00437

18

.00778

.00798

14

14

.00605

.00443

18

16

Factor

Gauge

Thermal conductivity, K

.000634

.000500

.000398

.000343

.000296

.000228

.000170

.000659

.000516

.000408

.000350

.000302

.000232

.000172

.000425

.000363

.000311

.000237

.000175

.000319

.000424

.000177

Carbon steel

25

.000251

.000199

.000158

.000136

.000118

.000091

.000067

.000261

.000205

.000162

.000139

.000120

.000092

.000068

.000169

.000144

.000123

.000094

.000069

.000127

.000096

.000070

Admiralty

63

Table 8.26B  Metal resistance of tubes and pipes.

.000178

.000141

.000112

.000096

.000083

.000064

.000048

.000185

.000145

.000114

.000098

.000085

.000065

.000048

.000119

.000102

.000087

.000067

.000049

.000090

.000068

.000754

.000596

.000474

.000408

.000353

.000272

.000202

.000784

.000614

.000485

.000417

.000359

.000276

.000204

.000506

.000432

.000370

.000282

.000208

.000380

.000288

.000932

.000736

.000585

.000504

.000436

.000336

.000250

.000967

.000758

.000599

.000515

.000444

.000341

.000252

.000625

.000534

.000458

.000349

.000257

.000469

.000356

.000261

Red brass 45% Ars. copper .000211

70-30 CU-NI

4-6% chrome ½% moly steel 80-20 CU-NI

.000050

17

21

89

.001085

.000857

.000682

.000587

.000508

.000391

.000291

.001128

.000883

.000698

.000599

.000516

.000397

.000294

.000728

.000621

.000533

.000406

.000299

.000547

.000414

.000303

Monel

14.6

Value of r w

.000067

.000053

.00042

.000036

.000031

.000024

.000018

.000069

.000054

.000043

.000037

.000032

.000024

.000018

.000045

.000038

.000033

.000025

.000018

.000034

.000025

.000019

Copper 99.9+CU

238

.000460

.000364

.000289

.000249

.000215

.000166

.000124

.000479

.000375

.000296

.000254

.000219

.000168

.000125

.000309

.000264

.000226

.000172

.000127

.000232

.000176

.000129

Nickel

34.4

.000186

.000147

.000117

.000101

.000087

.000067

.000050

.000194

.000152

.000120

.000103

.000089

.000068

.000050

.000125

.000107

.000092

.000070

.000051

.000094

.000071

.000052

Aluminum

85

.001584

.001251

.000995

.000857

.000741

.000571

.000425

.001647

.001289

.001019

.000875

.000754

.000579

.000429

.001063

.000907

.000778

.000593

.000437

.000798

.000605

.000443

Stainless AISI type 302 &-304

10

(Continued)

.00275

.000217

.000172

.000149

.000128

.000099

.000074

.000285

.000223

.000177

.000152

.000100

.000100

.000074

.000184

.000157

.000135

.000103

.000076

.000138

.000105

.000077

Yarkalbro, alum, brass

57.7

920  Chemical Process Engineering

2 in.

1

1 /2 in.

OD tube

.01197

.01499

8

.00722

14

.00961

.00560

16

10

.00419

18

12

.01545

8

.00831

.01226

10

13

.00979

.00732

14

12

.00566

16

.00845

.00422

18

13

Factor

Gauge

Thermal conductivity, K

.000600

.000479

.000384

.000332

.000289

000224

.000168

.000618

.000490

.000392

.000338

.000293

.000226

.000169

Carbon steel

25

.000238

.000190

.000153

.000132

.000115

.000089

.000067

.000245

.000195

.000155

.00134

.000116

.000090

.000067

Admiralty

63

.000168

.000134

.000108

.000093

.000081

.000063

.000047

.000174

.000138

.000110

.000095

.000082

.000064

.000714

.000570

.000458

.000396

.000344

.000267

.000200

.000736

.000584

.000466

.000402

.000349

.000270

.000882

.000704

.000565

.000489

.000124

.000329

.00246

.000909

.000721

.000576

.000497

.000431

.000333

.000248

Red brass 45% Ars. copper .000201

70-30 CU-NI

4-6% chrome ½% moly steel 80-20 CU-NI

.000047

17

21

89

Table 8.26B  Metal resistance of tubes and pipes. (Continued)

.001027

.000820

.000658

.000569

.000495

.000384

.000287

.001058

.000840

.000671

.000579

.000501

.000388

.000289

Monel

14.6

Value of r w

.000063

.000050

.000040

.000035

.000030

.000024

.000018

.000065

.000052

.000041

.000036

.000031

.000024

.000018

Copper 99.9+CU

238

.000436

.000348

.000279

.000242

.000210

.000163

.000122

.000449

.000356

.000285

.000246

.000213

.000165

.000123

Nickel

34.4

.000176

.000141

.000113

.000098

.000085

.000066

.000049

.000182

.000144

.000115

.000099

.000086

.000067

.000050

Aluminum

85

.001499

.001197

.000961

.000832

.000722

.000560

.000419

.001545

.001226

.000979

.000845

.000732

.000566

.000422

Stainless AISI type 302 &-304

10

(Continued)

.000260

.000207

.000167

.000144

.000125

.000097

.000073

.000268

.000212

.000170

.000146

.000127

.000098

.000073

Yarkalbro, alum, brass

57.7

Heat Transfer  921

Factor

.01055

.01504

.0299

.0363

.01308

.01863

.0275

.0422

Gauge

St’d

X Hvy

Sch. 160

XX Hvy

in. St’d

X Hvy

Sch. 160

XX Hvy .00169

.00110

.000745

.000523

.00145

.000916

.000602

.000422

Carbon steel

25

.000670

.000437

.000296

.000208

.000576

.000363

.000239

.000167

Admiralty

63

.000474

.000309

.000209

.000147

.000408

.000257

.000169

.00201

.00131

.000887

.000623

.00173

.001090

.000716

.00248

.00162

.001096

.000769

.00214

.001347

.000885

.000621

Red brass 45% Ars. copper .000502

70-30 CU-NI

4-6% chrome ½% moly steel 80-20 CU-NI

.000119

17

21

89

.00289

.00188

.001276

.000896

.00249

.00157

.001030

.000723

Monel

14.6

Value of r w

K in Btu/(hr)(ft2)(°F/ft)

rw in

1 Btu / (hr)(ft 2 )(°F)

.001227

.000799

.000542

.000380

.001055

.000666

.000437

.000307

Nickel

34.4

Everdur #50………….19 Wrought Iron…… .…40

.000177

.000166

.000078

.000055

.000153

.000096

.000063

.000044

Copper 99.9+CU

238

Used by permission: Griscom-Russell/Ecolaire Corporation.

rw for 1 in. O.D. 16 BWG steel tube with 18 BWG admiralty liner = .00031 For other materials, divide factor number by the thermal conductivity of various materials: 60-40 Brass…………….55 Chrome Vanadium Steel Tin ……………….35 Zinc…………………….64 SAE 6120…………………23.2 Lead………...........20

Pipe ¾ in. IPS

Pipe ¾ in. IPS

OD tube

Thermal conductivity, K

Table 8.26B  Metal resistance of tubes and pipes. (Continued)

.000496

.000324

.00029

.000154

.000427

.000269

.000177

.000124

Aluminum

85

.00422

.00275

.001863

.001308

.00363

.00229

.001504

.001055

Stainless AISI type 302 &-304

10

.000731

.000477

.000323

.000227

.000629

.000397

.000261

.000183

Yarkalbro, alum, brass

57.7

922  Chemical Process Engineering

Heat Transfer  923 Table 8.26C  Preliminary design resistances. Basis: Pressures used in Commercial Fractionations Heating side, rp′

Clean

Service

Condensing steam

0.0005

0.0010

Cooling hot water

0.0025

0.0045

Cooling hot oil

0.0080

0.0100

Combustion gases

*

*

Boiling side, rh′

Clean

Service

C2-C4 hydrocarbons

0.0030

0.0040

Gasoline and naphthas

0.0050

0.0060

Aromatics

0.0030

0.0040

C2-C7 alcohols

0.0040

0.0070

Water (atm. pressure)

0.0015

0.0025

*For direct-fired reboilers, estimate area on basis of heat flux: Radiant zone q/A = 10,000 Btu/(hr)(ft2)(°F) Convecton zone q/A = 3,5000 Btu/(hr)(ft2)(°F) Used by permission: Fair, J.R., Petroleum Refiner. Feb. 1960, reference 45. © Gulf Publishing Company, Houston, Texas. All rights reserved.

924  Chemical Process Engineering Table 8.27A  Thermal conductivity of metals used in heat exchangers. Heat exchanger tube material

k, W/m-K

k, Btu/h-ft-oF

Aluminum

147

85

Brass, Admiralty

111

64

Brass, Red

159

92

Carbon steel (0.5% C)

54 @ 20oC

31 @ 68 oF

Carbon steel (1.5% C)

36 @ 20oC

21 @ 68oF

33 @ 400oC

19 @ 750oF

Copper

386

223

Hastelloy C

8.7

5

Inconel

14.5

8.4

Monel

26

15

Nickel

90

52

Tantalum

54

31

Titanium

21

12

Type 316 stainless steel

16.3

9.4

Type 410 stainless steel

24.9

14.4

Table 8.27B  Thermal conductivity – special materials. Material

k, Btu/(h) (ft2) (°F)/(ft)

Carbon

3

Graphite

90

Karbate®, carbon base

3

Karbate®, graphite base

80

Teflon®

0.11

Glass (chemical resistant)

6.9

*To convert to Btu/(h) (ft2) (°F)/(in.), multiply by 12. To convert to gram calories/(sec) (cm2) (°C)/(cm), multiply by 0.004134.

Heat Transfer  925 Table 8.28A  Typical values of overall heat transfer coefficients in tubular heat exchangers U = Btu/h.ft2.oF. Shell-side

Tube-side

Design U

Includes total dirt

Aroclor – 1248

Jet fuels

100 – 150

0.0015

Cutback asphalt

Water

10 – 20

0.01

Demineralized water

Water

300 – 500

0.001

Ethanol amine (MEA or DEA) 10 – 25% solutions

Water or DEA, or MEA solutions

140 – 200

0.003

Fuel oil

Water

15 – 25

0.007

Fuel oil

Oil

10 – 15

0.008

Gasoline

Water

60 – 100

0.003

Heavy oils

Heavy oils

10 – 40

0.004

Heavy oils

Water

15 – 50

0.005

Hydrogen-rich reformer stream

Hydrogen-rich reformer stream

90 – 120

0.002

Kerosene or gas oil

Water

25 – 50

0.005

Kerosene or gas oil

Oil

20 – 35

0.005

Kerosene or jet fuels

Trichloroethylene

40 – 50

0.0015

Jacket water

Water

230 – 300

0.002

Lube oil (low viscosity)

Water

25 – 50

0.002

Lube oil (high viscosity)

Water

40 – 80

0.003

Lube oil

Oil

11 – 20

0.006

Naphtha

Water

50 – 70

0.005

Naphtha

Oil

25 – 35

0.005

Organic solvents

Water

50 – 150

0.003

Organic solvents

Brine

35 – 90

0.003

Organic solvents

Organic solvents

20 – 60

0.002

Tall oil derivatives, Vegetable oil, etc

Water

20 – 50

0.004

Water

Caustic soda solutions (10-30%)

100 – 250

0.003

Water

Water

200 – 250

0.003

Wax distillate

Water

15 – 25

0.005

Wax distillate

Oil

13 – 23

0.005

Liquid-liquid media

(Continued)

926  Chemical Process Engineering Table 8.28A  Typical values of overall heat transfer coefficients in tubular heat exchangers U = Btu/h.ft2.oF. Shell-side

Tube-side

Design U

Includes total dirt

Alcohol vapor

Water

100 – 200

0.002

Asphalt (450oF)

Dowtherm vapor

40 – 60

0.006

Dowtherm vapor

Tall oil and derivatives

60 – 80

0.004

Dowtherm vapor

Dowtherm liquid

80 – 120

0.0015

Gas-plant tar

Steam

40 – 50

0.0055

High-boiling hydrocarbons V

Water

20 – 50

0.003

Low-boiling hydrocarbons A

Water

80 – 200

0.003

Hydrocarbon vapors (partial condenser)

Oil

25 – 40

0.004

Organic solvents A

Water

100 – 200

0.003

Organic solvents high NC, A

Water

20 – 60

0.003

Organic solvents low NC, V

Water or brine

50 – 120

0.003

Kerosene

Water

30 – 65

0.004

Kerosene

Oil

20 – 30

0.005

Naphtha

Water

50 – 75

0.005

Naphtha

Oil

20 – 30

0.005

Stabilizer reflux vapors

Water

80 – 120

0.003

Steam

Feed water

400 – 1000

0.0005

Steam

No. 6 fuel oil

15 – 25

0.0055

Steam

No. 2 fuel oil

60 – 90

0.0025

Sulfur dioxide

Water

150 – 200

0.003

Tall-oil derivatives, vegetable oil (vapor)

Water

20 – 50

0.004

Water

Aromatic vapor-stream azeotrope

40 – 80

0.005

Air, N2, etc. (compressed)

Water or brine

40 – 80

0.005

Air, N2, etc. A

Water or brine

10 – 50

0.005

Water or brine

Air, N2 (compressed)

20 – 40

0.005

Water or brine

Air, N2, etc., A

5 – 20

0.005

Condensing vapor – liquid media

Gas – liquid media

(Continued)

Heat Transfer  927 Table 8.28A  Typical values of overall heat transfer coefficients in tubular heat exchangers U = Btu/h.ft2.oF. Shell-side

Tube-side

Design U

Includes total dirt

Water

Hydrogen containing natural – gas mixtures

80 – 125

0.003

Anhydrous ammonia

Steam condensing

150 – 300

0.0015

Chlorine

Steam condensing

150 – 300

0.0015

Chlorine

Light heat transfer oil

40 – 60

0.0015

Propane, butane, etc.

Steam condensing

200 – 300

0.0015

Water

Steam condensing

250 – 400

0.0015

Vaporizers

NC: non – condensable gas present; V: vacuum; A: atmospheric pressure. Dirt (or fouling factor) units are (h) (ft2) (oF)/Btu

K K

H K H K-U

Propylene (vaporization)

Propylene (vaporization)

Chilled water

Oil

Condensate and vapor

Chilled water

Propylene (refrigerant)

Transformer oil

Chlorinated Ci

Ethylene vapor

Propane liquid

Steam

Solvent

C4 unsaturates

Solvent

Oil

Ethylene-vapor

Ethylene vapor

Condensate

Chilled water

Calcium brine-25%

Ethylene liquid

Propane vapor

Lights and choir. HC U

H

K-U

H

H

H

H

Solvent

Solvent

H

Type equipment

Stream

Outside tubes

Butadiene mix. (super-heating

A. Heating

In tubes

…

…

…

1-2

…

…

…

…

…

…

20-40

1-2

…

25-35

Velocities tube

…

…

…

0.5-1.0

…

…

…

…

…

…

…

…

1.0-1.8

…

ft/s. shell

12-30

6-15

10-20

40-60

40-75

60-135

50-80

90-125

60-85

35-75

13-18

30-40

35-40

12

Overall coefficient

U, Overall heat transfer coefficient, Btu/(h) (ft2) (°F)

Table 8.28B  Overall heat transfer coefficients in typical petrochemical applications.

-30-260

-25-100

-170-(100)

-20-+20

75-50

60-30

270-100

600-200

150-100

115-40

100-35

40-0

110-30

400-100

Temp. range, °F

0.001

…

…

0.002

0.001

0.001

.001

0.002

0.0015

.003

…

…

…

…

Tube

0.001

…

…

0.005

0.001

0.001

.001

.001

.0015

.001

…

…

…

…

Shell

Estimated fouling

(Continued)

…

0.002

0.002

…

…

…

…

…

…

…

.005

0.006

0.0065

0.04

Overall

928  Chemical Process Engineering

H H H H H

H H H

Steam

Steam

Air mixture

Styrene and tars

Freon-12

Lean copper solvent

Treated water

C2-chlor HC, lights

Hydrogen chloride

Heavy C2-chlor.

Perchlorethylene

Air and water vapor

Engine jacket water

Absorption oil

Air-chlorine

Treated water

Unsat. Light HC, CO, CO2, HI2

Ethanolamine

Steam

Steam

Chilled Water

Water*

Water

Water

Water

Water

Water

Water

Water

Water

Water

Water

H

U

H

H

U (in tank)

U

H

H

Outside tubes

In tubes

Type equipment

5-7

4-7

…

…

…

…

…

…

2-3

3-5

4-5

4-7

…

…

…

…

Velocities tube

…

…

…

…

…

…

…

…

…

1-2

…

…

…

…

…

…

ft/s. shell

170-225

8-18

80-115

230-160

20-35

55-35

45-30

7-15

6-10

100-125

100-120

100-130

50-60

10-20

15-25

10-2

Overall coefficient

U, Overall heat transfer coefficient, Btu/(h) (ft2) (°F)

Table 8.28B  Overall heat transfer coefficients in typical petrochemical applications. (Continued)

200-90

250-90

130-90

175-90

370-90

150-90

300-90

230-90

360-100

90-110

180-90

90-25

190-230

-30-220

400-40

400-100

Temp. range, °F

0.001

…

0.0015

0.0015

0.0015

0.001

0.001

0.002

0.002

…

…

0.001

0.001

0.005

0.001

…

Tube

0.001

…

0.001

0.001

0.0015

0.001

0.001

0.001

0.001

…

…

0.001

0.002

0.0015

0.001

…

Shell

Estimated fouling

(Continued)

…

0.005

…

…

…

…

…

…

…

0.005

0.004

…

…

…

…

0.3

Overall

Heat Transfer  929

H H

Propylene refrig.

Propylene refrig.

Propylene refirg.

Propylene refrig.

Water

Water

Water

Water

Water

Propylene vapor

Propylene

Steam

Steam

Steam (exhaust)

Steam

Propylene cooling and cond.

Butadiene

Hydrogen chloride

Lights and chlori-ethanes

Ethylene

Unsat. Chloro HG

Unsat Chloro HG

Unsat Chloro HG

Chloro HG

Solvent and noncond.

Water

Water

Water

Water

Treated water

Oil

Water

H

H

H

H

H

H

KU

H

H

H

KU

KU

H

K

K

Propylene refrig.

HC unsat. lights

K

Type equipment

Propylene refrig.

Outside tubes

C4, unsat

B. Condensing

In tubes

…

…

…

…

…

…

2-3

…

…

6

3-8

7-8

…

…

…

v

v

v

Velocities tube

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

ft/s. shell

30-45 (C) 15-20 (Co)

110-150

375-130

220-130

230-130

300-90

130-90

200-90

260-90

110-(-10)

130-(-20)

110-90

145-90

120-(-10)

130-(-20)

0-15

20-35

45-3

60-35

Temp. range, °F

25-50

70-110

20-30

190-235

225-110

60-100

130-150

25-15

20-30

15-25

180-140

90-120

60-90

15-25

110-60

65-80

50-60

58-68

Overall coefficient

U, Overall heat transfer coefficient, Btu/(h) (ft2) (°F)

Table 8.28B  Overall heat transfer coefficients in typical petrochemical applications. (Continued)

0.0015

0.003

0.0001

0.0015

0.002

0.0015

…

0.0015

0.001

0.002

0.001

0.002

0.001

0.002

0.012

…

…

…

Tube

0.001

0.001

0.0001

0.001

0.0001

0.001

…

0.004

0.001

0.001

0.001

0.001

0.001

0.001

0.001

…

…

…

Shell

Estimated fouling

(Continued)

…

…

…

…

…

…

0.003

…

…

…

…

…

…

…

…

0.004

0.0055

0.005

Overall

930  Chemical Process Engineering

Ammonia

Ammonia

Freon

Water

Water

Air-Water vapor

Steam

Steam

Steam

Steam

Steam

Steam

Steam

Steam

Steam

Steam

Solvent, Copper-NH3

C4 Unsat.

Chloro HC

Chloro, unsat HC

Chloro ethane

Chloro ethane

Solvent (heavy)

Mono-diethanolamines

Organics, acid, water

Amines and water

C. Reboiling

Light HC, cool and cond.

Air-chlorine (part. cond.)

Chilled water

Water

Outside tubes

In tubes

VT

VT

VT

H

U

VT

VT

VT

H

H

KU

U

H

H

U

Type equipment

…

…

…

…

…

…

…

…

…

7-8

…

…

…

…

…

Velocities tube

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

ft/s. shell

120-140

60-100

210-155

70-115

50-70

90-135

100-140

35-25

95-115

130-150

10-20

10-50

280-300

140-65

360-250

450-300

450-350

375-300

30-190

300-350

230-130

300-350

95-150

180-160

60-10

110-90

120-90

270-90

10-15 (Co)

20-30 35-90

8-15 (C)

Temp. range, °F

8-15

Overall coefficient

U, Overall heat transfer coefficient, Btu/(h) (ft2) (°F)

Table 8.28B  Overall heat transfer coefficients in typical petrochemical applications. (Continued)

0.002

0.003

0.002

0.004

0.002

0.001

0.001

0.001

…

…

…

0.001

0.001

0.0015

0.0015

Tube

0.0015

0.0005

0.001

0.0005

0.001

0.001

0.001

0.001

…

…

…

0.001

0.001

0.003

0.005

Shell

Estimated fouling

(Continued)

…

…

…

…

…

…

…

…

0.0065

0.005

0.01

…

…

…

…

Overall

Heat Transfer  931

Naphtha frac.

C3

Butadiene, unsat.

Steam

Propylene

Propylene-butadiene

…

…

KU H

…

Velocities tube

Annulus, long F.N.

Type equipment

*Unless specified, all water is untreated, brackish, bay or sea. Notes: H = horizontal, fixes or floating tubesheet T = thermosyphon V = Vertical U = U-tube horizontal bundle v = variable r = reboiler (C) = cooling range t K = kettle type HC = hydrocarbon (Co) = condensing range t Data/results based on actual and specific industrial equipment.

Outside tubes

In tubes

25-35

…

…

ft/s. shell

15-18

120-140

15-20

Overall coefficient

U, Overall heat transfer coefficient, Btu/(h) (ft2) (°F)

Table 8.28B Overall heat transfer coefficients in typical petrochemical applications. (Continued)

400-100

-150-40

270-220

Temp. range, °F

…

0.001

0.0035

Tube

…

0.001

0.0005

Shell

Estimated fouling

0.02

…

…

Overall

932  Chemical Process Engineering

Heat Transfer  933 Table 8.56  Fault finding chart for Air-Cooled Heat Exchangers. Symptom

Possible faults

Solution

1. High tube-side outlet temperature

A. Cooler may be undersized

Perform design calculations, and if possible, use commercially tested software.

B. Excessive tube-side fouling

Clean the tubes, and ensure that there is equal airflow over all the bundles

C. Tube-side flow maldistribution

Redesign or fit tube-inserts or 1B.

D. Air-flow maldistribution

Check fan settings and adjust

E. Hot air recirculation.

Fit more efficient fan. Difficult-try wind fences or deflectors.

F. Excessive air-side fouling.

Clean-stream/water spray

G. Dirt in the tubes

Mesh upstream of cooler

H. Insufficient number of fans

Check calculations; experiment with different configuration, worst case: add new bundles with fans.

A. Excessive tube-side fouling.

See above 1A

B. Dirt in tubes

See above 1B

C. Pump is not adequate

Check; if problem persists explore other flow configurations; worst case: change pump

D. Presence of turbulence promoters

Reevaluate and if not possible to remove, then explore other configurations.

E. Overcooling/increased fluid viscosity.

Reduce air flow; or reduce number of bundles in operation

F. Failure to condense.

Increase air flow; or bring online more bundles is possible. Many require a trim cooler in some cases.

G. Dirt in the tubes

Mesh upstream of cooler

H. Insufficient number of fans

Check calculations; experiment with different configuration, worst case: add new bundles with fans.

A. Low air flow rate.

See above; check louvers; check blade pitch.

B. Tube side flow maldistribution

See above; check design; change configuration if required; evaluate inserts.

C. High ambient temperature

First check fan operation; use a different tubeside configuration.

2. High tube-side outlet pressure drop.

3. High air outlet temperature.

(Continued)

934  Chemical Process Engineering Table 8.56  Fault finding chart for Air-Cooled Heat Exchangers. (Continued) Symptom

Possible faults

Solution

4. Low air outlet temperature.

A. High air flow rate.

Check fan setting (pitch)

B. Tube side flow maldistribution

See above

C. Low ambient temperature

Check fan operation; adjust louvers if fitted.

A. Tube side maldistribution.

See above

5. Unequal exit temperatures from bundles for same flow.

B. Strong cross-winds C. Fans may differ in efficiency

Check fan operation, pitch, speed, etc.

Table 8.57  Checklist to decide between steam and electric heat tracing. Electric

Steam

Heat tracing recommended in company (Yes/No) engineering practices.

Yes

Yes

Plant preferences

-

Yes

Total feet of traced pipe

4,700

4.700

Cost of electricity ($/kWh) and steam energy ($/1,000 lb)

$0.067

Consider free

Estimated annual maintenance cost per foot of tracing ($/ft.)

$1.67

$1.33

Number of heat-tracing circuits required

50

65

Needed accuracy of temperature control (degrees)

± 50oF

± 50oF

Temperature control cost per circuit for needed accuracy ($)

No extra

No extra

Cost of monitoring one circuit in distributed control system ($)

NA*

NA*

Design time per circuit (h)

0.5

0.5

Design tools available for engineers (Good, Fair, Poor, None)

Good

Good

Capital cost of required electrical power ($)

Low

-

$30.00

$40.00

Pre-Existing Project Constraints

Project Design Phase Criteria

Other Project Installation Criteria Labor cost to install tracing and accessories ($/ft.)

(Continued)

Heat Transfer  935 Table 8.57  Checklist to decide between steam and electric heat tracing. (Continued) Electric

Steam

Training time per plant laborer (h)

20

20

Labor and overhead costs ($/h)

$23.50

$23.50

Total installed heat-tracing costs ($/ft.)

$62.00

$74.00

Annual maintenance required (h/ft.)

0.03

0.05

Annual cost for replacement parts ($/ft.)

$1.00

$0.80

Total annual maintenance cost ($)

$6,182

$6,807

Total annual operating cost ($)

$7,179

$6,807

Other Project Operation Criteria

Other *NA = not applicable as the plant does not have a distributed control system capable of monitoring heat tracing. Reproduced by permission of the American Institute of Chemical Engineers, © 1992, AIChE. All rights reserved.

936  Chemical Process Engineering Table 8.61  Description of typical saturated pool boiling curve of Figure 8.187. Regime

Description

a. The natural convection

The natural convection regime characterized by a ∆T less than about 10oF. In this region, the liquid in contact with the hot surface is superheated and rises by natural convection to the surface between the vapor and liquid where the superheat is released by quiescent vaporization of liquid. There is no vapor bubble formation in the bulk of the liquid and the heat transfer coefficients are characteristic of those of natural convection processes

b. The nucleate boiling

Here, vapor bubbles are formed at preferred nucleation sites – typically small pits or scratches on the hot surface. The liquid is superheated by direct contact with the solid surface. Once a vapor nucleus forms at the nucleation site, the bubbles grow very rapidly by desuperheating the surrounding liquid until buoyant forces pull them free from the surface and cause them to rise to the vapor-liquid interface. A large number of factors influence the heat transfer in nucleate boiling. Some of these are: the system pressure, the surface condition, the size and orientation of the surface, the wettability of the surface, the subcooling of the liquid, the hysteresis in the boiling curve, the presence of non-condensable gases and the gravitational acceleration,

c. Critical heat flux (CHF)

This is highest heat flux that can be supplied to the liquid and is referred to as the critical heat flux (CHF). At this point, the release of vapor is so intense that the flow of liquid to the surface is just adequate to supply the vapor. Any further increase in surface temperature results in some of the vapor being generated is unable to escape and the heat flux falls off. Patches of vapor form on the surface, and heat transfer at these locations occurs through the vapor film. It is no more nucleate boiling, and therefore this point is also known as the point of departure from the nucleate boiling (DNB) or burnout. The CHF depends on (a) the subcooling of the liquid (b) the liquid viscosity (c) the surface condition and the geometry and orientation of the surface. This is a phenomenon which is essentially a vapor hydrodynamic limit, and is nearly independent of the exact nature of the surface.

d. Transition boiling

This is an intermediate regime, which is characterized by the occasional generation of a vapor film at the surface that insulates the surface from the cooling liquid. This results in local hot spots and unstable operation. The film is unstable in the transition boiling regime, and after a short period of time the liquid will flood back to cool the surface and momentarily return into nucleate boiling regime. Gradually, more and more of the surface is covered by the vapor and less and less is in contact with the liquid, which results in a continuous fall in the heat flux as (Tw-Tsat) increases. For water at 1 atm, this occurs at a temperature difference of 100-260oF (37.7 – 126.7oC). Heat transfer equipment should be avoided in operating in this regime. Some of the factors that affect the transition boiling are (a) the surface condition (density of nucleation sites), (b) the temperature difference (Tw-Tsat), (c) the thermodynamic properties of the liquid (d) the thermodynamic properties of the heat transfer surface and (e) the frequency of contact between the liquid and tube wall at any given location. (Continued)

Heat Transfer  937 Table 8.61  Description of typical saturated pool boiling curve of Figure 8.187. (Continued) Regime

Description

e. Film boiling

This is stable at large temperature differences between the surface and the saturation temperature. In film boiling, a stable, almost quiescent, film of vapor exists between the surface and the liquid pool. Heat transfer is primarily by radiation at high surface temperature, although there is also some conduction and convection through the vapor film. The film eventually becomes unstable and releases large vapor bubbles at relatively infrequent intervals. The bubbles rise through the pool to the interface. This regime is characterized by large temperature differences, generally very low heat fluxes and correspondingly very low heat transfer coefficients. The surface may become hot enough to thermally degrade the substance being boiled. A deleterious effect is that of fouling, which takes place in this regime because any fouling deposit that forms on the surface cannot be redissolved or washed away by liquid. It is undesirable to operate in the film boiling regime. The heat flux in the early regions of the film boiling is less than that in the nucleate boiling, although the driving potential (Tw-Tsat) is significantly higher. Therefore, this is not a desired region for operating the process equipment. The point at which the film boiling starts is referred to as the Leidenfrost point. Some of the factors that affect this region are (a) the surface condition, (b) the surface geometry and orientation (c) the subcooling of the liquid (d) the properties of the vapor and (e) the temperature difference (Tw-Tsat).

938  Chemical Process Engineering Table 8.62  Advantages and disadvantages of various reboiler types.

Type

Advantages

Disadvantages

Remarks

Kettle reboiler

1. Most reliable in terms of operation

1. Expensive installation cost (large shell, connection piping and level control)

1. Multiple outlets can be designed to reduce shell size.

2. High vaporization percentage and good vapor quality

2. Long residence time

2. Continuous blowdown can be provided to avoid accumulation of heavy and polymerized materials and hence reduce fouling.

3. Equivalent to one theoretical stage.

3. Not good for high pressure boiling

4. Easy cleaning and maintenance

4. Lower heat flux and heat transfer rate.

5. Low circulation rate.

5. Accumulation of heavy polymerized substances.

6. Contains vapor disengaging space.

Easily fouled.

1. Low installation cost.

1. Lower heat transfer rate.

2. No space available in vicinity of the tower.

2. Process side cannot be isolated.

3. For very small reboiler duty.

3. Difficult for cleaning and maintenance

Internal reboilers

Normally not recommended.

4. Tube length limited by tower diameter. 5. Cannot be counted as one theoretical stage. Vertical thermosyphon reboiler

1. High heat transfer rate.

1. Maximum vaporization fraction shall not exceed 30% per HTRI.

1. For critical towers, dual reboilers are normally designed with 70% capacity and can be readily isolated for repair. (Continued)

Heat Transfer  939 Table 8.62  Advantages and disadvantages of various reboiler types. (Continued)

Type

Advantages

Disadvantages

Remarks

2. Occupy less space.

2. Limited tube length, normally not over 16 ft.

2. Overall heat transfer coefficient, Uo is in the range of 90-160 Btu/h ft2 oF in most hydrocarbons reboilers.

3. Simple piping.

3. Not easily accessible for maintenance and repair.

4. Low residence time

4. Some designs require expansion joint on shell.

5. Not easily fouled.

Additional column skirt required.

6. Good controllability

Equivalent to theoretical plate only at high recycle.

7. Low installation cost for fixed tube sheet design. Horizontal thermosyphon reboiler

1. Moderate heat transfer rate.

1. Extra piping required.

1. Overall heat transfer rate, Uo is in the range of 70-100 for heavy hydrocarbons (HCs), and up to 150 for light hydrocarbons (HCs).

2. Can be designed for very large heat duty.

2. Low vaporization fraction, normally not over 35%.

2. Careful baffle design to meet phase separation requirement and to eliminate tube vibration.

3. Low residence time

3. Phase separation may occur if shell side velocity is too low.

4. Not easily fouled

4. Uneven flow distribution if multishell and multi inlet are designed.

5. Good controllability

5. Extra piping and space required.

6. Ease for cleaning and maintenance.

6. Equivalent to theoretical plate only at high recycle. (Continued)

940  Chemical Process Engineering Table 8.62  Advantages and disadvantages of various reboiler types. (Continued)

Type

Advantages

Disadvantages

Remarks

Once-through natural circulation reboiler

1. As thermosiphon reboiler, has the flexibility to be either vertical or horizontal depending on tower elevation.

1. No control over circulation rate.

1. Vaporization can be up to 40% of total inlet flow.

2. Moderate to high heat transfer rate.

2. Danger of back-up in column

3. Equivalent to one theoretical stage.

3. Danger of excessive per pass vaporization.

4. Low residence time

4. Additional column skirt height required.

5. Not easily fouled.

5. Maintenance and cleaning can be awkward.

1. Suitable for viscous high-fouling and solid bearing boiling liquid.

1. Highest cost due to pump, piping and control instruments.

2. Circulation rate is well controlled.

2. Potential leaking from pump seal.

3. For very large circulation rate.

3. Additional area for pump installation.

Forced circulation reboiler

4. High operation cost. 5. Furnace reboiler 6. To avoid phase separation. 7. Enable erosioncorrosion balance. 8. Superheating is possible

5. Leaking of material at stuffing box.

Forced circulation reboiler will be considered only when kettle-type or horizontal thermosiphon reboiler cannot work.

Heat Transfer  941 Table 8.62  Troubleshooting of shell and tube heat exchanger (Continued). The following provides example causes of problems in heat exchangers, and offers solutions to remedy them. Pressure drops ( ps): ps are essential in analyzing performance of heat exchangers. The following relating to pressure drops are: 1. They provide a rough check of flowrates. 2. In the absence of fouling and for single phase streams, the calculated and measured pressure drops should be close. 3. If measured ps are lower than the calculated ps, this suggests fluid bypassing, as a low p on the tube-side indicates that not all the flow is entering the tubes. -- There may be a problem when the channel pass plates or floating head pass plates meet the tube sheets. In such a case, the tube bundle should be pulled and the pass plates and tube sheet gasket examined. The problem may be corrosion, a malfunction gasket or a manufacturing defect. 4. A shell-side p lower than the calculated indicates improper bundle sealing. Bundle bypass streams lower heat transfer. Any open areas above or below the bundle should have the cross-flow component of flow blocked by seal strips. -- This is especially important for the laminar flow region. If the exchanger is a two shell pass type, fluid may bypass the long baffle if it is not welded in as long baffles with leaf seals do not provide a perfect seal, and can result in their damage, or when the bundle is removed and later re-installed. 5. A high p could be caused by [136]: -- High fouling -- Debris from startup -- Improper venting -- Freezing of the process stream. -- Slug flow for two-phase streams. -- Fabrication problem. Improper or no venting causes a high p, and it should be analyzed first where this is established. Fouling: Heat exchanger fouling increases the p and thus reduces its efficiency. There are dedicated software programs that can give the available fouling as compared to design fouling (see Figure 8.26). A fouling phenomenon is rather a transient process and as such the actual fouling can be higher than the TEMA specifications. Where fouling is a problem or is suspected, check the exchanger’s operating history and ascertain as to whether: -- There are deviations from the design conditions -- Low velocities in the tubes streams flow rates are lower than design (see section on fouling in this text for its control) -- There are periods of operation where flowrates are lower than design. -- Heat exchangers will foul faster at low velocities. If water fouling is a problem, ensure that the flow is reduced during winter. Debris- check to ensure that there is a strainer in the piping ahead of the inlet nozzles, otherwise debris may be lodged in the exchanger. (Continued)

942  Chemical Process Engineering Table 8.62  Troubleshooting of shell and tube heat exchanger. (Continued) Excess surface problems: Generally, exchangers are designed for fouled conditions. However, there are situations where clean conditions require checking. An exchanger over surface means more deviations from outlet design temperatures and can cause problems. -- For high temperature applications, the outlet temperatures of the heated stream must be checked as it will be higher than the process design temperature. However, if this temperature is higher than what was used to select the material of construction (metallurgy), it can result in a problem. -- Another cause of a problem is degradation or lost in thermal stability of a liquid where higher than process design outlet temperatures are concerned. -- For cold applications, the outlet temperature of the stream to be cooled must be checked, otherwise the following can occur: • • • •

Stream freezing. Tube plugging. Brittle tubing. Tube failures.

Excess surface can pose a problem in the design of a vaporizer. If vaporizing is operating normally, a surge of vapor exits the exchanger. Gulley [137] described an experience with surging vapor to the reactor of an ammonia vaporizer in a nitric acid plant. All the liquid flashed to vapor inside the kettle as the liquid feed would surge in, followed by repeated flashing. The problem was resolved by plugging off some of the tubes. The kettle operation was normalized and the reactor efficiency improved. Excess surface problems can be resolved by plugging tubes in the inlet channels. There are different plug types, but the most common is the metal plugs with a slight taper. Wooden plugs can be used when the temperatures are not too high. Two-phase heat transfer: Adequate venting is essential for two-phase flow streams. Air may be introduced during startup, and non-condensables gases can occur from the process. These gases occur most often in condensers; therefore, vents on horizontal condensers should be located at the opposite end from the inlet. For vertical condensers where the vent is underneath the top tube sheet, there is a space where gases or vapors are trapped. It is important to get the vent connection as close to the tube sheet as possible. One solution is to use more than one vent nozzles [137]. Common problems with two-phase flow patterns are stratified and wave flows. For stratified flow pattern, there is little mixing of the liquid and vapor. The vapor with its lower thermal conductivity blankets some of the exchanger surface and reduces its film coefficient, which lowers the overall heat transfer coefficient. To check for stratified flow pattern or wave flow pattern, determine the gas velocity and liquid velocity as if each is alone (i.e., superficial velocity). Stratified flow pattern exists and there is a bad flow pattern for two-phase heat transfer, if the liquid velocity < 0.5 ft/s., and the gas velocity is below the calculated value from



Max. vsg = 3.5/(vs1)0.5

For a maximum liquid velocity of 0.5 ft/s, the gas velocity can be as high as 5 ft/s [137]. The solution for stratified and slightly wave flow patterns is to ensure that dry gas is kept away from the tube wall. Use twisted tape inserts, if the stream inside the tubes has low fouling characteristics. (Continued)

Heat Transfer  943 Table 8.62  Troubleshooting of shell and tube heat exchanger. (Continued) -- If the two-phase flow pattern is stratified or wave flow pattern, and it is boiling, the heat transfer surface should be submerged so that only the liquid is in contact with the tubing. This is achieved by using a weir for kettle reboilers, and using an external pipe loop in other exchanger types or arranging the unit in a vertical or slanted position. -- If the fluid condenses and no bubbling action thins the liquid film, then the liquid film needs to be thin for good heat transfer. A possible solution is to use inserts that provide the fluid with a higher velocity and a swirling action to thin the liquid film. Alternatively, arrange the exchanger to a vertical position and condense downward. -- Another problem is the holdup of the steam condensate, which thickens the liquid film so that part of the heat exchanger surface acts as a liquid cooler with lower heat transfer. A solution is a steam trap, which keeps the condensate from moving. It does not allow the condensate to build-up a thick film (see section on steam traps in [83]). -- Another aspect of condensate flow-hold up with low heat transfer is when there is one horizontal tube pass and the operating pressure is slightly above atmospheric. As there is insufficient driving force to keep the condensate from flowing normally, provide a sloping condenser so that the liquid condensate flows freely out of the tubes. -- Shell-side baffles can act as dams. Horizontal-cut baffles should not be used as vertical-cut baffles are suitable. Ensure that small baffle cuts do not flood too much of the bundle. -- For a superheated steam, a high amount at high operating pressures does not pose a problem. At low operating pressures, the mass velocity will be low and the gas heat transfer in the desuperheat zone will be low. This causes a bigger problem with more superheat and more of the exchanger surface will be in contact with dry steam with its low heat transfer. -- Film boiling can cause a problem, if the hot fluid temperature is much higher than the boiling stream temperature. The bubbling action can be so violent that only vapor contacts the exchanger tubing, resulting in the critical flux being exceeded. This can be cured with a reduction in steam pressure. -- Poor thermosyphon performance can be caused by an incorrectly set tower liquid level. Sufficient head is required to overcome the hydraulic resistance in the reboiler circuit. A tower with too high liquid level correspondingly raises the liquid level on the exchanger’s boiling side. This creates a zone of poor heat transfer where there is no boiling. -- A vertical thermosyphon having a mist flow pattern is caused when the percentage vaporization of the liquid is high, and there is a high circulation rate. There is no longer a liquid film on the tubes, as the liquid is entrained in the vapor. Mist flow results in a reduced heat transfer. Place a butterfly valve in the liquid feed line to the reboiler to control the feed rate and thus resolve the problem. Another solution is to use twisted tape inserts. Design and fabrication: Not removing tubes under the shell-side nozzles can cause high ∆p and vibration problems in the exchanger. This is because the entering shell-side fluid cannot be sufficiently distributed in all directions, as it can only flow in parallel to the tubes and down between the tubes. The reverse occurs at the exit. Thus, tubes too close to the nozzles will cause a high ∆p and possibly bundle vibration. -- This problem occurs when older exchangers are retrofitted in a new service. The problem can occur if the nozzles are enlarged to handle more flow for the new service with a change in the bundle layout. This can be resolved, if another nozzle is added so that two parallel streams enter or leave the exchanger. This can also be used if there is a vibration problem with the bundle end zones. Field mistakes: Wrong/incorrect piping of the heat exchanger nozzles during construction/retrofitting can cause problems. Gulley [136] provides an instance where a heat exchanger was piped backwards. The fluid that should have been on the shell-side was piped to the channel side and vice versa. When both streams are in turbulent flow, this connection may not be realized. However, where the fluid flow in the shell-side is semi viscous, the fluid would have been turbulent and provide a better heat transfer. When on the tube-side, the fluid flowed in the transition region between turbulent and viscous, thus producing a noticeable lower heat transfer. (Continued)

944  Chemical Process Engineering Table 8.62  Troubleshooting of shell and tube heat exchanger. (Continued) Operational Problems in a reboiler system: These are the following: -- The start-up should be gradual otherwise thermal stresses may occur. -- If steam is used for heating, inert gases must be vented by suitably located vents. The condensate formed should be drained effectively using a steam trap. If either of these is not adequately carried out, blockage of the heat transfer surface may occur with a reduced total amount of heat being transferred. -- Proper liquid level should be maintained, as a low liquid level will cause loss of thermosyphon. Film boiling might then set in, which can sharply reduce vapor generation rate. Also, too high a level will flood the reboiler outlet and can damage the distillation column by hydraulic hammer. -- Temperature difference (Tw –Tsat) should not be too high. A high-temperature driven potential > 90 – 100oF (> 50 – 55oC) can cause film boiling with a reduced heat flux and reduced vapor generation. -- Piping layout is essential, as improper piping can result in a manometer effect of connecting the column bottom to the kettle bottom. Because of the manometer effect, top tubes may be exposed when the kettle level is depressed resulting in product degradation or mechanical difficulty with the bundle [26]. Other operational problems are: pressure surging, low heat transfer, leakages and probable causes and cures are given by Lord et al. [138]. Unstable Operation with a reboiler: The following is a list of situations where this can occur: -- If the heat flux is high while the liquid distribution is non-uniform and inadequate to keep the tubes covered, local hot spots develop, and vapor is formed in a spurt as soon as any liquid reaches those hot spots. This results in an unstable operation. -- Wavy and slug flow patterns in the two-phase flow regimes are inherently unstable and must be avoided. -- Changes in the inlet flow rate, composition, and temperature of the evaporating and/or heating medium make a system depart from its currently steady state operation and try to seek another steady state. The new state may not be stable, and minor fluctuations would tend to throw the operation out of gear. -- If the circulation rate is low, the boil-off of the available volatile components will result in an increase in the boiling temperature of the remaining liquid, which reduces the vaporization rate further. Some liquid from the trays will be dumped on the base, which will replenish the volatile components in the circulating stream and the rate of vaporization will increase until the volatile components decrease again. Thus, surges in the vaporization rate will occur periodically resulting in an unsteady operation.

Heat Transfer  945 Table 8.62  Heat exchange operations. (Continued) Equipment designation

Process operation

Condenser

(a) Condenses all vapors (pure or mixed) entering. (b) Condenses all condensable vapor, cools the gases – termed a cooler-condenser.

Condenser

Condenses only part of the total entering vapors, condensed liquid removed as reflux or as “fractionation mixture,” vapor passes out unit to second condenser, or on for other processing

Cooler

Cools process stream, usually by water, but can be by air as in air cooler or by other process fluid.

Chiller

Cools process stream by refrigerant at temperature lower than prevailing water, can be chilled by water cooling the process fluid or by refrigerant such as ammonia, propylene, and freon. (Also see “Evaporator.”)

Evaporator

(a) Evaporates process fluid by some heating medium such as steam. (b) Evaporates refrigerant such as ammonia, propylene, etc., while cooling (or chilling or condensing) process fluid. Usually refrigerant on shell side of exchanger. (c) Evaporates part of process mixture while concentrating remainder as liquid. (See “Vaporizer.”)

Vaporizer

Vaporizes or evaporates all or part of liquid fed to unit by means of heating medium, such as steam, Dowtherm, etc.

Reboiler

Boils liquid by heating medium in a recirculation cycle. Feed may flow by (a) Pumped through tubes (usually) vaporizing main portion on leaving, termed “Forced Circulation Reboiler.” (b) Natural static and thermal heads through tubes, vaporizing part of fluid near outlet, termed “Natural Circulation” or “Thermosiphon Reboiler.”

(a) Forced Circulation (b) Natural Circulation or Thermosiphon Heater

Heats fluid (adds sensible heat) but does not vaporize except for effect of temperature on vapor pressure. Heating medium is usually steam, Dowtherm, or similar fluid that condenses at pressure and temperature desired, imparting its latent heat to fluid (gas or liquid).

Steam Generator

Produces steam from condensate or boiler feed water by combustion of waste oil, tars, or “off-gas” in direct-fired equipment.

Waste Heat-Boiler

Produces steam from condensate or boiler feed water by removal of sensible heat from high temperature level process or waste gas steams. (Sometimes liquid streams serve this function.)

Exchanger (a) Cross Exchanger

(a) Exchanges sensible heat between two process streams, either liquids or gases, cooling one while heating the other. Sometimes termed cross-exchanger. (b) May exchange heat for type of streams noted in (a), or any combination of specifically identified types mentioned previously, such as Cooler, Heater, etc. Usually limited to sensible heat exchange.

(b) Heat Exchanger

946  Chemical Process Engineering Table 8.62  Some considerations for the choice of heat exchanger design. (Continued) Exchanger type

Materials of construction

Cleaning

Comments

Shell and Tube

Most materials

Tubes relatively easy to clean, shell more difficult

Widely used.

Gasketed Plate

Stainless steel (usually)

Easy to clean

Compact

Double - Pipe

Commonly in carbon steel

Inner tube relatively easy, annular space more difficult or impossible (if welded)

Only useful for small heat transfer areas.

Immersed Coils

Most materials

Inside tubes impossible except by chemicals, outside of tubes possible but may be difficult

Limited application

Spiral

Most materials

Easy access to whole channel length

Compact, useful to slurries and fouling conditions.

Graphite Block

Graphite

Impossible to clean mechanically, chemical cleaning possible

Useful for corrosive conditions

Plate - fin

Aluminum, stainless steel, titanium

Only chemical cleaning possible

High compact

Air-Cooled

Aluminum fins or carbon steel tubes common, other combinations possible

Inside tubes relatively easy, finned surface more difficult

Large plot area required.

9 Process Integration and Heat Exchanger Network Introduction There have been several attempts to define process integration and a study of the most well-known definitions reveals that it has become difficult to describe the fundamental principle behind process integration (PI) [1]. However, the International Energy Agency (IEA) defined PI as systematic and general methods for designing integrated production systems, ranging from individual processes to total sites, with special emphasis on the efficient use of energy and reducing environmental effects [2]. Two main branches of PI can be recognized as: energy integration that deals with the global allocation, generation, and exchange of energy throughout the process, and mass integration that provides a fundamental understanding of the global flow of mass within the process and optimizes the allocation, separation and generation of streams and species. PI provides a framework for the holistic analysis of process performance and the generation of cost-effective and sustainable solution strategies. It is based upon fundamental chemical engineering and systems principles, and therefore provides a set of generally applicable tools. It allows the designer to see the overall concept and the details afterwards. With this approach, it is not only possible to identify the optimal process development strategy for a given task, but also to identify the most cost-effective way to accomplish the task. PI has a profound effect upon the chemical process industry and refinery in the form of pinch technology/analysis and heat-exchanger network optimization. However, it has mistakenly been interpreted as heat integration and probably because heat recovery studies inspired by the pinch concept initiated this field, which still remains the central part of PI. Process integration is a rather dynamic field with new methods and application areas emerging constantly such as mass pinch, water pinch, hydrogen pinch and latterly carbon capture pinch. Another interesting example of process integration is a dividing-wall column, which essentially integrated two distillation columns into one, thus eliminating two pieces of capital equipment – the condenser from the first column and the reboiler from the second. A typical process industry does not consist of independent process units. Instead, it is a network of units exchanging energy and energy media with each other. PI is the science of developing global tools and techniques for that purpose. It is a holistic approach to process design and operation, which emphasizes the unity of the process [3]. PI design tools have been developed over the past two decades to achieve process improvement, conservation in mass and energy resources, productivity enhancement, and reduction in the operating and capital costs of chemical processes. PI is a systematic and oriented approach to heating, cooling and power generation through process design and optimization, which exploits the interactions between different units, exchangers and utilities in order to employ resources effectively and minimize costs. PI provides a structured and disciplined knowledge of energy interactions on the site resulting in optimum overall solutions. PI has the objective of the design and optimization of integrated chemical manufacturing systems. It starts with the selection of a series of process steps and their interconnection to form a manufacturing system to transform raw materials into desired products (Figure 9.1). In PI, individual processes normally operate as part of an integrated manufacturing site that consists of a number of processes which are serviced by a common utility system. The common utility system creates interactions between the different processes which can be exploited to maximize the performance of the site as a whole. This approach is not limited to the design of new plants, but covers retrofit design and the operation of existing systems. By employing PI techniques, a process that uses the heat rejected by another unit, and thereby reducing the overall energy consumption can be identified, even if the units are not performing at optimum conditions on their own. Such an A. Kayode Coker and Rahmat Sotudeh-Gharebagh. Chemical Process Engineering: Design, Analysis, Simulation and Integration, and Problem-Solving With Microsoft Excel – UniSim Design Software, Volume 2, (947–1092) © 2022 Scrivener Publishing LLC

947

948  Chemical Processing Engineering

Process? Feed Streams

Product Streams

Figure 9.1  Process integration starts with the synthesis of a process to convert raw materials into desired products.

opportunity would be missed with an analytical approach, since this seeks to optimize each unit and therefore it would be impossible to reuse the heat internally. PI techniques are employed at the start of a new plant or the improvement of an existing one to screen out promising options to optimize the design and/or operation of a process plant. It is often employed in conjunction with simulation and mathematical optimization techniques to identify opportunities to integrate a system that results in optimum performance at reduced capital and/or operating costs. PI ranges from simple process flowsheets to sophisticated heat and mass balances, simulation plus a number of less obviously energy-related tools such as hazop analysis. Another aspect of PI is pinch analysis (PA). Generally, PI involves four key steps [4]: 1. T  ask identification: the explicit expression of the design in terms of actionable tasks. 2. Targeting: the identification of performance benchmarks before detailed design. The concept of targeting is one of the most powerful contributions of process integration. 3. Generation of alternatives (process synthesis): the use of process synthesis techniques to effectively identify those alternatives that meet the target at minimum economic and environmental cost. 4. Detailed analysis of selected alternatives: the use of process analysis, etc., to evaluate the alternatives generated based on various performance metrics. The principal benefits of employing PI are: • • • • •

Ensuring that new and retrofitted plants are inherently energy efficient and environmentally sound. Identifying opportunities for improved efficiency before carrying out detailed design. Achieving savings in total energy costs. Minimizing carbon emissions and environmental pollution. Optimum solutions for the total site, thereby avoiding wasted expenditure on non-optimal local solutions. • Identifying total site solution with maximum overall benefit. Chemical processing should increasingly form a part of a sustainable industrial activity by using raw materials as efficiently as is economic and practical, to prevent the production of waste that can be environmentally harmful and to preserve the source of raw materials as much as possible. Further, energy is not only used to reduce cost but used efficiently to prevent the build-up of carbon dioxide in the atmosphere from burning fossil fuels, and preserve the reserves of fossil fuels. Water should be consumed in sustainable quantities that does not cause any deterioration in the quality of the water source or the long-term quantity of the reserves. Atmospheric emissions and waste water effluents should be minimized, any waste must not be environmentally harmful, solid waste to landfill must be avoided and all aspects of industrial activity must feature proper health, engineering and safety practices. Sustainable development also requires that the process should use as little energy as practicable. The process also must meet required health and safety criteria. PI can be decomposed into various sub-problems following the pioneering studies of Rudd et al. [5]. The first sub-problem to benefit by the introduction of systematic techniques is the heat exchanger network (HEN). The design of a heat exchanger network first requires that the material and energy balances for a process have been established. Once this has been carried out, the process streams can be represented as sources of heat (i.e., hot

Process Integration and Heat Exchanger Network  949 streams) and sinks of heat (i.e., cold streams). If the energy consumption of the process is to be minimized, then the sources of heat should as much as possible provide heat for the sinks. Maximizing the heat recovery in this manner will minimize any demand for external heating and cooling from utilities. This will not only minimize the energy consumption, but also the emissions of greenhouse gases (e.g., CO2, SO2, NOx) from the combustion of fuels. Using PI tools, process design engineers can answer some basic questions about processes and the utility systems that surround them without resolving into detailed process simulation and optimization. Acquiring such knowledge enables the engineer to achieve two major goals: • Set process and utility system configurations before final detailed simulation and optimization. • Conduct the engineering of the process and utility systems in the sequence in which they will be commissioned. The hierarchical approach of process synthesis starts with the reactor and projects outward as illustrated in Figure 9.2. The reactor design determines the product and influences the separation and recycle structures (the second layer of the onion diagram), which are designed next. These provide the heat and mass balances, which dictate the overall heat recovery requirements, where the heat recovery system is designed (the third layer). Finally, the process utility systems are designed to provide additional minimum heating and cooling requirements, and consequently maximum energy recovery for the process. The onion model of process synthesis requires the use of process analysis aided by powerful simulation tools, where decisions are made at each layer of the onion model. Additionally, more compact and efficient equipment can be designed by applying the principles of process synthesis and intensification, where the overall integrated conceptual design shows a simpler flowsheet with lower energy consumption and equipment costs. Generally, process design consists of the optimal combination of technical, economic, ecological and social aspects in highly integrated processes. This ensures that a feasible process flowsheet is developed at each layer after which optimization can be performed to identify the optimum design variables. The design of any chemical process involves synthesis and analysis. Process synthesis is referred to as the overall development of a process flowsheet by combining individual steps into an optimal arrangement. Process analysis breaks down the flowsheet to determine the performance of each unit element as well as the overall performance of the process. This task is performed after the synthesis has been accomplished. Traditionally, this process is followed sequentially, because early decisions often influence the basic flowsheet structure. However, optimization of a completed flowsheet does not guarantee an optimal design. In a new process, it is important to recognize that decisions made in the conceptual design phase may affect the entire life cycle of the process facility. The complete engineering

Recycle structure

Reactors

at He

Separators Exchanger

ork

F+P

tw

Reactor

Ne

F

Separator

Heat and mass balances

Utilities

Process utility interface

Site – wide Utilities

Figure 9.2  The onion diagram of hierarchy in process design.

The heat and material balance is at this boundary

950  Chemical Processing Engineering phase of a project represents about 10% of the life cycle, while the process design phase represents 10% of the engineering effort. However, the process design effort is about 90% of the total capital investment [1]. In this aspect, PI allows the process engineer to develop a more cost-effective conceptual design for the process and utility system, thereby improving the life cycle value of the facility. The success of this technology depends upon the decisions made in the process integration phase of the project, which must be consistent with the defined requirements for material and energy efficiency based on sound engineering practice. Morgan [1] presents a work process that achieves these goals, where the design procedure begins by visualizing the process and utility systems together. Targets are set for the process-to-process heat transfer, and overall energy efficiency at an optimum minimum driving force (∆Tmin.,opt.), for the project. Thermodynamic principles are considered for process-to-process heat exchanger, while targets are set for energy, capital and shaft work. After these steps have been carried out, the process engineer evaluates and selects utility system configurations that best fit the process and determines the proper design of integration. This is then followed by optimizing the utility loads, and after some iteration an economic heat exchange network that will meet the energy targets is finalized. Using this approach, conceptual designs for the utility systems are developed and finalized in conjunction with the process facilities. Finally, the project team can carry out simultaneous design, engineering and procurement of the process and supporting utility systems thereby reducing the overall project schedule. Figure 9.3 illustrates a new work process that achieves these goals. Governments, companies and established institutions in the U.S., Europe and elsewhere in the world have created consortia to find alternative ways to mitigate CO2 emissions and other environmental pollutants and reduce energy costs. In particular, the Center for Process Integration at the University of Manchester in the U.K. has formed a consortium with blue chip companies where collaborative research works are carried out in the field of process integration, with the objectives reducing energy cost and the protection of the environment through the reduction of gaseous and CO2 emissions. A list of research activities on PI are shown on their website [6]. Recent texts and articles have provided much insight in Process Integration tools [7–10]. Dunn and El-Halwagi [3] list ten discouraging attitudes about process integration and suggested responses as illustrated in Table 9.1, and Table 9.2 shows a summary of industrial applications of process integration tools. Preliminary scoping activities

Detailed analysis

Conceptual phase

Process design phase

Detailed engineering phase

· Network designs · Utility loads and levels

Input

Start

Interact with client

Clarify client requirements · Turndown · Flexibility · Site · Other

Basic inputs · Technical proposal* · Proposal guarantees · Project design data · Third-party proposals · Project execution strategy *Includes base heat and material balance

· Preliminary targets · Unit interactions · Conceptual utility systems Conceptual Pinch studies to set design basis

Interact with client and project team · Process · Systems · Analytical · Control systems · Plant layout · Operations

Update and f inalize Pinch analysis

Finalize process f low alignment

Interact with project team

· Process · Systems · Plant layout · Operations · Cost services

Process design activities

· Flow diagrams · Material balances · Finalize heat balances · Equipment loads · Control strategy · Utility balances

Pinch specialist review interaction

Detailed engineering activities

Stop

· P & ID development · Utility f low diagrams · Plot plan development · Hazard reviews · Control system design · Operating philosophy

Figure 9.3  This new process design work process implements process integration effectively. (Used by permission: Stephen W. Morgan, “Use Process Integration to Improve Process Designs and the Design Process”, Chemical Engineering Progress, p. 62, September 1992.)

Process Integration and Heat Exchanger Network  951 Table 9.1  Examples of discouraging attitudes about process integration and suggested responses. Discouraging attitudes

Responses

We don’t have the resources to support this process integration initiative

Let us create resources that match the anticipated results or let us do the best we can within the available resources.

We have tried something similar before and it did not work.

Let us study the previous effort and see indeed if no more program can be made.

These concepts will not work in my plant. We have a very unique operation

There is now a track record of tens of very successful process integration projects that have applied to a wide variety of industrial processes; each of which is unique in its own right

Has anyone else applied it before?

See previous response.

Our process is too big/too small for this approach

See previous response

I am the process expert; there is no way that someone else can do better.

Let us incorporate your experience in a process integration framework. Time and again, track record has indicated that when proper process experience is incorporated into a process integration framework. Significant and intuitively non-obvious benefits have accrued.

You really don’t’ understand the issues and problems that we face

See previous two responses.

Sounds great buy you need to speak to someone else

Get suggestions on the ‘the someone else’ but also see if there is a legitimate role for the individual.

I don’t wish to participate in an initiative where I don’t’ feel comfortable with the tools and techniques

Provide appropriate training to develop the proper comfort level and understanding

Not now! We will include it in our long-term strategic planning

Each day without process integration implies missed opportunities.

Source: Dunn, Russel, F., and Mahmoud M. El-Halwagi, Review Process integration technology review: background and applications in the chemical process industry, J. Chem. Technol. Biotechnol., 78: 1011-1021 (online, 2003).

Process integration design tools were originally developed over the past two decades for heat exchanger networks (HENs) because escalating energy costs have caused operating companies to look for alternative ways to maximize production while reducing the energy consumption. Energy integration deals with all forms of energy such as cooling, heating, power generation and consumption. Much of the effort at the time focused on increasing heat recovery in chemical process industries and refineries. Industrial heat exchanger networks have played excellent roles in recovering process heat. Today, there is hardly any process in which a large amount of hot or cold fluid is allowed to be heated or cooled, due to the cost. The recovery of energy from heating and cooling may not only improve economy by reducing the energy cost, but also it will reduce operating costs and at the same time conform to environmental legislations. Process plants are now provided with HEN, in which the heat available from the hot process streams can be used to meet the heating demand, and the cold process streams can be used to meet the cooling demand. Matching heating and cooling duties in these process streams consequently reduces the use of hot and cold utilities considerably, by reducing their use to just the cases where internal matching of the streams cannot be achieved. HEN design is now the key aspect of chemical process integration, as energy savings, typically of 20-30%, coupled with capital savings can be realized in PI [11].

Debottlenecking of the process and hydrogen management

Water management and conservation

Production debottlenecking

Identification of sitewide water stream recycle opportunities to reduce river water discharges

Identification of sitewide energy conservation opportunities to reduce energy costs.

Identification of sitewide energy conservation opportunities to reduce energy costs

Reduce cost of industrial solvent

Recovery of lost fibers and management of water system

Identification of sitewide wastewater recycle opportunities

Develop power co-generation strategies and optimize utility systems.

Specialty chemical process

Kraft pulping process

Resin production facility

Organic chemicals production process

Polymer and monomer production processes

Specialty chemicals production process

Metal finishing process

Papermaking process

Polymer production processes

Petrochemical facility

Significant usage of steam for process uses and high cost of power usage.

Future expansion (wastewater discharge system expected to exceed its maximum capacity during the production process expansion)

7% losses of purchased fibers during processing and high usage of water

Major solvent losses leading to a large operating cost and environmental problems

High operating costs for utilities

Reduction in operating costs for manufacturing processes and the need for additional steam generation for production capacity expansion.

Pressure from local environmentalists and the need to meet more stringent environmental permit requirements

Sold out product with more market demands but a capped production capacity (bottlenecks)

High usage of water and buildup of non-process elements upon recycle

Sold out product with no additional capacity and significant cost for hydrogen consumption

Motivation

Energy integration with emphasis on combined heat and power optimization

Sitewide tracking of water followed by a mass integration study for water recycle opportunities and reverse osmosis treatment of select wastewater streams.

Integrated matching of properties of broke fibers with demands of paper machines (property integration)

Synthesis of an energy-efficient heat-induced separation network

Sitewide tracking of energy usage followed by a heat integration study to identify energy conservation opportunities.

Sitewide tracking of energy usage followed by a heat integration study to identify energy conservation opportunities.

Sitewide tracking of water followed by a mass integration study for water recycle opportunities and potential land treatment and reverse osmosis treatment of select wastewater streams.

Mass integration techniques to determine subtle causes of process bottlenecks and eliminate them at minimum cost

Sitewide tracking elements followed by a mass integration study for water minimization

Systematic elimination of two primary bottlenecks and sitewide integration of hydrogen generation, usage and discharge

Approach

25% reduction in steam cost and cogeneration of 20% of power requirement for the process. Payback period is four years.

24 process designs implemented resulting in a 30% reduction in site wastewater discharge and with a payback period of less than one year.

Recovery and reuse of 60% of lost fibers and reduction in water usage by 30% with a payback period of less than one year.

Recovery of 80% of lost solvent with a payback period of three years.

Five process designs implemented leading to a 25% reduction in energy usage with a payback period of less than one year.

A heat-exchange network and utility optimization process design implemented, resulting in a 10% reduction in site wastewater hydraulic load and a 5% production capacity increase; annual savings are in excess of $2.5 million/year

Nine process designs selected for implementation, including one separation system resulting in 5% wastewater reduction with a payback period of one year.

Increase in capacity by process debottlenecking: 4%(>$1 million/year additional revenue)

Key results: 55% reduction in water usage with a payback period of less than two years.

12% additional capacity and 25 % reduction in hydrogen cost with a payback period of less than one year.

Key results

Source: Dunn, Russell, and Mahmoud M. El-Halwagi, Review Process integration technology review: background and applications in the chemical process industry, J. Chem. Technol. Biotechnol., 78: 1011-1021, 2003.

Project objectives

Type of process

Table 9.2  Summary of industrial applications of process integration tools.

952  Chemical Processing Engineering

Process Integration and Heat Exchanger Network  953

Application of Process Integration Process integration concepts can be applied in various fields as: 1. Heat integration – heat exchange network. 2. Distillation column targeting 3. Cogeneration and total site targeting 4. Batch process integration and optimization 5. Emission targeting (GHG emission reduction) 6. Mass exchange network (waste and wastewater management and recovery of valuable materials) 7. Hydrogen management in refineries 8. Debottlenecking of criteria areas in process industries 9. Pollution prevention 10. Co-production system 11. Low temperature process 12. Supply-chain management 13. Financial management 14. Carbon-constrained energy-sector planning

Pinch Technology The recent staggering environmental, energy-related problems and increased global competition have caused manufacturers in the process industries, particularly petroleum refining and petrochemical, to improve the performance of their processes. Additionally, global warming and other emission issues are forcing governments and enterprises to review the way we consume fossil fuel resulting in carbon dioxide emission and other pollutants such as NOx, H2S and SO2 now recognized as a significant cause of the greenhouse effect. Further, wastewater and other organic substances have caused environmental pollution. The petroleum refining and petrochemical industries have recently dedicated much attention and resources to mitigate the detrimental impact of the environment by conserving resources and reducing the intensity of energy usage. The past two decades have resulted in significant industrial and academic efforts devoted toward the development of holistic process design methodologies that target energy conservation and waste reduction from a systems perspective. Petroleum refining is a complex operation involving many kinds of processes. All these processes have different principles; some involving fractionation, some include various reactions, and some have both. All these processes require energy that may be needed to heat (cold streams) or to make the required separation between cuts, to strip off unwanted gases, to perform a reaction, and so on. The processes also have energy-producing streams (hot streams). For example, column pump around, overhead streams, reactor effluents, and so on, which are available to supply a portion of the necessary heat such as furnaces burning fuel. Some processes are integrated where the product or residue of one process may act as the feed to another. The better the heat integration between the process units, the less fuel is burned in furnaces, which results in more profit. Pinch technology refers to a large and growing set of methods for analyzing process energy requirements to find economically optimal and controllable designs. The technology has proven to be robust and is successfully applied to process integration that encompasses overall plant integration and includes heat exchanger networks, heat and power integration and cogeneration, thermal integration of distillation columns. Industrial applications of this technology include capital cost reduction, energy cost reduction, emission reduction, operability improvement, and yield improvement for both new and revamp process designs. Pinch technology/analysis is a well-established concept, and a tool used to optimize waste heat recovery and design efficient heat integration schemes in a wide range of applications throughout the chemical process industry and refinery. The methodology is well documented in various process designs and no design involving the optimization of process heat recovery is carried out without applying some form of pinch analysis. Pinch technology is particularly

954  Chemical Processing Engineering 700 600

Cost Index

500 400 300 200 100 0 1990 1995 2000 2005 2010 2015 2020 2025 2030 Year 3% Fuel Oil Plant Cost

Figure 9.4  Projected energy versus plant cost trend (Source: Milosevic, Z., et al. www.digitalrefining.com/article/1000837, Sept. 2013).

useful when designing very complex processes such as refineries and petrochemical plants, aiming at achieving high energy efficiency of the individual processes, as well as the whole site. The technology, which is based on thermodynamic principles, is still relevant as the optimum in design is a moving target. Process plants that have been optimized today may not operate optimally in the future. Furthermore, many pinch revamps in existing refineries, and petrochemical plants have been carried out not because the original design was suboptimal at the time, but because the optimum has shifted since the plant was commissioned. A changing economic environment should ensure that the technology be reviewed because the cost of energy grows faster than the plant construction cost (Figure 9.4). Introducing this technology makes it viable to consider those projects that have previously been uneconomic. Pinch technology is a design tool that guides optimum retrofits. It aids the operating engineer to understand and manage a range of process issues that are related to daily operation of their process units. The Pinch principles will be described later in the chapter; however, the technology is a technique that is used to analyze heat availability in process hot streams and to match it against the heat demand of suitable cold streams in an optimum fashion. This process optimizes the preheating of the cold streams by using hot streams waste heat, and saves fuel in furnaces and other heaters. The technique owes its name to the discovery and the conceptual importance of the thermodynamic “pinch point,” i.e., the point of the closest temperature approach between the combined hot and cold heat availability curves. This thermodynamic bottleneck limits the recoverability of the hot stream’s energy. The four principal functions of Pinch Technology are [105]: • • • •

Energy versus capital targeting and optimization. Design of optimum heat exchanger networks. Optimization of the use of utilities. Revamping of existing networks.

Heat Exchanger Network Design A HEN consists of one or more heat exchangers that collectively satisfies the energy conservation task. In the chemical process industries, it is essential to create cost-effective HENs that can transfer heat among the hot and cold streams. The task in HEN involves using process and utility heat exchangers to heat and cool process streams from specified supplies to specified target temperatures. The objective is to minimize total costs; i.e., capital and operating costs expressed as annual charges. The network temperature pinch represents a bottleneck to feasible heat recovery in HEN design. Its location was first explained by Linnhoff et al. [12, 13] and Umeda et al. [14, 15], but its full significance for the design task was not recognized at the time. During the design stage, temperature specifications for the hot and cold streams must be met and a decision must be made about the use of a process stream or an external utility (e.g., steam, cooling water, refrigeration system, etc.) to accomplish the required heating duty. The exchange streams must be paired, and the sequencing of streams becomes important and

Process Integration and Heat Exchanger Network  955 Hot utilities Process streams to be cooled

ΔQH

NETWORK

Process streams to be heated

ΔQC QC – QH = ΔH Process streams Cold utilities

Figure 9.5  Maximum energy recovery.

therefore the use of systematic techniques becomes necessary. Figure 9.5 shows the schematic description of a network problem, with a number of hot and cold streams and hot as well as cold utilities. It should be noted that any additional heat exchanger for recovering heat from the hot stream would invariably increase the capital cost (however, it reduces the cost of utilities). The situation where no matching is made between the hot and cold streams, and all the heating or cooling duties are carried out by using utilities is called the minimum capital cost design. This corresponds to the maximum running cost and maximum utility cost as shown in Figure 9.6a. On the other hand, if all the hot and cold streams are used for heating and cooling duties and the utilities take care of only those extremes duties which cannot be met by mutual exchange of heat from the streams as shown in Figure 9.6b, the set-up is termed the maximum heat recovery at minimum energy cost, having minimum hot and cold utility requirements but higher capital cost. There are two basic thermodynamic effects that influence capital costs, namely the driving forces and the effects of heat load as depicted in Figure 9.7. Generally, as the designs are tightened (i.e., reducing the driving forces), less utility is required, and the overall heat load decreases. Invariably, this increases the capital cost with reduced driving forces, but decreases with reduced heat load. There is an actual optimum that lies between these two extreme cases, and the total annual cost, which is the sum of annual utility cost and annualized (capital cost per year life span plus interest) capital cost, should be minimized. The importance of optimization can be seen from the fact that, in a (a)

Heating utility H

Cooling utility H

(b)

Heating utility Cooling utility

H C

C C

H = Heater C = Cooler

H = Heater C = Cooler

Figure 9.6  Two extreme designs of heat exchanger network (a) Maximum capital cost, (b) Maximum heat recovery.

d

956  Chemical Processing Engineering

He at

lo a

Capital cost

D ri vin

gf orc e

Heat load Driving force

Figure 9.7  Effect of driving force and heat load on capital cost.

Table 9.3  Results of applying network analysis to projects. Process

Facility*

Energy savings available ($/yr)

Capital cost expenditure or saving $

Organic bulk chemical

New

800000

Same

Specialty chemical

New

1600000

Saving

Crude unit

Mod

1200000

Saving

Inorganic bulk chemical

New

320000

Saving

Specialty chemical

Mod

200000

160000

New

200000

Saving

General bulk chemical

New

2600000

Unclear

Inorganic bulk chemical

New

200000 to 360000

Unclear

Future plant

New

30 to 40%

30% saving

Specialty chemical

New

100000

150000

Unspecified

Mod

300000

1000000

New

300000

Saving

General chemical

New

360000

Unclear

Petrochemical

Mod

Phase I 1200000

600000

Phase II 1200000

1200000

*New means new plant; Mod means plant modification. Source: Linnhoff, B., et al. User Guide on Process Integration for the Efficient Use of Energy, IChemE., 1997.

process plant, the cost of heat exchangers can be as high as two-thirds of the plant cost and an energy cost saving of 20% to 30% is possible by optimizing the heat exchanger network. Table 9.3 shows capital savings achieved in practical case studies [16]. For a given system, the synthesis of HENs involves answering the following questions [1]: • Which heating/cooling utilities should be employed? • What is the optimal heat load to be removed/added by each utility?

Process Integration and Heat Exchanger Network  957 • How should the hot and cold streams be matched (i.e., stream pairings)? • What is the optimal system configuration (e.g., how should the heat exchangers be arranged? is there any stream splitting and mixing?) Numerous methods have been developed over the past two decades for the synthesis of HENs, and these have been reviewed by Linnhoff [16, 17], Shenoy [18], Douglas [19], Smith [20] and Kemp [21]. In a HEN, the analysis of driving forces is not only used to reduce the capital cost, but to distribute energy, which helps to clarify options in the design (e.g., for better operability and/or for lower capital costs at a constant level of energy recovery). Thus, thermodynamics can be used to identify options which point towards possible energy or capital savings or preferred integration alternatives, in the presence of constraints such as plant layout, control, safety, etc. In this chapter, HENs are reviewed using examples and case studies from the literature, and the applications of process integration and pinch analysis to technologies such as water and hydrogen pinch are then considered. Lam et al. [22] have provided an extensive review of commercial software tools in process integration, modeling and optimization for energy saving and pollution reduction. A further list of commercial software tools, their vendors and website addresses are provided by Klemes et al. [8]. These software tools provide the process designer with a practical, mature and powerful working environment that allows him/her to be in total control. They enable targets to be analyzed prior to design, thus allowing the designer to scope and screen broad design strategies. The scoping and screening process consider the overall economics and key feasibility features. Strategic alternatives can be selected for large and complex design problems. The Excel spreadsheet software provided by A User Guide on Process Integration for the Efficient Use of Energy, [21] is used to determine the minimum heating and cooling requirements for several example problems and case studies in this chapter. The main components of the spreadsheet are: 1. I nput of stream data, heat capacity flow rate (CP) values or heat contents (∆H) and a given ∆Tmin. 2. Calculation of composite curves (CCs), the problem table, energy targets and the pinch temperature, hot and cold pinch temperatures. 3. Plots of composite curves and grand composite curve. 4. Plots of the stream population over the temperature range of the problem and the basic grid diagram. 5. Tables and graphs of the variation in energy and pinch temperature over a range of ∆Tmin values. However, the software has no provision for cost targeting or area targeting; and no provision for the HEN grid of a given problem. UniSim ExchangerNet R460.2 provides these options for designers.

Energy and Capital Targeting and Optimization The energy targets for the optimum use of energy are evaluated before designing the unit. The procedure is based on the use of heat availability curves known as the composite curves for the hot and cold streams; the optimization of capital cost (exchanger area) versus energy cost (fuel), to determine energy “targets.” This is the optimum achievable heat recovery and therefore, the optimum energy consumption of a process. Composite curves represent heat availability, and heat demand profiles. When superimposed, they show the recoverable energy (where curves overlap), and the external heating and cooling requirements. Moving the curves apart illustrates the effect of increasing the temperature approach between the composites. This reduces the required exchanger area but also reduces the heat recovery between hot and cold composite and thereby increasing the consumption of both heating and cooling energy (Case B in Figure 9.8).

Optimization Variables The objective of the HEN synthesis problem is to design a network that meets an economic criterion such as the minimum total annualized cost. The total annualized cost is the sum of the annual operating cost (which consists mainly of energy costs), and the annualized capital cost. The capital cost of a network depends on parameters such as the total surface area, the number of shells, and the number of units that are installed. Additionally, the capital cost depends on the individual type of heat exchangers, their design temperature, pressure and material of construction.

958  Chemical Processing Engineering CASE A Tight approach, large exchanger are

400 350 250 200 150

DTmin = 30ºC

100

350 250 200 150

DTmin = 50ºC

100

5 0

DTmin 50ºC Heat Recovered 163 Gcal/h Exchanger Area 15,000 m2

350 Temperature, ºC

Temperature, ºC

400

DTmin 30ºC Heat Recovered 179 Gcal/h Exchanger Area 21,000 m2

350

CASE B Wider approach, smaller exchanger area

5 0

100

200

300

400

0

0

100

200

300

400

Figure 9.8  Different positioning of the composite curves (Source: Milosevic, Z., et al. www.digitalrefining.com/article/1000837, Sept. 2013).

Number of shells

Number of units

Total network area Design, T, P

Pumps, compressors

Materials of construction

Exchanger type Annualized capital cost

Plant lifetime

Interest rate

Cost of operability and flexibility

Total annualized cost

Fuel, steam Import/export, Power Import/export

Refrigeration loads and levels Operating cost

Steam loads and levels

Figure 9.9  Optimization variables in the design of heat exchanger networks [87].

Pumping cost

Process Integration and Heat Exchanger Network  959 T

T Hot utility

Hot utility

ΔTmin

Cold utility Section 1 Section 2 (a)

ΔTmin

Section 3

H

Section 1

Cold utility

Section 2 (b)

Section 3

H

Figure 9.10  Effects of on the energy, area, units and shells required for a heat exchanger system [87].

If the pressure drop incurred is included in a heat exchanger, then the capital and operating costs of the pumps must be considered. Figure 9.9 shows the variables that affect the optimization of a HEN. The network can be made operable or flexible by incurring additional costs, which may be in the form of added equipment, use of more utilities, additional area on some of the heat exchangers. The synthesis of HENs is a multivariable optimization problem as the design cannot violate the laws of thermodynamics. Therefore, the philosophy adapted in pinch technology is to establish targets for the various optimization variables based upon the thermodynamic principles. These targets set the boundaries and constraints for the design problem. Furthermore, targets help to identify the various trade-offs between the optimization parameters, and thus ensure to identify the optimal values. Once these values are identified, the design of the network is accomplished, which always results in an optimal design. The interaction between the different optimization variables (Figure 9.9) can be further understood by considering the heat curves with a small ΔTmin for a two–stream system as shown in Figure 9.10. Three different sections can be identified. Section 1 represents the cold utility requirement; Section 2 represents the process–process heat exchange, and Section 3 represents the hot utility requirement. From this set of heat curves, the utility requirements for the system are determined, and for each section, the area required is calculated since the duty, and the terminal temperatures are known, and each section is inferred to require one unit. The Bell’s method (Chapter 8) can be used to estimate the number of shells required for each unit that represents the different sections. In Section 2, two, shells are required. The heat curves for the hot and cold streams establish targets for energy, area, units and shells. These parameters are the major components that contribute towards the annualized cost of the network. For the same system, if ΔTmin is increased, then the new set of heat curves is shown in Figure 9.10b. The preceding exercise can be repeated to obtain targets for energy, area, units and shells. Figure 9.10b shows that when ΔTmin is increased, the utility requirements (i.e., hot and cold utilities) will increase and the total network area required will decrease. The number of units in this system remains the same, but the number of shells required will decrease. Section 2 now only requires one shell; thus, as the value of ΔTmin is increases, the utility cost increases and the capital cost decrease. This shows that ΔTmin is a single variable, which adjusts the major optimization variables shown in Figure 9.9. Therefore, the multivariable optimization problem is reduced to a single-variable optimization problem, which is ΔTmin. At the optimum value of ΔTmin, the other optimization variables, i.e., number of shells, number of units, total network area requirement, and the hot and cold utility requirements will be optimal [46, 47, 87].

Optimization of the Use of Utilities (Utility Placement) The utility placement function is based on the use of the grand composite curves (GCC) where the cost of the target energy is minimized by utilizing a cheaper utility, e.g., by using a low-pressure (LP) steam instead of high-pressure steam (HP) or fuel. While composite curves show the total demand of the heating and cooling utilities, the GCC

960  Chemical Processing Engineering T

HP

T

HP

LP

Figure 9.11  The use of Grand Composite Curve. (Source: Milosevic, Z., et al. www.digitalrefining.com/article/1000837, Sept. 2013.)

shows the distribution of this demand in various temperature intervals of the heat-transfer region, and is used to determine how much of the lower temperature utility can be optimally used. Figure 9.11 shows how the heating target can be met by using HP steam (left), but also illustrates the option of partly using LP steam and reducing the use of HP steam.

Heat Exchanger Network Revamp The network revamp algorithm is a complex and a developing feature of pinch technology. The algorithm is based on the path pinch concept and the methodology guides the process of adding new area strategically and economically with minimum network modifications [93, 95, 96]. The Excel spreadsheet software provided by A User Guide on Process Integration for the Efficient Use of Energy [21] is used to determine the minimum heating and cooling requirements for several example problems and case studies in this chapter. The main components of the spreadsheet are: 1. I nput of stream data, heat capacity flow rate (CP) values or heat contents (∆H) and a given ∆Tmin. 2. Calculation of Composite Curves (CCs), the problem table, energy targets and the pinch temperature, hot and cold pinch temperatures. 3. Plots of Composite Curves and Grand Composite Curve. 4. Plots of the stream population over the temperature range of the problem and the basic grid diagram. 5. Tables and graphs of the variation in energy and pinch temperature over a range of ∆Tmin values. However, the software has no provision for cost targeting or area targeting; and no provision for the heat exchanger network (HEN) grid of a given problem. UniSim Design software (UniSim Exchanger Net R460.2) provides many features for designing heat exchanger networks and details can be obtained from Honeywell International Inc.

Heat Recovery Problem Identification For efficient heat recovery, the relevant data must be stated and presented accordingly. The required data involve process streams heating and cooling information, utility system information, cost information and certain background information regarding the process and the site. The thermal data, which involve the stream heating, cooling and utilities information, are the most critical to the pinch analysis. The steps of extracting the thermal data for a given heat and material balance are:

Process Integration and Heat Exchanger Network  961 1. 2. 3. 4.

I nspect the general process flowsheet, which may contain heat recovery exchangers. Remove the recovery heat exchangers and replace them with equivalent virtual heaters and coolers. Lump all consecutive heaters and coolers. The resulting virtual heaters and coolers represent the net heating and cooling demands of the flowsheet streams. 5. The heating and cooling demands of the flowsheet streams are then listed in a tabular format in which each heating demand is referred to as a cold stream, and conversely, each cooling demand as a hot stream. In extreme cases, poor data extraction can falsely present the existing process flowsheet as optimal in terms of energy efficiency. If the data extraction accepts all the features of the existing flowsheet, then the scope for improvement is restricted; alternatively, if it does not accept any features of the existing flowsheet, then pinch analysis may overestimate the potential benefits. Appropriate data extraction depicts only the critical sections of the plant, which cannot be changed, details of which are provided elsewhere.

The Temperature-Enthalpy Diagram (T-H) Consider a general flow system with one inlet and one outlet as shown in Figure 9.12. The total energy of the system, ṁin and ṁout of the system, the general energy balance is:



dE system       P 1 P 1  in  u + + v 2 + gz  − m  out  u + + v 2 + gz  =Q−W+m ρ 2 ρ 2 dt   in   out

(9.1)

where ρ is the fluid density and the specific enthalpy, h (energy/mass) is:

h=u+



P ρ

(9.2)

The energy balance equation becomes:



dE system   1 1  in  h + v 2 + gz  − m  out  h + v 2 + gz  =Q−W+m   in   out 2 2 dt

For steady state operation,

(9.3)

dE system = 0 , ṁin = ṁout = ṁ, Equation 9.3 after rearranging becomes: dt



  1 1   h + v 2 + gz  −  h + v 2 + gz   Q = m  out   in  2 2  · Q

m· in

System

m· out

· W

Figure 9.12  General flow system.

(9.4)

962  Chemical Processing Engineering Assuming work done, W, kinetic energy and potential energy of the streams are negligible:

. Q = ṁ [hout − hin] = ΔḢ

(9.5)

where

ΔḢ = ṁCp • ΔT

(9.6)

and



CP = ṁ • Cp

(9.7)

The heat flow through the system is:

. Q = ΔḢ = CP • ΔT

(9.8)

where ∆Ḣ = heat content (kW)  kg kJ  ⋅ CP = heat capacity flowrate,  , (kW/K)  s kg.K  ∆T = temperature change for stream = (Tout − Tin) = (Ttarget – Tsupply), K where CP is assumed constant for a stream requiring heating (“cold” stream) from a supply temperature (Ts) to a target temperature, Tt, the total heat added will be equal to the stream enthalpy change, i.e.: Tt

∫

Q = CP dT = CP( Tt − Ts ) = ∆Η

(9.9)

Ts

and the slope of the line representing the stream is:

dT 1 = dQ CP



(9.10)

or CP can also be calculated from:

CP =



dQ dH ∆Η = = dT dT (Tt − Ts )

(9.11)

In a heat exchanger, the heat flow, Q is defined by:



Q = UAΔTLMTD

where U = overall heat transfer coefficient, (kW/m2 K) A = heat transfer area, m2. ΔTLMTD = log mean temperature difference, K. The T-H diagram can be used to represent heat exchange as shown in Figure 9.13.

(9.12)

Process Integration and Heat Exchanger Network  963 T Q = CP(TT - TS) TT

TS

ΔH

H

Figure 9.13  Representation of process streams in the T-H diagram.

Where a phase transition occurs, the latent heat is used instead of CP to calculate the stream duties as:

. Q= ṁλ

(9.13)

where ṁ = mass rate, kg/s λ = latent heat, kJ/kg.

Energy Targets Construction of Composite Curves Temperature–enthalpy (T-H) profiles of heat availability in the process (the hot composite curve) and the demands in the process (the cold composite curve) together form a graphical representation. Based on thermodynamic principles, pinch analysis offers a systematic approach to optimize energy integration in a process. One of the key advantages of pinch analysis is the ability to set an energy target for the design. The energy target is the minimum theoretical energy demand for the overall process. The second law of thermodynamics states that heat will flow from a region of higher temperature to one of lower temperature. As shown in Equation 9.12, in a heat exchanger the required heat transfer area is proportional to the temperature difference between the streams. In a heat exchanger network, the minimum approach temperature difference (∆Tmin) is the lower bound on any temperature difference to be encountered in any heat exchanger in the network. The value of ∆Tmin is a design parameter, which is determined by exploring the trade-offs between more heat recovery and the larger heat transfer area requirements. Any given pair of hot and cold process streams can exchange as much heat as permissible by their temperatures and the minimum approach temperature difference. Starting from the thermal data for a process, the hot and cold streams in a process can be represented on a temperature - heat content (enthalpy) graph once their input and output temperatures (i.e., supply and target temperatures), their flowrates and physical properties are known. Consider a single hot stream (heat source) and a single cold stream (heat sink) having initial and final temperatures (i.e., supply and target temperatures) and enthalpy change for both streams. For feasible heat exchange between the two streams, the hot stream must be hotter than the cold stream at all points. Figure 9.14a shows the temperature – enthalpy plot with a minimum temperature difference

964  Chemical Processing Engineering T(ºC)

T(ºC) 160

Steam

150

150

100

100

50

50 ∆Tmin = 10ºC

30

Steam

160

∆Tmin = 20ºC

30 CW

CW 0

∆H (MW)

QCmin = 1 MW Figure 16-9a:

QRec = 11 MW ΔTmin = 10ºC 100ºC

QHmin = 3 MW

0

∆H (MW)

QCmin = 2 MW

QRec = 10 MW 100ºC

ΔTmin = 10ºC H

150ºC

C QRec = 11 MW Cold Stream 30ºC

ΔTmin = 20ºC

H QHmin = 4 MW

QHmin = 3 MW

40ºC

Figure 16-9b:

ΔTmin = 20ºC

85ºC Hot Stream

QHmin = 4 MW

80ºC 30ºC QCmin = 1 MW

150ºC

Hot Stream

50ºC

C QRec = 10 MW

Cold Stream 30ºC

30ºC QCmin = 2 MW

Figure 9.14  Thermodynamic limits on heat recovery with one hot stream and one cold stream.

∆Tmin = 10oC. The region of overlap between the two streams in Figure 9.14a (i.e., the horizontal distance between the start of hot and cold streams), shows the amount of heat recovery possible (11 MW). The part of the cold stream that extends beyond the start of the hot stream in Figure 9.14a cannot be heated by recovery and therefore requires steam. This is the minimum hot utility or energy target QHmin = 3 MW. Correspondingly, the part of the hot stream which extends beyond the start of the cold stream in Figure 9.14a, cannot be cooled by heat recovery and requires cooling water. This is the minimum cold utility or energy target QCmin = 1MW. The temperature or enthalpy change for the streams and hence their slope, cannot be changed, but the relative position of the two streams can be changed by moving them horizontally relative to each other. This is possible because the reference enthalpy for the hot stream can be changed independently from the reference enthalpy for the cold stream. Figure 9.14b shows the two streams moved to a relative position such that ∆Tmin = 20oC. The amount of overlap between the streams is reduced and therefore the heat recovery is reduced to 10 MW. Further, more of the cold stream extends beyond the start of the hot stream, and hence the amount of steam is increased to 4 MW. Also, more of the hot stream extends beyond the start of the cold stream, increasing the cooling water demand to 2MW. To obtain the heat recovery targets for a practical HEN design problem, this principle is extended to handle multiple streams.

Heat Recovery for Multiple Systems Example 9.1. Setting Energy Targets and Heat Exchanger Network Consider a process flowsheet shown in Figure 9.15a involving a two-stage reactor and a distillation column. The process already has heat recovery represented by the two process-to- process heat exchangers. The hot utility demand of

Process Integration and Heat Exchanger Network  965 Table 9.4  Heat exchange stream data for the flowsheet in Figure 9.15. Stream

Type

Supply temp. oC

Target temp. oC

Heat capacity flow rate, CP kW/oC

∆H kW

Hot

H-1

190

85

20

-2100

Hot

H-2

140

50

40

-3600

Cold

C-1

60

100

80

3200

Cold

C-2

40

120

36

2880

the process is 1100 kW (shown by H) and the cold utility demand is 720 kW (shown by C). Determine the energy saving potential (or target) for the process and design a possible heat exchanger network to achieve the targeted saving.

Solution Pinch analysis principles are applied to identify the energy saving potential for the process in Figure 9.15a. However, in order to start the pinch analysis, the necessary thermal data must be extracted from the process, which involves identifying the process heating and cooling duties. Figure 9.15b shows the flowsheet representation of the process, which highlights the heating and cooling demands of the streams. This is called the data extraction flowsheet representation. The reboiler and condenser duties are excluded from the analysis for simplicity; however, these duties should be included for detailed analysis. Table 9.4 shows the thermal data for pinch analysis. “Hot streams” are the streams that require cooling (i.e., heat sources) while “cold streams” are the streams that require heating (i.e., heat sinks). The supply temperature of the stream is denoted as Ts and target temperature as Tt. The heat capacity flowrate CP is the mass flowrate times the specific heat capacity in Equation 9.7. That is,



CP = ṁ • Cp

(9.7)

The CP of a stream is measured as enthalpy change per unit temperature. A minimum temperature difference ∆Tmin = 10oC is assumed. The hot utility is steam available at 200oC and the cold utility is cooling water available between 25oC to 30oC.

Condenser 60ºC

Condenser ΔH = 2100 kW

85ºC

Stream 1 ΔH = 2000 kW

60ºC 190ºC

85ºC

120ºC ΔH = 1100 kW H

R2

C1

C1

R2

Reboiler

Reboiler R1

120ºC Stream 3 ΔH = 3200 kW Heat

CP = 80

140ºC

100ºC

140ºC

ΔH = 720 kW

Stream 2 Cool ΔH = 3600 kW

ΔH = 2880 kW

CP = 40

40ºC

50ºC (a) Process f lowsheet

Figure 9.15  Process and data extraction flowsheets for Example 9.1.

R1

100ºC

120ºC C

190ºC

Cool

CP = 20

Stream 4 ΔH = 2880 kW

120ºC Heat

CP = 36

40ºC

50ºC (b) Data Extraction f lowsheet

966  Chemical Processing Engineering Starting from the thermal data for a process as shown in Table 9.4, pinch analysis provides a target for the minimum energy consumption. The energy targets are obtained by means of the composite curves. Figure 9.16 illustrates the construction of the hot composite curve for the example process, which has two hot streams (streams 1 and 2). Their T-H representation is shown in Figure 9.16a, and their composite representation is shown in Figure 9.16b. Stream 1 has a CP of 20 kW/oC and is cooled from 190oC to 85oC, releasing 2100 kW of heat. Stream 2 is cooled from 140oC to 50oC and with a CP of 40kW/oC and losses of 3600kW. The construction of the hot composite curve (as shown in Figure 9.16b) simply involves the addition of the enthalpy changes of the streams in the respective temperature intervals. In the temperature interval 190oC to 140oC only stream 1 is present. Therefore, the CP of the composite curve equals the CP of stream 1, i.e., 20. In the temperature interval 140oC to 85oC, both streams 1 and 2 are present. Therefore, the CP of the hot composite equals the sum of the CP’s of the two streams, i.e., 20 + 40 = 60. In the temperature interval 85oC to 50oC, only stream 2 is present, therefore CP of the composite curve is 40. The construction of the cold composite curve is similar to that of the hot composite curve, and involves the combination of the cold stream T-H curves of the process. Figure 9.17 shows the composite curve of the cold streams.

200

200

150

1

=2

(b) T(ºC)

CP

(a) T (ºC)

0

The composite curves provide a counter-current picture of heat transfer and can be used to illustrate the minimum energy target of the process. This is achieved by overlapping the hot and cold streams as shown in Figure 9.18, separating them by the minimum temperature difference ∆Tmin of 10oC. The heat can be rejected vertically from the hot streams comprising the hot composite curve into the cold streams, which comprise the cold composite curve. The curves are constructed such that the hot composite curve decreases monotically while the cold composite curve increases monotically. This allows maximum overlap between the curves and hence maximum process heat recovery

150

0

CP=6

2 100

100

50

50

0

1000 2000 3000 4000 5000 6000 H (kW) The hot streams plotted separately

CP=4

1000 2000 3000 4000 5000 6000 H (kW) The composite hot stream

Figure 9.16  The hot streams can be combined to obtain a composite hot stream. (a) T(ºC)

(b) T(ºC)

200

200

150

150

100 50

0 CP= 8

2

1

=3

CP

6

=3

100 36 P=

16

CP=1

CP

6

50 C

1000 2000 3000 4000 5000 6000 H (kW) The cold streams plotted separately

1000 2000 3000 4000 5000 6000 H (kW) The composite cold stream

Figure 9.17  The cold streams can be combined to obtain a composite cold stream.

Process Integration and Heat Exchanger Network  967 possible, indicating that the remaining heating and cooling needs are the minimum hot utility requirement (QHmin) and the minimum cold utility requirements (QCmin) of the process for the chosen ∆Tmin. Figure 9.18 shows the composite curve at ∆Tmin = 10oC and the maximum heat recover, QRec is 5620 kW. Where the cold composite curve extends beyond the start of the hot composite curve in Figure 9.18, heat recovery is not possible, and the cold composite curve must be supplied with an external hot utility such as steam. This represents the target for hot utility, QHmin = 460 kW at ∆Tmin = 10oC, which is less than the existing process energy consumption of 1100 kW. The potential energy saving is therefore 1100 – 460 = 640 kW (58%). Correspondingly, where the hot composite curve extends beyond the start of the cold composite curve, the heat recovery is again not possible, and the hot composite curve must be supplied with an external cold utility such as cooling water. The target for cold utility, QCmin = 80 kW at ∆Tmin = 10oC. Specifying the hot utility or cold utility or ∆Tmin fixes the relative position of the two curves. However, this position can be altered by moving them horizontally relative to each other. In considering the heat recovery from hot streams into cold, the hot composite curve must be in a position such that everywhere, it is above the cold composite curve for feasible heat transfer. Therefore, the relative position of the curves at ∆Tmin = 20oC, and Figure 9.19 shows that hot and cold utility targets are now increased to 860 kW and 480 kW respectively. Tables 9.5, 9.6 and 9.7, respectively, show typical ∆Tmin values used in various types of processes, process utility matches and in retrofit targeting of various refinery processes respectively. However, experience-based ∆Tmin values can provide practical targets for retrofit modifications, which in certain situations may result in non-optimal solutions and therefore loss of potential opportunities. It is therefore advisable to use experience based ∆Tmin values with caution, and ensure that the choice is supported by quantitative information such as the ∆Tmin versus energy plot. Although the ∆Tmin – energy plot does not directly account for the capital cost dimension, it is expected that the dominant changes in the energy dimension will provide an impact on the capital energy trade-offs. Figure 9.20 shows composite curves for predicting energy targets, and Figure 9.21 shows what happens to the cost of the system as the relative position of the composite curves is changed over a range of values of ∆Tmin. When the curves just touch, there is no driving force of heat transfer at one point in the process, which would require an infinite heat transfer area, and therefore an infinite capital cost. As ∆Tmin between the curves increases, the energy target increases and consequently the capital cost decreases. This results from increased temperature differences throughout the process,

Figure 9.18  Screenshot of composite curves for hot and cold streams at ∆Tmin = 10oC for Example 9.1.

968  Chemical Processing Engineering

Figure 9.19  Screenshot of composite curves for hot and cold streams at ∆Tmin = 20oC for Example 9.1.

Table 9.5  Typical ∆Tmin values for various types of processes. No.

Industrial sector

Experience ∆Tmin values

Comments

1

Oil Refining

20-40 C

Relatively low heat transfer coefficients, parallel composite curves in many applications, fouling of heat exchangers

2

Petrochemical

10-20oC

Reboiling and condensing duties provide better heat transfer coefficients, low fouling.

3

Chemical

10-20oC

As for Petrochemicals

4

Low Temperature Processes

3-5oC

Power requirement for refrigeration system is very expensive ∆Tmin decreases with low refrigeration temperatures.

o

Source: Introduction to Pinch Technology, Linnhoff March, © 1998, Linnhoff March.

Table 9.6  Typical ∆Tmin values used for matching utility levels against process streams. Match

∆Tmin values

Comments

Steam against Process stream

10-20 C

Good heat transfer coefficient for steam condensing or evaporation

Refrigeration against Process Stream

3-5oC

Refrigeration is expensive.

Flue gas against Process Stream

40oC

Low heat transfer coefficient for flue gas

Flue gas against Steam Generation

25- 40oC

Good heat transfer coefficient for steam.

Flue gas against Air (e.g., air preheat)

50 oC

Air on both sides. Depends on acid dew point temperature

Cooling Water (CW) against Process Stream

15-20oC

Depends on whether or not CW is competing against refrigeration. Summer/Winter operations should be considered.

o

Source: Introduction to Pinch Technology, Linnhoff March, © 1998, Linnhoff March.

Process Integration and Heat Exchanger Network  969 Table 9.7  Typical ∆Tmin values used in retrofit targeting of various refinery processes. Process

∆Tmin

Comments

CDU

30-40oC

Parallel (tight) composites.

VDU

20-30oC

Relatively wider composites (compared to CDU) but lower heat transfer coefficients.

Naphtha Reformer/ Hydrotreater Unit

30-40oC

Heat exchanger network dominated by feed-effluent exchanger with DP limitations and parallel temperature driving forces. Can get closer ∆Tmin with Packinox exchangers (up to 10-20oC)

FCC

30-40oC

Similar to CDU and VDU.

Gas Oil Hydrotreater/ Hydrotreater

30-40 oC

Feed-effluent exchanger dominant. Expensive high pressure exchangers required. Need to target separately for high pressure section (40oC) and low pressure section (30oC).

Residue Hydrotreating

40oC

As above for Gas Oil Hydrotreater/Hydrotreater.

Hydrogen Production Unit

20-30oC

Reformer furnace requires high ∆Tmin (30-50oC). Rest of the process: 10-20oC

Source: Introduction to Pinch Technology, Linnhoff March, © 1998, Linnhoff March. External Heating

T

QHmin

Temperature, ºC Pinch Hot Overshoot

Cold Overshoot

Interchange

External Cooling QCmin Heat content, kW

H

Figure 9.20  Composite curves for predicting energy targets.

decreasing the heat transfer area. Correspondingly, the energy cost increases as ∆Tmin increases, and there is a trade-off between energy and capital cost, i.e., there is an economic degree of energy recovery which will be reviewed later in this chapter.

The Heat Recovery Pinch and Its Significance Figure 9.22a shows composite curves for a multi-stream problem, which is noted at the pinch. As illustrated earlier, the correct setting for the composite curves is determined by an economic minimum temperature difference ∆Tmin between the curves. If the correct economic ∆Tmin is known, this fixes the relative position of the composite curves and hence the energy target. The ∆Tmin for the composite curves and its location have important implications for the design if the energy target is to be achieved in the design of a heat exchanger network. The ∆Tmin is normally observed at only one point between the hot and cold composite curves, which is referred to as the heat recovery pinch.

970  Chemical Processing Engineering T

T

2

1

H

H

Total En

Cost

y

erg

Capital

2 ∆Tmin, opt

1

∆Tmin

Figure 9.21  The correct setting for ΔTmin is fixed by economic trade-offs. (a)

(b) T

T

QHmin

QHmin + α

Heat sink

Heat sink

ΔTmin

}

(c) QHmin T

{

Zero heat f low

α

Heat source

QCmin

Heat source

QCmin

H

Heat f low

+ α

H

QCmin

H

Figure 9.22  The pinch and its significance.

The trade-off between energy and capital in the composite curves suggests that individual exchangers should have a temperature difference no smaller than ∆Tmin. An initial assumption in the design of heat exchanger network is that no individual heat exchanger has a temperature difference smaller than the ∆Tmin between the composite curves. Figure 9.22a shows the process at the pinch; above the pinch, the process is in heat balance with the minimum hot utility QHmin. Heat is received from hot utility, and no heat is rejected. The process acts as a heat sink. Correspondingly, below the pinch, the process is in heat balance with the minimum cold utility QCmin. No heat is received, but heat is rejected to cold utility. The process acts as a heat source. The problem therefore falls into two thermodynamically distinct regions as shown in Figure 9.22b. Heat QHmin flows into the problem above the pinch, and QCmin out of the problem below, but the heat flow across the pinch is zero as shown in the shifted composite curves (Figure 9.23). It follows that any network design that transfers heat α across the pinch must by an overall enthalpy balance, require α more than the minimum from hot and cold utilities as shown in Figure 9.22c. As a corollary, any utility cooling α above the pinch must incur extra hot utility α, and vice versa below the pinch.

The Significance of the Pinch The pinch divides the system into two distinct thermodynamic regions. The region above the pinch can be considered a heat sink, with heat flowing into it from the hot utility, but not out of it. Below the pinch, the heat flows out of

Process Integration and Heat Exchanger Network  971

Figure 9.23  Screen-shot of shifted composite curves for hot and cold streams at ∆Tmin = 10oC for Example 9.1.

the region to the cold utility. But no heat flows across the pinch. If a network is designed that requires heat to flow across the pinch, then the consumption of the hot and cold utilities will be greater than the minimum values that could be achieved. Therefore, for the designer wishing to produce a design achieving minimum utility targets, the three principal rules are: 1. N  o heat transfer between process streams across the pinch temperature. 2. No external (utility) cooling above the pinch temperature. 3. No external (utility) heating below the pinch temperature. Violation of any of the above rules results in higher energy requirements than the theoretical minimum, which will adversely affect the energy efficiency. If a process uses more energy than its thermodynamic targets, its shows that one of the principal rules is being violated. It may be a conscious trade-off, but it is essential for the designer to comprehend that it is happening. The basic concepts in pinch analysis from Figure 9.22 are: • Minimum temperature approach ΔTmin: For a feasible heat transfer between the hot and cold composite streams, a minimum temperature approach must be specified. This corresponds to the closest temperature difference between the two composite curves on the T-H axis, and ΔTmin is termed as the network temperature approach. • Pinch point: The location of ΔTmin is called the process pinch. When the hot and cold composite curves move closer to a specified ΔTmin, the heat recovery reaches the maximum and the hot (QHmin) and cold (QCmin) utilities reach the minimum. Therefore, the pinch point becomes the bottleneck for further reduction of hot and cold utilities. Here, process changes must be considered if utility reductions are required. • Hot and cold utility requirements: The overshoot at the top of the cold composite curve represents the minimum amount of external heating (QHmin), while the overshoot at the bottom of the hot composite curve represents the minimum amount of external cooling (QCmin). • Maximum process heat recovery (Interchange in Figure 9.22). The overlap between the cold and hot composite curves represents the maximum amount of heat recovery (QRec) for a given ΔTmin. The heat available from the hot streams in the hot composite curve can be heat-exchanged with the cold streams in the cold composite curve in the overlap region.

972  Chemical Processing Engineering

The Plus-Minus Principle for Process Modifications The heat and material balances of the process determine the composite curves of the process. As the heat and material balances change, so do the composite curves. These curves provide valuable information about maximum heat recovery, QRec, minimum external heating QHmin, minimum external cooling QCmin, and location of the heat recovery pinch for a given value of ∆Tmin. Composite curves can be applied and provide valuable information whenever an amount (such as heat) has a quality (such as temperature). The advantages of graphical representations (Figures 9.19 and 9.21) include a pedagogic aspect of understanding by providing the engineer with an overview of the problem, illustrating important economic trades-offs, and finally representing information in a very concentrated form. The results can be extracted from Figures 9.17a and 9.17b, respectively, and shown in Table 9.8. Table 9.8 shows that the difference between the hot and cold pinch temperatures equals ∆Tmin, as also observed on the composite curves. A general strategy for process modifications can be established from Figure 9.24. In pinch analysis, this strategy is referred to as the plus/minus principle as proposed by Linnhoff and Vredeveld [23]. Considering Figure 9.24, any process change which: • • • •

increases the total hot stream heat duty above the pinch, decreases the total cold stream heat duty above the pinch, decreases the total hot stream heat duty below the pinch, increases the total cold stream heat duty below the pinch, Table 9.8  Results of pinch analysis for Example 9.1. ∆Tmin=10oC

∆Tmin=20oC

Minimum external heating, kW

460

860

Minimum external cooling, kW

80

480

Pinch temperature,oC

65

70

Hot stream pinch temperature, oC

70

80

Cold stream pinch temperature, oC

60

60

(a)

(b) Hot utility target

sit e po co m

sit e po Co

+

co m

-

Shift hot streams

ld

-

Temperature

+

Ho t

T Temperature

QHmin

T

Shift cold streams Excess energy f low

Enthalpy The plus-minus principle.

H

QCmin Cold utility target Enthalpy

H Shifting streams through the pinch in the right direction enacts the plus-minus principle.

Figure 9.24  The plus-minus principle guides process design changes to reduce utility consumption. (Used by permission: Smith, R. and Linnhoff, B. Trans. IChemE. ChERD, 66: 195, 1988).

Process Integration and Heat Exchanger Network  973 will result in a decrease in utility requirements. These guidelines provide a definite reference for appropriate design changes to improve the targets. Examples of such process modifications include changes in pressure for distillation columns and evaporators, changes in flow rates for some streams, and new target temperatures for streams when possible. Another way to remember these principles is that heat integration will always benefit by keeping hot streams hot and cold streams cold [16]. Although the plus/minus principle is a pertinent reference in guiding process changes to reduce utility costs, it does not, however, account for the capital costs. Process changes to reduce utility consumption normally result in a reduction in temperature driving forces as shown in Figure 9.24. Therefore, the capital energy trade-off (and hence ∆Tmin) should be readjusted after process changes, using any of the commercial software on cost estimation. While graphical diagrams such as the composite curves provide excellent tools for learning the methods and understanding the overall energy situation, minimum energy consumption and the heat recovery pinch are more often obtained by numerical procedures based on mathematical models. The heat cascade is a special case of the transshipment model and forms the basis for some of the optimization-based methods such as mathematical programming. For detail reviews, see references [2, 18, 24–26].

A Targeting Procedure: The Problem Table Algorithm The composite curves discussed earlier can be used to set energy targets; however, they can be inconvenient as they rely on graphical construction. Linnhoff and Fowler [12] developed a method of calculating energy targets algebraically, which is referred to as the Problem Table. The procedure is as follows: 1. S elect a global ∆Tmin for the calculation. 2. Convert the actual stream temperatures Tact into shifted temperatures Tshift by subtracting half the minimum temperature difference from the hot stream temperatures, and by adding half to the cold stream temperatures:



hot streams, Ts = Tact −

∆Tmin 2

(9.14)



cold streams, Ts = Tact +

∆Tmin 2

(9.15)



The use of the shifted temperature rather than the actual temperatures allows the minimum temperature difference to be taken into account, i.e., ∆Tmin 3. Note any duplicated shifted temperatures. These are bracketed. 4. Make a list of all the shifted temperatures Tshift at which streams (hot or cold) begin, and end or change heat capacity flowrate CP. 5. Rank the list of shifted temperatures in descending order (highest temperature at the top) showing the duplicated temperatures only once in the order. 6. In each temperature interval i, between two shifted temperatures, add together the heat capacity flowrates of all the hot streams which exist in that temperature interval and subtract the heat capacity flowrates of all the cold streams to give a net heat capacity flowrate CPnet 7. Multiply CPnet for each interval by the temperature range of the interval (Ti – Ti+1) to give the net heat released (positive) or required (negative) in the interval. For the ith interval:



where

∆Hi =

(∑CP −∑CP )(T − T h

c

ΔHi = net heat released (required) in the ith interval.

i

i +1

)

(9.16)

974  Chemical Processing Engineering



∑ CP = sum of the heat capacities of all hot streams in the interval. ∑ CP = sum of the heat capacities of all cold streams in the interval. h

c

(Ti − Ti+1) = interval temperature difference.

8. S tarting from a zero input at the highest temperature, work down the column in the table, adding on the net heat change in each temperature interval to give a heat cascade (cumulative heat passing through at a given shifted temperature). 9. The cascade in step 8 normally contains negative heat flows and is thermodynamically infeasible. Take the minimum net heat flow in the table (-Qmin) (i.e., largest negative value or zero) and add this amount of heat Qmin as hot utility to the first interval in the cascade. All the net heat flows in the cascade now increase by this amount, and the minimum value becomes zero. This is the feasible heat cascade or Problem Table. 10. The heat added to the first interval is the hot utility requirement (target) QHmin. The heat removed from the final interval is the cold utility target QCmin. The point(s) at which there is zero net heat flow in the cascade is the pinch. The plot of the net heat flow (horizontal axis) against the shifted temperature (vertical axis) is the grand composite curve, which will be reviewed later. 11. As a confirmation, the cold utility target minus the hot utility target in the Problem Table should equal the bottom line of the infeasible heat cascade. This provides a useful cross-check that the stream data and heat cascades have been evaluated correctly. Using Table 9.9 in Example 9.1 and ∆Tmin = 10oC the steps as described above are used to determine the targets (i.e., the minimum external utilities), the pinch temperature, the hot stream pinch temperature and the cold stream pinch temperature. Figure 9.25 shows the grid diagram of interval temperature against heat load capacity of hot and cold streams respectively. A heat balance is carried out within each shifted temperature interval according to Equation 9.16. The results show that some of the shifted intervals are seen to have a surplus of heat and some a deficit. The heat balance within each shifted interval allows maximum heat recovery within each interval. A cascade is carried out and any surplus heat flows down the temperature scale from interval to interval. This is possible because any heat available in interval i is hot enough to supply any duty in interval i+1. Figure 9.26 shows the cascade for Example 9.1. First, assume that no heat is supplied to the first interval from a hot utility. The first interval has a surplus of 1000kW, which is cascaded to the next interval. This second interval has a surplus of 600 kW, which increases the heat cascaded from this interval to 1600 kW. In the third interval, the process has a surplus of 480 kW, which leaves 2080 kW to the fourth interval. The fourth interval has a deficit of 1400kW, which reduces the heat cascaded from this interval to 680kW. The fifth interval has a deficit of 1140kW, which leaves -460kW to be cascaded to the next interval. In the sixth interval, there is a surplus of 80k, resulting in a 380kW. Looking at the heat flows in Figure 9.26, some are negative, which is infeasible, as heat cannot be transferred up the temperature scale. To make the cascade feasible, sufficient heat must be added from a hot utility to make the heat flows at least zero. The smallest amount of heat required from a hot utility is the largest negative heat flow from Figure 9.26, i.e., 460 kW. 460kW Table 9.9  Heat exchange stream data for the flowsheet in Figure 9.15. Stream

Type

Supply temp. oC

Target temp. oC

Shifted supply temp. oC

Shifted target temp. oC

Heat capacity flow rate, CP kW/oC

∆H kW

Hot

H-1

190

85

185

80

20

-2100

Hot

H-2

140

50

135

45()

40

-3600

Cold

C-1

60

100

65

105

80

3200

Cold

C-2

40

120

45()

125

36

2880

Process Integration and Heat Exchanger Network  975 Interval Temperature

Stream Population 1

185ºC

2

135C 125ºC 105ºC 80ºC 65ºC

3

45ºC CP

4 20

20

80

36

Figure 9.25  Grid diagram of interval temperature vs. heat capacity flow rate of hot and cold streams.

is added to the first interval from a hot utility (see column 9, Figure 9.26). This does not change the heat balance within each interval but increases all the heat flows between intervals by 460kW, giving one heat flow of zero at an interval temperature of 65oC. This temperature is referred to as the pinch temperature, (i.e., where the heat flow is zero). The minimum hot and cold utility requirements are QHmin = 460 kW and QCmin = 80 kW, respectively. Therefore, the actual hot and cold streams pinch temperatures are 70oC and 60oC, respectively. These results agree with the results from the composite curves in Figure 9.18. Further, the cold utility target minus the hot utility target (80 – 460kW) should equal the bottom line (-380kW) of the infeasible heat cascade in the Problem Table of Figure 9.26. These calculations provide useful cross-checks that the stream data and heat cascades have been determined correctly. The composite curves are useful in providing conceptual understanding of the process, but the Problem Table algorithm is a more convenient tool. There are commercial software packages such as UniSim Exchanger Net R460.2 that generate these and others such as the grand composite curve and the heat exchanger network grid. From the Problem Table (Figure 9.26), the following results are obtained: Pinch temperature

= 65oC

Hot stream pinch temperature

= 70oC

Cold stream pinch temperature

= 60oC

Minimum hot utility requirement

= 460 kW

Minimum cold utility requirement

= 80 kW

Maximum energy recovery

= 5620 kW

The Grand Composite Curve After maximizing heat recovery in the heat exchanger network, those heating and cooling duties not serviced by heat recovery are provided by external utilities, i.e., that outermost layer of the onion model as shown in Figure 9.4, and also shown in the composite curves Figure 9.18. However, these curves do not provide information about the

976  Chemical Processing Engineering Interval

(Ti – Ti+i)

(ΣCPh–ΣCPc)

∆Hi

∆Hi Heat

Temp.,

Surplus/ Cascade Def icit

ºC

20

1000

Utility

Utility

135 60

600

24

480

600 2060 480

480

105

2080 25

-56

-1400

2540 -1400

-1400

80

680 15

-76

-1140

-1140

65 6

1460

1600 20

5

1000

600

125

4

460

1000 10

3

Cascade

Hot

1000

1140 -1140

-460 20

4

80

80

45()

Feasible

Heat

0 50

2

∆Hi

Hot

185 1

Infeasible

0 80

-380

80

Cold

Cold

Utility

Utility

Figure 9.26  The problem table.

temperature levels at which the various utilities are used. As a pure thermodynamic analysis, it assumes that there is enough utility at the minimum and maximal heating and cooling temperature level, but in most processes, the utilities are used at different temperatures and pressures. Table 9.10 shows some typical values. There are various utilities, and the most common hot utility is steam. It is available at several levels. High temperature heating duties require furnace flue gas or a hot oil circuit. Cold utilities might be cooling water, air cooling, refrigeration, furnace air preheating, boiler feedwater preheating, or even steam generation at higher temperatures. Although the composite

Process Integration and Heat Exchanger Network  977 Table 9.10  Typical temperatures and pressures for utilities. Utility

Temperature, K

Pressure, bar

High pressure steam

703

26

Middle pressure steam

523

15

Low pressure steam

423

3

Water

293

-

Sole water

273

-

Mechanical cooling, I

253

-

Mechanical cooling, II

233

-

Liquid nitrogen

193

-

curves can be used to set energy targets, they are not a suitable tool for the selection of utilities. A more appropriate tool for understanding the interface between the process and the utility system is the grand composite curve (GCC) [27–29]. This diagram allows a better view of the amount of heat available at various temperatures to be achieved. It is also referred to as the heat surplus diagram and is generated by plotting the interval temperature against the corresponding flow of heat between the intervals in the cascade in the problem table algorithm (PTA). The shape of the GCC is dependent not only on process stream data, but also on ∆Tmin. A typical grand composite curve is shown in Figure 9.27. It shows the heat flow through the process against temperature after adding minimum hot and cold utility requirements. The modified temperatures (i.e., shifted temperatures) are simply the average between the hot and cold temperatures (+/- ∆Tmin/2), an adjustment that allows the drawing of hot and cold streams and utilities in the same temperature scale, while satisfying the need for the minimum driving forces. The point of zero heat flow in the grand composite curve in Figure 9.27 is the pinch. The open ‘jaws’ at the QHmin

Tshifted

HEAT SINK

Pockets of Heat Recovery

HEAT SOURCE

ΔH

QCmin

Figure 9.27  The grand composite curve shows the utility requirements in both enthalpy and temperature terms.

978  Chemical Processing Engineering top and bottom represent the minimum heating and cooling requirements (i.e., QHmin, QCmin) respectively. The heat sink above the pinch and heat source below the pinch can be identified in Figure 9.27. The shaded areas in the figure are known as pockets as these represent areas of additional process-to-process heat transfer. In these pockets, a local surplus of heat in the process is used at temperature differences in excess of ∆Tmin to satisfy a local deficit. Figure 9.28a shows the same grand composite curve with two levels of saturated steam used as a hot utility. The steam system in Figure 9.28a shows the low-pressure steam being desuperheated by injection of boiler feedwater after pressure reduction to maintain saturated conditions. Figure 9.28b shows the same grand composite curve but with hot oil used as a hot utility.

Placing Utilities Using the Grand Composite Curve Figure 9.28 shows several different examples of multiple utilities placement using the grand composite curve. A general guideline to follow when placing utilities is to maximize the use of the cheaper utilities subject to minimum overall energy use. Also, when placing utilities in the GCC, interval and not actual utility is represented. In Figure 9.28a, cooling water (CW), refrigerant (R), high pressure (HP) and low pressure (LP) steam utilities are available. First considering process cooling below the process pinch, the duty on CW is initially maximized as CW is the cheapest cold utility. The CW duty is set by the amount of heat indicated on the GCC at the CW interval temperature. Refrigeration is used to satisfy the remaining process cooling requirements. Above the process pinch, the use of LP steam is first maximized, since LP steam is cheaper than HP steam. However, unlike CW, the LP steam duty is not set by the enthalpy value of the GCC at the LP steam interval temperature. There is a “nose” in the GCC below which lies a region or “pocket” as stated earlier where excess process heat at a higher temperature can be used to satisfy lower temperature process heat requirements. Hence, LP steam is only satisfying that heat requirement not satisfied by excess process heat. HP steam is used to satisfy the remaining process heating requirements. Figure 9.28b, shows the same GCC, but there is also a medium pressure (MP) steam level available in the utility steam. The temperature of MP steam is such that it can be generated using the excess heat available in the pocket. This leads to increase in LP steam use to balance overall utility requirements. The GCC indicates just how much MP steam can be generated and how much additional LP steam is required. In such instances, a steam turbine is placed between the MP and LP steam levels, thereby converting process heat into power. The points where the MP and CW levels touch the grand composite curve are called the utility pinches since they are caused by utility levels. A violation of a utility pinch (cross utility pinch heat flow) results in shifting of heat load from a cheaper utility level to a more expensive utility level. A process pinch is caused by the process streams and violating a process pinch results in an overall heat load penalty for the utilities. Figure 9.28c, shows how a furnace may be matched to a process GCC. The cooling profile for furnace flue gas is assumed to be linear, cooling from a theoretical flame temperature. In order to minimize flue gas flow and therefore (a)

(b) HP

TShifted, ºC

TShifted, ºC

TShifted, ºC MP LP

LP

(c)

HP

Theoretical f lame Flue gas temperature

Utility pinches

Process pinch CW

Utility pinches Process pinch

CW R Enthalpy, kW

Figure 9.28  The grand composite curve for multiple utilities targeting.

R Enthalpy, kW

R Enthalpy, kW

Process Integration and Heat Exchanger Network  979

Figure 9.29  Screenshot of the grand composite curve at ΔTmin = 10oC for Example 9.1.

the fuel consumption, the flue gas line should touch the process GCC. The touch point does not have to be the process pinch, but may be at a different location as shown. The utility profile is often referred to as the utility grand composite curve, and each additional steam level increases the complexity of the utility system. Higher complexity has several negative consequences, including increased capital costs, greater potential for leaks, reduced safety, and more maintenance expenses. Therefore, limits are generally placed on the number of steam levels. Detailed illustrations of creating utility pinches are provided by Linnhoff et al. [16]. The grand composite curve has a number of industrial applications, mostly related to utility system and combined heat and power systems. It can be employed both quantitatively and qualitatively to provide the following [29]: 1. I dentify the potential for steam production below the pinch, if the process pinch is at a sufficiently high temperature. This implies that steam generation (typically low pressure steam (LP)) is acting as a cold utility. 2. Identify whether there is a scope for integrating of special equipment such as distillation columns or evaporators with the background process. 3. Identify a near-optimal set of utility types (both load and level) to cover the need for external heating and cooling in the process. A utility grand composite curve [28] consisting of available utilities, e.g., various steam levels, flue gas from a furnace or gas turbine, hot oil circuits, cooling water refrigeration, etc., can be combined in such a way that total utility cost is minimized. 4. Identify potential for utilizing so-called pockets in the grand composite curve for additional power production. If the temperature difference had been sufficiently large between the part of the process where the local heat surplus and the corresponding part where there is local heat deficit, there would have been some scope of producing steam that could have been used in a back pressure turbine. The turbine then borrows steam generated in the process and returns steam for heating at a lower level after power production. Figure 9.29 shows the Grand Composite Curve at ∆Tmin = 10oC for Example 9.1.

Stream Matching at the Pinch Linnhoff and Hindmarsh [30] introduced pinch decomposition of the hot and cold streams (i.e., above and below the pinch) for stream matching. They focused attention at the pinch where the temperatures of the hot and cold streams are separated by ∆Tmin, the location of the closest approach temperature.

980  Chemical Processing Engineering Consider the schematic of a counter-current heat exchanger in Figure 9.30. The hot stream having a heat capacity flow of CPh enters at Thi and exists at Tho. It transfers heat Q to the cold stream, which has a heat capacity flow rate of CPc that enters at Tci and exists at Tco. On the cold end of the heat exchanger where the temperatures of the hot and cold streams are the lowest, the approach temperature difference is ∆T1. Correspondingly, on the hot end where the temperatures are the highest, the approach temperature difference is ∆T2. The energy balance for the hot and cold streams is:

Q CP h Q Q = CPc (Tco – Tci) or  Tco − Tci = CP c

Q = CPh (Thi − Tho) or  Thi − Tho =



(9.17) (9.18)

Subtracting Equation 9.18 from Equation 9.17 gives:

(Thi − Tho ) − (Tco − Tci ) =



or

Q Q − CPh CP c

(9.19)

1   1 (Thi − Tco ) − (Tho − Tci ) = Q  −  CPh CPc 



DΤ 2 − DΤ1 =



(9.20)

Q(CPc − CPh ) CPh • CPc

(9.21)

Next, we can consider the potential locations for the heat exchanger at the pinch employing the approach introduced by Linnhoff and Hindmarsh [30]. When a heat exchanger is positioned on the hot side of the pinch, which is considered first arbitrarily, ΔT1 = ΔTmin and Equation 9.21 becomes DΤ 2 = DΤ min +



Q(CPc − CPh ) CPh • CPc

(9.22)

Ensuring that ΔT2 ≥ ΔTmin, since Q > 0 and the heat capacity flow rates are positive, it follows that CPh ≤ CPc is a necessary and sufficient condition. Therefore, for a match to be feasible at the pinch, on the hot side, CPh ≤ CPc must be satisfied. If two streams are matched at the pinch with CPc < CPh, the heat exchanger is infeasible because ΔT2 < ΔTmin. Correspondingly, when a heat exchanger is positioned on the cold side of the pinch ΔT2 = ΔTmin and Equation 9.21 becomes DΤ1 = DΤ min −

Hot stream

Q(CPc − CPh ) CPh • CPc

Thi

ΔT2 = Thi – Tco

Tco

Figure 9.30  Schematic of a counter current heat exchanger.

(9.23)

Tho

Q

CPh

ΔT1 = ΔTho – ΔTci

Tci Cold stream

CPc

Process Integration and Heat Exchanger Network  981 In this case, ensuring that there are no approach temperature violations (i.e., ΔT1 ≥ ΔTmin), it is necessary and sufficient that CPh ≥ CPc.

The Pinch Design Approach to Inventing a Network In designing a heat exchanger network that uses the minimum utilities for maximum heat recovery, we consider the following steps: 1. 2. 3. 4.

S elect a ∆Tmin. Calculate the minimum hot and cold utilities used based on this value of ∆Tmin. Using the grand composite curve, pick which utilities to use and their amounts. If the problem has a pinch point in it (which will occur, if step 2 discovers the need for both heating and cooling), divide the problem into two parts at the pinch. We shall design the two parts separately. Remember that the part above the pinch requires only hot utilities, and the part below only the cold utilities. 5. Estimate the number of exchangers for each partition as N-1, where N is the number of streams in that part of the problem. 6. Invent a network using all available knowledge. All exchangers that exist at the pinch point will have the minimum driving force at that point. A small driving force for heat transfer implies a large area. The exchangers near the pinch will tend to be large. Therefore, bad design decisions near the pinch point will tend to be more costly. Design decisions should generally be made in the vicinity of the pinch first. 7. Remove heat cycles if possible. For the designer wishing to produce a design that achieves minimum utility targets, the following rules are: • No heat transfer between the process streams across the pinch temperature. • No external (utility) cooling above the pinch temperature. • No external (utility) heating below the pinch temperature. Violation of any of the above rules results in higher energy requirements than the theoretically minimum requirements and will adversely affect the energy efficiency. These rules form the basis for the network design procedure for heat exchanger networks that ensures that there is no cross pinch heat transfer. For retrofits applications, the design procedure corrects the exchangers that are passing the heat across the pinch.

Heat Exchanger Network Design (HEN) The Design Grid The design of heat exchanger networks has been carried out using the classical pinch design method of Linnhoff and Hindmarch [30], which focused on minimum energy requirement and the fewest number of units. Later graphical and numerical additions made it possible to consider heat transfer area and total annual cost during design. The basic pinch design method respects the decomposition of process and utility pinch points and provides a strategy and matching rules that enable the engineer to obtain an initial network, which achieves the minimum energy target. The stream grid is very useful in the design phase and acts as a drawing board, where the engineer places one match at a time using these matching rules. The pinch design method also indicates situations where stream splitting is required to reach the minimum energy target. Stream splitting is also important in area considerations and the optimal use of temperature driving force, as will be reviewed later in the chapter. The design strategy is simply to start design at the pinch, where driving forces are limited and the critical matches for maximum heat recovery must be selected (i.e., the most restricted part of the design owning to temperature differences approaching ∆Tmin). The matching rules ensure sufficient driving forces, and they attempt to minimize the

982  Chemical Processing Engineering number of units. The design then gradually moves away from the pinch, making sure that hot streams are utilized above the pinch (limited resource) and cold streams are utilized below the pinch. Above the pinch, the hot streams are cooled from their supply temperatures to their pinch temperature, and the cold streams are heated from their pinch temperature to their target temperatures. Below the pinch, the position is reversed, with hot streams being cooled from the pinch to target temperatures and cold streams being heated from supply to pinch temperature. Therefore, for optimum performance above the pinch, no utility cooling should be used. This means that above the pinch, all hot streams must be brought to pinch temperature by interchanging with cold streams. Thus, the pinch design should commence at the pinch by finding matches that fulfill this condition. Cases may occur where CP inequality does not hold for a match; however, the match is still feasible because it is away from the pinch, as it is not a match that has to bring the cold or hot stream up to the pinch temperature. The pinch design method starts the design where the problem is most constrained; that is at the pinch. The thermodynamic constraint of the pinch is used by the designers to identify matches that must be made in order to produce efficient designs. When placing matches, several rules have to be followed in order to obtain a network that minimizes utility use [8]: 1. N  o exchanger may have a temperature difference smaller than ∆Tmin. 2. No process-to-process heat transfer may occur across the pinch. 3. No inappropriate use of utilities should occur. Before placing matches between the hot and cold streams, the target indicates that the number of units needed is equal to the number of streams (including the utility streams) minus one. The tick-off heuristic satisfies the heat duty on one stream, each time a unit is used, and therefore is no longer part of the remaining design problem. Sizing the matches follows the tick-off heuristic that stipulates that the heat exchange match should be as large as possible, so that at least one of the involved streams will be completely satisfied, and then ticked-off from the design. This ensures that once a unit is placed, and uses up one of the available units, it is removed from the problem. Once the matches around the pinch have been chosen to satisfy the criteria for minimum energy, the design should proceed in a manner that keeps capital costs to a minimum. An important criterion in the capital cost is the number of units, and keeping this to a minimum can be achieved using the tick-off heuristic. A stream is ticked-off when individual units are made as large as possible, (i.e., the smaller of the two heat duties on the streams being matched), although the tick-off heuristic can occasionally penalize the design. At the pinch, the enthalpy balance restrictions entail that certain matches must be made, if the design is to achieve minimum utility usage without violating the ∆Tmin constraint; these are known as the essential matches. Above the pinch, the hot streams should be cooled only by transferring heat to cold process streams, not to utility cooling. Therefore, all hot streams above the pinch must be matched up (i.e., ticked-off) with cold streams. That is, hot all streams entering the pinch must be given priority when matches are made above the pinch. Cooling water must not be used above the pinch; therefore, if there are hot streams above the pinch for which the duties are not satisfied by the pinch matches, additional process to process heat recovery must be performed. Finally, above the pinch, the residual heating duty on the cold stream must be satisfied. Since there are hot streams left above the pinch, hot utility is used. Conversely, below the pinch, all colds streams must be matched with hot streams, i.e., all cold streams entering the pinch must be given priority when matches (i.e., ticked-off) are made below the pinch. If there are any cold streams for which the duties are not satisfied by the pinch matches, then additional process-to-process heat recovery must be performed, since hot utility must not be used. Additional match may be used to satisfy the residual heating of the cold streams until the duty is maximized. Finally, the residual cooling duty on the hot streams must be satisfied. Since there are no cold streams left below the pinch, cold utility must be used. The three rules of the pinch principle as well as the CP rules are applied to design the network in Figure 9.31. On the left had side of the grid diagram, the CP rule is CPHot ≤ CPCold or CPleaving pinch ≥CPentering pinch and correspondingly, the right side of the grid diagram, CPHot ≥ CPCold or CPleaving pinch ≥CPentering pinch. According to the pinch rules, there must be no external cooling above the pinch (on the left side of the grid diagram) so hot streams on this side must be brought to pinch temperature by heat transfer with cold streams on the same side, i.e., on the left of the grid diagram.

Process Integration and Heat Exchanger Network  983 CPHot ≥ CPCold

CPHot≤ CPCold

Stream 1

2 3

4

20

36

40

80

Design away from the pinch

ΔH=2100 kW 190ºC 2 ΔH=2800 kW 140ºC

ΔTmin = 10ºC

Tph = 70ºC 85ºC

1

ΔH=2160 kW 118.3ºC 120ºC 2 H 60 kW 2100 kW

40

Design away from the pinch

36

CP (kW/ºC) ∆H (kW)

Tph = 70ºC ΔH= 800 kW 52ºC 3

ΔH=720 kW 3

C

80 kW

50ºC

40ºC

720 kW

ΔH=3200 kW 95.0ºC 60ºC H 1 100ºC 400 kW 2800 kW T = 60ºC pc

20

2100

40

3600

36

2880

80

3200

Tpc = 60ºC

QHmin = 460 kW (a) above the pinch

QCmin = 80 kW

(b) below the pinch

Figure 9.31  The CP table for the possible designs above and below the pinch for Example 9.1.

Similarly, cold streams on the right-hand side of the grid diagram must be brought up to the pinch temperature using hot streams on the right rather than utility heating. The ∆Tmin puts another constraint on the design because it has been defined as the minimum temperature difference for heat transfer anywhere in the system. In general, the grid representation reflects the counter-current nature of heat transfer that makes it easier to check temperature feasibility of the match that is being placed. The hot and cold temperature pinch points can be represented on the grid. The pinch design procedure can be summarized as follows: 1. D  ivide the problem at the pinch into separate problems. 2. Commence the design for the separate problem at the pinch where driving forces are limited and move away from it. 3. Satisfy the feasibility criterion on the CP values for matches (i.e., tick-off heuristic) between streams at the pinch. 4. Determine the loads on individual units using the tick-off heuristic to minimize the number of units; however, this can cause problems. 5. Create freedom of choice for matches away from the pinch. Here, the designer can be flexible on the basis of judgment and process knowledge. The matching rules for heat exchanger networks (i.e., those situated immediately above and below the pinch) can be expressed mathematically by: The minimum number of heat exchangers in a HEN is [31]:

uHX,min = Ns + Nu − 1

(9.24)

984  Chemical Processing Engineering where NS = number of streams NU = total number of distinct hot and cold utility sources. Thus, for hot utilities: fuel, steam at high pressure (hp), medium pressure (mp) and low pressure (lp), and for cold utilities: boiler feed water (bfw), cooling water (cw) and refrigeration; each counts as distinct utility sources. Above pinch

Below pinch

CPHot ≤ CPCold or CPleaving pinch ≥ CPentering pinch

CPHot ≥ CPCold or CPleaving pinch ≥ CPentering pinch

NCold ≥ NHot

NHot ≥ NCold

where CPHot = Capacity flow rate of hot stream. CPCold = Capacity flow rate of cold stream. NHot = Number of hot streams at the pinch (including full as well as split streams). NCold = Number of cold streams at the pinch (including full as well as split streams). Making sure that every unit fully satisfies the enthalpy change of either the hot or cold stream (the tick-off rule) minimizes the number of units. If the inequalities above are not satisfied for a complete set of pinch exchangers, stream splitting has to be considered in order to reach maximum energy recovery (MER). It is always possible to satisfy all the inequalities by stream splitting, since total CP for cold streams are larger than total CP for hot streams above the pinch, and vice versa below the pinch. Figure 9.31 illustrates a possible HEN for Example 9.1. The overall network resulting from the above and below pinch designs as shown in Figure 9.32 is known as a minimum energy requirement (MER) design since it meets the minimum energy target. The Problem Table shows the results as: Pinch temperature

= 65oC

Hot stream pinch temperature

= 70oC

Cold stream pinch temperature

= 60oC

Minimum hot utility requirement

= 460 kW

Minimum cold utility requirement

= 80 kW

Maximum energy recovery

= 5620 kW

Network Design Above the Pinch Applying:

or

CPHot ≤ CPCold

CPleaving pinch ≥ CPentering pinch

(9.25) (9.26)

1. S tream 1 is matched with stream 3, and transferring the full amount of heat required to bring stream 1 to the target temperature gives:

Process Integration and Heat Exchanger Network  985 CPHot ≤ CPCold

Stream No.

1

190ºC

ΔTmin10ºC

85ºC

2

2 140ºC

120ºC

H 60 kW

1

118.3ºC

CPHot ≥ CPCold

Design away from the pinch

CP (kW/ºC)

∆H (kW)

20

2100

80 kW 50ºC C

40

3600

40ºC 3

36

2880

Tph = 70ºC

Tph = 70ºC

2

3

52ºC

3 720 kW

2100 kW

100ºC

H 400 kW

95ºC

1 2800 kW

4 60ºC

80

Tpc = 60ºC QHmin = 460 kW

QCmin = 80 kW

H Hot utility C Cold utility

3200

Heat exchange between streams

Figure 9.32  A final grid representation of the heat exchanger network for Example 9.1.

ΔHex = CP ΔT or = CP (Ts – Tt) = 20 (190 – 85) = 2100 kW The heat load in stream 3 from the pinch temperature to its target temperature of 120oC is: ΔHex = CP ΔT = 36(120 – 60) = 2160 kW. This requires an excess of 60kW, which requires heating to bring the stream to its target temperature. Therefore, a heater is included to provide the remaining heat load: ΔHhot = 2160 − 2100 = 60kW 2. S tream 2 is matched with stream 4, while satisfying CP restriction, transferring the full amount of heat to bring stream 2 to the pinch temperature. ΔHex = CP ΔT = 40(140 – 70) = 2800kW. 3. The heat required to bring stream 4 to its target temperature from the pinch temperature is: ΔHex = CP ΔT = 80(100 – 60) = 3200kW Another heater is included in stream 4 to provide the remaining heat load: ΔHhot = 3200 – 2800 = 400kW

986  Chemical Processing Engineering This calculation checks with the value given by the problem table in Figure 9.26. The proposed network design above the pinch is shown in Figure 9.31.

The Intermediate Temperatures in the Streams are: Stream 4: the heat load is: = CP ΔT DΗ DT = CP 2800 (T − 60) = = 35 80 T = 95oC

ΔHex

The heater load = 400kW DΗ DT = CP 400 (T − 95) = =5 80 T = 100oC In stream 3: ΔHex = CP ΔT 2100 = 36(T – 60) 58.3 = T – 60 T = 118.3oC The heater load is 60kW ΔHhot = CP ΔT 60 = (T − 118.3) 36 1.7 = T – 118.3 T = 120oC

Network Design Below the Pinch Applying:

CPHot ≥ CPCold

(9.27)

or

CPleaving pinch ≥ CPentering pinch

(9.28)

1. Th  ere is one hot stream 2 and one cold stream 3 below the pinch, as stream 1 has its target temperature at 85oC > 70oC (the hot pinch temperature) and stream 3 starts at the supply temperature (40oC).

Process Integration and Heat Exchanger Network  987 So, stream 2 is matched with stream 3, transferring the full amount to bring stream 3 to its pinch temperature. ΔHex = CP ΔT = 36(60 – 40) = 720 kW. The amount of heat in stream 2 from the pinch temperature to its target temperature is: ΔHex = CP ΔT = 40 (70 – 50) = 800 kW.

A cooler is required in stream 2 as the remaining heat load is: ΔHCold = 800 – 720 = 80kW



This value also checks with the value by the problem table in Figure 9.26.

The Intermediate Temperatures in the Streams are: In stream 2: ΔHex = CP ΔT 720 40 18 T

= (70 − T) = (70 –T) = 52oC

The cooler load is 80kW and the target temperature is: ΔHex = CP ΔT 80 = (52 − T) 40 T = 50oC Verification of the temperature difference between the heat exchanger units in the network ≥ than the minimum temperature approach ∆Tmin = 10oC.

Above the Pinch The heat exchange between streams 2 and 4, unit 1, assuming counter current flow through unit 2 at constant CP is: 140°C ∆T1 = 140 – 95 = 45°C 95°C

1

70°C ∆T2 = 70 – 60 = 10°C 60°C

Here, the temperature difference at either end of the unit is ≥ ∆Tmin (10oC), indicating that unit 1 has not violated the minimum temperature approach; however, there is a temperature cross in this unit as the exit temperature of the cold stream is greater than the exit temperature of the hot stream.

988  Chemical Processing Engineering The heat exchange between streams 1 and 3, unit 2 assuming counter-current flow at constant CP is: 190°C T1 = 190 – 118.3 = 71.7°C

85°C ∆T2 = 85 – 60 = 25°C

2

118.3°C

60°C

The temperature difference at either end of the unit 2 is ≥ ∆Tmin (10oC), indicating that unit 2 has not violated the minimum temperature approach, but there is a temperature cross in the unit as the exit temperature of the cold stream is greater than the exit temperature of the hot stream.

Below the Pinch The heat exchange between streams 2 and 3, unit 3 assuming counter-current flow at constant CP is: 70°C ∆T1 = 70 – 60 = 10°C

52°C ∆T2 = 52 – 40 = 12°C

3

60°C

40°C

Here, the temperature difference at either end of unit 3 is ≥ ∆Tmin (10oC), indicating that unit 3 has not violated the minimum temperature approach. There is a temperature cross in this unit, which is tolerable.

Example 9.2 Consider the network of heat exchangers in Figure 9.33 with ∆Tmin = 10oF. Is the heat flowing across the pinch temperatures? If so, redesign the network for minimum utility requirements (i.e. QHmin and QCmin). Table 9.11 shows the input stream data.

400ºF

Steam

250 250ºF 300ºF CPh = 4 Btu/h. ºF

CW 150ºF CPc = 2 Btu/h. ºF

Figure 9.33  Heat exchanger network for Example 9.2.

100ºF

250ºF

Process Integration and Heat Exchanger Network  989 Table 9.11  Stream data for Example 9.2. Stream

Actual Ts oF

Temperature Tt oF

Shifted Ts oF

Temperature Tt oF

CP Btu/hr.oF

Hot

300

100

295

95

4

Cold

150

400

155

405

2

Solution The utilities in the network are: Cooling water, ΔHCW = CP ΔT = 4 (100 – 150) = -600 Btu/h (-ΔHCW) = 600 Btu/h. Steam, ΔHSteam = CP·ΔT = 2(400 – 250) = 300 Btu/h. Figure 9.34 shows the grid diagram at interval temperature vs. heat capacity for hot and cold streams respectively. Using the Problem Table in calculating the pinch temperature and the minimum utility requirements (i.e., targets) for the hot and cold streams is illustrated as follows: For ∆Tmin = 10oF The results from the Problem Table (Figure 9.35) show that: Pinch temperature

= 295oF

Hot stream pinch temperature

= 300oF

Cold stream pinch temperature

= 290oF

Minimum hot utility requirement

= 220 Btu/h.

Minimum cold utility requirement

= 520 Btu/h.

A possible HEN is shown in Figure 9.36, and one with the minimum utility requirements shown in Figure 9.37. To avoid heat flow across the pinch, use a larger heat exchanger. Stream Population

Interval Temperature 405ºC 295ºC

1

155ºC

2

95ºC CP

4

2

Figure 9.34  The grid diagram of interval temperature vs. heat capacity flow rate of hot and cold streams for Example 9.2.

990  Chemical Processing Engineering Interval

(Ti – Ti+i)

Temp.,

Infeasible

∆Hi

(ΣCPh–ΣCPc) ∆Hi

ºC

Heat

Surplus/Def icit

Cascade

Hot

Hot

Utility

Utility 0

110

-2

-220

-220 -220

140

2

280

0

280

280

155 3

220

-220

295 2

Heat

Cascade

405 1

Feasible

∆Hi

60 60

4

240

280

240

240

95

300

520

Cold

Cold

Utility

Utility

Figure 9.35  The problem table. CPh ≤ CPc

Thp = 300ºF

CPh ≥ CPc

ΔH= 800 Btu/h

230ºF

CP, ΔH Btu/ hr.ºF Btu/hr.

C

100ºF

4

800

520 Btu/h

400ºF

H

ΔH=280 Btu/h

220 Btu/h QHmin= 220 Btu/h

150ºF

280 Btu/h Tcp = 290ºF

QCmin = 520 Btu/h

Figure 9.36  A grid representation of the heat exchanger network for Example 9.2.

2

500

Process Integration and Heat Exchanger Network  991 400ºF

220 Btu/hr.

Steam CW 290ºF 230ºF

300ºF CPh = 4 Btu/hr. ºF

280 Btu/hr.

100ºF 520 Btu /hr.

150ºF CPc = 2 Btu/hr. ºF

Figure 9.37  Heat exchanger network for Example 9.2.

Design for Threshold Problems Generally, processes require both hot and cold utilities in the design of HEN. The philosophy in the pinch design method is to start the design where it is most constrained (i.e., at the pinch). If the design is pinched, then the problem is mostly referred to as a single pinch problem. However, if there is no pinch, then the most constrained part of the problem is the no-utility end [16]. A pinch does not occur in all HEN designs. Certain problems remain free of a pinch until the minimum allowed driving force; ∆Tmin is increased up to or beyond a threshold value ∆Tthreshold. The value of ∆Tmin at which one utility target falls to zero is referred to as ∆Tthreshold, and the condition where only one utility has a value of zero is called the threshold problem. For a pinch to occur, it is necessary to have ∆Tmin≥ ∆Tthreshold,, as it is also possible for HEN problems to contain more than a single pinch. This situation occurs when utilities are available at different temperature levels, e.g., high, medium and low pressure steam. An essential feature of threshold problems is that as ∆Tmin varies, demands for only one utility type (hot or cold) are identified over the variation range. Typical examples of threshold heat integration problems involve high-temperature fuel cells, which usually have large net cooling demands but no heat heating demands [32, 33]. There are two subtypes of threshold problems (see Figure 9.38). 1. L  ow-threshold ∆Tmin, where problems of this type can be treated exactly as pinch-type problems. 2. High-threshold ∆Tmin, where it is first necessary to satisfy the required temperature for the no-utility end before proceeding with the remaining design by applying the tick-off heuristic. Figure 9.39a shows a typical sketch of the closest temperature approach between the hot and cold composites is the non-utility and the curves diverge away from this point. Here, the design can start from non-utility end using the pinch design rules, and Figure 9.39b shows a typical sketch of the grand composite curve with zero heat flow. The relationship for threshold problems can be summarized as [13]: 0 ≤ ΔTmin < ΔTthreshold

Either hot or cold utility usage (but not both) is required and the problem is not pinched.

ΔTmin = ΔTthreshold

The same hot or cold utility requirement as for lower values of ΔTmin is required but the problem is now pinched.

ΔTmin > ΔTthreshold

Both hot and cold utilities are required. The problem is pinched.

992  Chemical Processing Engineering (a)

ST

T Utilities [MW]

CW ST

ΔTmin CW 10ºC

ΔTmin

DH

[MW]

Low Threshold ΔTmin (b)

ST T

Utilities [MW]

ST ΔTmin = 10ºC

CW

10ºC

ΔTmin

ΔH

[MW]

High Threshold ΔTmin

Figure 9.38  Threshold problems. (b)

Grand composite curve

Shifted temperature(ºC)

Hot and cold composite curves

Actual temperature(ºC)

(a)

Heat f low, kW

Net heat f low, kW

Figure 9.39  (a) Hot and cold composite curves; and (b) grand composite curve for threshold problems.

It is possible to apply the pinch design method to threshold problems providing that ∆Tmin, is adjusted to the threshold value, although in this instance, the designer would not be too concerned about a ∆Tmin, violation. Generally, threshold problems in industrial design are fairly rare. This is due to the fact that most industrial processes use more than one hot or cold utility. Further, savings can be made by utilizing cheaper grade utilities. In cases where only one

Process Integration and Heat Exchanger Network  993 hot or one cold utility is available, threshold problems can only exist if the process (e.g., reactors, separators, etc.) has large driving forces, and in today’s energy costs, processes such as these are less common.

Stream Splitting The principle of design at the pinch follows several rules and guidelines to allow design for minimum utility (or maximum energy recovery) in the minimum number of units. There are cases where it is not always possible to follow these basic rules, and it is necessary to split the streams so that heat exchange matches can be appropriately placed. Stream splitting may be considered in the following cases: 1. A  bove the pinch, where the number of hot streams is greater than the number of cold streams (NHot > NCold). 2. Below the pinch, where the number of cold streams is greater than the number of hot streams (NCold > NHot). 3. When the CP values do not provide any feasible match. The loads of the matches involving stream branches are determined using the tick-off heuristic because each stream splitter presents an additional degree of freedom; it is essential to decide how to divide the overall streams CP between the branches. Finally, when using stream splitting above and below the pinch for HEN design, the CP feasibility criterion for every pinch match must be satisfied. Above the pinch

Below the pinch

CPHot ≤ CPCold

CPHot ≥ CPCold

or CPleaving pinch ≥ CPentering pinch

or CPleaving pinch ≥ CPentering pinch

Figure 9.40 shows complete algorithm for stream splitting streams above and below the pinch, respectively.

Stream data at pinch

(a)

(b)

Below the pinch

Above the pinch NHot ≤ NCold ? Yes

Place matches

NHot ≥ NCold ?

No Split a cold stream

CPHot ≤ CPCold For every pinch match ? Yes

Stream data at pinch

No

Yes CPHot ≥ CPCold For every pinch match ? Yes

Split a stream (usually hot)

CPCold = Capacity f low rate of cold stream CPHot = Capacity f low rate of hot stream NCold = Number of cold streams NHot = Number of hot streams

Figure 9.40  Algorithm for stream splitting at the pinch.

Place matches

No Split a hot stream

No

Split a stream (usually cold)

994  Chemical Processing Engineering

Advantages and Disadvantages of Stream Splitting Advantage: Stream splitting removes the use of one extra heat exchanger in the network. Disadvantages: 1. I n stream splitting, control of the flows in two or more branches is required. 2. Splitting a stream means each branch has a lower flow rate than that of the entire stream. Where there is no phase change heat transfer, the lower flow rate means lower heat transfer coefficients and larger exchanger areas.

Example 9.3 (Source: Seider et al. Product and Process Design Principles – Synthesis, Analysis, and Evaluation 3rd ed. Wiley, 2009 [26]) Consider the process flowsheet in Figure 9.41, where the duties required for each heat exchanger are given in MW, and the source and target stream temperatures are shown in Table 9.12. a. Th  e flowsheet calls for 990 MW to be removed by cooling water and 750 MW to be provided by steam. It is claimed that this design does not meet MER targets for ∆Tmin = 10oC. Verify or refute this claim. b. If verified, design a HEN to meet MER targets for ∆Tmin = 10oC.

Solution Using the data in Table 9.12 and Figure 9.41, the stream data and the CP values are shown in Table 9.13. The Excel spreadsheet software in A User Guide on Process Integration for the Efficient Use of Energy, [21] is used to perform the following steps: a. C  onstruct the Problem Table. b. Determine the pinch problem; pinch temperature; hot and cold streams pinch temperatures, hot and cold utility requirements. c. Plot the composite curves and the grand composite curve. d. Determine the maximum energy recovery at ∆Tmin = 10oC. e. Plots of the hot and cold pinch temperatures at varying ∆Tmin (i.e., minimum to maximum values) and of the minimum utility requirements for hot and cold streams at varying ∆Tmin (i.e., minimum to maximum values). The results show the following at ∆Tmin = 10oC: Type of pinch problem

= Threshold problem

Pinch temperature

= 255oC

Hot stream pinch temperature

= 260 oC

Cold stream pinch temperature

= 250oC

Minimum hot utility requirement

= 0 MW

Minimum cold utility requirement

= 240MW

Maximum energy recovery

= 1400 MW

Process Integration and Heat Exchanger Network  995 Table 9.12  Stream data for Example 9.3. Process stream

Ts (oC)

Tt (oC)

Feed

25

200

Effluent

260

40

Recycle 1

40

200

Flash liquid

40

100

Recycle 2

50

200

Product

120

40

Feed

1

25ºC

Ef f luent

200ºC 350 MW st 200ºC

260ºC 450 MW 180 MW

Reactor

st 200ºC

2 300 MW

Recycle 2 cw

Recycle 1

cw Product 40ºC

790 MW

200 MW 50ºC

40ºC

40ºC

Flash Separator Flash Liquid

Distillation column

40ºC 3

100ºC 120MW

120ºC

Figure 9.41  Process flowsheet for Example 9.3. (Used by permission: Seider et al., Product and Process Design Principles Synthesis, Analysis and Evaluation, 3rd. ed., Wiley, 2009.)

996  Chemical Processing Engineering Table 9.13  Completed stream data from Figure 9.41 for Example 9.3. Stream

ID

Ts (oC)

Tt (oC)

Heat capacity flow, CP (MW/oC)*

ΔH (MW)

Effluent

H1

260

40

6.0

1320

Product

H2

120

40

4.0

320

Feed

C1

25

200

2.0

350

Recycle -1

C2

40

200

3.0

480

Flash liquid

C3

40

100

2.0

2000

Recycle- 2

C4

50

200

3.0

2000

Therefore, the proposed design does not meet the targets. The following Figures 9.42 to 9.51 show snapshots of the results for Example 9.3 and a possible HEN is shown in Figure 9.52. Figure 9.52 shows a three-way split of stream H1 to fully meet the heating requirements of streams C1 and C2 and partially meet the requirements of stream C4. Note that the stream-split fractions are also adjusted to ensure no violations of ΔTmin. Similarly, stream H2 is split two ways to complete the heating requirements of the two streams that remain. Finally, coolers are installed to close the energy balances on streams H1 and H2, with a total duty equal to the minimum energy requirement target. In both figures, seven heat exchangers are used.

Figure 9.42  Screenshot of the input data for Example 9.3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Process Integration and Heat Exchanger Network  997

Figure 9.43  Screenshot of the grid diagram showing the shifted temperature vs. heat capacity flow rate and the pinch location for Example 9.3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Figure 9.44  Screenshot of the grid diagram showing the actual temperature vs. heat capacity flow rate for Example 9.3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

998  Chemical Processing Engineering

Figure 9.45  Screenshot of the grid diagram showing the shifted streams, shifted temperature vs. heat capacity flow rate for Example 9.3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Figure 9.46  Screenshot of the Problem Table, heat cascade, pinch identification, problem type, minimum hot and cold utility requirements for Example 9.3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Process Integration and Heat Exchanger Network  999

Figure 9.47  Screenshot of hot and cold streams Composite Curves for Example 9.3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Figure 9.48  Screenshot of hot and cold streams shifted Composite Curves for Example 9.3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

1000  Chemical Processing Engineering

Figure 9.49  Screenshot of the Grand Composite Curve for Example 9.3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Figure 9.50  Screenshot of actual interval temperature of hot and cold duties for Example 9.3 Maximum energy recovery at ΔTmin = 10oC = 1640 – 240 = 1400 MW. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Process Integration and Heat Exchanger Network  1001

Figure 9.51  Screenshot of plots of pinch temperature of hot and cold streams and minimum utility requirements at varying ∆Tmin > (22.5oC) (i.e minimum to maximum values) for Example 9.3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.) Design away From the pinch

CPHot ≥ CPCold Nhot ≥ NCold

CP = 1.55

Thp = 260ºC

CP = 2.29

H1

CP = 2.16

34.2ºC

3 2

40ºC C 160 MW

107.2 ºC

1

CP = 2.0 120ºC

4

H2

CP (MW/ºC)

66.67ºC

50.4ºC

5

60ºC

40ºC 4.0 C 80 MW

CP= 2.0

200ºC

6.0

25ºC

3

∆H (MW) 1320

320

C1

2.0

350

C2

3.0

480

C3

2.0

120

C4

3.0

450

350 MW 200ºC

40ºC

2

480 MW 100ºC

Tcp = 250ºC 200ºC

90ºC

1

330 MW Q Hmin = 0 MW

40ºC

4

120 MW 5

50ºC

120 MW

H Hot utility

Q Cmin = 240 MW C Cold utility

Heat exchange between streams

CP = Heat capacity flow rate N = Number of streams

Figure 9.52  A possible grid representation of the heat exchanger network of Example 9.3.

1002  Chemical Processing Engineering

Example 9.4: Source - Manufacture of cellulose acetate fiber, by Robin Smith (Chemical Process Design and Integration, John Wiley, 2007 [34]) The process flowsheet for a cellulose acetate fiber process is shown in Figure 9.53. Solvent is removed from the fibers in a dryer by recirculating air. The air is cooled before it enters an absorber where the solvent is absorbed in water. The solvent–water mixture is separated in a distillation column and the water is recycled. The process is serviced by saturated steam at 150oC, cooling water at 20oC and refrigerant at -5oC. The temperature rise of both the cooling water and refrigerant can be neglected. Extract the stream data from the flowsheet and present them as hot and cold streams with supply and target temperatures and heat capacity flowrates. Sketch the composite curves for the process at ΔTmin = 10oC. Determine the maximum energy recovery (minimum heat and cold utilities), and design a network for the process which achieves maximum energy recovery in the minimum number of units when no cooling water is used, i.e., only steam and refrigeration. 80ºC

100ºC

Dryer Dryer

Steam

Air CP = 80

20ºC 10ºC

Water CP = 140 5ºC

30ºC

Refrigeration

59ºC

30ºC Refrigeration

CP = 5,000

CW

Fan

CW

60ºC

Absorption column

CW

30ºC CW Solvent CP = 5

Distillation column 90ºC 101ºC

Air/Solvent CP = 100

15ºC

8ºC

100ºC 100ºC Steam CP = 6,500

CP = kW/K Steam

Water/Solvent CP = 145

Figure 9.53  Flowsheet for the manufacture of cellulose acetate fiber. (Used by permission: Smith, R., Chemical Process Design and Integration. John Wiley, 2007.)

Table 9.14  Stream data from Figure 9.53 for Example 9.4. Stream

Ts (oC)

Tt (oC)

mCp (kW/K)

Heat load (kW)*

H1

80

15

100

-6500

H2

100

5

140

-13300

H3

59

30

5

-145

H4

60

59

5000

5000

C1

100

101

6500

6500

C2

8

90

145

11890

C3

20

100

80

6400

Process Integration and Heat Exchanger Network  1003

Stream Data Extraction The process flowsheet is shown in Figure 9.53 and the data extraction from the flowsheet is shown in Table 9.14.

Solution The Excel spreadsheet software in A User Guide on Process Integration for the Efficient Use of Energy, [21] is used for the following steps: a. C  onstruct the Problem Table. b. Determine the pinch problem; pinch temperature; hot and cold streams pinch temperatures, hot and cold utility requirements. c. Plot the composite curves and the grand composite curve. d. Estimate the maximum energy recovery at ∆Tmin = 10oC. e. Plots of the hot and cold pinch temperatures at varying ∆Tmin (i.e., minimum to maximum values) and of the minimum utility requirements for hot and cold streams at varying ∆Tmin (i.e., minimum to maximum values). The results show the following at ∆Tmin = 10oC: Type of pinch problem

= Two pinches

Pinch temperature

= 75oC

Hot stream pinch temperature

= 80oC

Cold stream pinch temperature

= 70oC

Minimum hot utility requirement

= 9000kW

Minimum cold utility requirement

= 9155kW

Maximum energy recovery

= 15790kW

Figure 9.54  Screenshot of the input data for Example 9.4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

1004  Chemical Processing Engineering

Figure 9.55  Screenshot of the grid diagram showing the shifted temperature vs. heat capacity flow rate and the pinch location for Example 9.4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Figure 9.56  Screenshot of the grid diagram showing the actual temperature vs. heat capacity flow rate for Example 9.4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Hot process streams - Cold utility = 6500 + 13300 +145 – 5000 – 9155 = 15790 kW Cold process streams – Hot utility = 6500 + 11890 + 6400 – 9000 = 15790 kW This is evident from the overlap of the composite curves in Figures 9.59 and 9.60. (Note: Example 9.4 is a problem with two pinches, in addition to the process pinch at 75oC, there is a utility pinch at 25oC corresponding to cooling water). Figures 9.54 to 9.63 show snapshots of the results of Example 9.4 and a possible HEN is shown in Figure 9.64. There is however a ΔTmin violation of heat exchanger unit 4 (i.e., 15°C – 8°C = 7°C, which is < ΔTmin).

Process Integration and Heat Exchanger Network  1005

Figure 9.57  Screenshot of the grid diagram showing the shifted streams, shifted temperature vs. heat capacity flow rate for Example 9.4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Figure 9.58  Screenshot of the Problem Table, heat cascade, pinch identification, problem type, minimum hot and cold utility requirements for Example 9.4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Heat Exchanger Area Targets The area of a single counter-current heat exchanger is defined by

where A = surface area for heat exchanger, m2 Q = heat transferred, kW

A=

Q U∆TLMTD

(9.29)

1006  Chemical Processing Engineering

Figure 9.59  Screenshot of hot and cold streams composite curves for Example 9.4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Figure 9.60  Screenshot of hot and cold streams shifted Composite Curves for Example 9.4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

U   = overall heat transfer coefficient, W/m2.oC. ΔTLMTD = log mean temperature difference, oC. If we have a pure counter-current heat exchanger where the hot stream enters at Th1 and leaves at Th2, and the cold stream enters at Tc1 and exits at Tc2, so that Tc1 and Th2 are at the cold end C, and Th1 and Tc2 are at the hot end H of the exchanger.



∆TLMTD =

∆TH − ∆TC ln ( ∆TH ∆TC )

(9.30)



Process Integration and Heat Exchanger Network  1007

Figure 9.61  Screenshot of the Grand Composite Curve for Example 9.4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Figure 9.62  Screenshot of actual interval temperature of hot and cold duties for Example 9.4. Maximum energy recovery at ΔTmin = 10oC = 24945- 9155 = 15790 kW (15.8 MW). (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

=

(Th1 − Tc2 ) − (Th2 − Tc1 ) T − T  ln  h1 c2   Th2 − Tc1 

For a multi-stream problem with several exchangers, the composite curves are divided into vertical segments, based on heat load. We can calculate the area value for each segment, k and sum them together to give a total area for the heat exchangers in the network. To calculate the network area from the composite curves, utility streams (i.e., hot and cold minimum requirements) must be included with the process streams in the composite curves to obtain

1008  Chemical Processing Engineering

Figure 9.63  Screenshot of plots of pinch temperature of hot and cold streams and minimum utility requirements at varying ∆Tmin (i.e minimum to maximum values) for Example 9.4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Design away From the pinch

CPHot ≤ CPCold NHot ≤ NCold

Tph = 80ºC

Design away CPHot ≥ CPCold From the pinch N ≥N Hot

15ºC

4 100ºC

CP = 86

1

Tph = 80ºC 60ºC 110ºC

6500 kW H 100ºC

90ºC

100ºC

89.3ºC H 1 2800 kW 100 kW 2400 kW H

5ºC 140 C 4010 kW

3

CC 59ºC 5000 kW

30ºC 59ºC C 145 kW

9000 13300

5

145 5000

6500

6500

8ºC

145

11890

20ºC

80

6400

3 2490 kW 4 CP = 105 6500 kW 2 4000 kW

∆H (kW)

5000

CP = 40 Tpc = 70ºC

Tpc = 70ºC

100

33.6ºC

2

CP = 54

CP (kW/ºC)

Cold

H Hot utility C Cold utility

Heat exchange between streams

CP = Heat capacity f low rate N = Number of streams

Figure 9.64  A grid representation of the heat exchanger network for Example 9.4.

the balanced composite curves to obtain the balanced composite curves (BCC). The segments should be chosen to start and finish at heat loads that correspond to gradient changes on the hot and cold composite curves (i.e., where streams start and finish or change CP, as with the temperature intervals when calculating the Problem Table). The total network area is:

Process Integration and Heat Exchanger Network  1009

1 A Total = U



Intervals k

∑

k =1,....K

Ηk TLMTD,k

(9.31)



where ATotal = heat exchange area for vertical heat transfer for the whole network. K = total number of enthalpy intervals. The problem with Equation 9.31 is that the overall heat transfer coefficient is not constant throughout the process. To overcome this, Equation 9.31 can be extended to allow for individual film heat transfer coefficients h, on each stream [33, 35]. Intervals k

∑

A Total =

k =1,....K



1 TLMTD,k

Cold streams J  Hot streams I q q j,k  i,k   + h  i =1,....I h i,k j,k  j=1,...J  

∑

∑

(9.32)

where qi = heat duty on hot stream i in enthalpy interval k. = heat duty on cold enthalpy j in enthalpy interval k. j hi, hj = film heat transfer coefficients for hot stream i and cold stream j (including wall and fouling resistances). I = total number of hot streams in enthalpy interval k. J = total number of cold streams in enthalpy interval k. K = total number of enthalpy intervals.

(a)

(b)

TºC

A CP = 10 h = 0.01 A

B

350º

CP = 50 h = 0.1 B 300º

AREA = 1616 m2 C

290º 250º D 200º

C CP = 50 h = 0.1

D

260º

A B

CP = 10 h = 0.01 CP = kWK-1 h = kWm-2 K-1

H (kW)

C D

AREA = 1250 m2

Figure 9.65  If film heat transfer coefficients differ significantly, then non vertical heat transfer is necessary to achieve the minimum area. (Used by permission: Linnhoff and Ahmad, 1990. Cost Optimum Heat Exchanger Networks: I. Minimum Energy and Capital Using Simple Models for Capital Cost. Computers Chem. Eng., 7, 729.)

1010  Chemical Processing Engineering Equation 9.32 allows the network area to be targeted based on a vertical heat exchange model, if film heat transfer coefficients vary. If there are large variations in film heat transfer coefficients, Equation 9.32 cannot predict the true minimum network area, and deliberate non-vertical matching may be required to achieve minimum area. Consider Figure 9.65a, where hot stream A with a low coefficient is matched against cold stream C with a high coefficient. Hot stream B with a high coefficient is matched with cold stream D with a low coefficient. In both matches, the temperature difference is taken to be the vertical separation between the curves. This arrangement requires 1616 m2 of area overall. Conversely, in Figure 9.65b, hot stream A with a low film heat transfer coefficient is matched with cold stream D which also has a low coefficient, but uses temperature differences greater than vertical separation. Hot stream B is matched with cold stream C, both with high heat transfer film coefficients but with temperature differences less than vertical. This arrangement requires 1250 m2 of area overall less than the vertical arrangement. Therefore, if film heat transfer coefficients vary significantly, then Equation 9.32 does not predict the minimum network area. If higher temperature differences (∆Ts) are used for matches with low film heat transfer coefficient and vice versa, the area target from criss-crossing can actually be lower than that from vertical matching, and Equation 9.32 does not predict the true minimum network area. The true minimum area must be predicted using linear programming [36, 37]. In practice, Equation 9.32 gives an area accurate to within 10%, unless film heat transfer coefficients differ by more than order of magnitude. All these methods require knowledge of film heat transfer coefficients, which are very seldom available in practice. However, possible ways of acquiring them are: 1. T  abulated experience values [38]. 2. By assuming a reasonable fluid velocity, together with fluid physical properties, standard heat transfer correlations can be used. 3. If the pressure drop available for the stream is known, the expressions of Polley et al. [39, 40] can be used.

Example 9.5. (Source: R. Smith, Chemical Process Design, McGraw-Hill, 1995 [20]) Table 9.15 shows the stream data together with utility data and streams heat transfer coefficients. Calculate the heat exchange area target for the network.

Solution Using the data in Table 9.15 at ∆Tmin = 10oC, the BCCs are determined as shown in Figure 9.66. These curves incorporate the steam within the construction of the hot composite curve, and the cooling water for the cold composite curve. Figure 9.66 shows the curves divided into enthalpy intervals, where there is either a change of slope on the Table 9.15  Complete stream and utility data for the Example 9.5 [20]. Stream

Supply temp. TS (oC)

Target temp. TT (oC)

∆H (MW)

Heat capacity flow rate, CP(MW/oC)

Heat transfer film coefficient (MW/m2.oC)

1. Reactor 1 feed

20

180

32.0

0.2

0.0006

2. Reactor 1 product

250

40

-31.5

0.15

0.0010

3. Reactor 2 feed

140

230

27.0

0.3

0.0008

4. Reactor 2 product

200

80

-30.0

0.25

0.0008

5. Steam

240

239

-7.5

7.5

0.0030

6. Cooling water

20

30

10.0

10

0.0010

Process Integration and Heat Exchanger Network  1011 T(ºC) 250 225 200 175 150

6

7

125

4

5

2

3

1

100 75 50 25 0

0

10

20

50

40

30

70

60

H(MW)

Figure 9.66  The enthalpy intervals for the balanced composite curves of Example 9.5. 1

3

2

Hot Stream 250ºC Temperature

240ºC Steam

239ºC

4 200ºC

6

5 150ºC

95ºC

7 80ºC

40ºC

CP=7.5 h = 0.003 CP=0.15 h= 0.001

2

4

CP=0.25 h = 0.0008 CP=0.2 h = 0.0006

CP=0.3 h = 0.0008

1

3 CP=1.0 h = 0.001

Cold Stream Temperature Enthalpy

230ºC

225ºC

199.5ºC

69 MW

67.5 MW

59.85 MW

180ºC 54 MW

CW

140ºC

30ºC

25ºC

20ºC

34 MW

12 MW

6 MW

0 MW

Figure 9.67  The enthalpy interval population for Example 9.5. (Used by permission: Smith, R., Chemical Process Design, McGraw-Hill, 1995.)

hot composite curve, or a change of slope on the cold composite curve. Figure 9.67 shows the stream population for each enthalpy interval together with the hot and cold stream temperatures. Calculations for in Table 9.21.

∑(q

i

hi) , k

∑(q

j

h j ) and (ΔTLMTD)k terms on the hot and cold streams at intervals of k given k

Enthalpy interval 1 Hot stream 250°C

240°C

∆TH = (Th1 – Tc2)

∆TC = (Th2 – Tc1)

= 250 – 230 = 20°C 230°C

225°C Cold stream

= 240 – 225 = 15°C

1012  Chemical Processing Engineering The log mean temperature difference is:

∆TLMTD =

Hot stream:

∑(q

h i ) , (kW/kW/m2.oC) = m2.oC

i

k

∑(q

Cold stream:

∑(q

(∆TH − ∆TC ) = (20 − 15) / ln(20 /15) = 17.38° C ln ( ∆TH ∆TC )

h j)

j

k

∑(CP

Ti h i ) =

∑(CP

Tj h j ) =

1

0.15(250 − 240) = 1500(m 2 .° C) 0.001

k

∑(q



hi) =

i

j

h j) = k

1

0.3(230 − 225) = 1875(m 2 .° C) 0.0008

Enthalpy interval 2 Hot stream 240°C

239°C

∆TH = (Th1 – Tc2)

∆TC = (Th2 – Tc1)

= 240 – 225 = 15°C 225°C

= 239 – 199.5 = 39.5°C 199.5°C Cold stream

The log mean temperature difference is:

∆TLMTD =

Hot stream:

∑(q

(∆TC − ∆TH ) = (39.5 − 15) / ln(39.5 /15) = 25.30° C ln ( ∆TC ∆TH )

h i ) , (kW/kW/m2.oC) = m2.oC

i

k



∑(q

Cold stream:

∑(q

i

j

hi) = k

h j)

i

i

2

1

k

∑(q



− 239) 0.15(240 − 239) + = 2650(m .° C) ∑(CP∆T h ) = 7.5(240 0.003 0.001

j

h j) = k

∑(CP∆T

j

hj ) = 1

0.3(225 − 199.5) = 9562.5(m 2 .° C) 0.0008

Enthalpy interval 3 Hot stream 239°C

200°C

∆TH = (Th1 – Tc2)

∆TC = (Th2 – Tc1)

= 239 – 199.5 = 39.5°C 199.5°C

= 200 – 180.0 = 20°C 180.0°C Cold stream

Process Integration and Heat Exchanger Network  1013 The log mean temperature difference is:

∆TLMTD =

Hot stream:

∑(q

h i ) , (kW/kW/m2.oC) = m2.oC

i

k

∑(q

Cold stream:

(∆TH − ∆TC ) = (39.5 − 20) / ln(39.5 / 20)° C = 28.65° C ln ( ∆TH ∆TC )

∑(q

j

h j)

hi) = k

− 200) = 5850(m .° C) ∑(CP∆T h ) = 0.15(239 0.001 i

2

i

1

k

∑(q



i

j

h j) = k

∑(CP∆T

j

hj ) = 1

0.3(199.5 − 180) = 7312.5(m 2 .° C) 0.0008

Enthalpy interval 4 Hot stream 150°C

200°C

∆TC = (Th2 – Tc1)

∆TH = (Th1 – Tc2)

= 150 – 140.0 = 10°C 140.0°C

= 200 – 180.0 = 20°C 180.0°C Cold stream

The log mean temperature difference is:

Hot stream:



∆TLMTD =

∑(q

∑(q

Cold stream:



(∆TH − ∆TC ) = (20 − 10) / ln(20 /10) = 14.43° C ln ( ∆TH ∆TC )

i

h i ) , (kW/kW/m2.oC) = m2.oC

i

hi) =

k

k

∑(q

∑(q

j

j

h j)

− 150) 0.25(200 − 150) + = 23,125(m .° C) ∑(CP∆T h ) = 0.15(200 0.001 0.0008 i

i

2

1

k

h j) = k

∑(CP∆T

j

hj ) = 1

0.2(180 − 140) 0.3(180 − 140) + = 28,333.3(m 2 .° C) 0.0006 0.0008

Enthalpy interval 5 Hot stream 150°C

95.0°C

∆TH = (Th1 – Tc2)

∆TC = (Th2 – Tc1)

= 150 – 140.0 = 10°C 140.0°C

= 95 – 30.0 = 65°C 30.0°C Cold stream

1014  Chemical Processing Engineering The log mean temperature difference is:

Hot stream:



∆TLMTD =

∑(q

Cold stream:

h i ) , (kW/kW/m2.oC) = m2.oC

i

∑(q

(∆TC − ∆TH ) = (65 − 10) / ln(65 /10) = 29.38° C ln ( ∆TC ∆TH )

k

hi) =

i

k

∑(q

h j)

j

− 95) 0.25(150 − 95) + = 25,437.5(m .° C) ∑(CP∆T h ) = 0.15(150 0.001 0.0008 i

2

1

k

∑(q



i

h j) =

j

k

∑(CP∆T

j

hj ) = 1

0.2(140 − 30) = 36,666.7(m 2 .° C) 0.0006

Enthalpy interval 6 Hot stream 95.0°C

80°C

∆TH = (Th1 – Tc2)

∆TC = (Th2 – Tc1)

= 95 – 30.0 = 65°C 30.0°C

= 80 – 30.0 = 55°C 25.0°C Cold stream

The log mean temperature difference is:

∆TLMTD =

Hot stream:

∑(q

Cold stream:



h i ) , (kW/kW/m2.oC) = m2.°C

i

k

∑(q ∑(q

(∆TH − ∆TC ) = (65 − 55) / ln(65 / 55) = 59.86° C ln ( ∆TH ∆TC )

j

hi) =

i

k

h j)

∑(q

j

− 80) 0.25(95 − 80) + = 6937.5(m .° C) ∑(CP∆T h ) = 0.15(95 0.001 0.0008 i

i

2

1

k

h j) = k

∑(CP∆T

j

hj ) = 1

0.2(30 − 25) 1.0(30 − 25) + = 6666.7(m 2 .° C) 0.0006 0.001

Enthalpy interval 7 Hot stream 40°C

80°C

∆TC = (Th2 – Tc1)

∆TH = (Th1 – Tc2)

= 40 – 20.0 = 20°C 20.0°C

= 80 – 30.0 = 55°C 25.0°C Cold stream

Process Integration and Heat Exchanger Network  1015 The log mean temperature difference is:

∆TLMTD =



Hot stream:

∑(q

h i ) , (kW/kW/m2.oC) = m2.oC

i

k

∑(q

Cold stream:

∑(q

j

h j)

∑(q



(∆TH − ∆TC ) = (55 − 20) / ln(55/20) = 34.6°C ln ( ∆TH ∆TC )

j

i

hi) = k

− 40) = 6000.0(m .° C) ∑(CP∆T h ) = 0.15(80 0.001 i

i

2

1

k

h j) = k

∑(CP∆T

j

hj ) = 1

0.2(25 − 20) 1.0(25 − 20) + = 6666.7(m 2 .° C) 0.0006 0.001

Table 9.16 shows the network area target at ΔTmin = 10°C is 7410 m2. Shenoy [18] provides detailed calculations of the area target for the network of 1-2 shell and tube heat exchangers as well as counter-current exchangers. For Example 9.5, the targets obtained using the procedure and software given by Shenoy are summarized as: Above Pinch + Below Pinch = Total 2706.94 + 4703.03 = 7409.97 (countercurrent area target) 3094.06 + 5795.63 = 8889.74 (1 – 2 shell and tube area target) 7 + 12 = 19 (number of shells target)

For a network of 1-2 exchangers, Equation 9.32 can be modified by introducing the FT correction factor for each enthalpy interval, which depends both on the assumed value of Xp, where Xp is a constant defined by the designer, and the temperatures of the interval on the composite curves. The overall area is [41]:

Table 9.16  Network area target for Example 9.5. Hot streams

Cold streams

Enthalpy interval

∆TLMTD

∑ (q

1

17.38

1500

1875

194.2

2

25.30

2650

9562.5

482.7

3

28.65

5850

7312.5

459.4

4

14.43

23,1250

28,333.3

3566.1

5

29.38

25,437.5

36,666.7

2113.8

6

59.86

6937.5

6666.7

227.3

7

34.60

6000.0

6666.7

366.1

∑A

Total

= 7409.6m 2 .

i

hi)

k

∑ (q

j

hj)

k

Ak =

1  TLMTD 

∑ (q

i

h i )k +

∑ (q

j

h j )k  

1016  Chemical Processing Engineering

Interval K

∑

A network ,1− 2 =

k



Cold stream, J   Hot stream, I x q i hi + q j hj  ∆TLMTDFT,k   j i  

∑

1

∑

(9.33)

A line of constant Xp is compared with a line of constant FT as shown in Figure 9.68, where the line of constant Xp avoids the regions of steep slope. Situations often occur where the FT is too low or the FT slope is too large. In such cases, either different types of shells or multiple shell arrangements as illustrate in Figure 9.69 must be considered.

1 Shell Pass - 2 Tube Passes

1.0 0.9 X

FT

p

0.8

0.3

0.4

0.5 P

0.6

R = 0.1

0.2

R = 0.5

0.1

R = 1.0

0

R = 2.0

0.6 0.5

.90

R = 10.0

0.7

=0

0.7

0.8

0.9

1.0

Figure 9.68  The XP parameter avoids steep slopes on the FT curves, whereas minimum FT does not. (Reprinted from Ahmad, Linnhoff and Smith, “Cost Optimum Heat Exchanger Networks: II Targets and Design for Detailed Capital Cost Models, Computer. Chem. Eng., 7: 751, 1990; Used by permission: R. Smith, Chemical Process Design, McGraw Hill, 1995.)

Temperature

Temperature

temperature cross large

Length

Enthalpy

(a) A single 1-2 shell is infeasible. Temperature

Temperature

temperature crosses smaller

Enthalpy

Length

(b) Putting shells in series reduces the temperature cross in individual exchangers.

Figure 9.69  A large overall temperature cross requires shells in series to reduce the cross in individual exchangers. (From Ahmad, Linnhoff, and Smith, Trans. ASME, J. Heat Transfer, 110: 304, 1988. Used by permission: R. Smith, Chemical Process Design, McGraw-Hill, 1995.)

Process Integration and Heat Exchanger Network  1017

Example 9.6 A hot stream is to be cooled from 300oC to 100oC by exchange with a cold stream heated from 60oC to 200oC in a single unit. 1-2 shell and tube exchangers are to be used subjected to Xp = 0.9. The duty of the exchanger is 3.5 MW and the overall heat transfer coefficient is estimated to be 100 W/m2 oC. Calculate the number of shells required and the heat transfer area.

Solution An Excel spreadsheet (Example 9.6.xlsx) has been developed to determine the FT-factor, and subsequently the logmean temperature difference, the corrected log mean temperature difference and the required number of shells required. The Excel spreadsheet calculations with the number of shells N = 3, shows FT is indeterminate, but another developed program shows FT = 0.8363, LMTD = 65.5 oC and CMTD = 56.6oC. The heat transfer area is:

A=



Q Q = U∆TLMTDFT UC MTD

3.5 × 106 = 619m 2 (100 × 56.55 ) Table 9.17 shows the results of the developed program and Excel spreadsheet calculations respectively. Table 9.17  Input data and computer results for the number of shells required of Example 9.6. DATA26.DAT 300.0

100.0

60.0

200.0

1 THE CORRECTED LMTD IN A SHELL AND TUBE HEAT EXCHANGER HOT FLUID INLET TEMPERATURE, oC:

300.000

HOT FLUID OUTLET TEMPERATURE, oC:

100.000

COLD FLUID INLET TEMPERATURE, oC:

60.000

COLD FLUID OUTLET TEMPERATURE, oC:

200.000

NUMBER OF SERIES EXCHANGER SHELLS:

1.0

THE PARAMETER P VALUE IS:

0.5833

THE PARAMETER R VALUE IS:

1.4286

THE NUMBER OF SHELLS REQUIRED

3.0

THE F-FACTOR:

0.8636

THE LOG MEAN TEMPERATURE DIFFERENCE, oC:

65.4814

The CORRECTED LMTD, oC:

56.5524

1018  Chemical Processing Engineering The Excel Spreadsheet (Example 9.6.xlsx) Results. RESULTS OF THE EXCEL SPREADSHEET CALCULATIONS OF EXAMPLE 9.6

THE CORRECTED LMTD IN A SHELL AND TUBE HEAT EXCHANGER

C

HOT FLUID INLET TEMPERATURE

300

o

HOT FLUID OUTLET TEMPERATURE

100

o

COLD FLUID INLET TEMPERATURE

60

o

COLD FLUID OUTLET TEMPERATURE

200

o

NUMBER OF SERIES EXCHANGER SHELLS

3

THE NUMBER OF SHELLS REQUIRED

3

THE F-FACTOR

#####

THE LOG MEAN TEMPERATURE DIFFERENCE

65.48

o

THE CORRECTED LOG MEAN TEMPERATURE DIFF.

#####

o

C C C

C C

HEN Simplification Cases often arise where the general results in HENs are rather complex with many units. There is scope to simplify minimum utility designs and reduce the number of units by transferring heat across the pinch and thus increasing the utility usage; correspondingly the number of capital items can thus be reduced. The simplification can be done in a more controlled and efficient manner from the standpoint concepts of heat load loops and heat load paths.

Heat Load Loops A heat load loop is a loop in the HEN around which duties can be shifted from one exchanger to another without affecting stream duties. Hohmann [31] was the first to observe and introduce the term heat load loop, and was later confirmed by Linnhoff et al. [13] to be generally true, based on Euler’s network theorem. Changing the duty on an exchanger may result in a violation of ΔTmin; however, the number of heat load loops is the difference between the actual number of units in the network and the minimum number of units calculated by Equation 9.24 (i.e., uHX, min = N-1) to the network as a whole, i.e., ignoring the pinch. We shall consider the data from Linnhoff and Hindmarsh [30], having two hot streams and two cold streams as shown in Table 9.18, referred to as Test Case 3 (TC3).

Table 9.18  Stream data for Example 9.7. Stream

Ts (oC)

Tt (oC)

mCp (kW/K)

Heat load (kW)*

H1

150

60

2.0

-180.

H2

90

60

8.0

-240

C1

20

125

2.5

262.5

C2

25

100

3.0

225.0

Process Integration and Heat Exchanger Network  1019

Example 9.7. Test Case 3, TC3 Linnhoff and Hindmarch [30] Using the data from Linnhoff and Hindmarch [30], TC3, determine the minimum utility requirements at ∆Tmin = 20oC and design a HEN for Test Case 3.

Solution The Excel spreadsheet software in A User Guide on Process Integration for the Efficient Use of Energy [21] is used to determine the following: a. C  onstruct the Problem Table. b. Determine the pinch problem, pinch temperature; hot and cold streams pinch temperatures, hot and cold utility requirements. c. Plot the composite curves and the grand composite curve. d. Estimate the maximum energy recovery at ∆Tmin = 20oC. e. Plots of the hot and cold pinch temperatures at varying ∆Tmin (i.e., minimum to maximum values) and of the minimum utility requirements for hot and cold streams at varying ∆Tmin (i.e., minimum to maximum values). The results show the following at ∆Tmin = 20oC from Excel spreadsheet (Example 9.7.xlsx) show the following: Type of pinch problem

= Single pinch problem

Pinch temperature

= 80oC

Hot stream pinch temperature

= 90oC

Cold stream pinch temperature

= 70oC

Minimum hot utility requirement

= 107.5kW

Minimum cold utility requirement

= 40kW

Maximum energy recovery

= 380kW

Figures 9.70 and 9.71 show the composite curves, the grand composite curve respectively, and Figure 9.72 from Excel spreadsheet (Example 9.7.xlsx) shows the screenshot of plots of temperature of hot and cold streams and utility requirements at varying ∆Tmin. Figures 9.73a, b and c show possible HEN of TC3, although Figure 9.73c has more units than Figures 9.73a or b. In trying to match the hot and cold streams respectively, the following inequalities should be noted:

CPHot ≤ CPCold   above the pinch.

(9.25)

and

CPHot ≥ CPCold   below the pinch.

(9.26)

These only apply at the pinch. Away from the pinch, temperature driving forces may have increased sufficiently to allow matches in which the CPs of the streams matched violate the inequalities. The CP difference criterion is [30] as follows: For a hot end pinch match:



CP difference = CPCold – CPHot

(9.34)

1020  Chemical Processing Engineering

Figure 9.70  Screenshot of the hot and cold composite curves for Example 9.7. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Figure 9.71  Screenshot of the grand composite curve for Example 9.7. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

For a cold end pinch match:



CP difference = CPHot – CPCold

Immediately above the pinch:



NCold

Overall CP difference =

∑ CP

Cold

1

(9.35)

NHot

−

∑CP

Hot

1



(9.36)

Process Integration and Heat Exchanger Network  1021

Figure 9.72  Screenshot of plots of pinch temperature of hot and cold streams and minimum utility requirements at varying ∆Tmin (i.e minimum to maximum values) for Example 9.7. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, - A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.) Stream No. 1

CPHot ≤ CPCold

CPHot ≥ CPCold

Tph = 90ºC 1

150ºC

4

80ºC

CP(kW/ºC) ∆H(kW)

C

60ºC 2

180

60ºC 8

240

20ºC 2.5

262.5

25ºC 3

225.0

40 kW CP= 4.5

2

Tph = 90ºC

2

3

CP= 3.5 3 125ºC

17.5 kW 118ºC H

1

120 kW 4 100ºC

H

90 kW

3

Tpc = 70ºC

28ºC 4

105 kW 20 kW 2

Tpc = 70ºC 135 kW

H Hot utility C Cold utility

Heat exchange between streams

Figure 9.73a  A grid representation of the heat exchanger network for Example 9.7.

Immediately below the pinch:



NHot

Overall CP difference =

∑ 1

NCold

CPHot −

∑ CP

Hot



(9.37)

1

The third feasibility condition states that the CP difference for any exchanger operating at the pinch must not exceed the overall CP difference. Where one exchanger has a CP difference greater than the total, then another must have a negative CP difference that violates the CP inequality. Table 9.19 shows the CP table for the hot end of TC3. By inspection, the number of hot streams is less than the number of cold streams, and the CP inequality is satisfied for each of the possible matches. The overall CP difference is from the total (5.5 – 2.0) = 3.5. The individual CP difference for the two possible matches is:

1022  Chemical Processing Engineering Stream No.

CPHot ≤ CPCold 150ºC

1

CPHot ≥ CPCold

Tph = 90ºC 1

4

80ºC

CP(kW/ºC)

C

60ºC 2

180

60ºC 8

240

40 kW CP = 3.5

2

Tph = 90ºC

3

∆H(kW)

2

CP=4.5 3

4

125ºC

17.5 kW 118ºC

28ºC

H

1

Tpc = 70ºC

120 kW

100ºC

3

20ºC

4

262.5

3

225.0

25ºC

2

H

2.5

105 kW 20 kW

Tpc = 70ºC 135 kW

90 kW

H Hot utility C Cold utility

Heat exchange between streams

Figure 9.73b  A grid representation of the heat exchanger network for Example 9.7.

Stream No. 1

CPHot ≤ CPCold 135ºC

2

150ºC

Tph = 90ºC CP = 3 107.5 kW 125ºC

H

82ºC

80ºC

CP(kW/ºC)

C

15 kW 3

C

100ºC

4

Tpc = 70ºC 1

90 kW

2

180

60ºC

8

240

20ºC

2.5

262.5

25ºC

3

225.0

4

34ºC

2

5

90 kW 35 kW 3

Tpc = 70ºC 135 kW

H Hot utility C Cold utility

Figure 9.73c  A grid representation of the heat exchanger network for Example 9.7.

Table 9.19  The CP table for the hot end of TC3 for Example 9.7. CPHot ≥ CPCold

NHot ≥ NCold

Stream number

Hot

Cold

Stream number

1

2

3

4

2.5

3

Total

2

∆H(kW)

60ºC

25 kW CP= 5

30 kW 4

5

1

2

3

CPHot ≥ CPCold

Tph = 90ºC

5.5

Heat exchange between streams

Process Integration and Heat Exchanger Network  1023 Stream 1 and stream 4: CP difference = 3 – 2 =1 Stream 1 and stream 3: CP difference = 2.5 – 2 = 0.5. Since both of these values are less than the overall CP difference, both satisfy all of the feasibility criteria. Table 9.20 shows the CP table for the cold end of TC3. It can be seen that hot stream 1 cannot be matched with either cold stream due to violation of the CP inequality. Hot stream 2 can be matched with either cold stream without violating the CP inequality, but the CP differences are 5 and 5.5 respectively for these matches while the overall CP difference is 4.5. Thus, neither of these matches is feasible. For feasible matches, stream splitting is required. If one of the cold streams is split to allow a match with stream 1, it will result in NCold ≥ NHot, thus requiring the split of a hot stream as well. Alternatively, hot stream 2 can be split to allow a match with either cold stream. Figures 9.73a and b show two possible splittings of hot stream 2. Figure 9.73a and b show seven units of HENs, whereas the minimum number is five. Hence, there are two loops shown in these figures, and formed by the two exchangers operating between streams 1 and 3. Both loops cross the pinch, therefore to simplify the HEN; consider first the loop formed by the exchangers operating between streams 1 and 4 in Figure 9.73a. The 20kW exchanger is eliminated by shifting it to the 120kW exchanger thus increasing its duty to 140 kW. The resulting HEN is shown in Figure 9.74. The heat balance calculation of the new load of 140kW shows that temperature on the cold end is 18oC (< ∆Tmin = 20oC), which is a violation of ∆Tmin (see Figure 9.75 for calculations), although there is no change in the utility consumption. Therefore, using heat load loop to transfer the 20kW across the pinch results in a violation of ∆Tmin, but no increase in utility use. Similarly, by eliminating the small 17.5 kW heater on stream 3 (on the second loop) and adding to the 105kW load on the cold side, this becomes Table 9.20  The CP table for the cold end of TC3 for Example 9.7. CPHot ≥ CPCold

Stream No. 1

NHot ≥ NCold

Stream number

Hot

Cold

Stream number

2

8

3.0

4

1

2

2.5

3

Total

10

5.5

CPHot ≤ CPCold

150ºC

1

CPHot ≥ CPCold

Tph = 90ºC

80ºC

80ºC

C

CP(kW/ºC) ∆H(kW) 60ºC

2

180

60ºC

8

240

20ºC

2.5

262.5

25ºC

3

225.0

40 kW CP= 4.5

2

Tph = 90ºC

2

3

CP= 3.5 3 125ºC

17.5 kW 118ºC H

1

140 kW 4

100ºC

H

90 kW

62ºC

3

Tpc = 70ºC

28ºC

105 kW 2

Tpc = 70ºC 135 kW

H Hot utility C Cold utility

Figure 9.74  Breaking the loop of the heat exchanger network for Example 9.7.

Heat exchange between streams

1024  Chemical Processing Engineering CP kW/ºC 80ºC

150ºC

118ºC 125ºC

H

62ºC

Tph = 90ºC

Tpc = 70ºC

CP kW/ºC

2

90ºC

60ºC

3.5

2.5

69ºC

20ºC

2.5

140 kW ∆H = CP ∆T In hot stream 1, 140 = 2 (150 -T) 70 = 150 -T T = 80ºC In cold stream 1, before breaking 120 = 2.5 (T – 70) the loop : 48 = T - 70 T = 118ºC

122.5 kW Assuming counter current f low through the heat exchanger

150ºC ∆T1 = 32ºC 118ºC

Breaking the loop by adding 20 kW to 120kW in the cold stream gives: 140 kW

80ºC ∆T2 = 18ºC 62ºC The temperature difference on the cold end is 18ºC < ∆Tmin (20ºC), which is a violation of ∆Tmin

Assuming counter current f low through the heat exchanger

Removing the 17.5 kW heating utility in the 90ºC cold stream above the ∆T1 = 11ºC pinch, and adding to 105 kW below the pinch 69ºC gives 122.5 kW ∆H = CP ∆T 122.5 = 2.5 (T – 20) 49 = T - 20 T = 69ºC

60ºC ∆T2 = 40ºC 20ºC

The temperature difference on the cold end is 11ºC < ∆Tmin (20ºC), which is a violation of ∆Tmin

140 = 2.5 (118 – T) 56 = 118 - T T= 62ºC

Figure 9.75  Calculations of the temperature differences resulting from the breaking of the loop for Example 9.7.

122.5 kW. The temperature difference between stream 2 (from the stream splitting of CP =8.0) and stream 3 is 11oC (see Figure 9.75 for calculations), which is again a violation of ∆Tmin = 20oC. An important feature of every loop is that heat loads can be shifted around it, which always maintains the correct stream heat loads, but the exchanger duties are altered, and this may cause a violation of ∆Tmin. The driven forces are often restored using heat load paths.

Heat Load Paths A heat load path is a continuous connection in the network between a heater, one or more heat exchangers and a cooler. Load shifts along paths follow equivalent rules to load shifts around a loop. This procedure has no effect on stream duties, but intermediate stream temperatures will change due to the change in exchanger duties. Therefore, a heat load path can be used to eliminate a ∆Tmin violation incurred during network simplification. Consider the 140kW exchanger in Figure 9.76, where there is an 18oC driving force on the cold end. However, to restore this value to 20oC, the exit temperature of stream 1 can be increased from 80oC to 82oC. Since the CP of stream 1 is 2 kW/oC, the exchanger duty must be reduced by 4kW to 136kW. The exchanger forms a path of a heat load path from the heater on stream 3 to the cooler on stream 1. The result of a HEN is by adding 4kW to the heater duty on stream 3, and 4kW to the cooler duty on stream 1 (see Figure 9.76). The HEN modification is that a 20kW exchanger has been eliminated from the network without violating the ∆Tmin on the remaining exchanger. The hot and cold utilities have subsequently increased by 4kW. In summary, the procedure for reducing units at minimum energy sacrifice is: • • • • •

Identify a loop (across the path), if one exists. Break it by subtracting and adding loads. Recalculate network temperatures and identify the ΔTmin violations. Find a relaxation path and formulate T = f(X). Restore ΔTmin.

The procedure can then be repeated for other loops and paths to give a range of options with different numbers of units and energy usage.

Process Integration and Heat Exchanger Network  1025 Stream No. 1

CPHot ≤ CPCold 1

150ºC

80ºC

Tph = 90ºC

CPHot ≥ CPCold Path 80ºC

CP(kW/ºC) C

∆H (kW)

60ºC

2

180

60ºC

8

240

20ºC

2.5

262.5

25ºC

3

225.0

(40+X) kW CP= 4.5 2

2

Tph = 90ºC

3

CP = 3.5 118ºC 3 125ºC

4 100ºC

62ºC

H

1

(17.5+X) kW

(140-X) kW

Tpc = 70ºC

28ºC 3 105 kW

2 Tpc = 70ºC 135 kW

H 90 kW X =4

H Hot utility C Cold utility

Heat exchange between streams

Figure 9.76  Identifying a path to restore the ΔTmin constraint for Example 9.7.

Number of Shells Target Multiple shells in series are required when a single shell does not provide a significantly high value of FT ≥ 0.75 [42] or the slope of FT (R, P) is too steep. In establishing the shell targets, start by dividing the composite curves into vertical enthalpy intervals as with the area target algorithm. It is always possible to design a network for the enthalpy interval with Sk – 1 matches, with each match having the same temperature profile as the enthalpy interval. If such a design is established within an interval, then the number of shells for each match in interval k will be the same. If each match in enthalpy interval k requires NSHELLS,k, then the number of shells using the temperatures interval k can be determined. The minimum shell count for the interval is:

NSHELLS, k (Sk – 1)

(9.38)

where



R=

CPc Th1 − Th2 t −t and P = c2 c1 = CPh t c2 − t c1 Th1 − t c1

(9.39)

FT depends on the inlet and outlet temperatures of the streams in a 1-2 exchanger. Figure 9.77 illustrates three situations that can be encountered, when using 1-2 exchangers. 1. F  igure 9.77a shows that the final temperature of the hot stream is higher than the final temperature of the cold stream. A temperature approach is observed, and can thus be accommodated in a single 1-2 shell exchanger. 2. Figure 9.77b indicates that the final temperature of the hot stream is slightly lower than the final temperature of the cold stream, where temperatures cross is observed. However, provided the temperature cross is small; this situation can be accommodated in a single shell. The decrease in FT significantly increases the heat transfer area requirements. 3. However, as the amount of temperature increases in Figure 9.77c, the logarithmic mean temperature difference (LMTD) correction factor, FT rapidly decreases, causing an increase in the heat transfer area requirements and thus indicating the need for multiple shell passes. The most common way of achieving multiple shell passes is by connecting E-shells in series, making these units relatively expensive compared to 1-2 or counter-flow exchangers that comprise a single shell. Furthermore, problems may

1026  Chemical Processing Engineering Temperature

(a)

Temperature approach

Enthalpy Temperature

(b)

Temperature cross

Enthalpy Temperature

(c)

Temperature cross

Enthalpy 1 Shell Pass - 2 Tube Passes

1.0 0.9 FT 0.75

feasible

0.8

feasible R = 0.1

R = 0.5

0.6

R = 1.0

R = 2.0

R = 10.0

0.7

infeasible

0.5 0

0.1

0.2

0.3

0.4

0.5

0.6 P

0.7

0.8

0.9

1.0

Figure 9.77  Designs with a temperature approach or small temperature cross can be accommodated in a single 1-2 shell, whereas designs with a large temperature cross becomes infeasible. (Ahmad, Linnhoff and Smith, Trans. ASME. J. Heat Transfer, 110: 304, 1988, Used by permission: R. Smith, Chemical Process Design, McGraw-Hill, 1995.)

occur where there is a local reversal of heat flow, which is wasteful in heat transfer area. In such cases, the design may become infeasible. If heat exchangers are counter-current devices, then the number of units equals the number of shells, providing individual shells do not exceed a certain upper size limit. If equipment used is not completely counter-current, as with 1-2 shell and tube heat exchanger, then:

NShells ≥ Nunits

(9.40)

Since the number of shells influences the capital cost, it is often useful to predict it as a target ahead of design. An algorithm has been developed to target the minimum total number of shells for a stream set based on the temperature distribution of the composite curves. The algorithm starts by dividing the composite curves into enthalpy intervals as in the case of the area target algorithm. The resulting number of shells is [43].

Process Integration and Heat Exchanger Network  1027

Intervals K

NShells =

∑

NSHELLS,k (SK − 1)

(9.41)

k

where NShells NSHELLS,k Sk K

= total number of shells over k enthalpy intervals = real (or fractional) number of shells resulting from temperatures of enthalpy interval k. = number of streams in enthalpy interval k. = Total number of enthalpy intervals on the composite curves.

Implications for HEN Design Temperature crosses present problems for U-tube exchangers and other types with multiple tube passes. For these matches that are near the pinch, it is best to use multiple shells or counter-current exchangers. If the shell side fluid is boiling or condensing at constant temperature, the U-tube unit is at no disadvantage as which fluid should be on the tube side and which on the shell side in a match. The following preferences may be applied [21]. • Put a condensing or boiling stream on the shell side (easier flows and better temperature differences). • Put the fluid with the lower temperature change (or higher CP) on the shell side (tends to give better temperature differences). • Put corrosive fluids on the tube side; it is cheaper to make tubes from exotic alloys than shells, and easier to repair than a shell if corrosion does occur. • Streams whose pressure drop must be minimized should go on the shell side (∆P through the exchanger is much lower). • In fixed tube plate units, heavily fouling fluids should go on the tube side; in U-tube units, they should go on the shell side. • Putting the hot fluid on the tube side minimizes structural heat losses. Floudas et al. [46] and Ciric and Floudas [47] discuss automatic synthesis of optimum HEN configurations and decomposition respectively.

Capital Cost Targets Generally, the purpose of synthesizing a counter-current HEN is to match hot and cold process streams in such a way that the expense for heating cold streams and cooling hot streams is reduced. The objective of the HEN synthesis is to develop a network of counter-current heat exchangers that minimizes capital investment and operational costs. It leads to the optimization of ΔTmin, which offers a trade-off between the capital costs and the energy costs. At an optimum ΔTmin, the total annual cost (TAC) of the HEN is minimized. The TAC of a HEN for a given ΔTmin is determined by targeting. The cost targeting is divided into two parts: a. C  apital cost targeting b. Operational cost targeting. The cost of a network is the sum of the capital cost (CC) and operating cost (OC). The operating cost is dependent on the energy requirements and is [18].

1028  Chemical Processing Engineering

Operating Cost (OC) = (Chu . QHmin) + (Ccu . QCmin)



(9.42)

where Chu = cost of unit load of hot utility. Ccu = cost of unit load of cold utility. QHmin = minimum hot utility requirement. QCmin = minimum cold utility requirement.

Capital Cost To predict the capital cost of a network, if A is the surface area, then a simple cost law typically used is: Installed capital cost of exchanger



(CC) = a + bAc

(9.43)

where a, b and c are the cost law coefficients which depend on the material of construction, the pressure rating and type of exchanger. When establishing capital cost targets for a network, the area distribution among the individual exchangers comprising the network is unknown. Therefore, to cost a network, using Equation 9.43 some area distribution must be assumed, the simplest being that all exchangers have the same area [18].

Network Capital Cost (CC)

CC = N[a+b(ANetwork/N)c]

(9.44)

For a network of counter-current exchangers:



CC = aN + bSmin (A12/Smin)c

(9.45)

for a network of 1-2 shell and tube exchangers. where N = minimum number of units in a MER network. ANetwork and A12 = appropriate area targets. = minimum number of shell target. Smin

Total Cost Targeting The cost is involved at two places in any heat exchanger network synthesis problem: • Capital cost of the heat exchangers, heaters and coolers • Utility costs. These two costs vary in opposite to each other as the driving force ΔTmin changes. For example, an increase in ΔTmin results in an increase in utility costs as the utility consumption increases. However, the capital cost decreases as the area of the heat exchanger network reduces. Therefore, it is better to consider both the costs during targeting a HEN and for further determination of optimum ΔTmin using Supertargeting. Capital cost (fixed cost) and operating cost (utility cost) are expressed in different time scales. For example, the capital cost is expressed for the operating useful life period of the exchanger whereas the operating cost is generally

Process Integration and Heat Exchanger Network  1029 Table 9.21  Cost data for various exchanger specifications [18]. Exchanger specification

Capital cost ($)

Identifier

Spiral (SS-SS)

30000 + 19700A0.59

HX1

Plate & frame (SS-SS)

30000 + 1900A0.78

HX2

Shell & tube (CS-CS)

30000 + 750A0.81

HX3

Shell & tube (SS-SS)

30000 + 1650A0.81

HX4

Shell & tube (CS-SS)

30000 + 1350A0.81

HX5

Note: A is exchanger area, m , SS is stainless steel and CS is carbon steel. 2

expressed on a per annum basis. Therefore, it is essential to determine a common time scale for these two costs. This is done by determining the annualized capital cost (i.e., expressing the capital cost on a per annum basis) before it is added to the operating cost in order to make the time scale consistent. Since the energy cost is a recurring expense whereas the capital cost is a one-time investment, the expected life of the plant has to be considered while calculating the annual cost. The total annual cost (TAC) is: Total Annual Cost (TAC) = Annualized capital cost + Annual utility cost That is,

TAC = OC + CC . Af



(9.46)

where Af is the annualized factor defined by:

Af =



i(1 + i)n (1 + i)n − 1

(9.47)

where i  = fractional interest rate per year. n = number of years. Shenoy [18] provides cost data for various heat exchanger specifications, as shown in Table 9.21. Examples for determining the total annual cost target for counter-current flow heat exchangers are given by Shenoy [18], Smith [20] and Ahmad, S. et al. [44].

Energy Targeting Heat exchanger network synthesis (HENS) involves computation of a cost-effective network that exchanges heat among a set of process streams, where any heating and cooling not satisfied by exchange among these streams must be provided by external utilities (e.g., steam, hot oil, cooling water, refrigerants, etc.). Other constraints such as safety, controllability, plant layout, flexibility, operability, and so on should also be in the mind of the engineer/ designer. MER implies use of the minimum amount of utilities. If QHmin is the heat supplied by hot utility and QCmin is heat removed by cold utility, then determination of energy targets involves the values of QHmin and QCmin respectively subject to thermodynamic constraints.

1030  Chemical Processing Engineering

Supertargeting or ∆Tmin Optimization The energy targeting is dependent on the minimum approach temperature ∆Tmin in order to provide a minimum driving force for heat transfer and Tables 9.5, 9.6 and 9.7 show values of ∆Tmin for different processes. The aim is to design a cost-effective heat exchanger network. The network should feature minimum utility requirements, minimum area and minimum number of units/shells. However, there are trades-offs among these features, which often require optimization, where the total cost of a network is the sum of the operating cost and the capital cost (Equation 9.46), both of which are dependent on ∆Tmin. The higher the value of ∆Tmin, the higher are the energy requirements (i.e. QHmin and QCmin), resulting in increased operating costs. Similarly, with increased ∆Tmin gives lower area requirements and consequently lower capital costs. As ∆Tmin decreases from its maximum value, the extent of heat recovery increases while the amount and cost of utility usage decreases. At the same time, the surface area required for process heat exchangers increases, due to greater total heat duty and smaller average driving force for heat transfer. There will be an optimum value of ∆Tmin for which the total annual cost is a minimum. Therefore, for any HEN problem, there is an optimal value of ∆Tmin that minimizes the total cost. The procedure for estimating this optimum is referred to as supertargeting. Linnhoff and Ahmad [33] coined the term “Supertargeting” where the process of pre-design optimization of ∆Tmin is based on the total cost with no specified piece of equipment. In supertargeting, the optimization is performed on the basis of operating and capital cost targets together, as this is in contrast to the conventional HEN design at an arbitrary value of ∆Tmin, that may not guarantee cost optimality. Therefore, supertargeting ensures that an initial design at an optimal ∆Tmin requires minimal computation and saves considerable effort in post-design optimization.

Example 9.8. HEN for Maximum Energy Recovery (Warren D. Seider et al. [26]) Design a heat exchanger network for maximum energy recovery with not more than 15 heat exchangers (including utility heaters) and ∆Tmin = 10oC for the streams in Table 9.22.

Solution The Excel spreadsheet software in A User Guide on Process Integration for the Efficient Use of Energy [21] is used to determine the following steps: Table 9.22  Stream data for Example 9.8. Stream

Feed temp. (oC)

Target temp. (oC)

Cp, kW/oC

∆H, kW

H1

140

50

10

900

H2

320

20

9

2700

H3

370

20

8

2800

C1

50

130

10

800

C2

130

430

8

2400

C3

100

300

6

1200

C4

30

230

5

1000

C5

30

130

4

400

C6

30

430

1

400

ΔH = CP . ΔT.

Process Integration and Heat Exchanger Network  1031 a. C  onstruct the Problem Table. b. Determine the pinch problem, pinch temperature; hot and cold streams pinch temperatures, hot and cold utility requirements. c. Plot the composite curves and the grand composite curve. d. Estimate the maximum energy recovery at ∆Tmin = 10oC. e. Plots of the hot and cold pinch temperatures at varying ∆Tmin (i.e. minimum to maximum values) and of the minimum utility requirements for hot and cold streams at varying ∆Tmin (i.e., minimum to maximum values) (see Excel spreadsheet, Examples 9.8.xlsx). The results show the following at ∆Tmin = 10oC: Type of pinch problem

= Single pinch problem

Pinch temperature

= 135oC

Hot stream pinch temperature

= 140 oC

Cold stream pinch temperature

= 130oC

Minimum hot utility requirement

= 960kW

Minimum cold utility requirement

= 760kW

Maximum energy recovery

= 5440kW

Figure 9.78 shows a grid representation of the heat exchanger network, and Figure 9.79 shows HEN design that meets MER targets. The total number of heat exchangers including the utilities = 13.

CPHot ≤ CPCold NHot ≤ NCold CP= 2.777 320ºC H2

Design away from the pinch

Tph = 140ºC ∆H=900 kW 5 H1 CP = 5

4

CP=5.66

3

1

∆H=1080 kW CP= 4 7 ∆H=960 kW CP= 7 CP= 1 ∆H=800 kW

8

9

300ºC

H

900 2700

8

2800

10

800

8

2400

C3

6

1200

C4

5

1000

30ºC C5

4

400

1

400

20ºC C 680 kW 40ºC 50ºC C1

800 kW

360ºC

560 kW

∆H(kW)

10 9

114.28ºC 105ºC

5

430ºC

CP (kW/ºC)

60ºC C 50ºC 40ºC 100 kW C 20ºC 180 kW

6

2

CP= 0.555 370ºC H3

CPHot ≥ CPCold NHot ≥ NCold

1

3

C2

1840 kW ∆H=180 kW

100ºC

8

1020 kW

180 kW Tpc = 130ºC

230ºC

430ºC

∆H=500 kW

∆H=500 kW 4

H

230ºC

200 kW QHmin = 760 kW

30ºC

6

500 kW

500 kW ∆H=400 kW 2

100 kW

7

∆H=100 kW 400 kW Tpc = 130ºC

9

100 kW

QCmin =960 kW

30ºC

C6

H Hot utility C Cold utility

Heat exchange between streams

CP = Heat capacity f low rate N =Number of streams

Figure 9.78  A grid representation of heat exchanger network for Example 9.8.

1032  Chemical Processing Engineering CP= 2.777 320ºC H2

H3

44

H1

CP=5.66

3

140ºC 5 CP= 5

2

CP= 0.555 370ºC

430ºC 300ºC

130ºC 1

H

560 kW

9

∆H=500 kW

230ºC

8

2800

10

800

8

2400

C3

6

1200

C4

5

1000

C5

4

400

C6

1

400

100ºC

8

4

H

20ºC C 680 kW 50ºC C1

180 kW

30ºC

6

500 kW

200 kW

900 2700

C2

500 kW 130ºC

430ºC

10 9

C

800 kW

1020 kW

230ºC

40ºC

1840 kW

3

50ºC 20ºC

C

114.28ºC 105ºC

8

CP= 7 130ºC CP= 1

5

360ºC

∆H (kW)

180 kW

7

CP= 4 1

40ºC

6

CP (kW/ºC)

100 kW

60ºC

30ºC

7

400 kW 2

9

100 kW

100 kW

QHmin =760 kW

30ºC

QCmin = 960 kW

H

Hot utility

C

Cold utility

Heat exchange between streams

CP= Heat capacity f low rate N =Number of streams

Figure 9.79  HEN design that meets MER targets for Example 9.8.

Summary: New Heat Exchanger Network Design We can summarize the steps being followed in network design for a grass roots project as: a. Develop a minimum energy requirement (MER) network. • • • • • • • •

Divide the problem at the pinch. Start at the pinch and move away. Start with biggest stream ‘IN’ Observe CPOUT > CPIN, splitting streams where necessary. Place all pinch matches first. Maximize loads on all pinch matches to minimize number of units (the tick-off rules). Fill in the rest. Merge above and below the pinch designs.

b. Evolve the MER network for network simplicity and capital energy trade-off • Exploit heat load loops and heat load paths. • Optimize network performance using advanced tools in SuperTarget Process. Retrofit design can be carried out using one of the following three methods. 1. P  inch design method with maximum reuse of existing exchangers. 2. Correction of cross-pinch exchangers. 3. Analysis of exchanger paths. Figure 9.80 shows a flow chart indicating which retrofit method is most suitable for a project.

Process Integration and Heat Exchanger Network  1033 Retrof it project with large scope for savings

Is the current heat integration signif icant?

Yes

No

Pinch Design Method

Are composite curves parallel with little use of intermediate utilities?

Re-use existing exchangers

No

Cross-Pinch Analysis

Yes

Path Analysis

Figure 9.80  Hierarchy of retrofit design.

Targeting and Design for Constrained Matches Process Constraints Generally, any hot stream could in principle be matched with any cold stream, providing there is feasible temperature difference between the streams. There are instances where practical constraints may prevent the matching, for example where the two streams are matched by a heat exchanger, which later develops a leak resulting in contact between the two streams; a hazardous situation can result in violation of safety or hygiene. In such a case, a constraint would be imposed to prevent the two streams being matched. Another constraint may be due to location, where the plant layout may prevent matches between the front end and back end of a process, or uncontrollable inoperable process disturbances may occur (e.g., during start up and shut down situations) when matches are made. Often common reason of imposing constraints may be due to areas of integrity. Here, a process is designed to have identifiable sections or areas, e.g., reaction area and separation area of the process. These areas are kept separate for reasons such as start-up, shutdown, operational flexibility, safety and so on. They are generally made operationally independent through the use of intermediate storage of process materials between the areas. Such independent areas are generally described as areas of integrity and impose constraints on the ability to transfer heat. In order to maintain operational independence, the two areas cannot be dependent on each other for heating and cooling by recovery as illustrated by Ahmad and Hui [37].

Targeting for Constraints When the above situations arise, a constraint on a heat exchange system exists. Such constraints often lead to an increased energy target compared to unconstrained situations. Such an increase in energy target is referred to as an energy penalty, where engineers often find it useful to quantify the energy penalty for disallowing the heat exchange

1034  Chemical Processing Engineering between certain streams. Sometimes, the magnitude of such energy penalties and their associated utility cost penalty cause the original design constraints to be relaxed. Cerda et al. [45] introduced procedures based on either linear programming or thermodynamic algorithms for predicting the minimum energy targets in the presence of constraints. After targeting, the engineer can proceed to use a systematic network design procedure to observe the constraints and approach the targets. This procedure first places the matches which exhibit the energy penalty and then remaining matches on either side of the pinch.

Heat Engines and Heat Pumps for Optimum Integration Chemical processes and their associated sites require not only heat but power. This power may be used to drive electric motors, compressors, pumps, lighting, instruments or visual displays. Most sites pay to import this power in the form of electricity from an external supply, but the power itself must ultimately be generated. Some countries produce a significant proportion by hydroelectric or using other renewable sources or by nuclear power, but in most cases, the vast majority of power is generated from heat engines. A heat engine is a device for converting heat into power. High temperature heat is provided by burning coal, natural gas or other fossil fuels or combustible materials. In most power stations, the heat is used to evaporate water to make high pressure steam. This steam is then passed into a turbine and exerts a force on the blade to rotate the turbine and produce shaft power. The exhaust steam emerges at low pressure, where it is condensed and cold water is recycled to the boilers to be reused. Latent heat of condensation of steam is thus wasted. As a result, the thermal efficiency of these processes (power produced divided by heat supplied from fuel) is about 40%. Other types of heat engines e.g., the internal combustion engine burns diesel oil, petrol (gasoline) or natural gas, producing power and releasing heat in the exhaust gases and in the water required to cool the cylinders. In the gas turbine, fuel is burned in a stream of compressed air to produce hot gas at a high pressure, which is passed through a turbine and produces power and emerges as hot gas at low pressure and about 500oC. This process is also about 40% efficient or less in producing power. This low efficiency of heat engines means that a substantial amount of heat is produced and wasted. The question that arises is why not use a heat engine at the site to produce power and simultaneously use the heat it rejects as hot utility on the processes, thereby giving a much more efficient system? The concept of combined heat and power system (CHP) thus arises, which must be designed to ensure that any heat produced is at a useful level. Ways then need to be found to use the CHP system to supply heat at the temperatures that are required on the site. Another system that links heat and power needs are heat pumps. These generally work as a reversed heat engine, using a power input to upgrade heat from a low temperature to a higher one. Heat pumps include vapor recompression systems. Heat engines apply a working fluid that absorbs the heat from a source that generates the work while passing through mechanical devices, and rejects the waste heat to a sink. Therefore, proper placement ensures that the work generating efficiency is 100%, but maximizing the amount of work that can be extracted at 100% efficiency requires minimizing the driving force losses between the engine working fluid and the process. Applying thermodynamics, the temperature-enthalpy diagram can be employed by matching the heat-absorbing and heat rejecting profiles of the engine with the source and sink profiles of the process. A heat pump is a device that increases the temperature of a waste heat source to a temperature at which the waste heat becomes useful. The waste heat can thus replace purchased energy and reduce energy costs. The increase in temperature also requires cost, as it requires an external mechanical or thermal energy source. Therefore, the aim is to design a system where the benefits of using the heat-pumped waste heat exceed the cost of driving the heat pumps. There are various types of heat pumps, of which some require external mechanical work, and others require external thermal energy.

Principle of Operation Heat pumps use waste heat that would otherwise be rejected to the environment, thereby increasing the air temperature to a more useful level. They operate on a thermodynamic principle known as the Carnot cycle. Figure 9.81 is a

Process Integration and Heat Exchanger Network  1035 Temperature (T1)

Reservoir Heat

Heat

Q1

Heat engine

Work

W

Q1

Heat pump

Temperature (T2) Heat

Q2

Heat Q2 Reservoir

Figure 9.81  Thermodynamic basis of heat engines and heat pumps.

schematic heat engine and heat pump. A heat engine is a device which accepts heat Q1 from a source at temperature T1, rejects heat Q2 to a sink at a lower temperature T2 and generates work W. From thermodynamics,



W = Q1 – Q2  first law.

(9.58)



W ≤ ηc   second law Q1

(9.59)

and



ηc = 1 −

T2   Carnot efficiency T1

(9.60)

However, since real heat engines are irreversible, the equation introducing machine efficiency ηe for the heat engine may be written as:



W = ηe ηc Q1  0 ≤ ηe < 1

(9.61)

A heat pump is a heat engine that operates in reverse, that is, it accepts heat Q2 from the sink at temperature T2, rejects heat Q1 into the source (i.e., higher temperature) at T1, and consumes work W. From thermodynamics:



W = Q1 – Q2  first law.

(9.62)



W ≥ ηc   second law Q1

(9.63)

and

ηc = 1 −

T2 T1

(9.64)

1036  Chemical Processing Engineering For real irreversible heat pumps:

W = ηc Q1 ηe =



Q1   0 ≤ ηe 0 indicates that there are enough manipulated variables in the HEN and you can implement more sophisticated control structures. The number of degrees of freedom is calculated using the following equation NDoF = NMW - NTS Direct heat exchange: Heat exchanged between two streams in the same time interval of a batch process. Direct contact heat transfer: Heat exchanged by two streams which mix directly (e.g., steam injection). Energy relaxation: Process of reducing energy recovery in a heat exchanger network for the purpose of design simplification. Energy targets heating: The minimum hot utility load required for the process streams in the HEN to achieve their final values, after the energy available in the hot process streams have been transferred to cold process streams. Cooling: the minimum cold utility load required for the process streams in the HEN to achieve their final values, after the energy available in the hot process streams have been transferred to cold process streams. Extracted streams or extracted process: A set of streams removed from the process stream data to test them for appropriate placement. Feasible cascade: Heat cascade in which net heat flow never becomes negative and is zero at the pinch. Flowing stream: A stream which receives or releases heat as it flows through a heat exchanger. Gantt chart: A representation of which streams exist in given time intervals of a batch process, also called a time event chart. Grand composite curve (GCC): Is a plot of shifted temperature vs. the cascaded heat between each temperature interval. It represents the difference between the heat available from the hot streams and the heat required by the cold streams, relative to the pinch, at a given shifted temperature. The GCC is a plot of the net heat flow against the shifted (interval) temperature, which is simply a graphical plot of the Problem Table (heat cascade). Grid: System of horizontal and vertical lines with nodes, for representing heat exchange networks. Heat cascade: A table of the net flow from high to low temperatures divided up into temperature intervals. Heat engine: System converting high-grade heat to lower-grade heat and producing power. Heat exchanger network (HEN): System of utility heaters and coolers and process interchangers. Heat pump: System upgrading heat from a lower to a higher temperature using power or high-grade heat. Heating: Minimum hot utility load required for the heat exchanger network. Heat storage: Heat recovery by taking heat out of one time interval in a batch or time-dependent process and supplying it to a later time interval. Hot stream: Process stream requiring cooling. Individual heat cascades: Heat cascades for a time interval considered in isolation from all other time intervals. Infeasibile cascade: Heat cascade with zero hot utility and some negative values of net heat flow. In-situ heating/cooling: A stream which is heated or cooled in a vessel over a period of time. Intermediate condenser: An additional condenser in a column working above the main condenser temperature. Interval temperature: Obsolete name for shifted temperature. Loop: System of connections in a heat exchanger network which form a closed pathway. That is, a set of connections that can be traced through a network that starts from one exchanger and returns to the same exchanger. A loop may

1084  Chemical Processing Engineering also pass through a utility. The existence of a loop implies that there is an extra exchanger in the network. If we break the loop, we can remove an exchanger. Maximum energy recovery (MER): Best possible energy recovery in a heat exchanger network for a given value of ΔTmin, also known as minimum energy requirement. Maximum heat exchanger (MHX): The maximum amount of heat which can be recovered by direct heat exchange in a batch process. Maximum heat recovery (MHR): The maximum amount of heat which can be recovered for a batch process at given process conditions by direct heat exchange and heat storage added together. Minimum approach temperature, ΔTmin: The closest temperature difference between the hot and cold composite curves. MHR or MHX network: A heat exchanger network achieving the MHR or MHX target. More in, more out: An off-target process requires more than the minimum external heating and therefore more than the minimum external cooling. Multiple utilities: Utility or utility system whose temperature or temperature range falls within the temperature range of the process stream data. Near-pinch: Point in a heat cascade where net heat flow is very small but increases at temperatures on either scale. Network optimization: Evolution of a heat exchanger network to give most convenient heat exchanger sizes, allowing for existing area. Network pinch: Point in heat exchanger network where temperature driving force is lowest. Number of units: Minimum total number of heat exchanger units for the heat exchanger network. Number of units targets total minimum: the minimum total number of units required for the HEN system. Minimum for MER: The minimum number of units required for the HEN system for MER design, the MER (Minimum energy requirement) design takes into account the pinch temperature. Operating cost index: Minimum operating cost, based on energy targets. Overall heat cascade: A time-dependent heat cascade for a batch process which includes the effects of heat storage. Path: System of connections in a heat exchanger network forming a continuous pathway between the utility heater and a utility cooler. That is a connection between a heater and a cooler in a network. Pinch: Point of zero heat flow in a cascade (alternatively, point of closest approach of composite curves in a [heating and cooling] problem). Pinch design method: Method of heat exchanger network design which exploits the constraints inherent at the pinch. Pinch match: Process interchanger which brings a stream to its pinch temperature (i.e., hot streams above the pinch, cold streams below). Pinch region: Range of temperature over which cascade net heat flow is zero (or very low). Pinch temperature: The point of closest approach between the hot and cold composite curves is the pinch temperature, and is where design is most constrained. At the pinch temperature, there is no energy transfer between the temperature intervals. Thus, the pinch temperature provides a decomposition of the design problem. That is, above the pinch temperature, the process requires external heating, whereas below the pinch temperature the process requires external cooling. Pocket: Region in the grand composite curve where neither external heating nor cooling is required. Problem table: System of analyzing process stream data for a heat recovery problem which exploits temperature interval sectioning of the problem, and predicts minimum utilities consumptions, pinch location, and cascade heat flows. Process change: Altering the stream data by changing the temperature and /or heat load of one or more streams. Process sink profile: Section of the grand composite curve above pinch temperature. Process source profile: Section of the grand composite curve below pinch temperature. Profile: Temperature-enthalpy plot of a stream or a composite stream. Pumparound: Liquid drawn from a distillation column which releases sensible heat and is returned to the column. Rescheduling: Altering the time period during which a stream exists. Retrofit or revamp: Any change to an existing chemical process, but in this context, mostly changes for improvement in energy efficiency. Shells: The total minimum number of shells required for the HEN system. The minimum number of shells is not necessarily equal to the minimum total number of heat exchangers due to restriction on maximum heat transfer area for a shell.

Process Integration and Heat Exchanger Network  1085 Shifted composite curves: Plots of combined enthalpy of all hot and all cold streams against shifted temperature, touching at the pinch. This plot is similar to the composite curve plot, except that the hot composite curve is shifted down by ΔTmin/2 and the cold composite curve is shifted up by ΔTmin/2. Shifted temperature: Stream temperatures altered to include the effect of the required ΔTmin, usually by reducing hot stream temperatures by ΔTmin/2 and increasing cold stream by ΔTmin/2. Site sink profile: Plot of heat required by all processes on a site at given temperatures. Site source profile: Plot of heat released by all processes on a site at given temperatures. Split grand composite curve: Plot of the grand composite curve for the back ground process and the extracted streams on the same graph. Stream splitting: Division of a process stream into two or more parallel branches. Subset: Set of process streams or process streams, plus utilities, within a heat recovery problem which are in overall enthalpy balance. Supply temperature: Temperature at which a process stream enters a heat recovery problem. Target: A design performance limit, determined prior to design. Targets are theoretical values that represent the ideal or perfect situation. They are very important as an analysis tool as it provides a comparison for how close the current design is to the optimal design. Target temperature: Temperature at which a process stream leaves a heat recovery problem. Temperature interval: Section of a heat recovery problem between two temperatures which contains a fixed stream population. T-H Plots: A series of values of ΔH for each temperature interval is plotted resulting in a T-H plot. The resulting T-H plot is a single curve representing all the hot streams, known as the hot composite curve, and correspondingly a similar procedure gives a cold composite curve of all the cold streams in a problem. The overlap between the composite curves represents the maximum amount of heat recovery possible within the process. The overshoot at the bottom of the hot composite represents the minimum amount of external cooling required and the overshoot at the top of the cold composite represents the minimum amount of external heating required. Threshold problem: Heat recovery problem that shows the characteristic of requiring either only hot or only cold utility, over a range of ΔTmin values from zero up to a threshold (or throughout). The value of ΔTmin at which one utility target falls to zero is termed ΔTthreshold, and a situation where only one utility is required is called a threshold problem. Ticking-off a stream: Heuristic of maximizing the heat load on an interchanger by completely satisfying the heat load on one stream. Heat exchanger network is to be designed keeping capital cost in mind. This essentially means that the number of utilities is to be reduced (for a given utility load). This can be done by crossing the heat exchanger in such a way that the smaller heat load of the two streams attains the target without the need of any utility. This stream is known to be ticked off. Time average model (TAM): Averaging heat flows by dividing the total heat load over the batch period by the total batch cycle time. Time-dependent heat cascade: A set of heat cascades for different time intervals forming a matrix. Time event chart: A Gantt chart, plotting the time periods when different streams exist. Time interval: A period of time during which stream conditions do not change appreciably and for which a target can be obtained. Time slice model (TSM): Division of a batch problem into time intervals and finding the targets for the individual cascades, with zero heat storage. Total area: Minimum total area when all exchangers are shell and tube type for the heat exchanger network. Total cost index: Minimum annualized cost, based on capital and operating targets. Total heat recovery: The total heat recovered by the heat exchange is found by adding the heat loads for all the hot streams and all the cold streams, respectively. Subtracting the cold and hot utility targets from these values gives the total heat recovery. The cold utility target minus the hot utility target should equal the bottom line of the infeasible heat cascade, which provides a useful cross-check that the stream data and heat cascades have been evaluated correctly. Top level analysis: Study of a site’s heat and power needs using existing utility consumption of plants, rather than targets.

1086  Chemical Processing Engineering Trade-offs: A similar relationship exists between the number of streams (process streams plus utilities) in a problem and the minimum number of heat exchanger units (i.e., heaters, coolers and interchangers). A network which achieves the minimum energy targets, with the heat source and heat sink sections separate, needs more units than if the pinch division had been ignored. This type of trade-off, between energy recovery and number of units, adds to the traditional concept of a trade-off between energy and surface area. UA analysis: Procedure of calculating UA values (= Q/ΔTLMTD) for matches in a heat exchanger network, for the purposes of preliminary costing and optimization. Utility: System of process heating or process cooling. Unit: Process interchanger, heater or cooler. CPHOT − CPCOLD where ΔHi (kW): The enthalpy balance is determined by (Ti − Ti +1 )

(∑

∑

)

i

i = interval, T = shifted temperature, CPHOT = heat capacity flow rate of the hot stream (kW/K), CPCOLD = heat capacity flow rate of the cold stream (kW/K). ΔTmin: Minimum temperature difference allowed in the process between hot and cold streams. For a given value ΔTmin, the utility quantities predicted are the minima required to solve the heat recovery problem. In general, ΔTmin occurs at only one point of closest approach, which is called the pinch. This means that it is possible to design a network which uses the minimum utility requirements, where only the heat exchangers at the pinch need to operate at ΔT values down to ΔTmin. A value of 10oC or 20oC is best, but in some industries, a very much lower or higher value is appropriate. ΔTmin contribution (ΔTcont): Temperature difference value assigned to individual process streams. Match-dependent ΔTmin values are given by the sum of the contributions in a match.

Summary and Heuristics A very simple procedure exists that makes it possible to calculate the minimum heating and cooling requirements for a process. Also, simple procedures exist for calculating the minimum number of exchangers required and for estimating the heat exchanger area required. These calculations are possible without even specifying a heat exchanger network and therefore are ideal for screening purposes. The results indicate that normally a process has a pinch temperature, and above this temperature heat should only be added to the process, whereas below this temperature heat should only be removed. Since this problem decomposition was not widely known two decades ago, it is often possible to significantly reduce the energy requirements of existing processes (that is, 30 to 50% energy savings have been obtained in industry).

Heuristics The following heuristics in the design of HEN are [19]: 1. O  nly add heat to a process above the pinch temperature. 2. Only remove heat from a process below the pinch temperature. 3. A feasible exchanger just above the pinch requires that CPHot ≤ CPCold, while the CPHot ≥ CPCold is true below the pinch. 4. To eliminate a heat exchanger from a network, we prefer to break a loop that includes the smallest heat load. 5. When we break loops that cross the pinch in order to eliminate heat exchangers from a network, we often violate the ΔTmin condition. 6. If we add extra heat to a process, we must remove this same amount of heat to a cold utility. 7. If possible, always install heat engines either above or below the pinch. 8. If possible, always install heat pumps across the pinch.

Process Integration and Heat Exchanger Network  1087 9. If possible, always install distillation columns either above or below the pinch. Three design heuristics have been proposed by Linnhoff and Hindmarsh [30]: • First, break the loop that includes the exchanger with the smallest possible heat load. • Always remove the smallest heat load from a loop. • If we break a loop that crosses the pinch, normally we violate the minimum approach temperature in the revised network. If we violate the minimum approach temperature, we must find some way of restoring it. The concept of paths is used for this purpose.

Nomenclature a A Ai Amin ATotal .M b CC CH CP NC NH NS NU ∆Hi Q QCmin QHim QRec Tcold Thot T S TT ∆T ∆TLMTD ∆Tmin U uHX, min

= Installed capital cost law coefficient. = Heat exchanger area = Contribution to overall area target from enthalpy interval I of the composite curves. = Minimum overall area target for a heat exchanger network = Minimum overall area for heat exchanger network after accepting match M. = Installed capital cost law coefficient = Annual operating capital cost of unit duty of cold utility. = Annual operating capital cost of unit duty of hot utility. = Heat capacity flowrate. = Number of cold streams in an enthalpy interval. = Number of hot streams in an enthalpy interval. = Number of streams. = Total number of distinct hot and cold utilities. = Total enthalpy change of enthalpy interval i on the composite curve. = Heat exchanger duty. = Minimum cold utility target. = Minimum hot utility target. = Maximum heat recovery = Temperature of cold composite curve. = Temperature of hot composite curve. = Supply temperature. = Target temperature. = Temperature difference. = Log mean temperature difference. = Minimum temperature difference on composite curves. = Overall heat transfer coefficient for a heat exchanger = Minimum number of heat exchanger in a HEN.

References 1. Morgan, S.W., Use Process Integration to Improve Process Designs and the Design Process, CEP, pp. 62-68, September, 1992. 2. Gundersen, Truls, A process integration primer, SINTEF Energy Research, Trondheim, Norway, 9 April, 2002.

1088  Chemical Processing Engineering 3. Dunn, Russel, F. and Mahmoud M. El-Halwagi, Process integration technology review: background and applications in the chemical process industry. J. Chem. Technol Biotechnol, 78: 1011-1021, 2003. 4. El-Halwagi, M. M., Process Integration, vol. 7. Process Systems Engineering Series, Elsevier, Amsterdam, The Netherlands, 2006. 5. Rudd, D. F., Powers, J.G. and J. J. Siirola, Process Synthesis, Prentice Hall, 1973. 6. http://www.ceas.manchester.ac.uk/research/centers/ceneterforprocessintegration 7. Dimian, A. and Costin Sorin Bildea, Chemical process design, Wiley – VCH, 2008. 8. Klemes, Jiri, Friedler, Ferenc, and Bulatov, Igor and Petar Varbanov, Sustainability in the process industry: integration and and optimization, McGraw-Hill Co, 2011. 9. Friedler, F., Process integration, modelling and optimisation for energy saving and pollution reduction, Appl. Thermal Eng., 30, 2270-2280, 2010. 10. Umeda, T., Expanding process integration, CEP, pp. 85, February, 2011. 11. Linnhoff, B., and J. A. Turner, Heat recovery networks: new insights yield big savings, Chem. Eng., pp. 56, Nov. 2, 1981. 12. Linnhoff, B., and J. R. Fowler, Synthesis of heat exchanger networks: I. Synthesis generation of energy optimal networks., AIChE J. July 1978; 24(4): 633-42. II Evolutionary Generation Networks with various critical of optimality, AIChE, J., July 1978; 24(4): 642-54. 13. Linnhoff, B., Mason, D.R., and I. Wardle, Comput., Chem. Eng., 3, 295, 1979. 14. Umeda, T., Itoh, J., and K. Shiroko, Chem. Eng. Prog., 75, 70, 1978. 15. Umeda, T., Niida, K., and K. Shirolo, AIChE J, 25, 423, 1979. 16. Linnhoff, B., Pinch Analysis - a state of the art review, Trans. IChemE. Res. Des. 71, Part A5: 503-522, 1993. 17. Linnhoff, B. Townsend, D. W., Boland D., G. F., Hewitt, B. E. A., Thomas, A. R., Guy., and R. H. A. Marshland., A user guide on process integration for the efficient use of energy, Revised 1st. ed., IChemE, 1994. 18. Shenoy, U. V., Heat exchanger network synthesis: process optimization by energy and resource analysis, Gulf Publishing Co., Houston, 1995. 19. Douglas, J.M., Conceptual design of chemical process, McGraw-Hill, New York, p. 216-288, 1986. 20. Smith, R., Chemical Process Design, McGraw-Hill, Inc., New York, 1995. 21. Kemp, I. C., A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed., Elsevier, 2007. 22. Lam, H. L., et al., Special theme review: software tools overview: process integration, modeling and optimization for energy saving and pollution reduction, Asia-Pac. J. Chem. Eng., Published online in Wiley Online library, wileyonlinelibrary.com. DOI:10.1002/apj.469, 2010. 23. Linnhoff, B, and D. R. Vredeveld, Pinch technology has come of age, Chem. Eng. Progr., 80, 33, July 1984. 24. Biegler, L. T., Grossmann, I. E. and A. W., Westerberg, Systematic methods of chemical process design. Upper Saddle River, New Jersey: Prentice Hall, 1997. 25. Floudas, C. A., Nonlinear and mixed – integer optimizations. In: Fundamentals and applications. Oxford University Press, 1995. 26. Seider, W. D., Seader, J. D., and D. R. Lewin, Product and process design principles, synthesis, analysis and evaluation, 3rd ed. Wiley; 2009. 27. Linnhoff, B., et. al., User guide on process integration for the efficient use of energy, Inst. Chem. Engrs., Rugby, U.K., 1982. 28. Hall, S. G., Targeting for multiple utilities in pinch technology, Ph.D. Thesis UMIST, Dept. of Process Integration, Manchester, November 1989. 29. Gundersen, Truls, “A Process Integration PRIMER”, International Energy Agency, SINTEF Energy Research, Dept. of Thermal Energy and Hydro Power Trondheim, Norway, 10 May 2000. 30. Linnhoff, B. and E. Hindmarsh, The Pinch Design Method for Heat Exchanger Networks, Chem. Eng., Sci., Vol. 38, No. 5, pp. 745-763, 1983. 31. Hohmann, E.C., “Optimum networks for heat exchanger”, PhD Thesis, University of S. California, 1971. 32. Varbanov, P. and J. Klemes, Analysis and integration of fuel cells combined cycles for development of low carbon energy technologies, Energy, 33 (10), 1508-1517, 2008. 33. Linnhoff, B., and S. Ahmad, “Cost Optimum Heat Exchanger Networks-1. Minimum Energy and Capital Using Simple Models for Capital Cost”, Computers & Chem. Eng., Vol. 14, No. 7, pp. 729-750, 1990. 34. Smith, R., Chemical process design and integration. John Wiley, 2007. 35. Townsend, D. W., Linnhoff, B., Surface area targets for heat exchanger networks., IChemE Annual Res. Meeting, Bath, April 1984. 36. Beck. Ron, Best practice in energy efficiency, www.digitalrefining.com/article/1001121, pp 1-4, PTQ, Q2, 2015. 37. Ahmad, S., and D.C.W. Hui, “Heat Recovery Between Areas of Integrity”, Computers & Chem. Eng., 15, No. 12, pp. 809-832, 1991.

Process Integration and Heat Exchanger Network  1089 38. Ludwig, Ernest, E., Applied Process Design for Chemical and Petrochemical Plants, Vol. 3, 3rd ed., Gulf Professional Publishing, 2001. 39. Polley, G.T., Panjeh Shahi, M.M., and F.O. Jegede, “Pressure Drop Considerations in Retrofit of Heat Exchanger Networks”, Trans. IChemE., Part –A, 68: 211, 1990. 40. Polley, G.T., and M.M. Panjeh Sahhi, “Synthesis and Detailed Heat Exchanger Design”, Trans. I.ChemE., Part A, 69: 445, 1991. 41. Ahmad, S., and R. Smith, “Targets and Design Multipass Heat Exchangers, An Alternative Approach”, Trans. ASME, J. Heat Transfer, 110: 304, 1988. 42. Kern, D.Q., Process Heat Transfer, McGraw-Hill, New York, 1950. 43. Ahmad, S., and R. Smith, “Targets and Design for Minimum Number of Shells and Heat Exchanger Networks”, IChemE, ChERD, 67: 481, 1989. 44. Ahmad, S., Linnhoff, B., and R. Smith., “Cost Optimum heat exchanger networks-2. Targets and design for detailed capital cost models”, Computers & Chem. Eng., Vol. 14, No. 7, pp. 751-767, 1990. 45. Cerda, J., Westerberg, A.W., Mason, D., and B. Linnhoff, “Minimum Utility Usage in Heat Exchanger Network Synthesis – A transportation Problem”, Chem. Eng. Sci, Vol. 38, pp. 373-387, 1983. 46. Floudas, C.A., Ciric, A.R. and I.E. Grossmann, “Automatic Synthesis of Optimum Heat Exchanger Network Configurations”, AIChEJ, Vol. 32, pp. 276-298, 1986. 47. Ciric, A. R. and C.A. Floudas, “Heat Exchanger Network Synthesis with Decomposition”, Comput. & Chem. Eng., Vol. 15, pp. 385-396, 1991. 48. Linnhoff March Introduction to Pinch Technology, 1998. 49. Ahmad, S., Polley, G.T. and E.A. Petela., Retrofit of heat exchanger networks subject to pressure drop constraints, Paper No. 34a, AIChE Spring Meeting, Houston, April 1989. 50. Nie, X. R. and X. X. Zhu, “Heat exchanger network retrofit considering pressure drop and heat transfer enhancement”, AIChEJ, 45(6), pp. 1239-1254, 1999. 51. Asante, N.D.K, and X. X. Zhu, “An Automated and interactive approach for heat exchanger network retrofit”, ChERD, 75 (part A), pp. 349-360, 1997. 52. Vaclavek, V., Novotna, A. and J. Dedkova, Pressure as a further parameter of composite curves in energy process integration, Applied Thermal. Eng., 23, (14), pp. 1785-1795, 2003. 53. Panjeh Shahi, M.H. and N. Tahoumi, Pressure drop optimization and debottlenecking of heat exchanger networks, Energy, 33(6), pp. 942-951, 2008. 54. Dhole, V.R., and B. Linnhoff, Total site targets for fuel, co-generation, emissions and cooling, Computers & Chem. Eng., 17 (Suppl.), pp. 101-109, 1993. 55. Raissi, K, Total site Integration, PhD Thesis, UMISIT, Manchester, U.K. 1994. 56. Klemes, J., Dhole, V.R., Raissi, K., Perry, S.J., and L. Puigjaner., Targeting and design methodology for reduction of fuel, power and CO2 on total sites, Applied Thermal Engineering, 17, (8/10), pp. 993-1003, 1997. 57. Mavromatis, S.P. and A.C. Kokossis., Conceptual optimization of utility networks for operation variations- 1., Targets and Level Optimisation, Chem. Eng. Sci., 53(8), pp. 1585-1608, 1998. 58. Verbanov, P.S., Doyle, S., and R. Smith., Modelling and Optimisation of utility systems, Trans. IChemE – Chem.Eng. Res. Dev., 82(45), pp. 561-578, 2004. 59. Verbanov, P.S. and J. Klemes, Total sites integrating renewable with extended heat transfer and recovery, Heat Transfer Engineering, 31(9), pp. 733-741, 2010. 60. Towler, G. P., Mann, R., Serriere, A. J., and C.M.D. Gabande, Refinery Hydrogen Management: Cost Analysis of Chemically Integrated Facilities, Ind. Eng. Chem. Res., Vol. 35, No.7, pp. 2378-2388, May 1996. 61. Alves, J, J. and G. P. Towler, Analysis of Refinery Hydrogen Distribution Systems, Ind. Eng. Chem. Res. 41, pp. 5759-5769, 2002. 62. Alves, J. J., Analysis and design of refinery hydrogen distribution systems, PhD Thesis, Dept. of Process Integration, University of Manchester, 1999. 63. Hallale, N. and F. Liu, Refinery hydrogen management for clean fuels production, Advances in Environmental Research, 6, pp. 81-98, 2001. 64. Agrawal, V. and U.V. Shenoy, Unified Conceptual Approach to Targetting and Design of Water and Hydrogen Networks, AIChE J., vol. 52, No. 3, pp. 1071-1082, March, 2006. 65. Wei, Z, J., Yuhang, L., Zhang, Nan., and K. Guy, Optimising and revamping a refinery hydrogen network, Revamps Petroleum Technology Quarterly, pp. 37-46, 2011. 66. Jla, N., Refinery hydrogen network optimization with improved hydroprocessor modeling, PhD Thesis, Centre for Process Integration, University of Manchester, 2010.

1090  Chemical Processing Engineering 67. Roozbeh, S., et al., Design of Oil Refineries Hydrogen Network Using Process Integration Principles, Iran J. Chem. Chem. Eng., vol. 27, No. 4, 2008. 68. Nelson, A.M., and Y.A. Liu, Hydrogen Pinch Analysis Made Easy, Chem. Eng., pp. 56-61, June 2008. 69. Zhelev, T., and L. Ntlhakana., Energy – environment closed loop through oxygen pinch, Computers and Chemical Engineering 23 (Suppl.), pp. 79-83, 1999. 70. Zhelev, T., and N. Bhaw., Combined water-oxygen pinch analysis for better waste water treatment, Management, Waste Management, 20, 8, pp. 665-670, 2000. 71. Clarke, S.C, CO2 Management – A Refiners Perspective, Foster Wheeler Energy Ltd., Shinfield Park, Reading, Berkshire, U.K. 72. Klemes, J., Bulatov, I. and T. Cockeril, Techno-economic modeling and cost functions of CO2 capture processes, Computers and Chemical Engineering, 31 (5-6), pp. 445-455, 2007. 73. Perry, S., Klemes, J. and I. Bulatov., Integrating waste and renewable energy to reduce the carbon footprint of locally integrated energy sectors, Energy, 33 (10), pp. 1487-1497, 2008. 74. Tan, R., and D.C. Y. Foo., Pinch analysis approach to carbon-constrained energy sector planning, Energy, 32 (8), pp. 14221429, 2007. 75. El-Halwagi, M. M., and V. Manousiouthakis, Synthesis of mass-exchange networks, AIChE J., 35, pp. 1233-1244, 1989. 76. El-Halwagi, M.M. and V. Manoussiouthakis, Simultaneous synthesis of mass-exchange and regeneration networks, AIChE J., 36, pp. 1209-1219, 1990. 77. Wang, Y.P., and R. Smith, Wastewater minimization, Chem. Eng. Sci., 49, pp. 981-1006, 1994. 78. Prakash, R. and Shenoy, U.V. Targeting and design of water networks for fixed flowrate and fixed contaminant load operations. Chem. Eng. Sci., 60, 255–268. (2005a). Prakash, R. and Shenoy, U.V. Design and evolution of water networks by source shifts. Chem. Eng. Sci., 60, 2089–2093, (2005b). 79. Chemical Processing Webcast: Boost Water Efficiency and Improve Wastewater Treatment”, Chemical Processing.com, December 2, 2011. 80. Foo, D., Water Pinch Analysis, Dept. of Chemical & Env. Eng., University of Nottingham, Malaysia Campus, http://inemaglow.dcs.unipannon.hu/summer_ws/lectures/Water/pinch/(Full).pdf. 81. Smith, R., and O. Delaby, Targeting Flue Gas Emissions, Trans. I. ChemE. Eng. Res. Des., 69, NoA6, pp. 492-505, 1991. 82. Linnhoff, B. and V.R. Dhole, Targeting for CO2 emissions for total site, Chem. Ind. Tech., 16, 256, 1993. 83. Smith, R., Petala, E.A. and H.D. Spriggs, Minimization of Environmental Emissions Through Improved Process Integration, Heat Recovery System & CHP, vol. 10, No. 4, pp. 329-339, 1990. 84. Smith, R., State of the art in process integration. Appl. Therm. Eng., 20: 1337-45, 2000. 85. Natural Resources Canada, Pinch Analysis for the Efficient Use of Energy, Water and Hydrogen, ISBN: 0-662-34944-4 © Her Majesty the Queen in Right of Canada, 2003. 86. Mehta, R., Crude unit integrated energy analysis, Petroleum Technology Quarterly, pp. 93-99, Summer 2002. 87. Kreith, F., and D.Y. Goswami, Handbook of Energy Efficiency and Renewable Energy, - Chapter 15, Process Energy Efficiency: Pinch Technology - Pinch Technology in Theory: Trivedi, Kirtan, K., Pinch Technology in Practice, Fouche, Ed, and Kelly, E. Parmenter, CRC Press, Taylor & Francis Group, 2007. 88. Shenoy, U.V., Targeting and design of energy allocation networks for carbon emission reduction, Chem. Eng. Sci., vol. 65: 6155-68, 2010. 89. Shenoy, A. U. and U.V. Shenoy, Targeting and design of energy allocation networks with carbon capture and storage, Chem. Eng. Sci., vol. 68, pp. 313-327, 2012 90. Shenoy, U. V., Unified targeting algorithm for diverse process integration problems of resource conservation networks, Chem. Eng. Res. Des., vol. 89, pp. 2686-2705, 2011. 91. Declerq, D., Private Communication, Pinch Technology Second Generation – Analysis with Crisscross for minimum area and minimum cost. http://www.pincho.com, 2014. 92. Weber, Claire., and Thomas Yeung, Energy management: raising profitability, reducing CO2 emissions. 93. Coker, A. K., Ludwig’s Applied Process Design for Chemical and Petrochemical Plants, vol. 3, Elsevier, 2015. 94. Worrel, E., and C. Galistsky, Energy Efficiency Improvement and Cost Saving Opportunities for Petroleum Refineries. An Energy Star ® Guide for Energy and Plant Managers. Berkeley, CA: Lawrence Berkeley National Laboratory (LBNL – 56183). 95. Kumana, J. D.,Corporate Energy Management Programs: A Case Study, Chemical News, pp. 38, 2010. 96. Zoran Milosevic, Rudman, A., and Richard Brown, Using pinch technology in operations? www.digitalrefining.com/ article/1000837, pp. 1, September 2013. 97. William, R. Morrow, III., John Marano., Jayant Sathaye., Ali Hasanbeigi, Eric Masanet, and Tengfang Xu., Energy efficiency improvements in the U.S. petroleum refining industry, ECEEE Industrial Summer Study Proceedings, p. 487., 2014.

Process Integration and Heat Exchanger Network  1091 98. Foo, D. C. Y. and R. R. Tan, Targeting for minimum low and zero-carbon energy resources in carbon-constrained energy sector planning using cascade analysis. Chemical Engineering Transactions, 12, pp. 139 – 144, 2007. 99. Foo, D. C. Y., Tan, R. R., and D. K. S. Ng., Carbon and footprint -constrained energy planning using cascade analysis technique., Energy, 33(10), 1480-1488, 2008.

Bibliography March Linnhoff, Introduction to Pinch Technology, © Linnhoff March, 1998. Varbanov, P., Klemes, J., Shah, R.K., and H. Shihn, Power cycle integration and efficiency increase of molten carbonate fuel cell system, Journal of Fuel Cell Science and Technology, 3 (4), 375-383, 2006. Gundersen, Truls., A Process Integration Primer, International Energy Agency. SINTEF Energy Research, 10 May 2000. Industrial Heat Pumps for Steam and Fuel Savings – A Best Practices Steam Technical Brief., US Department of Energy – Energy Efficiency and Renewable Energy, Nov. 2005/ www.eere.energy.gov.

10 Process Safety and Pressure-Relieving Devices Introduction The subject of process safety is so broad in scope that this chapter must be limited to the application, design, rating, and specifications for process over-pressure relieving devices for flammable vapors and external fires on equipment. The subject of fire protection cannot be adequately covered; however, the engineer is referred to texts dealing with the subject in a thorough manner [1–6]. The possibilities for development of excess pressure exist in nearly every process plant. Due to the rapidly changing and improved data, codes, regulations, recommendations, and design methods, it is recommended that reference be made to the latest editions of the literature listed in this chapter. It is important to understand how the over-pressure can develop (source) and what might be the eventual results. The mere solving of a formula to obtain an orifice area is secondary to an analysis and understanding of the pressure system. Excess pressure can develop from explosion, chemical reaction, reciprocating pumps or compressors, external fire around equipment, and an endless list of related and unrelated situations. In addition to the possible injury to personnel, the loss of equipment can be serious and an economic setback. Most states have laws specifying the requirements regarding application of pressure-relieving devices in process and steam power plants. In essentially every instance, at least part of the reference includes the A.S.M.E. Boiler and Pressure Vessel Code, Section VIII, Division 1 (Pressure Vessels) and/or Division 2 [1]; and Section VII, Recommended Rules for Care of Power Boilers [7]. In addition, the publications of the American Petroleum Institute are helpful in evaluation and design. These are API-RP-520 [8], Design and Installation of Pressure-Relieving Systems in Refineries; Part I-Design; Part II-Installation; and API-RP-521 [9], Guide for Pressure Relief and Depressurizing Systems, ANSI/ ASME B31.1 Power Piping; B16.34; and NFPA-1; [10], Sections 30, 68, and 69. The ASME Code requires that all pressure vessels be protected by a pressure-relieving device that shall prevent the internal pressure from increasing more than 10% above the maximum allowable working pressures (MAWP) of the vessel to be discussed later. Except where multiple relieving devices are used, the pressure shall not increase more than 16% above the MAWP or, where additional pressure hazard is created by the vessel being exposed to external heat (not process related) or fire, supplemented pressure-relieving devices must be installed to prevent the internal pressure from rising more than 21% above the MAWP. See Ref. [1] sections U-125 and UG-126. The best practice in industrial design recommends that (a) all pressure vessels of any pressure be designed, fabricated, tested and code stamped per the applicable ASME code [1] or American Petroleum Institute (API) Codes and Standards, Ref. [5] and (b) that pressure-relieving devices be installed for pressure relief and venting per codes [1, 5, 8, 9]. Although not specifically recognized in the titles of the codes, the rupture disk as a relieving device is, nevertheless, included in the requirements as an acceptable device. Usual practice is to use the terms “safety valve” or “relief valve” to indicate a relieving valve for system overpressure and this will be generally followed here. When specific types of valves are significant, they will be emphasized.

A. Kayode Coker and Rahmat Sotudeh-Gharebagh. Chemical Process Engineering: Design, Analysis, Simulation and Integration, and Problem-Solving With Microsoft Excel - UniSim Design Software, Volume 2, (1093–1252) © 2022 Scrivener Publishing LLC

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1094  Chemical Process Engineering

10.1 Types of Positive Pressure-Relieving Devices (See Manufacturers’ Catalogs for Design Details) Relief Valve: a relief valve is an automatic spring-loaded pressure-relieving device actuated by the static pressure upstream of the valve, and which opens further with increase in pressure over the opening pressure. It is used primarily for liquid service [1, 8] (Figures 10.1A and 10.1B). The rated capacity is usually attained at 25% overpressure. Safety Valve: this is an automatic pressure-relieving device actuated by the static pressure upstream of the valve and characterized by rapid full opening or “pop” action upon opening [1, 8], but does not reseat. It is used for steam or air service (Figure 10.2). The rated capacity is reached at 3%, 10% or 20% overpressure, depending upon applicable code. Safety Relief Valve: this is an automatic pressure-relieving device actuated by the static pressure upstream of the valve and characterized by an adjustment to allow reclosure, either a “pop” or a “non-pop” action, and a nozzle type entrance; and it reseats as pressure drops. It is used on steam, gas, vapor and liquid (with adjustments), and is probably the most general type of valve in petrochemical and chemical plants (Figures 10.3A, 10.3B, and 10.4). The rated capacity is reached at 3% or 10% overpressure, depending upon code and/or process conditions. It is suitable for use either as a safety or as a relief valve [1, 8]. It opens in proportion to an increase in internal pressure.

Pressure Relief Valve The term Pressure relief valve applies to relief valves, safety valves or safety relief valves [8]. CAP PRESSURE SCREW PRESSURE SCREW NUT SET SCREW SPRING WASHER BONNET SPRING SPRING WASHER SPINDLE WING VALVE BODY

FLOW

Figure 10.1A  Relief valve (Courtesy of Crosby – Ashton Valve Co.).

Process Safety and Pressure-Relieving Devices  1095 Pressure-Relieving Devices

Cap

Plug

Gasket Bonnet

Cotter Pin Cap Test Gag Cap Forked Lever Spindle Ajusting Bolt Lever Adj. Bolt Nut Gasket Bonnet

Spindle Spindle Lift Nut Forked Lever Pin Adjusting Bolt Adj. Bolt Lock Nut Cap Set Screw

REGULAR LIFTING GEAR Type C

SCREWED CAP Type A (Std.) Cap Spindle Nut Dog Shaft

SCREWED CAP AND TEST ROD Cap Type B Spindle Nut Dog “Pull-up” Shaft Stud

Gasket

Gasket

PACKED LIFTING GEAR Type D

Stud

PACKED LIFTING GEAR AND TEST ROD (Valve not shown gagged) Type E

Figure 10.1B  Accessories for all types of safety relieving valves (Courtesy of Crosby – Ashton valve Co.).

CAP SPINDLE NUT ADJ. BOLT BEARING FORKED LEVER ADJUSTING BOLT ADJ. BOLT NUT LEVER SPRING WASHER SPRING SPINDLE BONNET GUIDE GUIDE BEARING DISC NUT DISC HOLDER DISC INSERT GUIDE (ADJ.) RING GUIDE RING SET SCREW NOZZLE RING SET SCREW NOZZLE RING NOZZLE BODY

Figure 10.2  Safety valve (Courtesy of Croby-Ashton Valve Co.).

1096  Chemical Process Engineering 3

Bill of Materials-Conventional 10

ITEM 1

9 19

2

11 15 2 18 15

14 8

25 16

21 20 1

17

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

13

18

22

19 20 21 22 23 24 25 26

12 6 4 7 24 5

23 26

PART NAME 26( )A10 Body thru 26( )A26 26( )A32 thru 26( )A36 26( )A10 thru 26( )A26 Bonnet 26( )A32 thru 26( )A36

MATERIAL SA-216 GR. WCB, Carbon Steel SA-217 GR. WC6, Alloy St. (11/4 CR–1/2 Moly) SA-216 GR. WCB, Carbon Steel SA-217 GR. WC6, Alloy St. (11/4 CR–1/2 Moly) Carbon Steel Cap. Plain Screwed Stainless Steel Disc 316 St. St. Nozzle 300 Series St. St. Disc Holder 300 Series St. St. Blow Down Ring 300 Series St. St. Steeve Guide Stem Stainless Steel Spring Adjusting Screw Stainless Steel Jam Nut (Spr. Adj. Scr.) Stainless Steel Stainless Steel Lock Screw (B.D.R) Stainless Steel Lock Screw Stud Stainless Steel Stem Retainer Carbon Steel Spring Button Rust Proofed ASTM A193 Body Stud Gr. B7, Alloy St. ASTM A194 Hex Nut (Body) Gr. 2H, Alloy St. 26( )A10 Carbon Steel thru 26( )A16 Rust Proofed Spring High Temp. Alloy 26( )A20 Rust Proofed thru 26( )A36 Cap Gasket Soft Iron or Steel Soft Iron or Steel Body Gasket Bonnet Gasket Soft Iron or Steel Lock Screw Gasket Soft Iron or Steel Stainless Steel Hex Nut (B.D.R.L.S) Lock Screw (D.H.) Stainless Steel Steel Pipe Plug (Bonnet) Steel Pipe Plug (Body)

Also suitable for liquid service where ASME Code certif ication is not required.

Figure 10.3A  Conventional or unbalanced nozzle safety relief valve (By permission from Teledyne Farris Engineering Co.).

Pilot-Operated Safety Valves When properly designed, this type of valve arrangement conforms to the ASME code. It is a pilot-operated pressure relief valve in which the major relieving device is combined with and is controlled by a self-activating auxiliary pressure relief valve (See Figures 10.5A and B).

10.2 Types of Valves/Relief Devices There are many design features and styles of safety relief valves, such as flanged ends, screwed ends, valves fitted internally for corrosive service, high temperature service, cryogenic service/low temperatures, with bonnet or without, nozzle entrance or orifice entrance, and resistance to discharge piping strains on body. Yet most of these variations have little, if anything to do with the actual performance to relieve overpressure in a system/vessel. A few designs are important to the system arrangement and relief performance. These are as follows:

Conventional Safety Relief Valve This valve design has the spring housing vented to the discharge side of the valve. The performance of the valve upon relieving overpressures is directly affected by any changes in the back pressure on the valve (opening pressure, closing pressure, relieving capacity referenced to opening pressure) (see Figures 10.3, 10.6A and 10.6B) [11]. When

Process Safety and Pressure-Relieving Devices  1097 Process Safety and Pressure-Relieving Devices 10 11 9

3 4

23

6

22

5 20 16

5

3 6

4

18

18

20

19

19

21

7

21

7

2

2 12 14

8

13

13 8

17

1

15

17

12 14

15

SPINDLE

SPINDLE

SEAT RETAINER GUIDE GUIDE PLASTIC SEAT O-RING SEAT NOZZLE NOZZLE RETAINER SCREW

Figure 10.3B  Safety relief valve with rubber or plastic seats (By permission from Anderson, Greenwood and Co.).

connected to a multiple relief valve manifold, the performance of the valve can be somewhat unpredictable from a relieving capacity standpoint due to the varying backressure in the system.

Balanced Safety Relief Valve This valve provides an internal design (usually bellows) above/on the seating disk in the huddling chamber that minimizes the effect of back pressure on the performance of the valve (opening pressure, closing pressure and relieving capacity) [11] (see Figures 10.4, 10.5A and B, 10.6A and B).

Special Valves a. i nternal spring safety relief valve b. power-actuated pressure relief valve c. temperature-actuated pressure relief valve These last three are special valves from the viewpoint of chemical and petrochemical plant applications, but they can be designed by the major manufacturers and instrumentation manufacturers as these are associated with instrumentation controls (Figure 10.7A). Care must be taken in the system design to make certain it meets all ASME code requirements.

1098  Chemical Process Engineering Bill of Materials-BalanSeal ITEM 1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

PART NAME 26( )B10 Body thru 26( )B26 26( )B32 thru 26( )B36 26( )B10 thru 26( )B26 Bonnet 26( )B32 thru 26( )B36 Cap. Plain Screwed Disc Nozzle Disc Holder Blow Down Ring Sleeve Guide Stem Spring Adjusting Screw Jam Nut (Spr. Adj. Scr.) Lock Screw (B.D.R) Lock Screw Stud Stem Retainer Bellows Bellows Gasket

17 Spring Button 18 Body Stud 19 Hex Nut (Body) 26( )B10 thru 26( )B16 26( )B20 thru 26( )B36 Cap Gasket Body Gasket Bonnet Gasket Lock Screw Gasket Hex Nut (B.D.R.L.S) Lock Screw (D.H.) Pipe Plug (Body)

20 Spring 21 22 23 24 25 26 27

MATERIAL SA-216 GR, WCB, Carbon Steel SA-217 GR. WC6, Alloy St. (11/4 CR–1/2 Moly) SA-216 GR, WCB, Carbon Steel SA-217 GR. WC6, Alloy St. (11/4 CR–1/2 Moly) Carbon Steel Stainless Steel 316 St. St. 300 Series St. St. 300 Series St. St. 300 Series St. St. Stainless Steel Stainless Steel Stainless Steel Stainless Steel Stainless Steel Stainless Steel 316L St. St. Flexible Graphite Carbon Steel Rust Proofed ASTM A193 Gr. B7, Alloy St. ASTM A194 Gr. 2H, Alloy St. Carbon Steel Rust Proofed High Temp. Alloy Rust Proofed Soft Iron or Steel Soft Iron or Steel Soft Iron or Steel Soft Iron or Steel Stainless Steel Stainless Steel Steel

Also suitable for liquid service where ASME Code certif ication is not required.

3 9 11

10 21

2

17

14 20

8

17

23

15

22

18 1

19

13

6 16 4 7 26 5

12 24 25 27

Figure 10.4  Balanced nozzle safety relief valve, Balanseal® (By permission from Teledyne Farris Engineering Co.).

10.3 Rupture Disk A rupture disk is a non-reclosing thin diaphragm (metal, plastic, carbon/graphite (non-metallic)) held between flanges and designed to burst at a predetermined internal pressure. Each bursting requires the installation of a new disk. It is used in corrosive service, toxic or “leak-proof ” applications, and for required bursting pressures not easily accommodated by the conventional valve such as explosions. It is applicable to steam, gas, vapor, and liquid systems (Figures 10.7B, 10.8A-F). There are at least four basic types of styles of disks, and each requires specific design selection attention. An explosion rupture disc is a special disc (or disk) designed to rupture at high rates of pressure rise, such as runaway reactions. It requires special attention from the manufacturer [11]. Other rupture devices suitable for certain applications are [11]: a. b  reaking pin device b. shear pin device c. fusible plug device Set Pressure: The set pressure, in pounds per square inch gauge (barg), is the inlet pressure at which the safety or relief valve is adjusted to open [8, 9]. This pressure is set regardless of any back pressure on the discharge of the valve, and is not to be confused with a manufacturer’s spring setting. Overpressure: Pressure increase over the set pressure of the primary relieving device is overpressure. It is the same as accumulation when the relieving device is set at the maximum allowable working pressure (MAWP) of the vessel [8].

Process Safety and Pressure-Relieving Devices  1099 Set Pressure Adjustment Pilot Main Valve

Sense Diaphragm

Dome Feedback Piston Inlet Seat Outlet Seat

Piston

With no system pressure, the pilot inlet seat is open and outlet seat is closed. As pressure is admitted to the main valve inlet, it enters the pilot through a filter screen and is transmitted through passages in the feedback piston, past the inlet seat, into the main valve dome to close the main valve piston. As system pressure increases and approaches valve set pressure, it acts upward on the sense diaphragm, with the feedback piston moving upward to close the inlet seat, thus sealing in the main valve dome pressure, as the outlet seat is also closed. A small, further increase in system pressure opens the outlet seat, venting the main valve dome pressure. This reduced dome pressure acts on the unbalanced feedback piston to reduce feedback piston lift, tending to “lock in” the dome pressure. Thus, at any stable inlet pressure there will be no pilot flow (i.e. zero leakage)

As inlet pressure rises above set pressure, dome pressure reduction will be such as to provide modulating action of the main valve piston proportional to the process upset. The spool/feedback piston combination will move, responding to system pressure, to alternately allow pressure in the main valve dome to increase or decrease, thus moving the main valve piston to the exact lift that will keep system pressure constant at the required flow. Full main valve lift, and therefore full capacity, is achieved with 5% overpressure. As system pressure decreases below set pressure, the feedback piston moves downward and opens the inlet seat to admit system pressure to the dome, closing the main valve. Due to the extremely small pilot flow, the pilot on gas/vapor valves normally discharge to atmosphere through a weather and bug-proof fitting. Pilots for liquid service valves have their discharge piped to the main valve outlet.

Figure 10.5A  Pilot – operated safety relief valve (By permission from Anderson, Greenwood and Co.).

Accumulation: Pressure increase over the maximum allowable working pressure of the vessel during discharge through the safety or relief valve, expressed as a percentage of that pressure, pounds per square inch (bar), is called accumulation [8]. Blowdown: Blowdown is the difference between the set pressure and the reseating pressure of a safety or relief valve, expressed as a percent of the set pressure, or pounds per square inch (bar) [8]. Back Pressure: This is the pressure existing at the outlet or discharge connection of the pressure-relieving device, resulting from the pressure in the discharge system of the installed device [11]. This pressure may be only atmospheric if discharge is directly to atmosphere, or it may be some positive pressure due to pressure drops of flow of discharging vapors/gases (or liquids where applicable) in the pipe collection system or a common header, which in turn may be connected to a blowdown or flare system with definite back pressure conditions during flow, psig (gauge). The pressure drop during flow discharge from the safety relief valve is termed “built-up back pressure”. Burst Pressure: This is the inlet static pressure at which a rupture disk pressure-relieving device functions or opens to release internal pressure. Design Pressure: This is the pressure used in the vessel design to establish the minimum code permissible thickness for containing the pressure in pounds per square inch gauge (barg).

1100  Chemical Process Engineering

Main Valve

Dome

Pilot

TAG Piston Seal Seat

Pressure Pickup

Figure 10.5B  Safety relief valve mechanism as connected to a non-flow (zero flow) pilot safety valve (By permission from Anderson Greenwood and Co.).

P2

P2 P2

P1

AD> AN

P1 AN = FS - P2 (AD - AN)

Back Pressure Decreases Set Pressure

P2 P2 P2

P1 P1 AN = FS + P2 AN

Back Pressure increases Set Pressure

P2

Vented Bonnet

P2

DISK P2

P2

DISK

Vented Bonnet Vent

P2

P2 P1

P1 AN2 FS

Bellows Type

Vented Bellows

FS

Spring Bonnet

DISK P2

P2

B - BALANCED SAFETY VALVES

Balanced Disk and Vented Piston Type Spring FS

Disk Guide

Spring FS

Spring FS DISK

Vented Bonnet

Non-Vented Bonnet

PISTON

A - CONVENTIONAL SAFETY VALVES

Bonnet Vented to Atmosphere

AP = AN

P1

Set Press. P1 = FS = Spring Force

AB = AN

AN Nozzle Seat Area

Back Pressure Has Very Little Effect on Set Pressure Note: P1 = Valve Set-pressure P2 = Vent Line Back pressure FS = Force of Valve Spring AN = Nozzle Seat Area AP = Piston Face Area AB = Bellows Area AD = Valve Disc Area

Figure 10.6A  Effect of back pressure on set pressure of safety or safety relief valves (By permission from Recommended Practice for Design and Construction of Pressure – Relieving Systems in Refineries, API RP – 520, 5th. Ed., American Petroleum Institute (1990)).

Maximum Allowable Working Pressure (MAWP): This is the maximum pressure in pounds per square inch gauge (barg) permissible at the top of a completed vessel in its operating position for a specific designated temperature corresponding to the MAWP pressure. This pressure is calculated in accordance with the ASME code (Par. UG-98) [1] for all parts or elements of the vessel using closest next larger to calculated value nominal thickness (closest standard for steel plate) (see Par. UG-A22) but exclusive of any corrosion allowance or other thickness allowances for loadings (see ASME Par.-UG-22) on vessels other than pressure (e.g., extreme wind loadings for tall vessels). The MAWP is calculated using nominal standard steel plates (but could be other metal-use code stresses) thickness, using maximum vessel operating temperature for metal stress determinations. See Ref [1] Par. UG-98.

Process Safety and Pressure-Relieving Devices  1101

% of Set Pressure

100 80

Ope Clo

ning

sin

essure ing Pr Open Pressure Closing

100

Pres s

ure

gP res

100

Opening Pressure Closing Pressure

80

80

sur e

Conventional Valve

Balanced Valve

(b) Backpressure Increases Set Pressure

(c) Backpressure Has Little Effect on Set Pressure

Conventional Valve (a) Backpressure Decreases Set Pressure

% of Backpressure

Figure 10.6B  Diagram of approximate effects of back pressure on safety relief valve operation (Adapted by permission from Teledyne Farris Engineering Co.).

Example 10.1 Hypothetical Vessel Design, Carbon Steel Grade A-285, Gr C

Then

Normal operating: 45 psig at 600°F Design pressure: 65 psig at 700°F corres. to the 65 psig. Assume calculated thickness per ASME code Par. UG- 27: 0.43 in. Closest standard plate thickness to fabricate vessel is 0.50 in. with -0.01 in. and + 0.02 in. tolerances at mill. 1. U  sing 0.50 in. - 0.01 in. (tolerance) = 0.49 in. min. thickness. 2. Using 0.50 in. + 0.02 in. (tolerance) = 0.52 in. max. thickness.

Generally, for design purposes, with this type of tolerance, nominal thickness = 0.50 in. can be used for calculations. Now, using Par. UG-27, 0.50 in. thickness and ASME code stress at 750°F (estimated or extrapolated) per Par. UCS23 at 750°F, the maximum allowable stress in tension is 12,100 psi. Recalculate pressure (MAWP) using Par. UG-27 [1] For cylindrical shells under internal pressure: (1) Circumferential stress (longitudinal joint)

Pd = SEt/(Ri + 0.6t), psi = psig

(10.1)



(10.2)

t = PR/[SE − 0.6P]

where t = minimum actual plate thickness of shell, no corrosion, = 0.50ʹʹ Pd = design pressure, for this example equals the MAWP, psi Ri = inside radius of vessel, no corrosion allowance added, in. S = maximum allowable stress, psi, from Table UCS-23 E = joint efficiency for welded vessel joint, plate to plate to heads. See ASME Par. UW-12, nominal = 85% = 0.85 t = required thickness of shell, exclusive of corrosion allowance, inches (2) Longitudinal stress (circumferential joints).

1102  Chemical Process Engineering Pressure Vessel Requirements

Vessel Pressure

Typical Characteristics of Pressure Relief Valves

121

Maximum relieving pressure for f ire sizing

Maximum allowable accumulated pressure (f ire exposure only)

120

Maximum allowable accumulated pressure for multiple-valve installation (other than f ire exposure)

Multiple valves Maximum relieving pressure for process sizing

116 115

Maximum allowable accumulated pressure for single-valve installation (other than f ire exposure)

Maximum allowable working pressure or design pressure

Percent of maximum allowable working pressure (gauge)

Single valve Maximum relieving pressure for process sizing Maximum allowable set pressure for supplemental valves (f ire exposure)

110

Overpressure (maximum) Maximum allowable set pressure for additional valves (process)

105

100

Simmer (typical)

Maximum allowable set pressure for single valve Start to open Blowdown (typical) (see Note 6)

95 Closing pressure for a single valve Maximum expected operating pressure (see Notes 5 and 6)

Leak test pressure (typical)

90

85 Notes: 1. This figure conforms with the requirements of Section VIII of the ASME Boiler and Pressure Vessel Code. 2. The pressure conditions shown are for pressure-relief valves installed on a pressure vessel. 3. Allowable set-pressure tolerances will be in accordance with the applicable codes.

4. The maximum allowable working pressure is equal to or greater than the design pressure for a coincident design temperature. 5. The operating pressure may be higher or lower than 90. 6. Section VIII, Division 1, Appendix M, of the ASME Code should be referred to for guidance on blowdown and pressure differentials.

Figure 10.7A  Pressure level relationship for pressure – relief valve installed on a pressure vessel (vapor phase) Single valve (or more) used for process or supplemental valves for external fire (see labelling on chart) (Reprinted by permission from Sizing, Selection and Installation of Pressure Relieving Devices in Refineries, Part 1 “Sizing and Selection”, API RP-520, 5th ed., Jul 1990, American Petroleum Institute).

Pd = 2SEt /(R – 0.4t)

(10.3)



(10.4)

t = PR/[2SE + 0.4P]

The vessel shell wall thickness shall be the greater of Equation 10.2 or 10.4, or the pressure shall be the lower of Equation 10.1 or 10.3 [1].

Process Safety and Pressure-Relieving Devices  1103 Pressure Vessel Requirements

Vessel Pressure

Maximum allowable accumulated pressure (f ire exposure only)

Maximum allowable accumulated pressure for installation of a multiple rupture disk device (other than fire exposure)

Maximum allowable working pressure or design pressure (see Note 3)

Maximum expected operating pressure (see Notes 5 and 6)

121 120

Maximum relieving pressure for f ire sizing

116

Maximum relieving pressure for process sizing

115

Percent of maximum allowable working pressure (gauge)

Maximum allowable accumulated pressure for installation of a single rupture disk device (other than f ire exposure)

Typical Characteristics of a Rupture Disk Device

110

Multiple-rupture-disk device Single-rupture-disk device

Maximum allowable burst pressure for supplemental (f ire exposure) rupture disk device (see Note 6) Overpressure (maximum)

105

Maximum allowable burst pressure for additional rupture disk device (see Note 6)

100

Maximum allowable burst pressure for single rupture disk device (see Note 6)

95

90

85 Notes: 1. This f igure conforms with the requirements of Section VIII of the ASME Boiler and Pressure Vessel Code. 2. The pressure conditions shown are for rupture disk devices installed on a pressure vessel. 3. The margin between the maximum allowable working pressure and the operating pressure must be considered in the selection of a rupture disk.

4. The allowable burst-pressure tolerance will be in accordance with the applicable code. 5. The operating pressure may be higher or lower than 90 depending on the rupture disk design. 6. The stamped burst pressure of the rupture disk may be any pressure at or below the maximum allowable burst pressure.

Figure 10.7B  Pressure level relationships for rupture disk devices (Reprinted by permission from Sizing, Selection and Installation of Pressure Relieving Devices in Refineries, Part 1 “Sizing and Selection”, API RP-520, 5th ed., Jul 1990, American Petroleum Institute).

For the above example, assume calculated MAWP (above) = 80 psig. This is the maximum pressure that any safety relief valve can be set to open. For pressure levels for pressure relief valves referenced to this MAWP, see Figures 10.7A and B. Operating Pressure: This is the pressure, psig (barg), to which the vessel is expected to be subjected during normal or, the maximum probable pressure during upset operations. There is a difference between a pressure generated internally due to controlled rising vapor pressure (and corresponding temperature) and that

1104  Chemical Process Engineering

Figure 10.8A  Metal type frangible disk (above) with cross section (below) (Courtesy of Black, Sivalis and Bryson Safety Systems, Inc.).

Figure 10.8B  Standard rupture disk  A prebulged rupture disk available in a broad range of sizes, pressures, and metals (By permission from B.S. & B. Safety Systems, Inc.).

Figure 10.8C  Disk of Figure 10.8B after rupture. Note 30° angular seating in holder is standard for prebulged solid metal disk (By permission from B.S. & B. Safety Systems, Inc.).

Process Safety and Pressure-Relieving Devices  1105

Figure 10.8D  Disk of Figure 10.8B with an attached (underside) vacuum support to prevent premature rupture in service with possible less than atmospheric pressure on underside and/or pulsation service (By permission from B.S. & B. Safety Systems, Inc.).

Figure 10.8E  Rupture disk (top) with Teflon® or other corrosion-resistance film/sheet seal, an open retaining ring. For positive pressure only (By permission from Fike Metal Products Div., Fike Corporation, Blue Springs, MO).

Figure 10.8F(a)  Rupture disk (top), similar to Figure 10.8E, except a metal vacuum support is added (see Figure 10.8F(b)) (By permission from Fike Metal Products Div., Fike Corporation, Blue Springs, MO).

SLOTTED TOP SECTION

SEAL MEMBER

VACUUM SUPPORT

Figure 10.8F(b)  Cross section of disk assembly for Figure 23.8F(a) (By permission from Fike Metal Products Div., Fike Corporation, Blue Springs, MO).

1106  Chemical Process Engineering Features: • Isolates Safety Relief Valves • No Fragmentation • Operates up to 90% Rated Pressure • Can Withstand Full Vacuum without Supports • Available in Sizes 1¯ thru 36¯ • Wide material Availability • U.S. Patent Number 3,294,277

Unburst

Burst

Figure 10.8G  Reverse buckling® disk, showing top holder with knife blades (underside) that cut the disk at time of rupture (By permission, B. S., & B. Safety Systems, Inc.).

Figure 10.8H  Standard non-metal frangible disk (graphite); Teflon® coatings or linings are available on entire disk (By permission from Zook enterprises).

Armor

Rupture disc installation

Figure 10.8I  Armored graphite disk. Note: steel ring bonded to circumference of disk to increase safety in toxic or flammable services and improve reliability by preventing unequal piping stress from reaching the pressure membrane. Teflon® coatings or linings are available on the entire disk (By permission from Zook Enterprises).

Process Safety and Pressure-Relieving Devices  1107 generated due to an unexpected runaway reaction, where reliance must depend on the sudden release of pressure at a code conformance pressure/temperature. In this latter case, careful examination of the possible conditions for a runaway reaction should be made. This examination is usually without backup data or a firm basis for calculating possible maximum internal vessel pressure to establish a maximum operating pressure and from this, a design pressure.

10.4 Design Pressure of a Vessel This is the pressure established as a nominal maximum above th e expected process maximum operating pressure. This design pressure is based on experience/practice and suggests a percentage increase of the vessel design pressure above the expected maximum process operating pressure level. There is no code requirement for establishing the design pressure. Good judgment is important in selecting each of these pressures. See operating pressure description in above paragraph. Depending on the actual operating pressure level, the increase usually varies from a minimum of 10% higher or 25 psi, whichever is greater, to much higher increases. For instance, if the maximum expected operating pressure in a vessel is 150 psig, then experience might suggest that the design pressure be set for 187 to 200 psig. Other factors known regarding the possibility of a run-away reaction might suggest setting it at 275 psig. A good deal of thought needs to enter into this pressure level selection. (Also see section on explosions and DIERS technology in this chapter [12, 13].) Relieving Pressure: This is the pressure relief device’s set pressure plus accumulation or overpressure (see Figures 10.7A and 10.7B). For example, at a set pressure equal to the maximum allowable at the MAWP of the vessel of 100 psig, and for process internal vessel pressure, the pressure relief device would begin relieving at nominal 100 psig (actually begins to open at 98 psig, see figures above) and the device (valve) would be relieving at its maximum conditions at 110 psig (the 10 psig is termed the accumulation pressure) for a single valve installation, or 116 psig, for a multiple valve installation on the same vessel. These are all process situations, which do not have an external fire around the vessel (see External Fire discussion later in this chapter and Figures 10.7B, 10.32A, B for these allowable pressure levels) and in no case do the figures apply to a sudden explosion internally. Resealing Pressure: This is the pressure after valve opening under pressure that the internal static pressure falls to when there is no further leakage through the pressure relief valve (see Figure 10.7A). Closing Pressure: This is the pressure established as decreasing inlet pressures when the disk of the valve seats and there is no further tendency to open or close. Simmer: This is the audible or visible escape of fluid between the seat and disk of a pressure-relieving valve at an inlet static pressure below the popping pressure, but at no measurable capacity of flow (for compressible fluid service). Popping Pressure: This is the pressure at which the internal pressure in a vessel rises to a value that causes the inlet valve seat to begin to open and to continue in the opening direction to relieve the internal overpressure greater than the set pressure of the device (for compressible fluid service).

10.5 Materials of Construction Safety and Relief Valves; Pressure-Vacuum Relief Values For most process applications, the materials of construction can be accommodated to fit both the corrosive-erosive and mechanical strength requirements. Manufacturers have established standard materials, which will fit a large percentage of the applications, and often only a few parts need to be changed to adapt the valve to a corrosive service. Typical standard parts are (see Figures 10.3A, 10.3B and 10.4) as follows:

1108  Chemical Process Engineering Option 1 (typical only) Body

carbon steel, SA 216, gr. WCB

Nozzle

316 stainless steel

Disc/Seat

stainless steel

Blow Down Ring

300 Ser. stainless steel

Stem or Spindle

stainless steel

Spring

C.S. rust proof or high temp. alloy, rust proof

Bonnet

SA-216, Gr. WCB carbon steel

Bellows

316L stainless steel Option 2 (typical only)

Body

316 stainless steel

Nozzle

17-4 stainless steel or 316 stainless steel

Disc/Seat

Teflon, Kel-F, Vespel or Buna-N

Blow Down Ring

316 stainless steel

Stem or Spindle

17-4 stainless steel or 316 SS

Spring

316 stainless steel

Bonnet

316 stainless steel

Bellows

−

For pressure and temperature ratings, the manufacturers’ catalogs must be consulted. In high pressure and/or temperature, the materials are adjusted to the service. For chemical service the necessary parts are available in 3.5% nickel steel; monel; Hastelloy C; Stainless Type 316, 304, and so on; plastic coated bellows; nickel; silver; nickel plated springs and other workable materials. The designer must examine the specific valve selected for a service and evaluate the materials of construction in contact with the process as well as in contact or exposed to the vent or discharge system. Sometimes the corrosive nature of the materials in the vent system presents a serious corrosion and fouling problem on the back or discharge side of the valve while it is closed. For these special situations, properly designed rupture disks using corrosion-resistant materials can be installed both before the valve inlet as well as on the valve discharge. For these cases, refer to both the valve manufacturer and the rupture disk manufacturers. See later discussion of code requirements for this condition.

10.6 Rupture Disks Rupture disks are available in: 1. P  ractically all metals that can be worked into thin sheets, including lead, Monel, nickel, aluminum, silver, lnconel, 18-8 stainless steel, platinum, copper, Hastelloy and others. 2. Plastic coated metals, lead lined aluminum, lead lined copper. 3. Plastic seals of polyethylene, Kel-F®, and Teflon®. 4. Graphite, impregnated graphite or carbon. The selection of the material suitable for the service depends upon the corrosive nature of the fluid and its bursting characteristics in the pressure range under consideration. For low pressure, a single standard disk of some materials

Process Safety and Pressure-Relieving Devices  1109 would be too thin to handle and maintain its shape, as well as give a reasonable service life from the corrosion and fatigue standpoints. See section on Selection and Application.

General Code Requirements [1] It is essential that the ASME code requirements be understood by the designer and individual rating and specifying the installation details of the safety device. It is not sufficient to merely establish an orifice diameter, since process considerations which might cause overpressure must be thoroughly explored in order to establish the maximum relieving conditions. An abbreviated listing of the key rating provisions is given in paragraphs UG-125 through 135 of the ASME code, Section 8, Div. 1, for unfired pressure vessels [1]. 1. A  ll pressure vessels covered by Division 1 or 2 of Section VIII are to be provided with protective over pressure devices. There are exceptions covered by paragraph U-l of the code, and in order to omit a protective device this paragraph should be examined carefully. For example, vessels designed for above 3000 psi are not covered; also, vessels with < 120 gallons of water, vessels with inside diameter not over 6 inches (at any pressure), vessels having internal or external operating pressures not over 15 psig (regardless of size), and a few other conditions may not be subject to this code. 2. Unfired steam boilers must be protected. 3. Pressure relief must be adequate to prevent internal pressures from rising over 10% above the MAWP, except when the excess pressure is developed by external fire or other unforseen heat source (see design details in later paragraph). Papa [17] proposes an improved technique for relief sizing. (Also see Figures 10.7A and B.) 4. When a pressure vessel is exposed to external heat or fire, supplemental pressure relieving devices are required for this excessive pressure. These devices must have capacity to limit the overpressure to not more than 21% above the MAWP of the vessel (see Figures 10.7A and B). A single relieving device may be used to handle the capacities of paragraph UG-125 of the code, provided it meets the requirements of both conditions described. 5. Rupture disks may be used to satisfy the requirements of the code for conditions such as corrosion and polymer formations, which might make the safety/relief valve inoperative, or where small leakage by a safety valve cannot be tolerated. They are particularly helpful for internal explosion pressure release. 6. Liquid relief valves should be used for vessels that operate full of liquid.

Relief Mechanisms Reclosing Devices, Spring Loaded Safety and relief valves must be the direct spring-loaded type, and for pressure ranges noted below the code [1] requires the following: Set pressure

Max. spring reset referenced to set pressure*

≤250 psig

±10%

≥250 psig

±5%

*Marked on value.

The set pressure tolerances of pressure relief valves are not to exceed ±2 psi for pressures up to and including 70 psig and ±3% for pressures above 70 psig. Indirect operation of safety valves, for example, by pilot valve, is not acceptable

1110  Chemical Process Engineering unless the primary unloading valve will automatically open and will operate fully in accordance with design relieving capacity conditions if some essential part of the pilot or auxiliary device should fail [1]. The pilot valve is a self-actuated pressure relief valve that controls the main valve opening.

Non-Reclosing Pressure-Relieving Devices Rupture disks must have a specified bursting pressure at a specified temperature. There must be complete identification of the metallurgy (if metal) or other properties if graphite or plastic, and the disk must be guaranteed by the manufacturer to burst within ±5% of the specified bursting pressure at the rated temperature. The connection nozzle holding the disk must have a net cross-sectional area no less than that required for the designrated conditions of the disk. The certification of disk performance is to be based on actual bursting tests of two or more disks from a lot of the same material of the exact same size as the disk to be sold by the manufacturer. The holder for the test disks must be identical to the design, dimensions, and so on for the disk being certified (for details, see ASME code, Par. UG-127 [1]).

Pressure Settings and Design Basis Unfired steam boilers, that is, nominally termed “waste heat boilers” or “heat exchangers”, which generate steam by heat interchange with other fluids (see ASME code [1] Par. U-1 (g)), should be equipped with pressure-relieving devices required by the ASME Code, Section 1, as far as applicable; otherwise, use Par. UG-125. Vessels, which per Par. U-1(g), follow Par. UG-125ff are: 1. E  vaporators or heat exchangers 2. “Vessels in which steam is generated by the use of heat resulting from operation of a processing system containing a number of pressure vessels such as used in the manufacturer of chemical and petrochemical products” [1]. 3. Par. U-1 (h) “Pressure vessels or parts subject to direct firing from the combustion of any fuel, which are not within the scope of Sections I, III or IV, may be constructed in accordance with the rules of Section VIII, Div. I, Par. UW-2 (d)” [1]. To meet code requirements, the relieving device must be directly open to the system to be relieved, see Figures 10.9, 10.10 and 10.11. For Figures 10.9, 10.10 and 10.11, the rupture disk and the relief valve must be designed to handle the relieving capacity at the relieving temperature without allowing more than a 10% pressure build-up above the MAWP of the unfired pressure vessel (or corresponding overpressure for other code requirements). Figure 10.10 requires that the rupture disk be designed the same as for Figure 10.9, 10.12A and 10.12B and Figure 10.11 requires that the relief valve be the primary device and meets the process relief requirements; it may have additional capacity to accommodate such conditions as external fire, or this additional requirement may be installed in a separate relief valve or rupture disk as shown. Also, the separate rupture disk may be in a secondary function not covered by the code for such conditions as runaway reactions and internal explosion. For these conditions the setting of the rupture disk is left up to the designer, and may be higher than that for the usual relief. Of course, it should be set sufficiently below the rupture condition for the vessel or component in order to avoid a hazardous condition and meet Code requirements.

10.7 Unfired Pressure Vessels Only, But Not Fired or Unfired Steam Boilers Non-fire exposure Single pressure relief valve installation must be set to operate at a pressure not exceeding the MAWP of the vessel, Ref [1] Par. UG-134, but may be set to operate at pressures below the MAWP. The device must prevent the internal pressure from rising more than 10% above the MAWP.

Process Safety and Pressure-Relieving Devices  1111 SRV Excess f low *Metal rupture disk only. Disk set lower than SRV*

*Rupture disk set higher than SRV for emergency relief

SRV*

Tell-tale

Vessel

Vessel

(b)

(a)

Note:* All reliefs must conform to code. Low pressure rupture disk to prevent manifold contents from backf lowing into SRV

Rupture disk

To vent manifold

SRV

Vessel

(c)

Note: Rupture disk my also be installed here, see (a)

Vessel

(d)

Figure 10.9  Rupture disk installations.

Figure 10.9A  Non-metal frangible disk. Ruptured disk showing complete breakout of membrane (Courtesy of Frails Industries, Inc.).

1112  Chemical Process Engineering

Figure 10.9B  Standard non-metal frangible disk (graphite); Teflon® coatings or linings are available on entire disk (By permission from Zook enterprises).

Armor

Rupture dics installation

Figure 10.9C  Armored graphite disk. Note: steel ring bonded to circumference of disk to increase safety in toxic or flammable services and improve reliability by preventing unequal piping stresses from reaching the pressure membrane. Teflon® coatings or linings are available on the entire disk (By permission from Zook Enterprises).

For multiple pressure relief valves installation, if the required capacity is provided using more than one ­pressure-relieving device, (i) only one device must be set at or below the MAWP of the vessel, and, (ii) the additional device(s) may be set to open at higher pressures, but in no case at a pressure any higher than 105% of the MAWP. The combination of relieving valves must prevent the pressure from rising more than 16% above the MAWP. See ASME Ref [1] Par. UG-125C and G-1 and Par. UG-134a.

External Fire or Heat Exposure Only and Process Relief Valves to protect against excessive internal pressures must be set to operate at a pressure not in excess of 110% of the MAWP of the vessel (ASME Par. UG-134b). When valves are used to meet the requirements of both Par. UG-125(c) and UG-125c-(2); that is, both internal process pressure and external fire/heat requirements, the valve(s) must “be set to operate not over the MAWP of the vessel. For these conditions of the additional hazard of extreme fire or heat, supplemental” pressure-relieving devices must be installed to protect the vessel. The supplemental devices must be capable of preventing the pressures from rising more than 21% above the MAWP (Note: this is not the setting). The same pressure-relieving devices may be used to satisfy the capacity requirements of Par. UG-125c or C(1) and Par. UG-125c-(2) provided the pressure setting requirements of Par. UG-134(a) are met. See Par. (A) 1 and 2 above and see Figure 10.7A.

Process Safety and Pressure-Relieving Devices  1113

Vent side (lower pressure side)

Product side (higher pressure side)

Figure 10.9D  Protection against two different pressures from opposite directions using graphite disks, such as in closed storage tanks; particularly API-type to guard against failure of primary breathers, conservation vents, and so on. These require a differential of at least 10 psig between the two burst ratings, depending on diameters of disks (By permission from Continental Disk Corporation).

When pressure relief devices are intended primarily for protection against overpressure due to external fire or heat, have no permanent supply connection, and are used for storage at ambient temperature of non-refrigerated liquefied compressed gases, they are excluded from requirements of Par. UG-125c (1) and C (2), with specific provisions. See ASME code [1] for detailed references and conditions. • Vessels operating completely filled with liquid must be equipped with liquid relief valves, unless otherwise protected (Par. UG-125-3(g)). • Safety and safety relief valves for steam service should meet the requirements of ASME Par. UG-131 (b), Ref [1]. Note that the requirements for these valves are slightly different than for process type valves.

10.8 Relieving Capacity of Combinations of Safety Relief Valves and Rupture Disks or Non-Reclosure Devices (Reference ASME Code, Par. UG-127, U-132) Primary Relief A single rupture disk can be used as the only overpressure protection on a vessel or system (Figure 10.10). The disk must be stamped by the manufacturer with the guaranteed bursting pressure at a specific temperature. The disk must rupture within ±5% of its stamped bursting pressure at its specified burst temperature of operation. The expected burst temperature may need to be determined by calculation or extrapolation to be consistent with the selected pressure. The set burst pressure should be selected to permit a sufficiently wide margin between it and the vessels used or design operating pressure and temperature to avoid premature failure due to fatigue or creep of metal or plastic coatings.

1114  Chemical Process Engineering

FLOW

Std ANSI flange Flow arrow Gaskets

Optional TFE liner blocks water and dirt from disks in open vents. Std ANSI flange

FLOW

Flow arrow Gaskets

Duplex DUPLEX Disks extend corrosion resistance to highly oxidizing agents, halogens except free fluorine, and virtually all other corrosives. A sheet of PTFE is used as a barrier on the service side of the disk. Additionally, these disks are processed to accommodate temperatures up to 392°F without insulation.

Std ANSI flange

FLOW

Flow arrow

FLOW

Gaskets TFE liner

Std ANSI flange

FLOW

Flow arrow (2)

*Insulated INSULATED Disks are available in MONO, INVERTED, and DUPLEX styles to accommodate temperature exceeding 388–700°F. They are furnished as an attached unit as shown because the nameplate rating of the disk must be established at the cold face temperature of the insulation.

Gaskets

Std ANSI flange Flow arrow

FLOW

Insulation nameplate Gaskets (all included)

Std AAR vent

FLOW

(a)

(b)

Figure 10.9E (a) & (b)  Duplex and insulated disks (By permission from Zook Enterprises).

Process Safety and Pressure-Relieving Devices  1115

Figure 10.9F  For pressure ratings of 15 psig or lower, subject to internal vacuum conditions, a vacuum support is required that is an integral part of the rupture disk and cannot be added in the field (By permission from Falls Industries).

Figure 10.10  Safety valve and rupture disk installation using pressure rupturing disk on inlet to safety relief valve, and low pressure disk on valve discharge to protect against backflow/corrosion of fluid on valve discharge side, possibly discharge manifold (By permission from Fike Metal Products Div., Fike Corporation, Inc.).

1116  Chemical Process Engineering Pressure Gauge or Pressure Switch

Safety Relief Valve

Nozzle

Excess Flow Valve Safety Heads J-Bolt Test Pressure Connection

Rupture Disk

Flange

Figure 10.11  Rupture disk mounted beneath a pressure – relieving spring – loaded valve  A reverse buckling® disk arrangement is often recommended here (By permission from B. S. & B. Safety Systems, Inc.).

Vent

Flanges Gaskets (Soft Material such as Neoprene Rubber Preferred for Top Gasket.)

Rupture Disk

Vessel Nozzle Install Disk with Pressure Membrane up. When inverted, the Disk Bursts at about 65% Increase in Pressure. Disk Must be Positioned True Center of Vent Line and Nozzle. If Eccentric, Burst Characteristics Might Not Hold True.

Figure 10.12A  Installation of graphite rupture disk (Adapted by permission from Falls Industries, Inc.).

Vent

Flanges Graphite disk may be inverted Gaskets

Inverted graphite disk bursts at higher pressure than with flat surface on top.

Figure 10.12B  Inverted graphite disk bursts at higher pressure than with flat surface on top (Adapted by permission from Falls Industries, Inc.).

Process Safety and Pressure-Relieving Devices  1117

Selected Portions of ASME Pressure Vessel Code, Quoted by Permission [1] Section VIII, Division I Superscript = Footnote reference July 1, 1989 Edition in Code Figure No., for this text. Rupture Disk Devices, [44] Par UG-127 1. G  eneral a. Every rupture disk shall have a stamped bursting pressure within a manufacturing design range [11] at a specified disk temperature [18] and shall be marked with a lot number, and shall be guaranteed by its manufacturer to burst within 5% (plus or minus) of its stamped bursting pressure at the coincident disk temperature. 2. C  apacity Rating a. The calculated capacity rating of a rupture disk device shall not exceed a value based on the applicable theoretical formulas (see Par. UG-131) for the various media multiplied by K = coefficient = 0.62. The area A (square inches) in the theoretical formula shall be the minimum net area existing after burst [19]. 3. A  pplication of Rupture Disks a. A rupture disk device may be used as the sole pressure relieving device on a vessel. Note: When rupture disk devices are used, it is recommended that the design pressure of the vessel be sufficiently above the intended operating pressure to provide sufficient margin between operating pressure and rupture disk bursting pressure to prevent premature failure of the rupture disk due to fatigue or creep. Application of rupture disk devices to liquid service should be carefully evaluated to assure that the design of the rupture disk device and the dynamic energy of the system on which it is installed will result in sufficient opening of the disk. b. A rupture disk device may be installed between a pressure relief valve [20] and the vessel provided. (See Figure 10.10.) i. The combination of the spring loaded safety or safety relief valve and the rupture disk device is ample in capacity to meet the requirements of UG-133 (a) and (b). ii. The stamped capacity of a spring loaded safety or safety relief valve (nozzle type) when installed with a rupture disk device between the inlet of the valve and the vessel shall be multiplied by a factor of 0.80 of the rated relieving capacity of the valve alone, or alternatively, the capacity of such a combination shall be established in accordance with Par. 3 below. iii. The capacity of the combination of the rupture disk device and the spring loaded safety or safety relief valve may be established in accordance with the appropriate paragraphs of UG-132, Certification of Capacity of Safety Relief Valves in Combination with Nonreclosing Pressure Relief Devices. iv. The space between a rupture disk device and a safety or safety relief valve shall be provided with a pressure gauge, a try cock, free vent, or suitable telltale indicator. This arrangement permits detection of disk rupture or leakage [21]. v. The opening [22] provided through the disk, after burst, is sufficient to permit a flow equal to the capacity of the valve (Par. 2 and 3 above) and there is no chance of interference with proper functioning of the valve; but, in no case shall this area be less than 80% of the area of the inlet of the valve unless the capacity and functioning of the specific combination of rupture disk and valve been established by test in accordance with UG-132. Note that in lieu of testing, Par (b) 2 and (b) 3 above allow the use of a capacity factor of 0.80 as a multiplier on the stamped capacity of the spring-loaded safety relief valve (nozzle type). Some manufacturers test specific valve/rupture disk combinations and determine the actual capacity factor for the combination, and then use this for the net capacity determination. See Figures 10.9, 10.10, 10.11, 10.12, 10.13A and 10.13B. c. A rupture disk device may be installed on the outlet side [23] of a spring-loaded safety relief valve which is opened by direct action of the pressure in the vessel provided (Figure 10.12).

1118  Chemical Process Engineering Def ine Protected System

Locate Relief Devices

Def ine Overpressure Scenarios

Choose Relief Device Types

Acquire Data

Two-phase Flow?

Single-phase Flow?

Specify Design Basis

Design Relief System

Figure 10.13  The relief-device sizing procedures involves three steps [90].

1. Th  e valve is so designed that it will not fail to open at its proper pressure setting regardless of any back pressure that can accumulate between the valve disk and the rupture disk. The space between the valve disk and rupture disk shall be vented or drained to prevent accumulation of pressure due to a small amount of leakage from the valve [24]. 2. The valve is ample in capacity to meet the requirements of UG-133 (a) and (b). 3. The stamped bursting pressure of the rupture disk at the coincident disk temperature plus any pressure in the outlet piping shall not exceed the design pressure of the outlet portion of the safety or safety relief valve and any pipe or fitting between the valve and the rupture disk device. However, in no case shall the stamped bursting pressure of the rupture disk at the coincident operating temperature plus any pressure in the outlet piping exceed the maximum allowable working pressure of the safety or safety relief valve. 4. The opening provided through the rupture disk device after breakage is sufficient to permit a flow equal to the rated capacity of the attached safety or safety relief valve without exceeding the allowable overpressure. 5. Any piping beyond the rupture disk cannot be obstructed by the rupture disk or fragment. 6. The contents of the vessel are clean fluids, free from gumming or clogging matter, so that accumulation in the space between the valve inlet and the rupture disk (or in any other outlet that may be provided) will not clog the outlet. 7. The bonnet of the safety relief valve shall be vented to prevent accumulation of pressure.

Process Safety and Pressure-Relieving Devices  1119 Vent

Flanges

Gaskets (Soft Material such as Neoprene Rubber Preferred for Top Gasket.)

Rupture Disk

Vessel Nozzle Install Disk with Pressure Membrane up. When inverted, the Disk Bursts at about 65% Increase in Pressure. Disk Must be Positioned True Center of Vent Line and Nozzle. If Eccentric, Burst Characteristics Might Not Hold True.

Figure 10.13A  Installation of graphite rupture disk (Adapted by permission from Falls Industries, Inc.).

Vent

Flanges Graphite disk may be inverted Gaskets

Figure 10.13B  Inverted graphite disk bursts at higher pressure than with flat surface on top (Adapted by permission from Falls Industries, Inc.).

Footnotes to ASME Code 47. The minimum net flow area is the calculated net area after a complete burst of the disk with appropriate allowance for any structural members which may reduce the net flow through the rupture disk device. The net flow area for sizing purposes shall not exceed the nominal pipe size area of the rupture disk device. 48. Use of a rupture disk device in combination with a safety or safety relief valve shall be carefully evaluated to ensure that the media being handled and the valve operational characteristics will result in pop action of the valve coincident with the bursting of the rupture disk. 49. Users are warned that a rupture disk will not burst at its design pressure if back pressure builds up in the space between the disk and the safety or safety relief valve which will occur should leakage develop in the rupture disk due to corrosion or other cause. 50. This use of a rupture disk device in series with the safety or safety relief valve is permitted to minimize the loss by leakage through the valve of valuable or of noxious or otherwise hazardous materials and where a rupture disk alone or disk located on the inlet side of the valve is impracticable, or to prevent corrosive gases from a common discharge line from reaching the valve internals. 51. Users are warned that an ordinary spring-loaded safety relief valve will not open at its set pressure if back pressure builds up in the space between the valve and rupture disk. A specially designed valve is required, such as a diaphragm valve or a valve equipped with a bellows above the disk. (Source: Reprinted with ASME permission. ASME Pressure Vessel Code, Section VIII, Division I, UG-127, 1989 edition, pp. 86-88.)

1120  Chemical Process Engineering

10.9 Establishing Relieving or Set Pressures The pressure at which the valve is expected to open (set pressure) is usually selected as high as possible consistent with the effect of possible high pressure on the process as well as the containing vessel. Some reactions have a rapid increase in temperature when pressure increases, and this may fix the maximum allowable process pressure. In other situations, the pressure rise above operating must be kept to some differential, and the safety valve must relieve at the peak value. A set pressure at the maximum value (whether MAWP of vessel, or other, but insuring protection to the weakest part of the system) requires the smallest valve. Consult manufacturers for set pressure compensation (valve related) for temperatures >200°F (> 93.3 oC). When the pressure rise in a system is gradual and not “explosive” in nature, a safety or safety relief valve is the proper device, but when it is critical to completely depressurize a system or the rate of pressure increase might be expected to be rapid, then a rupture disk is the proper device. Properly designed, a pilot-operated valve may be selected after checking its performance with the manufacturer. Often a system (a group of vessels not capable of being isolated from each other by block valves, or containing restriction to flow and release of pressure) may need a relief valve set reasonably close, set 15% - 20% when system is below 1000 psig; above, typically use 7% - 15% above as set criteria related to normal operating pressure to catch any pressure upswing. Then this may have a backup valve set higher (but within code) to handle further pressure increase. Or, the second device may be a rupture disk. It is not unusual to have two relief devices on the same equipment set at different pressures. For situations where explosion may involve chemical liquid, vapor or dust; it is generally advisable to obtain rate of pressure rise data and peak explosion pressure data in order to intelligently establish the design parameters. Such data are available [25–32]; however, it is important to evaluate whether the conditions are comparable between the systems when selecting the values for design. In general, the lower the setting for pressure relief; the lower will be the final internal peak pressure in the vessel. It is extremely important to realize that the higher the system pressure before relief, the higher will be the peak pressure attained in the vessel. In some difficult cases it may be advisable to set relief devices at two pressures, one lower than the other. Each must be designed for the conditions expected when it relieves, and one or all must satisfy code requirements or be more conservative than the code. For pulsating service, the set pressure is usually set greater than the nominal 10% or 25 psig above the average operating pressure of the system in order to avoid unnecessary releases caused by surging pressure peaks, but still not exceeding the MAWP of the vessel/system. Careful analysis must be made of the proper set condition. Safety relief valves are available for relieving or set pressures as low as 2, 10, and 20 psig, as well as higher pressures. Lower pressures are available on special order. Usually, a more accurate relief is obtained from the higher pressures. Safety relief valves are normally tested in the shop, or even on the equipment at atmospheric temperature. The set tolerances on the valves as manufactured are established by the Code as discussed earlier. In order to recognize the difference between the test temperature and the actual operating temperature at actual relief, the corrections shown in Table 10.1A and 10.1B are applied. An increase in temperature above design causes a reduction in valve set pressure due to the effects of temperature on the spring and body. Testing of pressure-relieving spring-loaded valves at atmospheric temperature requires an adjustment in set pressure at ambient conditions to compensate for higher operating temperatures. For process services see Table 10.1A and for saturated steam, use Table 10.1B.

Safety and Safety Relief Valves for Steam Service Pressure-relieving devices in process plants for process and utility steam systems must conform to the requirements of ASME [1] Par. UG-131b. This is not necessarily satisfactory to meet the ASME Power Boiler Code for applications on power generating equipment.

Process Safety and Pressure-Relieving Devices  1121 Table 10.1A  Compensation factors for safety relief valves between atmospheric test temperatures and actual operating temperature [34]. Operating temperature oF

Percent increase in set pressure at atmospheric temperature

−450 − 200

None

201 − 450

2

451 − 900

3

901 − 1200

4

By permission, Teledyne Farris Engineering Corp., Cat. FE-316, p. 12.

Table 10.1B  Set Pressure compensation for saturated steam service safety-relief valves between atmospheric test temperature and actual operating temperature. Saturated steam pressure set pressure (psig)

% Increase in spring settling

10 − 100

2

101 − 300

3

301 − 1000

4

1001 − 3000

5

By permission, Teledyne Farris Engineering Corp., Cat. FE-316, p. 12.

Vessels or other pressure containing equipment that operates filled with liquid must be provided with liquid relief valves, unless protected otherwise [1]. Any liquid relief valve must be at least ½ in. in pipe size, [1] Par UG-128 (see [33]).

10.10 Selection and Application Causes of System Overpressure Figure 10.13, Operational Check Sheet [34], lists 16 possible causes of overpressure in a process system and Figures 10.14 and 10.14A show typical relief valve process data sheets. There are many others, and each system should be reviewed for its peculiarities. System evaluation is the heart of a realistic, safe and yet economical overpressure protection installation on any single equipment or any group of equipment. Solving formulas with the wrong basis and/ or data can be disastrous. The following should be reviewed: 1. 2. 3. 4.

t he sources of possible overpressure. maximum overpressure possible from all sources. maximum rate of volume increase at the burst pressure, and temperature at this condition. length of duration of overpressure.

10.11 Capacity Requirements Evaluation for Process Operation (Non-Fire) Each system and item of equipment should be examined for operational safety as set forth by specific plant area (and process fluids) requirements and the codes previously cited. The codes particularly [5a-d, 8-10] establish guides based on wide experience, and are sound requirements for design. Relief capacity is based on the most severe requirement of a system, including possible two-phase flow [13]. A system is generally equipment or groups of equipment which is

1122  Chemical Process Engineering

Figure 10.14  Safety valve design operational check sheet (Adapted and added to by permission from N.E. Sylvander and D. L. Klatz, Design and Construction of Pressure Relieving Systems, Univ. of Michigan, Ann Arbor (1948). Six items of overpressure list above by E. E. Ludwig [37] and from API Rec. Practice 521 (1982)).

isolated by shut-off valves. Within these isolated systems, a careful examination of the probable causes of overpressure is made [35]. Figures 10.15, 10.16 and 10.17 are suggested guides [34]. Capacities are calculated for conditions of temperature and pressure at actual state of discharge. Final discharge pressure is the set pressure plus overpressure. It must be emphasized that the determination of the anticipated maximum overpressure volume at a specified pressure and temperature is vital to a proper protection of the process system. The safety relief calculations should be performed at the actual worst conditions of the system, for example, at the allowable accumulated pressure and its corresponding process temperature. These can be tedious and perhaps time-consuming calculations, but they must not be “glossed” over but developed in a manner that accounts for the seriousness of the effort. They must be documented carefully and preserved permanently. The situation is just as critical, if not more so, for runaway reactions or reaction conditions that are not adequately known. They should be researched or investigated by laboratory testing for possible runaway conditions and then the kinetic and heat/pressure rise calculations should be performed, even if some assumptions must be made to

Process Safety and Pressure-Relieving Devices  1123

Figure 10.14A  Relief valve process data sheet.

establish a basis. Refer to later paragraphs and the American Institute of Chemical Engineers Design Institute for Emergency Relief (AIChE/DIERS) [13]. At the time of a vessel or pressure/vacuum system failure, the calculations for the effected pressure relief devices are always reviewed by plant management and the Occupational Safety and Health Administration (OSHA) inspectors. A few notes on causes of process system failures are noted below, with additional comments in API-521 [5a - d] [9]. Failure of Cooling Water: Assume all cooling media fail; determine relief capacity for the total vapors entering the vessel, including recycle streams (see [36] and [8]).

1124  Chemical Process Engineering Safety Valve SV-2

Safety Valve SV-1

Steam Exhaust Block valve

High Pressure Steam

Reducing Station Driven Equipment (Centrifugal Compressor Pump., etc) Steam Turbine Driver

Safety Valve Required to Protect Reducing Station. Discharge Pressure in Case of Valve Failure. SV-1 is Set at Slightly Above Downstream Pressure of Reducing Station, and Protects All Equipment Operating at this Pressure on Steam Header.

Safety Valve SV-2 is Set to Protect Discharge Side of Turbine, as it is Not Designed to Withstand Inlet Steam Pressure on Exhaust Side.

Figure 10.15  Safety valve protecting specific equipment operating.

Safety Valve

Block Valve

Driver

Inlet Positive Displacement Pump or Compressor

Figure 10.16  Safety valve in positive displacement system.

Reflux Failure: (a) At the top of a distillation column, the capacity is total overhead vapor [8], (b) when source of heat is in feed stream, the capacity is vapor quantity calculated in immediate feed zone [36], (c) when reboilers supply heat to system, the capacity is feed plus reboil vapors [36]. Each situation must be examined carefully. Blocked Outlets on Vessels: (a) For liquid, the capacity is the maximum pump-in rate. (b) For liquid-vapor system, the capacity is total entering vapor plus any generated in the vessel [8]. Blocked Outlets and Inlets: For systems, lines or vessels capable of being filled with liquid and heated by the sun or process heat require thermal relief to accommodate the liquid expansion (assuming vaporization is negligible).

Process Safety and Pressure-Relieving Devices  1125 A

Safety Valve

Condenser

B Receiver

To Pumps Distillation Column

This is acceptable as there is no block valve isolating any item. If a block valve installed at A, a safety valve would be required to protect condenser and receiver. If an additional block valve installed at B, a safety valve would be required for the condenser and also for the receiver.

Figure 10.17  System protected by safety valve on a distillation column.

Instrument Failure: Assume instrument control valves freeze or fail in open position (or closed, which ever is worse), determine the capacity for relief based on flows, temperatures, or pressures possible under these circumstances. The judicious selection of instrument failure sequence may eliminate or greatly reduce relief valve requirements. Equipment Failure: Pumps, tubes in heat exchangers and furnaces, turbine drivers and governor, compressor cylinder valves are examples of equipment which might fail and cause overpressure in the process. If an exchanger tube splits or develops a leak, a high-pressure fluid will enter the low side, over pressuring either the shell or the channels and associated system as the case may be. Vacuum: (a) Removal of liquid or vapor at greater rate than entering the vessel, the capacity is determined by the volume displaced. (b) Injecting cold liquid into hot (steamed out) vessel, the condensing steam will create vacuum, and must be relieved. Capacity is equivalent to vapor condensed. In-breathing and Out-breathing Pump In and Out: See section on Pressure-Vacuum Relief for Low Pressure Storage Tanks.

Installation Never place a block valve on the discharge side of a pressure relief device of any kind, except see [1] Par. U-135 (e). Never place a block valve on the inlet side of a pressure relief device of any kind, unless it conforms to the code practice for rupture disks or locking devices. See [1] Par. UG-135 (e) and Appendix M, ASME code. Note that the intent of the ASME code is to ensure that under those circumstances where a pressure-relieving device can be isolated by a block valve from its pressure, or its discharge, a responsible individual locks and unlocks the block valve to the safe open position and that this individual remains at the block valve the entire time that the block valve is closed. Safety (relief, or safety relief) valves are used for set pressures from 10 psig to 10,000 psig (0.69-690 bar) and even higher. At the low pressures, the sensitivity to relieving pressure is not always as good as is required for some processes, and for this reason most valve installations start at 15 to 20 psig (1.03 – 1.38 bar). Figures 10.9 and 10.18 illustrate a few typical safety valve installations. Care must be shown in designing any manifold discharge headers collecting the vents from several valves. Sharp bends are to be avoided. Often two or more

1126  Chemical Process Engineering collection systems are used in order to avoid discharging a high-pressure valve into the same header with a low-­ pressure valve. The simultaneous discharge of both valves might create too great a back pressure on the low-pressure valve, unless adequate arrangement has been made in the valve design and selection. The balanced safety relief valve can overcome most of the problems of this system. Whenever possible the individual installation of valves is preferred, and these should be connected directly to the vessel or pipe line [1, 37]. If a block-type valve is considered necessary for a single valve installation, it must be of the full open type, and locked open with the key in responsible hands, as stated earlier. Dual installations are frequently made in continuous processes, to allow switching from one valve to another without shutdown of the pressure system. A special three-way plug of full open type is installed directly on the vessel, and the safety valves are attached to it with short piping (Figure 10.18). The three-way valve ensures that one side of the safety valve pair is always connected to the vessel, as this pattern valve does not have a blind point during switching. (Also, see Figure 10.19.) One of the important justifications for this dual arrangement is that safety relief valves may leak on reseating after discharging. This leak may be caused by a solid particle lodged on the seat. This valve can be removed for repair and cleaning after the process has been switched to the second valve. Each valve must be capable of relieving the full process requirements. Multiple valves may also be individually installed separately on a vessel. Figure 10.19A shows a photo of a relief valve installed horizontally. Figure 10.19 illustrates a newer approach at simplifying the dual safety relief valve installation, ASME Sect. VIII, Div. 1, UG-135(b) [1] and API RP-520, Part II Conformance [5]. Note that the SRV valves are mounted on top of each of one dual vertical connection and are bubble tight. Also see cross section view. The flow Cv valves for each size device are available from the manufacturer. The Anderson Greenwood & Co. (AGCO) Safety Selector Valve body houses a uniquely designed switching ­mechanism. The internal rotor smoothly diverts flow to either safety relief valve. Conventional direct spring-­operated valves or pilot-operated valves may be used. The inactive valve is totally isolated by external adjustment. To begin the switchover, the retraction bushing is rotated to its stop. This separates the isolation disk from the standby valve channel and temporarily “floats” it in the main valve cavity. The index shaft is then rotated 180o to the alternate channel. The retraction bushing is then returned to its original position, securely seating the isolation disk beneath the valve taken out of service. A red pointer indicates which valve is in service and double padlocking provisions allow the safety selector valve to be locked in either safety relief valve position. The padlocks or car seals can only be installed with the internals in the proper position. No special tools are necessary for switching. Pivot Lid

Vent or Discharge Header

Interconnected Locking Device Free−Opening To Manifold Covered Discharge

Dual or Duplicate Safety Relief Valves Safety relief valves

Safety Relief Valve SRV

Inlet

Full-open Gate Valve 3-way Plug Valve Locked open

Liquid Drain Hole

Vessel Or Pipe Discharge, Alternate Arrangements

Figure 10.18  Safety relief valve installations.

Special 3-way Plugs or Fullyopen Gate valve

Locked positions

Vessel Or Pipe

Vessel Or Pipe

Inlet, Alternate Arrangements

Vessel

Vessel

Process Safety and Pressure-Relieving Devices  1127

(a) Retraction Bushing

Index Shaft

Indicator A

Isolated Valve

Flow

A

Field Test Connection and Bleed Port for standby SRV

Active

Less than 3% pressure loss at rated f low

Body

Spare

Rotor Base Isolation Disc (Soft Seated) Companion Inlet Flange (By others)

(b)

Figure 10.19  Safety selector valve for dual relief valve installation with switching (By permission from Anderson, Greenwood and Co.® AGGO.).

Figure 10.19A  Relief valve installed horizontally. The markings on the bonnet result from the spring working its way out (Source: Chris Flower and Adam Wills, The Chemical Engineer, U.K., pp. 24-31, June 2017).

1128  Chemical Process Engineering Weather cap (may be required)

Pressurerelief valve

If pressure-relief valve is connected to a closed system, care should be taken to keep piping strains away from the valve under all conditions of process operation

Support to resist weight and reaction forces Long-radius elbow Pressurerelief valve

Pressure drop not more than 3 percent of set pressure

Body drain Pressure drop not more than 3 percent of set pressure

Purge or vent valve may be required at stop valve or in spool piece See note

Vessel

Optional low-point drain

Vessel

Nominal pipe diameter no less than valve inlet size

Note: The stop valve must have a full port area greater than or equal to the inlet size of the pressure-relief valve. The stop valve should be used only as permitted by the applicable codes.

Typical pressure-relief valve without a stop valve

TYpical pressure-relief valve with a stop valve Pressurerelief valve

Discharge piping

Inlet piping sized so that pressure drop from vessel to pressure-relief valve inlet flange does not exceed 3 percent of valve set pressure

Vessel Typical pressure-relief valve mounted on process line

Typical pressure-relief valve mounted on long inlet pipe

Figure 10.20A  Recommended API – 520 piping for safety relief valve installations (Reprinted by permission from American Petroleum Institute, Sizing, Selection and Installation of Pressure Relieving Devices in Refineries, Part II – Installations, API RP – 520, 3rd. ed., Nov. 1988).

Pilot valve Main valve Integral pressure pickup

Optional remote pressure pickup

Figure 10.20B  Typical pilot – operated pressure relief valve installation.

Process Safety and Pressure-Relieving Devices  1129 F Ao (cross-sectional area)

Vent pipe

Long-radius elbow

Pressurerelief valve Free support to resist weight and reaction forces Vessel

Figure 10.20C  Typical pressure – relief valve installation with vent pipe. Pressure-relief valve Process laterals should generally not be connected to pressure-relief valve inlet piping

Vessel

Figure 10.20D  Typical installation avoiding process laterals connected to pressure-relief valve inlet piping.

The alternate concept which has been in use for many years is to fabricate or purchase a tee connection upon which the two safety relief valves can be mounted on top of their full-port plug or gate valve with required locking lugs. Rupture disks are often used in conjunction with safety valves as shown in Figures 10.9, 10.10, 10.11, and 10.18. Inlet piping is held to a minimum, with the safety device preferably mounted directly on the equipment and with the total system pressure drop loss to pressure relief valve inlet not exceeding 3% of the set pressure in psig, of maximum relief flowing conditions [8]. To conform to the code (see ASME code, Sect. VIII, Div. 1-UG-127 [1]) avoid high inlet pressure drop and possible valve chatter: 1. N  ever make pipe connection smaller than valve or disk inlet. 2. Keep friction pressure drop very low, not over 1 to 2% of allowable pressure for capacity relief [1, 5, 8, 34, 37]. 3. Velocity head loss should be low, not over 2% of allowable pressure for capacity relief [34]. Discharge piping must be sized for low pressure drop at maximum flow not only from anyone valve, but for the combined flow possibilities in the discharge collection manifold all the way to the vent release point, whether it be a flare, incinerator, absorber or other arrangement [9]. (See Figures 10.20A-F.)

1130  Chemical Process Engineering

Pressure gauge

Excess f low valve (optional) Bleed valve (may be car-sealed open)

Figure 10.20E  Typical rupture disk assembly installed in combination with a pressure – relief valve.

Conventional safety relief valves, as usually installed, produce unsatisfactory performance when variable back pressure exists [5, 8] (see Figure 10.6). Additionally, the same variable back pressure forces affect the set pressure release. At low back pressures, the valve flow falls rapidly as compared with the flow for a theoretical nozzle (see Figures 10.19 and 10.20A-H) [5a]. For conventional valves, pressure drop or variations in back pressure should not exceed 10% of set pressure. Because most process safety valves are sized for critical pressure conditions, the piping must accommodate the capacity required for valve relief and not have the pressure at the end of vent or manifold exceed the critical pressure. Designing for pressure 30% to 40% of critical with balanced valves, yields smaller pipes yet allows proper functioning of the valve. The discharge line size must not be smaller than the valve discharge. Check the manufacturer for valve performance under particular conditions, especially with balanced valves which can handle 70 - 80% of set pressure as back pressure. For non-critical flow the maximum back pressure must be set and pressure drop calculated by the usual friction equations (see Chapter 3). When process conditions permit, the low-pressure range is handled by bursting disks which will relieve down to 2 psig. These disks are also used up to 100,000 psig and above. The rupture pressures and manufacturing ranges of metal disks are given in Tables 10.2 and 10.3. For non-metallic materials such as graphite, bursting pressures are available from the manufacturers. From these manufacturing tolerances it can be seen that the relation of disk bursting pressure to the required relieving pressure must be carefully considered. Manufacturing practice is to furnish a disk, which will burst within a range of pressures and tolerances, and whose rated pressure is the result of bursting tests of representative sample disks which burst within the range specified. The engineer should specify only ASME code certified disks. It is not possible to obtain a disk for the usual process application set to burst at a given pressure,

Process Safety and Pressure-Relieving Devices  1131

Inlet f langes Inlet pipe Branch connection

Run pipe

Not less than 10 pipe diameters from any device that causes turbulence

Figure 10.20F  Typical installation avoiding excessive turbulence at pressure – relief valve inlet.

Figure 10.20G  Inlet piping expanding into the relief valve. Incorrect installation may lead to valves chattering (Source: Chris Flower and Adam Wills, The Chemical Engineer, U.K., pp. 24-31, June 2017).

as is the relieving pressure of a safety valve. An increase in temperature above the disk rating temperature (72°F) decreases the bursting pressure 70-90% depending upon the metal and temperature (see Tables 10.4A and B). The minimum rupture pressure of disks of various metals and combinations varies so widely that individual manufacturer must be consulted.

1132  Chemical Process Engineering

Figure 10.20H  An unrestrained metal cover placed over an outlet pipe could become a missile (Source: Chris Flower and Adam Wills, The Chemical Engineer, U.K., pp. 24-31, June 2017).

Table 10.2  Typical prebulged solid metal disk manufacturing ranges and tolerances at 72oF. Manufacturing range (%) Specified burst pressure rating, psig

Under

Over

Rated (stamped) burst tolerance %

2–5

–40

+40

± 25

6–8

–40

+40

± 20

9 – 12

–30

+30

± 15

13 – 14

–10

+20

± 10

15 – 19

–10

+20

±5

20 – 50

–4

+14

±5

51 – 100

–4

+10

±5

101 – 500

–4

+7

±5

501 – up

–3

+6

±5

Note: 1. Special reduced manufacturing ranges can be obtained for the STD prebulged metal disk, ¼, ½, and ¾ ranges are available upon request. Please consult your representative or the factory for additional information. 2. Burst tolerances are the maximum expected variation from the disk’s rated (stamped) burst pressure. 3. Standard–type rupture disk comply with ASME code requirements. Manufacturing Range The manufacturing range is defined as the allowable pressure range within which a rupture disk is rated. It is based upon the customer specified burst pressure. The manufacturing ranges for Continental’s standard rupture disk are outlined in this table. Burst Tolerance After the disk has been manufactured and tested, it is stamped with the rated burst pressure. The rated (stamped) burst pressure is established by bursting a minimum of two disks and averaging the pressures at which the disks burst. This average is the rated (stamped) burst pressure of the disk. Standard rupture disks above 15 psig at 72oF are provided with a burst tolerance of ±5% of the rated (stamped) burst pressure. This is in accordance with the ASME code. Burst tolerances for disks below 15 psig at 72oF are outlined in this table. Burst tolerance applies only to the rated (stamped) burst pressure of the disk. Burst certificates are provided with each disk lot. By permission, Continental Disk Corporation, Catalog STD–1184.

Process Safety and Pressure-Relieving Devices  1133 Table 10.3  Typical metal disk (single) bursting pressures at 72oF using different metals. Disk minimum burst pressure (psig) (without liners) Size (in.)

Alum

Silver

Nickel

Monel

Inconel

316SS

¼

160

450

600

700

1120

1550

½

65

220

300

350

560

760

1

29

120

150

180

250

420

1½

22

80

100

116

160

275

2

13

48

60

70

110

150

3

10

35

45

50

80

117

4

7

26

35

40

70

90

6

5

20

25

30

47

62

8

4

15

20

23

34

51

10

4

–

16

17

30

43

12

3

–

13

15

25

36

14

3

–

11

13

21

31

16

3

–

10

12

19

28

18

3

–

9

11

17

24

20

3

–

8

9

16

22

24

3

–

–

–

–

–

30

–

–

–

–

–

–

36

–

–

–

–

–

–

(–) = Consult factory. *Special designs of some manufacturers may exceed 150,000 psi for small sizes. The pressures listed are generally typical but certainly not the only ones available for the size shown. Note: 1. Maximum burst pressure depends upon disk size and application temperature. Pressures to 80,000* psig are available. 2. Other materials and sizes are available upon request. 3. Other liner materials are available upon request. Minimum burst pressures will change with change in liner material. 4. For larger sizes or sizes not shown, consult your representative, or the factory. Courtesy, Continental Disk Corp., Bul. 1184, p. 4–5.

For the usual installation, the rupture disk is installed as a single item between special flanges which hold the edges securely and prevent pulling and leakage. If the system is subject to vacuum or pressure surges, a vacuum support must be added to prevent collapse of the sealing disk. The flanges which hold the disk may be slip-on, weld neck, and so on. Disks to fit screwed and union-type connections are also available (see Figures 10.7 and 10.8). The service life of a rupture disk is difficult to predict, since corrosion, cycling pressures, temperature and other process conditions can all affect the useful life and cause premature failure. A graphite-type disk is shown in Figure 10.8. In some processes, it is safer to replace disks on a schedule after the life factor has been established, as a planned shutdown is certainly less costly than an emergency one.

1134  Chemical Process Engineering Table 10.4A  Typical recommended maximum temperatures for metals used in disks. Metals

Maximum temperature, (oF)

Aluminum

250 – 260

Silver

250 – 260

Nickel

750 – 800

Monel

800

Inconel

900 – 1000

316 Stainless Steel

900

Source: Various manufacturers’ technical catalogs.

Table 10.4B  Typical recommended maximum temperatures for linings and coatings with metals used with disks. Metal

Maximum temperature (oF)

Teflon®FEP Plastic

400

Polyvinylchloride

150 – 180

Lead

250

Source: Various manufacturers’ technical catalogs.

Rupture disks are often placed below a safety valve to prevent corrosive, tarring or other material from entering the valve nozzle. Only disks which do not disintegrate when they burst (Figures 10.9, 10.10, 10.11, and 10.18) can be used below a safety valve, as foreign pieces which enter the valve might render it useless. This is acceptable to certain code applications [1]. These disks are also used to provide secondary relief when in parallel with safety valves set at lower pressures. They can also be installed on the discharge of a safety valve to prevent loss of hazardous vapors, but caution should be used in any serious situation.

10.12 Selection Features: Safety, Safety Relief Valves, and Rupture Disks Referring to the description and definitions in the introduction for this chapter, it is important to recognize that in order to accomplish the required pressure relief the proper selection and application of device type is essential. Safety Valve: This is normally used for steam service, but is suitable for gases or vapors. When used in steam generation and process steam service the valves conform to the ASME Power Boiler Code as well as the ASME Pressure Vessel Code, Section VIII, and are tested at capacity by the National Board of Boiler and Pressure Vessel Inspectors. This type of valve characteristically “pops” full open and remains open as long as the overpressure exists. Relief Valve: This is normally selected for liquid relief service such as hydraulic systems, fire and liquid pumps, marine services, liquefied gases, and other total liquid applications. The valve characteristically opens on overpressure to relieve its rated capacity, and then reseats. Safety Relief Valve: This is normally selected for vapors and gases as may be found in all types of industrial processes. Characteristically, this valve will open only enough to allow the pressure to drop below the set pressure, and then it will reseat until additional overpressure develops. If the pressure persists or increases, then the valve will remain open or increase its opening up to the maximum design, but as the pressure falls the valve follows by closing down until it is fully reseated. However, as in any installation of any “safety” type valve, the valve may not reseat completely gas tight. In such cases it may be necessary to switch to a stand-by valve and remove the leaking valve for repair (see Figures 10.7A and 10.7B).

Process Safety and Pressure-Relieving Devices  1135 Special Valves: Because of the difficult and special sealing requirements of some fluids such as chlorine and Dowtherm, special valves have been developed to handle the requirements. Vacuum Relief and Combined Pressure-Vacuum Relief for Low-Pressure Conditions: This is normally used for low pressures such as 1-ounce water to 1.5 psig above atmospheric by special spring or dead weight loading; and for vacuum protection such as 0.5 psi below atmospheric. Usually these conditions are encountered in large process – that is, processing of crude oil, ammonia, and so on – storage tanks. Rupture Disks: This is used for low- as well as high-pressure protection of vessels and pipelines where sudden and total release of overpressure is required. Once the disk has ruptured, the process system is exposed to the environment of the backpressure of the discharge system, whether atmospheric or other. The process system is depressurized and the disk must be replaced before the process can be restarted. Typically, the types of disks available are as follows: 1. S olid metal rupture disk (Figure 10.8). This is the original type of rupture device, available in various metals and non-metals. It should normally not be used for operating pressures greater than 70% of rupture pressure in a non-corrosive environment. The metal disks are designed with a domed or hemispherical shape, with pressure on the concave side. As the pressure internally increases, the metal wall thins as the metal stretches to achieve a smaller radius of curvature. After the wall has thinned sufficiently, it will burst to relieve the pressure and tension loading on the metal. The accuracy of metal disks is ±5%, except for the Reverse Buckling Disk Assembly, which is ±2%. The usual recommended maximum operating temperatures for metal rupture disks is given in Tables 10.4A and B. a. Solid metal disk with vacuum support: When vacuum can occur internally in the system, or when external pressure on the convex side of the disk can be greater than the pressure on the concave side of the disk, a vacuum support is necessary to prevent reversal of the disk, Figure 10.8D. b. Solid metal disk with rating near minimum for size: With a rating pressure near the minimum available for the size and material of construction a special thin disk is attached to the lower and possibly the upper sides of the rupture disk to ensure freedom from deformity caused by the condition of the disk holding surfaces, Figure 10.8E. There are several versions of what to include under such conditions, therefore it is advisable to clearly explain the installation conditions and application to the manufacturer. c. Composite rupture disk: This type consists of a metal disk (not necessarily solid, it may have slots) protected by an inner and/or an outer membrane seal, Figure 10.8E. There are several possible arrangements, including vacuum support, as for the styles of paragraph (b) above. This general class has the same use-rating limitation as for the solid disk. d. Reverse acting or buckling disk assembly: This design allows the disk to be operated in a system at up to 90% of its rated burst pressure. The pressure is operating on the convex side of the disk and when bursting pressure is reached, the disk being in compression reverses with a snap action at which time the four knife edges (Figure 10.8G) cut the metal and it clearly folds back without fragmentation. There is another version of the same concept of reverse buckling, but it uses a pre-scored disk and thereby omits the knife blades. These types of disks do not need vacuum supports, unless there is unusually high differential pressure across the disk. 2. G  raphite Rupture Disk (Figure 10.9). There are special designs of disks and disk assemblies for specific applications, and the manufacturer should be consulted for his recommendation. Disks are available for pressure service, pressure-vacuum applications, high-temperature conditions, and close tolerance bursting conditions. The bursting accuracy of most designs is ±5% for rated pressures above 15 psig and ±0.75 psig for rated pressures 14 psig and below. It should be noted that these ratings are not affected by temperature up to 300°F. A new concept in graphite disks includes addition of a fluorocarbon film barrier between the process and the disk, and is termed a duplex disk. These disks are suitable for temperatures to 392°F, with accuracies as just mentioned.

1136  Chemical Process Engineering Graphite disks are normally used in corrosive services and/or high-temperature situations where metal wall thickness and corrosion rates make the metal units impractical because of unpredictable life cycles. The disks are available down to 1 psig ±0.75 psig, and are not affected by fatigue cracking. An interesting feature is the use of standard ASA (ANSI) flanges rather than special flanges (see Figure 10.8I). It is important to recognize here also that once the disk bursts the system is depressured, and there will be fragments of graphite blown out with the venting system. Special discharge designs are often used to prevent plugging of discharge pipe and fragments from being sprayed into the surrounding environment.

10.13 Calculations of Relieving Areas: Safety and Relief Valves References to the ASME Code [1] and the API Code [5, 8] are recommended in order that the design engineer may be thoroughly aware of the many details and special situations that must be recognized in the final sizing and selection of a pressure-relieving device. All details of these codes cannot be repeated here; however, the usually important requirements are included for the typical chemical and petrochemical application for the guidance of the engineer. Before performing sizing/design of relief valves calculations, a thorough examination of the possible causes and flow conditions of temperature and pressure should be determined. From this list, select the most probable and perhaps the worst-case possibility and establish it as a design basis, Figures 10.14 and 10.14A [38]. When the possibilities of internal explosion or a runaway chemical reaction exists, or are even suspected, they must also be rigorously examined and calculations performed to establish the magnitude of the flow, pressure, and temperature problems. Select the worst condition and plan to provide for its proper release to prevent rupture of equipment. This latter situation can only be handled by application of rupture disks and/or remote sensing and predetermined rupture of the disks (see Figures 10.5A, 10.8K and 10.8L) or remote sensing and application of quenching of the reaction/developing explosive condition by automatic process action and/or commercial application of quenching medium.

10.14 Standard Pressure Relief Valves Relief Area Discharge Openings The “orifice” area of these devices (see table below) is at the outlet end of the SRV nozzle through which the discharging vapor/gases/liquids must pass. These values are identified in industry as: (valve body inlet size in.) × (orifice letter) × (valve body outlet size, in.). For example, a valve would be designated 3E4. The standard orifice area designations are (also refer to mechanical illustrations of valves, previously shown in this chapter): Orifice letter

D

E

F

G

H

J

Area, sq. in.

0.11

0.196

0.307

0.503

0.785

1.287

Area, sq. cm2

0.71

1.27

1.98

3.25

5.06

8.30

Orifice letter

K

L

M

N

P

Q

Area, sq. in.

1.838

2.853

3.600

4.340

6.380

11.05

Area, sq. cm2

11.85

18.4

23.2

28.0

41.20

71.30

Orifice letter

R

T

V*

W

W2*

X*

Process Safety and Pressure-Relieving Devices  1137 Area, sq. in.

16.0

26.0

Area, sq. cm2

103.20

167.70

42.19

57.26

93.6

101.8

AA

BB

BB2

60.75 Orifice letter

Y*

Z*

Area, sq. in.

128.8

159.0

-

-

-

-

82.68

90.95

108.86

136.69

168.74 185.0

*Note: These letters and orifice areas are not consistent for these large orifices between various manufacturers. Some sizes go to 185 in2., which is a very large valve. When two valves are shown, they represent two different published values by manufacturers.

10.15 Sizing Safety Relief Type Devices for Required Flow Area at Time of Relief Before initiating any calculations, it is necessary to establish the general category of the pressure relief valve being considered. This section covers conventional and balanced spring-loaded types. Given the rate of fluid flow to be relieved, the usual procedure is to first calculate the minimum area required in the valve orifice for the conditions contained in one of the following equations. In the case of steam, air or water, the selection of an orifice may be made directly from the capacity tables if so desired. In either case, the second step is to select the specific type of valve that meets the pressure and temperature requirements. General equations are given first to identify the basic terms which correlate with ASME Pressure Vessel Code, Section VIII. It is recommended that computations of relieving loads avoid cascading of safety factors or multiple contingencies beyond the reasonable flow required to protect the pressure vessel.*

10.16 Effects of Two-Phase Vapor-Liquid Mixture on Relief Valve Capacity Many process systems where conditions for safety relief valve discharge are not single phase of all liquid (through the valve) or all vapor, but a mixture either inside the “containing” vessel or quite often as the fluid passes through the valve orifice; the liquid flashes to partial vapor, or the flashing starts just ahead of the orifice. Here, a mixture attempts to pass through the orifice, and the size must be sufficient or a restriction will exist and pressure will build up in the vessel due to inadequate relief. This problem was of considerable concern to the Design Institute for Emergency Relief of the American Institute of Chemical Engineers during their studies [13]. As a result, considerable research was performed leading to design techniques to handle this problem. A review of two-phase relief shall be presented. Also see Leung [39] for detailed procedure and additional references.

10.17 Sizing for Gases or Vapors or Liquids for Conventional Valves with Constant Backpressure Only This type of valve may be used when the variations in backpressure on the valve discharge connection do not exceed 10% of the valve set pressure, and provided this back pressure variation does not adversely affect the set pressure.

*Extracted by permission from Teledyne-Farris Engineering Catalog.

Ar C6H6 C4H10

iC4 nC4 iC4 nC4

4. Argon

5. Benzene

6. Iso–Butane

7. n–Butane

8. Iso–Butylene

9. Butylene

– Cl2 – C10H22

nC10 C2

12. Carbureted Water Gas (3)

13. Chlorine

14. Coke Oven Gas (3)

15. n–Decane

16. Ethane

nC6

23. n–Hexane

CH4

26. Methane CH3OH

H2S

25. Hydrogen Sulfide

27. Methyl Alcohol

H2

24. Hydrogen

C

C7H16

nC7

22. n–Heptane C6H14

He

21. Helium

C2H4

19. Ethylene –

C2H4Cl

18. Ethyl Chloride

20. Flue Gas (2)

C2H5OH

17. Ethyl Alcohol

C2

CO

11. Carbon Monoxide

C2H6

CO2

10. Carbon Dioxide

C4H8

C4H10

C4H8

NH3

C2H2

3. Ammonia

1. Acetylene

Chemical formula

N2+O2

C2

Gases and vapors

2. Air

Hydrocarbons reference symbols

Table 10.5  Properties of gases and vapors.

32.04

16.04

34.08

2.02

86.17

100.20

4.00

30.00

28.05

64.52

46.07

30.07

142.28

11.16

70.91

19.48

28.01

44.01

56.10

56.10

58.12

58.12

78.11

39.94

17.03

28.29

26.04

Mol. wt.

48.3

96.4

45.3

765.0

17.9

15.4

386.0

51.5

55.1

23.9

33.5

51.5

10.9

138.5

21.8

79.5

55.1

35.1

27.5

27.5

26.6

26.6

19.8

38.7

90.8

53.3

59.5

R = 1545/ mol. wt.

1157

673

1306

188

434

397

33

563

749

764

927

708

312

407

1119

454

514

1073

583

580

551

529

714

705

1657

547

905

Pressure (Psia)

924

344

673

60

915

973

9

265

510

829

930

550

1115

197

751

235

242

548

756

753

766

735

1013

272

731

239

557

Temperature (oR)

Critical conditions

148.1

–258.8

–76.5

–423.0

155.7

209.2

–450.0

–

–154.7

54.4

172.9

–127.5

345.2

–

–29.6

–

–313.6

–109.3

20.7

19.6

31.1

10.9

176.2

–30.3

–28.1

–317.7

–118.7

Boiling point (F) @ 14.7 Psia

*

23.50

11.00

187.80

*

*

94.91

12.63

13.40

5.59

*

12.52

*

34.10

5.25

19.60

13.55

8.53

6.54

6.54

6.25

6.26

*

9.50

22.10

13.09

14.37

Specific volume cu ft/lb @ 14.7 Psia & 60F (Z factor accounted for)

473.0

219.7

236.0

194.0

144.8

136.2

9.9

–

207.6

168.5

368.0

210.7

120.0

–

123.8

–

91.0

248.8

(1)

167.9

169.5

165.9

157.8

169.3

71.7

590.0

91.8

256.0

Latent heat of vaporization (Btu/lb @ 14.7 Psia)

0.330

0.526

0.254

3.41

0.398

0.399

1.24

0.240

0.361

0.274

0.370

0.410

0.401

0.679

0.115

0.281

0.275

0.402

0.192

2.42

0.375

0.379

0.748

0.174

0.291

0.230

0.328

0.343

0.387

0.514

0.084

0.208

0.177

0.153

0.199 0.248

0.292

0.333

0.363

0.352

0.215

0.075

0.399

0.171

0.320

1.20

1.31

1.32

1.41

1.06

1.05

1.66

1.38

1.24

1.19

1.13

1.19

1.03

1.32

1.36

1.35

1.40

1.30

1.11

1.10

1.09

1.10

1.12

1.66

1.31

1.40

1.24

Specific heat ratio K= Cp/ Cv

(Continued)

Specific heat constant volume (Cv @ 60F)

0.327

0.368

0.397

0.387

0.240

0.125

0.523

0.240

0.397

Specific heat constant pressure (Cp @ 60F)

1138  Chemical Process Engineering

– N2 C9H20

nC9 iC5 nC5 C5 nC8

29. Natural Gas (3)

30. Nitrogen

31. n–Nonane

32. Iso–Pentane

33. n–Pentane

34. Pentylene

35. n–Octane

C3H8

C3 C3

37. Propane

38. Propylene

– SO2 H2O

40. Refinery Gas (High Olefin) (4)

41. Sulphur Dioxide

42. Water Vapor 18.02

64.06

26.26

28.83

42.08

44.09

32.00

114.22

70.13

72.15

72.15

128.25

28.02

18.82

50.49

Mol. wt.

85.8

24.1

58.8

53.6

36.7

35.1

48.3

13.5

22.0

21.4

21.4

12.0

55.1

82.1

30.6

R = 1545/ mol. wt.

3208

1142

639

674

668

617

730

362

586

485

483

335

492

675

968

Pressure (Psia)

1166

775

456

515

658

666

278

1025

854

847

830

1073

228

379

750

Temperature (oR)

Critical conditions

212.0

14.0

–

–

–53.9

–43.7

–297.4

258.2

86.0

96.9

82.1

303.4

–320.0

–

–10.8

Boiling point (F) @ 14.7 Psia

*

5.80

14.40

13.20

8.86

8.45

11.85

*

*

*

*

*

13.53

20.00

6.26

Specific volume cu ft/lb @ 14.7 Psia & 60F (Z factor accounted for)

970.3

168

–

–

188.2

183.5

92.0

131.7

149.0

153.8

145.7

125.7

85.8

–

184.2

Latent heat of vaporization (Btu/lb @ 14.7 Psia)

0.445

0.147

0.397

0.395

0.354

0.388

0.219

0.400

0.382

0.397

0.388

0.400

0.248

0.485

0.200

Specific heat constant pressure (Cp @ 60F)

0.332

0.118

0.33

0.33

0.307

0.342

0.156

0.382

0.353

0.370

0.361

0.385

0.177

0.382

0.167

Specific heat constant volume (Cv @ 60F)

1.33

1.24

1.20

1.20

1.15

1.13

1.40

1.05

1.08

1.07

1.08

1.04

1.40

1.27

1.20

Specific heat ratio K= Cp/ Cv

*These substances are not in a vapor state at 14.7 psia and 60oF and therefore sp. Vol. values are not listed. NOTES: Most values taken from Natural Gasoline Supply Men’s Association Engineering Data Book, 1951 – 6th.Ed. 1. Heat of Sublimation. 2. Flue gas – Approximate values of based on 80.5% N2, 16% CO2, 3.5% O2. Actual properties depend on exact composition. Reference: Mark’s Engineering Handbook. 3. Carbureted Water Gas, Coke Oven Gas and Natural Gas. Based on average compositions. Actual properties will differ depending on exact compositions. Reference: Perry’s Handbook (3rd Edition). 4. Refinery gas (High Paraffin) – Has a greater mol. Percent of saturated hydrocarbons (example C2H6) Refinery gas (High Olefins) – Has a greater mol. Percent of unsaturated hydrocarbons (example C2H4) Reference: Perry’s Handbook (3rd ed.)

By permission, Elliott Turbomachinery Co., Inc.

–

39. Refinery Gas (High Paraffin) (4)

C3H6

O2

36. Oxygen

C8H18

C5H10

C5H12

C5H12

CH3Cl

Chemical formula

28. Methyl Chloride

Gases and vapors

Hydrocarbons reference symbols

Table 10.5  Properties of gases and vapors. (Continued)

Process Safety and Pressure-Relieving Devices  1139

1140  Chemical Process Engineering Table 10.6  Values of coefficient C. k

C

k

C

k

C

k

C

1.00

315a

1.30

347

1.60

372

1.90

394

1.01

317

1.31

348

1.61

373

1.91

395

1.02

318

1.32

349

1.62

374

1.92

395

1.03

319

1.33

350

1.63

375

1.93

396

1.04

320

1.34

351

1.64

376

1.94

397

1.05

321

1.35

352

1.65

376

1.95

397

1.06

322

1.36

353

1.66

377

1.96

398

1.07

323

1.37

353

1.67

378

1.97

398

1.08

325

1.38

354

1.68

379

1.98

399

1.09

326

1.39

355

1.69

379

1.99

400

1.10

327

1.40

356

1.70

380

2.00

400

1.11

328

1 41

357

1.71

381

—

—

1.12

329

1.42

358

1.72

382

—

—

1.13

330

1.43

359

1.73

382

—

—

1.14

331

1.44

360

1.74

383

—

—

1.15

332

1.45

360

1.75

384

—

—

1.16

333

1.46

361

1.76

384

—

—

1.17,

334

1.47

362

1.77

385

—

—

1.18

335

1.48

363

1.78

386

—

—

1.19

336

1.49

364

1.79

386

—

—

1.20

337

1.50

365

1.80

387

—

—

1.21

338

1.51

365

1.81

388

—

—

1.22

339

1.52

366

1.82

389

—

—

1.23

340

1.53

367

1.83

389

—

—

1.24

341

1.54

368

1.84

390

—

—

1.25

342

1.55

369

1.85

391

—

—

1.26

343

1.56

369

1.86

391

—

—

1.27

344

1.57

370

1.87

392

—

—

1.28

345

1.58

371

1.88

393

—

—

1.29

346

1.59

372

1.89

393

—

—

1.30

347

1.60

373

1.90

394

—

—

a The limit of C, as k approaches 1.00 is 315. (Source: Sizing, Selection and Installation of Pressure – Relieving Devices in Refineries, Part 1 – Sizing and Selection, API RP 520, 7th ed., January 2000).

Process Safety and Pressure-Relieving Devices  1141

Procedure 1. F  or a new installation, establish pressure vessel normal maximum operating pressure, and temperature, and then the safe increment above this for vessel design conditions and determine MAWP of the new vessel. (Have qualified fabricator or designer establish this). 2. Establish the maximum set pressure for the pressure-relieving valves as the MAWP, or lower, but never higher. 3. Establish actual relieving pressure (and corresponding temperature) from Figure 10.7A (at 110% of set pressure for non-fire and non-explosive conditions). Explosive conditions may require total separate evaluation of the set pressure (never above the MAWP), which should be lower or staged; or, most likely, will not be satisfied by a standard SRV due to the extremely rapid response needed. The capacity for flow through the valve is established by these conditions. 4. For existing vessel and re-evaluation of pressure relieving requirements, start with the known MAWP for the vessel, recorded on the vessel drawings and on its ASME certification papers. Then follow steps 2 and 3 above.

Establish Critical Flow for Gases and Vapors Critical or sonic flow will usually exist for most (compressible) gases or vapors discharging through the nozzle orifice of a pressure-relieving valve. The rate of discharge of a gas from a nozzle will increase for a decrease in the absolute pressure ratio P2/Pl (exit/inlet) until the linear velocity in the throat of the nozzle reaches the speed of sound in the gas at that location. Thus, the critical or sonic velocity or critical pressures are those conditions that exist when the gas velocity reaches the speed of sound. At that condition, the actual pressure in the throat will not fall below P1/rc even if a much lower pressure exists downstream [15]. The maximum velocity at the outlet end (or restriction) in a pipe or nozzle is sonic or critical velocity. This is expressed [40] as:

v s = kgRT = kg (144 )P′V = 68.1 kP′V

 kT  = 223    M



0.5

(10.5)

In Metric units

v s = γRT = γP′V = 316.2 γp′V

 γT  = 91.2    M



0.5

(10.5A)

Table 10.7  Actual Kd values of a selection of relief valves. Gas duty valves

Liquid duty valves

Manufacturer and model

Actual Kd

Manufacturer and model

Actual Kd

Brody 3500

0.957

Farris 1850

0.724

Farris 1850

0.724

Lesser 488

0.524

Lesser 488

0.801

Safety Systems WB100

0.653

Safety Systems WB400

0.975

Crosby 900 Series

0.735

Crosby JOS–E

0.961

1142  Chemical Process Engineering where k vs g R

= ratio of specific heats at constant pressure/constant volume, Cp/Cv see Table 10.6. = sonic velocity of gas, ft/sec (m/s) = acceleration of gravity, 32.2 ft/s2 = individual gas constant = (MR/M) = 1545/M

In Metric units R = Ro/M J/kg K where Ro = 8314 J/kg mol K, M = molecular weight of the gas MR = universal gas constant = 1545 M = molecular weight T = upstream absolute temperature, oR = oF + 460 (K = oC + 273.15) V = specific volume of fluid, cu ft/lb (m3/kg) P1 = Pʹ = upstream pressure, psi abs (N/m2 absolute (pascal)) pʹ = pressure, bars absolute. d = pipe inside diameter, in. W = gas rate, lb/h Z = gas compressibility factor Pc = Pcrit = critical pressure, psia γ = ratio of specific heat at constant pressure to specific heat at constant volume = Cp/Cv. The critical pressure at a pipe outlet is [5c]:



 W   ZT  1 2 Pcrit =   , psia 2   (408d )   M 

(10.6)

The velocity vs will occur at the outlet end or in a restricted area [43] when the pressure drop is sufficiently high. The condition of temperature, pressure and specific volume are those occurring at the point in question. Critical pressure will normally be found between 53 and 60% of the upstream pressure, P’, at the time of relief from overpressure, including accumulation pressure in psia. That is, P’ represents the actual pressure at which the relief device is “blowing” or relieving, which is normally above the set pressure by the amount of the accumulation pressure, (see Figure 10.7A). Thus, if the downstream or backpressure on the valve is less than 53-60% (should be calculated) of the values of P’, note above, critical (sonic) flow will usually exist. If the downstream pressure is over approximately 50% of the relief pressure, P’, the actual critical pressure should be calculated to determine the proper condition. Calculation of critical pressure [41]: k



 2  (k −1) Pc = P1    (k + 1) 



Pc  2  (k −1) = rc =   P1  (k + 1) 

(10.7)

k

For critical flow conditions at β ≤ 0.2. This equation is conventionally solved by Figure 10.21. At critical conditions, the maximum flow through the nozzle or orifice is: [41]

(10.8)

Process Safety and Pressure-Relieving Devices  1143 0.60 0.59 0.58 0.57 0.56

k

2 k –1 Pc / P = k +1 Pc = Critical Pressure, psia. P = Total Absolute Pressure Upstream of Safety Valve of Full Relief, Equals Set Pressure plus Overpressure, psia.

Critical Pressure Ratio, PC / P .

0.55 0.54 0.53 0.52 0.51 0.50 0.49 0.48 0.47 0.46 0.45 0.44 1.0 1.1

1.2 1.3 1.4 1.5 1.6 1.7 1.8 Ratio of Specif ic Heats, k = CP/CV

1.9 2.0

Figure 10.21  Critical back pressure ratio for vapors and gases. (k +1)

Wmax(critical flow) = C o APo



kgM  2  (k −1)   R g To  k + 1 



(10.9)

where = molecular wt of vapor or gas lbm/lb mol. = temperature of service, oR = (oF + 460). = ideal universal gas constant = 1545, ft lbf/lb-mol-oR, also = MR. = discharge coefficient for sharp-edged orifice. = 0.61 for Reynolds Number > 30,000 and not sonic. = 1.0 for sonic flow, Co increases from 0.61 to 1.0. (use 1.0 to be conservative [19, 44], 5th ed.) A = area of opening, orifice, or hole, or nozzle, ft2. P1 = Po = upstream pressure, lb/ft2, abs, (psfa). = 32.174 lbf/lbm · ft/s2. gc β = ratio of orifice diameter/pipe diameter (or nozzle inlet diameter). Wmax = maximum mass flow at critical or choked conditions, lb/s Pc = Pcrit = critical flow throat pressure, psia = sonic = choked pressure = maximum downstream pressure producing maximum flow. M To Rg Co

If the downstream pressure exceeds the critical flow pressure, then sub-critical pressure will occur and the equations for sub-critical flow should be used.

1144  Chemical Process Engineering When the downstream pressure is less than (or below) the critical or choked pressure, the velocity and fluid flow rate at a restriction or throat will not/cannot be increased by lowering the downstream pressure further, and the fluid velocity at the restriction or throat is the velocity of sound at the conditions [41]. The critical or sonic ratio is conveniently shown on Figure 10.21, but this does not eliminate the need for calculating the Pc/P1 ratio for a more accurate result. Table 10.5 shows the properties of gases and vapors at critical conditions. Table 10.6 shows the k (=Cp/Cv) values of gases, and Table 10.7 shows Kd values of a selection of relief valves for liquid and gases from manufacturers respectively.

Example 10.2 Flow through Sharp Edged Vent Orifice (Adapted after Ref. [41]) A small hole has been deliberately placed in a vessel near the top to provide a controlled vent for a nitrogen purge/ blanket. The hole is 0.2 in. diameter with the vessel operating at 150 psig at 100°F. Determine the flow through this vent hole. Assume it acts as a sharp edged orifice. k (for nitrogen) = 1.4 From Eq. 10.7, 1.4 (1.4 −1)

 2  = 87.0 psia, critical pressure Pc = (150 + 14.7)    (1.4 + 1)  Hole area = A = πd2/4 = π (0.2)2/4 = 0.0314 in2. = 0.0002182 ft2 Discharge coef. Co = assumed = 1.0 (Note, could calculate Re to verify) Inside pressure = 150 psig + 14.7 = 164.7 psia To = 100 + 460 = 560oR

(1.4 +1) (1.4 −1)    (1.4)(32.2)(28)   2  Wmax = 1.0(0.0002182)(164.7)(144sq.in sq.ft.)       (1545)(560)  1.4 + 1    = 0.1143 lb/s

critical flow rate, Wmax = 0.11443lb/sec

10.18 Orifice Area Calculations [42] Calculations of orifice flow area for conventional pressure-relieving valves, and flow is critical (sonic) through part of relieving system, i.e., backpressure is less than 55% of the absolute relieving pressure (including set pressure plus accumulation). See Figure 10.7A, use Kb = 1.0 (Figure 10.26), constant backpressure with variation not to exceed 10% of the set pressure. a. for vapors and gases, in lb/hr; Kb = 1.0; “C” from Figure 10.25, P is the relieving pressure absolute, psia



A=

W TZ , in2. CK d P1K b M

(Effective net discharge area) where C = gas or vapor flow constant Kb = 1 when back pressure is below 55% of absolute relieving pressure. Kd = coefficient of discharge (0.953)

(10.10)

Process Safety and Pressure-Relieving Devices  1145 M = molecular weight of gas or vapor. P1 = relieving pressure, psia = set pressure + overpressure + 14.7 W = required vapor or gas capacity, lb/h. T = inlet temperature, oR = oF + 460. Z = compressibility factor corresponding to T and P. Metric units in kg/h

A=



1.317W TZ . cm2 CK d P1K b M

(10.10A)

where A = required orifice area in cm2 C = Gas or vapor flow constant W = required vapor capacity, kg/h T = inlet temperature, K = (oC + 273.15) Kb = vapor or gas flow correction factor for constant back pressure above critical pressure, = 1 when back pressure is below 55% of absolute relieving pressure. Kd = Coefficient of discharge (0.953 for vapors, gases). P1 = relieving pressure in bar abs = set pressure + overpressure + 1.013 Z = compressibility factor corresponding to T and P (Z = 1.0) b. For vapors and gases, in scfm, Kb = 1.0

A=



V GTZ , in2. 1.175CP1K d K b

(10.11)

where G = specific gravity of gas (Molecular weight of gas /Molecular weight of air = 29.0) T = inlet temperature, oR = oF + 460 P1 = relieving pressure, psia = set pressure + overpressure + 14.7 V = required gas capacity, scfm Z = compressibility factor corresponding to T and P (Z = 1.0) Metric units in Normal m3/h

A=



V GTZ , cm2 3.344CK d P1K b

where A = required orifice area in cm2. C = Gas or vapor flow constant. G = Specific gravity of gas (Molecular weight of gas /Molecular weight of air = 29.0) V = required gas capacity, m3/h T = inlet temperature, K = (oC + 273.15) Kd = Coefficient of discharge (0.953 for vapors, gases). Kb = vapor or gas flow correction factor for constant back pressure above critical pressure (Kb = 1.0) P1 = relieving pressure in bar abs = set pressure + overpressure + 1.013 Z = compressibility factor corresponding to T and P (Z = 1.0)

(10.11A)

1146  Chemical Process Engineering Pressure relief devices in gas or vapor service that operate at critical conditions may be sized using the following equations [5d]: US Customary units:

A=



W CK d P 1 K b K c

TZ M

(10.11B)

or

V TZM 6.32CK d P 1 K b K c

(10.11C)

A=

V TZG 1.175CK d P 1 K b K c

(10.11D)

A=

13,160W CK d P 1 K b K c

(10.11E)

A=

or

SI Units:



TZ M

or



A=

35,250V TZM CK d P 1 K b K c

(10.11F)

A=

189,750V TZG CK d P 1 K b K c

(10.11G)

or



where A = required effective discharge area of the device, in2 (mm2) W = required flow through the device, lb/h, (kg/h) C = coefficient determined from an expression of the ratio of the specific heats (k = Cp/Cv) of the gas or vapor at inlet relieving conditions (see Figure 10.25) or



 2  C = 520 k   k + 1 

(k +1) (k −1)



(10.11H)

Kd = effective coefficient of discharge. For preliminary sizing, use the following values: (i) 0.975, when a pressure relief valve is installed with or without a rupture disk in combination. (ii) 0.62, when a pressure relief valve is not installed and sizing is for a rupture disk. P1 = upstream relieving pressure, psia (kPaa). This is the set pressure plus the allowable overpressure plus atmospheric pressure. Kb = capacity correction factor due to back pressure. The back pressure correction factor applies to balanced bellows valves only. For conventional and pilot-operated valves, Kb = 1.0 Kc = combination correction factor for installation with a rupture disk upstream of the pressure relief valve T = relieving temperature of the inlet gas or vapor, oR = oF + 460 (K = oC + 273)

Process Safety and Pressure-Relieving Devices  1147 Z = compressibility factor for the deviation of the actual gas from a perfect gas, a ratio evaluated at inlet relieving conditions. M = molecular weight of the gas or vapor at inlet relieving conditions. V = required flow through the device, scfm at 14.7 psia and 60oF (Nm3/min at 0oC and 101.3 kPaa) G = specific gravity of gas at standard conditions referred to air at standard conditions (normal conditions). G = 1.00 for air at 14.7 psia and 60oF (101.3 kPaa and 0oC) c. F  or steam, in lb/hr; Kb = 1.0 and Ksh = 1.0 for saturated steam when backpressure is below 55% of absolute relieving pressure.

A=



Ws , in2. 51.5P1K d K bK c K nK sh

(10.12)

SI units:

A=



190.4 × W s ,mm 2 . P1K d K bK c K nK sh

(10.12A)

where Ws = required steam capacity in lb/hr (kg/h). Kd = effective coefficient of discharge. For preliminary sizing, use the following values: (i) 0.975, when a pressure relief valve is installed with or without a rupture disk in combination. (ii) 0.62, when a pressure relief valve is not installed and sizing is for a rupture disk. Kb = 1 when back pressure is below 55% of absolute relieving pressure. The back pressure correction factor applies to balanced bellows valves only. For conventional valves, use a value for Kb = 1.0 Kc = combination correction factor for installation with a rupture disk upstream of the pressure relief valve. (i) 1.0, when a rupture disk is not installed. (ii) 0.9, when a rupture disk is installed in combination with a pressure relief valve and the combination does not have a published value. Kn = Napier steam correction factor for set pressures between 1500 and 2900 psig (Table 10.11). = 1 when P1 ≤ 1500psia(10,339kPaa) =

0.1906 × P1 − 1000 (US Customary units) 0.2292 × P1 − 1061

=

0.02764 x P1 − 1000 (SI units) 0.03324 x P1 − 1061

where P1 ≥ 1500 psia (10,339 kPaa) and ≤ 3200 psia (22,057 kPaa). Khs = 1 for saturated steam. P1 = relieving pressure, psia = set pressure + overpressure + 14.7 = relieving pressure, kPaa = set pressure + overpressure + 101.3 Metric units in kg/h



A=

Ws , cm2 52.49P1K d K bK sh

(10.12B)

1148  Chemical Process Engineering where Ws = required steam capacity, kg/h. Kb = 1 when back pressure is below 55% of absolute relieving pressure. Kd = coefficient of discharge (Kd = 0.953) Khs = 1 for saturated steam. P1 = relieving pressure, bara = set pressure + overpressure + 1.013. d. For air, in scfm; Kb = 1.0 when the back pressure is below 55% of absolute relieving pressure

A=



Va T 418K d P1K b

(10.13)

where Va = relieving air capacity, scfm Kb = 1 when back pressure is below 55% of absolute relieving pressure. Kd = coefficient of discharge (Kd = 0.953) P1 = relieving pressure, psia = set pressure + overpressure + 14.7. T = inlet temperature, oR = oF + 460. Metric units in m3/h



A=

Va T , cm2 1189.3K d PK b

(10.13A)

where Va = Required air capacity in m3/h. Kb = 1 when back pressure is below 55% of absolute relieving pressure. Kd = coefficient of discharge (Kd = 0.953). P = relieving pressure, bara = set pressure + overpressure + 1.013 T = inlet temperature, K = (oC + 273.15) e. For liquids, GPM Kp  = 1.0 at 10% overpressure Ku  = 1.0 at normal viscosities ΔP = P1 − P2 = upstream pressure, psig (set + overpressure) − total backpressure, psig.

10.19 Sizing Valves for Liquid Relief: Pressure Relief Valves Requiring Capacity Certification [5d] Section VIII, Division I, of the ASME code requires that capacity certification be obtained for pressure relief valves designed for liquid service. The procedure for obtaining capacity certification includes testing to determine the rated coefficient of discharge for the liquid relief valves at 10% overpressure. ASME Code valves: Board Certified for liquids only [5d].



A=

VL G , in2 38K d K w K c K u P1 − P2

(10.14)

Process Safety and Pressure-Relieving Devices  1149 SI units

A=



where

11.78 × VL G , mm2 K d K w K c K u P1 − P2

(10.14A)

A = required effective discharge area, in2 (mm2) G = specific gravity of the liquid at the flowing temperature referred to water at standard conditions (density of liquid/density of water ≈ 62.3 lb/ft3) VL = required liquid capacity, U.S. gpm (l/min) Kd = rated coefficient of discharge that should be obtained from the valve manufacturer. For a preliminary sizing, = 0.65 when a pressure relief valve is installed with or without a rupture disk in combination. = 0.62 when a pressure relief valve is not installed and sizing is for a rupture disk. Kc = combination correction factor for installations with a rupture disk upstream of the pressure relief valve. Kw = variable or constant back pressure sizing factor, balanced valves, liquid only (Figure 10.28). If the back pressure is atmospheric, Kw = 1.0. Balanced Bellows valves in back pressure service will require the correction factor. Conventional and pilot-operated valves require no special correction. Kc = combination correction factor for installation with a rupture disk upstream of the pressure relief valve. = 1.0 when a ruptured disk is not installed. = 0.9 when a rupture disk is installed in combination with a pressure relief valve and the combination do not have a published value. Ku = viscosity correction factor (Ku = 1 at normal viscosities).

2.878 342.75  =  0.9935 + 0.5 + 1.5  

Re

Re

−1.0



P1 = upstream relieving pressure, psig (kPag). This is the set pressure plus allowable overpressure. P2 = back pressure at outlet, psig (kPag).

10.20 Sizing Valves for Liquid Relief: Pressure Relief Valves Not Requiring Capacity Certification [5d] Before the ASME code incorporated requirements for capacity certification, valves were generally sized for liquid service, which assumes an effective coefficient of discharge, Kd = 0.62, and 25% overpressure. This method will typically result in an oversized design where a liquid valve is used for an application with 10% overpressure. A Kp correction factor of 0.6 is used for this situation [5d].

A=



VL G , in2 38K d K w K c K pK u 1.25P1 − P2

(10.15)

SI Units

A=

11.78 × VL G K d K w K c K u K p 1.25P1 − P2

, mm2

where A = required effective discharge area, in2 (mm2) G = specific gravity of liquid at flowing temperature referred to water at standard conditions.

(10.15A)

1150  Chemical Process Engineering VL = required liquid capacity, U.S. gpm (l/min). Kd = 0.62 for a preliminary sizing estimation, otherwise rated coefficient of discharge should be obtained from the valve manufacturer. Kw = variable or constant back pressure sizing factor, balanced valves, liquid only (Figure 10.28). If the back pressure is atmospheric, Kw = 1.0. Balanced bellows valves in back pressure service will require the correction factor. Conventional and pilot-operated valves require no special correction. Kc = combination correction factor for installation with a rupture disk upstream of the pressure relief valve. = 1.0, when a ruptured disk is not installed. = 0.9, when a rupture disk is installed in combination with a pressure relief valve and the combination do not have a published value. Kp = liquid capacity correction factor for overpressures. At 25% overpressure, Kp = 1.0. For overpressure other than 25%, Kp is determined from Figure 10.22. Ku = viscosity correction factor (Ku = 1 at normal viscosities).

2.878 342.75  =  0.9935 + 0.5 + 1.5  

Re

Re

−1.0



P1 = set pressure, psig (kpag) P2 = total back pressure, psig (kPag). Metric units in dm3/min



A=

VL G , cm2 84.89K d K pK u 1.25P1 − P2

(10.15B)

where A = required effective discharge area, cm2 G = specific gravity of liquid at flowing temperature referred to water at standard conditions. VL = required liquid capacity, U.S. gpm (l/min).

OVERPRESSURE SIZING FACTOR KP OTHER THAN 25% OVERPRESSURE Conventional and BalanSeal Valves—Non-Code Liquids Only

1.1 1.0 .9 .8 .7

EXAMPLE

OVERPRESSURE FACTOR KP

1.2

.6

EXAMPLE: FIND KP FACTOR FOR 15% OVERPRESSURE: FOLLOW DOTTED LINE FROM 15% OVERPRESSURE TO CURVE. KP = 0.79 CAPACITY AT 15% O.P. = 0.79 X RATED CAPACITY AT 25% O.P.

.5 10

15

20

25

50

% ALLOWABLE OVERPRESSURE Note: Pressure-Relief Valve liquid capacities cannot be predicted by a general curve for overpressures below 10%

Figure 10.22  Liquids overpressure sizing factor, Kp, for other than 25% overpressure. Applies to non-code liquids only using conventional and balanced valves. (By permission from Teledyne Farris Engineering Co.).

Process Safety and Pressure-Relieving Devices  1151 Kd = 0.62 for a preliminary sizing estimation, otherwise rated coefficient of discharge should be obtained from the valve manufacturer. Kp = liquid capacity correction factor for overpressures. At 25 %. Overpressure, Kp = 1.0. For overpressure other than 25%, Kp is determined from Figure 10.22 Ku = viscosity correction factor (Ku = 1 at normal viscosities). P1 = set pressure at inlet, barg. P2 = back pressure at outlet, barg. When sizing a relief valve for viscous liquid service, the orifice area is first calculated for non-viscous service to obtain a preliminary discharge area. The next standard orifice size is used to calculate the Reynolds number. To apply the viscosity correction Ku, a preliminary or trial calculation should be made for the areas required using the equation of paragraph (e) above or the modified equation (still ASME conformance [5] but not capacity certified). A simplified equation based on the ASME Pressure Vessel code equations, Section VIII, Div. 1, Mandatory Appendix XI uses K coefficient of discharge in the equations, where K is defined as 90% of the average Kd of certified tests with compressible or incompressible fluids, see [42], pg 40. For first trial, assume Ku for viscosity = 1.0 For final calculation use Ku from Figures 10.23 and 10.24 or a correlation equation defined by:

K u = −2.38878 + 1.2502(lnRe) − 0.17510(lnRe)2 + 0.01087(lnRe)3 − 0.00025(lnRe)4





(10.15C)

Ku is then substituted in Equations 10.15 and 10.15A (S.I. units). Determine the needed Reynolds number, Re, using the next size larger orifice. Area is determined from that made in the first trial calculation [5].

Re = VL



(2800G) , or µ A

(10.16)

or

Re =

12,700VL , (Do not use when U < 100 SUS) U A

(

)

(10.17)

SI units

Re = VL



(18,800G) µ A

(10.16A)

or

Re =



(85,220VL ) U A

where Re = Reynolds number μ = absolute viscosity at the flowing temperature, cP P1 = set pressure, psig U = viscosity at the flowing temperature, Saybolt Universal Seconds P2 = total backpressure, psig

(10.17A)

1152  Chemical Process Engineering

Figure 10.23  Liquids viscosity correction using chart method for Ku (By permission from Teledyne Farris Engineering Co.).

10.21 Reaction Forces The discharge of a pressure relief valve with unsupported discharge piping will impose a reactive load on the inlet of the valve as a result of the reaction force of the flowing fluid. This is particularly essential where piping discharging to atmosphere includes a 90o turn and has no support for the outlet piping. All reactive loading due to the operation of the valve is then transmitted to the valve and inlet piping. The following formula is based on a condition of critical steady-state flow of a compressible fluid that discharges to the atmosphere through an elbow and a vertical discharge pipe. The reaction force (F) includes the effects of both momentum and static pressure [5d]. The formula is applicable for any gas, vapor or steam and is expressed by



F=

W kT + (AP) 366 (k + 1)M

(10.17B)

In Metric units



F = 129W

kT + 0.1(AP) (k + 1)M

(10.17C)

Process Safety and Pressure-Relieving Devices  1153

Figure 10.23A  Viscous liquid valve sizing using the method of API RP – 520 (Reprinted by permission from Teledyne Farris Engineering Co., and Sizing, Selection and Installation of Pressure Relieving Devices in Refineries, Part I “Sizing and Selection”, API RP – 520, 5th ed., July 1990, American Petroleum Institute).

A = πd2/4 A = πd2/4

(a)

A = πdh

(b)

Figure 10.24  (a): Orifice area in a relief valve (green); (b) Orifice area in a relief valve (green), Curtain area (purple). This valve will have a low discharge coefficient as the curtain area is lower than the orifice area (Source: Chris Flower and Adam Wills, The Chemical Engineer, U.K., pp. 24-31, June 2017).

1154  Chemical Process Engineering where A = area of the outlet at the point of discharge, in2 (mm2) Cp = specific heat at constant pressure. Cv = specific heat at constant volume. F = reaction force at the point of discharge to the atmosphere, lbf (N) k = ratio of specific heats (Cp/Cv) at the outlet conditions. M = molecular weight of the process fluid P = static pressure within the outlet at the point of discharge, psig (barg) T = temperature at the outlet, oR (K ) W = flow of any gas or vapor, lbm/h (kg/s)

Example 10.3 In a process plant, ammonia is used to control the pH during a production process to obtain maximum yield of a product. For this purpose, liquid ammonia is vaporized by passing steam through a coil in a vaporizer. A relief valve from the vaporizer is set at a pressure of 290 psig. If the relieving rate of ammonia vapor is 620 lb/h, determine the size of the relief valve required to relieve ammonia vapor during an emergency. Design data: Ratio of specific heat capacities (Cp/Cv) = 1.33 Molecular weight of ammonia = 17.03 Critical pressure, Pc = 111.3 atm. Critical temperature, Tc = 405.6 K Constants in Antoine Equation: A = 16.9481 B = 213.25 C = -32.98

Solution From Antoine’s equation

lnP = A −

B T+C

Relieving pressure = mm Hg. Relieving temperature = K Relieving pressure = set pressure + over pressure + atmospheric pressure = 290 + (290 × 0.1) + 14.7 = 333.7 psia. Conversion 1 psi = 51.715 mm Hg. 1 atm = 14.7 psi Relieving pressure = 17,257.3 mm Hg. Relieving temperature from Antoine’s equation

lnP = A −

B T+C

Process Safety and Pressure-Relieving Devices  1155

ln(17,257.296) = 16.9481 −

2132.5 (T − 32.98)

−7.192(T – 32.98) = −2132.5 −7.192T + 237.19) = −2132.5

T=

2369.69 7.192

= 329.5 K (593.45 oR) Critical pressure = 1636.1 psia Critical temperature = 703.41 oR Since compressibility factor Z is a function of temperature Tr and Pr, then Tr = T/Tc = 593.45/730.41   = 0.812 Pr = P/Pc = 333.71/1636.11   = 0.204 From the Nelson and Obert chart, Z = 0.837 Coefficient “C” for gas related to specific heats. Substituting the value for k in Eq. 10.11H 0.5

(k +1)   (k −1) 2     C = 520 k     (k + 1)     (1.33+1) 0.5   (1.33−1) 2  = 520 (1.33) 1.33 + 1     = 350

{

}

For vapor, the orifice area (from Eq. 10.10) is:

A=

W TZ , in2. CK d PK b M

A=

620 (593.45)(0.812) (350)(0.953)(333.7)(1) 17.03

= 0.0296 in 2 The nearest standard orifice area is 0.110 in2, having an inlet and outlet valve body sizes of 1 and 2 in. The designation is 1D2 pressure relief valve. The maximum vapor rate with the nearest standard orifice area is:

W = ACK d PK b M ( TZ ) = (0.11)(350)(0.953)(333.7)(1) 17.03 (593.45 × 0.81) = 2305 lb/h. The Excel spreadsheet (Example 10.3xlsx) shows the calculations of Example 10.3, and Table 10.8 shows the results of the Excel spreadsheet program.

1156  Chemical Process Engineering Table 10.8  The results of the Excel spreadsheet calculations of Example 10.3. Results of relief valve sizing for vapor flow Flow type

Vapor

Set Pressure

290

psig

Relieving Pressure

333.7

psia

Inlet Temperature

132.5

o

Inlet Temperature

592.5

o

Ratio of Specific heat capacities, k

1.33

Constant Coefficient, C

349.8

Gas Compressibility factor Z

0.812

Relieving flow rate

620

Kb=

1

Kd=

0.953

Molecular weight of vapor, Mw

17.03

Calculated orifice area

0.03

in2

Nearest orifice area

0.11

in2

Orifice Size

D

Maximum vapor rate

2302

F R

lb/h

lb/h

Example 10.4 A bellows type pressure relief valve is required to protect a vessel containing an organic liquid. The required relieving capacity is 310 US gpm. The inlet temperature is 170oF and the set pressure is 100 psig. Allowable over pressure is 25% with a built-up back pressure is 25 psig. The fluid’s physical properties such as the specific gravity and viscosity are 1.45 and 3200 cP respectively. Determine the orifice size of the valve. Take the correction factors

Kd = 0.62, Kw = 0.92, Kc = Kp = Ku = 1

Solution Non-ASME Code Liquid Valves [5c] non-board certified for liquids, but code acceptable for other services. Kp from Figure 10.22, Kd = 0.62, and 25% overpressure. Substituting values in Eq. 10.15,



A=

VL G , in2 38K d K w K c K pK u 1.25P1 − P2

Process Safety and Pressure-Relieving Devices  1157

A=

(310) 1.45 38(0.62)(0.92)(1.0)(1.0)(1.0) 1.25(100) − 25

= 1.722 in 2

The next standard orifice area is 1.838 in2 having an inlet and outlet valve body sizes of 3 and 4 in. The designation is 3K4 pressure relief valve. The maximum flow rate with the standard orifice area is:

VL = A(38)(K d )(K w )(K c )(K p )(K u ) (1.25P1 − P2 ) / G = 1.838(38)(0.62)(0.92)(1.0)(1.0)(1.0) (1.25(100) − 25) / 1.45

= 330.85 gpm.

Next, calculate the Reynolds number using the manufacturer’s orifice area:

Re = VL



(2800G) , or µ A

(10.16)

(310)(2800 × 1.45) (3200) 1.838 = 290.0

Re =

Determine the viscosity correction factor Ku from Eq. 10.15C:

K u = −2.38878 + 1.2502(lnRe) − 0.17510(lnRe)2

+ 0.01087(lnRe)3 − 0.00025(lnRe)4 K u = −2.38878 + 1.2502(ln 290) − 0.17510(ln 290)2 + 0.01087(ln 290)3 − 0.00025(ln 290)4 = 0.794



The required orifice area with calculated Ku = 0.794 is:

A=

(310) 1.45 38(0.62)(0.92)(1.0)(1.0)(0.794) 1.25(100) − 25

= 2.17 in 2 .

The nearest standard orifice area is 2.853 in2., with L designation having preferred valve body sizes, 3-4 or 4-6. The maximum liquid flow rate with the standard orifice area is:

VL = A(38)(K d )(K w )(K c )(K p )(K u ) (1.25P1 − P2 )/G

= 2.853(38)(0.62)(0.92)(1.0)(0.794)(1.0) (1.25(100) − 25)/1.45 = 407.76 gpm.

1158  Chemical Process Engineering ASME code valves: Board Certified for liquids only. Substituting the values in Eq. 10.14,

A=



A=

VL G 38K d K w K c K u P1 − P2

(310) 1.45 38(0.62)(0.92)(1)(1) 100 − 25

= 1.989 in 2 .



The error in the orifice area between the ASME code and Non-ASME code is

ε=



(1.989 − 1.722) × 100% = 15.5% 1.722

Percentage deviation in the calculated orifice areas between the ASME code valves and Non-ASME Code Liquid valves [5a] non-board certified for liquids is 15.5%. This is because the Non-ASME Code uses a 25% over pressure, whereas the ASME Code formula is based on only 10%. It should be noted that Equation 10.15 is applicable only to relief valves not requiring capacity certification (Section 4.6 of API 520). The Excel spreadsheet (Example 10.4.xlsx) shows the calculations of Example 10.4 and Table 10.9 shows the results of the Excel spreadsheet program.

10.22 Calculations of Orifice Flow Area using Pressure-Relieving Balanced Bellows Valves, with Variable or Constant Back Pressure Must be used when back pressure variation exceeds 10% of the set pressure of the valve. Flow may be critical or non-critical for balanced valves. All orifice areas, A, in square inches [42]. The sizing procedure is the same as for conventional valves listed above (Equations 10.10), but uses equations given below incorporating the correction factors Kv and Kw. With variable backpressure, use maximum value for P2 [5a, 42]. a. For vapors or gases, lb/hr



A=

W TZ , in2. CK d P1K v M

(10.18)

A=

1.317W TZ , cm2 CK d P1K v M

(10.18A)

A=

V GTZ , in2 1.175CK d P1K v

(10.19)

A=

V GTZ , cm2 3.344CK d P1K v

(10.19A)

Metric units in kg/h



b. For vapors or gases, scfm

In Metric units in Normal m3/h For vapor or gases, Normal m3/h

c. For steam, lb/h

Process Safety and Pressure-Relieving Devices  1159 Table 10.9  The results of the Excel spreadsheet calculations of Example 10.9. Results of relief valve sizing for liquid flow Flow type

Liquid

Set Pressure at inlet

100

psig

Back Pressure at outlet

25

psig

Specific gravity of liquid

1.45

 

Viscosity of Liquid

3200

cP

Relieving flow rate

310

US gal.

Kd

0.62

 

Kw

0.92

 

Kc

1

 

Kp

1

 

Ku

1

 

Calculated orifice area

1.722

in2

Nearest orifice area

1.838

in2

Orifice Size

K

 

Maximum Liquid flow rate

330.8

US gal.

Reynolds number

290

 

Calculated Ku

0.794

 

Calculated orifice area

2.17

in2

Nearest orifice area

2.853

in2

Orifice Size

L

 

Maximum Liquid flow rate

407.6

US gal.

A=



Ws , in2. 51.5K d K v K sh K nP1

(10.20)

Metric units, kg/h

A=



Ws , cm2 52.49K d K v K sh K nP1

(10.20A)

d. For air, scfm

Metric units, Normal m3/h

A=

Va T , in2. 418K d P1K v

(10.21)

1160  Chemical Process Engineering

A=



Va T , cm2 1189.3K d P1K v

(10.21A)

e. For liquids, GPM; ASME Code valve

A=



VL G , in2. 38.0K d K w K u ∆P

(10.22)

f. For liquids, GPM, non-ASME Code valve

A=



VL G , in2. 38.0K d K pK w K u (1.25P1 − P2 )

(10.23)

Metric unit in dm3/min.



A=

VL G , cm2 84.89K d K pK w K u (1.25P1 − P2 )

(10.23A)

When the backpressure, P2 is variable, use the maximum value. where (Courtesy of Teledyne Farris Engineering Co. [45]): A = required orifice area in square inches. This is as defined in the ASME Code and ANSI/API Std 526. W = required vapor capacity in lb/h Ws = required steam capacity in lb/h V = required gas capacity in scfm Va = required air capacity in scfm VL = required liquid capacity, gal/min (dm3/min). G = specific gravity of gas (air = 1.0) or specific gravity of liquid (water = 1.0) at actual discharge temperature. A specific gravity at any lower temperature will obtain a safe valve size. M = average molecular weight of vapor. P1 = relieving pressure in lbs per square inch abs. = [set pressure, psig + over pressure, psig + 14.7] psia. Minimum overpressure = 3 psi. P1 = set pressure at inlet, psig. P2 = back pressure at outlet, psig. ΔP = Set pressure + over pressure, psig - back pressure, psig. At 10% overpressure delta P equals 1.1 P1-P2. Below 30 psig set pressure, ΔP = P1 + 3 – P2. T = inlet temperature of absolute, oR = (oF + 460). Z = compressibility factor corresponding to T and P. If this factor is not available, compressibility correction can be safely ignored by using a value of Z = 1.0. C = gas or vapor flow constant, see Figure 10.25. k = ratio of specific heats, Cp/Cv. If a value is not known the use of k = 1.001, C = 315 will result in a safe valve size. Isentropic coefficient, n, may be used instead of k (Table 10.5). Kp = liquid capacity correction factor for overpressures lower than 25% for non-code liquids equations only; (see Figure 10.22). Kb = vapor or gas flow correction factor for constant back pressures above critical pressure (see Figure 10.26). Kv = vapor or gas flow factor for variable back pressures for balanced seal valves only (see Figures 10.27A and B). Kw = liquid flow factor for variable back pressures for balanced seal valves only (see Figure 10.28). For atmos., Kw = 1.0. Ku = liquid viscosity correction factor (see Figure 10.23 or Figure 10.24).

Process Safety and Pressure-Relieving Devices  1161 400

Coef f icient C

380

360

340

320 1.0

1.2

1.4

1.6

1.8

2.0

Specif ic Heat Ratio, k = Cp /Cv Notes: 1. The equation for this curve is C = 520 k

2 (k +1)/(k − 1) k+1

2. The units for the coef f icient C are lbmlbmole ºR/ lb f hr .

Figure 10.25  Constant “C” for gas or vapor related to specific heats (By permission from Sizing, Selection and Installation of PressureRelieving Devices in Refineries, Part I “Sizing and Selection”, API RP – 520, 5th ed., July 1990).

CONSTANT BACK PRESSURE SIZING FACTOR Kb 1.1

.9 .8 .7 .6 .5 .4 .3 .2

EXAMPLE: SET PRESSURE = 100 PSIG CONSTANT BACK PRESSURE = 80 PSIG (k = 1.30) 80+14.7 % ABSOLUTE B.P. = × 100 = 76% 100 + 10 + 14.7 FOLLOW DOTTED LINE. Kb = 0.89 (FROM CURVE) CAPACITY WITH B.P. = 0.89 × RATED CAPACITY WITHOUT B.P.

Kb =

.1 0

10

20

30

40

% ABSOLUTE BACK PRESSURE =

50

EXAMPLE

CAPACITY WITH BACK PRESSURE RATED CAPACITY WITHOUT BACK PRESSURE

1.0

60 70 80 BACK PRESSURE, PSIA SET PRESSURE + OVERPRESSURE, PSIA

90

100

× 100

Figure 10.26  Constant back pressure sizing factor, Kb, conventional valves – vapors and gases (By permission from Teledyne Farris Engineering Co.).

Ksh = steam superheat correction factor (see Table 10.10). Kn = Napier steam correction factor for set pressures between 1500 and 2900 psig (see Table 10.11). Kd = coefficient of discharge [42]:** 0.953 for air, steam, vapors and gases**

1162  Chemical Process Engineering

CAPACITY WITH BACK PRESSURE RATED CAPACITY WITHOUT BACK PRESSURE

VARIABLE OR CONSTANT BACK PRESSURE SIZING FACTOR Kv 10% OVERPRESSURE BalanSeal Valves Only—Vapors & Gases

1.00 .90 ABOVE 200 PSIG

.80 EXAMPLE: SET PRESSURE = 100 PSIG BACK PRESSURE = ZERO TO 60 PSIG 60 % GAUGE B.P. = 100 ×100 = 60% MAX. FOLLOW DOTTED LINE. KV = 0.88 (FROM CURVE) CAPACITY WITH B.P. = 0.88 × RATED CAPACITY WITHOUT B.P.

.60

KV=

.50

200 100 50 25

EXAMPLE

.70

SET PRESS PSIG

.40

0

10

20

30

40

50

60

70

80

90

100

BACK PRESSURE, PSIG X 100 % GAUGE BACK PRESSURE = SET PRESSURE, PSIG

Figure 10.27A  Variable or constant back pressure sizing factor Kv, at 10% overpressure. BalanSeal® valves only – vapors and gases (By permission from Teledyne Farris Engineering Co.).

CAPACITY WITH BACK PRESSURE KV = RATED CAPACITY WITHOUT BACK PRESSURE

VARIABLE OR CONSTANT BACK PRESSURE SIZING FACTOR KV 21% OVERPRESSURE BalanSeal Valves Only—Vapors & Gases

1.00

ABOVE 200 PSIG

.90

200 100 50 SET PRESS PSIG

.80

.60 .50

25

EXAMPLE

EXAMPLE: SET PRESSURE = 25 PSIG BACK PRESSURE = ZERO TO 17.5 PSIG % GAUGE B.P. = 17.5 x 100 70% MAX. 25 FOLLOW DOTTED LINE. KV = 0.87 (FROM CURVE) CAPACITY WITH B.P. = 0.87 X RATED CAPACITY WITOUT B.P.

.70

.40 0

10

20

30

40

50

% GAUGE BACK PRESSURE =

60

70

BACK PRESSURE, PSIG X 100 SET PRESSURE, PSIG

80

90

100

Figure 10.27B  Variable or constant back pressure sizing factor, Kv, at 21% overpressure, BalanSeal® valves only – vapors and gases (By permission from Teledyne Farris Engineering Co.).

0.724 for ASME Code liquids 0.64 for non-ASME Code liquids 0.62 for rupture disks and non-reclosing spring loaded devices ASME [1], Par. UG - 127 **0.975 per API RP-520, balanced valve. To convert flow capacity from SCFM to lb/h use

W=

(M)(V) 6.32

Process Safety and Pressure-Relieving Devices  1163

1.00 .90 EXAMPLE

KW = CAPACITY WITH B.P.

RATED CAPACITY BASED ON ∆P

VARIABLE OR CONSTANT BACK PRESSURE SIZING FACTOR KW

.80 .70

EXAMPLE: SET PRESSURE = 100 PSIG BACK PRESSURE = ZERO TO 40 PSIG 40 % GAUGE B.P. =100 X100 = 40% MAX. FOLLOW DOTTED LINE. KW = 0.88 (FROM CURVE) CAPACITY WITH B.P. = 0.88 X RATED CAPACITY (FPR 10% OVERPRESSURE, NON-CODE VALVES, MULTIPLY BY KP FACTOR 0.6 IN CAPACITY FORMULA

.60 .50 .40 0

10

20

30 40 50 60 70 80 % GAUGE BACK PRESSURE = BACK PRESSURE, PSIG X 100 SET PRESSURE, PSIG

90

100

Figure 10.28  Variable or constant back pressure factor, Kw, for liquids only, BalanSeal® valves. Use this factor as a divisor to results of constant back pressure equations or tables (By permission from Teledyne Farris Engineering Co.).

where M  = molecular weight of flowing media. V  = flow capacity, scfm W = flow capacity, lb/h Where the pressure relief valve is used in series with a rupture disk, a combination capacity of 0.8 must be applied to the denominator of the referenced equations. Refer to a later section of this text or to specific manufacturers. **Some manufacturers’ National Board-Certified Tests will have different values for some of their valves. Be sure to obtain the manufacturer’s certified coefficient for the valve you select.

10.23 Sizing Valves for Liquid Expansion (Hydraulic Expansion of Liquid-Filled Systems/Equipment/Piping) The API Code RP-520 [5a] suggests the following to determine the liquid expansion rate to protect liquid-filled (full) systems or locations where liquid could be trapped in parts of a system or an area could be subjected to blockage by process or operational accident. When thermal input from any source can/could cause thermal expansion of the enclosed liquid:



GPM = BH/(500 G Ch)

(10.24)

This relation can be converted to solve for the required orifice area at 25% overpressure for non-viscous liquids discharging to atmosphere [43]



A = BH/(13600)(P1G)0.5, in2.

where GPM = flow rate at the flowing temperature, gpm

(10.24A)

Saturated steam temperature ° F.

250

259

278

308

324

338

350

361

371

380

385

395

403

409

416

422

436

448

460

470

480

489

497

506

513

520

527

533

540

546

552

Set pressure psig

15

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

100D

100

280

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

100

100

100

300

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

100

100

100

100

320

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

100

100

100

99

99

340

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

100

100

100

99

99

99

99

360

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

100

100

100

100

99

99

99

98

98

380

Total temperature in degrees fahrenheit

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

100

100

100

100

100

99

99

99

98

98

98

98

400

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

100

100

100

100

99

99

99

99

98

98

98

87

97

97

97

420

-

-

-

-

-

-

-

-

-

-

-

-

-

-

100

100

100

99

99

99

99

98

98

98

97

97

97

96

96

96

96

440

Table 10.10  Steam superheat correction factors, Ksh.

-

-

-

-

-

-

-

-

-

-

-

-

-

100

100

99

99

98

98

98

97

97

97

96

96

96

96

95

95

95

95

440

-

-

-

-

-

-

-

-

-

-

-

100

100

99

99

98

97

97

97

96

96

96

95

95

95

95

94

94

94

94

94

430

-

-

-

-

-

-

-

-

-

100

100

99

99

98

97

96

96

96

-

-

-

-

-

-

100

100

100

99

99

98

97

96

96

95

95

94

94

94

95 95

93

93

93

93

93

93

92

92

92

92

92

520

95

95

94

94

94

94

93

93

93

93

93

500

-

-

-

100

100

100

100

99

99

98

97

96

96

95

94

93

93

93

93

93

92

92

92

92

92

92

91

91

91

91

91

540

1000

100

100

100

99

99

98

97

97

96

95

94

94

93

93

92

92

92

92

92

91

91

91

91

91

91

90

90

90

90

90

560

100

99

99

99

99

98

97

96

95

94

94

93

93

92

92

91

91

91

91

91

90

90

90

90

90

90

89

89

89

89

89

580

99

35

98

97

97

96

95

94

94

93

92

92

92

91

91

90

90

90

90

90

89

89

89

89

89

89

89

88

88

88

88

600

97

96

96

95

95

94

94

93

92

92

91

91

91

90

90

89

89

89

89

89

88

88

88

88

88

88

88

87

87

87

87

620

95

94

94

93

93

92

92

91

91

90

90

90

89

89

89

88

88

88

88

88

87

87

87

87

87

87

87

87

87

86

86

640

93

93

92

92

92

91

90

90

90

89

89

89

88

88

88

87

87

87

87

87

86

86

86

86

86

86

86

86

86

86

86

660

92

91

91

90

90

90

89

89

89

88

88

88

87

87

87

86

86

86

86

86

86

86

86

85

85

85

85

85

85

85

85

680

90

90

89

89

89

88

88

88

87

87

87

87

86

86

86

86

85

85

85

85

85

85

85

85

85

85

84

84

84

84

84

700

89

89

88

88

88

87

87

87

86

86

86

86

86

85

85

85

85

85

84

84

84

84

84

84

84

84

84

84

84

83

83

720

88

87

87

87

87

86

86

86

86

85

85

85

85

84

84

84

84

84

84

84

83

83

83

83

83

83

83

83

83

83

83

740

87

86

86

86

86

85

85

85

85

84

84

84

84

84

83

83

83

83

83

83

83

82

82

82

82

82

82

82

82

82

82

760

86

85

85

85

85

84

84

84

84

84

83

83

83

83

83

82

82

82

82

82

82

82

82

82

82

82

82

82

82

81

81

780

85

84

84

84

84

84

83

83

83

83

82

82

82

82

82

82

82

81

81

81

81

81

81

81

81

81

81

81

81

81

81

800

84

83

83

83

83

83

83

82

82

82

82

82

82

81

81

81

81

81

81

81

81

80

80

80

80

80

80

80

80

80

80

820

83

83

82

82

82

82

82

81

81

81

81

81

81

81

81

80

80

80

80

80

80

80

80

80

80

80

80

80

79

79

79

840

82

82

82

81

81

81

81

81

81

80

80

80

80

80

80

80

80

79

79

79

79

79

79

79

79

79

79

79

79

79

79

860

81

81

81

81

80

80

80

80

80

80

80

79

79

79

79

79

79

79

79

79

79

79

79

78

78

78

78

78

78

78

78

880

80

80

80

80

80

80

79

79

79

79

79

79

79

79

78

78

78

78

786

78

78

78

78

78

78

78

78

78

78

78

78

900

80

79

79

79

79

79

79

79

78

78

78

78

78

78

78

78

78

78

78

78

77

77

77

77

77

77

77

77

77

77

77

920

79

79

79

79

78

78

78

78

78

78

78

78

78

77

77

77

77

77

77

77

77

77

77

77

77

77

77

77

77

77

76

940

77

77

77

77

77

77

77

77

77

76

76

76

76

76

76

76

76

76

76

76

76

76

76

76

76

76

76

75

75

75

75

980

77

77

77

77

76

76

76

76

76

76

76

76

76

76

76

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

1000

(Continued)

78

78

78

78

78

78

77

77

77

77

77

77

77

77

77

77

77

76

76

76

76

76

76

76

76

76

76

76

76

76

76

960

1164  Chemical Process Engineering

558

563

569

574

579

584

588

593

597

606

615

622

630

636

644

650

658

663

669

675

680

686

691

1100

1150

1200

1250

1300

1350

1400

1450

1500

1600

1700

1800

1900

2000

2100

2200

2300

2400

2500

2600

2700

2800

2900

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

280

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

300

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

320

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

340

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

360

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

380

Total temperature in degrees fahrenheit 400

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

420

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

440

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

Courtesy of Teledyne-Farris Engineering Co., Cat. 187C.

Saturated steam temperature ° F.

Set pressure psig

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

440

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

430

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

500

Table 10.10  Steam superheat correction factors, Ksh. (Continued)

520

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

540

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

560

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

580

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

100

100

100

600

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

100

100

100

100

99

99

99

620

-

-

-

-

-

-

-

-

-

-

-

-

100

100

100

100

100

99

99

99

98

98

98

640

-

-

-

-

-

-

-

-

-

-

100

99

99

99

99

99

99

98

98

97

97

96

95

660

-

-

-

-

-

-

100

100

100

100

98

98

97

97

97

97

97

96

96

95

95

94

94

680

-

-

-

100

98

98

98

98

98

98

97

97

96

96

96

95

95

94

94

93

93

92

92

700

-

100

100

96

95

95

95

95

95

96

96

95

95

94

94

94

93

93

92

92

91

91

90

720

100D

95

95

93

93

93

93

93

93

93

93

93

93

93

92

92

92

91

91

90

90

90

89

740

90

90

90

90

90

91

91

91

91

91

91

91

91

91

91

90

90

90

89

89

89

88

88

760

87

88

88

88

88

89

89

89

89

89

89

89

89

89

89

89

89

88

88

88

87

87

87

780

8B4

85

85

85

86

87

87

87

87

87

88

88

88

88

88

88

88

87

87

87

86

86

86

800

82

82

83

84

84

85

85

85

86

86

86

86

86

86

87

86

86

86

86

85

85

85

85

820

80

80

81

82

83

83

84

84

84

84

85

85

85

85

86

85

85

85

85

85

84

84

84

840

78

78

79

80

81

82

82

82

83

83

84

84

84

84

84

84

84

84

84

84

83

83

83

860

76

76

78

79

80

80

81

8

82

82

82

82

83

83

84

83

83

83

83

83

82

82

82

880

75

75

76

77

78

79

79

80

81

81

81

81

82

82

83

82

82

82

82

82

81

81

81

900

73

74

75

76

77

78

78

79

79

80

80

80

81

81

82

81

81

81

81

81

81

81

81

920

72

73

74

75

76

77

77

78

78

79

79

79

79

80

81

80

81

80

80

80

80

80

80

940

71

72

73

74

75

76

76

77

77

78

78

79

79

79

80

80

80

80

79

79

79

79

79

960

70

71

72

73

74

75

75

76

77

77

78

78

78

78

79

79

79

79

79

79

78

78

78

980

69

70

71

72

73

74

75

75

76

76

77

77

77

78

78

78

78

78

78

78

78

78

78

68

69

70

71

72

73

74

74

75

76

76

76

77

77

78

78

78

78

77

77

77

77

77

1000

Process Safety and Pressure-Relieving Devices  1165

1.005

1.005

1.006

1.007

1.007

1.008

1.009

1.009

1.010

1.011

1.011

1.012

1.013

1.014

1500

1510

1520

1530

1540

1550

1560

1570

1580

1590

1600

1610

1620

1630

1770

1760

1750

1740

1730

1720

1710

1700

1690

1680

1670

1660

1650

1640

Set pres. psig

1.024

1.023

1.023

1.021

1.021

1.020

1.019

1.019

1.018

1.017

1.016

1.016

1.015

1.014

Kn

1910

1900

1890

1880

1870

1860

1850

1840

1830

1820

1810

1800

1790

1780

Set pres. psig

1.036

1.035

1.034

1.033

1.032

1.031

1.031

1.030

1.029

1.028

1.027

1.026

1.026

1.025

Kn

Courtesy Teledyne-Farris Engineering Co., Cat. 187C.

Kn

Set pres. psig

Kn Napier correction factor for set pressures between 1500 and 2900 at 10% overpressure

Sizing factors for steam

2050

2040

2030

2020

2010

2000

1990

1980

1970

1960

1950

1940

1930

1920

Set pres. psig

1.049

1.048

1.047

1.046

1.045

1.044

1.043

1.042

1.041

1.040

1.040

1.039

1.038

1.037

Kn

2190

2180

2170

2160

2150

2140

2130

2120

2110

2100

2090

2080

2070

2060

Set pres. psig

1.049

1.063

1.062

1.061

1.060

1.059

1.058

1.057

1.055

1.054

1.053

1.052

1.051

1.050

Kn

2330

2320

2310

2300

2290

2280

2270

2260

2250

2240

2230

2220

2210

2200

Set pres. psig

1.082

1.081

1.079

1.078

1.077

1.075

1.074

1.073

1.072

1.070

1.069

1.068

1.067

1.066

Kn

Table 10.11  Napier steam correction factors, Kn, for set pressures between 1500 and 2900 psig.

2470

2460

2450

2440

2430

2420

2410

2400

2390

2380

2370

2360

2350

2340

1.102

1.101

1.099

1.098

1.096

1.095

1.093

1.092

1.090

1.089

1.087

1.086

1.085

1.083

Kn

0.1906P -1000 0.2292P -1061

Set pres. psig

Kn =

Equation:

2610

2600

2590

2580

2570

2560

2550

2540

2530

2520

2510

2500

2490

2480

Set pres. psig

1.126

1.124

1.122

1.121

1.119

1.117

1.115

1.114

1.112

1.110

1.109

1.107

1.105

1.104

Kn

2750

2740

2730

2720

2710

2700

2690

2680

2670

2660

2650

2640

2630

2620

Set pres. psig

where P = relieving pressure, psia

1.155

1.152

1.150

1.148

1.146

1.144

1.142

1.140

1.138

1.136

1.134

1.132

1.130

1.128

Kn

1.189 1.192

2900

1.187

1.184

1.181

1.179

1.176

1.174

1.171

1.169

1.166

1.164

1.161

1.159

1.157

Kn

2890

2880

2870

2860

2850

2840

2830

2820

2810

2800

2790

2780

2770

2760

Set Pres. psig

1166  Chemical Process Engineering

Process Safety and Pressure-Relieving Devices  1167 Table 10.8  Excel spreadsheet results for vapor relief valve sizing of Example 10.3. Vapor relief valve sizing:    Valve name:        Example 10.3 Required relief vapor rate, lb/hr.:

620.000

Valve set pressure, psig:

290.000

Percentage of valve overpressure, (%):

10.000

Upstream fluid temperature, deg. F:

133.4000

Fluid compressibility factor:

0.8370

Fluid molecular weight:

17.030

Ratio of specific heats of fluid k=Cp/Cv:

1.310

Gas constant determined by ratio of k:

347.913

Calculated valve orifice area, in2:

.030

Nearest standard orifice area, in2:

.110

Nearest standard orifice size:

D

Preferred valve body size. (In-out) inches:

1-2

Maximum vapor flowrate with std. Orifice, lb/hr.

2305.658

Reaction force, lb:

28.0

B H G Ch A P1

= cubical expansion coefficient per degree F for the liquid at the expected temperature. For values, see specific liquid data or see table below for typical values. = total heat transfer rate, Btu/h. For heat exchangers, Ref [5a] recommends that this value be taken as the maximum exchanger duty during operation. = specific gravity referred to water. Ignore fluid compressibility. = specific heat of the trapped fluid, Btu/lb/oF = required orifice area, in2. = set pressure of valve, psig

Reference [5a] in Appendix D cautions that if the vapor pressure of the fluid at the temperature is greater than the relief set/design pressure that the valve must be capable of handling the rate of vapor generation. Other situations should be examined as the thermal relief by itself may be insufficient for total relief. Typical values for cubic expansion coefficient. Liquid

Value

3−34.9o API gravity

0.0004

35−50.9o API gravity

0.0005

51−63.9o API gravity

0.0006

64−78.9o API gravity

0.0007

79−88.9o API gravity

0.0008

89−93.9o API gravity

0.00085

1168  Chemical Process Engineering Table 10.9  Excel spreadsheet results for liquid relief valve sizing of Example 10.4. Liquid relief valve sizing:    Valve name:        Example 10.4 Required liquid flow rate, U.S. gpm:

310.000

Valve set pressure, psig:

100.000

Valve back pressure, psig:

25.000

Fluid specific gravity:

1.4500

Fluid viscosity, cP:

3200.000

Viscosity correction factor:

1.000

Back pressure correction factor:

.920

Overpressure correction factor:

1.000

Calculated valve orifice area, in^2:

1.722

Nearest standard orifice area, in^2:

1.838

Nearest standard orifice size:

K

Preferred valve body size, (in-out), inches:

3-4

Maximum liquid flow rate with std. Orifice, lb/hr.:

330.845

Viscosity correction factor:

.794

Reynolds number:

290.

Calculated valve orifice area, in2:

2.170

Nearest standard orifice area, in2:

2.853

Nearest standard orifice size:

L

Preferred valve body size, (in-out) inches:

3-4 or 4-6

Maximum liquid flow rate, gpm:

408.

94−100o API gravity and lighter

0.0009

Water

0.0001

(Source: By permission API, Ref [5a].)

Note: Reference of the API gravity values to refinery and petrochemical plant fluids will show that they correspond to many common hydrocarbons.

10.24 Sizing Valves for Subcritical Flow: Gas or Vapor but not Steam [5d] If the ratio of backpressure to inlet pressure to valve exceeds the critical pressure ratio, Pc/P1. From Eq. 10.7,



 Pc   2   P  =  (k + 1)  1  

k/(k −1)

Process Safety and Pressure-Relieving Devices  1169 the flow through the valve is subcritical. The required area (net, free unobstructed) is calculated for a conventional relief valve, including sizing a pilot-operated relief valve [5d]:



A=

W 735 × F2K d K c

ZT , in2. MP1 (P1 − P2 )

(10.25A)

A=

V 4645 × F2K d K c

ZTM , in2. P1 (P1 − P2 )

(10.25B)

A=

V 864 × F2K d K c

ZTG , in2. P1 (P1 − P2 )

(10.25C)

A=

17.9 × W ZT , mm2 F2K d K c MP1 (P1 − P2 )

(10.26A)

47.95 × V ZTM , mm2 F2K d K c P1 (P1 − P2 )

(10.26B)

258 × V ZTG , mm2 F2K d K c P1 (P1 − P2 )

(10.26C)

or



or



In SI Units:

or

A=



or

A=



When using a balanced/bellows relief valve in the subcritical, use Eqs. (10.18 - 10.22); however, the backpressure correction factor for this condition should be supplied by the valve manufacturer [5d]. For subcritical, conventional valve:



(k −1)/k  k  2/k  1 − (r) (r) F2 =   1− r  k − 1  

  

(10.27)

where A = required effective discharge area of the device, in2 (mm2) W = required flow through the device, lb/h (kg/h) F2 = coefficient of subcritical flow =

(k −1)/k   k  2/k  1 − r (r)     (Figure 10.29) k −1  1− r 

r = ratio of back pressure to upstream relieving pressure, P2/P1 Kd = effective coefficient of discharge. For preliminary sizing (i) 0.975, when a pressure relief valve is installed with or without a rupture disk in combination. (ii) 0.62, when a pressure relief valve is not installed and sizing is for a rupture disk. Kc = combination correction factor for installation with a rupture disk upstream of the pressure relief valve. = 1.0, when a rupture disk is not installed. = 0.9, when a rupture disk is installed in combination with a pressure relief valve and the combination does not have a published value.

1170  Chemical Process Engineering 1.0

0.9

1

1.

2

k=

CRITICAL FLOW LINE

k=

1.

k=

00

6

1. 4

1. 1. k=

0.7

8

0.8

k=

F2

0.6 0.4

0.7

0.6

0.5

0.8

0.9

1.0

P2 r= P1

Figure 10.29  Values of F2 for subcritical flow of gases and vapors (By permission from Sizing, Selection and Installation of PressureRelieving Devices in Refineries, Part I “Sizing and Selection”, API RP – 520, 5th ed., July 1990, American Petroleum Institute).

Z = compressibility factor for the deviation of the actual gas from a perfect gas, evaluated at relieving inlet conditions. T = relieving temperature of the inlet gas or vapor, oR = oF + 460 (K = oC + 273) M = molecular weight of the gas or vapor. P1 = upstream relieving pressure, psia (kPaa). This is the set pressure plus the allowable overpressure plus atmospheric pressure. Fire Sizing Vessel (Tank) Selection Diagram L

D

Spherical Tank

F

Cylindrical Tank

D

H

H

D

Cylindrical Vessel (tank) Orientation Diagram L L Horizontal

D

F

H

Figure 10.30  Vessel types for external fires.

H

Vertical

F

Process Safety and Pressure-Relieving Devices  1171 P2 = back pressure, psia (kPaa). V = required flow through the device, scfm at 14.7 psia and 60oF (Nm3/min at 101.325 kPaa and 0oC) G = specific gravity of gas at standard conditions referred to air at standard conditions (normal conditions). G = 1 for air at 14.7 psia and 60oF (101.325 kPaa and 0oC)

10.25 Emergency Pressure Relief: Fires and Explosions Rupture Disks Process systems can develop pressure conditions that cannot timely or adequately be relieved by pressure relieving valves as described earlier. These conditions are primarily considered to be (1) internal process explosions due to runaway reactions (see Design Institute for Emergency Relief Systems (DIERS) [13]) in pressure vessels or similar containers such as an atmospheric grain storage silo (dust explosion typically) or storage bin; (2) external fires developed around, under, or encompassing a single-process vessel or a system of process equipment, or an entire plant; and (3) other conditions in which rapid/instantaneous release of developed pressure and large volumes of vapor/ liquid mixture is vital to preserve the integrity of the equipment. For these conditions, a rupture disk may perform a vital safety relief function. Sometimes the combination of a rupture disk and pressure-relieving valve will satisfy a prescribed situation, but the valve cannot be relied on for instantaneous release (response time lag of usually a few seconds). The ASME Pressure Vessel Code [1] and the API codes or recommended procedures [5, 8, 9] recognize and set regulations and procedures for capacity design, manufacture and installation of rupture disks, once the user has established the basis of capacity requirements.

10.26 External Fires There have been at least six different formulas proposed and used to determine the proper and adequate size of rupture disk openings for a specific relieving condition. The earlier studies of Sylvander and Katz [34] led to the development of the ASME and API recommendations. This approach assumes that a fire exists under or around the various vessels in a process. This fire may have started from static discharge around flammable vapors, flammable liquids released into an area drainage ditch, combustible gas/vapors released through flange leaks or ruptures, over pressure, or many other potential hazards. The codes [9] suggest typical lists of potential hazards and some approach to determine the types of process conditions that can cause a fire. A suggested extended list (Figure 10.14A) is presented earlier in this chapter and in the following paragraphs. There are no formulas to establish a code capacity for the volume of vapors to be released under any one of the possible plant “failure” conditions. Therefore, the codes assume, based on evaluation of test data, that fire is under or around the various vessels and that absorbed heat vaporizes the contained fluid. The information presented is taken from API-RP-520/521 latest editions [5, 8, 9] and the ASME code [1]. The designer should be familiar with the details in these codes.

10.27 Set Pressures for External Fires The MAWP (discussed earlier) for the vessel or each vessel should be the maximum set pressure for the rupture disk. Furthermore, estimated flame temperatures of usually 2500-3500°F should be used to establish the reduced vessel metal wall temperatures (recognizing the benefits of code recommended fireproof insulation if properly applied to prevent dislodging by fire water hose pressures impacting on the insulation). The MAWP should then be reestablished by calculation using the metal wall code allowable stresses at the new estimated reduced metal temperature. This should be the maximum set pressure for the rupture disk provided the new lower value does not cause it to be below or too close to the usual expected process operating temperature. In such a case, the set pressure should be 25% above the operating condition, exclusive of fire, not exceeding the MAWP values [44].

1172  Chemical Process Engineering When a rupture disk relieves/blows/ruptures, it creates a rapid depressuring of the process system and a likely discharge of some or all vapor/liquid in the vessel(s), discharging to the properly designed disposal system. Therefore, great care should be given to setting the rupture disk pressure because it does not have an accumulation factor, but bursts at the prescribed pressure of the disk, taking into account the code allowed manufacturing tolerances. Twophase flow will most likely occur when the disc (or safety relief valve) blows (see later references to explosions and DIERS work [13, 25]). Figure 10.30 shows vessels for external fires. For unexpected runaway or process overpressure not subject to external fire, the rupture disk set pressure, which is the bursting pressure, should be sufficiently higher than the expected “under acceptable control” conditions for the operation to avoid the frequent burst and shutdown of the process. Usually this is found to be about 20-30% above the maximum expected peak operation pressure. Again, recognize the requirements for the relieving device set pressure not to exceed the actual vessel MAWP at the expected relieving temperature (by calculation or pilot plant test data).

10.28 Heat Absorbed The amount of heat absorbed by a vessel exposed to an open fire is markedly affected by the size and character of the installation and by the environment. These conditions are evaluated by the following equivalent formulas, in which the effect of size on the heat input is shown by the exponent of Aw, the vessel wetted area, and the effect of other conditions, including vessel external insulation is included in a factor F [5]:



q = 21,000FA −w0.18

(10.28)



Q = 21,000FA +w0.82

(10.29)

The Severe Case Where the facility does not have prompt fire-fighting equipment and inadequate drainage of flammable materials away from the vessel:

Q = 34,500FA +w0.82



(10.30)

where q = average unit heat absorption, in Btu/h ft2 of wetted surface. Q = total heat absorption (input) to the wetted surface, in Btu/h. Aw = total wetted surface, in ft2. The expression A −w0.18 is the area exposure factor or ratio. This recognizes that large vessels are less likely to be completely exposed to the flame of an open fire than small vessels. It is recommended that the total wetted surface (A in the foregoing formulas) be limited to that wetted surface included within a height of 25 ft above “grade” or, in the case of spheres and spheroids, to the elevation of the maximum horizontal diameter or a height of 25 ft, whichever is greater. (A more conservative approach is recommended.) The term “grade” usually refers to ground grade, but may be any level at which a sizable area of exposed flammable liquid could be present [5, 8]. F = environment factor, values of which are shown in Table 10.12 for various types of installation. Surface areas of vessel elliptical heads can be estimated by 1.15 x cross-sectional area of vessel. These are the basic formulas for the usual installation, with good drainage and available fire-fighting equipment. These formulas are plotted on Figure 10.31 showing curves for Q for various values of factor F. The approximate amount of insulation corresponding to the factors is indicated.

Process Safety and Pressure-Relieving Devices  1173 Table 10.12  Environmental factor, F. Type of installation

Factor*

Bare vessel

1.0

Insulated vessel† (These arbitrary insulation conductance values are shown as examples and are in British Thermal Units per hour per square foot per oF) (a) 4.0 Btu/hr/sq ft/oF

(1 in thick)

0.3

(b) 2.0 Btu/hr/sq ft/oF

(2 in thick)

0.15

(c) 1.0 Btu/hr/sq ft/oF

(4 in thick)

0.075

(d) 0.67 Btu/hr/sq ft/oF

0.05

(e) 0.5 Btu/hr/sq ft/oF

0.0376

(f) 0.4 Btu/hr/sq ft/oF

0.03

(g) 0.32 Btu/hr/sq ft/oF

0.026

Water–application facilities, on bare vessel**

1.0

Depressurizing and emptying facilities††

1.0

Underground storage

0.0

Earth–covered storage above grade

0.03

* These are suggested values for the conditions assumed in code [36] Par D 5.21. When these conditions do not exist, engineering judgment should be exercised either in selecting a higher factor in providing means of protecting vessels from fire exposure as suggested in [36], par. D.8. † Insulation shall resist dislodgement by fire hose streams. For example, a temperature difference of 1600oF was used. These conductance values are based on insulation having conductivity of 48TS/hr–ft–oF per inch at 1600oF and correspond to various thicknesses of insulation between 1 and 12 inches. ** See code for recommendations regarding water application and insulation. †† Depressurizing will provide a lower factor if done promptly, but no credit is to be taken when safety valves are being sized for fire exposure. See [36], Part I, par. D. 8.2. By permission, API–RP–520, American Petroleum Institute, Div. of Refining (1967) and adapted for this current edition by this author from later editions of the code (197) and (1990). Items d, e, and f above from API–RP–520, 5th Ed. (1990). For complete reference, see the latest code cited in its entirety.

Referring to the wetted surface, Aw, the surface areas of ASME flanged and dished head, ASME elliptical heads, hemispherical heads, and so on are often the end assemblies on a cylindrical vessel. If a formula is not available to accurately estimate the wetted surface, or the blank diameters used for fabrication which would give a close approximation of the inside surface of the head, use an estimated area for the dished or elliptical heads as 1.2 × cross-section area of the vessel based on its diameter.

10.29 Surface Area Exposed to Fire The surface area of a vessel exposed to fire which is effective in generating vapor is that area wetted by its internal liquid contents. The liquid contents under variable level conditions should ordinarily be taken at the average inventory (see note below). 1. Liquid-full vessels (such as treaters) operate liquid full. Therefore, the wetted surface would be the total vessel surface within the height limitation.

2

su

la tio

nT hi

ck

100 8 6 5 4 3 2 10 10,000

2

1. 0

1,000 8 6 5 4 3

In

A = Wetted Surface Area, ft.2

2

F=

10,000 8 6 5 4 3

ne ss Ab ou t4 Ab in . ou Co t2 nd in Ab uc . ou ta nc t1 eB in TU . (S /(H pr r.) in En (ft kl vi . 2) er ro (ºF Pr nm ) ot en ec 1 t ta ed Ba lF re Ve ac Ve ss to F 2 el ss = r, s) el 0. F 07 5 F= 4 0. 15 F= 0. 3

1174  Chemical Process Engineering

Notes: Based on API RP-520, 1988 Q = 21,000 FA.82 On Insulated Vessels Insulation shall resist Dislodgement by Fire Hose Streams. Surface Area shall include only Totally Wetted Surface within a Height of 25 ft. Above Grade or in the case of Spheres or Spheroids to the Elevation of the Maximum Horizontal Diameter. The term Grade usually Refers to Ground Grade but may be any Level at which a Sizable Area of Exposed Flammable Liquid may be Present. For Flammable Insulation use F = 1.0 or Bare Vessel Equivalent.

3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 100,000 1,000,000 10,000,000 Q = Heat Absorbed, BTU/Hr.

3 4 56 8 100,000,000

Figure 10.31  API formula for heat absorbed from fire on wetted surface of pressure vessel. (By permission from Sizing, Selection and Installation of Pressure-Relieving Devices in Refineries, Part I “Sizing and Selection”, API RP – 520, 5th ed., July 1990).

2. Surge drums (vessels) usually operate about half full. Therefore, the wetted surface would be calculated at 50% of the total vessel surface, but higher if design is based on greater figure. 3. Knockout drums (vessels) usually operate with only a small amount of liquid. Therefore, the wetted surface would be in proportion, but to maximum design liquid level. 4. Fractionating columns usually operate with a normal liquid level in the bottom of the column and a level of liquid on each tray. It is reasonable to assume that the wetted surface be based on the total liquid within the height limitation – both on the trays and in the bottom. 5. Working storage tanks’ wetted surface is usually calculated on the average inventory, but at least 25 ft height, unless liquid level can reasonably be established as higher; if established as higher, then use higher value. This should be satisfactory not only because it conforms to a probability, but also because it provides a factor of safety in the time needed to raise the usually large volume of the liquid’s sensible heat to its boiling point.   It is recommended that the wetted area be at least to the height as defined in the definition of area, Aw. Note: E.E. Ludwig [44] suggested that determining Aw values may be more conservative and not conform exactly to Code [5a, c, and d] recommendations. The Code [5a, Part 1, Sect D, Par. D.4] reads, “to determine vapor generation, only that portion of the vessel that is wetted by its internal liquid and is equal to or less than 25 ft above the source of flame needs to be recognized”. 6. E. E. Ludwig’s experience [44] in investigating many industrial fires and explosions, it is suggested that the height limit of 25 ft above “grade” or fire source level is too low for many process plants, and therefore, the effect of a large external fire around equipment can reach to 100 ft with 75 ft perhaps being acceptably conservative. Ludwig expressed concern in using the 25-ft limit, for example, for a horizontal butane storage “bullet” tank, 15 ft diameter and raised 15 ft off grade to its bottom. Furthermore, the fact that any fire will engulf the entire vessel should be considered and the wetted surface should be the entire vessel. The same concern applies to a vertical distillation column over 25 ft high. He suggested that the wetted surface should be at least 80% of the vessel height and further recognized that

Process Safety and Pressure-Relieving Devices  1175 the tray liquid will wet the walls and be evaporated only as long as there is liquid to drain off the trays. But for a conservative approach, he assumed that there are always wetted walls in the column. Each situation must be evaluated on its own merits or conditions and operating situation, and even its environment with respect to the plant flammable processing equipment.

10.30 Relief Capacity for Fire Exposure In calculating the relief capacity to take care of external fire the following equation is used:



W = Q/L

(10.31)

where W = weight rate of flow of vapors, lb/h L = latent heat at allowable pressure, Btu/lb Q = total heat absorption from external fire, Btu/h

10.31 Code Requirements for External Fire Conditions Paragraph UG-125 (3) of the ASME code [1] requires that supplemental relieving capacity be available for an unfired pressure vessel subject to external accidental fire or other unexpected source of heat. For this condition, relieving devices must be installed to prevent the pressure from rising more than 21% [9] above the MAWP of the vessel. The set pressure should not exceed the vessel MAWP. A single relief device may be used for this capacity as long as it also meets the normal overpressure design for other possible causes of 10%. If desirable, multiple separate devices can be installed to satisfy both potential overpressure situations. For this condition, the API-RP-521 code [9] (Figure 10.7A) shows an allowable 16% maximum accumulation relieving pressure above the set pressure. For external fire conditions on a vessel, the maximum allowable accumulation pressure is 21% above the set pressure [9] for both single or multiple relieving devices (Figure 10.7A).

10.32 Design Procedure The usual procedure for determining relief area requirements is as follows: 1. Determine the external surface area exposed to fire, as set forth by Eq. 10.29,



Q = 21,000FA +w0.82 and Table 10.10 and the paragraph on Surface Area Exposed to Fire. 2. Determine the heat absorbed, Q, from Figure 10.30. 3. Calculate the rate of vaporization of liquid from Eq. 10.31



W=

Q L

4. V  erify critical pressure from Eq. 10.7 and establish actual back pressure for relieving device. 5. Calculate relieving area by applicable equation for critical or non-critical flow, using the flow rate determined in (3) above. (See Eq. 10.10 and following.) The area actually selected for orifice of safety type valve must have orifice equal to or greater than calculated requirements. For a rupture disk

1176  Chemical Process Engineering application, the full free open cross-sectional area of pipe connections in inlet and exit sides must be equal to or be greater than the calculated area. 6. Select a valve or rupture disk to accommodate the service application. 7. To provide some external protection against the damage that an external fire can do to a pressure relief valve or rupture disk, Ludwig [44] recommends that these devices be insulated after installation in such a manner as not to restrict their action but to provide some measure of reliable performance, even if the vessel is not insulated.

Example 10.5 Calculate the required area for the relief valve for a horizontal non-insulated storage tank, exposed to fire and containing liquid vinyl chloride monomer (CH2 = CHCl). The tank dimensions are shown in Figure 10.32. The design pressure is 100 psig, and the discharge from the relief valve will be vented to a gas holder operating at 0.5 psig. A 20% accumulation (over pressure) is assumed over the design pressure. The average inventory of the tank contents will equal 75% of the vessel’s inside diameter.

Solution The wetted surface for the vessel equals the wetted area of the two heads plus that of the cylindrical section. Thus:

Aw =



2π(yD1 )2 + D2Lπ 4

where y   = the fraction of the vessel’s internal diameter (ID) that is equivalent to average liquid inventory. D1 = diameter of circular blank from which head is shaped (D1 will depend on the type of head). D2 = y times the ID of the tank. L   = tangent-to-tangent length of the cylindrical section. D1 = 11 ft.



2π [(0.75)(11)] + (0.75)(10)(20)π 4 = 578.15 ft 2 . 2

Aw =

20 ft. Vent to gas holder Relief valve

Uninsulated tank

10 ft.

Figure 10.32  A horizontal, non-insulated storage tank of Example 23.5.

Grade

Process Safety and Pressure-Relieving Devices  1177 The heat input to the wetted surface of the vessel is given by Eq. 10.29,

Q = 21,000FA +w0.82

where

F  = environmental factor, F = 1.0 (Bare vessel, Table 10.12).

Q = 21,000(1)(578.15)0.82 = 3.864 × 106 Btu/hr. The mass flow rate of vinyl chloride m, lb/h is:

m = Q/λ = 3.864 × 106 /116 = 33,314.6 lb/hr. The relieving temperature at the set pressure plus 20% over pressure plus 14.7 is 135oF. At this temperature, the latent heat of vaporization is 116 Btu/lb. Molecular weight of vinyl chloride is: M = 62.5. Ratio of specific heat capacities k = 1.17 The relieving pressure, P P = set pressure + over pressure + atmospheric pressure    = 100 + (100 × 0.2) + 14.7    = 134.7 psia. The critical properties of vinyl chloride are: Pc = 809 psia. Tc = 313.7°F Pr = P/Pc = 134.7/809 =0.167 Tr = T/Tr = (135 + 460)/(313.7 + 460) = 0.77 From the compressibility factor chart, Z = 0.86 The value of C with k = 1.17 is obtained by substituting the value of k in Eq. 10.11H,

 2  C = 520 k   k + 1 

(k +1)/(k −1)

 2  C = 520 1.17   1.17 + 1  C = 334.17

(1.17 +1)/(1.17 −1)

For vapors and gases, in lb/hr; Kb = 1.0; “C” from Figure 10.25, P is the relieving pressure absolute, psia. Substituting the value of k in Eq. 10.10.

A=

W TZ , in2. CK d PK b M

1178  Chemical Process Engineering

A=

(33314.5) (595)(0.86) (334.17)(0.953)(134.7)(1) 62.5

= 2.22 in 2 . The nearest standard orifice area is 2.853in2. The pressure relief valve designation is L and the preferred valve body size is 3-4 or 4-6. The maximum vapor rate with the nearest standard orifice area is:

W = ACK d PK b M/(TZ) = (2.853)(334.17)(0.953)(134.7)(1) 62.5 / (595 × 0.86) = 42,772.2 lb/hr. The Excel spreadsheet (Example 10.5.xlsx) shows the calculations of Example 10.5 and the results are shown in Table 10.13.

Table 10.13  Excel spreadsheet results of relief valve sizing for fire of Example 10.5. Results of relief valve sizing for fire flow Relief type

Fire

Set Pressure at inlet

100

psig

Relieving Pressure

134.7

psig

Relieving Temperature

135

o

Molecular weight, Mw

62.5

 

Compressibility factor, Z

0.86

 

Kd

0.953

 

Kb

1

 

Ratio of specific heat capacities, k=Cp/Cv

1.17

 

Environmental factor, F

1

 

Latent heat of vaporization, λ

116

Btu/lb

Calculated heat input, Q

3864493

Btu/h

Calculated mass flow rate of liquid, m

33314.6

lb/h

Calculated constant, C

334.17

 

Calculated area, A

2.22

in2

Nearest orifice area

2.853

in2

Orifice Size

L

 

Maximum Liquid flow rate

42772.2

lb/h

Reaction Force

297.70866

lbf

F

Process Safety and Pressure-Relieving Devices  1179

10.33 Runaway Reactions: DIERS One of the standardized methods for predicting or controlling runaway reaction that may lead to explosions (deflagration or detonations) is the Fauske approach (Figure 10.33). Others are presented elsewhere [45]. Accordingly, to emphasize the safety problems affecting all industrial process plants and laboratories, the AIChE established the industry-supported Design Institute for Emergency Relief Systems (DIERS). The purposes of the Institute are [24]: • • • •

Reduce the frequency, severity, and consequences of pressure producing accidents. Promote the development of new techniques that will improve the design of emergency relief systems. Understand runaway reactions. Study the impact of two-phase flow on pressure-relieving device systems.

In the refineries and CPI, chemical manufacture especially in the fine, pharmaceutical and specialty chemical industries involves the processing of reactive chemicals, toxic or flammable liquids, vapors, gases and powders. The safety records of these industries have improved in recent years; however, fires, explosions and incidents involving hazardous chemical reactions do still occur. A basis for good engineering practice in assessing chemical reaction hazards is essential, with the aim to help designers, engineers and scientists responsible for testing and operating chemical plants to meet the statutory duties of safety imposed by governmental organizations (e.g., U.S. Environmental Protection Agency (EPA), Occupational Safety and Health Administration (OSHA), USA, Health & Safety Executive, UK and others). The control of chemical reactions (e.g., esterification, sulfonation, nitration, alkylation, polymerization, oxidation, reduction, and halogenation) and associated hazards are an essential aspect of chemical manufacture in the refineries

Cutaway of containment vessel

Figure 10.33  Reactive System Screening Tool (RSST) for evaluating runaway reaction potential (By permission from Fauske and Associates, Inc.).

1180  Chemical Process Engineering and CPIs. The industries manufacture nearly all their products such as inorganic, organic, agricultural, polymers and pharmaceuticals through the control of reactive chemicals. The reactions that occur are generally without incident. Barton and Nolan [46] examined exothermic runaway incidents and found that the principal causes were as follows: • • • • • •

inadequate temperature control. inadequate agitation. inadequate maintenance. raw material quality. little or no study of the reaction chemistry and thermochemistry. human factors.

Other factors that are responsible for exothermic incidents are as follows; • poor understanding of the reaction chemistry resulting in badly designed plant. • underrated control and safety back-up systems. • inadequate procedures and training. The research and technical evaluations have provided industry with extremely valuable information and design procedures, including, but not limited to, two-phase flow phenomena and runaway reactions during safety/over-­pressure relief.

10.34 Hazard Evaluation in the Chemical Process Industries The safe design and operation of chemical processing equipment require detailed attention to the hazards inherent in certain chemicals and processes. Chemical plant hazards can occur from many sources; the principal ones arise from: • • • •

fire and explosion hazards. thermal instability of reactants, reactant mixtures, isolated intermediates and products. rapid gas evolution which can pressurize and possibly rupture the plant. rapid exothermic reaction, which can raise the temperature or cause violent boiling of the reactants and also lead to pressurization.

Earlier reviews have been concerned with energy relationships for a particular chemical process, which are based upon two general classifications of chemical processes, conventional and hazardous [47]. The former is used to describe a non-explosive non-flammable reaction and the latter to describe an explosive and flammable type reaction. The division of reactions does not account for the varying degree of safety or hazards of a particular reaction, which may lie between these extremes, and consequently becomes too limiting in the design. Safety is most likely to be neglected with conventional reactions while over design may be the expected practice with hazardous reactions. These limitations can be avoided by introducing a third class of reactions, “special,” that covers the intermediate area between conventional and hazardous where reactions are relatively safe. Shabica [48] has proposed some guidelines for this third classification and Figure 10.34 shows the increasing degree of hazard of a particular process. Chemical reaction hazards must be considered in assessing whether a process can be operated safely on the manufacturing scale. Furthermore, the effect of scale-up is particularly important. A reaction, which is innocuous on the laboratory or pilot plant scale, can be disastrous on a full-scale manufacturing plant. Therefore, the heat release from a highly exothermic process, for example, the reduction of an aromatic nitro compound, can be controlled easily in laboratory glassware. However, if the same reaction is carried out in a full-scale plant reactor with a smaller surface area to volume ratio, efficient cooling is essential; otherwise a thermal runaway and violent decomposition may occur. Similarly, a large quantity of gas produced by the sudden decomposition of a diazonium compound can be easily vented on the laboratory scale, but the same decomposition on the large scale could pressurize and rupture a full-scale plant.

Process Safety and Pressure-Relieving Devices  1181 6

Substances

l na tio en nv Co

4 3 2

l ia ec s ou rd za Ha

1

Sp

Degree of hazard

5

A

B

C

D

E

Processes Degree of Hazard

Figure 10.34  The increasing degree of hazard of matter plotted against the increasing hazard of a process (Source: Shabica [48].)

In addition, consequences of possible process maloperations, such as incorrect charging sequence, contamination of reactants, agitation failure and poor temperature control, addition of reactants too quickly, omitting one of the reactants and incorrect reactant concentration (recycling) must be considered. A number of parameters govern the reaction hazards associated with a process. These include the following: • • • • • • • • •

chemical components. process temperature. process pressure. thermochemical characteristics of the reaction. reaction rate. reaction ratios. solvent effects. batch size. operational procedure.

The assessment of the hazards of a particular process requires investigations of the effects of these parameters by experimental work, the interpretation of the results in relation to the plant situation, and the definition of a suitable basis for safe operation.

10.35 Hazard Assessment Procedures Hazard assessments are essential, and should be performed on all chemical processes. The reactors such as batch, semi-batch and continuous can be employed for carrying out various operations. Many industrial reactions are exothermic (i.e., are accompanied by the evolution of heat) and therefore overheating can occur. In batch operations, all the reactants are added to the reactor at the start of the reaction. In semi-batch operations, one or more of the reactants are charged to the reactor at the start, and others are then metered in, giving some control over the rate of reaction, and thus the rate of heat production. Overheating often results in thermal runaway, which is characterized by progressive increases in the rate of heat generation, and hence temperature and pressure. Thermal runaway is a particular problem in unsteady state batch reactions, where the rate of reaction and therefore the rate of heat production vary with time. The consequences of thermal runaway can sometimes be very severe as in

1182  Chemical Process Engineering the incidents at Seveso [49]. In this case, a bursting disk ruptured on a reactor. The reactor was used to manufacture trichlorophenol at a temperature of 170 - 185°C and it was heated by steam at 190°C. The batch had been dehydrated and left at a temperature of 158°C over the weekend. Ethylene glycol and caustic soda give exothermic secondary reactions producing sodium polyglycolates, sodium oxalate, sodium carbonate and hydrogen thus exhibiting an autocatalytic behavior. These reactions caused a temperature rise allowing the production of tetrachlorodioxin and the subsequent vessel pressurization. The Bhopal fatal incident [50] (is not a thermal runaway) involved a toxic release of an intermediate, methyl isocyanate (MIC), which resulted in the death of over 2,000 people. A runaway polymerization of highly toxic MIC occurred in a storage tank. The runaway polymerization caused an uncontrolled pressure rise, which caused a relief valve to lift and discharge a plume of toxic vapor over the city. The task of specifying the design, operation and control of a reactor with stirrer, heating or cooling coils, reflux facilities and emergency relief venting can pose a problem if all the time-dependent parameters are not considered. The use of batch processing techniques in the fine chemical industry is often characterized by: • • • •

multi-product plant (must have adaptable safety system). complex developing chemistry. high frequency of change. process control is simpler than continuous processes.

These factors are attributed to batch and semi-batch processes rather than continuous processes. However, the use of continuous processes on fine chemical manufacturing sites is limited. It is often preferable to use semi-batch mode as opposed to batch processes.

10.36 Exotherms Temperature-induced runaways have many causes including the following: • loss of cooling. • loss of agitation. • excessive heating. During a temperature-induced upset, the reactor temperature rises above the normal operating target. When any of the temperature elements senses a high reactor temperature, the programmable logic controller (PLC) software shutdown system automatically puts the reactor on idle (isolates). This action doubles the cooling water flow to the reactor by opening a bypass valve. If these reactions are unsuccessful in terminating the temperature rise, the shutdown system opens the quench valves, dumping the reaction mass into the water-filled quench tank. If the dump valves fail to operate, the reactor contents soon reach a temperature where a violent self-accelerating decomposition occurs. The uncontrolled exotherm generates a large volume of gas and ejects the process material out of the reactor into the containment pot.

10.37 Accumulation It is important to know how much heat of reaction can accumulate when assessing the hazards relating with an exothermic reaction. Accumulation in a batch or semi-batch process can be the result of: • • • • •

adding a reactant too quickly. loss of agitation. carrying out the reaction at too low a temperature. inhibition of the reaction. delayed initiation of the desired reaction.

Process Safety and Pressure-Relieving Devices  1183 Reactants can accumulate when the chosen reaction temperature is too low, and as such the reaction continues even after the end of the addition. In such a case, a hazardous situation could occur if cooling were lost as exemplified [51]. Impurities or the delayed addition of a catalyst causes inhibition or delayed initiation resulting in accumulation in the reactors. The major hazard from accumulation of the reactants is due to a potentially rapid reaction and consequent high heat output that occurs when the reaction finally starts. If the heat output is greater than the cooling capacity of the plant, the reaction will runaway. The reaction might commence if an agitator is restarted after it has stopped, a catalyst is added suddenly, or because the desired reaction is slow to start.

10.38 Thermal Runaway Chemical Reaction Hazards Thermal runaway reactions are the results of chemical reactions in batch or semi-batch reactors. A thermal runaway commences when the heat generated by a chemical reaction exceeds the heat, which can be removed to the surroundings as shown in Figure 10.35. The surplus heat increases the temperature of the reaction mass, which causes the reaction rate to increase, and subsequently accelerates the rate of heat production. Thermal runaway occurs as follows: as the temperature rises, the rate of heat loss to the surroundings increases approximately linearly with temperature. However, the rate of reaction, and thus the rate of heat generation, increases exponentially. If the energy release is large enough, high vapor pressures may result or gaseous products may be formed which can finally lead to over pressurization, and possible mechanical destruction of the reactor or vessel (thermal explosion). The energy released might result from the wanted reaction or from the reaction mass if the materials involved are thermodynamically unstable. The accumulation of the starting materials or intermediate products is an initial stage of a runaway reaction. Figure 10.36 illustrates the common causes of reactant accumulation. The energy release with the reactant accumulation can cause the batch temperature to rise to a critical level thereby triggering the secondary (unwanted) reactions. Thermal runaway starts slowly and then accelerates until finally it may lead to an explosion.

10.39 Heat Consumed Heating the Vessel. The ϕ-Factor The fraction of heat required to heat up the vessel, rather than its contents, depends on the heat capacity of the vessel (i.e., how much energy is required to raise the temperature of the vessel with respect to the reaction mass). The heat loss to the vessel is known as the ϕ-factor [52]. The ϕ-factor is the ratio of the total heat capacity of sample and vessel to that of the sample alone, and is defined by

Unstable operation point Point where heat generation and removal rates are equal

Heat rate

Heat removal Heat generation

Temperature Temperature of cooling medium

Figure 10.35  A typical curve of heat rate vs. temperature.

1184  Chemical Process Engineering Low heat transfer capacity. Too much thermal insulation.

High heat of desired reaction. Wrong kinetic assumption Too high feed rate. Too low temperature. Incorrect initiation. Insufficient mixing. Impurities (inhibitors).

Thermally hazardous material.

Wrong assumption on heat transfer Loss of agitation. Loss of cooling.

Accumulation of reactants or intermediates

Insuf f icient heat removal.

AND

Wrong choice of T. Unintentional heating. Mechanical friction. Intrusion of reactive material (heat transfer fluid). Intrusion of decomposition catalysts. Too high temperature.

AND

Excursion Thermal Runaway

Figure 10.36  Causes of runaways in industrial reactors (Source: W. Regenass, Safe Operation of Exothermic Reactions, Internal Ciba-Geigy Publication, 1984).

φ=



M sC ps (sample) + M v C pv (vessel) M sC ps (sample)

(10.48)

where Ms = mass of the sample (kg). Cps = specific heat capacity of sample (J/kg.K). Mv = mass of the vessel (kg). Cpv = specific heat capacity of vessel (J/kg.K). The ϕ-factor does not account for the heat loss to the environment. It is used to adjust the self-heating rates as well as the observed adiabatic temperature rise. As the scale of operation increases, the effect of the heat consumption by the plant typically reduces, and thus the extent to which the kinetics of the runaway reaction is influenced by the plant is reduced. For plant scale vessels, the ϕ-factor is usually low (i.e., 1.0 – 1.2) depending on the heat capacity of the sample and the vessel fill ratio. Laboratory testing for vent sizing must simulate these low ϕ-factors. If the laboratory ϕ-factor is high, several anomalies will occur. • • • •

The rate of reaction will be reduced (i.e., giving incorrect reaction rate data for vent sizing). The magnitude of the exotherm will be smaller by a factor of ϕ. Measured pressure effects will be smaller than those that would occur on the plant. The induction period of a thermal runaway reaction will be increased compared to the plant.

The consequences of these erroneous anomalies will be: • inadequate safety design system. • undersized emergency relief system. • unknown decompositions may occur at elevated temperatures, which may not be realized in the laboratory.

Process Safety and Pressure-Relieving Devices  1185

10.40 Onset Temperature The reaction onset temperature is that temperature where it is assumed that significant fuel consumption begins. The onset temperature is expressed by

Tonset = where

B  x o∆HRx .A  ln  •   C.φ.Tex  B=



EA R

(10.49)

(10.50)

A = Rate constant (Pre-exponential factor from Arrhenius equation k = A exp(−EA /RT), sec-1 (i.e. for a first order reaction) B = Reduced activation energy, K C = Liquid heat capacity of the product (J/kg.K) EA = Activation energy (J/mol) R = Gas constant (8.314 J/mol.K) Tonset = Onset temperature, K = Initial mass fraction xo ΔHRx = Heat of decomposition, J/kg ϕ = Dimensionless thermal inertial factor for the sample holder or product container (PHI-factor). • Tex = Bulk heat-up rate driven by an external heat source (oC/sec).

10.41 Time-to-Maximum Rate We may select an onset temperature based upon an arbitrary time-to-maximum-rate from the relation



t mr =

C.φ.T 2 exp(B/Tonset ) x o .∆HRx .A.B

(10.51)

Rearranging Eq. 10.51 yields



Tonset =

B  t mr .x o .∆HRx .A.B  ln   C.φ.T 2  

(10.52)

Eq. 10.52 gives an onset temperature Tonset that corresponds to a time-to-maximum rate tmr (min) using a successive substitution solution procedure. An initial guess of T = 350K in the RHS of Eq. 10.52 will give a solution value of Tonset on the LHS of Eq. 10.52 within 1% or on an absolute basis ±3°C. Convergence is reached within several successive substitution iterations.

10.42 Maximum Reaction Temperature Once we have determined the onset temperature, we can then obtain the maximum reaction temperature by the adiabatic temperature rise and any contribution due to external heat input. The theoretical adiabatic temperature increase is



∆Tadia =

x o .∆HRx C.φ

(10.53)

1186  Chemical Process Engineering The contribution to the overall temperature increase from external heat input is defined by

Tex• .t mr 2

∆Tex =



(10.54)

where ΔTex = The temperature increase attributed to external heating effects, oC. Tex• = Bulk heat-up rate due to external heating alone, oC/min tmr = Time-to-maximum rate as determined by Eq. 10.52 with temperature T set equal to Tonset, min From these expressions, the maximum reaction temperature Tmax is defined by

Tmax =Tonset + ΔTadia + ΔTex

(10.55)

To obtain updated listing of the published information on this research, contact the AIChE office in New York. The work is original and conducted by thoroughly qualified researchers/engineers. The work on runaway reactions is the first systematized examination of the subject and is really the only design approach available, which requires careful study. Two-phase flow is an important aspect of venting relief as well as of runaway reactions, and is a complicated topic when related to liquid flashing in a vessel as it discharges on pressure relief. It cannot be adequately covered by conventional fluid two-phase flow. The following briefly reviews different calorimetric methods employed for screening and testing a two-phase relief system. Other techniques are illustrated elsewhere [45].

10.43 Vent Sizing Package (VSP) The vent sizing package (VSP) was developed by Fauske & Associates Inc. The VSP and its latest version VSP2 employ the low thermal mass test cell stainless steel 304 and Hastelloy test cell with a volume of 120 ml contained in a 4 L high pressure vessel as shown in Figure 10.39. The typical ϕ-factor is 1.05 – 1.08 for a test cell wall thickness of 0.127 mm to 0.178 mm. Measurements consist of sample temperature T1 and pressure P1, external guard

Containment Vessel ~4000 cc T1

P2 Bypass

4

P1 Bypass

Exhaust

Test Cell

3

T2

2

120cc

5

N2 Supply Legend Item 1 - Magnetic Stirrer Bar 2 - Test Cell Heater 3 - Guard Heater Assembly with Aluminum Can and Lid 4 - Fiberfrax Insulation 5 - Magnetic Stirring T - Thermocouple P - Pressure Transducer

Figure 10.37  Vent sizing package (VSP) apparatus (By permission from Fauske and Associates, Inc.).

Process Safety and Pressure-Relieving Devices  1187

Figure 10.38  The Vent Sizing package 2TM (VSP 2TM) apparatus (By permission from Fauske and Associates, Inc.).

temperature T2 and containment pressure P2. During the runaway or the self-heating period, the guard heater assembly serves to provide an adiabatic environment for the test sample by regulating T2 close to T1. For closed (non-vented) test cells, the containment vessel serves to prevent bursting of the test cell by regulating its own pressure P2 to follow the test cell sample pressure P1. This pressure-tracking feature makes possible the utilization of the thin wall (low ϕ-factor) test cell design. Vented or open tests, where the vapor or gas generated is vented either into the containment vessel or to an external container are unique capabilities of the VSP instruments. The typical onset sensitivity is 0.1oC/min for the VSP and 0.05oC/min for the VSP2. Figure 10.37 shows the vent sizing package (VSP) apparatus. The VSP experiments allow the comparison of various process versions, the direct determination of the wanted reaction adiabatic temperature rise and the check of the possible initiations of secondary reactions. If no secondary reaction is initiated at the wanted reaction adiabatic final temperature, a further temperature scan allows the determination of the temperature difference between the wanted reaction adiabatic final temperature and the subsequent decomposition reaction onset temperature. The VSP experiments are not suitable to measure the controlling reactant accumulation under normal process conditions. This is obtained using reaction calorimeters. The VSP experiments are suitable to assess the consequences of runaway decomposition reactions after their identification using other screening methods (Differential Thermal Analysis (DTA), Differential Scanning Calorimetry (DSC) and Accelerating Rate Calorimeter (ARC)). The decomposition is then initiated by a temperature scan or an isothermal exposure, depending on the known kinetic behavior of the reaction. In some instances where a reliable baseline cannot be determined on DTA thermograms, a VSP experiment enables a better and safer determination of the decomposition exotherm. The VSP experiments provide both thermal information on runaway reactions and information on pressure effects. The type of pressurization, following the DIERS methodology (i.e., vapor pressure, production of non-­condensable gases or both) can be determined from VSP experiments. The following experimental conditions are readily achievable using the VSP. • Temperature up to 350°C − 400°C under temperature scan conditions. • Pressure up to 200 bar. • Closed or open test cells. Open test cells are connected to a second containment vessel. Test cells of various materials including stainless steel, Hastelloy C276 and glass test cells. Glass test cells of various sizes and shape are suitable for testing fine chemical and pharmaceutical products/reaction conditions, when the process is in glass vessels only or when small samples only are available, or if the samples are very expensive. • Mechanical stirring is recommended for testing polymerization reactions or viscous reaction mixtures. This requires the use of taller containment vessels than the original one to install the electric motor for the agitator.

1188  Chemical Process Engineering

Figure 10.39A  The Advanced Reactive System Screening ToolTM (ARSSTTM) (By permission from Fauske and Associates, Inc.).

Syringe External Sample Fill

Thermocouple Connection

TC Gland

Heater Gland

Fill Tube

1 TC

Heater Connection

Rupture Disc and Holder

Insulation Shealth

Gas Inlet and Vent Valve

Bottom Heater with Belt Test Cell TC1

Stir Bar Insulation

Containment Vessel Material: 316 SS Effective Volume: 350cc

Figure 10.39B  Schematic of the Advanced Reactive System Screening ToolTM (ARSSTM) containment vessel and internals (By permission from Fauske and Associates, Inc.).

Process Safety and Pressure-Relieving Devices  1189 TC2

TC2

TC1

TC1

1/8” 1/4”

Foam

q

q

Sample

1/8”

(a) Sample Non-Foamy

(b) Foamy TC2 ≈ TC1

TC2 > TC1

Figure 10.39C  The Advanced Reactive System Screening ToolTM (ARSSTTM) flow regime detector (By permission from Fauske and Associates, Inc.).

Self-Heat Rate (ºC/min)

1000

ARSST-HWS

ARSST-scan

VSP2-closed

100 10 1 0.1 0.01 25

50

75

100 125 Temperature (ºC)

150

175

200 225 250 275

Figure 10.40  Self – heat rate data for 25% DTBP in Toluene (By permission from Fauske and Associates, Inc.).

10.44 Vent Sizing Package 2TM (VSP2TM) Figure 10.38 shows the Vent Sizing Package 2 system. It uses a patented low thermal mass temperature and pressure equalized 120 ml test cell configuration. The equipment is versatile and enables users to obtain accurate adiabatic temperature and pressure rate data for the fastest runaway reactions. The test data can directly be applied to process scale without performing tedious computations. VSP2 tests are employed to model upset conditions as: • • • • •

loss of cooling. loss of stirring. mischarge of reagents. batch contamination. fire exposure heating.

The VSP2 provides vent sizing and thermal data under adiabatic runaway reaction conditions, which can be directly applied to process scale.

1190  Chemical Process Engineering dT/dt (ARSST)

Self-Heat Rate (ºC/min) or First Order Rate Constant (1/sec)

1.0E+02

dT/dt (VSP2)

k1 (ARSST)

k1 (VSP2)

1.0E+01 1.0E+00 1.0E–01 1.0E–02 1.0E–03 1.0E–04 1.0E–05

40

20

100 80 Temperature (ºC)

60

120

140

160

180

Figure 10.41  Self-heat rate data and first-order rate constant for Methanol/Acetic Anhydride (By permission from Fauske and Associates, Inc.).

1999 DIERS Round Robin 1000

Self-Heat Rate (ºC/min)

ARSST

ARSST

VSP2

HSE

VSP2

100

10

1 50.

75.

100.

125.

150.

175.

225.

200.

Temperature (ºC)

Figure 10.42  Composite self-heat plot of selected Round Robin data (By permission from Fauske and Associates, Inc.).

Self Heat Rate (ºC/min)

Self-Heat Rate or Pressure Rate

100000.0

Pressure Rate (psi/min)

10000.0 1000.0 100.0 10.0 1.0 0.1

0

100 Temperature (ºC)

200

300

400

500

Figure 10.43  Self-heat rate and pressure rate data for neat DTBP at 300 psig in the ARSST (By permission from Fauske and Associates, Inc.).

Process Safety and Pressure-Relieving Devices  1191

Temperature (ºC)

300. Styrene - w/0.5% BPO CONSTANT 15W Power 5 ml sample

200.

100.

0. 0.0

1.0 TC1 (sample)

2.0 Time (min)

3.0

4.0

TC2 (FRED)

Figure 10.44  Example of flow regime detection with the ARSST (By permission from Fauske and Associates, Inc.).

10.45 Advanced Reactive System Screening Tool (ARSST) Fauske & Associates Inc. developed the ARSST, as an easy and inexpensive screening tool for characterizing chemical systems and acquiring relief system design data. It can safely identify potential chemical hazards in the process industry. The ARSST (Figures 10.39A, B and C) consists of a spherical glass test cell, and immersion heater. It has surrounding jacket heater and insulation, thermocouples and a pressure transducer, a stainless-steel containment vessel that serves as both a pressure simulator and safety vessel. The ARSST uses a small magnetic stir bar which is placed in the test cell and driven by an external magnetic stirrer. The sample cell volume is 10 ml and the containment volume is 350 ml. The apparatus has a low effective heat capacity relative to that of the sample whose value, expressed as the capacity ratio is approximately 1.04 (i.e., quite adiabatic). This key feature allows the measured data to be directly applied to process scale. The ARSST features a heat-wait-search (HWS) mode of operation that provides onset detection sensitivity as low as 0.1 oC/min, and isothermal operation at elevated temperature. It can readily cope with endothermic behavior (phase change) and an optical flow regime detector enables the ARSST operator to distinguish between “foamy” and “non-foamy” runaway reactions (Figure 10.41C). The ARSST is computer controlled, which records time, temperatures and pressure and heater power during a test. Figures 10.40–10.44 show typical plots generated by the equipment.

10.46 Two-Phase Flow Relief Sizing for Runaway Reaction Many methods have been used to size relief systems: area/volume scaling, mathematical modeling using reaction parameters and flow theory, and empirical methods by the Factory Insurance Association (FIA). The DIERS of the AIChE has carried out studies of sizing reactors undergoing runaway reactions. Intricate laboratory instruments as described earlier have resulted in better vent sizes. A selection of relief venting as the basis of safe operation is based upon the following considerations [53]. • • • • • •

compatibility of relief venting with the design and operation of the plant/process. identifying the worst scenarios. type of reaction. means of measuring the reaction parameters during the runaway reaction. relief sizing procedure. design of the relief system including discharge ducting and safe discharge area.

1192  Chemical Process Engineering

10.47 Runaway Reactions A runaway reaction occurs when an exothermic system becomes uncontrollable. The reaction leads to a rapid increase in the temperature and pressure which if not relieved can rupture the containing vessel. A runaway reaction happens because the rate of reaction, and therefore the rate of heat generation, increases exponentially with temperature. In contrast, the rate of cooling increases only linearly with temperature. Once the rate of heat generation exceeds available cooling, the rate of increase in temperature becomes progressively faster. Runaway reactions nearly always result in two-phase flow reliefs. In reactor venting, reactions essentially fall into three classifications: 1. V  apor pressure systems. 2. Hybrid (gas + vapor) systems. 3. Gassy systems. The significance of these categories in terms of relief is that, once the vent has opened, both vapor pressure and hybrid reactions temper by losing enough heat through vaporization, to maintain temperature and pressure at an acceptable level. In a gas generating system, there is negligible or sometimes no control of temperature during venting, such that relief sizing is based upon the peak gas generation rate. Experimental studies conducted by the testing methods must not only be able to differentiate between the reaction types, but must also simulate large-scale process conditions. The results of the experimental studies should greatly enhance the design of the relief system. We shall review the reactor venting categories as follows:

10.48 Vapor Pressure Systems In this type of reaction, no permanent gas is generated. The pressure generated by the reaction is due to the increasing vapor pressure of the reactants, products and/or inert solvent as the temperature rises. It is the rate of temperature increase (i.e., power output) between the set pressure and the maximum allowable pressure, which determines the vent size and not the peak rate. Boiling is attained before potential gaseous decomposition, (i.e., the heat of reaction is removed by the latent heat of vaporization). The reaction is tempered, and the total pressure in the reactor is equal to the vapor pressure. The principal parameter determining the vent size is the rate of the temperature rise at the relief set pressure. Systems that behave in this manner obey the Antoine relationship between pressure P and temperature T as represented by



ln P = A + B/T

(10.56)

where A and B are constants and T is the absolute temperature. An example is the methanol and acetic anhydride reaction.

10.49 Gassy Systems Here, the system pressure is due entirely to the pressure of non-condensible gas rather than the vapor pressure of the liquid. The gas is the result of decomposition. The exothermic heat release is largely retained in the reaction mass since the cooling potential of volatile materials is not available. As such, both the maximum temperature and maximum gas generation rate can be attained during venting. Gaseous decomposition reactions occur without tempering. The total pressure in the reactor is equal to the gas pressure. The principal parameter determining the vent size is the maximum rate of pressure rise. Unlike the vapor-pressure systems, the pressure is controlled (and reduced) without cooling the reaction.

Process Safety and Pressure-Relieving Devices  1193 A survey within the Fine Chemical Manufacturing Organization of ICI has shown that gassy reaction systems predominate due to established processes such as nitrations, diazotizations, sulphonations and many other types of reactions [64]. Very few vapor pressure systems have been identified which also generated permanent gas, i.e., hybrid type.

10.50 Hybrid Systems These are systems that have a significant vapor pressure and at the same time produce non-condensible gases. Gaseous decomposition reaction occurs before boiling: the reaction is still tempered by vapor stripping. The total pressure in the reactor is the summation of the gas partial pressure and the vapor pressure. The principal parameters determining the vent size are the rates of temperature and pressure rise corresponding to the tempering condition. A tempered reactor contains a volatile fluid that vaporizes or flashes during the relieving process. This vaporization removes energy via the heat of vaporization and tempers the rate of temperature rise due to the exothermic reaction. In some hybrid systems, the vapor generation in a vented reaction is high enough to remove sufficient latent heat to moderate or “temper” the runaway, i.e., to maintain constant temperature. This subsequently gives a smaller vent size. Richter and Turner [54] have provided systematic schemes for sizing batch reactor relief systems. They employed logic diagrams that outlined the various decisions to produce a model of the system. Figure 10.45 reviews the reaction kinetics and thermodynamics required to create a reactor model. Figure 10.46 shows a sequence of steps used to model flow from the reactor, assuming relief is occurring as a homogeneous vapor-liquid mixture. The DIERS program has supported the use of a homogeneous vapor-liquid mixture (froth) model, which relies on the assumption that the vapor phase is in equilibrium with the batch liquid phase [55]. Figure 10.47 shows the steps used to model compressible vapor venting from the reactor. Table 10.14 lists formulae for computing the area of the three systems.

10.51 Simplified Nomograph Method Boyle [56] and Huff [57] first accounted for two-phase flow with relief system design for runaway chemical reactions. Computer simulation approaches to vent sizing involve extensive thermokinetic and thermophysical characterization of the reaction system. Fisher [58] has provided an excellent review of emergency relief system design involving runaway reactions in reactors and vessels. The mass flux through the relief device representing choked two-phase 0.5 flow through a hole is expressed as: Q m ∆H v  g c  G= = (10.57)  

A



υ fg  C p Ts 



For two-phase flow through pipes, we apply an overall dimensionless discharge coefficient ψ. Eq. 10.57 is referred to as the equilibrium rate model (ERM) for low quality choked flow. Leung [59] indicated that Eq. 10.57 be multiplied by a factor of 0.9 to bring the value in line with the classic homogeneous equilibrium model (HEM). Eq. 10.57 becomes

∆H v  g c  Q G = m = 0.9ψ A υ fg  C p Ts 

where A = area of the hole, m2.

kg.m N. sec 2 Qm = mass flow through the relief, kg/s. ΔHv = the heat of vaporization of the fluid, J/kg. υfg = the change of specific volume of the flashing liquid, m3/kg.

gc = correction factor 1.0

0.5



(10.58)

1194  Chemical Process Engineering Start 1 Runaway reaction possible?

No

Use conventional sizing method for pressure safety valve (PSV) or rupture disk (RD).

No

5 Reevaluate physical properties, thermodynamics, kinetics, and program parameters.

Yes

7 Modify model to reflect heat input. Consider if vessel/jacket mass also absorbs part or total heat from reaction and other sources.

Yes 2 Input physical properties of system, thermodynamics, kinetics model, and program parameters.

3 Model adiabatic temperature and pressure rise with time due to reaction.

4 Is model consistent with client experience?

Yes 6 Does f ire or other heating occur during venting?

No 8 Input PSV/RD set pressure, trial orifice diameter of PSV or RD, diameter pf vent pipe to relief device and equivalent length of this pipe.

11 Make new assumption on PSV or RD data or vent pipe.

9 From onset of runway reaction, calculate conditions at relief set pressure. 10 Does vap./liq. phase separation occur inside reactor?

Yes

No

20 Calculate relieving rates assuming homogeneous mixture (vap./liq.) of instantaneous reactor contents. 30 Calculate relieving rates assuming compressible vapor flow. Liquid is totally reparated and retained in reactor.

3

2

4

Figure 10.45  Block flow diagram showing the reaction kinetics and thermodynamics needed to create a reactor model (Reproduced with the permission from the AIChE copyrights © 1996 AIChE, All rights reserved.).

CP = the heat capacity of the fluid, J/kg.K. TS = the absolute saturation temperature of the fluid at the set pressure, K. The result is applicable for homogeneous venting of a reactor (low quality, not restricted just to liquid inlet condition). Figure 10.48 gives the value of ψ for L/D ratio. For a pipe length zero, ψ = 1 as the pipe length increases, the value of ψ decreases. Eq. 10.58 can be further rearranged in terms of a more convenient expression as follows:



∆H v dP = Ts υ fg dT

(10.59)

Process Safety and Pressure-Relieving Devices  1195 2

4

21 Assume reactor pressure starting from PSV/RD set pressure.

22 Calculate volumetric expansion of reactor contents by vapor generated from reaction/fire heat during time increment. Relief f low is homogeneous difference between expanded and former reactor volume at start of time increment. The former reactor remains in the reactor for the next time interval, but has the new properties of the relief flow.

23 Use adiabatic flashing of the relief flow’s liquid phase, and adiabatic expansion of the relief flow’s vapor phase to calculate the relief flow’s homogenous foam properties. Then calculate the critical flow outlet pressure at the throat of the PSV/RD.

24 Using small pipe length increments of 1 ft, calculate total pressure drop frome choke point ( where flow becomes critical) back reactor. Include equivalent lengths of open RD or PSV piping, fittings, and exit effects at the reactor nopzzle.

25 Does calculated reactor pressure equal assumed reactor pressure?

Assume a new reactor pressure.

No

Yes 26 Save data calculated for sizing of relief headers separation vessels, and modeling vent stack dispersion.

27 is reactor pressure below closing pressure for PSV or 50 psig for rupture disks?

No 29 Are the selected relief device and piping satisfactory?

Yes

No

Yes

28 Set assumed reactor pressure for next interval at pressure just calculated. Adjust the remaining reactor content for conversion due to reaction and venting losses during time increment.

Calculation is completed.

Figure 10.46  Steps used to model flow from the reactor, assuming relief is occurring as a homogeneous vapor – liquid mixture (Reproduced with the permission from the AIChE copyrights © 1996 AIChE, All rights reserved.).

Substituting Eq. 10.59 into Eq. 10.58 gives



dP  g c Ts  G = 0.9ψ dT  C p 

0.5



(10.60)

The exact derivative is approximated by a finite difference derivative to yield



dP  g c Ts  G ≅ 0.9ψ dT  C p 

0.5



(10.61)

1196  Chemical Process Engineering

4

3 31 Assume reactor pressure starting from PSV/RD set pressure

32 Calculate vapor generate by heat of reaction/f ire during time increment.

33 Calculate vapor properties assuming adiabatic expansion, and calculate the criminal f low outlet pressure at the throat area of the PSV/RD.

34 Using small pipe length increment of 1 ft, calculate total pressure drop from choke point (where flow becomes critical) back to reactor. Include equivalent lengths of open RD or PSV piping, fittings, and exits effects at the reactor nozzle.

35 Does calculated reactor pressure equal assumed reactor pressure?

Assume a new reactor pressure.

No

Yes 36 Save data calculated for sizing of relief headers, separation vessel, and modeling vent stack dispersion.

37 Is reactor pressure below closing pressure for PSV or 50 psig for rupture disks?

Yes

39 Are the selected relief device and piping satisfactory?

No 38 Set assumed reactor pressure for next interval at pressure just calculated. Adjust the remaining reactor content for conversion due to reaction and venting loses during time increment.

Calculation is completed.

Figure 10.47  Steps used to model compressible vapor venting from the reactor (Reproduced with the permission from the AIChE copyrights © 1996 AIChE, All rights reserved.).

where ΔP = the overpressure. ΔT = the temperature rise corresponding to the overpressure. Fauske [60] has developed a simplified chart for the two-phase calculation. He expressed the relief area as:



A=

Vρ G∆t v

(10.62)

Process Safety and Pressure-Relieving Devices  1197 Table 10.14  Vent areas and diameters of the three systems. Vapor system

Gassy system

Hybrid system

dT   mo  dt  A = 1.5 × 10 −5  F.Ps   

 dP    1 m     A = 3 × 10 −6    o   dt 1.5   F   m t  PMAP  

 dP    1 m     A = 5.6 × 10 −6    o   dt  F   m t  Ps1.5   

 4A  d=  π 

0.5

 4A  d=  π 

0.5

 4A  d=  π 

0.5

L/D=0,

F=1.00

L/D=0

F=1.00

L/D=0,

F=1.00

L/D=50, F=0.85

L/D=50, F=0.70

L/D=50, F=0.70

L/D=100, F=0.75

L/D=100, F=0.60

L/D=100, F=0.60

L/D=200, F=0.65

L/D=200, F=0.45

L/D=200, F=0.45

L/D=400, F=0.50

L/D=400, F=0.33

L/D=400, F=0.33

1.1

Correction Factor, ψ

1.0 0.9 0.8 0.7 0.6 0.5

0

100

200 L/D

300

400

Figure 10.48  Correction factor versus L/D for two-phase flashing flow through pipes (Source: J. C. Leung and M. A. Grolmes, “The Discharge of Two-Phase Flashing Flow in a Horizontal Duct”, AIChE J., Vol. 33, No. 3, p. 524, 1987.).

where A = the relief vent area, m2. V = reactor volume, m3. ρ = density of the reactants, kg/m3. G = mass flux through the relief, kg/sec. m2. Δtv = venting time, sec. Boyle [56] developed Eq. 10.62 by defining the required area as that size which would empty the reactor before the pressure could rise above some allowable pressure for a given vessel. The mass flux G is given by Eq. 10.58 or Eq. 10.61, and the venting time is given by



∆t v =

(∆T)(C p ) qs

(10.63)

1198  Chemical Process Engineering where ΔT = the temperature rise corresponding to the overpressure ΔP. T = the temperature. CP = the heat capacity. qS = the energy release rate per unit mass at the set pressure of the relief system. Combining Eqs. 10.62, 10.63 and 10.57 yields

A = Vρ(g c C p Ts )−0.5



qs ∆P

(10.64)

Eq. 10.64 gives a conservative estimate of the vent area and the simple design method represents overpressure (ΔP) between 10 and 30%. For a 20% absolute overpressure, a liquid heat capacity of 2510 J/kg.K for most organics, and considering that a saturated water relationship exists, the vent size area per 1,000 kg of reactants is given by:

 dT  0.00208    m   dt  °C/min. A= =  Ps bar  1,000kg  2



(10.65)

Figure 10.49 shows a nomograph for determining the vent size. The vent area is calculated from the heating rate, the set pressure and the mass of reactants. The nomograph is used for obtaining quick vent sizes and checking the results of the more rigorous computation. Crowl and Louvar [41] have expressed that the nomograph data of Figure 10.49

RELIEF SET PRESSURE (psia)

10−2

1 2 5 30 0 4 60 0 8 1 0 18 20 2 0 32 40 48 0 0

VENT SIZE AREA PER 1000 kg OF REACTANTS, m2

10−1

10−3

10−4 1

10

100

SELF-HEAT RATE, ºC/min

Figure 10.49  A vent sizing nomograph for tempered (high vapor-pressure) runaway chemical reactions (Source: H. K. Fauske, “Generalized Vent Sizing Monogram for Runaway Chemical Reactions”, Plant/Operations Prog., Vol. 3, No. 4, 1984. Reproduced with permission from the AIChE, Copyrights © 1984, All rights reserved).

Process Safety and Pressure-Relieving Devices  1199 applies for a discharge coefficient of ψ = 0.5, representing a discharge L/D of 400.0. However, use of the nomograph at other discharge pipe lengths and different ψ requires a suitable conversion.

10.52 Vent Sizing Methods Vents are usually sized on the assumption that the vent flow is: • all vapor or gas. • all liquid and • a two-phase mixture of liquid and vapor or gas. The first two cases represent the smallest and largest vent sizes required for a given rate at increased pressure. Between these cases, there is a two-phase mixture of vapor and liquid. It is assumed that the mixture is homogeneous, that is, that no slip occurs between the vapor and liquid. Furthermore, the ratio of vapor to liquid determines whether the venting is closer to the all vapor or all liquid case. As most relief situations involve a liquid fraction of over 80%, the idea of homogeneous venting is closer to all liquid than all vapor. Table 10.15 shows vent area for different flow regimes.

10.53 Vapor Pressure Systems These systems are called “tempering” (i.e., to prevent temperature rise after venting) systems as there is sufficient latent heat available to remove the heat of reaction, and to temper the reaction at the set pressure. The vent requirements for such systems are estimated from the Leung’s Method [61, 62].

A=

M oq

2

0.5  V  dP  0.5 (C ∆T) Ts + G   v   M o dT  

(10.66)

Alternatively, the vent area can be expressed as:



A=

where

M oq   V ∆H  0.5 v 0.5  G  (C ∆T) + v   M o υ fg  

2



Table 10.15  Vent areas for different flow regimes. Type of flow

Required vent area as a multiple of all vapor vent area

All vapor

1

Two–phase: Churn turbulent

2–5

Bubbly

7

Homogeneous

8

All liquid

10

(10.67)

1200  Chemical Process Engineering Mo = the total mass contained within the reactor vessel prior to relief, kg J W q = the exothermic heat release rate per unit mass, , kg.sec kg V = the volume of the vessel, m3 CV = the liquid heat capacity at constant volume, J/kg.K ΔHv = heat of vaporization of the fluid, J/kg υfg = change of specific volume of the flashing liquid, (υg − υf ), m3/kg The heating rate q is defined by

1  dT   dT   q = C v   +    2  dt  s  dt  m 



(10.68)

The first derivative Eq. 10.68, denoted by the subscript “s”, corresponds to the heating rate at the set pressure and the second derivative, denoted by subscript “m”, corresponds to the temperature rise at the maximum turnaround pressure. The above equations assume the following: • • • • •

Uniform froth or homogeneous vessel venting occurs. The mass flux, G, varies little during the relief. The reaction energy per unit mass, q, is treated as constant. Constant physical properties Cv, ΔHv, and υfg. The system is a tempered reactor system. This applies to the majority of reaction systems.

We should take care of using consistent units in applying the above two-phase equations. The best procedure is to convert all energy units to their mechanical equivalents before solving for the relief area, especially when Imperial (English) units are used. To be consistent, use the SI unit. The vapor pressure systems obey the Antoine relationships given by Eq. 10.56:

lnP = A +



B T

Differentiating Eq. 10.56, yields,



1 dP B =− 2 P dT T

(10.69)



dP B =− 2 P dT T

(10.70)

An equation representing the relief behavior for a vent length L/D < 400 is given by [62]

(DP )2 (∆PS )  TS  MO ⋅  dT   C S  2.769    dt  S



0.5



where MO = allowable mass of the reactor mixture charge (kg) to limit the venting overpressure to PP (psig) DP = rupture disk diameter, inches

(10.71)

Process Safety and Pressure-Relieving Devices  1201 ΔPS

= the allowable venting overpressure (psi), that is the maximum venting pressure minus the relief device set pressure = maximum venting pressure (psig) PP = the relief device set pressure (psig). Note that the relief device set pressure can range from the PS vessel’s MAWP to significantly below the MAWP = the equilibrium temperature corresponding to the vapor pressure where the vapor pressure is TS the relief device set pressure (K)  dT  = the reactor mixture self-heat rate  °C  at temperature T (K) as determined by a DIERS or     s dt S min  equivalent test = specific heat of the reactor mixture (cal/g-K or Btu/lb oF) CP Eq. (10.71) is a dimensional equation; therefore, the dimensions given in the parameters must be used.

10.54 Fauske’s Method Fauske [60, 62] represented a nomograph for tempered reactions as shown in Figure 10.49. This accounts for turbulent flashing flow and requires information about the rate of temperature rise at the relief set pressure. This approach also accounts for vapor disengagement and frictional effects including laminar and turbulent flow conditions. For turbulent flow, the vent area is

 dT  MO   (α D − α O )  dt  S 1 A= 2  TS  0.5 F   ∆P(1 − α O )  CS 



  for 0.1PS ≤ ΔP ≤ 0.3PS

where MO = Initial mass of reactants, kg  dT  = Self-heat rate corresponding to the relief set pressure, (K/sec)   dt S  dT  = Self-heat rate at turnaround temperature, (K/sec)   dt m = Relief set pressure (Pa) PS = Vessel void fraction corresponding to complete vapor disengagement. αD = Initial void fraction in vessel αO = Temperature corresponding to relief actuation, K TS = Liquid specific heat capacity, J/kg.K CS ΔP = Equilibrium overpressure corresponding to the actual temperature rise, Pa. ΔT = Temperature rise following relief actuation, K F = Flow reduction correction factor for turbulent flow (L/D=0, F≈1.0; L/D=50, F≈0.85; L/D=100, F≈0.75; L/D=200, F≈0.65; L/D=400, F≈0.55). where L/D is the length-to-diameter ratio of the vent line. Figure 10.50 shows a sketch of temperature profile for high vapor pressure systems.

(10.73)

1202  Chemical Process Engineering

TWO-PHASE FLOW

W=F

NONEQUILIBRIUM

∆P

T C

∆T

1 – 2

A

TURNAROUNDCOMPLETE VAPOR DISENGAGEMENT TEMPERATURE

(dT/dt)s ∆T ∆t =

VENTING

2∆t (dT/dt)s

αo

TIME

RUNAWAY REACTION

mo

mo

A = 1–2

(αo−αo) = W ∆t (1−αo)

mo (dT /dt)s (αo−αo) F (T/C)1/2 ∆P (1−αo)

Figure 10.50  Vent sizing model for high vapor-pressure systems; due to non-equilibrium effects turnaround in temperature is assumed to coincide with the onset of complete vapor disengagement.

The VSP bench scale apparatus can be employed to determine the information about the self-heat-rate and vapor disengagement when this is not readily available. In addition, the VSP equipment can be used for flashing flow characteristics using a special bottom vented test cell. Here, the flow rate, GO (kg/sm2) is measured in a simulated vent line (same L/D ratio) of diameter DO using the vent sizing package (VSP) apparatus. The following recommended scale-up approach in calculating the vent size is:

D   ∆P   TS  GO  T  ≥ G T ≅ F   ∆T   C P,S   DO 



0.5

where DT is the vent diameter required for turbulent flow, and is expressed by 0.5



D   ∆P   TS  GO  T  ≤ G T ≅ F   ∆T   C P,S   DO 



dT   0.25 (α − α O )  M 3  O dt D  C P,S  DT ≅  2  FPS (1 − α O )   TS   

0.5

, the required vent diameter for laminar flow DL is given by

G   DL =  D2T DO T   GO 

0.33

10.55 Gassy Systems The major method of vent sizing for gassy system is two-phase venting to keep the pressure constant. This method was employed before DIERS with an appropriate safety factor [62]. The vent area is expressed by:

Process Safety and Pressure-Relieving Devices  1203

A=



Q g (1 − α )ρf Q g M = G1 GV

(10.73)

where Qg = volumetric gas generation rate at temperature and in reactor during relief, m3/sec M = mass of liquid in vessel, kg = liquid density, kg/m3 ρf G, G1 = mass vent capacity per unit area, kg/s m2 α = void fraction in vessel V = total vessel volume, m3 Unlike systems with vapor present, gassy systems do not have any latent heat to temper the reaction. The system pressure increases as the rate of gas generation with temperature increases, until it reaches the maximum value. The vent area could be underestimated, if sizing is dependent on the rate of gas generated at the set pressure. Therefore, it is more plausible to size the vent area on the maximum rate of gas generation. Homogeneous two-phase venting is assumed even if the discharge of liquid during venting could reduce the rate of gas generation even further. The vent area is defined by

M  A = 3.6 × 10 Q g  O   VPm  −3



0.5



(10.74)

dP The maximum rate of gas generation during a runaway reaction is proportional to the maximum value of and dt can be calculated from

Q g1 =



M O  Vt dP  M t  Pm dt 

(10.75)

An equation representing the relief behavior for a length L/D Vυ fg (1 − α )2



(10.78)

is satisfied at the point of disengagement.

10.57 Two-Phase Flow Through an Orifice Sizing formulae for flashing two-phase flow through relief devices were obtained through DIERS. It is based upon Fauske’s equilibrium rate model (ERM), and assumes frozen flow (non-flashing) forms a stagnant vessel to the relief device throat. This is followed by flashing to equilibrium in the throat. The orifice area is expressed by 0.5



W  xVG   (VG − VL )2 C L T1   + A=   λ2 C D  kP1   

where A = Vent area, m2 CD = Actual discharge coefficient CL = Average liquid specific heat, J/kg.K k = isentropic coefficient

(10.79)

Process Safety and Pressure-Relieving Devices  1205 P1 = Pressure in the upstream vessel, N/m2 T1 = Temperature corresponding to relief actuation, K x = Mass fraction of vapor at inlet VG = Specific volume of gas, m3/kg VL = Specific volume of liquid, m3/kg W = Required relief rate, kg/s λ = Latent heat, J/kg Theoretical rate is given by



W = Af (2ΔP · ρ)0.5

(10.80)

For a simple sharp-edged orifice, the value of CD is well established (about 0.6). For safety relief valves, its value depends upon the shape of the nozzle and other design features. In addition, the value of CD varies with the conditions at the orifice. For saturated liquid at the inlet, Eq. 10.79 simplifies to yield

A=

W(VG − VL )(C L T1 )0.5 = C Dλ



W  dP   T  CD    1   dT   C L 

(10.81)

0.5



These equations are based upon the following assumptions: • • • •

Vapor phase behaves as an ideal gas. Liquid phase is an incompressible fluid. Turbulent Newtonian flow. Critical flow. This is usually the case since critical pressure ratios of flashing liquid approach, the value of 1.

It is recommended that a safety factor of at least 2.0 be used [63]. In certain cases, lower safety factors may be employed. The designer should consult the appropriate process safety section in the engineering department for advice.

10.58 Conditions of Use • If Fauske’s method yields a significantly different vent size, then the calculation should be reviewed. • The answer obtained from the Leung’s method should not be significantly smaller than that from Fauske’s method. • ICI recommends a safety factor of 1-2 on flow or area. The safety factor associated with the inaccuracies of the flow calculation will depend on the method used, the phase nature of the flow, and the pipe friction. For two-phase flow, use a safety factor of 2 to account for friction or static head. • Choose the smaller of the vent size from the two methods. A systematic evaluation of venting requires information on: • • • •

the reaction - vapor, gassy or hybrid. flow regime - foamy or non-foamy. vent flow - laminar or turbulent. vent sizing parameters are dT/dt, ΔP/ΔT and ΔT.

It is important to ensure that all factors (e.g., long vent lines) are accounted for, independent of the methods used. Designers should ascertain that a valid method is chosen rather than the most convenient or the best one. For ease

1206  Chemical Process Engineering of use, the Leung’s method for vapor pressure systems is rapid and easy. Different methods should give vent sizes within a factor of 2. Nomographs give adequate vent sizes for long lines to L/D of 400, but sizes are divisible by 2 for nozzles. A computer software VENT has been developed to size two-phase relief for vapor, gassy and hybrid systems.

10.59 Discharge System Design of the Vent Pipe The nature of the discharging fluid is necessary in determining the relief areas. DIERS and ICI techniques can analyze systems that exhibit “natural” surface active foaming and those that do not. The DIERS further found that small quantities of impurities can affect the flow regime in the reactor. In addition, a variation in impurity level could arise by changing the supplier of a particular raw material. Therefore, care is needed in sizing emergency relief on homogeneous vessel behavior, that is, two-phase flow. In certain instances, pressure relief during a runaway reaction can result in three-phase discharge, if solids are suspended in the reaction liquors. Solids can also be entrained by turbulence caused by boiling/gassing in the bulk of the liquid. Caution is required in sizing this type of relief system. Especially, where there is a significantly static head of fluid in the discharge pipe. Another aspect in the design of the relief system includes the possible blockage in the vent line. This could arise from the process material being solidified in cooler sections of the reactor. It is important to consider all discharge regimes when designing the discharge pipe work.

10.60 Safe Discharge Reactors or storage vessels are fitted with overpressure protection vent directly to roof level. Such devices (e.g., relief valves) protect only against common process maloperations and not runaway reactions. The quantity of material ejected and the rate of discharge are low, resulting in good dispersion. The increased use of rupture (bursting) discs can result in large quantities (95% of the reactor contents) being discharged for foaming systems. The discharge of copious quantities of chemicals directly to the atmosphere can give rise to secondary hazards, especially if the materials are toxic and can form a flammable atmosphere (e.g., vapor or mist) in air. In such cases, the provision of a knockout device (scrubber, dump tank) of adequate size to contain the aerated/foaming fluid will be required. The regulatory authorities can impose restrictions on the discharge of the effluent from the standpoint of pollution. Therefore, reliefs are seldom vented to the atmosphere. In most cases, a relief is initially discharged to a knockout system to separate the liquid from the vapor. The liquid is collected and the vapor is then discharged to another treatment unit. The vapor treatment unit depends upon the hazards of the vapor, which may include a vent condenser, scrubber, incinerator, flare or a combination of these units. This type of system is referred to as the total containment system as shown in Figure 10.51. The knockout drum is sometimes called a catch tank or blowdown drum. The horizontal knock-out serves both as a vapor-liquid separator as well as a holdup vessel for the disengaged liquid. These types are commonly used where there is greater space as in the petroleum refineries and petrochemical plants. The two-phase mixture enters at one end, and the vapor leaves at the opposite end. Inlets may be provided at each end with a vapor outlet at the center of the drum to minimize vapor velocities involving two-phase streams with very high vapor flow rates. When there is limited space in the plant, a tangential knock-out drum is employed as illustrated in Figure 10.52. Coker [64] has given detailed design procedures of separating gas-liquid separators.

10.61 Direct Discharge to the Atmosphere Careful consideration and analysis by management are essential before flammable or hazardous vapors are discharged to the atmosphere. Consideration and analysis must ensure that the discharge can be carried out without creating a potential hazard or causing environmental problems. The possible factors are:

Process Safety and Pressure-Relieving Devices  1207 • • • •

exposure of plant personnel and/or the surrounding population to toxic vapors or corrosive chemicals. formation of flammable mixtures at ground level or elevated structures. ignition of vapors at the point of emission (blowdown drum vent nozzle). air pollution.

These factors and methods for evaluating their effects are elaborated in API publications (API RP521) [5c]. We should take special care in the design of the vapor vent stack, to ensure that the tip faces straight up (i.e., no goose-neck) in order to achieve good dispersion. The stack should not be located near a building so as to avoid vapor drifting into the building. However, if the drum is near a building, the stack should extend at least 12 ft above the building floor. Grossel [65] has provided various descriptions of alternative methods of disposal.

Example 10.6 Tempered Reaction An 800-gal reactor containing a styrene mixture with a specific heat of 0.6 cal/gm oC, has a 10-inch rupture disk and a vent line with equivalent length of 400. The vessel MAWP is 100 psig and the rupture disk set pressure is 20 psig. The styrene mixture had a self-heat rate of 60oC/min at 170oC as it is tempered in a DIERS venting test. What is the allowable reactor mixture charge to limit the overpressure to 10% over the set pressure?

Solution Using Eq. 10.69, we have

(D p )2 (∆PS )  TS  MO = ⋅  dT   C p  2.769    dt  S



0.5

where MO DP P S PP ΔPS

= allowable mass of the reactor mixture charge (kg) to limit the venting overpressure to PP (psig). = 10 in. = the relief device set pressure = 20 psig = maximum venting pressure = 1.10(20) = 22.0 psig = the allowable venting overpressure (psi), i.e., the maximum venting pressure minus the relief device set pressure. (22.0 – 20) = 2 psi = the equilibrium temperature corresponding to the vapor pressure where the vapor pressure TS is the relief device set pressure (K) = 170 oC (170 + 273.15 = 443.15K) dT   = the reactor mixture self-heat rate  °C  at temperature T (K)     S dt S min  o = 60 C/min = specific heat of the reactor mixture (cal/g-K ) = 0.6 cal/gm.K. CP

(102 )(2.0)  443.15    (2.769)(60)  0.6  = 32.72 kg

MO = MO

0.5

1208  Chemical Process Engineering The density of styrene is 0.9 g/cm3. Therefore, the quantity charged in the reactor is:

(32.72) kg (103 ) g 1 cm 3 1 gal 11 × × 3 3× 1 kg 0.9 g 10 cm 3.7851 = 9.6 gal (≈ 10 gal). The reactor charge is quite small for an 800-gal reactor. If the pressure is allowed to rise to 10% above MAWP, then

∆PS = 1.1(100) − 20 = 90 psi. The amount charged is:

MO =

(102 )(90)  443.15    (2.769)(60)  0.6 

0.5

M O = 1472.2 kg 1472.2 gal = (0.9)(3.785) = 432 gal. This shows that a much larger initial charge will be required. An Excel spreadsheet program (Example 10.6.xlsx) has been developed for this example, and the results of the calculations are shown below. Results of the calculations of two-phase flow with tempered reaction. Type of two-phase flow reaction

Tempered

Density of reactor mixture

0.9

g/cm3

Rupture disk diameter

10

in.

The relief device set pressure

20

psig

Maximum allowable working pressure

100

psig

Maximum venting pressure

22

psig

The allowable venting overpressure

2

psi

The equilibrium temperature

170

°C

The reactor mixture self-heat rate

60

°C/min

Specific heat of the reactor mixture

0.6

cal/g-K

Mass of the reactor mixture charge, Mo.

32.72

kg

Quantity charged in the reactor

9.6

gal

An increase in the pressure above the MAWP

90

psi

The amount charged, Mo

1472.2

kg

The quantity charged to the reactor

432.2

gal

Process Safety and Pressure-Relieving Devices  1209

Example 10.7 A 700 gal reactor with a net volume of 850 gal containing an organic mixture has a 10-inch rupture disk and a vent line with an equivalent length L/D = 400. The vessel MAWP = 100 psig and the rupture disk set pressure is 20 psig. A venting test that was carried out showed that the reaction was “gassy”. The test mass was 30g, the peak rate of pressure rise was 550 psi/min., and the maximum test temperature was 300oC. Determine the allowable reactor mixture charge to limit the overpressure to 10% of the MAWP.

Solution Using Eq. 10.76 for “gassy” reaction, the amount charge is: 1/3

2   (DP )2 (M S )(PP )   M O =  VP ∆PP     (2.07)(TT )(dP/ dt)   

where

VP = vessel total volume (gal) = 850 gal PP = maximum allowable venting pressure (psia) 1.10 (100) + 14.7 = 124.7 psia. MS = sample mass used in a DIERS test or equivalent test, g. = 30 g dP = pressure rise in test (psi/sec). = 550 psi/min = 9.17 psi/sec dt TT = maximum temperature in test (K). (300oC = 573.15K) ΔPP = PP − Pamb = 124.7 – 14.7 = 110 psi Pamb = ambient pressure at the end of the vent line = 14.7 psia 1/3



  (10)2 (30)(124.7)   M O = (850)(110)    (2.07)(573.15)(9.17)    M O = 479.9 kg

The amount charge to the reactor is 480 kg. A Microsoft Excel spreadsheet (Example 10.7.xlsx) has been developed for this example. The table below shows the results of the spreadsheet calculations. Results of the calculations of two-phase flow with vapor reaction. Type of two-phase flow reaction

Gassy

Rupture disk diameter

10

in.

The relief device set pressure

20

psig

Maximum allowable working pressure

100

psig

Sample mass used in a diers test, Ms

30

g

Maximum temperature in test

300

o

Vessel total volume, Vp

850

gal

Pressure rise in test

550

psi/min.

C

1210  Chemical Process Engineering Pressure rise in test

9.17

psi/s.

Ambient pressure at the end of the vent line

14.7

psia

Maximum allowable venting pressure

124.7

psia

The allowable venting overpressure

110

psi

The amount charged, Mo

479.94

kg

Example 10.8 Determine the vent size for a vapor pressure system using the following data and physical properties. Reactor Parameters: Volume, V=10m3. Mass, M = 8,000 kg Vent opening pressure = 15 bara. (217.5 psia) Temperature at set pressure Ts=170oC (443.15K) Overpressure allowed above operating pressure = 10% = 1 bar (105 Pa). Material Properties: Specific heat, Cp=3000 J/kg.K. Slope of vapor pressure and temperature curve dP/dT=20,000 Pa/K. Rate of Reaction ΔT = dP/20,000 = 105/20,000 = 5K. Rate of set pressure, (dT/dt)s = 6.0K/min. Rate of maximum pressure = 6.6 K/min. Average rate = 6.3 K/min.    = 0.105 K/s.

Solution Using Fauske’s nomograph of Figure 10.49 at a self-heat rate of 6.3K/min and a set pressure of 217.5 psia, the corresponding vent are per 1,000 kg of reactants = 0.0008m2. The vent area of 8,000 kg reactants = 0.0064m2. The vent size



 4 Area  d=  π 

0.5

= 90.27 mm (3.6 in.) .

If Figure 10.51 applicable for F=0.5, then for F=1.0, the area is



 0.5  A = (0.0064 m 2 )  = 0.0032m 2  1.0 

The area assumes a 20% absolute overpressure

Process Safety and Pressure-Relieving Devices  1211 The result can be adjusted for other overpressures by multiplying the area by a ratio of 20/(new absolute percent overpressure). Using the Leung’s method: Assuming L/D=0, F=1.0 Two-phase mass flux from Eq. 10.61 gives

 1.0 × 443.15  G = (0.9)(1.0)(20,000)  3,000  = 6918.1



Rate of heat generation: q

q = Cp



0.5

kg . ms 2

W W dT  J.K  . 315 (3.000)(0.105) = = kg kg dt  kg.K.s 

From Eq. 10.66, the vent area A is:



A=

8,000 × 315 0.5   10  6918.1  × 443.15 × 20,000 + (3,000 × 5.0)0.5    8,000 

2

A= 7.024 × 10-3m2. d = 94.6mm (3.72 in). The vent size is about 4.0 in. Using the Fauske’s method: Assuming α = 1.0, αO = 0.0, F = 1.0 ΔP = 1bar = 105 N/m2. From Eq. 10.72, the vent area is

1 A= ⋅ 2

(8,000)(0.105)(1 − 0) 0.5  443.15  (1.0) (105 )(1 − 0)  3,000 

A= 10.927 × 10-3m2. d = 117.95mm (4.64 in).

Example 10.9 A 3500-gallon reactor with styrene monomer undergoes adiabatic polymerization after being heated inadvertently to 70oC. The MAWP of the reactor is 5 bara. Determine the relief vent diameter required. Assume a set pressure of 4.5 bara and a maximum pressure of 5.4 bara. Other data and physical properties are given as follows:

1212  Chemical Process Engineering Data Volume (V)

= 13.16 m3, (3,500 gal)

Reaction mass (mo), kg. = 9,500 Set temperature (Ts) = 209.4 oC = 482.5K Data from VSP: Maximum temperature (Tm) 219.5oC = 492.7K

 dT  29.6oC/min = 0.493 K/s (sealed system)   dt s  dT  39.7oC/min = 0.662 K/s   dt m

Physical property data: 4.5 bar set.

5.4 bar set.

vf, m /kg

0.001388

0.001414

vg, m3/kg; ideal gas assumed

0.08553

0.07278

Cp, kJ/kg.K

2.470

2.514

ΔHv, kJ/kg.

310.6

302.3

3

Solution The heating rate q is determined by Eq. (10.68)

1  dT   dT   q = C v   +    2  dt  S  dt  m 

Assuming Cv = CP

1 q = (2.470 kJ/ kg.K)[0.493 + 0.662](K/s) 2 kJ = 1.426 kg.s



The mass flux through the relief G is given by Eq. 10.58, assuming L/D = 0 and ψ = 1.0



∆H V  g c  Q G = m = 0.9ψ A υ fg  C P TS 

0.5

0.5

 (0.9)(1.0)(310660 J/ kg)[1(Nm)/ J]  [1(kgm/ s 2 ) / N] G=   3 (0.08553 − 0.001388)m / kg  (2,470J/ kg K)(482.5K)[1(Nm)/ J]  = 3043.81

kg m2s

The relief area is determined by Eq. 10.67

Process Safety and Pressure-Relieving Devices  1213

A=

M Oq   V ∆H  0.5 V 0.5  G  (C ∆T) + V   M O υ fg  

2

The change in temperature ΔT is Tm − Ts



ΔT = 492.7 – 482.5 = 10.2K (9500 kg)(1426J/ kg.s)[1(Nm)/ J]

A=

0.5   13.16m3   310660 J/kg[1(Nm)/ J] 0.5    J  2 (10.2K)[1(Nm) / J]  (3043.81kg / m s)    +  2470 kg.K  0.08414 m3 /kg     9500 kg      2 A = 0.0839m .

2

The required relief diameter is

 4A  d=  π 





0.5

 (4)(0.0839m 2 )  =  3.14 

0.5

= 0.327m

d = 327 mm (12.87 inches).

We shall consider the situation that involves all vapor relief. The size of a vapor phase rupture disk required is determined by assuming that all of the heat energy is absorbed by the vaporization of the liquid. At the set temperature, the heat release rate q is given by:



K kJ    dT   0.493  q = C V   =  2.470    dt  s  s kg.K   q = 1.218



kJ kg.s

The vapor mass flow through the relief is then

qmo ∆H v (1218J/ kg)(9500 kg) = (310660J/ kg)

Qm =

= 37.25

kg s

The required relief area for vapor is determined by 0.5



 γ +1    Q m  R g T  2   γ −1   A=   C oP  γg c M  γ + 1    

1214  Chemical Process Engineering To Condenser, Flare Stack, or Scrubber

Long Radius

Rupture Disc Reactor

Blowdown Drum

Figure 10.51  Relief containment system with blowdown drum. The blowdown drum separates the vapor from the liquid (Source: Grossel [65]). Vent to Atmosphere or Flare Stack or Scrubber

Long Radius

Tangential Knock-Out Drum

Reactor

Catchtank

Rupture Disc Located as Close to Vessel as Possible

Figure 10.52  Tangential inlet knockout drum with separate liquid catch-tank (Source: Grossel [65]).

where Qm = discharge mass flow, kg/s Co = discharge coefficient A = area of discharge P = absolute upstream pressure γ = heat capacity ratio for the gas gc = gravitational constant M = molecular weight of the gas (M=104 for styrene) Rg = ideal gas constant (8314 Pa m3/kg mol K) T = absolute temperature of the discharge Assuming Co = 1 and γ = 1.32 0.5



 (8314Pa m3 / kg − mol)(482.5K)[1(N/ m 2 )/Pa]  (37.25kg/s) A=   (1.0)(4.5bar)(105 Pa / bar)[1(N/ m 2 )/Pa]  (1.32)[1(kg m/ s 2 )/ N](104 kg / kg − mol)  0.5



 2.32     2   −0.32   ×      2.32 

Process Safety and Pressure-Relieving Devices  1215

A = 0.0242 m2. The relief diameter = 0.176 m d = 176mm (6.9 inches). Thus, the size of the relief device is significantly smaller than for two-phase flow. Sizing for all vapor relief will undoubtedly give an incorrect result, and the reactor would be severely tested during this runaway occurrence. Articles describing procedures related to the DIERS development of this entire subject have been published by some members of the DIERS group. These are referenced here and the detailed descriptions and illustrations in the noted articles can be most helpful to the potential user. A useful website for two-phase runaway flow system is www.fauske. com.

10.62 DIERS Final Reports Refer to the bibliography at the end of this chapter for a listing of the final reports of this program [13].

10.63 Sizing for Two-Phase Fluids Sizing for two-phase fluids is based upon the procedures outlined in API RP 520 [5]. In this design, the physical parameters are established carefully because a little change in the physical parameters may alter the results substantially. The design procedure uses the following definitions: Noncondensible gas: This is a gas that is not easily condensed under normal pressure and temperature conditions. The common noncondensible gases are air, nitrogen (N2), oxygen (O2), hydrogen (H2), carbon dioxide (CO2), hydrogen sulfide (H2S) and carbon monoxide (CO). Highly subcooled liquid: It is a liquid that does not flash after passing through the PRV. Subcooled liquid: It is a liquid that flashes after passing through the PRV. The following three different types are possible for designing a two-phase PRV: Type 1 (omega method): Subcooled (including saturated) liquid enters the PRV and flashes. No condensable vapor or noncondensable gas is present. This calculation follows the method defined in Section D 2.2 in API RP 520 [5]. Type 2 (omega method): All other cases. This calculation follows the method defined in Section D.2.3 in API RP 520 [5]. Type 3 (integration method): For all cases using the numerical integration method. This calculation follows the method defined in Section D2.1 in API RP 520 [5]. Type 1 (omega method) This method is used for sizing pressure relief valves handling a subcooled (including saturated) liquid at the inlet. No condensable vapor or non-condensable gas should be present at the inlet. The subcooled liquid either flashes upstream or downstream of the pressure relief valve throat depending on which subcooling region the flow falls into. The equations also apply to all liquid scenarios. The steps are as follows:

Step 1. Calculate the Saturated Omega Parameter, ωs For multicomponent systems with nominal boiling range* less than 150 oF or single component systems, use either Eq. 10.82 or 10.83. If Eq. 10.82 is used, the fluid must be far from its thermodynamic critical point (Tr ≤ 0.9 or Pr ≤ 0.5)**

1216  Chemical Process Engineering 2

υ  ω s = 0.185 ρ lo C p To Ps  vls   h vls 



(10.82)

where ρlo = liquid density at the PRV inlet, lb/ft3 Cp = liquid specific heat at constant pressure at the PRV inlet (Btu/lb oR) To = temperature at the PRV inlet (oR) Ps = saturation (vapor) pressure corresponding to To (psia). For a multicomponent system, use the bubble point pressure corresponding to To. υvls = difference between the vapor and liquid specific volumes at Ps (ft3/lb) hvls = latent heat of vaporization at Ps (Btu/lb). For multicomponent systems, hvls is the difference between the vapor and liquid specific enthalpies at Ps * The nominal boiling range is the difference in the atmospheric boiling points of the lightest and heaviest components in the system. ** Other assumptions that apply include: heat of vaporization and the heat capacity of the fluid are constant through the nozzle, behavior of the fluid vapor pressure with temperature follows the Clapeyron equation, and isenthalpic (constant enthalpy) flow process. For multicomponent systems with nominal boiling range greater than 150oF or single component systems near the thermodynamic critical point use Eq. 10.83.

ρ  ω s = 9  lo − 1  ρ9 



(10.83)

where ρlo = liquid density at the PRV inlet, lb/ft3 ρ𝟿  = density evaluated at 90% of the saturation (vapor) pressure Ps corresponding to the PRV inlet temperature To, lb/ft3. For a multicomponent system, use the bubble point pressure corresponding to To for Ps. When determining ρ9, the flash calculation should be carried out isentropically, but an isenthalpic (adiabatic) flash is sufficient.

Step 2. Determine the Subcooling Region The subcooling region is determined as:

Ps ≥ ηst Po ⇒ low subcooling region (flashing occurs upstream of throat)

(10.84)

Ps ≤ ηst Po ⇒ high subcooling region (flashing occurs at the throat).

(10.85)

where ηst = transition saturation pressure ratio



ηst =

2ω s 1 + 2ω s

(10.86)

Process Safety and Pressure-Relieving Devices  1217 Po = pressure at the PRV inlet (psia). This is the PRV set pressure (psig) plus the allowable overpressure (psi) plus atmospheric pressure.

Step 3. Determine if the Flow is Critical or Subcritical For the low subcooling region, the flow behavior is determined by:

Pc ≥ Pa ⇒ critical flow

(10.87)

Pc ≤ Pa ⇒ subcritical flow

(10.88)

For the high subcooling region, the flow behavior is determined by:

Ps ≥ Pa ⇒ critical flow

(10.89)

Ps ≤ Pa ⇒ subcritical flow

(10.90)

where

Pc = critical pressure, psia = ηcPo



(10.91)

ηc = critical pressure ratio and is estimated from Figure 10.53 using the value of ηs where

ηs = saturation pressure ratio =

Ps Po

(10.92)

Pa = downstream back pressure (psia).

Step 4. Calculate the Mass Flux In the low subcooling region, use Eq. 10.93. If the flow is critical, use ηc for η, and if the flow is subcritical, use ηa for η. In the high subcooling region, use Eq. 10.94. If the flow is critical, use Ps for P and if the flow is subcritical (all – liquid flow), use Pa for P

   η  68.09  2(1 − ηs ) + 2 ω s ηs ln  s  − (ω s − 1)( ηs − η)  η    G= η  ω s  s − 1 + 1  η 



0.5

Po ρlo

G = 96.3[ρlo (Po – P)]0.5

(10.93)

(10.94)

where G = mass flux (lb/s ft2)

ηa = back pressure ratio/subcritical pressure ratio =

Pa Po

(10.95)

1218  Chemical Process Engineering where Pa = downstream back pressure (psia).

Step 5. Calculate the Required Area of the PRV The following equation is applicable to turbulent flow systems, as most two-phase relief scenarios are within the turbulent flow regime. Qρlo

A = 0.3208



Kd K b Kc G



(10.96)

where A = required effective discharge area, in2. Q = volumetric flow rate, gpm Kd = discharge coefficient that should be obtained from the valve manufacturer. For a preliminary sizing estimation, a discharge coefficient 0.65 for subcooled liquids and 0.85 for saturated liquids. Kb = back pressure correction factor for liquid that should be obtained from the valve manufacturer. For a preliminary sizing estimation, use Figure 10.54. Kc = combination correction factor for installations with a rupture disk upstream of the pressure relief valve. = 1.0 when a rupture disk is not installed. = 0.9 when a rupture disk is installed in combination with a pressure relief valve and the combination does not have a published value.

SI Units For ηs ≤ ηst

ηc = ηst

(10.97)

For ηs ≥ ηst, the value of ηc is calculated using Eq. 10.98 or approximated using Eq. 10.99



1    ω s + ω − 2 η  s ηc2 − 2(ω s − 1)ηs + ω s ηs ln  c  + 1.5ω s ηs − 1 = 0  ηs  2 ηs



1  2ω − 1    2ω   1− 1−  ηc = ηs     2ω − 1   2ω   η s  

(10.98)

(10.99)

The mass flux for the low subcooling region is calculated by:



    ηs   2 (1 − ηs ) + 2 ω s ηs 1n  η  − ( ω s − 1)( ηs − η)    G= η   ω s  s + 1  η 

0.5

Poρ1o

(10.100)

Process Safety and Pressure-Relieving Devices  1219 In the above equation, if the flow is critical, use ηc for η, and if the flow is subcritical, use ηa for η. The mass flux for the high subcooling region is calculated by:



G = 1.414[ρlo (Po − P)]0.5

(10.101)

In the above equation, if the flow is critical, use Ps for P, and if the flow is subcritical, use Pa for P. The PRV area is calculated by:

A = 16.67



Qρlo Kd K b K v G



(10.102)

where A = required effective discharge area, mm2. Q = volumetric flow rate, l/min Kd = discharge coefficient that should be obtained from the valve manufacturer. For a preliminary sizing estimation, a discharge coefficient 0.65 for subcooled liquids and 0.85 for saturated liquids. Kb = back pressure correction factor for liquid that should be obtained from the valve manufacturer. For a preliminary sizing estimation, use Figure 10.54 Kv = viscosity correction factor. G = mass flux, kg/(s m2) ωs = saturated omega parameter ρlo = liquid density at the PRV inlet, kg/m3 ρ9 = density evaluated at 90% of the saturation (vapor) pressure, Ps, corresponding to the PRV inlet relieving temperature, To, kg/m3 Ps = saturation vapor pressure, Pa Po = PRV relieving pressure, Pa Pc = critical pressure, Pa Pa = downstream back pressure, Pa To = relieving temperature, oC ηa = subcritical pressure ratio/back pressure ratio = Pa/Po ηc = critical pressure ratio ηs = saturation pressure ratio = Ps/Po ηst = transition saturation pressure ratio.

Example 10.10 The following relief requirements are given: a.

Required propane volumetric flow rate caused by blocked in pump

= 100 gal/min

b

Relief valve set at the design pressure of the equipment

= 260 psig

c

Downstream total back pressure of (superimposed back pressure = 0 psig, built – up back pressure = 10 psig)

= 10 psig (24.7 psia)

d

Inlet temperature at the PRV

= 60oF (519.7oR)

e

Inlet liquid propane density at the PRV

= 31.92 lb/ft3

f

Inlet liquid propane specific heat at constant pressure at the PRV

= 0.6365 Btu/lboR

1220  Chemical Process Engineering g

Saturation pressure of propane corresponding to 60oF

107.6 psia

h

Specific volume of propane liquid at the saturation pressure

0.03160 ft3/lb

i

Specific volume of propane vapor at the saturation pressure

1.001 ft3/lb

j

Latent heat of vaporization for propane at the saturation pressure

152.3 Btu/lb

The following data are derived: a. P  ermitted accumulation is 10% b. Relieving pressure of 1.10 × 260 = 286 psig (300.7 psia) c. Percent of gauge back pressure = (10/260) × 100 = 3.8%. Since the downstream built-up back pressure is less than 10% of the set pressure, a conventional pressure relief valve may be used. Thus, the back pressure correction factor Kb = 1.0 (Figure 10.55). d. Since the propane is subcooled, a discharge coefficient Kd of 0.65 can be used.

Solution Step 1. Calculate the saturated omega, ωs Since the propane system is a single-component system, the saturated omega parameter is calculated from Eq. 10.82

 1.001 − 0.0316  ω s = 0.185(31.92)(0.6365)(519.67)(107.6)   152.3

= 8.497

Step 2. Determine the Subcooling Region The transition saturation pressure ratio ηst is calculated from Eq. 10 – 86

2 × 8.497 1 + 2 × 8.497 = 0.9444

ηst =

The liquid is determined to fall into the high subcooling region since Ps < ηst Po i.e. 107.6 < 0.9444 × 300.7 = 283.98 Step 3. Determine if the flow is Critical or Subcritical The flow is determined to be critical since Ps > Pa i.e. 107.6 > 24.7 Step 4. Calculate the Mass flux Since the flow is critical, substitute Ps for P, and the mass flux from Eq. 10.94 is: G = 96.3[(31.92)(300.7 − 107.6)]0.5    = 7560.5 lb/s-ft2 Step 5. Calculate the required area of the PRV from Eq. 10.96:

A = 0.3208

(100)(31.92) (0.65)(1.0)(1.0)(7560.5)

= 0.208 in 2

2

Process Safety and Pressure-Relieving Devices  1221 The table below shows the orifice designation and effective area from the Crosby Catalog. Thus, the next standard orifice area is “F” orifice pressure relief valve = 0.307 in2 The maximum flow, W = (0.307) (0.65) (1) (1) (7560.5) (60)/(0.3208 × 7.4805) = 37721.5 lb/h Microsoft Excel spreadsheet (Example 10.10.xlsx) shows the calculations of Example 10.10, and the results are shown below. Results of Type 1 omega method (Subcooled) for liquid flow. Flow type

Type 1 omega method

 

Volumetric flow rate of liquid

100

US gal./min

Set Pressure at inlet

260

psig

Downstream total back pressure

10

psig

Inlet temperature at the PRV

60

o

Inlet liquid density at the PRV

31.92

lb/ft3

Inlet liquid specific heat at constant pressure at the PRV

0.637

Btu/lboR

Saturation pressure of propane corresponding to 60oF

107.6

psia

Specific volume of liquid propane at the saturation pressure

0.0316

ft3/lb

Specific volume of propane vapor at the saturation pressure

1.001

ft3/lb

Latent heat of vaporization for propane at the saturation pressure

152.3

Btu/lb

Relieving pressure

300.7

psia

Kb

1

 

Kd

0.65

 

Kc (rupture disk not installed)

1

 

Kc (rupture disk installed)

0.9

 

Saturated Omega Parameter, ωs

8.5203

 

Saturation pressure, Pst

284

psia

Flow Type

Critical flow

 

Mass flux, G

7560

lb/(s.ft2)

Effective required area, A

0.208

in2

Next standard orifice area

0.307

in2

Maximum flow rate with the next standard orifice size

37721

lb/h

F

Orifice designation and effective area: crosby catalog. Orifice designation

in2

mm2

D

0.11

71

1222  Chemical Process Engineering E

0.196

126

F

0.307

198

G

0.503

325

H

0.785

506

J

1.287

830

K

1.838

1186

–

2.461

1588

L

2.853

1841

M

3.6

2323

N

4.34

2800

–

5.546

3578

P

6.379

4116

–

9.866

6365

Q

11.05

7129

R

16

10323

–

22.22

14335

T

26

16774

–

39.51

25490

Example 10.11 Design a pressure-relieving valve for a subcooled liquid that enters a PRV and flashes, using the following parameter: Flow rate = 15,000 kg/h Liquid density at the PRV inlet = 700 kg/m3 PRV set pressure = 1000 kPaG Bubble point pressure = 850 kPaG Density at 90% of bubble point pressure = 600 kg/m3 PRV back pressure = 50 kPaG Allowable overpressure = 10% Type of PRV = Conventional

Solution 1. The saturated omega parameter from Eq. 10.83 is:



ρ  ω s = 9  lo − 1  ρ9 

Process Safety and Pressure-Relieving Devices  1223

700  ω s = 9  −1  600  = 1.5



2. The transition saturation pressure ratio, ηst from Eq. 10.86 is:

2 × 1.5 1 + 2 × 1.5 = 0.75

ηst = 3. Determine the Subcooling Region The subcooling region is determined as:

Ps > ηst Po ⇒ low subcooling region (flashing occurs upstream of throat)

(10.84)

Ps < ηst Po ⇒ high subcooling region (flashing occurs at the throat).

(10.85)

The saturation pressure, Pst is: Pst = ηst Po   = 0.75 (1.1 × 1000 + 101.35)   = 901.0 kPaa Bubble point pressure, Ps = 850 + 101.35 = 951.35 kPaa   Since the bubble point pressure > saturation pressure, then it will be in the low subcooling region. i.e. 951.35 > 901.0 4. Saturation pressure ratio, ηs from Eq. 10.92 is: ηs = saturation pressure ratio =

Ps 951.35 = Po 1201.35 = 0.792

Since the saturated pressure ratio > the transition pressure ratio, i.e., ηs > ηst, 0792 > 0.75, then the critical pressure ratio, ηc can be determined from Eq. 10.99



1  2ω − 1    2ω   1− 1−  ηc = ηs       2ω − 1  ηs  2ω   



1  2 × 1.5 − 1    2 × 1.5   1− 1− ηc = 0.792       2 × 1.5 − 1  0.792  2 × 1.5    = 0.716 5. The critical pressure, Pc is determined from Eq. 10.91 Pc = ηc Po = 0.716 × 1201.35    = 860.2 kPaa The back pressure, Pa = 50 + 101.35 = 151.35 kPaa Since the critical pressure > the back pressure, i.e., Pc > Pa, then the flow is critical.

(10.99)

1224  Chemical Process Engineering 6. The mass flux, G for the low subcooling region is calculated from Eq. 10.100, and for critical flow, use ηc for η



    ηs  2(1 ) 2 ln ( 1)( ) − ω − η − η − η + ω η s s s s s     η     G= η  ω s  s − 1 + 1  η 

0.5

1000Po ρlo

    0.792   2(1 − 0.792) + 2 (1.5)(0.792) ln  0.716  − (1.5 − 1)(0.792 − 0.716)   G=  0.792  1.5  −1 +1  0.716 

0.5

1201.35 × 700 × 1000

= 19037.5 kg / (s m 2 ) 7. The volumetric flow rate, Q is:

Q=



W 15,000  kg m 3 103 l h  = ⋅ 3⋅  ⋅ , 700  h kg m 60min  ρlo



= 357.14 l/min. Since the region is low subcooling, the discharge coefficient, Kd is assumed as 0.85 8. The effective PRV area is calculated from Eq. 10.102





A = 16.67

Qρlo Kd K b K v G

A = 16.67

(357.14)(700) (0.85)(1)(1)(19037.5)

= 257.54 mm 2 The next standard orifice size is G with area = 325 mm2. The maximum flow with the standard size is: W = (325) (0.85) (1) (1) (19037.5) (60)/(16.67 × 1000.)   = 18929 lb/h

Microsoft Excel spreadsheet (Example 10.11.xlsx) shows the calculations of Example 10.11, and the results are shown below. Results of Type 1 omega method (subcooled) for liquid flow. Flow type

Subcooled

Volumetric flow rate of liquid

357.14

l/min

Set Pressure at inlet

1000

kPaG

Downstream total back pressure

50

kPaG

Inlet liquid density at the PRV

700

kg/m3

Process Safety and Pressure-Relieving Devices  1225 Flow rate

15000

kg/h

Allowable overpressure

10

%

Type of PRV

Conventional

Relieving pressure of 1.1 × 1000 + 101.35

1201.4

kPaa

Kb

1

 

Kd

0.85

 

Kc (rupture disk not installed)

1

 

Kc (rupture disk installed)

0.9

 

Kv

1

 

Saturated Omega Parameter, ωs

1.5

 

Saturation pressure, Pst

901.01

kPaa

Bubble point pressure

951.35

kPaa

Type of liquid phase

Low subcooling

Saturation pressure, ratio, Ps/Po

0.792

 

Type of pressure phase

Critical

 

Critical pressure ratio

1.1879

 

Critical pressure

859.57

kPaa

1.00 ηc = ηst

0.95

Critical Pressure Ratio, ηc

0.90

ωs = 40 20

0.85

ηs = ηs

15 10

0.80

7 Low subcooling

High subcooling

0.75

5

0.70

0.65 0.60 0.75

0.80

0.85

0.90

0.95

1.00

1.05

Saturation Pressure Ratio, ηs

Figure 10.53  Correlation for nozzle critical flow of inlet subcooled liquids (Source: API RP 520, Sizing Selection, and Installation of Pressure – Relieving Devices in Refineries, Part 1- Sizing and Selection, 7th ed., 2020).

1226  Chemical Process Engineering Back pressure

151.35

kPaa

Mass flux, G

19050

kg/(s.m2)

Effective required area, A

257

mm2

Next standard orifice area

325

mm2

Maximum flow rate with the next standard orifice size

151.4

kg/h

Type 2. (Omega Method): Sizing for Two-Phase Flashing Flow with a Noncondensable Gas Through a Pressure Relief Valve [5] In this method, the term vapor (subscript v) will be used to refer to the condensable vapor present in the two-phase flow and the term gas (subscript g) will be used to refer to the non-condensable gas. The following procedure is as follows: Step 1. Calculate the inlet void fraction, αo

αo =



x o υ vgo υo

(10.103)

1.00 0.95 0.90 0.85

Kb

0.80 0.75 0.70 0.65 0.60 0.55 0.50

0

10

20 30 40 Percent of guage back pressure = (Pa /PS) x 100

50

Kb = correction factor due to back pressure. Pa = back pressure, in psig. PS = set pressure, in psig. Note: The curve above represents values recommended by various manufacturers. This curve may be used when the manufacturer is not known. Otherwise, the manufacturer should be consulted for the applicable correction factor.

Figure 10.54  Back pressure correction factor, Kb for balanced – bellows pressure relief valves (Liquids) (Source: API RP 520, Sizing Selection, and Installation of Pressure – Relieving Devices in Refineries, Part 1- Sizing and Selection, 7th ed., 2020).

Process Safety and Pressure-Relieving Devices  1227 where xo = gas or combined vapor and gas mass fraction (quality) at the PRV inlet υvgo = specific volume of the gas or combined vapor and gas at the PRV inlet, ft3/lb υo = specific volume of the two-phase system at the PRV inlet, ft3/lb Step 2. Calculate the Omega Parameter, ω For systems that satisfy all of the following conditions, use Eq. 10.104 a. b. c. d.

 ontains less than 0.1 weight % hydrogen C Nominal boiling range* less than 150oF. Either Pvo/Po less than 0.9 or Pgo/Po greater than 0.1 Far from its thermodynamic critical points (Tr ≤ 0.9 or Pr ≤ 0.5)** 2

α υ  ω = o + 0.185(1 − α o )ρlo C p To Pvo  lo   h vlo  k



(10.104)

where Pvo = saturation (vapor) pressure corresponding to the inlet temperature To (psia). For a multicomponent system, use the bubble point pressure corresponding to To. Po = pressure at the PRV inlet (psia). This is the PRV set pressure (psig) plus the allowable overpressure (psi) plus atmospheric pressure. Pgo = noncondensable gas partial pressure at the PRV inlet (psia). k = ratio of specific heats of the gas or combined vapor and gas. If the specific heat ratio is unknown, a value of 1 can be used. ρlo = liquid density at the PRV inlet, lb/ft3 Cp = liquid specific heat at constant pressure at the PRV inlet, Btu/lb - oR To = temperature at the PRV inlet, oR = (oF + 460) υvlo = difference between the vapor† (not including any condensable gas present) and liquid specific volumes at the PRV inlet, ft3/lb hvlo = latent heat of vaporization at the PRV inlet, Btu/lb. For multicomponent systems, hvlo is the difference between the vapor and liquid specific enthalpies.  o to Step 3 to determine if the flow is critical or subcritical. For systems that satisfy one of the following condiG tions, use Eq. 10.105 a. b. c. d.

 ontains more than 0.1 weight % hydrogen C Nominal boiling range greater than 150oF. Either Pvo/Po greater than 0.9 or Pgo/Po less than 0.1 Near its thermodynamic critical point

υ  ω = 9  9 − 1  υo 



(10.105)

where υ9 = specific volume evaluated at 90% of the PRV inlet pressure Po (ft3/lb). When determining υ9, the flash calculation should be carried out isentropically, but an isenthalpic (adiabatic) flash is sufficient. Go to Step 4 to determine if the flow is critical or subcritical. Step 3. Determine if the flow is Critical or Subcritical

1228  Chemical Process Engineering Pc > Pa ⇒ critical flow Pc < Pa ⇒ subcritical flow where Pc = critical pressure, psia = [ygo ηgc + (1 − ygo)ηvc]Po ygo = inlet gas mole fraction in the vapor phase. Can be determined using given mole composition information or the following equation = Pgo/Po ηgc = nonflashing critical pressure ratio from (Figure 10.56) using the value of ω = αo/k ηvc = flashing critical pressure ratio from Figure 10.56 using the value of ω Pa = downstream back pressure, psia Go to Step 5. Step 4. Determine if the flow is Critical or Subcritical (Eq. 10.105) Pc > Pa ⇒ critical flow Pc < Pa ⇒ subcritical flow where

Pc = critical pressure, psia = ηc Po

(10.106)

ηc = critical pressure ratio from Figure 10.58. This ratio can also be obtained from the following expression:

ηc2 + (ω 2 − 2ω )(1 − ηc )2 + 2ω 2 ln ηc + 2ω 2 (1 − ηc ) = 0



(10.107)

Pa = downstream back pressure (psia). Step 5. Calculate the Mass Flux (ω calculated from Eq. 10.104) From critical flow, use Eq. 10.108

 Po  y go η2gc k  (1 − y go ) η2vc  G = 68.09    + ω  υo  α o  

1/2





(10.108)

where G = mass flux, lb/s – ft2

For subcritical flow, and iterative solution is required. Eqs. 10.109 and 10.110 are solved simultaneously for ηg and ηv:

ηa = ygo ηg + (1 − ygo)ηv   1  αo  1 − 1 = ω  − 1  k  ηg   ηv 



where ηg = nonflashing partial pressure ratio. ηv = flashing partial pressure ratio.

(10.109) (10.110)

Process Safety and Pressure-Relieving Devices  1229 1.00

Backpressure Correction Factor, Kb

0.95 0.90

16% Overpressure (see Note 2)

0.85 10% Overpressure

0.80 0.75 0.70 0.65 0.60 0.55 0.50

0

5

10

15 20 25 30 35 Percent of Gauge Pressure = (PB /PS) x 100

40

45

50

PB = back pressure, in psig. PS = set pressure, in psig. Notes: 1. The curves above represent a compromise of the values recommended by a number of relief valve manufacturers and may be used when the make of the valve or the critical flow pressure point for the fluid is unknown. When the make of the valve is known, the manufacturer should be consulted for the correction factor. These curves are for the set pressures of 50 psig and above. They are limited to back pressure below critical flow pressure for a given set pressure. For set pressures below 50 psig or subcritical flow, the manufacturer must be consulted for vakues of Kb. 2. See paragraph 3.3.3. 3. For 21% overpressure, Kb equals 1.0 up to PB /PS = 50%.

Figure 10.55  Back pressure correction factor, Kb for balanced bellows pressure relief valves (vapors and gases) (Source: API RP 520, Sizing Selection, and Installation of Pressure – Relieving Devices in Refineries, Part 1- Sizing and Selection, 7th ed., 2020).

Calculate the mass flux by:

G =  y goG 2g + (1 − y go ) G 2v  0.5



(10.111)

where Gg = nonflashing mass flux, lb/s-ft2 0.5



 α  α  68.09 −2  o ln ηg +  o − 1 (1 − ηg )   k    k Gg =   αo 1 −1 +1 k  η 

Po vo

(10.112)

Gv = flashing mass flux, lb/s – ft2

68.09 {−2[ ω ln ηv + (ω − 1)(1 − ηv )]} Gv =  1  ω − 1 + 1  ηv 

0.5



Po vo

(10.113)

1230  Chemical Process Engineering Go to Step 7 Step 6. Calculate the Mass Flux (ω is calculated from Eq. 10.105) For critical flow, use Eq. 10.114. For subcritical flow, use Eq. 10.115

 P  G = 68.09 ηc  o   υ oω 

G=

0.5



68.09 {−2[ω ln ηa + (ω − 1)(1 − ηa )]} 0.5 Po vo  1  ω  − 1 + 1  ηa 

(10.114)



(10.115)

where G = mass flux, lb/s-ft2 P ηa = back pressure ratio = a Po Step 7. Calculate the required area of the PRV

A=



0.04W Kd K b Kc G

(10.116)

where A = Required effective discharge area, in2 W = Mass flow rate, lb/h Kd = discharge coefficient that should be obtained from the valve manufacturer. For a preliminary sizing estimation, a discharge coefficient of 0.85 can be used. Kb = back pressure correction factor for vapor that should be obtained from the valve manufacturer. For a preliminary sizing estimation, use Figure 10.55. The back pressure correction factor applies to balanced bellows valves only. Kc = combination correction factor for installations with a rupture disk upstream of the pressure relief valve. = 1.0 when a rupture disk is not installed. = 0.9 when a rupture disk is installed in combination with a pressure relief Valve and the combination do not have a published value.

* The nominal boiling range is the difference in the atmospheric boiling points of the lightest and heaviest components in the system. ** Other assumptions that apply include: ideal gas behavior, heat of vaporization and the heat capacity of the fluid are constant throughout the nozzle, behavior of the fluid vapor pressure with temperature follows the Clapeyron equation, and isenthalpic (constant enthalpy) flow process. † To obtain the vapor specific volume when a noncondensable gas is present at the PRV inlet, use the vapor partial pressure (from the mole composition) and the ideal gas law to calculate the volume.

Example 10.12 The following requirements are given as follows: a.

Required gas oil hydrotreater (GOHT) flow rate caused by operational upset.

= 160,000 lb/h

Process Safety and Pressure-Relieving Devices  1231 b.

Inlet temperature at the PRV.

= 450oF (909.67oR)

c.

Relief valve set pressure design of the equipment.

= 600 psig

d.

Downstream total back pressure (superimposed back pressure = 0 pisg, built-up back pressure = 55 psig)

= 55 psig (69.9 psia)

e.

Two- phase specific volume at the inlet of PRV

= 0.1549 ft3/lb

f.

Mass fraction of the vapor and gas at the inlet of PRV

= 0.5596

g.

Combined specific volume of the vapor and gas at the inlet of PRV

= 0.2462

h.

Inlet gas mole fraction in the vapor phase. Non condensable gases in the GOHT system include hydrogen, nitrogen and hydrogen sulfide

= 0.4696

i.

Specific heat ratio, k

=1

Here, the following data are as follows: a. O  verpressure of 10%. b. Relieving pressure of 1.10 × 600 = 660 psig (674.7 psia) c. Percent of gauge back pressure = (55/600) × 100 = 9.2% Since the downstream back pressure is less than 10% of the set pressure, a conventional pressure relief valve is used. Thus, the back pressure correction factor Kb = 1.0 Step 1. Calculate the inlet void fraction, The inlet void fraction αo is determined by Eq. 10.103

αo =



x o υ vgo υo

0.5596 × 0.2462 0.1549 = 0.8894 =



Step 2. Calculate the Omega Parameter, ω Since the gas oil hydrotreater has a nominal boiling range greater than 150oF, Eq. 10.105 is used to calculate ω. The specific volume calculated at 0.9 × 674.7 = 607.2 psia using the results of an isenthalpic (i.e., adiabatic) flash calculation from a process simulator is 0.1737 ft3/lb. The ω parameter is determined by Eq. 10.105:

υ  ω = 9  9 − 1  υo 



 0.1737  = 9 −1  0.1549  = 1.0923



Step 3. Determine if the Flow is Critical or Subcritical The critical pressure ratio, ηc is 0.62 from Figure 10.58 with ω = 1.0923 or from Eq. 10.117.

ηc = 1 + (1.0446 − 0.0093431ω 0.5 )ω −0.56261 

= 0.62

( −0.70356 + 0.014685ln ω )

1232  Chemical Process Engineering The critical pressure Pc is: Pc = ηc × Po = 0.62 × 674.7    = 418.3 psia The flow is determined to be critical since Pc > Pa, i.e. 418.3 > 69.7 Step 4. Calculate the Mass flux G The mass flux G is calculated from Eq. 10.114

 P  G = 68.09 ηc  o   υ oω 



0.5



674.7   G = 68.09(0.62)  0.1549 × 1.0923 

0.5

= 2665.2 lb/s − ft 2



Step 5. Calculate the required area of the PRV from Eq. 10.116

A=

=

0.04W Kd K b Kc G

0.04(160,000) (0.85)(1.0)(1.0)(2665.2)

= 2.825 in 2 .



The next recommended standard orifice pressure relief size is “L” = 2.853 in2. The maximum flow with the standard orifice size is: W = (2.853) (0.85) (1.0) (1.0) (2665.2)/0.04    = 161,581 lb/h Microsoft Excel spreadsheet (Example 10.12.xlsx) shows the calculations of Example 10.12.

SI Units The ω parameter is calculated from:

υ  ω = 9  9 − 1  υo 

where

υ9 = specific volume evaluated at 90% of the PRV inlet pressure, m3/kg υo = specific volume of the two-phase system at the PRV inlet, m3/kg The flow condition is calculated as: Pc > Pa ⇒ critical flow Pc < Pa ⇒ subcritical flow

(10.105)

Process Safety and Pressure-Relieving Devices  1233 where

Pc = critical pressure, psia = ηc Po

(10.106)

where Pc is the critical pressure, Pa Pc = ηc Po The critical pressure ratio ηc is obtained from Figure 10.56 or can be calculated by:

ηc2 + (ω 2 − 2ω )(1 − ηc )2 + 2ω 2 ln ηc + 2ω 2 (1 − ηc ) = 0



(10.107)

Or

ηc = 1 + (1.0446 − 0.0093431ω 0.5 )ω −0.56261 



( −0.70356 + 0.014685ln ω )



(10.117)

where Po = PRV relieving pressure, Pa Pa = downstream back pressure, Pa

The mass flux is calculated as follows: Critical flow

 P  G = ηc  o   υ oω 



0.5



(10.118)

Subcritical flow: 0.5 −2[ω ln ηa + (ω − 1)(1 − ηa )]} { G=



 1  ω  − 1 + 1  ηa 

Po vo

(10.119)

where G  = mass flux, kg/s m2 Po = PRV relieving pressure, Pa υo  = specific volume at the PRV inlet, m3/kg ηa  = back pressure ratio, = Pa/Po The effective discharge area is calculated by:



A=

277.8W Kd K b Kc K v G

where A = effective discharge area, mm2 W = mass flow rate, kg/h Kd = discharge coefficient, the preliminary value of 0.85. Kc = combination correction factor Kv = viscosity correction factor.

(10.120)

1234  Chemical Process Engineering Microsoft Excel spreadsheet (Example 10.12.xlsx) shows the calculations of Example 10.12 and the results are shown below. Results of Type 2 omega method for two-phase flashing. Flow type

Two-phase flashing

 Unit

Flow rate

160000

lb/h

Set Pressure at inlet

600

psig

Downstream total back pressure

55

psig

Inlet temperature at the PRV

450

o

Two-phase specific volume at the inlet of PRV

0.1549

ft3/lb

Specific volume at 90% at the inlet of the PRV

0.1737

ft3/lb

Mass fraction specific volume at the inlet of PRV

0.5596

 

Combined specific volume of the vapor and gas at the inlet of PRV

0.2462

ft3/lb

Inlet gas mole fraction in the vapor phase

0.4696

 

Specific heat ratio, k

0.1737

 

Relieving pressure of 1.1 × 260 + 14.7

674.7

psia

Kb

1

 

F

1.4

1.2 Non-f lashing f low

F lashing f low

Critical Pressure ratio, ηc

1.0

0.8

0.6

0.4 ηc2 + (ω2–2ω)(1 – ηc)2 + 2ω2/nηc + 2ω2 (1 – ηc) = 0

0.2

0.0 0.01

0.1

1

10

100

Omega Parameter, ω

Figure 10.56  Correlation for nozzle critical flow of flashing and nonflashing systems (Source: API RP 520, Sizing Selection, and Installation of Pressure – Relieving Devices in Refineries, Part 1- Sizing and Selection, 7th ed., 2020).

Process Safety and Pressure-Relieving Devices  1235 Kd

0.85

 

Kc (rupture disk not installed)

1

 

Kc (rupture disk installed)

0.9

 

Calculate the inlet voild fraction:

0.8894

 

Saturated Omega Parameter, ωs

1.092

 

The critical pressure, Pc is:

416.89

psia

Total back pressure, Pa

69.7

psia

Flow Type

Critical

 

Mass flux, G

2657.16

lb/(s.ft2)

Effective required area, A

2.834

in2

Next standard orifice area

2.853

in2

Maximum flow rate with the next standard orifice size

161093.6

lb/h

Example 10.13 Design a pressure-relieving valve for a two-phase fluid at the inlet of the PRV. The following process parameters are to be used for the design: Mass flow rate = 10,000 kg/h Specific volume at PRV relieving pressure = 0.1 m3/kg Specific volume at 90% of relieving pressure = 0.15 m3/kg PRV set pressure = 1000 kPaG PRV back pressure = 150 kPaG Discharge coefficient = 0.85 Overpressure = 10% Type of PRV = balanced bellow

Solution Omega parameter, ω from Eq. 10.105

 0.15  ω = 9 − 1  0.1  = 4.5



The critical pressure ratio ηc is obtained from Figure 10.56 or can be calculated from Eq. 10.107 or 10.117.

ηc2 + (ω 2 − 2ω )(1 − ηc )2 + 2ω 2 ln ηc + 2ω 2 (1 − ηc ) = 0



Using the Solver from Excel spreadsheet for Eq. 10. 107 gives ηc = 0.779

1236  Chemical Process Engineering Critical pressure ratio from Eq. 10.107, Pc = ηc Po    = 0.779 × (1.1 × 1000 + 101.35)    = 935.85 kPaa Since the critical pressure > back pressure, the flow is critical i.e., 935.85 > 251.35 kPa The mass flux for critical flow is from Eq. 10.118 is:

 P  G = ηc  o   υ ω

0.5



o



 1201.350 × 1000  G = 0.779    0.1 × 4.5

0.5

= 1272.8 kg/(s m 2 )



The effective discharge area is calculated from Eq. 10.120:

A=

277.8 × 10,000 (.85)(1)(1)(1)(1272.8)

= 2567.7 mm 2



The next standard orifice size is N, area = 2800 mm2 The maximum flow rate with the standard orifice is: W = (2800) (0.85) (1) (1) (1) (1272.8) / 277.8    = 10904.5 kg/h Microsoft Excel spreadsheet (Example 10.13.xlsx) shows the calculations of Example 10.13, and the results of the calculations are shown below. Results of Type 2 omega method for two-phase flashing. Flow type

Two-phase flashing

 

Flow rate

10000

kg/h

Set Pressure at inlet

1000

kPag

Downstream total back pressure

150

kPag

Allowable overpressure

10

%

Specific volume at PRV relieving pressure

0.1

m3/kg

Tpe of PRV

balanced bellow

 

Relieving pressure of 1.1 × 1000 + 101.35

1201.35

kPag

Kb

1

 

Kd

0.85

 

Process Safety and Pressure-Relieving Devices  1237 Kc (rupture disk not installed)

1

 

Kc (rupture disk installed)

0.9

 

Viscosity correction factor, Kv

1

 

Saturated Omega Parameter, ωs

4.5

 

The critical pressure Pc is:

937.02

kPaa

Total back pressure, Pa

251.35

kPaa

Flow Type

Critical

 

Mass flux, G

1274.41

(kg/m2.s)

Effective required area, A

2564.5

mm2

Next standard orifice area

2800

mm2

Maximum flow rate with the next standard orifice size

10918.27

kg/h

Type 3 Integral Method [5] In the integration, the mass flux is calculated by:

  P  dP   G = ρ12  −2   ρ    Po   max

∫

2



(10.121)

The value of the integral can be approximated by: Pt

∫



Po

dP ≅ ρ

t



− Pi   i +1 − ρi 

∑ 2 ρP i=0

i +1

(10.122)

And the overall mass density of the fluid is:

ρm = αρv + (1−α)ρ1 where G = mass flux, kg/(s -m2 ) υ = specific volume of the fluid, m3/kg ρ = mass density of the fluid, kg/m3. ρm = mixed density, kg/m3 ρ1 = density of liquid, kg/m3. ρv = density of vapor, kg/m3 P = stagnation pressure of the fluid, Pa o = condition at the inlet of the nozzle. t = condition at the throat of the nozzle. The effective orifice area is calculated from Eq. 10.120



A=

277.8W Kd K b Kc K v G

(10.123)

1238  Chemical Process Engineering where A = effective discharge area, mm2 W = mass flow rate, kg/h Kd = discharge coefficient = 0.85 for a two-phase fluid at the PRV inlet = 0.65 for a single liquid phase = 0.975 for a single vapor phase. Kb = back pressure correction factor (Figure 10.55) Kc = combination correction factor Kv = viscosity correction factor.

Example 10.14 [66] Using the integration method, design a PRV for the following process parameters. Type of fluid = two – phase saturated Mass flow rate = 15,000 kg/h PRV set pressure = 1726.1 kPaG End pressure for integration = 288.7 kPaG PRV back pressure = 100 kPaG Valve discharge coefficient = 0.85 Overpressure =10% The pressure – density relationship is given by: Pressure kPaa

Density kg/m3

Pressure kPaa

Density kg/m3

2000

15.281

1160

9.634

1930

14.826

1090

9.141

1860

14.368

1020

8.643

1790

13.908

950

8.137

1720

13.444

880

7.634

1650

12.98

810

7.634

1580

12.511

740

6.596

1510

12.041

670

6.068

1440

11.566

600

5.531

1370

11.088

530

4.985

1300

10.607

460

4.429

1230

10.122

390

3.858

Solution Value of integral at 2000 kPaa = 0 Value of integral at 1930 kPaa = -2 × 70,000 / (15.281 + 14.826) = -4650.1 m2/s2

Process Safety and Pressure-Relieving Devices  1239 Mass flux t 1930 kPaa = 1429.7 kg/(s – m2) Value of integral at 1860 kPaa = -4650.1 – 4795.5 = -9445.6 m2/s2 Mass flux at 1860 kPaa = 1977.5 kg/(s – m2) This calculation continues till the maximum mass flux is achieved. The maximum mass flux achieved at 1160 kPaa = 3564.3 kg/(s – m2) The effective orifice area is calculated from Eq. 10.120

A=



A=

277.8W Kd K b Kc K v G

277.8(15,000) (0.85)(1.0)(1.0)(1.0)(3564.3)

= 1375.4 mm 2 Arun Datta [66] has provided Excel Visual Basic software programs on the 3 Omega Parameter methods for sizing relief valves.

Glossary Accumulation: The build-up of unreacted reagent or intermediates, usually associated with reactant added during a semi-batch operation. Activation energy Ea: The constant Ea in the exponential part of the Arrhenius equation, associated with the minimum energy difference between the reactants and an activated complex (transition state which has a structure intermediate to those of the reactants and the products), or with the minimum collision energy between molecules that is required to enable a reaction to occur. Adiabatic: A system condition in which no heat is exchanged between the chemical system and its environment. Adiabatic induction time: Induction period or time to an event (spontaneous ignition, explosion, etc.) under adiabatic conditions, starting at operating conditions. Adiabatic temperature rise: Maximum increase in temperature that can be achieved. This increase occurs when the substance or reaction mixture decomposes or reacts completely under adiabatic conditions. The adiabatic temperature rise follows from:



ΔTadia = xo (ΔHRX)/ϕ

where xo = Initial mass fraction, ΔHRX = Heat of reaction J/kg, C= Liquid heat capacity J/kg.K, ϕ = Dimensionless thermal inertial factor (Phi- factor). Autocatalytic reaction: A reaction, the rate of which is increased by the catalyzing effect of its reaction products. Autoignition temperature: The autoignition temperature of a substance, whether solid, liquid or gaseous is the minimum temperature required to initiate or cause self-sustained combustion (e.g., in air, chlorine or other oxidant) with no other source of ignition. For example, if a gas is flammable and its autoignition temperature (AIT) is exceeded, there is an explosion. Back pressure: The static pressure existing at the outlet of a pressure relief device as a result of the pressure in the discharge system. It is the sum of the superimposed and built-up back pressure.

1240  Chemical Process Engineering Blowdown: Is the difference between actual popping pressure of a pressure relief valve and actual re-seating pressure expressed as a percentage of set pressure. Blowdown pressure: Is the value of decreasing inlet static pressure at which no further discharge is detected at the outlet of a safety relief valve of the resilient disk type after the valve has been subjected to a pressure equal to or above the popping pressure. Boiling-Liquid-Expanding-Vapor-Explosive (BLEVE): Is the violent rupture of a pressure vessel containing saturated liquid/vapor at a temperature well above its atmospheric boiling point. The sudden decrease in pressure results in explosive vaporization of a fraction of the liquid and a cloud of vapor and mist, with accompanying blast effects. The resulting flash vaporization of a large fraction of the liquid produces a large cloud. If the vapor is flammable and if an ignition source is present at the time of vessel rupture, the vapor cloud burns in the form of a large rising fireball. Built-up back pressure: Pressure existing at the outlet of a pressure relief device caused by flow through that particular device into a discharge system. Burst pressure: Is the value of inlet static pressure at which a rupture disc device functions. Chatter: Is abnormal rapid reciprocating motion of the movable parts of a pressure relief valve in which the disk contacts the seat. Combustible: A term used to classify certain liquids that will burn on the basis of flash points. Both the National Fire Protection Association (NFPA) and the Department of Transportation (DOT) define “combustible liquids” as having a flashing point of 100°F (37.8°C) or lower. Combustible Dusts: Dusts are particularly hazardous; they have a very high surface area-to- volume ratio. When finely divided as powders or dusts, solids burn quite differently from the original material in the bulk. Many combustible dusts produced by industrial processes are explosible when they are suspended as a cloud in air. A spark may be sufficient to ignite them. After ignition, flame spreads rapidly through the dust cloud as successive layers are heated to ignition temperature. Condensed phase explosion: An explosion that occurs when the fuel is present in the form of a liquid or solid. Confined explosion: An explosion of a fuel-oxidant mixture inside a closed system (e.g.. a vessel or building). Confined Vapor Cloud Explosion (CVCE): Is a condensed phase explosion occurring in confinement (equipment, building or/and congested surroundings). Explosions in vessels and pipes, processing or storing reactive chemicals at elevated conditions are examples of CVCE. The excessive build-up of pressure in the confinement leads to this type of explosion leading to high overpressure, shock waves and heat load (if the chemical is flammable and ignites). The fragments of exploded vessels and other objects hit by blast waves become airborne and act as missiles. Containment: A physical system in which under all conditions no reactants or products are exchanged between the system and its environment. Cubic law: the correlation of the vessel volume with the maximum rate of pressure rise. V1/3 (dP/dt)max = constant = Kmax Decomposition energy: The maximum amount of energy which can be released upon decomposition. The product of decomposition energy and total mass is an important parameter for determining the effects of a sudden energy release, e.g., in an explosion. Deflagration: The chemical reaction of a substance in which the reaction front advances into the unreacted substance at less than sonic velocity. Where a blast wave is produced that has the potential to cause damage, the term explosive deflagration is used.

Process Safety and Pressure-Relieving Devices  1241 Detonation: A release of energy caused by the extremely rapid chemical reaction of a substance in which the reaction front advances into the unreacted substance at equal to or greater than sonic velocity. Design Institute for Emergency Relief Systems (DIERS): Institute under the auspices of the American Institute of Chemical Engineers funded to investigate design requirements for vent lines in the case of two-phase venting. Disk: Is the pressure containing movable element of a pressure relief valve which effects closure. Dow Fire and Explosion Index (F&EI): A method (developed by Dow Chemical Company) for ranking the relative fire and explosion risk associated with a process. Analysts calculate various hazard and explosion indexes using material characteristics and process data. Dust: Solid mixture with a maximum particle size of 500 µm. Dust explosion class, St: Dusts are classified in accordance with the Kmax values. Dust explosion constant (Kst): Kst is defined as the maximum rate of pressure rise during a dust explosion in an equi-dimensional vessel, times the cube root of the vessel volume, i.e., Kst = (dP/dt)max V1/3. Kst (bar m/s) is numerically equal to the maximum rate of pressure rise (bar/s) in the 1 m3 standard ISO (International Standards Organization, 1985) test. The St class was determined using the modified Hartmann tube with a hinged lid at the top. St 1 dust means Kst ≤ 200 bar m/s, St 2 dust means that 200 bar m/s ≤ Kst < 300 bar m/s, and St 3 dust means that Kst ≥ 300 bar m/s. Exotherm: A reaction is called exothermic if energy is released during the reaction. Explosion: Propagation of a flame in a premixture of combustible gases, suspended dust(s), combustible vapor(s), mist(s), or mixtures of thereof, in a gaseous oxidant such as air, in a closed, or substantially closed vessel. Explosion rupture disk device: Is a rupture disk device designed for use at high rates of pressure rise. Fail-safe: Design features which provide for the maintenance of safe operating conditions in the event of a malfunction of control devices or an interruption of an energy source (e.g., direction of failure of a motor operated valve on loss of motive power). Failure: An unacceptable difference between expected and observed performance. Fire point: The temperature at which a material continues to burn when the ignition source is removed. Flammability limits: The range of gas or vapor compositions in air that will burn or explode if a flame or other ignition source is present. Importance: The range represents an unsafe gas or vapor mixture with air that may ignite or explode. Generally, the wider the range the greater the fire potential. Flammable: A “flammable liquid” is defined as a liquid with a flash point below 100°F (37.8°C). Flammable liquids provide ignitable vapor at room temperatures and must be handled with caution. Flammable liquids are: Class I liquids and subdivided as follows: Class 1A: Those having flash points below 73°F and having a boiling point below point below 100°F. Class 1B: Those having flash points below 73°F and having a boiling point at or above 100°F. Flares: Flares are used to burn the combustible or toxic gas to produce combustion products, which are neither toxic nor combustible. The diameter of a flare must be suitable to maintain a stable flame and prevent a blowdown (when vapor velocities are greater than 20% of the sonic velocity). Flash fire: The combustion of a flammable vapor and air mixture in which flame passes through that mixture at less than sonic velocity, such that negligible damaging overpressure is generated.

1242  Chemical Process Engineering Flash point: The lowest temperature at which vapors above a liquid will ignite. The temperature at which vapor will burn while in contact with an ignition source, but which will not continue to burn after the ignition source is removed. Gases: Flammable gases are usually very easily ignited if mixed with air. Flammable gases are often stored under pressure, in some cases as a liquid. Even small leaks of a liquefied flammable gas can form relatively large quantities of gas, which is ready for combustion. Gassy system: In gassy systems, the pressure is due to a permanent gas which is generated by the reaction. Hazard: An inherent chemical or physical characteristic that has the potential for causing damage to people, property or the environment. Hazard analysis: The identification of undesired events that lead to the materialization of a hazard, the analysis of the mechanisms by which these undesired events could occur and usually the estimation of the consequences. Hazard and Operability (HAZOP): A systematic qualitative technique to identify process hazards and potential operating problems using a series of guide words to study process deviations. A HAZOP is used to question every part of the process to discover what deviations from the start of the design can occur and what their causes and consequences may be. This is done systematically by applying suitable guide words. This is a systematic detailed review technique for both batch and continuous plants, which can be applied to new or existing processes to identify hazards. Hazardous chemical reactivity: Any chemical reaction with the potential to exhibit rates of increase in temperature and/or pressure too high to be absorbed by the environment surrounding the system. Included are reactive materials and unstable materials. Hybrid mixture: A suspension of dust in air/vapor. Such mixtures may be flammable below the lower explosive limit of the vapor and can be ignited by low energy sparks. Hybrid system: Hybrid systems are those in which the total pressure is due to both vapor pressure and permanent gas. Inherently safe: A system is inherently safe if it remains in a non hazardous situation after the occurrence of non acceptable deviations from normal operating conditions. Inhibition: A protective method where the reaction can be stopped by addition of another material. Interlock system: A system that detects out-of-limits or abnormal conditions or improper sequences and either halts further action or starts corrective action. Isothermal: A system condition in which the temperature remains constant. This implies that temperature increases and decreases that would otherwise occur are compensated by sufficient heat exchange with the environment of the system. Likelihood: A measuring of the expected frequency which an event occurs. This may be expressed as a frequency (e.g., events per year), a probability of occurrence during a time interval (e.g., annual probability), or a conditional probability (e.g., probability of occurrence, given that a precursor event has occurred). Limiting oxygen concentration (LOC): Minimum concentration of oxygen in a mixture with gas, vapor or dust that will allow it to burn. Liquids: A vapor has to be produced at the surface of a liquid before it will burn. Many common liquids give off a flammable concentration of vapor in air without being heated, sometimes at well below room temperature. Gasoline, for example, gives off ignitable vapors above about -40oC, depending on the blend. The vapors are easily ignited by a small spark of flame. Lower Explosive Limit (LEL): The concentration of a powder finely dispersed in air, below which no mixture likely to explode will be present.

Process Safety and Pressure-Relieving Devices  1243 Lower Flammable Limit (LFL): The lowest concentration of a vapor or gas (the lowest percentage of the substance in air) that will produce a flash of fire when an ignition source (heat, arc or flame) is present. Maximum allowable working pressure (MAWP): The maximum allowed pressure at the top of the vessel in its normal operating position at the operating temperature specified for that pressure. Maximum explosion overpressure, Pmax: The maximum pressure reached during an explosion in a closed vessel through systematically changing the concentration of dust-air mixture. Maximum reduced explosion overpressure, Pred, max: The maximum pressure generated by an explosion of a dust-air mixture in a vented or suppressed vessel under systematically varied dust concentrations. Maximum explosion constant, Kmax: Dust and test-specific characteristic calculated from the cubic law. It is equivalent to the maximum rate of pressure rise in a 1 – m3 vessel. Maximum explosion pressure (Pmax): the maximum expected pressure for an explosion of the optimum concentration of the powder concerned in air, in a closed vessel under atmospheric starting conditions. Maximum explosion pressure rise (dP/dt)max: The maximum pressure rise for an explosion of the optimum concentration of the powder concerned in air, in a closed vessel under atmospheric starting conditions. This explosion property depends on the volume of the vessel. Minimum Ignition Energy (MIE): Is used to measure the lowest energy at which an electrical discharge is just able to ignite the most sensitive mixture of the material in air. Minimum ignition temperature (MIT): The lowest temperature of a hot surface which will cause a dust cloud to ignite and flame to propagate. Minimum Oxygen Concentration (MOC): the concentration of oxygen in air, below which no mixture likely to explode will be formed with the present of dust/air/inert mixture. Mitigation: Lessening the risk of an accident event. A sequence of action on the source in a preventive way by reducing the likelihood of occurrence of the event, or in a protective way by reducing the magnitude of the event and for the exposure of local persons or property. Onset temperature: Is the temperature at which the heat released by a reaction can no longer be completely removed from the reaction vessel, and consequently, results in a detectable temperature increase. The onset temperature depends on detection sensitivity, reaction kinetics, on vessel size and on cooling, flow and agitation characteristics. Oxidant: Any gaseous material that can react with a fuel (either gas, dust or mist) to produce combustion. Oxygen in air is the common oxidant. Overpressure: A pressure increase over the set pressure of the relief device usually expressed as a percentage of gage set pressure. Phi-factor ϕ: A correction factor which is based on the ratio of the total heat capacity (mass x specific heat) of a vessel and the total heat capacity of the vessel contents.



φ=

Heat capacity of sample + Heat capacity of vessel Heat capacity of sample

The ϕ factor enables temperature rises to be corrected for heat lost to the container or vessel. The ϕ factor approaches the value of one for large vessels and for extremely low mass vessels.

1244  Chemical Process Engineering Pressure relief device: Is designed to open to prevent a rise of internal fluid pressure in excess of a specified value due to exposure to emergency or abnormal conditions. It may also be designed to prevent excessive internal vacuum. It may be a pressure relief valve, a non-reclosing pressure relief device or a vacuum relief valve. Process safety: A discipline that focuses on the prevention of fires, explosions and accidental chemical releases at chemical process facilities. Excludes classic worker health and safety issues involving working surfaces, ladders, protective equipment, etc. Purge gas: A gas that is continuously or intermittently added to a system to render the atmosphere nonignitable. The purge gas may be inert or combustible. Quenching: Rapid cooling from an elevated temperature, e.g., severe cooling of the reaction system in a short time (almost instantaneously), “freezes” the status of a reaction and prevents further decomposition. Relieving pressure: Is set pressure plus overpressure. Risk: The likelihood of a specified undesired event occurring within a specified period or in specified circumstances. Risk analysis: A methodical examination of a process plant and procedure which identifies hazards, assesses risks and proposes measures which will reduce risks to an acceptable level. Runaway: A thermally unstable reaction system, which shows an accelerating increase of temperature and reaction rate. The runaway can finally result in an explosion. Rupture disk device: Is a non-reclosing pressure relief device actuated by inlet static pressure and designed to function by the bursting of a pressure containing disk. Safety relief valve: Is a pressure relief valve characterized by rapid opening pop action or by opening generally proportional to the increase in pressure over the opening pressure. It may be used for either compressible or incompressible fluids, depending on design, adjustment or application. Set pressure: The inlet pressure at which the relief device is set to open (burst). Stagnation pressure: The pressure that would be observed if a flowing fluid were brought to rest along an isentropic path. Static activation pressure, Pstat: Pressure which activates a rupture disk or an explosion door. Superimposed back pressure: The static pressure existing at the outlet of a pressure relief device at the time the device is required to operate. It is the result of pressure in the discharge system from other sources. Temperature of no-return: Temperature of a system at which the rate of heat generation of a reactant or decomposition just exceeds the rate of heat loss and will lead to a runaway reaction or thermal explosion. Thermally unstable: Chemicals and materials are thermally unstable if they decompose, degrade or react as a function of temperature and time at or about the temperature of use. Thermodynamic data: Data associated with the aspects of a reaction that are based on the thermodynamic laws of energy, such as Gibbs’ free energy, and the enthalpy (heat) of reaction. Time to maximum rate (TMR): The time taken for a material to self-heat to the maximum rate of decomposition from a specific temperature. Unconfined Vapor Cloud Explosion (UCVE): Occurs when sufficient amount of flammable material (gas or liquid having high vapor pressure) gets released and mixes with air to form a flammable cloud such that the average concentration of the material in the cloud is higher than the lower limit of explosion. The resulting explosion has a

Process Safety and Pressure-Relieving Devices  1245 high potential of damage as it occurs in an open space covering large areas. The flame speed may accelerate to high velocities and produce significantly blast overpressure. Vapor cloud explosions in densely packed plant areas (pipe lanes, units, etc.) may show accelerations in flame speeds and intensification of blast. Upper Explosive Limit (UEL) or Upper Flammable Limit (UFL): The highest concentration of a vapor or gas (the highest percentage of the substance in the oxidant) that will produce a flash or fire when an ignition source (heat, arc or flame) is present. Vapor specific gravity: The weight of a vapor or gas compared to the weight of an equal volume of air, an expression of the density of the vapor or gas. Materials lighter than air have vapor specific gravity less than 1.0 (examples: acetylene, methane, hydrogen). Materials heavier than air (examples: ethane, propane, butane, hydrogen, sulphide, chlorine, sulfur dioxide) have vapor specific gravity greater than 1.0. Vapor pressure: The pressure exerted by a vapor above its own liquid. The higher the vapor pressure, the easier it is for a liquid to evaporate and fill the work area with vapors which can cause health or fire hazards. Vapor pressure system: A vapor pressure system is one in which the pressure generated by the runaway reaction is solely due to the increasing vapor pressure of the reactants, products and/or solvents as the temperature rises. Venting (emergency relief): Emergency flow of vessel contents out of the vessel. The pressure is reduced by venting, thus avoiding a failure of the vessel by overpressurization. The emergency flow can be one-phase or multiphase, each of which results in different flow and pressure characteristics. Multiphase flow, e.g., vapor and or gas/liquid flow, requires substantially larger vent openings than single phase vapor (and/or gas) flow for the same depressurization rate. Vent area, A: Area of an opening for explosion venting.

Acronyms and Abbreviations AGA AIChE AIChE/CCPS AIChE/DIERS AIT API ARC ASME ASTM bar-m/sec BLEVE CFD CSB CPI DIERS DOE EFCE EPA HAZOP HAZAN HMSO HRA

American Gas Association American Institute of Chemical Engineers American Institute of Chemical Engineers – Center for Chemical Process Safety American Institute of Chemical Engineers – Design Institute for Emergency Relief Systems Auto-Ignition Temperature American Petroleum Institute Accelerating Rate Calorimeter American Society of Mechanical Engineers American Society of Testing Materials Bar-meter per second Boiling Liquid Expanding Vapor Explosion Computational fluid dynamics U.S. Chemical Safety and Hazard Investigation Board Chemical Process Industry Design Institute for Emergency Relief Systems. Department of Energy European Federation of Chemical Engineers U.S. Environmental Protection Agency Hazard and Operability Hazard Analysis Her Majesty’s Stationery Office Human Reliability Analysis

1246  Chemical Process Engineering HSE Health and Safety Executive, United Kingdom IChemE Institution of Chemical Engineers (U.K.) ICI Imperial Chemical Industries LFL Lower Flammable Limit LNG Liquefied Natural Gas LPG Liquefied Petroleum Gas MSDS Material safety data sheet NFPA National Fire Protection Agency NIOSH National Institute for Occupational Safety and Health OSHA Occupational Safety and Health Administration PE Process Engineer PFD Process Flow Diagram PHA Preliminary Hazard Analysis P&ID Piping and Instrumentation Diagram TNT Trinitrotoluene TLV Threshold Limit Values UFL Upper Flammable Limit VCDM Vapor Cloud Dispersion Modeling VCE Vapor Cloud Explosion VDI Verein Deutscher Ingenieure VSP Vent Sizing Package

Nomenclature a ap A or A

= area, in2. = cross-sectional area of the inlet pipe, ft2 = area, in2, ft2, m2; consistent with equation units = nozzle throat area, or orifice flow area, effective discharge area (calculations required) or from manufacturer’s standard orifice areas, in2. = initial vessel relief area, in2, m2 Al = second vessel relief area, in2, m2 A2 = exposed surface area of vessel, ft2 A3 = internal surface area of enclosure, ft2 or m2 As = -vent area, ft2, m2 Av = total wetted surface area, ft2 Aw AIT = auto-ignition temperature B = cubical expansion coefficient per of liquid at expected temperature (see tabulation in text) BP = boiling point, °C or oF B.P. = burst pressure, either psig or psi abs Bar = 14.5 psi = 0,987 atmosphere = 100 k Pa atmosphere; 14.7 psia = 1.01 bars C1 = c = C = gas/vapor flow constant depending on ratio of specific heats Cp/Cv (see Figure 10.25 sonic) = ratio of specific heats Cp/ Cv = specific heat of trapped fluid, Btu/lb/oF Ch = subsonic flow constant for gas or vapor, function of k = Cp/Cv, (Table 10.11) C2 c = orifice coefficients for liquids d = diameter, inches (usually of pipe) dp/dt = rate of pressure rise, bar/sec or psi/sec E = joint efficiency in cylindrical or spherical shells or ligaments between openings (see ASME Code Par. UW-12 or UG-53) e = natural logarithm base, e = 2.718

Process Safety and Pressure-Relieving Devices  1247 F Fgs′ F’ F Fl or F2 F2 o F G GPM g H h Kp

= environment factor for Table 10.10 = relief valve factor for non-insulated vessels in gas service exposed to open fires = operating environment factor for safety relief of gas only vessels = Flow gas/vapor, cubic feet per minute at 14.7 psia and 60°F = relief area for vessels 1 or 2 resp., ft2 = coefficient of subcritical flow (see Figure 10.29) = temperature, °Fahrenheit = specific gravity of gas (air = 1), or specific gravity of liquid (water = 1) at actual discharge temperature = gallons per minute flow = acceleration of gravity, 32.0 ft/s2 = total heat transfer rate, Btu/h = head of liquid, ft = liquid capacity correction factor for overpressures lower than 25% from Figure 10.22. Non-code equations only. = vapor or gas flow correction factor for constant back pressures above critical pressure from curve on Kb Figure 10.26 = vapor or gas flow factor for variable back pressures from Figure 10.27A or 27B. Applies to Balanced Kv Seal valves only. = liquid correction factor for variable back pressures from Figure 10.28. Applies to balanced seal valves Kw only. Conventional valves require no correction. = liquid viscosity correction factor from chart Figure 10.24 Ku = steam superheat correction factor from Table 10.8 Ksh = Napier steam correction factor for set pressures between 1500 and 2900 psig from Table 10.9 Kn = coefficient of discharge:* K = Kd = 0.975 for air, steam, vapors and gases = 0.724 for ASME Code liquids** = 0.64 for non-ASME Code liquids = 0.62 for bursting/rupture disk   *Where the pressure relief valve is used in series with a rupture disk, a combination capacity factor of 0.8 must be applied to the denominator of the above valve equations. Consult the valve manufacturer (also see specific section this chapter of text). For higher factors based on National Board flow test results conducted with various rupture disk designs/arrangements   **For saturated water see ASME Code, Appendix 11.2. = discharge coefficient orifice or nozzle Kd = deflagration index, maximum rate of pressure rise for gases, bar-meter/second = bar-m/sec Kc = variable or constant back pressure sizing factor, balanced valves, liquids only (Figure 10.28) Kw k = ratio of specific heats, Cp/ Cv L = liquid flow, gallons per minute = latent heat of vaporization, Btu/lb Lv = L L/D = length-to-diameter ratio, dimensionless M = molecular weight MAWP = maximum allowable working pressure of a pressure vessel, psi gauge (or psi absolute if so specifically noted) MR = universal gas constant = 1544 ft lbf/lbm s2. Units depend on consistency with other symbols in equation, or manufacturing range for metal bursting/rupture disks. n = moles of specified components P = relieving pressure, psia = valve set pressure + permissible overpressure, psig, + 14.7, or any pressure, bar (gauge), or a consistent set of pressure units. Minimum overpressure is 3 psi = stamped bursting pressure, plus overpressure allowance (ASME 10% or 3 psi, whichever is greater) plus Pb atmospheric pressure (14.7), psia Pc = Pcrit = critical pressure of a gas system, psi abs

1248  Chemical Process Engineering Pd Pd P1 P2 p Po p’ ΔP

= design pressure of vessel or system to prevent deformation due to internal deflagration, psig = ASME Code design pressure (or maximum allowable working pressure), psi = upstream relieving pressure, or set pressure at inlet to safety relief device, psig (or psia, if consistent) = back pressure or downstream at outlet of safety relief device, psig, or psia, depending on usage = rupture pressure for disk, psig or psia = overpressure (explosion), psi. = pressure, psia = pressure differential across safety relief valve, inlet pressure minus back pressure or downstream pressure, psi. Also = set pressure + overpressure, psig-back pressure, psig. At 10% over-pressure delta P equals 1.1 P1 -P2. Below 30 psig set ΔP equals P1 + 3 -P2. ΔP = differential pressure across liquid relief rupture disk, usually equals p, psi Q = total heat absorption from external fire (input) to the wetted surface of the vessel, Btu/h Q’ = liquid flow, ft3/s = required flow, ft3/min at actual flowing temperature and pressure, acfm QA = heat released by flame, Btu/h Qf = heat release, lower heating valve, Btu/h Qr = required flow, cu ft/min at standard conditions of 14.7 psia and 60°F, scfm Qr q = Average unit heat absorption, Btu/h/ft2 of wetted surface R = individual gas constant = MR/M = 1544/M R’ = adjusted value of R, for NFPA Code-69 = distance from center of explosion source the point of interest, ft. Rexp Re = Reynolds number (or sometimes, NRe) = Universal gas constant = 1544 = MR Rg = individual gas constant = MR/M Rgc = inside radius of vessel, no corrosion allowance added, in. Ri o R = temperature, absolute, degrees Rankine r = rc = ratio of back pressure to upstream pressure, P2/P1, or critical pressure ratio, Pc/P1 = relative humidity, percent rl S’ = SpGr = specific gravity of liquid, referenced to water at the same temperature SG = Sg = SpGr of gas relative to air, equals ratio of mol wt of gas to that of air, or liquid fluid specific gravity relative to water, with water = 1.0 at 60°F SpGr = specific gravity of fluid, relative to water = 1.0 SSU = viscosity Saybolt universal seconds o S = degrees of superheat, oF T = absolute inlet or gas temperature, degrees Rankine oR = oF + 460, or temperature of relief vapor [26]; oR = normal operating gas temperature, oR Tη = operating temperature, °C (NFPA Code-59) T1 o = temperature of service, oR T UEL = upper explosive or flammable limit, percent of mixture of flammable gases only in air V = vessel volume, ft3, or m3, or required gas capacity in scfm or, V = vapor flow required through valve (sub-critical), -Std ft3/min at 14. 7psia and 60°F V = specific volume of fluid, ft3/lb = required air capacity, scfm Va = flow rate at flowing temperature, US gpm, or required liquid capacity in US gpm VL v = shock velocity, ft/s or ft/min (depends on units selected) = specific volume of gas or vapor at upstream or relief pressure and temperature conditions, ft3/1b V1 = sonic velocity of gas, ft/s vs = volume percent of each combustible mixture, free from air or inert gas V1, V2 W = required vapor capacity in pounds per hour any flow rate, lb/h Z = compressibility factor, deviation of actual gas from perfect gas law. Usually Z = 1.0 at low pressure below 300 psig.

Process Safety and Pressure-Relieving Devices  1249

Subscripts 1 = condition 1 2 = condition 2

Greek Symbols β = beta ratio orifice diameter to pipe diameter (or nozzle inlet diameter) μ = (mu) absolute viscosity at flowing temperature, centipoise (cP) π = (pi), 3.1418 ρ = (rho) fluid density, lb/ft3

References 1. American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code, Section VIII, Pressure Vessels, American Society of Mechanical Engineers, New York, 1989. 2. Kirkwood, J. G. and Wood, W. W., ed., Shock and Detonation Waves, Gordon and Breach, London and New York. 3. Tuve, R. L. Principles of Fire Protection and Chemistry, National Fire Protection Association, Inc., 1976. 4. Handbook of Industrial Loss Prevention, Factory Mutual Engineering Corp., 2nd ed., McGraw-Hill Book Co., 1967. 5(a). Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries, Part I- Sizing and Selection; API Recommended Practice 520, 5th Ed., July 1990, American Petroleum Institute. 5(b). Ibid. Part II-Installation, API Recommended Practice 520, 3rd Ed. Nov. 1988, American Petroleum Institute. 5(c). Guide for Pressure-Relieving and Depressuring Systems, API Recommended Practice 521, 3rd ed. Nov. 1990, American Petroleum Institute. 5(d). Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries, Part I- Sizing and Selection; API Recommended Practice 520, 7th Ed., July 2000, American Petroleum Institute. 6. Fire Protection Handbook, 17th ed., National Fire Protection Association, Quincy, MA. 02269, 1991. 7. American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code, Section VII, Power Boilers, 1974. 8. “Design and Installation of Pressure Relieving Devices”, Part I-Design; Part ll-:-Installation, API-RF.520, American Petroleum Institute, New York, 1967. 9. “Guide for Pressure Relief and Depressuring Systems”, API-RP-521, American Petroleum Institute, New York, 1990. 10. Venting of Deflagrations, NFPA-68, National Fire Protection Association, 1988 ed., Quincy, MA 02269. 11. “Terminology of Pressure Relief Devices”, American National Standards Institute (ANSI) No. B95, 1 (latest ed.). 12. Explosions Prevention Systems (1986) NFPA #69, National Fire Protection Association (1986) Quincy, MA 02259. 13. Fisher, H. G., “An Overview of Emergency Relief System Design Practice”, Plant/Operations Progress, Vol 10; No. 1, 1991.

Listing of Final Reports from the DIERS Research Program (Design Institute for Emergency Relief Systems) Used by permission and courtesy of the Committee on Chemical Process Safety of the American Institute of Chemical Engineers.

Project Manual “Emergency Relief System Design Using DIERS Technology”, Fisher, H. G., et al., The Design Institute for Emergency Relief Systems of the American Institute of Chemical Engineers, New York, July 1992.

Technology Summary 1. “Emergency Relief Systems for Runaway Chemical Reactions and Storage Vessels: A Summary of Multiphase Flow Methods”, DIERS/AIChE. 1986, 206 p.

1250  Chemical Process Engineering

Sm 540 All/Large-Scale Experimental Data and Analysis 2. “Large Scale Integral Tests-Facility Description”, DIERS/AIChE, 1986, 48 p. 3. “Equipment Design and Pretest Analysis for Series I Tests”, DIERS/AIChE, 1986, 45 p. 4. “Experimental Results for Series I Tests”, DIERS/AIChE, 1986, 163 p. 5. “Experimental Results for Series II Tests”, DIERS/AIChE, 1986, 224 p. 6. “Experimental Results for Series III Tests”, DIERS/AIChE, 1986, 95 p. 7. “Experimental Results for Series IV Tests, Analysis and Program Summary”, DIERS/AIChE, 1986, 259 p. 8. “Large Scale Rubber Cement High Viscosity Two-Phase Flow Test Report”, DIERS/AIChE, 1986, 114 p. 9. “Large Scale Polystyrene-Ethylbenzene High Viscosity Two-Phase Flow Test Report”, DIERS/AIChE, 1986, 76 p. 10. “Analysis of DIERS Phase III Blowdown Tests”, DIERS/AIChE, 1986, 151 p. 11. “Test T-I0A/Digitized Data”, DIERS/AIChE, 1986, 43 p.

Bench-Scale Apparatus Design and Test Results 12. “Bench Scale ERS Sizing Tools-Acquisition of Thermal Data-Apparatus Design and Sample Thermal Data for 5 Systems”, DIERS/AIChE, 1986, 159 p. 13. Final Report, “Bench Scale ERS Sizing Tools-Acquisition of Flow Regime Data-Prototype Test Results”, DIERS/AIChE, 1986, 31 p. 14. “Immiscible Two Fluid Mixture Tests”, DIERS/AIChE, 1986, 7 p. 15. “A Direct Experimental Approach to Sizing Emergency Relief Systems - Prototype and Data with Scale-up Procedure”, DIERS/AIChE, 1986, 36 p. 16. “Bench Scale ERS Sizing Tools: Equipment Details, Test Procedures and illustrations”, DIERS/ AIChE, 1986, 53 pages. 17. Papa, D. M., “Clear Up Pressure Relief Sizing Methods”, Chem. Eng. Prog., V. 87, No. 8, 1991, p. 81. 18. Perry, R H. and Green, Don, Perry’s Chemical Engineers’ Handbook, 6th ed., 1984. 19. Nazario, F. N., “Rupture Discs, a Primer”, Chem. Eng., June 20, 1988, p. 86. 20. Pitman, J. F., Blast and Fragments from Superpressure Vessel Rupture, Naval Surface Weapons Center, White Oak Silver Springs, Maryland, Report #NSWC/WOL/TR. 75-87, 1976. 21. Suppressive Shield Structural Design and Analysis Handbook, U.S. Army Corps of Engineers, Huntsville, Div. No. HNDM1110-1-2, 1977. 22. Albaugh, L. R. and Pratt, T. H., “Flash Points of Aqueous Solutions”, Newsletter No. 6, Hazards Evaluation and Risk Control Services, Hercules, Inc., 1979. 23. Structure to Resist the Effects of Accidental Explosions, U.S. Army TM 5-1300, NAVFAC-P-397 (Navy), AFM-88-22 (Air Force). 24. Fisher, H. G., The DIERS Users Group, AICHE, National Meeting, New Orleans, La. March 6, 1988. 25. Cousins, E. W. and P. E. Cotton, “Design Closed Vessels to Withstand Internal Explosions”, Chem. Eng., No. 8, 1951, p. 133. 26. Cousins, E. W. and P. E. Cotton, “Protection of Closed Vessels Against Internal Explosions”, Presented at. annual meeting National Fire Protection Assoc., May 7-11, 1951, Detroit, MI. 27. Jacobson, M., et al., “Explosibility of Dusts Used in the Plastics Industry”, U.S. Bureau of Mines, RI-5971, 1962. 28. Jacobson, M., et al., “Explosibility of Agricultural Dusts”, U.S. Bureau of Mines, RI-5753, 1961. 29. Jacobson, M., et al., “Explosibility of Metal Powders”, U.S. Bureau of Mines, RI-6516, 1964. 30. Nagy, J. et al., “Explosibility of Carbonaceous Dusts”, U.S. Bureau of Mines, RI-6597, 1965. 31. Stull, D. R., Fundamentals of Fire & Explosion, Monograph Series, No. 10, Vol 73, Dow Chemical Co., Published Amer. Inst. Chem. Engrs., 1977. 32. Bartknecht, W., Explosions-Course Prevention Protection, Translation of 2nd Ed., Springer-Verlag, 1981. 33. Bravo, F. and Beatty, B. D., “Decide Whether to Use Thermal Relief,” Chem. Eng. Prog., V. 89, No. 12, 1993, p. 35. 34. Sylvander, N. E. and D. L. Katz, “Design and Construction of Pressure Relieving Systems”, Engineering Research Bu. No. 31, Univ. of Michigan Press, Ann Arbor, Mich., 1948. 35. Conison, J., “Why a Relief Valve”, Inst. & Auto., 28, 1955, 988. 36. Bigham, J. E., “Spring-Loaded Relief Valves”, Chem. Eng., Feb. 10, 1958, p. 133. 37. Weber, C. G., “How to Protect Your Pressure Vessels”, Chem. Eng., Oct. 1955. 38. Cassata, J. R., Dasgupta, S. and Gandhi, S. L., “Modeling of Tower Relief Dynamics”, Hydro. Proc., Part I, V. 72, No. 10; Part 2, V. 72, No. 11, 1993.

Process Safety and Pressure-Relieving Devices  1251 39. Leung, J. C., “Size Safety Relief Valves for Flashing Liquids”, Chem. Eng. Prog. V. 88, No.2, 1992, p. 70. 40. Crane Technical Manual No. 410, Crane Co., Chicago, Ill. 41. Crowl, D. A. and Louvar, J. F., Chemical Process Safety: Fundamentals with Applications, Prentice-Hall, 1990. 42. Teledyne Farris Engineering Catalog 187 C., Teledyne Farris Engineering Co., Palisades Park, NJ. 43. Safety and Relief Valves, Cat. FE-316, Farris Engineering, Palisades Park, NJ. 44. Ludwig, E. E., “Applied Process Design for Chemical and Petrochemical Plants”, Vol. 1, 3rd, 1995 Gulf Publishing Company, Houston. 45. White, R. E. and C. J. Oswald, Mitigation of Explosion Hazards of Marine Vapor Control Systems, Report SWRI Project No. 064116 for American Petroleum Institute, Oct., 1992. 46. Barton, J. A., and Nolan, P.F., “ Incidents in the Chemical Industry due To Thermal runaway Reactions, Hazards X, Process Safety in Fine and Specialty Chemical Plants”, I. ChemE Symp., Ser. No. 115, pp. 3-18, 1989. 47. Lees, F. P., Loss Prevention in the Process Industries, Vol. 1, Butterworth-Heinemann, Ltd. 48. Shabica, A. C., “Evaluating the Hazards in Chemical Processing”, Chem, Eng., Prog., Vol. 59, No. 9, pp. 57-66, 1963. 49. Bodurtha, Frank T., Industrial Explosion Prevention and Protection, McGraw-Hill, Inc., 1980. 50. Mumford, C. J., “PSI Chemical Process Safety”, Occupational Health And Safety Training Unit, University of Portsmouth Enterprise Ltd., Version 3, 1993. 51. Dow Chemical Co., Dow’s Fire and Explosion Index, Hazard Classification Guide, American Institute of Chemical Engineers, 6th ed., 1987. 52. Baker, W. E., Explosions in Air; 2nd ed., Wilbert E. Baker Engineering Co., U. of Texas Press Pub. 1st ed., Austin, Texas, 1973 and 1983. 53. Wells, G. L., Safety in Process Plant Design, George Godwin /Longman Group UK, Ltd., London, John Wiley and Sons, NY, 1980. 54. Ritcher, S. H., and Turner, F., “Properly Program the Sizing of Batch Reactor Relief Systems”, Chem. Eng., Prog., pp 46-55, 1996. 55. Fisher, H., et al., “Emergency Relief System Design Using DIERS Technology”, AIChE’s Design Institute for Emergency Relief Systems, AIChE, New York, 1992. 56. Boyle, W. J., “Sizing Relief Area for Polymerization Reactors”, Chem. Eng. Prog. 63 (8), p. 61, 1967. 57. Huff, J. E., CEP Loss Prevention Technical Manual, 7, 1993. 58. Fisher, H. G., “An Overview of Emergency Relief System Design Practice”, Plant/Operations, Prog. 10 (1), pp 1-12, January, 1991. 59. Leung, J. C., “Simplified Vent Sizing Equations for Emergency Relief Requirements in Reactors and Storage Vessels”, AIChE J, Vol. 32, No. 10, pp. 1622-1634, 1986. 60. Fauske, H. K., “Generalized Vent Sizing Monogram for Runaway Chemical Reactions”, Plant/Operation, Prog. Vol. 3, No. 3, October 1984. 61. Leung, J. C., and H. K. Fauske, Plant/Operation Progress, 6 (2), pp 77-83, 1987. 62. Fauske, H. K., "Emergency Relief System Design For Runaway Chemical Reaction", Extension of the DIERS Methodology, Chem. Eng. Res. Dev., Vol. 67, pp. 199-202, 1989 63. Duxbury, H. A., and A. J. Wildly, “The Design of Reactor Relief Systems”, Trans. I. ChemE., Vol, 68, Part B, pp. 24-30, February 1990. 64. Coker, A. K. “Computer program enhances guidelines for gas-liquid separator designs”, Oil and Gas Journal, pp. 55-62 May 10, 1993. 65. Grossel, S. S., “Design and Sizing of Knock-out Drums/Catchtanks for Reactor Emergency Relief Systems”, Plant/ Operations Prog. Vol. 5, No. 3, pp. 129-135, 1986. 66. Arun Datta, Process Engineering and Design Using Visual Basic ® 2nd. ed., CRC Press, Taylor & Francis Group, 2014.

11 Chemical Kinetics and Reactor Design INTRODUCTION Chemical reactors are the core features of a chemical process. A reactor is an equipment in which the feedstock is converted into the desired products. The choice of chemical reactors for specific tasks depends on availability and cost of raw materials, equipment costs, profits, yields and purity, pollution control, and so on. Furthermore, the requirements imposed by the reaction mechanisms, rate expression and the production capacity should also be met. Other pertinent parameters are hydrodynamics, reaction heat, reaction rate constant, heat transfer coefficient and reactor size and operating conditions [1]. An important factor in reactor operation is the overall conversion. However, the optimal reactor size depends on operation mode (continuous, tubular/plug flow, semi-batch and batch) and the arrangement of multiple reactors in series or parallel. The operation of the reactors could be isothermal or adiabatic, single-pass or an operation with a recycle depending on the desired degree of conversion, which highly affects the economics of the process. Another classification of the reactors is based on the shape of the vessels [1]. At laboratory scale, a vessel with a stirrer is classified as a stirred tank or well-mixed reactor where the composition and temperature are homogeneous. If there is no mixing in the direction of flow as in the cylindrical vessels, it is classified as a plug flow or tubular flow reactor. Knowledge of the concentration, pressure and temperature at each point of the reactor enables the designer to describe the behavior of a chemical reaction. Concentrations of species and temperature at any point may change due to either reaction, mass or heat transfer. The rates of mass and heat transfer depend on the reactor properties, such as the size of the vessel, the size and speed of the impeller and the area of heat exchanging surfaces. Therefore, the process design is highly dependent to reactor design and choice, and it continues outward as shown in Figure 11.1. The reactor design determines the product and influences the whole process through the separation units, recycles structures and other downstream unit operations. Therefore, it is of prime importance in terms of the heat and mass

R e a c tors

Sep

Hea

a r a ti o n s

t E xc h

a n g e r N et

wo r

k

U tiliti e s

Figure 11.1  The onion diagram in process design. A. Kayode Coker and Rahmat Sotudeh-Gharebagh. Chemical Process Engineering: Design, Analysis, Simulation and Integration, and Problem-Solving With Microsoft Excel – UniSim Design Software, Volume 2, (1253–1334) © 2022 Scrivener Publishing LLC

1253

1254  Chemical Process Engineering balances which dictate the overall heat recovery requirements and production capacities. Engineers, technologists, and scientists have employed different approaches to design the reactors and adapt various numerical techniques to solve the resulting equations. Several reactor types are used in laboratory scale, pilot scale or industrial scales, and they are all associated with various forms of chemical reactions or biochemical reactions. The reactions may also be used in columns and separators (with some limitations on the phases used by the reactions). There are many schemes for the classification of chemical reactions. The reactions may take place in one, or more phases; or at the interfaces of phases; the reactants and products may be distributed among the phases or contained within a single phase. In the most useful scheme, the reactions are classified according to the number and types of phases as homogeneous and heterogeneous reactions [2]. The key difference between these reactions is that the reactants and products that take part in homogeneous reactions are in the same phase (gaseous, liquid, or solid) whereas the reactants and products in heterogeneous reactions are in different phases where at least two phases exist. From the theoretical point of view, homogeneous reactions are the simpler of these two classes because the chemical changes that take place are solely dependent on the nature of the interactions of the reacting substances. Sometimes the distinction between homogeneous and heterogeneous systems may not be sharp enough due to non-homogeneity in composition and temperature; e.g., biological reactions, the enzyme-substrate reactions or the very rapid chemical reactions. Such borderline can be treated based on the description we provide for the problem. Cutting line between this classification is the catalytic reaction whose rate is altered by foreign materials, called catalysts, that are neither reactants nor products. These materials are not present in large amounts. Catalysts are either accelerating or inhibiting the reaction. Table 11.1 shows the general classification for chemical reactions according to this view with a few examples of typical reactions for each type. However, the reactions involved in this classification could be single, reversible or irreversible, parallel or in series or complex. The kinetic expressions can reflect these reactions in reactor design. Coker [3] provided extensive coverage of reaction rate expressions for these reactions. Several excellent textbooks and references, e.g., [2–5] are available on chemical reaction kinetics and reactor design involving the basics to complex reactions, and presenting the design equations for ideal and non-ideal reactors. Coker [1] provides a good coverage of industrial and laboratory reactors, chemical reaction hazards and process integration of reactors. The aim of this chapter is to present some aspects of reactor design with the use of the UniSim design simulator and the Excel spreadsheet. For this purpose, the various reactions types are introduced and then the common reactors are presented listing the types of reactions used in each reactor type. Information provided by Penn [6] on chemical reactions/reactors in the HYSYS simulation software also helps the UniSim design users due to its similarities with previous versions of the HYSYS simulation programs. Additionally, a short review will be provided on the simulation of non-ideal reactors using the UniSim design simulation software, and some general comments will be also Table 11.1  Common Classification of Chemical Reactions (Source: Levenspiel [2]). Homogeneous

Non-catalytic

Catalytic

Most gas phase reactions

Most liquid-phase reactions

Fast reactions such as burning of a flame

Reactions in colloidal systems Enzyme and microbial reactions

Heterogeneous

Burning a coal in air

Ammonia sysnthesis

Roasting of ores

Oxidation of ammonia to produce nitric acid

Attach of solids by acids

Cracking of crude oil Oxidation of SO2 to SO3

Gas-liquid absorption with reaction Reduction of iron ore to iron and steel

Chemical Kinetics and Reactor Design  1255 given on multiscale modeling. Hands-on problems are presented at the end of the chapter for showing the step-bystep solution with the UniSim design and the Excel spreadsheet. Finally, a review of safety in reactor with a case study of an industrial incident is presented.

INDUSTRIAL REACTION PROCESSES Many processes in linear or circular economy, e.g., various chemical production, waste-to-energy-management, residue hydrotreating, are industrially applied or under development. All these processes involve some sort of chemical reactions conducted in various devices. Some common types of the reactors used in various processes are described as the following:

Conventional Reactors The conventional reactors used in the Chemical, Biochemical and Mining (CBM) industry are classified into three main categories as fixed bed reactors, fluidized bed reactors (also called ebullated-bed reactors) and slurry reactors with the following general descriptions: i.

 fixed bed reactor consists of a cylindrical tube filled with catalyst pellets with reactants flowing A through the bed and being converted into products. The pellets may have multiple configurations including one large bed, several horizontal beds, several parallel packed beds, multiple bed in their own shells. The various configurations are adapted depending on the need to maintain temperature control within the reactor. The pellets may be spherical, cylindrical or randomly shaped. They range from 2.5 to 10 mm in diameter. The flow of a fixed bed reactor is typically downward. A trickle-bed reactor is a fixed bed where the gas and liquid flow co-currently downward over a packed bed of catalyst particles. It is the simplest reactor type for catalytic reactions where a gas and a liquid are present in the reactor and accordingly it is extensively used in chemical and biochemical processing plants. Typical examples are liquid phase hydrogenation, hydrodesulfurization, and hydro-de-­ nitrogenation in refineries and oxidation of harmful chemical compounds in wastewater streams or of cumene in a cumene process. ii. In a fluidized bed reactor, gas and liquid flow upward and keep the catalyst particles in suspension. In principle, the catalyst remains in the reactor. The catalysts are much smaller, in the range of 10 – 1000 microns. A key advantage of a fluidized bed reactor is its ability to achieve a highly uniform temperature in the reactor. iii. In slurry reactors, the catalyst is very finely divided and is carried through the reactor with the liquid fraction. This reactor is typically used when one reactant is a gas and the other a liquid while the catalyst is a solid. The reactant gas is put through the liquid and dissolved. It then diffuses onto the catalyst surface. Slurry reactors are usually mechanically stirred, but in slurry reactors for the conversion of heavy petroleum fractions, suspension of the catalyst particles creates no problem as the liquid/solid slurry behaves as a homogeneous phase. Slurry reactors can use very fine particles, and this can lead to problems of separation of catalyst from the liquid. The most important advantages of the fluidized bed reactors are the excellent heat-transfer properties, the option to use highly dispersed catalyst systems and highly exothermic reactions, and the ease of addition and removal of catalyst particles. Compared to fixed bed reactors, the particle size can and must be much smaller, and consequently, the apparent activity and the capacity for metal removal are higher. In slurry reactors, the particle size is even smaller with the accompany advantages. However, the separation of the fine particles from the product is often a problem, e.g., in residue processing, recovery of the catalyst is usually not practical; therefore it is discarded with the unconverted residue. Figures 11.2, 11.3, 11.4 and 11.5 show examples of the various reactor types used with two or three phases are present; gas (e.g.; H2), liquid (e.g., residual oil), and solid (e.g., catalyst). Figures 11.6, 11.7, 11.8 and 11.9 and 11.10 show the photos of various industrial reactors.

1256  Chemical Process Engineering Gas + liquid

Product (+ cat.)

Product Distributor Inert beads

Catalyst addition

Catalyst bed Support grid

Gas bubble

Catalyst suspension Gas bubbles

Catalyst in suspension

Gas

Gas Catalyst removal

Product

Liquid + cat.

Liquid

Figure 11.2  Fixed bed (left), Fluidized bed (middle), and Slurry reactor (right) (Source [7], p. 88).

Feed

Figure 11.3  A battery of continuous stirred tank reactors (Source: Mann U. [8]). Syngas

Catalyst Steam

BFW Gaseous products

Wax

Figure 11.4  Multitubular Fixed Bed Reactor (Source [7], p. 205).

Chemical Kinetics and Reactor Design  1257 Gas in

Liquid in

Liquid distributor

Water in Packing

Cooling jacket

Water out

Gas out

Liquid out

Figure 11.5  Scheme of a trickle-bed reactor (Source: https://en.wikipedia.org/wiki/Trickle-bed_reactor, accessed January 2021).

Figure 11.6  A Packed bed reactor (Source: https://www.tessa.eu/en/product/packed-bed-reactors, accessed January 2021).

1258  Chemical Process Engineering

Setting Hopper

Riser

Standpipe

Figure 11.7  Straight through a transport reactor of 38 m tall and 3.5 m in diameter (Source: https://image.slideserve.com/314741/straightthrough-transport-reactor-l.jpg, accessed January 2021).

Figure 11.8  CSTR/batch reactor with different impeller types (Source: https://ptgmedia.pearsoncmg.com/images/chap1_9780135486221/ elementLinks/fogler_f01_07a.jpg, accessed January 2021).

Chemical Kinetics and Reactor Design  1259

Figure 11.9  A series of continuous flow stirred tank reactors (Source: https://tennessine.com.br/reator-cstr-tanque-perfeitamente-agitadoamar, accessed January 2021).

Figure 11.10  Plug Flow Reactor, 243’ Long, 8” S40 CS Pipe, (Source: https://i.ebayimg.com/images/g/pvUAAOSw2xRYiTE2/s-l1600.jpg, accessed January 2021).

Membrane Reactors Membrane reactors are devices that integrate the hydrodynamic and a chemical reaction with a membrane separation process to add reactants and to remove products of the reactions. The membrane can be used for different tasks, namely: • Separation (selective extraction of products, retention of the catalyst) • Distribution/dosing of a reactant • Catalyst support (often combined with distribution of reactants).

1260  Chemical Process Engineering Membrane reactors are an example for the combination of two-unit operations in one step, e.g., membrane separation with the chemical reaction. The integration of reaction section with selective extraction of a reactant allows an enhancement of the conversions compared to the equilibrium value. This characteristic makes membrane reactors suitable to perform equilibrium-limited endothermic reactions. Generally, membrane reactors can be classified based on the membrane position and reactor configuration. If the catalyst is installed inside the membrane, the reactor is referred to as catalytic membrane reactor (CMR). If the catalyst and the support are packed and fixed inside, the reactor is called packed bed membrane reactor. If the speed of the gas is high enough, and the particle size is small enough, fluidization of the bed particle occurs, and the reactor is called fluidized bed membrane reactor. A good example for the application of membrane reactors is the production of Hydrogen. Hydrogen is increasingly used as a possible replacement of fossil fuels as energy carrier and as fuel in fuel cells. Additionally, it is used in the chemical industry as a reactant in ammonia production, and methanol synthesis and in refinery processes for hydrotreating and hydrocracking. More than 50% of hydrogen is currently produced from steam reforming of natural gas due to its low costs. Traditional processes are composed of a steam reforming section to produce syngas from natural gas, two water gas shift reactors which enhance hydrogen in syngas and a pressure swing adsorption unit for hydrogen purification. Figure 11.11 shows the schematic of the packed bed and fluidized bed membrane reactors. Membrane reactors are suitable for hydrogen production which make a process intensification by integrating reactions and separation in one single unit with significant economic and environmental benefits. The membranes must have a high flux, high selectively towards hydrogen, low costs and high stability. Among the membrane type reactors dense inorganic types are the most suitable having a selectivity orders of magnitude bigger than porous ones. The metallic ones are the most used due to higher fluxes compared to ceramic ones. The most used material in hydrogen separation membranes is palladium, particularly its alloy with silver. This metal is of very high solubility towards hydrogen. The transport mechanism of hydrogen inside palladium membranes follows a solution/diffusion mechanism as the hydrogen molecule is adsorbed onto the surface of the membrane. Then, it is split into hydrogen atoms where they transverse across the membrane through diffusion and then recombine again into hydrogen molecule on the low-pressure side of the membrane, where it is then desorbed from the surface. Recently, studies have been conducted with palladium membranes inside fluidized bed membrane reactors for hydrogen production [9]. Figure 11.12 shows the schematic of a Pd-Ag membrane reactor to produce hydrogen.

permeate

retentate

packed bed with support and catalyst

retentate

permeate membrane

bubbles

membrane

feed

feed

FIXED BED

FLUIDIZED BED

Figure 11.11  Packed bed and fluidized bed membrane reactors (Source: M. Ongis https://en.wikipedia.org/wiki/File:Packed_bed_and_ fluidized_bed_membrane_reactors.png, accessed January 2021).

Chemical Kinetics and Reactor Design  1261 Inert gas

Catalyst bed

H2 CO + H2O

H2

CO + H2O

H2

Pd-Membrane

H2

H2 + CO2

H2

CO2

H2

Permeate

Figure 11.12  Schematic of the Pd-Ag membrane reactor (Source: [10]).

Spherical Reactors Spherical reactors have been found to be an effective solution to the challenging pressure drop in a chemical reactor as compared to the conventional tubular reactors having considerable pressure drop across the bed, high manufacturing costs resulting from large wall thickness and low production capacity. A photo of a 12-in. diameter spherical reactor is shown in Figure 11.13. There are two types of spherical reactors, namely: radial flow and axial flow spherical reactors: i.

 radial flow spherical reactor is constructed of two concentric spheres and the catalysts fill the free A space between them. The reactants radially flow from the outside surface through the inner one or vice versa. The radial flow direction in spherical reactors possess a larger cross-sectional area and smaller reactor thickness in comparison with traditional tubular reactors. Consequently, the radial flow pattern leads to a significantly lower pressure drop. The radial flow spherical configuration has been applied to many processes, e.g., reforming of naphtha into hydrogen and aromatics. It is also used in hydrocracking as it is a key sector of refineries. It is now considered as an alternative to the tubular catalytic reactor in the hydrocracking process and important parameters of the reactors such

Figure 11.13  A 12-in. diameter spherical reactor (Source: https://i.redd.it/5m5lf72b9j521.jpg, accessed January 2021).

1262  Chemical Process Engineering

Figure 11.14  A photo of three Spherical Reactors (Source: http://www.umich.edu/~essen/html/01chap/html/reactors/pics/3sphere.gif, accessed January 2021).

as the pressure drop, yield and temperature profile were compared with the conventional reactor. The results showed an improved value of pressure drop and increased product yields in the spherical geometry in comparison with a tubular reactor operating in the same conditions and catalyst load. Furthermore, an increase in the catalyst loading in the spherical configuration results in more productivity, while the increase of the catalyst weight in the tubular reactor could damage the catalyst and the reactor structure. Recently, these reactors have been found useful in steam reforming of methanol, which is one of the principal routes to produce hydrogen, leading to minimum amount of required feed, and maximum reactor efficiency and productivity. ii. The axial flow spherical reactor (AFSR) is where a fixed catalytic bed is placed between the two perforated screens as the feed enters the top of the reactor and flows axially towards the bottom of the reactor. This configuration leads to a uniform flow distribution and studies regarding mathematical modeling and simulation of AFSR show that the axial flow pattern is dominant (i.e., radial flow is neglected). However, a significant hurdle to commercialization of axial flow reactors is to provide a uniform feed distribution in a way to avoid a two-dimensional flow regime. Thus, it is necessary to use flow distributors along the reactor axis. The AFSR has been investigated for different processes such as hydrocarbons reforming, dehydrogenation of paraffins into olefins and gasoline production. This reactor shows a lower pressure drop, higher production rate, suitable flow distribution, and desirable temperature profile. More importantly, a membrane reactor has the advantages as an AFSR because of its axial structure [11]. A photo of three Spherical Reactors is shown in Figure 11.14.

Bioreactors Bioreactors are vessels that support a biologically active environment. A chemical process is carried out which involves organisms or biochemically active substances derived from such organisms. This process can either be aerobic1 or anerobic2. These bioreactors are cylindrical, ranging in size from liters to cubic meters and are often of stainless steel. It is also referred to as a device or system designed to grow cells or tissues in the context of cell culture. These devices are being developed for use in tissue or biochemical or bioprocess engineering. Figure 11.15 shows an overview of a bioreactor/fermenter. *

1 1

*

2 2†

†

An aerobic organism or aerobe is an organism that can survive and grow in an oxygenated environment. An anaerobic organism (anaerobe) is any organism that does not require oxygen for growth.

Chemical Kinetics and Reactor Design  1263 Agitation system Feeding pump System monitor Medium Sensors probes Air

Reactor tank

Thermal jacket

Submerged aerator Effluent

Figure 11.15  An overview of a bioreactor/fermenter (Source, https://en.wikipedia.org/wiki/Industrial_microbiology, accessed January 2021).

A bioreactor may be classified as batch, fed batch or continuous (e.g., a continuous stirred tank reactor model). An example of a continuous bioreactor is the chemostat bio reactor [3] to which fresh medium is continuously added, while culture liquid containing leftover nutrients, metabolic end products and microorganisms are continuously removed at the same rate to keep the culture volume constant. By changing the rate with which medium is added to the bioreactor, the specific growth rate of the microorganism can be easily controlled within limits. Chemostats in research are used for investigations in cell biology as a source for large volumes of uniform cells or protein. An enclosed chemostat vessel is shown in Figure 11.16. The chemostat is often used to gather steady-state data about an organism in order to generate a mathematical model relating to its metabolic processes. They are also used as microcosms in ecology and evolutionary biology. In one case, mutation/selection is a nuisance, while in another case, it is the desired process under study. Chemostats can also be used to enrich specific types of bacterial mutants in culture such as auxotrophs3 or those that are resistant to antibiotics4 for further scientific study. Variations in the dilution rate permit the study of the metabolic strategies pursued by the organisms at different growth rates. Chemostats are frequently used in the industrial manufacturing of ethanol. In this instance, several chemostats are used in series, each maintained at decreasing sugar concentrations. They also serve as an experimental model of continuous cell cultures in the biotechnological industry. ‡

§

Organisms growing in bioreactors may be submerged in liquid medium or may be attached to the surface of a solid medium. Submerged cultures may be suspended or immobilized. Suspended bioreactors can use a variety of organisms, since special attachment surfaces are not required and can operate at a much larger scale than immobilized cultures. In a continuously operated process, the organisms will be removed from the reactor with the effluent. Immobilization is a general term describing a wide variety of methods for cell or particle attachment or entrapment. It can be applied to all types of biocatalysts including enzymes, cellular organelles, animal and plant cells. Immobilization is useful for continuously operated processes, since the organisms will not be removed with the reactor effluent, but is limited in scale because the microbes are only present on the surfaces of the vessel. Figures 11.17 and 11.18 show the photos of bioreactors. Kinetics studies of biochemical reactions are provided later in the chapter. Auxotrophy is the inability of an organism to synthesize an organic compound required for its growth. An auxotroph is an organism that displays these characteristics. 4 Antibiotic is a type of antimicrobial substance for fighting bacterial infections, and antibiotic medications are widely used in the treatment of such infections. They may either kill or inhibit the growth of bacteria. 3

‡

§

1264  Chemical Process Engineering

Inflow of fresh sterile medium

Inflow of sterile air

Flow-rate control valve Air opening

Gaseous headspace

Culture

Stirring apparatus

Outflow of media and microbial cells to collection vessel

Figure 11.16  An enclosed chemostat vessel with a continuous and adjustable inflow of medium and outflow of effluent, used for controlled growth of microorganism (Source: https://en.wikipedia.org/wiki/Chemostat#/media/File:Chemostat_Vessel_Diagram.png, accessed January 2021).

Figure 11.17  A photo of bioreactors at the BTEC facility (Source: Rick Lawless, BTEC, https://en.wikipedia.org/wiki/File:BTEC_ Bioreactors.jpg, accessed January 2021).

Chemical Kinetics and Reactor Design  1265

Figure 11.18  World’s largest industrial fermenter, 200 ft tall and 25 ft in diameter from Chem. Eng. News, 10 April 1978 (Source: https:// image.slideserve.com/227283/slide5-l.jpg, accessed January 2021).

CHEMICAL REACTIONS This section covers the common chemical reactions. Since most of the problems at the end of the chapter are solved with the UniSim design simulator, the focus is given to the reactions defined in the simulator. However, these are common reactions found in most reaction engineering texts, e.g.; [2–5]. There are currently three different reaction types simulated in the UniSim design simulator and these are identical to those used in previous versions of the HYSYS simulation software [6]. Common to all reactions is to enter the stoichiometry coefficients with a negative sign for reactants and a positive sign for products. In the stoichiometry tab of the reaction window, one must make sure to have the balance error equal to zero which shows the stoichiometry balance. In the same window, the heat of reaction is also shown with a negative sign for exothermic and a positive sign for endothermic reactions. The reaction types are:

Conversion Type This type of reaction requires the stoichiometry and the conversion data of the Basis Component without any thermodynamic knowledge. The reaction normally proceeds until the specified conversion is reached or a limiting component is exhausted. The maximum conversion in the reaction can reach to 100%. This reaction cannot be grouped with other reaction types in a reaction set, but multiple conversion reactions may occur sequentially or simultaneously. The following expression used to calculate the conversion is:



X(%) = C0 + C1T + C2T2

(11.1)

where T is in Kelvin. For fixed conversion, C1= C2= 0

Equilibrium Type This reaction requires the relation between the equilibrium constant, Keq, and temperature based on reaction stoichiometry. The equilibrium constants, Keq as reported in the UniSim design software [12] are: a. ln(Keq) Equation:

ln(keq) = a + b

(11.2)

1266  Chemical Process Engineering

a =A+



B + C ln(T) + DT T

b = ET2 + FT3 + GT4 + HT5

(11.3) (11.4)

In this equation, the temperature (T) is always considered in Kelvin regardless of the units set for simulation and therefore all coefficients, (A-H) must be adjusted accordingly to meet this condition. b. Gibbs Free Energy: This is based on the minimization of Gibbs free energy of all components. The Gibbs free energy vs. Keq is calculated with the following Equation:



ln(K eq ) =

−∆GR RT

(11.5)

c. F  ixed Keq or ln(Keq) d. Keq vs. T Table; the coefficients of equilibrium constants are predicted within the UniSim design or tools provided in Chapter 1.

If the equilibrium reaction is chosen from the library of Equilibrium Reactions in the UniSim design, no additional equilibrium data is needed by the user to define the reaction. Like the conversion reactions, equilibrium reactions may be also defined in parallel or series and only regrouped with their types.

Kinetic Type 1. Kinetic (standard): This reaction needs an expression for the rate of the reaction as the following;



r = k × f(Basis) − k′ × f′ (Basis)

(11.6)

where: r is the reaction rate k and k′ are the pre-exponential factors for forward and reverse reactions respectively. f and f ’ are the Basis functions for forward and reverse reactions respectively. The reaction rate constants are:



k = A × exp(−

E ) × Tβ RT

 E′  × T β′ k ′ = A′ × exp  −  RT 

(11.7)

where E and E’ are the activation energies for forward and reverse reactions, respectively A and A’ are the pre-exponential factors for forward and reverse reactions, respectively T is the temperature in Kelvin R is the universal gas constant. β is a dimensionless number of order 1 regarded as a purely empirical correction or fudge factor to make the model fit the data. If no values are given for A′ and E′, no reverse reaction would take place. It is worthy to mention that the UniSim design does not show the units for the Pre-exponential factor and it is the user’s responsibility to initially set units for Basis and Rate Units.

Chemical Kinetics and Reactor Design  1267 The f(Basis) and f′(Basis) are the products of the concentrations (or partial pressures, mole fractions, etc.) of any of the reactants including the Base Component or products to their relevant powers (order of reaction) which could be positive and negative numbers or decimals. In the UniSim design simulation, by default, the stoichiometry parallels the order of the reaction as shown in Figure 11.19 for the Acetone reaction (CH3COCH3 → CH2CO + CH4) where Stoich Coeff and Forward Reaction Order have similar values. This means that the absolute values of stoichiometry are used as the order of the reactions for both forward and reverse reactions by default, however, the reaction order for a given component is an input by the user so that UniSim Design software may know how to treat the reaction as a function of the concentrations. 2. S imple Rate: This is like the standard kinetic equation and the difference is related to the reverse rate constant, which is predicted from equilibrium data:

k′ =



k K′

(11.8)

where K′ is predicted from the equilibrium data





f' (Basis)   r = k × f (Basis) − k ′ f' (Basis) = k ×  f (Basis) − k/k ′   f' (Basis)   = k ×  f (Basis) − K'   K' = A +

B + C × ln(T) + D × T T

(11.9)

(11.10)

where T is in Kelvin. 3. H  eterogeneous Catalytic Reaction: This is a rather complicated kinetic form that is mainly used to model heterogeneous catalysis [6]. The rate of reaction is gradually slowed when some of the catalyst active sites may become blocked by the products being formed with the completion of the reaction. Therefore, a denominator is added to the standard kinetic to represent the adsorption term. This form

Figure 11.19  The Stoichiometry versus reaction order by default in the reaction of Acetone (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

1268  Chemical Process Engineering can also represent the enzyme catalytic reactions. The rate of reaction of a heterogeneous catalytic reaction is expressed as:



rate = Numerator / Denominator

(11.11)



Numerator = k × f(Basis) – k′ × f′ (Basis)

(11.12)



Denominator = [1 + K1 × f1 (Basis) + K2 × f2(Basis)]n

(11.13)



 E  K1 = A1 × exp  − 1   RT 

(11.14)



 E  K 2 = A 2 × exp  − 2   RT 

(11.15)



 Ej  K j = A j × exp  −  RT 

(11.16)

where: The functions of the Basis (f, f′, f1 and f2) are the products of “concentrations” (in the Basis units) to the power of specified exponents. n is the denominator exponent The indexes 1, 2, …j, in the constants K, A and E show the row number in the matrix of denominator terms. The choice of the reactive phases is important in the reaction and one must ensure finding the correct phases in which a reaction occurs. All other reaction types can be fairly converted to one of the above-mentioned forms to be used in the simulation.

IDEAL REACTORS The common ideal reactor types in the UniSim Design software library are shown in Table 11.2: All reactors can be modeled as adiabatic until an external heating or cooling energy stream is attached (at which point some further specification such as outlet temp or energy input is required). The summary of common Reactors in the UniSim design simulation with their relevant Reaction Types is given in Table 11.3. It is important to mention that like HYSYS [13], the reaction rates are given in units of volume of gas phase in the UniSim design simulator. For the catalytic reactions in CSTR or PFR, the reaction rate is normally provided per units of kg of catalysts, therefore, it should be converted to the volume of gas as the following: Table 11.2  Common ideal reactor types in the UniSim design simulation library. Type

Conversion

Equilibrium

C

E

Gibbs

Library Models G

CSTR

PFR

Chemical Kinetics and Reactor Design  1269 Table 11.3  UniSim design reactors with their relevant reaction types. Reactors

Reaction type

Conversion

Conversion; one or multiple reactions (series/parallel)

Equilibrium

Equilibrium: one or multiple reactions (series/parallel)

Gibbs

Equilibrium: one or multiple reactions (series/parallel) Minimization of Gibbs free energy for all components

CSTR

Kinetic, Simple Rate, Heterogeneous Catalytic or their combinations, multiple reactions (series/parallel)

PFR

Kinetic, Simple Rate, Heterogeneous Catalytic or their combinations, multiple reactions (series/parallel)

The rection rate unit for the catalytic reactions is:

r[=]



mol kg cat .s

(11.17)

It can be converted to the form used by simulators as:

rUniSim = rρc



mol (1 − ϕ ) mol kg cat m3cat [=] × 3 × 3 [=] 3 kg cat .s mcat mGas mGas .s ϕ

(11.18)

where:  mol  rUniSim is the reaction rate unit used in the simulator  3   mGas .s   mol  r is the reaction rate unit per weight of catalyst   kg cat .s   kg  ρc is the density of catalyst  3cat   mcat  φ is the void fraction The details of all common reactors are found in process simulator guidelines [12] and reaction engineering textbooks, e.g., [2–5]. Brief descriptions are also provided in this chapter. The information provided here can be used in conjunction with the UniSim design Manuals. We also assume readers possess certain basic information that is best explained in Chapter 1 through examples.

Conversion Reactor This reactor type deals with conversion reactions when one knows how much of the reactants are converted into products. It can also handle multiple reactions ranked to occur simultaneously or sequentially. The conversion reactions with the same ranking are considered simultaneous and the total conversion of the base reactant cannot exceed 100% subject to limiting reagents. It is worth mentioning that the product of one reaction may be the feed/reactant of another reaction. The conversion reactor can be used to easily perform some tedious calculations or generate hands-on curves in chemical reaction engineering. In this chapter, we will show how this reactor is used to calculate, e.g., the adiabatic flame temperature (AFT) and the heat of reaction at a given temperature with relevant flowsheets and hypotheses.

Adiabatic Flame Temperature When a combustion reaction takes place in a chemical reactor, the energy is released to the products. If there is no heat loss in this process, the outlet temperature is called the adiabatic flame temperature (AFT). This is the

1270  Chemical Process Engineering Table 11.4  AFT of selected common fuels [14]. Fuel

Oxidizer

Temperature (°C)

Acetylene

Oxygen

3480

Acetylene

Air

2500

Butane

1970

Ethane

1955

Gasoline

2138

Hydrogen

2254

Kerosene

2093

Methane

1963

Natural gas

1960

Pentane

1977

Propane

1980

maximum temperature achievable for a given mixture. When a flame loses heat to the surrounding environment or it is diluted with an inert material or excess air, the outlet stream is heated with the heat released by the highly exothermic combustion reaction, therefore, the actual temperature would be significantly less than the ideal adiabatic flame temperature. For initial conditions of 1 bar and 20 °C in a stoichiometric fuel-oxidizer mixture, Table 11.4 shows the typical AFT for common fuels under constant pressure conditions. The AFT can be also calculated with the numerical solution of thermodynamic and reaction Equations as shown in the literature [15] for the combustion of liquid octane at 25°C with 400% theoretical air. The reaction is

C8 H18 (l) + 4 × 12.5(O2 + 3.76N2 ) → 8CO2 + 9H2 O + 37.5O2 + 188N2

(11.19)

The value of AFT calculated for this example was reported 962 K and the reader can redo the calculations with Excel spreadsheet and compare the results. However, since finding the physical properties is the main challenge in this type of calculations, the use of process simulators is highly recommended. In Example 11.2, AFT is calculated using the UniSim Design simulator and its variation is plotted with excess air with a flowsheet and some hypotheses.

Heats of Reaction If a process involves any chemical reactions, heat effects will invariably be present in the process. The amount of heat produced/consumed in a chemical reaction depends on operating conditions. The standard heat of reaction, ∆H°R , is the enthalpy variation when the reaction is carried out at 1 atm and usually at 298 K. The values of ∆H°R may be found in the literature, calculated by thermodynamic methods or process simulators. In process design, it is usually more convenient to express the heat of reaction in terms of the enthalpy per mole of product formed or reactant consumed. Calculating the heat of reaction is a multi-step process as illustrated by Coker [3]. This begins with the standard heats of formation at 298 K, where the standard heat of reaction and the heat of reaction for the actual system temperature and pressure are calculated respectively. The heat of reaction at reference temperature (298 K) is usually referred as the standard heat of reaction. This can be readily calculated from the standard heats of formation of the reaction components. For the following general reaction:



α1A + α2B → α3C + α4D

(11.20)

Chemical Kinetics and Reactor Design  1271 The standard heat of reaction would be expressed by:

∆H0R =



(∑ α

poducts

(

. ∆H0f

)

product

) − (∑ α

reacrants

(

. ∆H0f

)

reacrants

)

(11.21)

while, the heat of reaction for a given temperature is [3]:

DHR = DHR0 + Da(T − TR ) +



∑α ∆b = ∑ α ∆c = ∑ α ∆d = ∑ α ∆a =



Db 2 Dc 3 T − TR3 T − TR2 + 2 3

(

)

∑α − ∑α − ∑α − ∑α

(

poducts

. a products −

reactants

. a reactants

poducts

. bproducts

reactants

. a reactants

poducts

. c products

reactants

. a reactants

poducts

. d products

reactants

)

. a reactants

(11.22)

where: ∆H0R is heat of reaction at the reference temperature (TR) ∆HR is heat of reaction at a given temperature (T) α is the stochiometric coefficients of reactants and products ∆H0R is the standard heat of formation of each component T is the system temperature, K TR is the reference temperature, K α1, α2, α3, α4, are the stoichiometric coefficients of a chemical rection a, b, c, d are the coefficients of specific heats usually expressed as quadratic or polynomial function of temperature. For quadratic Equation only a, b and c are used.

The details of steps leading to Equation 11.22 are provided by Coker [3]. Besides the equations presented above, the UniSim design simulation can also be used to find the heat of reaction at a given temperature with conversion reactor introduced in Chapter 1. The following hypothesis are made in the simulation of the conversion reactor to find the heat of reaction: a. Th  e conversion is assumed 100%. b. The feed enters at stochiometric conditions. c. The outlet temperature is assumed equal to the inlet temperature with Set function. Upon completing the simulation of the reactor, the heat duty of the reactor is calculated. If the duty is divided to mole of product formed or reactant consumed, it would give the heat of reaction at a given conditions. The calculation of the heat of reaction is illustrated in Example 11.1 with the Excel spreadsheet and the UniSim design simulation.

Equilibrium Reactor In the equilibrium reactor, only equilibrium reactions with proper equilibrium data are considered. The reactor has one inlet and one outlet streams. Before simulating the reactor, all components are entered, the fluid package is selected, and the reactions are defined. These reactions should be then assigned to the reactor in the simulation environment. In this reactor, the reactions are in equilibrium in the phases in which they occur, therefore the choice

1272  Chemical Process Engineering of reaction phase is of prime importance in the simulation. There are various sources to extract the equilibrium data as explained in the previous section. Only reacting components listed in the Reaction Set undergo the reaction.

Gibbs Reactor This reactor is unique among the chemical reactors and it is suitable for use when reaction equilibrium constants are not known in advance, but the reaction phase is known. It requires knowledge of enthalpy that includes the formation terms. In this reactor, the reaction equilibrium is calculated by minimizing the Gibbs free energy at specified temperature and pressure where all possible equilibrium reactions are found and allowed to be in equilibrium. Therefore, there is no need to have information on the individual reactions. The Gibbs reactor can be used for single-­ phase systems where the equilibrium constants are not known in advance which is the case with complex reactions while equilibrium reactions should be performed in the equilibrium reactor. In Gibbs reactor, the reaction phase must be specified. Generally, it is recommended to use the Gibbs reactor over the Equilibrium reactor. However, Gibbs reactor behaves like an equilibrium reactor if equilibrium reactions are attached or it behaves like a separator if no reaction is attached. A problem is solved at the end of the chapter to show the similarities and differences between the Gibbs and the Equilibrium reactors.

CSTR Reactor The CSTR (Continuously Stirred Tank Reactor) reactor is a standard model that was in process simulators for several years. The reactor content is assumed single phase and well mixed with one inlet and two outlet streams. It is primarily for liquid reactions, of course, but it is also used for the gaseous reactions. The less the “liquid” volume, the more of the total volume would be available for the vapor phase reactions. In the UniSim Design like most process design simulators, the total volume minus the volume of the liquid phase is used to calculate the volume of the gas, whether any liquid is present in the reactor. Before running the CSTR, one should provide homogeneous or heterogeneous reaction data within a reaction set assigned to the reactor.

PFR Reactor The Plug Flow Reactor (PFR), is a 1-dimensional reactor, generally consists of a bank of cylindrical tubes where the flow is modeled as plug flow. This implies that at every cross-section along the reactor length, the velocity, pressure, temperature and concentrations of the reactive phase are constant, and the axial mixing is negligible. However, the reactive phase flows through the length of the reactor and the reactants are gradually consumed leading to an axial variation in the concentration. The PFR has one inlet and one outlet; it is implemented as a single phase reactor and the reaction phase must be specified. Only reactions that take place in the specified phase should be selected. The reactor is solved by dividing the volume into small and spatially uniform segments like a series of CSTRs and a sequential solution is found for each segment. The reactor includes the calculations of energy balances and pressure drop which are a standard feature in catalytic or fixed bed reactors. The reactor also provides the axial profiles of compositions, temperature and pressure, etc., as a function of length or volume of the reactor. Only Kinetic type reactions (Kinetic, Simple Rate and Heterogeneous Catalytic) are allowed in the PFR with unlimited number of reactions.

NON-IDEAL REACTORS Modular Analysis The knowledge of ideal reactors mentioned in previous sections is important, because some industrial multiphase flow reactors may approach an idealized type or may be simulated by the combination of ideal reactors through Sequential Modular Simulation (SMS) models or compartmental models (CM) [1]. These reactors can be modelled using the combination of several ideal reactors and simple unit operations, e.g., heater, mixer, splitter, etc., with some addition

Chemical Kinetics and Reactor Design  1273 Table 11.5  Examples for the simulation of non-ideal reactors with process simulators. Reactor type

Description

Reference

Circulating fluidized bed

Coal combustion, NOX and SOX formation/reduction

[17, 18]

Turbulent fluidized bed

Catalytic combustion of methane

[19]

Membrane fluidized bed

Reforming reactions, hydrogen production

[20, 21]

Fluidized bed combustor

Coal volatile and natural gas combustion

[22, 23]

Photocatalytic reactors

VOC5 photodegradation

[24]

Combustors

Heavy fuel combustion

[25]

Gasifier

Gasification of biomass

[26, 27]

Fluidized bed bioreactor

Ethanol production

[28]

Fluidized bed reactor

Gas phase polyethylene

[29]

of hydrodynamic details in separate subroutine. SMS/CM models are an intermediate approach between ideal reactors (e.g., CSTR and PFR) found in the UniSim design simulator and more detailed multiscale computer programs are provided in the next section on multiscale analysis. These models are used to simulate the mixing behaviour in industrial reactors without a need to solve complicated partial differential equations integrating hydrodynamics to chemical reaction. The modeling is based on a combination of ideal or simple non-ideal reactors (i.e., dispersion model) to simulate the industrial reactors [16]. The dispersion model is used most often for non-ideal tubular reactors. In these models, two sub-models on hydrodynamics and chemical reactions are simultaneously integrated. The reactor is divided into various axial (radial) sections or compartments depending on the configuration of the reactor, mixing patterns (at the injection points, inside of the reactor and exits), leading phases and presence of solid, liquid or gas phases. At each section/compartment, various ideal reactors and units normally found in process simulators are combined and additional subroutines are added to manage the flow distribution and mass transfer calculations among unit operations and ideal reactors. In this way, the hydrodynamic and reactions are integrated in an intelligent way inside of the process simulators or mathematical software to represent the non-ideal multiphase flow reactors. In case of using a process simulator, this modeling approach enables the use of simulator facilities; e.g., databanks, property packages and solvers, in the design, simulation, scale-up and optimization of large scale non-conventional processes with a reasonable computational time and cost. Example of multiphase flow reactors simulated in this way could be fixed and fluidized bed reactors, combustors, gasifiers, bubble columns, catalytic and photocatalytic reactor, fluidized catalytic cracking (FCC) units. Table 11.5 shows some examples where ideal reactors are combined in a sophisticated way through subroutines to simulate the behaviour of non-ideal reactors in a simplified way. It is important to mention that the experimental data from laboratory or pilot plants or the measured residence time distribution (RTD) is used to adjust the number of ideal unit and the dispersion coefficient in the dispersion model. The importance of RTD in flow processes was first introduced by Danckwerts [30]. The RTD simply shows the age, E(t), of the individual molecules staying in the vessel, or more precisely, the distribution of residence times of the fluid elements. The RTD is obtained by injecting a tracer at the inlet and measuring the tracer concentration at the outlet and it shows the bulk flow patterns or macromixing. The typical RTD calculation is provided in Example 11.12.

Multiscale Analysis In order to predict the performance of real pilot and industrial scale reactors, one must couple hydrodynamics with chemical reactions and solve the resulting equations simultaneously. The results should be then validated 5

Volatile Organic Compounds (VOC).

1274  Chemical Process Engineering

Particle

Phases

Fluid

Scales Micro

Meso

Micro

Continuum (1D)

Continuum (local averaging)

Flow around (individual particles)

TPM

TFM

DNS-DEM

Continuum (1D)

Continuum (multi-dimension)

CFD-DEM

Individual particles (trajectories)

Figure 11.20  Multiscale analysis of a fluid–particulate reactor (TPM6, TFM7, CFD8-DEM9, DNS10-DEM) [31].

with experimental data in order to make sure if the modeling is performed with an acceptable accuracy. The main complexity in these reactors is mostly related to the hydrodynamics of the reactive flows rather than the chemical reactions. The reactive flows exist in many pilot and industrial reactors such as gas-solid or liquid-solid fluidized beds, spotted beds, three-phase gas-liquid-solid fluidized beds, bubble columns, membrane reactors and so on. A detailed knowledge of these flows is crucial for design, scale-up, optimization, and troubleshooting of chemical reactors. Although this may be achieved by experimental techniques, modeling can be considered as an alternative tool for exploring different micro-, meso- and macroscales structure coexisting in multiphase flows. With modeling, one can understand different phenomena occurring in these reactors, perform sensitivity analysis on different input parameters and test different configurations and operational conditions at lower expense compared to experiments. Norouzi et al. [31] provided comprehensive coverage of the advanced simulation techniques applied to multiphase flow systems. Generally, real reactors are rather complex, and the modeling allows the analysis and simulation of these reactors to be conducted with more accuracy. Depending on the length scales of fluid and particle systems, various combinations of modeling scales can be used. These are classified as a macro-, meso-, and micro-scale as shown in Figure 11.20 [31]: • In the macro-scale model, the fluid length scale is in the order of the flow field motions of the fluid within the fluid phase and the assemblage of particles as solid phase are treated in one dimension. This approach can be implemented in process simulators with the combination of ideal reactors as explained in the previous section. • In the meso-scale, both gas and solid phases are considered as interpenetrating continua. The conservation equations are solved over a given mesh to capture main features of the flow, like bubble motions and clusters. • In the micro-scale, trajectories of individual particles are obtained through the equations of motion, while the fluid length scale is the same as the particle size or even smaller. At the same time, local flow field around individual particles are calculated. It is worth mentioning that in multiscale analysis, scales may interact with each other; e.g., particle might be in micro-scale interacting with gas in the meso scale. For moving from micro- to meso- and macro-scale, one needs to use proper averaging for the properties in question in order to use in upper scales. Figure 11.21 shows the coexistence and interaction of various scales in gas-solid fluidized beds at various scales with main leading phenomena at each scale. Advanced computational tools can be used to deal with multiscale analysis in industrial reactors and one needs to find the trade-off between the complexity considered and accuracy expected. Two-Phase Model (TPM). Two-Fluid Model (TFM). 8 Computational Fluid Dynamics (CFD). 9 Discrete Element Method (DEM). 10 Direct Numerical Simulation (DNS). 6 7

Chemical Kinetics and Reactor Design  1275

Eddies, Particles and flow around particles (pattern scale)

Micro Meso

Small Bubbles Clusters Agglomerates (cell scale)

Macro Bubbles and emulsion (vessel level)

Figure 11.21  Various scales in gas-solid fluidized beds.

BIOCHEMICAL REACTIONS The processing of waste, biomass and biological materials with cells, enzymes, or antibodies consists the core of the biochemical reaction engineering. In biochemical reactions, both cellular and enzymatic processes simultaneously occur; however, the main differences between the biochemical and chemical reactions is related to the nature of the living systems, although the design basics explained in previous sections on chemical reaction and hydrodynamic considerations remain the same. Small living systems known as microorganisms interact in many ways with human activities as they are responsible in closing the cycles of carbon, oxygen, nitrogen, and other elements necessary for life. The use of microorganisms is fully restricted with feed and operating conditions, e.g., contents of nutrients, temperature, pressure and pH at which they operate. Thus, successful operation depends on the correct choice of organisms or enzymes while preventing the entry of foreign impurities, which could impair the process [3]. The major characteristics of microbial processes that contrast with those of ordinary chemical processing is covered by Coker [3]. In biochemical reactions, the reactant is referred to as a substrate. Alternatively, it may be a nutrient for the growth of cells, or its main function may require being transformed into some desirable chemical. The cells use reactants that will be combined and molecules that may be decomposed by using enzymes. These are produced only by living organisms, and commercial enzymes are produced by bacteria. Enzymes are proteins that act as biological catalysts (biocatalysts). Catalysts accelerate chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules know as products. Almost all metabolic processes in the cell need enzyme catalysis in order to occur at rates fast enough to sustain life. Enzymes are known to catalyze more than 5,000 biochemical reaction types. Like all catalysts, enzymes increase the reaction rate by lowering its activation energy. Enzymes operate under mild conditions of temperature and pH. Therefore, understanding the kinetics of biochemical reactions are critical in any design process. This section solely reviews the kinetics of enzyme reactions; modeling, simulation and scaleup of biochemical reactors are covered in some excellent books; e.g., [2–4, 32] which are beyond the scope of this section.

Models of Enzyme Kinetics Consider the reaction S → P occurs with an enzyme as a catalyst. It is assumed that the enzyme, E, and substrate, S combine to form a complex ES*, which then dissociates into product P and free (uncombined) enzyme E. k



1 E +S  ES* (11.23) k



ES *  → E + P (11.24)

2

k3

1276  Chemical Process Engineering The net rate of disappearance of S, in Equation 11.23 is:

(−rS)net = k1CECS – k2CES*

(11.25)

where k1 and k2 are the reaction rate constants for forward and reverse reactions, respectively. At pseudo-equilibrium conditions when the steps are very rapid, (−rS)net = 0 and the Equation 11.25 would become [3]:

k1CECS = k2CES*

k 2 C ECS = k 1 C ES∗

Km =

(11.26) (11.27)

where Km = dissociation equilibrium constant for ES* CE   = enzyme concentration, E CS   = substrate concentration, S CES* = concentration of the complex, ES* Therefore, the concentration of the enzyme-substrate complex from Equation 11.27 is:

C ES∗ =



k1 C ECS k2

(11.28)

Decomposition of this complex to the product and free enzyme (Equation 11.24) is assumed irreversible, and rate controlling. Therefore, the formation of product would be:

rP = k3CES*

(11.29)

CES* and CS are related by a material balance on the total amount of enzyme, CET. The total amount of enzyme consumed during the process would be (CET) using CB from Equation 11.28:



C ET = C B + C ES∗ =

Or



C ES∗ =

k 2C ES∗ + C ES∗ k 1C S

C SC ET  k2   k + C S  1

(11.30)

(11.31)

If this Equation is inserted to Equation 11.29, the formation of product can be



rP

v

k 3C SC ET (K m C S )

(11.32)

where: Km is the Michaelis-Menten [33] constant and it is equal to k2/k1 rp is the reaction rate like conventional reactions. Equation 11.32 rearranged to the following form:



v

VmaxCS (K m C S )

(11.33)

Chemical Kinetics and Reactor Design  1277 where



Vmax = k3CET

(11.34)

The Equation 11.33 is known as the Michaelis-Menten (MM) equation which represents the kinetics of many simple enzyme-catalyzed reactions involving a single substrate. Generally, assuming Km as an equilibrium constant is not always valid due to the nature of the reversible reactions. The Equation 11.33 is not suitable for the estimation of the kinetic parameters Vmax and Km through linear regression. However, by rearranging this equation, proper forms can be obtained for estimating of the parameters based on the procedure introduced in Chapter 1. Rearrange equation 11.33 as:



1 1 K 1 = + m v Vmax Vmax C S

(11.35)

This equation is referred as the Lineweaver-Burk equation involving separate dependent and independent variables, 1/v and 1/CS, respectively. However, various other arrangements may be also possible, however, by using the experimental data, one can estimate the constants of these equations. Example 11.13 illustrates the calculation of Michaelis (Km) and the catalytic constant (k3) constants with this Equation. Briggs and Haldane [34] proposed a general mathematical model for the enzymatic kinetic reaction to modify the MM constant for broad applications. The model assumes the concentration of the enzyme substrate complex at a pseudo-steady state (PSS) conditions after a short initial startup period. With this general model, the following expression can be derived for the MM constant [3]:

Km



k2 k3 k1

(11.36)

Constant Volume Batch Reactor For a constant volume batch reactor, the MM equation can be linearized [3]. Equation 11.33 can be rewritten to the following form:



rP = −rS = −

dC S V C = max S dt (K m + C S )

(11.37)

dC S = − Vmax dt CS

(11.38)

or



(K m + C S )



−K m

dC S − dC S = Vmax dt CS

(11.39)

Equation 11.39 can be integrated with the following boundary condition:



at t = 0, CS = CS0

(11.40)

C  −K m ln  S  − (C S − C S0 ) = Vmax t  C S0 

(11.41)

and gives the following equation:



1278  Chemical Process Engineering The equation can be further rearranged to give:



1  C S0 − C S  1  C S  Vmax ln  = −    t  C S0  K m K m  t

(11.42)

The equation can be written to the following simple form:



Y = A − BX

(11.43)

where:



1 C  Y = ln  S  t  C S0  A=

Vmax Km

B=− X=

(11.44)

1 Km

C S0 − C S t

With these simplifications, the parameters Km and Vmax can be estimated from Equation 11.42 using measured values of CS as a function of t for a given CS0 as illustrated in Example 11.14. However, The linearized form of the MM equation does not allow to obtain accurate estimates of Km and Vmax. Non-linear regression technique is needed to estimate the values of Km and Vmax. This technique is more complex than the linear regression method and provides additional benefits [3] as explained in Chapter 1. First, accurate non-biased estimates of Km and Vmax can be determined. Second, non-linear regression may allow the errors (or confidence intervals) of the parameters to be evaluated. The non-linear regression technique is illustrated in Example 11.15. Coker [3] has also treated the enzyme kinetics in the presence of inhibitors, design, modeling and scale-up of bioreactors, batch fermenter, fed-batch reactor. The basics provided in previous sections of this chapter can also be applied to bioreactors. However there are specific simulators, e.g., SuperPro Designer® [35] which is widely used by engineers and scientists in biotech, pharmaceutical, food processing, wastewater treatment, etc., for biochemical process development, engineering, and manufacturing. It also facilitates modeling, evaluation and optimization of integrated batch and continuous biochemical reactors and processes.

CHEMICAL REACTION HAZARDS INCIDENTS Reactive Hazards Incidents US Chemical Safety and Hazard Investigation Board (CSB) published a report in 2002 in which it listed 167 serious incidents involving uncontrolled chemical reactions between January 1980 and June 2001 [36]. There were 108 fatalities resulting from 48 of these incidents. In addition to causing injuries and fatalities to plant personnel and the public, reactive incidents can also result in environmental harm and equipment damage. These impacts may be due to fires, explosions, hazardous liquid spills, toxic gas releases, or any combination of such. Fires and explosions are the most frequent occurrence in CSB data (in 42% of incidents) followed by toxic gas releases (37%) [36]. CSB has several reports on these and more recent incidents that should be required reading for anyone involved in reactor design and control. A lack of awareness and prevention against chemical hazards is a recurring feature in

Chemical Kinetics and Reactor Design  1279 Table 11.6  Common types of reactive hazards incidents [36]. Type of reactive hazard

Contribution

Chemical incompatibility

36 %

Runaway reactions

35 %

Impact-sensitive or thermally sensitive materials

10 %

Unknown

19 %

Table 11.7  Common types of reactive hazards incidents [36]. Type of hazard

Contribution

Material handling

21 %

Lack of study on chemistry

20 %

Temperature control

19 %

Maintenance

15 %

Mixing/Agitation

10 %

Raw material quality

9%

Human factor

6%

many of these accidents [37]. These are, however, well known, and, in most cases, are addressed by local, state, or national codes, standards, or regulations. It is worth mentioning that each accident is unique and presents its own lessons, and taken together all accidents reported by CSB can shed light on major chemical accidents and their recurring characteristics. A common perception is that reactive incidents are primarily the results of runaway reactions. However, analysis of data from 167 incidents as shown in Table 11.6 suggests that other types of reactive hazards are of great concern in the chemical process industry. Causal data are reported for only 37 of the 167 incidents, and analysis of this limited set of data showed a variety of causes as detailed in the CSB report [36]. Further, more than 60% of reactive incidents for which some causal information was available involved inadequate management systems for identifying hazards or conducting process hazard evaluations; nearly 50% involved lack of adequate procedures for storage, handling, or processing of chemicals11. ¶

Barton and Rogers [38] reported the analysis of 189 incidents in the U.K. chemical industry involving thermal runaway chemical reactions in batch/semi-batch reactors. Their results showed that in eleven chemical processes, polymerization reactions were involved in the most incidents, followed by nitration, sulfonation and hydrolysis. Table 11.7 shows the causes of reactive hazard and their proper contributions. The general observations of reactive hazards incidents from this table are: • • • • 11 ¶

A basic lack of proper understanding of the process chemistry and thermochemistry. Inadequate engineering design for heat transfer. Inadequate control system and safety back-up systems (including venting). Inadequate operational procedures, including training.

The sum of causal factor exceeds 100% because each major incident may have more than one cause.

1280  Chemical Process Engineering Generally, there is no standard procedure for evaluating chemical reaction hazards, as evaluation must correlate with both process development stage ranged from the lab-scale to pilot plant, full-scale, manufacturing and modifications, and the degree to which the process has been defined. In order to minimize the likelihood of an incident occurring or to minimize the consequences, the following is considered [36]: • Establish a strategy for chemical reaction hazards assessment procedures and responsibilities and process risk analysis. • Evaluate the general hazards of plant operation, particularly fire and explosion and toxic hazards. • Select and specify a basis of safety, considering inherent safety considerations, preventive measures, protective measures including emergency relief (see Chapter 9) and inhibiting the reaction and containment. • Establish operating procedures and instructions. • Process instructions and normal operating procedures • Process changes requiring a reassessment of the hazard. • Product (and personnel) changeover procedures • Operator training • Plant maintenance • Routine checks on safety systems • Emergency procedures.

Chemical Reactivity Worksheet (CRW) Reactivity is the tendency of substances to undergo chemical change, which can result in hazards – such as explosions or the generation of toxic gas. The Chemical Reactivity Worksheet (CRW) is a free software program [39] to find out the chemical reactivity of thousands of common hazardous chemicals, compatibility of absorbents, and suitability of materials of construction in chemical process industry. Versions of the CRW were developed by collaboration of several organizations including the Center for Chemical Process Safety, Environmental Protection Agency, NOAA’s Office of Response and Restoration, the Materials Technology Institute, Dow Chemical Company, Dupont, and Phillips. The program allows users to view the reactivity hazards of individual chemicals and to predict the hazards that could occur if chemical substances were to mix. The key features of the software are [39]: • Chemicals: The CRW contains a database of chemical datasheets for thousands of chemicals which describe their reactive hazards, such as flammability, peroxidizability, polymerizability, explosivity, strong oxidizer or reducer capability, water or air reactivity, pyrophoricity, known catalytic activity, instability, and radioactivity. Datasheets also contain general descriptions of the chemicals, their physical properties and toxicity information. • Mixtures of chemicals: The CRW includes a reactivity prediction worksheet which allows to simulate mixing of chemicals to find out dangers arising from accidental mixing. • Customized chemical datasheets: The chemical data sheets of CRW have been reduced to include primarily reactivity-related information allowing the user to add his/her own customized chemical datasheets to the database. The link to download the CRW is: https://www.aiche.org/ccps/resources/chemical-reactivity-worksheet (Accessed January 2021).

Protective Measures for Runaway Reactions Protective measures have been employed to ensure safe operation either to deal with or to mitigate the consequences of the runaway reaction. They are seldom used on their own and some preventive measures are usually included to reduce the demand on the protective system. Protective measures include emergency relief systems, quenching or inhibition and containment. It is important that a full evaluation of the hazards of the process is reviewed before

Chemical Kinetics and Reactor Design  1281 the type of protective measures is chosen. The identification and definition of the worst-case scenario is particularly important as any protective measure must be able to cope with this worst-case runaway reaction. Additionally, the course of the runaway reaction must be carefully analyzed and evaluated using Figure 11.22, and as illustrated in the literature [3, 36, 40–44] CCPS [45] provides potential failure mechanisms for reactors and suggests design alternatives for reducing the risks associated with such failures covering batch and semi-batch reactors, CSTR and PFR, plug flow tubular reactors, fixed and fluidized bed reactors and packed-tube reactors. However, generic failure scenarios pertaining to vessels and heat exchangers may also be applicable to reactors as detailed in this guideline. Table 11.8 shows some failure characteristics in reactors and details of these scenarios are provided elsewhere [45]. The following case study shows the consequences of the runaway reaction that happened at T2 Laboratories Inc., Jacksonville, Florida, as detailed in the CSB Investigation Report [46] (Courtesy of Chemical Safety and Hazard Investigation Board, CSB). T2 Laboratories manufactured Methylcyclopentadienyl Manganese Tricarbonyl (MCMT), which is a combustible liquid. The explosion at T2 laboratories was due to a runaway chemical reaction. In the incident, the reactor’s relief system could no longer control the rapidly increasing temperature and pressure of the runaway reaction. The explosion killed the owner/chemical engineer and process operator who were in the control room (50 ft. from the reactor) and two outside operators who were leaving the reactor area. Another outside operator and the plant mechanic were injured. Figures 11.23 and 11.24 show an aerial view of T2 Laboratories site and the control room after the explosion.

Explosibility

Detonation Deflagration

Chemical structure Oxygen balance High rate test Explosibility tests

Reaction profile

Normal reaction

Heat flow calorimetry Effect of change

Screen

Differential Scanning Calorimetry (DSC) Differential thermal analysis (DTA)

Identification of exothermic activity Programmed tests

Minimum exotherm temperature Establish minimum temperature

Adiabatic Dewar Adiabatic calorimetry

Gas evolution Adiabatic Dewar Consequence of runaway reaction

Temperature Adiabatic calorimetry Pressure

Figure 11.22  Typical testing procedure (Source: Barton and Rogers [38]).

Deviations

Overpressure (Batch, Semi-batch and CFSTR Reactors)

Overpressure (Batch and Semi-batch Reactors)

No.

1

2 Addition of a reactant too rapidly resulting in runaway reaction.

Loss of agitation resulting in runaway reaction or hot bearing/seals causing ignition of flammables in vapor space.

Characteristics

Table 11.8  Failure characteristics in Reactors [45].

• Manual activation of bottom discharge valve to drop batch into dump tank with diluent, poison or shortstopping agent, or to an emergency containment area. • Procedural controls of concentration of reactants.

• Pressure or temperature sensors actuating bottom discharge valve to drop batch into a dump tank with diluent, poison or shortstopping agent, or to an emergency containment area. • Automatic addition of diluent, poison, or short-stopping agent directly to reactor. • High flow shutdown alarm and interlock. • Vessel design accommodating maximum expected pressure. • Select feed system pressure so that feed cannot continue at reactor overpressure. • Use different type of reactor.

(Continued)

• Manual addition of diluent, poison, or short-stopping agent directly to reactor. • Manual shutdown on high flow alarm.

• Operators to visually check mechanical seal fluid on regular basis. • In-vessel agitation (velocity) sensor with alarm. • Mechanical seal fluid reservoir low level sensor with alarm. • Speed or vibration sensor with alarm. • Manual activation of bottom discharge valve to drop batch into dump tank with diluent, poison, or shortstopping agent, or to an emergency containment area. • Manual activation of inert gas sparging of reactor liquid to effect mixing.

Procedural

• Temperature or pressure sensor interlocked to a shutoff valve in the feed line. • Emergency relief device.

• Agitator power consumption or rotation indication interlocked to cutoff feed of reactants or catalyst or activate emergency cooling. • Uninterrupted power supply backup to motor. • Emergency relief device. • Pressure or temperature sensors actuation bottom discharge valve to drop batch into a dump tank with diluent, poison, or shortstopping agent, or to an emergency containment area. • Inerting of vapor space. • Provide nitrogen buffer zone round seal using enclosure around seal. • Automatic agitator trip on low agitation (velocity) sensor, low, seal fluid, or low shaft speed.

Active

• Limit delivery capacity of feed system to within safe feed rate limitations (e.g., screw feeder for solids or flow orifice for liquids).

• Vessel design accommodating maximum expected pressure. • Use different type of reactor (plug flow). • Alternative agitation methods (e.g., external circulation eliminates shaft seal as a source of ignition in vapor space).

Inherently Safer/Passive

Procedural design solutions

1282  Chemical Process Engineering

Deviations

Overpressure (Batch, Semi-batch and Plug flow reactors)

Overpressure (Batch and Semi-batch Reactors)

No.

3

4 Overcharge or overfeed of reactant resulting in runaway reaction.

Overcharge of catalyst resulting in runaway reaction.

Characteristics

Table 11.8  Failure characteristics in Reactors [45]. (Continued)

• Use of dedicated reactant charge tank sized only to hold amount of reactant needed. • Vessel design accommodating maximum expected pressure. • Use of continuous reactor.

• Use dedicated catalyst charge tank sized to hold only the amount of catalyst needed. • Vessel design accommodating maximum expected pressure. • Use different type of reactor.

Inherently Safer/Passive

• Emergency relief device. • Reactant feed charge interlocked via feed totalizer or weight comparison in charge tank. • Pressure or temperature sensors actuating bottom discharge valve to drop batch into a dump tank with diluent, poison, or shortstopping agent or to an emergency containment area. • Automatic addition of diluent poison, or short-stopping agent directly to reactor.

• Emergency relief device • Pressure or temperature sensors actuating bottom discharge valve to drop batch into a dump tank with diluent, poison or shortstopping agent, or to an emergency containment area. • Automatic addition of diluent, poison or short-stopping agent directly to reactor. • Limit quantity of catalyst added by flow totalizer.

Active

Procedural design solutions

(Continued)

• Manual feed charge shutdown via indication from feed totalizer or weight comparison in charge tank. • Manual activation of bottom discharge valve to drop batch into dump tank with diluent, poison, or shortstopping agent, or to an emergency containment area.

• Procedural controls on the amount or concentration of catalyst to be added. • Manual activation of bottom discharge valve to drop batch into dump tank with diluent, poison, or shortstopping agent, or to an emergency containment area. • Manual addition of diluent, poison, or short-stopping agent directly to reactor. • Intermediate location of pre-weighed catalyst charges.

Procedural

Chemical Kinetics and Reactor Design  1283

Deviations

Overpressure

Overpressure

No.

5.

6. Loss of cooling resulting in runaway reaction.

Addition of incorrect reactant resulting in runaway reaction.

Characteristics

Table 11.8  Failure characteristics in Reactors [45]. (Continued)

• Vessel design accommodating maximum expected pressure.

• Use of dedicated feed tank and reactor for production of one product. • Vessel design accommodating maximum expected pressure. • Elimination of cross-connections. • Use of dedicated hoses and incompatible couplings for reactants where hose connections are used.

Inherently Safer/Passive

• Loss coolant flow or pressure or high reactor temperature to actuate secondary cooling medium via separate supply line (e.g. city water or fire water). • Automatic isolation of feed on detection of loss of cooling. • Emergency relief device. • Pressure or temperature sensors actuating bottom discharge valve to drop batch into a dump tank with diluent, poison or shortstopping agent, or to an emergency containment area (not be effective for systems such as polymerization reactions where there is a significant increase in viscosity). • Automatic addition of diluent poison, or short-stopping agent directly to reactor.

• Emergency relief device. • Automatic feed shutdown based on detection of unexpected reaction progress (i.e. abnormal heat balance).

Active

Procedural design solutions

(Continued)

• Manual activation of secondary cooling system. • Manual activation of bottom discharge valve to drop batch into dump tank with diluent, poison or shortstopping agent, or to an emergency containment area. • Manual addition of diluent, poison, or short-stopping agent directly to reactor.

• Procedures to shutdown feed based on indication of unexpected reaction progress. • Procedure for double checking reactant identification and quality. • Dedicated storage areas/ unloading facilities for reactants.

Procedural

1284  Chemical Process Engineering

Deviations

Overpressure (Batch and Semi-batch)

Overpressure

Over-pressure

No.

7.

8.

9. External fire initiates runaway reaction.

Feed of monomer emulsion breaks into a separate oil phase on top of a water phase while being fed to the reactor leading to runaway reaction.

Reactants added in incorrect order.

Characteristics

Table 11.8  Failure characteristics in Reactors [45]. (Continued)

• Fireproof insulation (reduced heat input). • Slope-away grading under reactor to remote spill collection. • Locate reactor outside of fire affected zone.

• Vessel design accommodating the maximum pressure arising from run-away reaction of bulk (nonemulsified) monomer phase. • Static mixer ahead of reactor.

• Vessel design accommodating maximum expected pressure.

Inherently Safer/Passive

• Automatically activated fixed fire protection – water spray (deluge) and/ or foam systems. • Emergency relief device. • Automatic reactor dump to dump tank with diluent, poison, or short stopping agent. • Automatic injection of diluent poison or short-stopping agent into reactor.

• Emergency relief device. • Automatic feed shut-off or dumping on change of heat balance.

• Sequence control via programmable logic controller. • Interlock shutdown of reactant addition based on detection of mis-sequencing. • Automatic isolation of feed based on detection of unexpected reaction progress (i.e. abnormal heat balance).

Active

Procedural design solutions

• Manual activation of fixed fire protection. • Manual reactor dump to dump tank with diluent, poison or short-stopping agent. • Manual injection of diluent, poison or short-stopping agent into reactor.

• Operator samples the monomer emulsion feed and observes that sample is stable without agitation for a predetermined length of time before feed is begun. • Manual feed shut-off or dumping on change of heat balance.

• Manual isolation of feed based on detection of unexpected reaction progress. • Manual isolation of feed based on indication of mis-sequencing.

Procedural

Chemical Kinetics and Reactor Design  1285

1286  Chemical Process Engineering

Figure 11.23  Aerial photography of T2 Laboratories (Source: www.csb.gov [46]).

Figure 11.24  Control room (Source: www.csb.gov [46]).

Chemical Kinetics and Reactor Design  1287 Figure 11.25 shows a photo of the fire after the explosion at T2 laboratory Inc. The explosion leveled the plant, propelling debris in all directions (Figure 11.26). Two large steel support columns from the reactor structure traveled about 1,000 ft. along the site plant road in both directions, and a 2,000-lb section of the 3-inch-thick reactor (Figure 11.27) impacted railroad tracks adjacent to T2 site, pushing a rail out of place, before impacting and damaging a building about 400 ft. from the reactor. The explosion threw piping from inside the reactor hundreds of feet onto the other businesses and wooden areas surrounding T2 site. The 4-inch diameter agitator shaft from the reactor was thrown about 350 ft. across the road in two large pieces that imbedded in a sidewalk and the ground (Figure 11.28).

Injured Killed Faye R oa

Building damaged Building condemned

d

T2 Reactor

Railro

ad Tr ack

250 feet

Figure 11.25  Injury and business locations (Source: www.csb.gov [46]).

Figure 11.26  Jackson Fire Rescue Department (JFRD) responders in Self Containing Breathing Apparatus (SCBA) battle fire (Source: www. csb.gov [46]).

1288  Chemical Process Engineering

Figure 11.27  Portion of the 3-inch thick reactor (Source: www.csb.gov [46]).

Figure 11.28  Agitator shaft pieces (Source: www.csb.gov [46]).

PROBLEMS AND SOLUTIONS Example 11.1 Calculate the heat of reaction per mole of N2 reacted for the synthesis of ammonia from nitrogen and hydrogen (N2 + 3H2 → 2NH3) at 1 atm and 155°C [3]. The heats of formation and heat capacities of the components are given in Table 11.9.

Solution The Excel spreadsheet program, Example 11.1.xlsx, determines the values of the standard heat of reaction and the heat of reaction at 155°C. The value of heat of reaction at the reference temperature is -22,040 kcal per kmol of N2

Chemical Kinetics and Reactor Design  1289 Table 11.9  Heats of formation and heat capacities of the components. Component

∆H 0rxnT kcal/kmol

Cp, kcal/kmol ∙ K

N2(g)

0.0

6.457 + 1.39 × 10 3T − 0.069 × 10 6T2

H2(g)

0.0

6.946 − 0.196 × 10 3T + 0.476 × 10 6T2

NH3(g)

-11,020

5.92 + 8.963 × 10 3T − 1.764 × 10 6T2

reacted. The minus sign shows that the reaction is exothermic. The value of the heat of reaction at 155 °C is calculated -23,326 kcal per mole of N2 reacted. For the reaction given in this problem, the standard heat of reaction is:

(



∆H0R = 2 ∆H0f

)

NH3

(

)

(

)

− 3 ∆H0f H2 − ∆H0f N 2

(11.45)

Figure 11.29 shows the snapshot of the Excel spreadsheet calculations of the heat of reaction. The UniSim Design program, Example 11.1.usc, determines the values of the standard heat of reaction and the heat of reaction at 155°C using the conversion reactor. The following steps are followed to simulate the reactor: 1. 2. 3. 4. 5. 6. 7. 8.

 pen a new case. O Add a new component list and choose all components from the Components list. Select the Fluid Package (make sure selecting Component List -1 in the component list). Add a new Fluid Package and select the Peng Robinson from the Fluid Package. Close the Fluid Package by clicking on cross button. Go to the Reaction button, choose “add Rxn” button to enter the reaction data. Select the Conversion Reaction and then click on the Add Reaction button. Select the components from the drop-down menu and then enter the stoichiometry (-1 for N2, -3 for H2 and +2 for NH3). At this stage, the standard heat of reactions can be obtained from the thermodynamic calculations as shown in Figure 11.30.

Once the stoichiometric coefficients are provided, the Balance Error cell will show zero, which indicates that the reaction is mass balanced. The UniSim Design simulator will also calculate and display the heat of reaction in the

Figure 11.29  Snapshot of the Excel spreadsheet calculations of the heat of reaction.

1290  Chemical Process Engineering

Figure 11.30  The Stoichiometry tab for the Conversion Reaction (Courtesy of Honeywell UniSim Design software. Honeywell UniSim Design are registered trademarks of Honeywell International Inc.).

and

Reaction Heat cell. For this problem, the value of heat of reaction at the reference temperature is - 2.2×10-4 kcal per kmol of N2 reacted. The result is very close to the Excel spreadsheet calculations. The simulation is now continued to calculate the heat of reaction in the simulation environment. 9. C  lick on the Basis button, select Base Component (N2) from drop down menu and enter the conversion for the base component (100 %). 10. Close the active window and return to the following window: The reaction Rxn-1 is added. Add a reaction set by clicking on the Add Set button. 11. In the Active List, select Rxn-1 from the drop down menu. Check mark the reaction set and close the active window. 12. Click on the Add FP button (This makes the reaction available for the simulation). 13. Click on Add Set to Fluid Package Button. 14. The Basis-1 property model is now added to the Fluid Package. Then Enter to Simulation Environment (Figure 11.31). 15. Go to Tools/Preference to change the Unit Set to EuroSi (to show Q in kcal/h).

Figure 11.31  Reactions tab in the Simulation Basis Manager window (Courtesy of Honeywell UniSim Design software. Honeywell UniSim Design are registered trademarks of Honeywell International Inc.).

and

Chemical Kinetics and Reactor Design  1291 16. Draw the flowsheet with the heat and stream materials and enter the information as explained in Chapter 1 (P = 1 atm, T = 25 or 155 °C, N2 = 1 kmol/h, and H2= 3 kmol/h). Use the Set function to relate the output temperature of Stream Vap to feed temperature as explained in Chapter 1 (Figure 11.32). 17. If we consider the input temperature equal to T, the value of heat stream (Q-100) divided to the flow of N2 in the feed stream shows the heat of reaction at T. If T=25°C, the value would be -2.188×104 kcal/ kmol which is the standard heat of reaction. For T=155 °C, the value is -2.312×104 kcal/kmol which shows the heat of reaction at 155 °C. 18. With the simulation, we can also plot the variation of heat of the reaction as a function of temperature in the Data Book with case studies option in the simulator as explained in chapter 1. In Figure 11.33, the value of the heat of reaction is calculated in the UniSim Design spreadsheet and then it is exported to data book (Ctrl-D) as dependent variable. The feed temperature, which also shows the reactor temperature, is considered as independent variable. 19. The results are illustrated in Figure 11.34. The values of the heat of the reaction are calculated and are shown in Table 11.10. As seen in this table, the results are identical and are almost the same as those calculated from other programs and spreadsheet.

Example 11.2 Calculate the adiabatic flame temperature for the combustion of propane with air and plot its variation as a function of excess air in the range of -50 to 250%. The feed enters the reactor at T=25°C and P=1 atm where the following reaction occurs:

C3H8 + 5O2 → 3CO2 + 4H2O

Figure 11.32  The Conversion Reactor in the PFD of UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell UniSim Design are registered trademarks of Honeywell International Inc.).

(11.46)

and

1292  Chemical Process Engineering

Figure 11.33  Adding the data for independent variable in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Heat of reaction (kcal/kmol)

Case Study 1 –2.120e+004

Heat of reaction (kcal/kmol)

–2.140e+004 –2.160e+004 –2.180e+004 –2.200e+004 –2.220e+004 –2.240e+004 –2.260e+004 –2.280e+004 –2.300e+004 –2.320e+004 –40.00

–20.00

0.0000

20.00

40.00

60.00

80.00

100.0

120.0

140.0

160.0

Temperature (C)

Figure 11.34  A plot of Heat of reaction with Temperature (Courtesy of Honeywell UniSim Design software. Honeywell Design are registered trademarks of Honeywell International Inc.).

and UniSim

Solution The UniSim Design program, Example 11.2.usc, shows the results for both cases. 1. W  ith the procedure shown in the previous example and steps explained in Chapter 1, all components are entered to the simulation, the proper physical property model (Peng- Robinson Equation of state) is chosen and the reaction is defined with 100% conversion with propane as base component. We then enter to Simulation Environment (Figure 11.35): 2. Draw the flowsheet with the heat and stream materials and enter necessary input data as explained in Chapter 1 (P=1 atm, T=25°C, air consists of 79% nitrogen and 21% oxygen, mole flow of propane is 1 kmol/h). As discussed in the text, the reactor is considered adiabatic and no heat flow is needed. The total air flow rate is calculated in the UniSim Design spreadsheet (Figure 11.36) and it is then exported to flowrate cell in the Air stream:

Chemical Kinetics and Reactor Design  1293 Table 11.10  Calculated heat of the reaction. ∆H 0rxnT (kcal/kmol)×10-4 Temperature (°C)

Excel spreadsheet

UniSim Design software

UniSim (Basis)

FORTRAN [3]

25

-2.204

-2.188

-2.2

-2.204

155

-2.333

-2.312

-

-2.323

Figure 11.35  The Simulation Basis Manager window (Courtesy of Honeywell UniSim Design software. Honeywell are registered trademarks of Honeywell International Inc.).

and UniSim Design

Figure 11.36  Calculation of the total air flow rate in the UniSim Design spreadsheet (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

1294  Chemical Process Engineering

v Figure 11.37  PDF for the calculation of AFT in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell Design are registered trademarks of Honeywell International Inc.).

and UniSim

Figure 11.38  Independent Variable Setup and plot of Temperature versus Excess-Air (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

3. The simulation flowsheet looks like the following Figure. The program calculates the adiabatic flame temperature (AFT) equal to 2091°C with zero excess air as shown in cell B6 in the spreadsheet (Figure 11.37). 4. If the excess air is varied from -50 to 250% in the spreadsheet with the case study option (Ctrl-D), we can then see the variation of adiabatic flame temperature as a function of the excess air. The excess air equal to zero shows the adiabatic flame temperature in stochiometric conditions as calculated before. As seen in Figure 11.38, the maximum AFT for a given mixture occurs on stoichiometric conditions in which all fuel and all oxidizer are consumed. The amount of excess air can be varied as part of the design to control the AFT. Therefore, by increasing the excess air, the AFT drops because the part of reaction energy is consumed to heat up the excess air.

Example 11.3 Styrene is widely used in the production of many plastics. It is made from the gas phase dehydrogenation of ethylbenzene:

Chemical Kinetics and Reactor Design  1295

C6 H5 – C2 H5 → C6 H5 – CH = CH2 + H2

(11.47)

The conversion of this reaction is limited by equilibrium with the following Equation.



ln(K) = −13.21 −

13,122.5 + 4.354 ln(T) − 0.0033T T

(11.48)

The pure ethylbenzene with molar flow rate of 152.2 mol/s enters to an isothermal equilibrium reactor at 880 K and 1.378 bar. Using the reaction with corresponding equilibrium data and the UniSim Design software library of reactions, calculate the conversions and compare the results with those reported in the literature [47].

Solution The UniSim Design Program, Example 11.3.usc, shows the conversion results for both cases and compared the results with those reported in the literature. With the procedure shown in previous examples, all components are entered to the simulation, and the PRSV Equation of state is chosen as the fluid package. This is the Peng-Robinson Equation of state modified by Stryjek and Vera [48] representing the nonpolar, polar non-associating and associating compounds by the cubic equation of state. 1. I n this example, the equilibrium Equation is introduced to the simulator. There are two ways to introduce the equilibrium constants; these should be either entered by the user or if one chooses the reaction from the UniSim Design library, those constants will be chosen from the UniSim Design library and bring all equilibrium data available for the reaction. The Equilibrium Reaction window contains five tabs. The Stoichiometry and Basis tabs are like the Conversion Reaction as explained earlier. For this problem, we need two reactions, one with stoichiometry and user Keq from Equation 11.48 (case 1) and second reaction is chosen from the library (case 2). In case 1, the equilibrium coefficients are entered in Keq tab as shown in Figure 11.39: In case 2, the predefined equilibrium reaction is chosen from the Library tab and is then added to the simulation by clicking on Add Library Rxn (Figure 11.40). The UniSim Design program then determines Keq from the Ideal Gas Gibbs Free Energy Coefficients. 2. For both cases separately, we now need to close the active windows. At this stage, by clicking on Add Set in the Reaction Sets, a new reactions set is added, and it is associated to fluid Pkgs by clicking on add to FP (Figure 11.41). The reaction is now available for the simulation. After completing these steps, enter to Simulation Environment:

Figure 11.39 Keq tab in the Equilibrium Reaction window of UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

1296  Chemical Process Engineering

Figure 11.40  Library Equilibrium Reactions window in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Figure 11.41  Reactions tab in the Simulation Basis Manager window in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Figure 11.42  The flowsheet and spreadsheet results (Courtesy of Honeywell UniSim Design software. Honeywell are registered trademarks of Honeywell International Inc.).

and UniSim Design

Chemical Kinetics and Reactor Design  1297 Table 11.11  The conversion results for the Equilibrium reactor. UniSim Desing software Hand calculation [47]

Keq

Library

HYSYS [47]

37.4

37.44

40.03

40.03

The procedure is repeated for both reactions in order that they become available for the simulation. 1. D  raw the flowsheet with the heat and stream materials and enter necessary information to define the feed stream and reactors. The feed consists of pure ethylbenzene with molar flow rate of 152.2 mol/s which enters to the reactor at 880 K and 1.378 bar. By entering the input data and choosing the reaction set, the simulation of both reactors can be completed. The flowsheet and results are shown in Figure 11.42. Table 11.11 compares the results obtained by the UniSim Design (Keq and Library reaction) and hand calculations: As seen in this table, the results are identical and are almost the same from various ways of calculations.

Example 11.4 Repeat the previous problem with the Gibbs Reactor and compare the overall conversion and exit concentration of the vapor stream with the Equilibrium Reactor for similar input data.

Solution The UniSim Design Program, Example 11.4.usc, shows the overall conversion results and exist composition of both reactors. The solution for the Equilibrium Reactor is obtained in the previous problem. Since the Gibbs reactor does not need any reactions, we only need to choose the unit operation and connect the inlet and outlet stream. We will start with the previous problem where all components are entered to the simulation, the PRSV equation of state is chosen as the fluid package and the feed stream is defined. 1. In this example, the Gibbs Reactor is installed to the simulation. Draw the flowsheet with the heat and stream materials and enter necessary information to define the feed stream and the reactor. The feed for both reactors consists of pure ethylbenzene with molar flow rate of 152.2 mol/s which enters to the reactor at 880 K and 1.378 bar. The flowsheet and conversion results are shown in Figure 11.43. Since we did not define the reaction for the Gibbs Reactor, the overall conversion cannot be obtained from the simulator for a given reaction and it can be calculated by the minimization of Gibbs free energy of all components. On the molar flow rate of ethylbenzene in the input and exit streams. The exit composition of vapor stream for both reactors are given in Table 11.12: Notice that the results are close together and for the Gibbs Reactor, we did not specify the stoichiometry of the reaction and only the reactor temperature and pressure, or pressure and enthalpy are needed. It is worthy to mention that the differences shown in the table contributed to the choice of the property package. The Gibbs reactor considers any non-ideal behavior predicted by a thermo package such as Peng-Robinson. An ideal fluid package like Antoine would give the same results for these two reactors.

Example 11.5 The vapor-phase reaction of acetone is conducted in an adiabatic tabular reactor as:

CH3 COCH3 → CH2CO + CH4

(11.49)

1298  Chemical Process Engineering

Figure 11.43  The flowsheet and conversion results window in UniSim Design soft (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Table 11.12  Comparison of Equilibrium and Gibbs Reactor. Exit mole fraction Component

Equilibrium

Gibbs

Ethylbenzene

0.428

0.430

Styrene

0.286

0.285

Hydrogen

0.286

0.285

This reaction is first-order with respect to acetone with the following reaction rate:

ln(k) = 34.34 −



34222 T

(11.50)

where: k is the rate constant (s-1) and T is temperature in Kelvin. The feed stream, which consists of pure acetone with the mass flow rate of 7,850 kg/h, enters the reactor at 1035 K and 162 kPa. The reactor consists of a bank of 1000 one-inch schedule 40 tubes with the volume of 1 m3 [4]. a. C  alculate the conversion of the adiabatic reactor. b. Plot the actual conversion as a function of volume. c. What would be the volume of the reactor to reach the conversion of 20%?

Solution The UniSim Design Program, Example 11.5.usc, shows the results for all three cases as detailed below: 1. W  ith the procedure shown in previous example and steps explained in Chapter 1, all components are entered to the simulation, and the physical property model is chosen. The choice of the physical property model is important for the gas phase cracking problem, therefore, the PRSV Equation of state is selected.

Chemical Kinetics and Reactor Design  1299 2. S ince the kinetic data is available, in the Reactions tab, the kinetic reaction is chosen (Figure 11.44). 3. Add Reaction and then enter the stoichiometry data as shown in Figure 11.45. 4. In the Basis tab, enter Basis, Base Component, Rxn Phase, Base Units and Rate Units as shown in Figure 11.46. 5. In the Parameters tab, the kinetic data explained in Equation 11.7 including A, E and β should be entered. These are the constants of the modified Arrhenius kinetic equation. Since the kinetic equation given in this problem is not in the form of Arrhenius kinetic equation, it should be rearranged to this form for the extraction of the constants needed for the simulation. Rearranging the Equation 11.48 gives:



34222  34,222  → k = 8.211014 exp  − →  T T   284,522  k = 8.21014 exp  −   RT 

ln(k) = 34.34 −

Figure 11.44  Reactions tab in the Simulation Basis Manager window (Courtesy of Honeywell UniSim Design software. Honeywell UniSim Design are registered trademarks of Honeywell International Inc.).

(11.51)

and

Figure 11.45  Stoichiometry tab in Kinetic Reaction window in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

1300  Chemical Process Engineering

Figure 11.46  Basis tab in Kinetic Reaction window in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell UniSim Design are registered trademarks of Honeywell International Inc.).

and

where: A = 8.2×1014 E = 284,522 kJ/kmol R = 8.314 J/mol.K β=0 The constants A, E and β are now entered to Parameters tab for the forward reaction. Since there is no reverse reaction for this problem, the corresponding cells will be kept as is . This completes the definition of the kinetic reaction as shown in Figure 11.47: 6. C  lose the active window. As explained earlier, at this stage, by clicking on Add Set in the Reaction Sets, new reactions set is added, and it is associated to fluid Pkgs by clicking on add to FP. The reaction is now available for the simulation. After completing these steps, enter to Simulation Environment (Figure 11.48): 7. Draw the flowsheet with the heat and stream materials and enter necessary information to define the feed stream and reactor. Feed consists of pure acetone with mass flow of 7850 kg/h, P = 1 62 kPa, T = 1035 K. The reactor is considered adiabatic with no heat flow and consists of a bank of 1000 oneinch schedule 40 tubes (d =1.05 in = 0.0267 m) with the volume of one cubic meter. The reaction set ­(set-1), should be attached to the reactor as explained earlier. The flowsheet for part a) looks like as Figure 11.49: 8. The program calculates the reactor conversion equal to 18.16% (Figure 11.50). Since ketene is an unstable component in the product tending to explode, at the industrial scale the conversion should be kept low for safety considerations. 9. For part b), the conversion is plotted versus the reactor volume using the case study feature. The reactor volume and the actual % conversion are chosen as the independent dependent variables respectively as shown below (Figure 11.51) with a plot:

Chemical Kinetics and Reactor Design  1301

Figure 11.47  Parameters tab in Kinetic Reaction window in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Figure 11.48  Reactions tab the Simulation Basis Manager window in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

10. For part c), the volume of the reactor is calculated with Adjust feature explained in Chapter 1 as shown in Figure 11.52: 11. The program calculates the reactor volume of 1.495 m3 for the conversion of 20% (Figure 11.53). The solution of this problem is also reported by Fogler [4] and is in good agreement.

Example 11.6 Repeat the Example 11.5 with one PFR, one CSTR and four CSTRs with the volume of 1.5 m3, pressure drop of zero and similar feed conditions and compare the results.

Solution The UniSim Design program, Example 11.6.usc, shows the results for all three cases as shown in Figures 11.49– 11.54. Start with the previous example where the components, fluid package and reaction are introduced. It is worth mentioning that when we use 4 CSTRs, the volume of each CSTR would be 0.25×1.5 m3.

1302  Chemical Process Engineering As shown in Figure 11.55, the conversion for CSTR is smaller than that for PFR and the overall conversion forfour CSTRs lies between the conversion of CSTR and PFR. This is the case when kinetic orders are positive. On the other hand, the choice of the reactor would affect the conversion. For the constant conversion, the volume of PFR is smaller than the volume of CSTR and this leads to a significant reduction in the capital expenditure of a project.

Figure 11.49  Rating tab in PFR window in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell Design are registered trademarks of Honeywell International Inc.).

and UniSim

Figure 11.50  Reactions tab in PFR window in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell Design are registered trademarks of Honeywell International Inc.).

and UniSim

Chemical Kinetics and Reactor Design  1303

Figure 11.51  Independent Variable Setup and a plot of conversion versus volume (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Figure 11.52  Connection tab in Adjust window of UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell UniSim Design are registered trademarks of Honeywell International Inc.).

Figure 11.53  Monitor tab in Adjust window of UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell Design are registered trademarks of Honeywell International Inc.).

and

and UniSim

1304  Chemical Process Engineering

Figure 11.54  PFR, CSTR and cascade of CSTRs in PFD of UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Figure 11.55  Spread calculations for PFR and CSTRs in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell UniSim are registered trademarks of Honeywell International Inc.).

and

Example 11.7 Consider the following catalytic reaction for the gas-phase oxidation of chloroform [49]:

2CHCl3 + 2H2 O + O2 → 2CO2 + 6HCl The kinetics of the reaction is expressed as:

(11.52)

Chemical Kinetics and Reactor Design  1305

Figure 11.56  Stoichiometry tab in the Heterogeneous Catalytic Reaction window in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim are registered trademarks of Honeywell International Inc.).

 21,700  3.72 × 105 exp  −  C CHCl3  RT  r=    2,440   5,330  3 3 C 1.23 10 exp 1 5.97 10 exp + × + × HCl     C CHCl3    RT  RT 



(11.53)

kmol where: r is the rate of reaction  3   ms kmol  C is the concentration   m3  J  E is the activation energy   mol  The feed stream consists 40, 40 and 20 kmol/h of CHCl3, H2O and O2 respectively and enters to an isothermal reactor with the volume of 0.25 m3 at T = 100°C and P = 1 bar. If the reaction takes place in a gas phase, calculate the conversion for PFR and CSTR reactors with no pressure drop.

Solution The UniSim design program, Example 11.7.usc, shows the results for both reactors. With the procedure shown in an earlier example, all components are entered to the simulation, and the PSRV Equation of state is chosen as the fluid package. 1. S ince the kinetic data for the catalytic reaction is available, in the Reactions tab, the Heterogeneous Catalytic is chosen. The heterogeneous Catalytic Reaction window contains 4 tabs to be filled out as shown in Figure 11.56: a. I n the Stoichiometry tab, the stichometry data for the reaction are entered and this allows the standard heat of the reaction is calculated. The reaction is exothermic with the negative sign shown in the Reaction Heat (25°C) cell. b. In the Basis tab, the Basis, Base Component, Reaction (Rxn) Phase, Basis Units and Rate Units are chosen. It is worth mentioning that the choice of Basis and Rate Units is very important since this determines the units for rate constants (Figure 11.57). c. In the Numerator tab, the kinetic data are introduced as shown in Figure 11.58. The constants A, E and β are the constants of the modified Arrhenius kinetic equation and entered for the Forward Reaction in the same way we introduced in kinetic reactions in Parameters tab. Since there is no Reverse Reaction for this example, the corresponding cells for kinetic data and reaction order will be kept .

1306  Chemical Process Engineering

Figure 11.57  Basis tab in the Heterogeneous Catalytic Reaction window in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Figure 11.58  Numerator tab in the Heterogeneous Catalytic Reaction window in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Figure 11.59  Denominator tab in the Heterogeneous Catalytic Reaction window in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Chemical Kinetics and Reactor Design  1307 d. In the Denominator tab, the adsorption term is introduced as shown in Figure 11.59. This is the only tab that differs with kinetic reactions and should be filled with care as it shows the effect of mass transfer related to the presence of the catalysts. 2. C  lose the active window. As explained before, at this stage, by clicking on Add Set in the Reaction Sets, new reactions set is added, and it is associated to fluid Pkgs by clicking on add to FP. The reaction is now available for the simulation as in chapter 1. After completing these steps, enter to Simulation Environment (Figure 11.60): 3. Draw the flowsheet with the heat and stream materials and enter necessary information to define the feed stream and reactors. Feed consists 40, 40 and 20 kmol/h of CHCl3, H2O and O2 respectively, the reactor is isothermal with the volume of 0.25 m3 operating at T = 100°C and P = 1 bar. The flowsheet and conversion results are shown in Figure 11.61:

Example 11.8 N-butane (A) is converted to i-butane (B), which is a valuable product used in the manufacture of gasoline additives [4]. Th reversible reaction (A ↔ B) takes place in an adiabatic plug-flow reactor in the liquid phase at high pressure. This reaction rate is given with the following expression:

Figure 11.60  Reactions tab in the Simulation Basis Manager window in Unisim Design (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Figure 11.61  Spreadsheet calculations for the calculation of PFR and CSTR volumes (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

1308  Chemical Process Engineering



C   kmol   −rA = k  C A − B   3   K  m h 

(11.54)



J    65,700    mol   1 − 1   ,R = 8.314  J .K  k = 31.1exp  −    mol  R T 360     

(11.55)



1   6,900[J/ mol]  1 −  K = 3.03exp  −   R 333 T  

(11.56)

The feed consists a mixture of 90% (mol) A and 10% (mol) B with flow rate of 163 kmol/h enter the reactor at 330 K and 15 atm. If the pressure drop in the reactor is neglected. a. C  alculate the PFR volume necessary to reach 70% conversion of n-butane. b. Plot the conversion and temperature down the volume of the reactor.

Solution The UniSim Design Program, Example 11.8.usc, shows the results for both cases. With the procedure shown in previous examples, all components are entered to the simulation, and the PR Equation of state is chosen as the fluid package. 2. S ince the form of kinetic expression is different from kinetic and heterogenous forms, in the Reactions tab, the Simple Rate is chosen. The Simple Rate Reaction window contains 3 tabs to be filled out as shown in Figure 11.62: a. Th  e Stoichiometry tab is exactly like the reactions explained before where the Stoichiometry Coefficients are entered with negative and positive signs (i.e., negative for reactants and positive for products).

Figure 11.62  The Stoichiometry tab in the Simple Rate Reaction window (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Chemical Kinetics and Reactor Design  1309 b. I n the Basis tab, the Basis, Base Component, Reaction (Rxn) Phase, Basis Units and Rate Units are chosen (Figure 11.63). It is worth mentioning that the choice of Basis and Rate Units is very important since this determines the units for rate constants. c. In the Parameters tab, the data for forward reaction and reverse reaction are provided. This differs from the Parameters tab of the Kinetic Reaction, since here, the Reverse Reaction is defined based on equilibrium constant as explained in kinetic type section under the Simple rate. The kinetic expressions for forward reaction (k) and reverse reaction (K) provided in the problem (Equation 11.52 and Equation 11.53) are not ready to be used and these should be transformed to the suitable formats for the UniSim Design simulator. For k (forward reaction)

1   65,700  1 k = 31.1exp  −  −   R T 360    65,700   65,700  = 31.1exp  exp   RT   8.314 360 



(11.57)

 65,700  = 1.1 1011 exp  −   RT  With this transformation, we will get the following data for simulator as:



A = 1.1×1011, E = 65,700 [J/mol], β = 0

(11.58)

For K (reverse reaction)



6,900  1   6,900  1  6,900  exp  −   = 3.03exp  K = 3.03exp  −    8.314 × 333   RT   R 333 T   830  6,900  → ln(K) = −1.4 + = 0.25exp   8.314 × T  T



(11.59)

With this transformation, we will get the following data for simulator as:



Aʹ = −1.4, Bʹ = 830, Cʹ = 0, Dʹ =0

Figure 11.63  The Basis tab in the Simple Rate Reaction window (Courtesy of Honeywell UniSim Design software. Honeywell UniSim Design are registered trademarks of Honeywell International Inc.).

(11.60)

and

1310  Chemical Process Engineering With these mathematical operations on kinetic expressions, we are now ready to enter the information to the Parameters tab as (Figure 11.64): 3. C  lose the active window. As explained before, at this stage, by clicking on Add Set in the Reaction Sets, new reactions set is added, and it is associated to fluid Pkgs by clicking on add to FP. The reaction is now available for the simulation. After completing these steps, enter to Simulation Environment (Figure 11.65): 4. Draw the flowsheet with the heat and stream materials and enter necessary information to define the feed stream and reactors. The feed consists a mixture of 90% (mol) n-Butane and 10%(mol) i-Pentane with flow rate of 163 kmol/h and enter the reactor at 330 K and 15 atm. If the pressure drop in the reactor is neglected. The flowsheet is shown in Figure 11.66. 5. For the solution of part a), the adjust function is used with the following Solving Parameters (Figure 11.67): The solution is shown in the Monitor Tab as (Figure 11.68): As shown in this Figure, in order to reach 70% conversion, the volume of the reactor would be 3.477 m3.

Figure 11.64  The Parameters tab in the Simple Rate Reaction window (Courtesy of Honeywell UniSim Design software. Honeywell UniSim Design are registered trademarks of Honeywell International Inc.).

and

Figure 11.65  The Reactions tab of the Simulation Basis Manager window (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Chemical Kinetics and Reactor Design  1311

Figure 11.66  The PFR reactors with/without the Adjust function (Courtesy of Honeywell UniSim Design software. Honeywell UniSim Design are registered trademarks of Honeywell International Inc.).

Figure 11.67  The Parameters tab in the Adjust function (Courtesy of Honeywell UniSim Design software. Honeywell are registered trademarks of Honeywell International Inc.).

and

and UniSim Design

6. F  or the solution of part b), the conversion and outlet temperature are plotted as a function of the reactor volume with case study feature explained in Chapter 1 (Figure 11.69). The hand calculation of this problem is rather tedious and time consuming as shown by Fogler in the tabs 512-518 [4]. Fogler’s results are slightly different from the UniSim Design results due to the differences in the estimation of physical properties which are the challenging part of the hand calculation. This problem can be also solved by Kinetic Reaction in the UniSim Design simulator, if the transformations are made to kinetic expressions to find the parameters of the forward and reverse reactions as required by the UniSim Design as explained in the standard kinetic form in the chemical reaction section of the book.

Example 11.9 100 lb/h methane is passing through 1.5-inch pipe with 60-ft length packed with catalyst pellets of 0.25 inch in diameter. The temperature is constant along the length of pipe at 200°F. The entering pressure is 200 psi. Plot the pressure drop as a function of void fraction in the range of 0.4-1.

1312  Chemical Process Engineering

Figure 11.68  The Monitor tab in the Adjust function (Courtesy of Honeywell UniSim Design software. Honeywell are registered trademarks of Honeywell International Inc.).

and UniSim Design

Figure 11.69  Case Studies Setup and a plot of conversion versus volume (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Solution The UniSim design program, Example 11.9.usc, shows the plot of the pressure drop as a function of bed void fraction for packed bed. The PFR reactor is used for this purpose with hypothetical kinetic reaction where the pressure drop is calculated with Ergun equation. In this example, the combustion of methane with oxygen is defined as the reaction. The kinetic data for this reaction are chosen in the way that no reaction occurs. This allows the simulator to calculate the pressure drop calculations. With the procedure shown in previous examples, all components including those added with reaction are entered to the simulation, and the PR equation of state is chosen as the fluid package. 1. Th  e Kinetic Reaction window contains 3 tabs to be filled out. The Stoichiometry and Basis tabs are exactly like the reactions explained before where the Stoichiometry Coefficients are entered with

Chemical Kinetics and Reactor Design  1313 negative and positive signs. In the Parameters tab, the data for Forward Reaction are provided as shown below (Figure 11.70).



A = 0, E = 1 1010 [J/mol], β = 0

(11.61)

With these data, no reaction occurs but the pressure drop calculations can be performed. 2. C  lose the active window. At this stage, by clicking on Add Set in the Reaction Sets, a new reactions set is added, and it is associated to fluid Pkgs by clicking on add to FP. The reaction is now available for the simulation. After completing these steps, enter to Simulation Environment (Figure 11.71): 3. Draw the flowsheet with the heat and stream materials and enter necessary information to define the feed stream and reactors. The feed contains methane with mass flow rate of 100 lb/h passing through 1.5 inch pipe with 60-ft length packed with catalyst pellets of 0.25 inch in diameter. The temperature is constant along the length of pipe at 200°F and the entering pressure is 200 psi. The reactor configuration data are entered in the Rating/Sizing tab as shown in Figure 11.72:

Figure 11.70  The Parameters tab in the Kinetic Reaction window (Courtesy of Honeywell UniSim Design software. Honeywell UniSim Design are registered trademarks of Honeywell International Inc.).

and

Figure 11.71  The Reactions tab in the Simulation Basis Manager window (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

1314  Chemical Process Engineering

Figure 11.72  The Rating tab in the PFR setup window in UniSim Design (Courtesy of Honeywell UniSim software. Honeywell UniSim Design are registered trademarks of Honeywell International Inc.).

and

Figure 11.73  The Design tab in the PFR setup window in UniSim Design (Courtesy of Honeywell UniSim Design software. Honeywell UniSim Design are registered trademarks of Honeywell International Inc.).

and

Choose the Ergun equation in the Design/Parameters tab for the calculation of pressure drop and enter the initial value of 0.5 for void fraction (11.73). In this tab the pressure drop is calculated as 56.77 psi for the void fraction of 0.5 as shown in Figure 11.73. 4. W  ith base case calculations, we can now choose the void fraction in the Tube packing section as the intendent and the pressure drop as the dependent variables respectively and plot the variation of pressure drop as a function of void fraction as shown in Figure 11.74: As seen in this Figure, as the bed voidage increase, the packed bed becomes less dense and the pressure drop decreases dramatically. However, the smaller the void fraction, the greater would be the pressure drop in the packed bed.

Chemical Kinetics and Reactor Design  1315

Figure 11.74  The Independent Variable Setup and a plot of pressure versus Bed voidage (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Example 11.10 A feed containing 100 kmol/h CO2 and 400 kmol/h H2 enters an isothermal catalytic bed with the diameter of 0.25 m at 314°C and 30 atm where the following gas phase reaction occurs:

CO2 + 4H2 → CH4 + 2H2O

(11.62)

Th reaction rate expression is:



−rCO2 =

7PCO2 PH42 [1 + 1.73PH2 + 0.3PCO2 ]5

  kmol  5   kg catalyst .h.atm 

(11.63)

The bed voidage (φ) and density of catalyst (ρcatalyst) are assumed 0.4 and 2,500 kg/m3, respectively [50]. What would be the catalyst weight to reach 20% conversion in the reactor?

Solution The UniSim Design program, Example 11.10.usc, shows the calculation of the weight of catalyst in the PFR reactor. The problem is like the catalytic reactions solved in previous examples with a small difference in the unit of the reaction rate expression. We can now transform the rate equation to the unit suitable for the UniSim design simulator using Equations 11.17 and 11.18.

− rCO2 =

= =

ρcatalyst × (1 − ϕ ) / ϕ × 7PCO2 PH42

[1 + 1.73PH

+ 0.3PCO2 ]

5

2

4 2500 × (1 − 0.4) / 0.4 × 7PCO2 PH2 )

[1 + 1.73PH2 + 0.3PCO2 ]

5

26,250PCO2 PH42

[1 + 1.73PH

2

+ 0.3PCO2 ]

5



(11.64)

  kmol  m3 .h. atm5   Gas 

The kinetic expression shown in Equation 11.64 is now used to define the Heterogeneous Catalytic Reaction and then the PFR reactor is applied to obtain the required results. With the procedure shown in previous examples, all components are entered to the simulation, and the PR Equation of state is chosen as the fluid package.

1316  Chemical Process Engineering

Figure 11.75  The Basis tab in the Heterogeneous Catalytic Reaction window (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

1. Th  e Heterogeneous Catalytic Reaction window contains four tabs to be filled out. The Stoichiometry tab is like the reactions explained before where the Stoichiometry Coefficients are entered with negative and positive signs. In the Basis tab, the following data are entered (Figure 11.75). In the Numerator tab (Figure 11.76), the data for Forward Reaction and the Forward Order are provided as shown below. In the Denominator tab (Figure 11.77), the following data are provided as shown below. 2. C  lose the active window. As explained before, at this stage, by clicking on Add Set in the Reaction Sets, new reactions set is added, and it is associated to fluid Pkgs by clicking on add to FP. The reaction is now available for the simulation. After completing these steps, enter to Simulation Environment (Figure 11.78): 3. Draw the flowsheet with heat and stream materials and enter necessary information to define the feed stream and reactor. The feed containing 100 kmol/h CO2 and 400 kmol/h H2 enters an isothermal PFR reactor with the diameter of 0.25 m at 314°C and 30 atm. The initial tube length is considered 2 m, the void fraction is 0.4, the solid density is 2,500 kg/m3 and the particles are considered spherical with diameter of 1 mm. The reactor configuration data are now entered in the Rating/Sizing tab as shown in Figure 11.79: In the Design/Parameters tab, set the pressure drop to zero (Figure 11.80).

Figure 11.76  The Numerator tab in the Heterogeneous Catalytic Reaction window (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Chemical Kinetics and Reactor Design  1317

Figure 11.77  The Denominator tab in the Heterogeneous Catalytic Reaction window (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

Figure 11.78  The Reactions tab in the Simulation Basis Manager window (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim Design are registered trademarks of Honeywell International Inc.).

4. A  t this stage, the base case calculation is performed, and it is time to use adjust feature to find the tube length for reaching 20% conversion. The simulation results and the weight of catalyst are shown in the spreadsheet (Figure 11.81): The weight of the catalyst to reach 20% conversion is 247.4 kg and this is the same as reported by hand calculations [50].

Example 11.11 The following multiple reactions take place in an adiabatic reactor:

CH4 + H2O → 3H2 + CO

CO + H2O → H2 + CO2

(11.65)

These reactions are mostly used in the early production stages of some chemicals, e.g., ammonia and methanol, starting with a Natural Gas feed. The first reaction is the endothermic reforming reaction in which methane is reacted

1318  Chemical Process Engineering

Figure 11.79  The Rating tab in the PFR window (Courtesy of Honeywell UniSim Design software. Honeywell registered trademarks of Honeywell International Inc.).

and UniSim Design

are

Figure 11.80  The Design tab in the PFR window (Courtesy of Honeywell UniSim Design software. Honeywell registered trademarks of Honeywell International Inc.).

and UniSim Design

are

with steam to form hydrogen and carbon monoxide. The second reaction is the exothermic water gas shift reaction limited by equilibrium in which the CO is converted to CO2. The rate expressions, kinetic and catalyst data for these reactions are (Table 11.13):



 E  k 01 exp  − 1  P.y CH4  RT  −r1 = 1 + K.P.y H2



y .y   E  −r2 = K 02 exp  − 2   y CO .y H2O − CO2 H2   RT   K eq  The feed of 2,000 mol/s enters to the reactor at 350°C and 30 atm with the following composition:

(11.66)

Chemical Kinetics and Reactor Design  1319

Figure 11.81  Calculations of Weight of Catalyst in the Spreadsheet window (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim are registered trademarks of Honeywell International Inc.).

Table 11.13  Kinetic and hydrodynamic data. Parameter

Symbol

Value

Unit

Particle Density

ρcata

3000

kg/m3

Pre-exponential Rate Constant, Reaction 1

k01

3.32×103

kmol/(kg.s.atm)

Activation energy, Reaction 1

E1

1 ×105

J/mol

Universal Gas Constant

R

8.314

J/mol.K

Pressure

P

30

atm

Adsorption parameter

K

4.053

atm-1

Pre-exponential Rate constant, Reaction 2

k02

2.95×105

kmol/(kg.s)

Activation energy, Reaction 2

E2

1.163×105

J/mol

Bed Voidage

ϕ

0.6

-

Spherical Particle Diameter

dp

1

mm

Equilibrium constant

Keq

4897   exp  −4.946 +   T 

( T in K)

Reactants

CO

H2O

CO2

H2

CH4

N2

Mole (%)

10

31

4

30

10

15

For the reactor volume of 40 m3 and diameter of 2 m, calculate the pressure drop and overall conversions for the reactions, and plot the temperature profile along the length of the reactor [6, 51, 52] using Peng-Robinson Equation of State.

Solution The UniSim design program, Example 11.11.usc, shows the calculation of the pressure drop and the overall conversions, and plots the temperature profile through the length of the reactor. The problem is identical to the catalytic

1320  Chemical Process Engineering reactions solved in the previous examples with small difference in the units of the reaction rate expressions and ways to implement multiple reactions. With the procedure shown in previous examples, all components are entered to the simulation, and the PR Equation of state is chosen as the fluid package. We must define two different reactions in the UniSim design; the first reaction is the Heterogeneous Catalytic Reaction and the second reaction is the Simple Rate Reaction as follows: 1. H  eterogenous Reaction: In the Reactions tab in the Simulation Basis Manager, the Heterogeneous Catalytic reaction is chosen (Rxn-1) which shows four tabs to be completed. a. Th  e definition of the Stoichiometry tab has been provided earlier. b. In the second tab (Basis), make sure to choose the partial pressure as the Basis with the proper reaction phase and Base and Rate Units as shown below (Figure 11.82):

In the Numerator tab (Figure 11.83), the information for the Forward Reaction is entered based on the data provided in the example and rate expression for reaction one. Since the UniSim design simulation program does not provide the unit for A, it is the responsibility of the user to check the unit based on

Figure 11.82  The Basis tab in the Heterogeneous Catalytic Reaction window (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim are registered trademarks of Honeywell International Inc.).

Figure 11.83  The Numerator tab in the Heterogeneous Catalytic Reaction window (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim are registered trademarks of Honeywell International Inc.).

Chemical Kinetics and Reactor Design  1321



Base and Rate Units as shown in Equation 11.67a. For the value of the activation energy, E, the UniSim design simulation allows the possibility to change the unit as desired; however, care is needed to enter the parameters in their proper units. Since the reaction is first order with to respect to Methane, the value of one is entered in the Forward Order cell relevant to methane. The value of A and E can be obtained with the following equations:

A = k 01 × ρcat

(1 − φ) (1 − 0.6) = 3.32e3 × 103 × 3000 φ 0.6

 kmol  = 6.63 × 106  3   mGas . atm. s  J  E = 1 × 105   mol 





(11.67)

Where the unit for A is determined based on the multiplication of units of pre-exponential rate constant for reaction 1, density of catalyst and bed voidage as:

A[=]





 kmol  kg m3 kmol × 3cat 3cat [=] 3 kg cat . atm. s mcat mGas  mGas . atm. s 

(11.67a)

c. I n the Denominator tab (Figure 11.84), Component Exponents and Denominator Exponent are entered from the data provided in the denominator of rate expression. It is shown as:

The definition of the first reaction is now finished, and we can close the active window and move to the definition of the second reaction.

2. H  omogenous Reaction: In the Reactions tab in the Simulation Basis Manager, the Simple Rate reaction is chosen (Rxn-2) which shows the following windows which shows three tabs to be completed. a. Th  e definition of the Stoichiometry tab is like what was explained before. b. In the second tab (Basis) (Figure 11.85), make sure to choose the mole fraction as the Basis with the proper reaction phase and suitable Rate Units as shown below: c. In the Parameters tab, the data for the Forward Reaction and Reverse Reaction are provided based on the Equation Help shown in Figure 11.86.

Figure 11.84  The Denominator tab in the Heterogeneous Catalytic Reaction window (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim are registered trademarks of Honeywell International Inc.).

1322  Chemical Process Engineering

Figure 11.85  The Basis tab in the Simple Rate Reaction window (Courtesy of Honeywell UniSim Design software. Honeywell UniSim are registered trademarks of Honeywell International Inc.).

and

Figure 11.86  The Parameters tab in the Simple Rate Reaction window (Courtesy of Honeywell UniSim Design software. Honeywell UniSim are registered trademarks of Honeywell International Inc.).



Forward Reaction: the value of A can be obtained with the following equation.

A = k 02 × ρcat

(1 − φ) (1 − 0.6)  kmol  = 2.95 × 105 × 3000 × = 5.9 × 108  3  φ 0.6  mGas .s  J  E = 1.163 × 105   mol  β=0







(11.68)

Backward Reaction: For this reaction the values of A′ and B′ are obtained from the Equilibrium Constant Equation provided Table 11.14.

4897  4897  K eq = exp  −4.946 + → ln(K eq ) = −4.946 +   T  T

and

A′ = 4.946 B′ = 4.897



(11.69)

Chemical Kinetics and Reactor Design  1323 Table 11.14  Tracer experiments data. θ

E(θ)

θ

E(θ)

0.000

0.000

1.243

0.403

0.113

0.308

1.356

0.355

0.226

0.995

1.469

0.313

0.339

0.876

1.582

0.275

0.452

0.786

1.695

0.237

0.565

0.720

1.808

0.213

0.678

0.663

1.921

0.171

0.791

0.606

2.034

0.142

0.904

0.545

2.147

0.123

1.017

0.497

2.260

0.109

1.130

0.450

2.373

0.095

Source: Coker [53].

These data are entered for the second reaction in the Parameters tab. Both reactions are now defined. 3. C  lose the active window (front window). Clicking on Add Set in the Reaction Sets, new reactions set is created with two reactions as shown in Figure 11.87: 4. Close the active window and associate the Reaction Sets (Set-1) to fluid Pkgs by clicking on add to FP (Figure 11.88). The reaction is now available for the simulation. After completing these steps, enter to Simulation Environment by clicking on the Return to Simulation Environment tab: 5. Draw the flowsheet with heat and stream materials and define the feed stream and reactor. The feed of 2,000 mol/s enters to the reactor, which has the volume of 40 m3 and diameter of 2 m, at 350°C and 30 atm with the following composition: Reactants

CO

H2O

CO2

H2

CH4

N2

Mole (%)

10

31

4

30

10

15

Figure 11.87  Activation of the Reaction Set (Courtesy of Honeywell UniSim Design software, Honeywell trademarks of Honeywell International Inc.).

and UniSim

are registered

1324  Chemical Process Engineering

Figure 11.88  The Reactions tab in the Simulation Basis Manager window (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim are registered trademarks of Honeywell International Inc.).

The reactor configuration data are now entered in the Rating/Sizing tab as shown in Figure 11.89: 6. I n the Design/Parameters tab (Figure 11.90), choose the Ergun Equation to calculate the pressure drop. The conversion of the reactions and the Pressure Drop can now be exported to the UniSim design flowsheet as shown in Figure 11.91: 7. N  ow click on the Reactor and choose the Performance/Conditions tab where the various profiles; pressure, flow and composition are shown in Figure 11.92. 8. Click on Plot and you can now see the temperature and pressure profiles along the reactor length as shown in Figure 11.93:

Example 11.12 A tracer experiment was carried out in a nozzle type reactor of volume V = 5.13L with liquid rate at 2.9 l/min. Table 11.14 shows data for the exit age distribution E(θ) against the dimensionless residence time θ. Determine the area under the distribution curve using Simpson’s Rule.

Figure 11.89  The Rating tab in the PFR window (Courtesy of Honeywell UniSim Design software. Honeywell registered trademarks of Honeywell International Inc.).

and UniSim

are

Chemical Kinetics and Reactor Design  1325

Figure 11.90  The Design/Parameters tab in the PFR window (Courtesy of Honeywell UniSim Design software. Honeywell are registered trademarks of Honeywell International Inc.).

and UniSim

Figure 11.91  The PDF and Spreadsheet tabs in the Spreadsheet window (Courtesy of Honeywell UniSim Design software. Honeywell UniSim are registered trademarks of Honeywell International Inc.).

and

Solution Figure 11.94 shows the exit age distribution versus dimensionless time (θ). The Excel spreadsheet program, Example 11.12.xlsx, calculates the area of a function defined by the uniform spacing of the independent θ values using Simpson’s rule. This gives the area of the exit age distribution of a tracer from a nozzle reactor. The area under the curve is approximated using the following equation: n



∫

I = Edθ ≈ 0

∆θ [E 0 + 4(E1 + E 3 + E 5 + ) + 2(E 2 + E 4 + E 6 + ) + E n ] 3

The calculated area is I = 0.986. The Excel snapshot in Figure 11.95 shows the details.

(11.70)

1326  Chemical Process Engineering

Figure 11.92  The performance/Conditions tab to show the various profiles for PFR (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim are registered trademarks of Honeywell International Inc.).

Temperature

350.0 345.0

Pressure 3100

Fluid

Pressure 3000

335.0

Pressure (kPa)

Temperature (C)

340.0

330.0 325.0 320.0 315.0 310.0

2800 2700 2600

305.0 300.0 0.0000

2900

2.000

4.000

6.000

8.000

10.00

12.00

14.00

2500 0.0000

2.000

4.000

Reactor Length (m)

6.000

8.000

10.00

12.00

14.00

Reactor Length (m)

Figure 11.93  Temperature and pressure profiles as a function of reactor length (Courtesy of Honeywell UniSim Design software. Honeywell and UniSim are registered trademarks of Honeywell International Inc.).

Example 11.13 The triose phosphate isomerase catalyzes the interconversion of D-glyceraldehyde 3–phosphate (S) and dihydroxyacetone phosphate (P). The following results show the initial reaction rate, v, with S as a substrate at a total enzyme concentration of CET = 2.22×10-10 M, pH = 7.42 and T = 30°C [3]. 103 [S]/M

0.071

0.147

0.223

0.31

0.602

1.47

2.6

107 v/Ms-1

1.31

2.45

3.37

3.9

5.63

7.47

8.17

Determine Km and the catalytic constant k3 for the enzyme under these conditions.

Solution The Excel spreadsheet program, Example 11.13.xlsx, determines the values of the Michaelis constant, Km and the catalytic constant, K3, for the enzyme. The regression analysis of the Equation 11.35 with two Excel spreadsheet functions; Slope and Intercept, provides the value of Vmax and Km and Equation 11.34 can be then used to calculate the

Chemical Kinetics and Reactor Design  1327 1.2

Exit age distribution E (θ)

1

0.8

0.6

0.4

0.2

0

0

0.5

1 1.5 Dimensionless residence time (θ)

2

2.5

Figure 11.94  The residence time distribution E versus dimensionless time.

Figure 11.95  Snapshot of the Excel spreadsheet calculations using the numerical integration functions.

catalytic constant, k3. Figure 11.96 shows the snapshot of the Excel calculation of the constants and the LineweaverBurk plot of 1/v versus 1/CS.

Example 11.14 At a given room temperature, results for the hydrolysis of sucrose, S, catalyzed by the enzyme invertase (CET = 1 × 10–5 mol L–1) in a batch reactor are shown in Table 11.15 [54]: Determine the values of the kinetic parameters Vmax, Km, and k3.

1328  Chemical Process Engineering

Figure 11.96  Snapshot of the Excel spreadsheet program for calculating the enzyme reaction constants.

Table 11.15  Concentration data. t (h)

CS (mmol/L)

0

1

1

0.84

2

0.68

3

0.53

4

0.38

5

0.27

6

0.16

7

0.09

8

0.04

9

0.018

10

0.006

11

0.0025

Solution The Excel spreadsheet program, Example 11.14.xlsx, determines the values of the Michaelis constant Km and the catalytic constant k3 for the hydrolysis of sucrose. The regression analysis of the Equation 11.42 with the transformation shown in Equation 11.43 provides the values of Vmax and Km, and Equation 11.34 is used to calculate the catalytic constant, k3. Figure 11.97 shows the snapshot of the Excel spreadsheet calculations. As shown in the Figure in cell $F$46, the value of the PEARSON correlation coefficient (r) is close to -1, this indicates a strong negative correlation. This means that when one of the variables increases, the other tends to decrease, and vice versa.

Chemical Kinetics and Reactor Design  1329

Figure 11.97  Snapshot of the Excel spreadsheet for calculating the reaction constants for the hydrolysis of sucrose.

Example 11.15 Determine the values of Km and Vmax for the following reaction using the Lineweaver-Burk and non-linear regression methods and compare the results. k1

urea + urease  [urea ⋅ urease]∗ + H 2O k2



3 [urea ⋅ urease] + H 2O k → 2NH3 + CO2 + urease

∗

The rate of reaction is given as a function of urea concentration in the following table [3]: CUrea (kmol/m3)

vUrea (kmol/m3.s)

0.6

1.8

0.4

1.45

0.2

1.07

0.02

0.54

0.01

0.36

0.005

0.19

0.002

0.085

0.001

0.06

Solution The Excel spreadsheet program, Example 11.15.xlsx determines the values Km and Vmax with linear and non-linear regression analyses. The linear regression is the same as shown in Example 11.13. The non-linear analysis with

1330  Chemical Process Engineering the Solver function uses Michaelis-Menten (MM) formula to compute v*(predicted value). In Figure 11.98, an example of the SOLVER parameters window is shown (see Chapter 1 for more details). In this problem, the residual sums of squares between v and v* is then calculated. Using guessed values of Km and Vmax, the Solver uses a search optimization technique to determine MM parameters as shown in Figure 11.99. The following table shows the comparion of results.

Figure 11.98  An example of the SOLVER parameters window.

Figure 11.99  Snapshot of the Excel spreadsheet for calculating the values of Km and Vmax using the linear and non-linear regression analyses.

Chemical Kinetics and Reactor Design  1331 Method Parameter

Lineweaver-Burk

Non-linear regression

Percentage deviation (%)

Vmax (kmol/m3.s)

0.852

1.703

50

Km (kmol/m3)

0.0143

0.0539

73.6

As seen in this table, there is a significant deviation between linear and non-linear regression, For the non-linear analysis, the Excel spreadsheet Solver function uses a search optimization technique to determine MM parameters. This also shows that the MM method does not provide sufficient accuracy for estimating reaction parameters due to the simplifying hypothesis made in the development of the kinetic expression.

References 1. A. K. Coker, Ludwig’s Applied process design for chemical and petrochemical plants, 4th ed., vol. 3, Gulf Professional Publishing, 2013. 2. O. Levenspiel, Chemical Reaction Engineering, 3rd ed., New York: John Wiley & Sons, 1999. 3. A. K. Coker, Modeling of Chemical Kinetics and Reactor Design, Gulf Professional Publishing, 2001, p. 81. 4. H. S. Fogler, Elements of chemical reaction engineering, 5th ed., Prentice-Hall, 2016. 5. G. F. Froment, K. B. Bischoff† e J. De Wilde, Chemical Reactor Analysis and Design, 3rd ed., John Wiley & Sons, 2011. 6. A. H. Penn, “Reactions in HYSYS,” August Fall 2005. [Online]. Available: http://www.owlnet.rice.edu/~ceng403/hysys/ reactions.html. [Accessed November 2020]. 7. J. Moulijn, M. Makkee e A. van Diepen, Chemical Process Technology, 2nd ed., Wiley, 2013. 8. U. Mann, Principles of Chemical Reactor Analysis and Design: New Tools for Industrial Chemical Reactor Operations, 2nd ed., Wiley-Interscience, April 13, 2009. 9. A. Arratibel, A. Pacheco Tanaka, I. Laso, M. van Sint Annaland e F. Gallucci, “Development of Pd-based double-skinned membranes for hydrogen production in fluidized bed membrane reactors,” Journal of Membrane Science, vol. 550, pp. 536544, March 2018. 10. I. Eddi e L. Chibane, “Parametric study of high temperature water gas shift reaction for hydrogen production in an adiabatic packed bed membrane reactor,” Revue Roumaine de Chimie, vol. 65, no. 2, pp. 149-164, January 2020. 11. S. Saeidi, D. Iranshahi e F. Gallucci, “Recent advances on spherical reactors for chemical and refinery industries.” TU/e Eindhoven University of Technology, Eindhoven, 2018. 12. Honeywellprocess, “UniSim Design,” [Online]. Available: https://www.honeywellprocess.com/en-US/online_campaigns/ connected_plant/Pages/process-simulation.html. [Accessed November 2020]. 13. R. P. Hesketh, “Catalytic Rates & Pressure Drop in PFR Reactors,” Spring 2003. [Online]. Available: http://users.rowan. edu/~hesketh/0906-316/handouts/catalytic%20rates&delp.pdf. [Accessed January 2021]. 14. Wikipedia, “Adiabatic flame temperature,” June 2020. [Online]. Available: https://en.wikipedia.org/wiki/Adiabatic_flame_ temperature. [Accessed October 2020]. 15. Z. S. Spakovszky, “Thermodynamics and Propulsion- 15.5: Adiabatic Flame Temperature,” [Online]. Available: https://web. mit.edu/16.unified/www/SPRING/propulsion/notes/notes.html. [Accessed October 2020]. 16. O. Levenspiel, Chemical Reaction Engineering, 3rd ed., New York: John Wiley & Sons, 1999. 17. R. Sotudeh-Gharebaagh, R. Legros, J. Chaouki e J. Paris, “Simulation of circulating fluidized bed reactors using ASPEN PLUS,” Fuel, vol. 77, no. 4, pp. 327-337, March 1998. 18. B. Liu, X. Yang, W. Song e W. Lin, “Process Simulation Development of Coal Combustion in a Circulating Fluidized Bed Combustor Based on Aspen Plus,” Energy & Fuels, vol. 25, no. 4, pp. 1721-1730, 2011. 19. R. Sotudeh-Gharebagh e N. Mostoufi, “Simulation of a Catalytic Turbulent Fluidized Bed Reactor using the Sequential Modular Approach,” Fuel Processing Technology, vol. 85, no, 2-3, pp. 189-200, 2004. 20. A. Sarvar-Amini, R. Sotudeh-Gharebagh, H. Bashiri, N. Mostoufi e A. Haghtalab, “Sequential Simulation of a Fluidized Bed Membrane Reactor for the Steam Methane Reforming using ASPEN PLUS,” Energy & Fuels, vol. 21, no. 6, pp. 35933598, 2007. 21. Y. Jin, Z. Rui, Y. Tian, Y. Lin e Y. Li, “Sequential Simulation of Dense Oxygen Permeation Membrane Reactor for Hydrogen Production from Oxidative Steam Reforming of Ethanol with ASPEN PLUS,” International Journal of Hydrogen Energy, vol. 35, no. 13, pp. 6691-6, 2010.

1332  Chemical Process Engineering 22. A. Eslami, A. Hashemi Sohi, A. Sheikhi e R. Sotudeh-Gharebagh, “Sequential Modeling of Coal Volatile Combustion in Fluidized Bed Reactors,” Energy & Fuels, vol. 26, no. 8, pp. 5199-5209, 2012. 23. A. Hashemi Sohi, A. Eslami, A. Sheikhi e R. Sotudeh-Gharebagh, “Sequential-based Process Modeling of Natural Gas Combustion in a Fluidized Bed Reactor,” Energy & Fuels, vol. 26, no. 4, pp. 2058-2067, 2012. 24. H. Asadi Saghandi, R. Sotudeh-Gharebagh, A. M. Dashliborun, H. Kakooei e M. Hajaghazadeh, “Sequential Based Process Modelling of VOCs Photodegradation in Fluidized Beds,” Canadian Journal of Chemical Engineering, vol. 92, no. 11, pp. 1865-1874, 2014. 25. A. Yousefifar, R. Sotudeh-Gharebagh, N. Mostoufi e S. S. Mohtasebi, “Sequential Modeling of Heavy Liquid Fuel Combustion in a Fluidized Bed,” Chemical Engineering & Technology,, vol. 38, no. 10, pp. 1853-1864, 2015. 26. H. Hasanzadeh-Shahrivar, A. Sheikhi e R. 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Symp. on Runaway Reactions, Boston, March 1989.. 44. D. Townsend, H. Ferguson e H. Kohlbrand, “Application of ARCTM Thermokinetic data to the design of safety schemes for industrial reactors.,” Process Safety Prog., vol. 14, no. 1, pp. 71-76, 1995. 45. Center for Chemical Process Safety (CCPS), Guidelines for Design Solutions for Process Equipment Failures, Center for Chemical Process Safety of the American Institute of Chemical Engineer, 1998. 46. U.S. Chemical Safety and Hazard Investigation Board,, “Investigation Report: T2 Laboratories, Inc., Runaway Reaction,” U.S. Chemical Safety and Hazard Investigation Board, September 2009. 47. R. P. Hesketh, “Equilibrium Constant in a Reaction rate in a PFR Reactors: HYSYS,” Spring 2003. [Online]. Available: http://users.rowan.edu/~hesketh/0906-316/handouts/equilibriumconstantpfrstyrene.pdf. [Accessed November 2020]. 48. R. Stryjek e J. H. Vera, “PRSV: An Improved Peng- Robinson Equation of State for Pure Compounds and Mixtures,” Canadian Journal of Chemical Engineering, vol. 64, pp. 323-333, April 1986. 49. K. I. Al-Malah, Aspen Plus: Chemical Engineering Applications, Wiley, 2016. 50. M. Sohrabi, Introduction to the Design of Catalytic Reactors, Tehran: Amirkabir University Publciation Press, 2010. 51. R. Sotudeh-Gharebagh e E. Jabbari, Computer-Aided Process Simulation in Chemical Engineering, Tehran: University of Tehran Press, 2020.

Chemical Kinetics and Reactor Design  1333 52. R. Sotudeh-Gharebagh, N. Mostoufi e A. Kiashemshaki, Steady State Process Simulation using HYSYS, Tohfeh and Boshra., 2006. 53. A. K. Coker, A Study of Fast Reactions in Nozzle-Type Reac-tors, Ph.D. Thesis, Aston University, U.K., 1985. 54. R. W. Missen, C. A. Mims e B. A. Saville, Introduction to Chemical Reaction Engineering and Kinetics, New York: Wiley, 1999.

12 Engineering Economics INTRODUCTION Project evaluation enables the technical and economic feasibility of a chemical process to be assessed using preliminary process design and economic evaluations. Once a process flowsheet is available, these evaluations can be classified into several steps: material balance calculations, equipment sizing, equipment cost determination, utility requirements, investment cost estimation, sales volume forecasting, manufacturing cost estimation, and finally profitability and sensitivity analysis. The results of an economic evaluation are reviewed together with other relevant aspects, such as competition and likely product life in arriving at project investment decisions. These decisions are essential in order properly to both plan and allocate the long-term use of available resources. Several excellent textbooks, book chapters and documentations are available in the literature to address the chain of project evaluation and feasibility analysis in chemical engineering where various aspects of plant design and engineering economics are addressed and reviewed comprehensively [1–5]. The objectives of an economic appraisal are: • To ensure that the expected future benefits justify the expenditure of resources. • To choose the best project from among alternatives to achieve future benefits. • To use all available resources. These objectives ensure that the right project is undertaken and is likely to attain the desired profitability. In the chemical process industries, an investment project may arise from any of a range of activities. It may be a minor modification to an existing plant, a major plant expansion or revamping, a completely new plant (on an existing or greenfield site) or the development of an entirely new process or product. For a major or a new plant, economic assessment with increasing degrees of accuracy may be carried out at different stages as the plant progresses. This may be based on an initial research and development (R&D), through various stages of the project (e.g., pilot plants, energy and material balance, preliminary plant design), which leads to the decision whether or not to proceed with investment in a full-scale plant for the process. Table 12.1 lists examples of the use of engineering economics for the evaluation of various projects. The approach used depends on the quality of the information, that is, the stage in the project at which it is undertaken.

GROSS PROFIT ANALYSIS With gross profit analysis (GPA)*, we can perform fast economic profit analysis on multiple reactions based on raw materials and products to determine which pathway to follow in the design tree. Raw materials

Plant

Products

The following formula is used to calculate the gross profit per unit of product.



Gross profit ($) = revenue of product − cost of raw materials

(12.1)

*University of Colorado Boulder, Department of Chemical and Biological Engineering (https://www.youtube.com/watch?v=0GfES6dgg_8). A. Kayode Coker and Rahmat Sotudeh-Gharebagh. Chemical Process Engineering: Design, Analysis, Simulation and Integration, and Problem-Solving With Microsoft Excel – UniSim Design Software, Volume 2, (1335–1362) © 2022 Scrivener Publishing LLC

1335

1336  Chemical Process Engineering Table 12.1  Use of chemical engineering economics (Courtesy of Chapman and Hall [6]). Production or Plant Technical Services A. Plant equipment continuously needs repair, replacement, or modernization. The responsible engineer should know roughly what the comparative performance, costs, and payout periods are, even if there is a plant engineering group to do that type of analysis, or a firm price quotation will be obtained later. B. Plant changes, such as those initiated by the ever-increasing costs of energy and environmental requirements, necessitate that many energy-saving, pollution, and hazardous waste control possibilities must be considered. To make intelligent recommendations, the responsible engineer should personally conduct design and cost estimates, payback, and economic calculations on the alternatives before making even preliminary recommendations. C. Competitors’ processing methods, as well as R&D, sales, or management suggested changes must be continuously examined. Supervisors or other groups may be responsible, but the staff engineer can help a great deal by making preliminary cost estimates and economic analyses of the changes to guide his or her own thinking (and hopefully the group’s position). D. All engineers should have a feel for their company’s business, products, and economics. This requires occasional economic reading, and a basic understanding of the company’s annual reports and general industry economic news. Research and Development A. In the process of being creative, one thinks of many novel ideas. During the analytical phase of creative thinking many of the ideas will require a quick cost estimation and economic analysis to provide a better idea of their merit. Even though supervisors or others may be assigned to do this work, the chances of conceiving good ideas and having them accepted increases immensely if some economic screening can be done by the originator. B. While conducting R&D or heat and mass integration studies, there are always many stumbling points or alternative directions that may be taken to solve problems. Often brief cost estimates and economic analyses will help the engineer in deciding which are the most promising directions to pursue. C. After an early or intermediate stage of an R&D program has been successful, new funding requests usually are required to continue the study. These requests can always benefit from having potential preliminary economic analyses. Later, in the final stages of a successful project, the engineer may be part of a team assigned to provide a more definitive preliminary economic projection and analysis. D. In dealing with production, sales, or management personnel, one can usually gain more respect, and be considered more practical and less “theoretical,” by having a reasonable knowledge of the costs and economics of the projects under study, and general industry economics. Sales A. A general knowledge of company costs, profits, and competition are very helpful for more effective salesmanship. B. Salesmen often recommend new products, improvements, or pricing ideas to their management. A cost and economic estimate for these ideas should be helpful in the proposal report. C. Salesmen sometimes perform market surveys. Again, a general economic knowledge of the industries and companies surveyed may be essential and is always useful. D. Salesmen may move into management, where economic knowledge is a major part of the job. Engineering A. Because of the extreme specialization of most engineering companies and many company engineering departments, cost estimating and economics may not be directly required in many engineering company or department jobs. However, other jobs will deal exclusively with cost estimating and economic analysis, and all will benefit from a good, fluent knowledge of the basic economic procedures. Engineering departments or companies usually have well developed in-house methods and data that must be used, but the basics are still applicable. (Continued)

Engineering Economics  1337 Table 12.1  Use of chemical engineering economics (Courtesy of Chapman and Hall [6]). (Continued) General A. All chemical engineers are assumed to know the rudiments of cost estimating, economic evaluation, and the economics of their industry. A high percentage will find this knowledge useful or necessary throughout their careers. Therefore, it is important for chemical engineers to be familiar with different type of contracts as cost engineer as shown in Table 12.2. B. All work situations are competitive, and one means of maintaining the highest advancement potential with most jobs is to convince superiors of your knowledge and interest in management, business, and economics. Associated with this is the demonstration of ability, an interest in accepting responsibility, and ability to communicate. Many companies promote people whom they think can “manage,” such as those with MBA1 degrees or with perceived equivalent capabilities, ahead of people with a better performance record. Basically, a confidence that you can learn managerial skills as you need them, and a knowledge of economics should make most chemical engineers equal or preferred candidates for advancement. Master of Business Administration.

1

Table 12.2  Typical contract types1. Type

Description

EPC

Engineering, Procurement, and Construction design, procurement, construction, to commissioning and handover of the project to the end-user or owner (EPC/Turnkey)

LSTK

Lump Sum Turn Key

EPIC

Engineering, Procurement, Installation & Commissioning

EPCC

Engineering, Procurement, Construction and Commissioning

EPCM

Engineering, Procurement, and Construction Management within the infrastructure, mining, resources and energy industries

EPCF

Engineering, Procurement, Construction and Finance 

https://en.wikipedia.org/wiki/Engineering,_procurement,_and_construction, accessed August, 2020.

1

As seen in the formula, no cost is assumed for the production and the conversion of reactions (best cases) is considered 100%. The gross analysis shows the suitability of raw materials for the process considered. This is a starting point and after passing this step, one can make the decision to follow with the next steps.

CAPITAL COST ESTIMATION Capital cost estimation is an essential part of investment appraisal. Many types of capital cost estimates are made, ranging from the order of magnitude to detailed estimates requiring the collection of accurate technical data. The choice of any estimate type depends upon the amount of detailed information available, and the accuracy desired. Various methods are reported in the literature for the capital cost estimation. Peter et al. [2] outlined and provided the details of seven methods: detailed item estimate, unit cost estimate, percentage of delivered-equipment estimate, approximation by Lang factor, power factor or capacity ratio, investment per unit of capacity, turnover ratio. Coker [1, 4] presented capacity ratio, factored cost estimates, detailed factorial cost estimates to estimate the cost of plant and equipments. Various correlations and software are readily available to estimate the purchased cost of the individual equipments which could then be used to determine the capital costs. McGraw-Hill provided an online cost estimator tool†‡ to estimate the purchased cost of equipments with minimal design data based on figures provided in Plant Design and Economics for Chemical Engineers Book, 5th edition [2]. The purchased costs of the following equipment can be easily estimated from this online tool: http://www.mhhe.com/engcs/chemical/peters/data/, accessed August 2020. http://www.mhhe.com/engcs/chemical/peters/data/ce.html, accessed August 2020.

† ‡

1338  Chemical Process Engineering 1. 2. 3. 4. 5. 6. 7. 8. 9.

a gitators, autoclaves, bayonet heaters, blenders, blowers centrifuges, chutes & gates, columns and connections compressors, condensers, solid conveyors, crushers, cutters, disintegrators drivers, dryers, dust collectors, ejectors, electric motors, evaporators expanders, extruders, fans, filters, furnaces, grinders, heat exchangers heaters, hoists, immersion heaters, insulation, kettles, kneaders, mixers mixing tanks, packed columns, packing, piping, pulverizers, pumps reactors, separators, storage tanks, trays (distillation), turbines, valves vaporizers and vibrating screens

The costs are for January 2002. The Chemical Engineering Plant Cost Index (CEPCI) can be used to update the cost to any appropriate date. This index is often referred to as the CE index. CE is a composite index for US Chemical Process Industry published monthly in the Journal of Chemical Engineering. Chemical Engineering also publishes the Marshall and Swift index (M&S Equipment Cost Index) [3]. In this chapter, five methods are listed based on the classification made by American Association of Cost Engineers [7]. Each method requires progressively less detailed data and preparation time. The defined five types of cost estimates are: Detailed estimate (tender or contractor’s estimate). Requires completed engineering drawings, specifications and site surveys. Probable accuracy of estimate is within ±5%. Definitive estimate (project control estimate). Based on considerable data obtained before preparing completed drawings and specifications. Probable error within 10%. Probable accuracy of estimate is within ±10%. Preliminary estimate (budget authorization estimate). More detailed information required than for study estimate. It is applied after a study estimate acceptance. However, further engineering information is needed; e.g., preliminary material and energy balances, P&IDs, equipment lists and material specifications, duty rating and sizing of all process equipment, and instrumentation and control devices. Probable accuracy of estimate is within ±20%. Study estimate (factored estimate). Better than order-of-magnitude but requires knowledge of major items of equipment. Used for feasibility study. Probable accuracy of estimate is within ±30%. Order-of-magnitude estimate (ratio estimate). Approximate method based on cost data for previous similar types of plant. Probable accuracy of estimate is within ±30%. Table 12.3 below provides each type of estimate with their range of accuracy [8]. Process plant designs start from preliminary designs based on approximate technical data, calculations, and cost data to final designs that require detailed and accurate data, calculations, and quotations. Cost estimates of a proposed plant are continuously carried out during the development of a process from the laboratory to construction. Because of the wide variation of various plant design projects, predesign cost estimates presented in process design, plant design and engineering economics documents should be used only when more accurate data are not available. Table 12.3  Each type of estimate with their range of accuracy. Class

Accuracy range (%)

Cost per project expenditure (%)

Detailed estimate

±2 to 5

5 to 10

Definitive estimate

±5 to 15

1 to 3

Preliminary estimate

±10 to 25

0.4 to 0.8

Study estimate

±20 to 30

0,1 to 0.2

Order of magnitude

±30 to 50

0 to 0.1

Engineering Economics  1339 The total capital cost, CTC, of a project consists of the fixed capital cost (CFC), the working capital (CWC) and the cost of land and any other non-depreciable assets (CL). This is given by:

CTC = CFC + CWC + CL

(12.2)

The fixed capital cost, CFC, is the capital required to provide all the depreciable facilities. It may be divided into two classes known as the battery limits and auxiliary facilities. The boundary of battery limits includes all manufacturing and processing equipment. The auxiliary facilities are the storage areas, administration offices, utilities and other essential and non-essential supporting facilities. Here, four methods are presented to calculate the capital cost of an investment for equipment and process.

Equipment/Plant Cost Estimations by Capacity Exponents It is often necessary to calculate the cost of a piece of equipment when there are no available cost data for the particular size or capacity. If the cost of a piece of equipment or plant size or capacity, Q1, is C1, the cost C2 of a similar piece of equipment or plant size or capacity, Q2, can be calculated from the equation m

Q  C 2 = C1  2   Q1 



(12.3)

where C1 = cost of plant or section of plant of original capacity “1” C2 = cost of plant or section of plant of new capacity “2” Q1 = capacity of plant or section of original requirements Q2 = capacity of plant or section of new requirements m  = cost exponent (or capacity factor) The value of m depends on the type of equipment or plant. It is generally taken as 0.6, the well-known six-tenths rule [2]. This value can be used to get a rough estimate of the capital cost, if there are insufficient data to calculate the index (m) for the size of equipment required. It is worth mentioning that in some literature, m is referred as power sizing component. Its value is usually less than 1. Coker has also reported the capacity exponent for process units ranging from 0.6-0.8 [1]. The value of m typically lies between 0.5 to 0.85 depending on the type of plant; however, care is needed for its utilization to each estimating situation. Table 12.4 lists values of m for various types of equipment. Table 12.4  Typical capacity exponents for equipment. Equipment

Exponent (m)

Reciprocating compressor Turbo blowers compressor Electric motors Evaporators Heat exchangers Piping Pumps Rectangular tanks Spherical tanks Towers, constant diameter Towers, constant height

0.75 0.5 0.8 0.5 0.65–0.95 0.7–0.9 0.7–0.9 0.5 0.7 0.7 1.0

(Source: Institution of Chemical Engineers [9]).

1340  Chemical Process Engineering Cost indices should be used to bring the cost data to a desired year. A cost index is a value for a given point in time showing the cost at that time relative to a certain base time. If the cost (Ct1) and index (Index1) at some time 1 in the past is known, the equipment cost at the time 2 (Ct1) can be determined from the following equation if index (Index1) at some time 2 is known:

 Index 2  C t2 = C t1   Index1 



(12.4)

Cost indices are used to give a general estimate, but no index can account for all the factors. Many different types of cost indices are published in the literature such as the Chemical Engineering index (CE), Marshall and Swift Cost Index (M&S), Intratec Chemical Plant Construction Index (IC), Nelson-Farrar indexes (NF) [1]. Table 12.5 shows the CE cost index for the years 1963-2000 [10] and Table 12.6 shows the updated overall CE index from 2001 to 2019.

Table 12.5  Annual plant cost indices [10]. Year

Composite CE index

Equipment

Construction labor

Buildings

Engineering & supervision

1963

102.4

100.5

107.2

102.1

103.4

1964

103.3

101.2

108.5

103.3

104.2

1965

104.2

102.1

109.7

104.5

104.8

1366

107.2

105.3

112.4

107.9

106.8

1367

109.7

107.7

115.8

110.3

108.0

1968

113.7

109.9

121.0

115.7

108.6

1969

119.0

116.6

128.3

122.5

109.9

1970

125.7

123.8

197.3

127.2

110.6

1971

132.3

130.4

146.2

135.5

111.4

1972

137.2

135.4

152.2

142.0

111.9

1973

144.1

141.8

157.9

150.9

122.8

1974

165.4

171.2

163.3

165.8

134.4

1975

182.4

194.7

168.6

177.0

141.8

1976

192.1

205.8

174.2

187.3

150.8

1977

204.1

220.9

178.2

199.1

162.1

1978

218.8

240.3

185.9

213.7

161.9

1979

238.7

264.7

194.9

228.4

185.9

1980

261.2

292.6

204.3

238.3

214.0

1981

297.0

323.9

242.4

274.9

268.5

1982

314.0

336.2

263.9

290.1

304.9

1983

317.0

336.0

267.6

295.6

323.3 (Continued)

Engineering Economics  1341 Table 12.5  Annual plant cost indices [10]. (Continued) Year

Composite CE index

Equipment

Construction labor

Buildings

Engineering & supervision

1984

322.7

344.0

264.5

300.3

336.3

1985

325.3

347.0

265.3

304.4

338.9

1986

318.4

336.3

263.0

303.9

341.2

1987

323.8

343.9

262.6

309.1

346.0

1988

342.5

372.7

265.6

319.2

343.3

1989

355.4

391.0

270.4

327.6

344.8

1990

357.6

392.2

271.4

329.5

355.9

1991

361.3

396.9

274.8

332.9

354.5

1992

358.2

392.2

273.0

334.6

354.1

1993

359.2

391.3

270.9

341.6

352.3

1994

368.1

406.9

272.9

353.8

351.1

1995

381.1

427.3

274.3

362.4

347.6

1996

381.7

427.4

277.5

356.1

344.2

1997

386.5

433.2

281.9

371.4

342.5

1998

389.5

436.0

287.4

374.2

341.2

1999

390.6

435.5

292.5

380.2

339.9

2000

394.1

438.5

299.2

385.6

340.6

Table 12.6  Overall CE index from 2001 to 2019. Year

Index

Year

Index

2000

394

2010

551

2001

394

2011

586

2002

396

2012

585

2003

402

2013

567

2004

444

2014

576

2005

468

2015

557

2006

500

2016

542

2007

525

2017

567.5

2008

575

2018

603.1

2009

521

2019

607.5

1342  Chemical Process Engineering

Factored Cost Estimate The purchased cost of an item of equipment, free on board (FOB) is quoted by a supplier and may be multiplied by a factor of 1.1 to give the approximate delivered cost. The factorial methods for estimating the total installed cost of a process plant are based on a combination of materials, labor, and overhead cost components. The fixed capital cost, CCF , of a plant based on design can be estimated using the Lang Factor method [11] given by the equation:

C FC = fL



∑C

EQ

(12.5)



where fL = 3.10 for solids processing fL = 3.63 for mixed solids-fluid processing fL = 4.74 for fluid processing ∑C EQ is the sum of the delivered costs of all the major items of process equipment. The major advantage of the Lang method is that the cost of equipment is available.

Functional-Unit Estimate This method considers the fixed capital investment required as a separate unit. These are also known as the process step scoring method or the modular estimate. The functional unit may be characterized as a unit operation, unit process, or separation method that involves energy transfer, moving parts, or a high level of internals. The unit includes all process streams together with side or recycle streams. Bridgwater [12] proposed seven functional units, namely, compressor, reactor, absorber, solvent extractor, solvent recovery column, main distillation column, and furnace and waste heat boiler. Taylor [13] developed the step counting method, based on a system in which a complexity score accounting for factors such as throughput, corrosion problems, and reaction time is estimated for each process step. The modular estimate considers individual modules in the total system with each module consisting of a group of similar items. For the modular estimate, all heat exchangers are classified in one module, all furnaces in another, all vertical process vessels in another, etc. The total cost estimate is considered under six general groupings. These are chemical processing, solids handling, site development, industrial buildings, off-site facilities, and project in-directs [4]. Various cost estimation methods used have been reported in the literature for chemical process industry in order to estimate the cost of equipment and fixed capital cost [1, 2].

Percentage of Delivered Equipment Cost This method requires the determination of the delivered equipment costs, E. The other items are then estimated based on E. The following cost equation is used for this method [2]:



C FC =

∑(E+ f E+ f E+ f E+ + f E) 1

2

3

n

(12.6)

where f1, f2, f3, …, fn are multiplying factors for piping, electrical and indirect costs and are determined based on the process used. This method is commonly used for preliminary and study estimates [2] with the expected accuracy in the range of ±20-30. It can yield more accurate results if applied to projects similar to recently constructed plants.

PROJECT EVALUATION Investment decisions are often based upon several criteria, such as annual return on investment (ROI), payback period (PBP), net present value (NPV), the average rate of return (ARR), present value ratio (PVR) or the internal rate of return (IRR). Discounted cash flow rate on return (DCFRR) is another popular means of evaluating the economic viability of a proposed project. The DCFRR is also called the internal rate of return (IRR) and both account for the time value of money. It is important to mention that the given cash flows may result in more than one IRR.

Engineering Economics  1343

Recovered Capital = Land value + Salvage value + Working capital

Cumulative cash flow

F

Start-up

+ Land value

A

-

E

O

Project time (years)

B

C Working capital D

Effect of tax credits

Figure 12.1  Cumulative cash flow diagram for a project.

Powell [14] reviewed the basics of various discounted cash flow techniques for project evaluation. Discounting is a method that accounts for the time value of money to provide either for the capital or to convert the cash flows to a common point in time so that they are summed. Ward [15] proposed a new concept known as the net return rate (NRR) that provides a better indication of a project’s profitability. Techniques and criteria for economic evaluation of projects are widely available in the literature and texts [1–4, 6]. A summary of the conventional decision criteria is given here.

Cash Flow It is the money that is flowing in and out of an industrial operation. It is coming in from customers or clients who are buying the products or services. Cash is going out of your business in the form of payments for operating costs, taxes and other accounts payable.

Cumulated Cash Flow Cumulative or net cash flow in the sum of net cash flow which flows from industrial operations. The total equals the net cash flow for a given period. A positive number indicates that the company generated more value than expenditures and a negative number indicates that it spent more than it generated. Figure 12.1 shows the cumulative cash flow diagram for a project [4].

Return on Investment (ROI) In engineering economic evaluation, rate of return on investment is the percentage ratio of average yearly profit (net cash flow) over the productive life of the project, divided by the total initial investment. This is calculated after income taxes have been deducted from the gross or pre-tax income. The remainder or net income may be used either for paying dividends, reinvestment, or can be spent for other means. ROI is defined by



 Annual return  ROI =  ∗100  Investment 

(12.7)

The annual return may be the gross income, net pre-tax income, net after-tax income, cash flow, or profit. These may be calculated for one particular year or as an average over the project life. Investment may be the original

1344  Chemical Process Engineering total investment, depreciated book-value investment, lifetime average investment, fixed capital investment, or equity investment. The investment includes working capital and sometimes capitalized expenses such as interest on capital during construction.

Payback Period (PBP) Payback period is widely used when long-term cash flows are difficult to forecast, because no information is required beyond the break-even point. It may be used for preliminary evaluation or as a project screening device for high-risk projects in times of uncertainty. Payback period is usually measured as the time from the start of production to recovery of the capital investment. The payback period is the time taken for the cumulative net cash flow from start-up of the plant to equal the depreciable fixed capital investment (CFC — S). It is the value of t that satisfies the equation: PBP

∑(C



) = C FC − S

CF t

(12.8)

0

where CCF = net annual cash flow CFC = fixed capital cost    S   = salvage value In the cumulative cash flow diagram for a project, the PBP is the time that elapses from the start of the project, A, to the break-even point, E, where the rising part of the curve passes the zero cash position line. The PBP thus measures the time required for the cumulative project investment and other expenditure to be balanced by the cumulative income.

Present Worth (or Present Value) In an economic evaluation of a project, it is often necessary to evaluate the present value of funds that will be received at some definite time in the future. The present value (PV) of a future amount can be considered as the present principal at a given rate and compounded to give the actual amount received at a future date. The relationship between the indicated future amount and the present value is determined by a discount factor. Discounting evaluates each year’s flow on an equal basis. It does this by means of the discount, or present value factor, and the reciprocal of the compound interest factor (l +i)n with i  = interest rate n = the year in which the interest is compounded



The discount factor =

1 (1 + i)n

(12.9)

If Cn represents the amount available after n interest periods, p is the initial principal and the discreet compound interest rate is i. The present value, PV, is expressed as



PV

p

Cn (1 i)n

(12.10)

Net Present Value (NPV) The net present value of a project is the cumulative sum of the discounted cash flows including the investment. The NPV corresponds to the total discounted net return, above and beyond the cost of capital and the recovery of the investment. The NPV represents a discounted return or profit but is not a measure of the profitability. Figure 12.2 shows the typical form of Net present value (NPV) of a project [4]. Each cash flow is evaluated by computing its present value. This is done by taking a cash flow of year n and multiplying it by the discount factor for the nth year.

Engineering Economics  1345

Cumulative net present value

Curve 1

Curve 2

Curve 3

Project time (years)

Figure 12.2  Net present value (NPV) of a project.



pn

1

Cn



(1 i)n

(12.11)

For a complete project, the earlier cash flows are usually negative and the later ones positive. The net present value, NPV, is the sum of the individual present values of the yearly cash flows. This is expressed as: n



NPV =

∑ p = C + (1C+ i) + (1C+ i) 0

1

2

1

2

+ +

0

Cn (1 + i)n

(12.12)

Equation 12.12 can be expressed as: n

NPV =



∑ (1C+ i) n

n



(12.13)

0

The life of the project (n years) must be specified together with the estimated cash flows in each year up to n.   NPV = net present value C0  = initial investment Cn  = cash flow n   = year n i    = interest rate of return (ROI/100) Assuming that the investment is made in year 0 (C0 = I), and the cash flows over the project life are constant, then Equation 12.12 is simplified to give



NPV C

(1 i)n 1 i(1 i)n

I

(12.14)

The NPV measures the direct incentive to invest in a proposal as a bonus or premium over the amount an investor could otherwise earn by investing the same money in a safe alternative, which would yield a return calculated at the rate, i. The resulting NPV from a project’s cash flow is a measure of the cash profit that the project will produce after recovering the initial investment and meeting all costs, including the cost of capital. The more positive the NPV is,

1346  Chemical Process Engineering the more attractive the proposition. If NPV is 0, the viability of the project is marginal; if it is negative, the proposal is unattractive.

Discounted Cash Flow Rate of Return (DCFRR) The discounted cash flow rate of return (DCFRR) is known by other terms, for example, the profitability index, the true rate of return or the investor’s rate of return. The DCFRR is also called the internal rate of return (IRR) and this is also the commonly used term in the literature. It is a metric used in financial analysis to estimate the profitability of potential investments. As DCFRR, the IRR is a discount rate that makes the NPV of all cash flows equal to zero in a discounted cash flow vector. IRR calculations rely on NPV equation (12.12). The DCFRR for a project measures the efficiency of the capital and determines the earning power of the project investment. Therefore, a DCFRR or IRR of say 20% per year implies that this amount will be earned on the investment, in addition to which the project generates enough money to repay the original investment, any interest payable on borrowed capital plus all taxes and expenses.

Net Return Rate (NRR) The net return rate is analogous to the rate of return and is the net average discounted “return” on the investment over and above the cost of capital. This is defined by:

NRR =



NPV × 100 (Discounted investment)(Project life)

(12.15)

where the investment is discounted to the same point as the NPV. Holland et al. [16] introduced the NPV/ investment ratio as a normalized measure of the total discounted return over the life of the investment. Ward [15] showed that the NPV can be divided by the number of cash flow increments (venture lifetime) so that the NRR corresponds to the average discounted net return on investment. The cost of capital is already accounted for by the discount rate in the NPV computation, and therefore the NRR is the true return rate.

Depreciation Estimation of depreciation may be based on: 1. 2. 3. 4.

c ost of operation tax allowance means of building up a fund to finance plant replacement measure of falling value

The annual depreciation can be calculated using “straight line” depreciation as:



D=

C FC − S n

(12.16)

where D  = annual depreciation CFC = initial fixed capital cost n  = n years of projected life S  = salvage value Assuming that CFC is the initial fixed capital investment, and S is the projected salvage value at the end of n years of projected life, then the depreciated rate, d, for any particular year, j, is:



D j = (C FC − S)d j

(12.17)

Engineering Economics  1347 where Dj = annual depreciation charge With the straight-line procedure, where dj is constant, combining Equations 12.16 and 12.17 gives:

d=



1 n

(12.18)

The various components of a plant such as equipment, buildings, and improvements are characterized by projected lifetimes. During this period, each item depreciates from its initial investment cost, CFC, to a salvage value, S, over the period of n years of its projected lifetime. At the end of any particular year, k, the depreciated value or book value, Vk, is: k

Vk = C FC −



∑ Dj

(12.19)

1

where Dj is the annual depreciation charge for year j. Substituting Equation 12.17 into Equation 12.19 gives k



Vk = C FC −

∑(C

k

FC

∑d

− S)d j = C FC − (C FC − S)

1

j

(12.20)

1

For the straight-line depreciation procedure, k



k

∑d =∑d = kd = n1

(12.21)

k Vk = C FC − (C FC − S) n

(12.22)

j

1

1

and



Double Declining Balance (DDB) Depreciation Equipment and complete plants depreciate and lose value more rapidly in the early stages of life. The depreciation based upon the declining book value balance can be expressed as:

Djk = djVj−1

(12.23)

The rate of depreciation, dj, is the same for each year, j; however, the depreciation charges decrease each year because the book value decreases each year. For a declining balance method, the depreciation rate of decline is up to twice, but no more than twice the straight-line rate. This is given by:



dj = d =

2 n

(12.24)

Capitalized Cost The capitalized cost, CK, of a piece of equipment of a fixed capital cost, CFC, having a finite life of n years and an annual interest rate, i, is defined by:

(Ck – CkFC)(1 + i)n = CK – S

(12.25)

1348  Chemical Process Engineering where S = salvage or scrap value CK is in excess of CFC by an amount, which, when compounded at an annual interest rate, i, for n years, will have a future worth of CK less the salvage or scrap value, S. If the renewal cost of the equipment and the interest rate are constants at (CFC - S) and i, then CK is the amount of the capital required to replace the equipment in perpetuity. Rearranging Equation 12.20 gives:

S   (1 + i)n   C K = C FC − (1 + i)n   (1 + i)n − 1  

or

CK = (CFC − Sfd)fk

(12.26) (12.27)

where fd = discount factor  (1 + i)n  f  = the capitalized cost factor   (1 + i)n − 1 

Average Rate of Return (ARR) The average rate of return (ARR) method averages out the cash flow over the life of the project. This is defined by:

ARR =



average cash flow × 100 original investment

(12.28)

The higher the percentage value of the ARR, the better the profitability of the project would be.

Present Value Ratio (Present Worth Ratio) A commonly used profitability index in conjunction with the NPV method shows how closely a project has met the criterion of economic performance. This index is known as the present value ratio (PVR) or present worth ratio (PWR), and is defined as:

PVR =



value of all positive cash flows × 100 value present value of all negative cash flows

(12.29)

The present value ratio (PVR) gives an indication of how much the project makes relative to the investment. A ratio of 1.0 shows that the income just matches the expected income from capital invested for a given interest rate. A ratio of less than 1.0 indicates that the income does not come up to the minimum expectations. A ratio of more than 1.0 means that the project exceeds the minimum expectations.

Profitability A project is profitable if its earnings are greater than the cost of capital. In addition, the larger the additional earnings, the more profitable the venture, and the greater the justification for putting the capital at risk. Therefore, a profitability estimate attempts to quantify the risk taken. The methods used to assess profitability are: 1. 2. 3. 4. 5. 6. 7.

r eturn on investment (ROI) payback period (PB) net present value (NPV) discounted cash flow rate of return (DCFRR) net return rate (NRR) interest recovery period (IRP) rate of return on depreciated investment

Engineering Economics  1349 8. rate of return on average investment 9. capitalized cost 10. average rate of return (ARR) 11. present value ratio (PVR) There are some other methods listed in the literature for assessing a project’s profitability [4].

ECONOMIC ANALYSIS The Excel spreadsheet programs have been developed to estimate the net present value (NPV), present value ratio (PVR), net return rate (NRR), average rate of return (ARR), payback period (PBP) and discounted cash flow rate of return (DCFRR). These analyses are done for a given cash flow over the operating life of a project. In addition, a detailed computer program has been developed to review an economic project using Kirkpatrick’s input data [4]. These data are defined as follows: Annual Revenue, $. The money received (sales minus the cost of sales) for one-year production from the plant. This is assumed as being constant for the life of the project. Annual Operating Cost, $. The cost of raw materials, labor, utilities, administration, insurance, and royalties, etc., but does not include debt service payments. Depreciating Base, $. The capitalized cost of the facility and less non-depreciable items, such as land and inventory. No salvage is subtracted because double declining balance depreciation is used. Project Life, Years. The length of time for which the facility is to be operated. It is also the term of the loan and the depreciation time. Initial Loan, $. The capitalized cost minus owner equity. Payments/Year. The number of payments on the loan per year: 1-annually, 2-biannually, 4-quarterly, and 12-monthly. Periodic Interest Rate. The annual interest rate divided by the payments per year. For a 10% annual interest rate and monthly repayments, this is 0.10/12. Investment Tax Credit, $. The percentage of the initial investment allowed as a tax credit in the year the investment is made. Tax Rate. The percentage tax that must be paid on the project’s pretax income. This rate is assumed to remain constant during the life of the project. Debt Service/Period, $. The amount of each loan payment, that is:

L=



(loan)[i] − (n∗p y ) 1 − [1 + i]

(12.30)

where: L  = Constant payment $/month py = payment per year n   = years i   = annual interest per py The Salvage Value (or Scrap Value). The projected salvage value of equipment at the end of the project lifetime. Land Value. Land is not considered depreciable. It can be used indefinitely for succeeding projects on a specific site, or it can be sold. Working capital. The capital invested in various necessary inventoried items, which are completely recoverable at any time. The calculations for every year of the project life are: 1. C  alculate the depreciation as double declining (that is, twice the depreciation based divided by project life), and subtract it from the depreciation base.

1350  Chemical Process Engineering 2. C  alculate the yearly interest and principal of the debt service payments. 3. Subtract from the revenue, the operating cost, annual depreciation, and interest. 4. Subtract from positive pre-tax income, until no negative pre-tax income remains, if the pre-tax income is negative or has been negative in a prior year. 5. Calculate the income tax due at the given rate and apply the investment tax credit against the income tax due until the credit is exhausted, if after Step 4, the pre-tax income is still positive. 6. Deduct the income tax remaining after Step 5 from the pre-tax income, leaving the after-tax income. 7. Add the after-tax income to the depreciation for the year, yielding the cash flow. 8. Determine the loan balance at the end of the year. 9. Determine the amount of unused depreciation after the last year of the project’s life. Because double declining depreciation does not totally exhaust the depreciation account, the unused depreciation should be added to the cash flow of the last year as salvage value recovered at the termination of the project. 10. Calculate the net present value, NPV, for a known discount rate. 11. Determine the present value ratio, PVR. 12. Calculate the net return rate (NRR) 13. Calculate the average rate of return (ARR). 14. Estimate the payback period, PBP. For a given discount rate, calculate the discount factor during the operating life of the project. Multiply the discount factor by the cash flow and obtain the net present value and the net return rate. Cash flows into a project can be time-­dependent, in which the cash flows occur in a continuous process rather than on a one-time basis. Figure 12.4 illustrates a continuous cash flow diagram. Continuous cash flows into the project are from sales revenues, and cash flows out are for out-of-pocket expenses. The difference between the incoming and outgoing cash flow is the net cash flow generated by the project. The combined net cash flow generated by all the company’s projects is reduced by the income tax payment to yield the net continuous cash flow as shown in Figure 12.3. Expressing the definition of profit with the continuous cash flow results in the following:



Profit before taxes = countinous cash flow − depreciation before taxes Cash flow in (from sales)

Cash flow out (Out- of pocket cash)

Project Net cash flow generated by project Net cash flow from other projects

Income tax Cash flow (after taxes) to corporation Corporation

Figure 12.3  A continuous cash flow diagram. Source: Valle-Riestra [17].

(12.31)

Engineering Economics  1351

Figure 12.4  Gross economic profit analysis for the production vinyl chloride monomer (VCM).



Profit after taxes = countinous cash flow − depreciation after taxes

(12.32)

It is useful to keep in mind that the cash flow differs from profit. i.e, Cash flow ≠ Profit. Allen [18] has provided a systematic procedure for assessing investment proposals for new plant and equipment, exploiting new technology, and replacing uneconomic, inefficient, and obsolete plants, process, and equipment.

Inflation A decrease in the average purchasing value of currency is referred to as inflation. An inflation rate of 15%, for example, means that the average cost of goods and services will increase 15% in one year. The result is that commencing construction one year early will reduce the amount of money expended by 15%. Since the 1980s, inflation has been considered in most economic project evaluations. When inflation is used in economic evaluations, all items except interest on a loan and depreciation are considered to increase in value at the same rate as inflation. Generally, interest is set at the time a loan is negotiated and does not change with inflation. In addition, depreciation depends on the method (for example, straight line or double declining balance) used and the capital charges incurred before start-up are not affected by the inflation rate after start-up. Determining the profitability of a project (for example, NPV), the interest rate is assumed to be greater than the inflation rate. Money may be lost on the project while the net present value indicates the opposite, if the inflation rate is greater than the interest rate. There are cases in which the interest rate is set at the expected inflation rate plus a real expected interest rate. The real expected interest rate is the interest rate that is used to calculate the net present value when there is no inflation. Alternatively, the present value is calculated using the inflation rate as the interest rate, the net present value is then determined using the real expected interest rate.

EXAMPLES AND SOLUTIONS Example 12.1 Prepare a gross economic profit analysis on the following reactions for the production of vinyl chloride monomer (VCM) to determine which pathway should be followed in the process design [19].



(1) C 2H 2 + HCl → C 2H3Cl

1352  Chemical Process Engineering



(2) C 2H 4 + HCl + 1 2 O2 → C 2H3Cl + H 2O

Solution The Excel spreadsheet program, Example 12.1.xlsx, calculates the gross profit for these two reactions based in the chemical cost data§ as shown in Figure 12.4. The results show that the reaction 2 may generate possible revenue depending on the production costs since the sum is positive. If the sign of the sum is negative, this means that the plant does not generate any value even by ignoring production costs. On the other hand, in this case, the raw materials are more expensive than products. However, a detailed projects evaluation of the whole project is needed before one can make any decisions.

Example 12.2 Estimate the fixed capital investment if the delivered equipment cost is $2,500,000 based on the following multiplying factors reported by Peters et al. [2]. Component

Ratio factor (%)

Purchased equipment cost (E)

100

Purchased equipment installation

39

Instrumentation

43

Piping

31

Electrical

10

Buildings

15

Yard improvement

12

Service facilities

55

Engineering and supervision

32

Construction expenses

34

Legal expenses

4

Contractor’s fee

19

Contingency

37

Solution The Excel spreadsheet program, Example 12.2.xlsx, provides the calculation for estimating the fixed capital investment by the delivered equipment percentage as shown in Figure 12.5.

Example 12.3 Plot the cumulative cash flow for the following projects and determine the payback period (PBP) for each.

§

University of Colorado Boulder, Department of Chemical and Biological Engineering (https://www.youtube.com/watch?v=​ 0GfES6dgg_8).

Engineering Economics  1353

Figure 12.5  Estimating the fixed capital investment by the delivered equipment percentage.

Year

Project A ($)

Project B ($)

0

-100,000

-100,000

1

10,000

80,000

2

20,000

70,000

3

30,000

60,000

4

40,000

50,000

5

45,000

40,000

6

55,000

30,000

7

60,000

20,000

8

70,000

10,000

Solution The Excel spreadsheet program, Example 12.3.xlsx, shows the results. Figure 12.6 shows a plot of the cumulative cash flow diagram against the project life for both projects and as it can be seen from this figure, the PBP for project A is about 4 years and for product B is about 1.3 years. Sign changes in the cumulative cash flow shows the PBP and the exact value between two consecutive years can be obtained by the Excel LINEST and GOAL SEEK functions. The results using these functions, as shown in the Figure, are the same as those observed visually.

Example 12.4 Consider a plant costing $1,000,000 to build that produces a product A. For the same capital outlay, a different plant can be erected to produce an alternative product B. Conditions are such that each plant will only be in operation for eight years and then both will be scrapped. The cash flows in each of the eight years obtained by selling A and B are shown in the following table. Calculate and plot the NPV at various discount rate from 5 to 75%. Which plant is more profitable?

1354  Chemical Process Engineering

Figure 12.6  Calculation of the payback period (PBP) for the projects.

Year

Product A ($)

Product B ($)

0

-1,000,000

-1,000,000

1

100,000

800,000

2

200,000

700,000

3

300,000

600,000

4

400,000

500,000

5

500,000

400,000

6

600,000

300,000

7

700,000

200,000

8

800,000

100,000

Solution The Excel spreadsheet program, Example 12.4.xlsx, shows the details of the calculation using NPV formula (Equation 12.12) and built-in NPV function. This function returns the Net Present Value (NPV) of an investment and can be entered as part of a formula in a cell of a worksheet. Chapter 1 and this Excel spreadsheet tutorial explain how to use the Excel spreadsheet NPV function with syntax and examples¶. The syntax for the NPV function in Excel ­spreadsheet is: NPV(discount_rate, value1, [value2, ... value_n]) discount_rate: the discount rate for the period. value1, value2, ... value_n: cash fow vector (up to 29 values) The NPV function returns a numeric value. With a given discount rate, the value of NPV can be calculated with this function. Figure 12.7 shows the calculation and plot of NPV values for both products against the discount rate of 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, and https://www.techonthenet.com/Excel/formulas/npv.php, accessed on July 2020.

¶

Engineering Economics  1355

Figure 12.7  Plot of NPV for both products against various discount rate.

75% with two methods and the results are similar. As seen in the figure, plant B generates the more positive NPV, therefore, it is the more attractive proposition.

Example 12.5 For the cash flow vectors given in Example 12.3, calculate DCFRR (IRR) and make a choice about which plant is more profitable.

Solution The Excel spreadsheet program, Example 12.5.xlsx, determines the discounted cash flow rate of return (DCFRR) using IRR function. The cash flows must occur at regular intervals, but do not have to be the same amounts for each interval. The IRR function is a built-in function in the Excel spreadsheet categorizes and returns the DCFRR for a series of cash flows with the following syntax: IRR (cash flow vector, [estimated_irr]) where: Cash flow vector: represent the series of cash flows. [estimated_irr]: optional. It is the guess for the internal rate of return. If this is deleted, it assumes an estimated_irr of 0.1 or 10%. The following results can be obtained using the IRR function for the input data (Figure 12.8). The results show that The DCFRR of product for A is 28%, and that of product B is 65%. The results further confirm that product B is more promising than product A. We can then conclude that product B is more profitable than product A. DCFRR is a discount rate that makes the net present value (NPV) of all cash flows equal to zero in a discounted cash flow analysis. In this figure, the Excel spreadsheet built-in NPV function is used to show the at IRR, the NPV value becomes zero for both cases. It is also important to mention that the IRR can be calculated by solving either NPV equation (12.12) or Excel NPV function with the Goal seek function. These will be illustrated in the next Example. In general, IRR can be determined in four different ways: a) Graphically: by plotting NPV vector with discount rate and finding the value for which NPV is shown zero, b) Excel IRR function, c) the Excel NPV function by setting the cell to zero and finding the relevant IRR that satisfies this equation with the Goal Seek function or the Excel Solver, and d) Direct solution of Equation 12.12 with the Excel spreadsheet with the Goal Seek function or the Excel Solver.

1356  Chemical Process Engineering

Figure 12.8  Calculation of the DCFRR using IRR function.

Example 12.6 Using the cash flow of product, A shown below, determine the discount cash flow rate of return (DCFRR) using a) the NPV curve, b) NPV function and c) the Equation 12.12.

Solution The Excel spreadsheet program, Example 12.6.xlsx, determines the discounted cash flow rate of return (DCFRR) using three methods as detailed below: a. N  PV curve: The intersection of NPV curve against the discount rate with y = 0 gives the value of DCFRR as shown in the following figure. The Excel spreadsheet forecast function with Goal Seek solver are used to find the value of DCFRR between 20 and 25% with the linear interpolation for which gives NPV = 0. This gives value of 21%. This is the same as the internal rate of return (IRR) (Figure 12.9).

Figure 12.9  Snapshot of Excel spreadsheet for calculating DCFRR with the NPV curve and Excel function.

Engineering Economics  1357 b. Th  e Excel NPV function: The Excel NPV equation can be solved by trial and error using Goal Seek. The root of this non-linear equation gives the value of DCFRR as shown in the following snapshots. In order to start the calculation, the value of NPV is calculated in cell ($D$41) is calculated for a given discount rate in cell ($D$40). After this step, Goal Seek is chosen from data toolbar menu (What-if Analysis) and the cell related to NPV is set to zero and the cell related to DCFRR is chosen as the changing cell. The Goal Seek function is explained in chapter 1. c. The NPV function: The NPV equation (12.12) is used with an initial discount rate to directly calculate the yearly present value and then sum up to reach the NPV. Then the initial discount rate is iterated to reach NPV = 0 with Goal Seek function as explained in previous section. The value of discount rate obtained in this way would be DCFRR or IRAA. The result obtained with this method is the same as previous methods as shown in Figure 12.10.

Example 12.7 Calculate the salvage value for the depreciation base of 10,000,000 $ using double declining balance (DDB) and plot the depreciation flow.

Solution The Excel spreadsheet program, Example 12.7.xlsx, shows the depreciation flows and salvage value for a given investment as Figure 12.11.

Example 12.8 For the cash flow vectors given in Example 12.3, calculate the net present value (NPV), the present value ratio (PVR), the net return rate (NRR) and the average rate of return (ARR) at discount rate of 10% for both products.

Solution The Excel spreadsheet program, Example 12.8.xlsx, shows the snapshot for calculating the economic indexes; the net present value (NPV), the present value ratio (PVR), the net return rate (NRR) and the average rate of return (ARR) at discount rate of 10% for both products as shown in Figure 12.12. These indexes suggest that product B is a better choice than product A.

Figure 12.10  Snapshot of the Excel spreadsheet results for the calculation of DCFRR with NPV equation.

1358  Chemical Process Engineering

Figure 12.11  The depreciation flows and salvage value for a given investment Example 12.8.

Figure 12.12  Calculation of the economic indexes (NPV, PVR, NRR and ARR).

Example 12.9 A loan of $10,000,000 at the interest rate of 10% per year is made for the repayment during the project life for 10 years. Calculate the constant payment, interest and principal paid on monthly and yearly bases. Assume 12 payments per year.

Solution The Excel spreadsheet program, Example 12.9.xlsx, shows the calculation for loan payment. The equation 12.30 is used to calculate the constant monthly payment for 120 months and each month interest of 0.1/12 is applied to remaining loan. The differences between the constant monthly payment and interest is deduced from the base loan. Make sure after the end of project, the final remaining principal becomes zero. The details are given in the following snapshot (Figure 12.13).

Engineering Economics  1359

Figure 12.13  The calculation of the constant monthly payment for a given loan.

Example 12.10 Calculate the yearly return of investment on the following data [4]: Financing data Item

Description

Value

1

Annual revenue, $

9,000,000

2

Annual operating cost, $

1,200,000

3

Depreciating base, $

40,000,000

4

Project life, years

10

5

Initial loan, $

30,000,000

6

Number of payments per year

12

7

Annual interest, %

10

8

Investment credit, %

10

9

Tax rate, %

50

10

Rate of return, %

5

Solution The Excel spreadsheet program, Example 12.10.xlsx, computes the depreciation flow, salvage value, monthly and yearly loan payment, interest, yearly and cumulative cash flows, the payback period and economic analysis of the project in details. Figure 12.14 shows the snapshot of the Excel spreadsheet which the input data, depreciation flow and salvage value. The double declining balance (DDB) is used for depreciation. This part is like Example 12.7 where more detailed are provided. The computed salvage value of the investment is $4,294,967. The Figure 12.15 shows the constant loan and interest flow on monthly and yearly basis. This is like Example 12.9 where more details are provided for the loan calculation. Figure 12.16 shows the cash flows during 10 years of the project life considering the depreciation, loan and interest flows.

1360  Chemical Process Engineering

Figure 12.14  Snapshot of the Excel spreadsheet with the depreciation flow and salvage value.

Figure 12.15  Calculation of the constant loan and interest flow on monthly and yearly basis.

The Figure 12.17 shows the economic indicators of the projects, e.g., the net present value ($), present value ratio, net return rate, average rate of return, payback period, discounted cash flow return rate (DCFRR). The value of DCFRR of the investment is 6.4%.

Nomenclature ARR

= average rate of return

C = equal cash flow for each year

CCF CFC CK CL C0 Cn CTC CWC

= net annual cash flow = fixed capital cost = capitalized cost = land cost = initial investment cost = cash flow = total capital cost = working capital cost C1 = capital cost of the designed plant

Engineering Economics  1361

Figure 12.16  The cash flows during the project life with the depreciation, loan and interest flows.

Figure 12.17  The economic indicators of the projects.

C2 = capital cost of the existing plant D = annual depreciation DCFRR = discounted cash flow rate of return

Dj dj

= annual depreciation rate = depreciation rate EMIP = equivalent maximum investment period = discount factor fd = capitalized cost factor fk I = investment cost IRP = interest recovery period IRR = internal rate of return i = interest rate of return (ROI/100) m = exponential power for cost capacity relationships NPV = net present value NRR = net return rate n = years of project life PBP = payback period

1362  Chemical Process Engineering

PV = present value PVR = present value ratio PWR = present worth ratio

Q1 Q2

= capacity of the designed plant = capacity of the existing plant ROI = return of investment S = salvage value

Carbon Tax The impact of rising greenhouse gas levels on climate change is one of the biggest issues facing the world. A carbon tax (pollution tax) is a tax levied on the carbon emissions required to produce goods and services. Carbon taxes are intended to make visible the hidden social costs of carbon emissions, which are otherwise felt only in indirect ways like more severe weather events. They are designed to reduce carbon dioxide (CO2) emissions by increasing prices. This invariably decreases demand for such goods and services and incentivizes efforts to make them less carbon-­intensive. A carbon tax covers only CO2 emissions; however, they can also cover other greenhouse gases such as methane (CH4) or nitrous oxide (NOx) by calculating their global warming potential relative to CO2. Research has shown that carbon taxes effectively reduce emissions and economists argue that carbon taxes are the most efficient (lowest cost) way to curb climate change as countries worldwide are committed to achieving net zero emissions by 2050. Chemical/process engineers could incorporate carbon tax into the cashflow and profitability analyses, which enable them to carry out any major decision. A carbon tax would allow the ingenuity of the engineering profession to flourish and thus find the best solution through the innovative power of the crowd.

References 1. A. K. Coker, Ludwig’s Applied process design for chemical and petrochemical plants, 4th ed., vol. 1, Gulf Professional Publishing, 2007. 2. M. S. Peters, K. D. Timmerhaus and R. E. West, Plant Design and Economics for Chemical Engineers, McGraw-Hill Education, 2003. 3. G. Towler and R. Sinnott, Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design, 2nd ed., Butterworth-Heinemann, 2012. 4. A. K. Coker, Fortran Programs for Chemical Process Design, Analysis, and Simulation, Gulf Professional Publishing, 1995. 5. R. Smith, Chemical Process Design and Integration, 2nd ed., Wiley, 2016. 6. D. E. Garrett, Chemical Engineering Economics, New York: Van Nostrand, 1989. 7. AACE, Inc., “COST ESTIMATE CLASSIFICATION SYSTEM – AS APPLIED IN,” 2005. [Online]. Available: https://www. costengineering.eu/Downloads/articles/AACE_CLASSIFICATION_SYSTEM.pdf. [Accessed August 2020]. 8. M. Gerrard, Guide to Capital Cost Estimating, 4th ed., IChemE, 2000. 9. Institution of Chemical Engineers, A New Guide to Capital Cost Estimating, London: Institution of Chemical Engineers, 1977. 10. W. Vatavuk, “Updating the CE Plant Cost Index,” Chem. Eng., vol. 1, p. 62, 2002. 11. H. J. Lang, “Simplified Approach to Preliminary Cost Estimates,” Chem. Eng., vol. 55, p. 112, 1948. 12. A. V. Bridgwater, “The Functional Unit Approach to Rapid Cost Estimation,” ACCE Bull, vol. 18, no. 5, p. 153, 1976. 13. J. H. Taylor, “The Process Step Scoring Method For Making Quick Capital Estimates,” Eng. & Process Economics, vol. 2, p. 259–267, 1977. 14. T. E. Powell, “A review of recent developments in project evaluation,” Chem. Eng., p. 187, 1985. 15. T. J. Ward, “Estimate Profitability Using Net Return Rate,” Chem. Eng., pp. 151–155, 1989. 16. F. A. Holland, F. A. Watson and J. K. Wilkinson, Introduction to Process Economics, 2nd ed., New York: John Wiley & Sons Ltd., 1976. 17. J. E. Valle-Riestra, Project Evaluation in the Chemical Process Industries, New York: McGraw-Hill Book Company, 1983. 18. D. H. Allen, A Guide to the Economic Evaluation of Projects, 2nd ed., England: The Institution of Chemical Engineers, 1980. 19. University of Colorado Boulder, “Gross Economic Profit Analysis,” 2012. [Online]. Available: https://www.youtube.com/ watch?v=0GfES6dgg_8. [Accessed August 2020].

13 Optimization in Chemical/Petroleum Engineering Optimization is the use of specific techniques to evaluate the most cost-effective and efficient solution to a problem or design for a process. This technique is one of the major quantitative tools in industrial decision making. A wide range of problems in the design, construction, operation and analysis of chemical plants and industrial processes can be resolved by optimization. Optimization covers the fields of science, engineering, and business. For example, a process can be represented by some equations or by experimental data, and there is a simple performance in mind such as minimum cost or maximum production. The goal of optimization is to find the values of the variables in the process that yield the best value of the performance criterion. Often, a trade-off exists between capital and operating costs; the described factors involving the process or model and the performance criterion constitute the optimization. Typical problems in chemical engineering process design or plant operation have an infinite number of solutions. Optimization technique can be employed by selecting the best among the entire set by efficient quantitative methods. Engineers work to improve the initial design of equipment and strive to enhance the operation of that equipment once it is installed in order to realize the largest production, the greatest profit, the minimum cost, the least energy usage and so on. In plant operations, benefits occur from improved plant performance such as improved yields of valuable products or reduced yield of contaminants, reduced energy consumption, higher processing rates and longer times between shutdowns. Optimization technique can result in reduced maintenance costs, less equipment wear, and better staff utilization. Additionally, benefits arise from the interactions amongst plan operators, engineers, and management. It is helpful to identify the objective, constraints, and degrees of freedom in a process or a plant, resulting in improved quality of design, faster and more reliable troubleshooting, and faster decision making. Computers and proprietary software are increasingly employed in optimization problems, as these make the necessary computations feasible and cost-effective. Obtaining useful information using computers requires: • Critical analysis of the process or design. • Insight about what the appropriate performance objectives are. • Use of experience, referred to as engineering judgement. Optimization can be applied in various ways to chemical processes and plants, and typical projects where it can be utilized are: 1. Sizing and establishing the best layout of a pipeline. 2. Designing equipment and an entire plant for an optimum cost and highest yields. 3. Determining the best sites for plant location. 4. Routing tankers for the distribution of crude and refined products. 5. Scheduling maintenance and equipment replacement at an optimum time. 6. Operating equipment, such as reactors, columns, and absorbers. 7. Evaluating plant data to construct a model of a process. 8. Minimizing inventory charges. 9. Allocating resources or services among several processes. 10. Planning and scheduling construction. These examples show the types of variables, objective functions and constraints that will be encountered, and we shall review the basic characteristics of optimization problems and their solution techniques and describe some typical benefits and applications in the chemical and petroleum industries. A. Kayode Coker and Rahmat Sotudeh-Gharebagh. Chemical Process Engineering: Design, Analysis, Simulation and Integration, and Problem-Solving With Microsoft Excel – UniSim Design Software, Volume 2, (1363–1404) © 2022 Scrivener Publishing LLC

1363

1364  Chemical Process Engineering

Optimal Operating Conditions of a Boiler An optimization can take place in the operation of a boiler, where engineers focus attention on utilities and operations within refineries and process plants because of the large amounts of energy consumed by these plants and potential for a significant reduction in the energy required for utilities generation and distribution. Furthermore, complexity and constraints arise in optimizing boiler operations due to the control of emissions. In a boiler, it is desirable to optimize the air-fuel ratio such that the thermal efficiency is maximized; however, environmental regulations encourage operations under fuel-rich conditions and lower combustion temperatures in order to reduce the emissions of nitrogen oxides (NOx). However, such operating conditions also reduce efficiency because some unburned fuel escapes through the stacks, resulting in an increase in undesirable hydrocarbon (HC) emissions, resulting in a conflict in operating criteria. Figure 13.1a shows the trade-offs between efficiency and emissions.

Thermal efficiency

Emissions

0

1.0 Air–fuel ratio

2.0

thermal efficiency nitrogen oxides emissions hydrocarbon emissions (a)

Linear response Nonlinear response

Fuel input

0

Idle 0

Minimum

Maximum Steam output

(b)

Figure 13.1  (a) Efficiency and emissions of a boiler as a function of air-fuel (1.0 = stoichiometric air-fuel ratio.) [1]. (b) Discontinuity in operating regimes [1].

Optimization in Chemical/Petroleum Engineering  1365 The engineer is now required to consider maximizing efficiency versus minimizing emissions, resulting in some compromise of the two objectives. Another feature of a boiler operation is the varying demands caused by changes in process operations, plant unit start-ups and shutdowns, and daily and seasonal cycles. Because utility equipment is often operated in parallel, demand varies and is commonly affected when another boiler, turbine or other piece of equipment is brought on-line and which should be used. Determining this is complicated by the feature that most powerhouse equipment cannot be operated continuously to the idle state as shown in Figure 13.1b for boilers and turbines. Instead, a range of continuous operation may exist for certain conditions, but a discrete jump to a different set of conditions may be required if demand changes. Constraint

Constraint

Region of feasible operation Cost of heat (high fuel cost) Value of products

Optimal profit

$/time

Optimal profit Cost of heat (low fuel cost)

R1*

R2* Reflux, or heat duty (a)

Constraint

Constraint

Region of feasible operation

$/time Total profit, low fuel cost Optimum

Optimum R* 1

Total profit, high fuel cost R2*

Reflux, or heat duty (b)

Figure 13.2  (a) Illustration of optimal reflux for different fuel costs [1]. (b) Total profits for different fuel costs [1].

1366  Chemical Process Engineering

Optimum Distillation Reflux When fuel costs were low, distillation column trains employed a strategy involving the substantial consumption of utilities such as steam, and cooling water in order to maximize separation (i.e., product purity) for a given tower. However, the operation of any tower involves certain limitations or constraints on the process, such as tower tray maloperations, channelling, weeping, flooding, condenser and reboiler duties. The requirement for energy conservation suggests a different objective, namely minimizing the reflux ratio. In this instance, the process engineer is required to set the reflux ratio from the viewpoint of optimization. Furthermore, there is an economic minimum value below which the energy savings are less than the cost of product quality degradation as illustrated by Figures 13.2a and 13.2b, respectively. Operators tend to over reflux a column because this strategy makes it easier to stay well within the product specifications, although columns are operated with a fixed flow control of reflux so that the reflux ratio is higher than required when feed rates drop off. Edgar et al. [1] studied this case and showed that optimization of reflux ratio is particularly attractive for columns that operate with 1. 2. 3. 4. 5.

 igh reflux ratio. H High differential products values (between overhead and bottoms). High utility costs. Low relative volatility. Feed light key far from 50%.

They employed a one-dimensional search technique of obtaining the optimal reflux ratio in a distillation column.

Features of Optimization Problems Since the solution of optimization problems involves many features of mathematics, the formulation of an optimization problem requires the use of mathematical expressions. Such expressions do not need to be complex as not all problems can be stated or analyzed quantitatively; however, from a practical viewpoint, it is essential to coordinate the problem statement with the anticipated solution technique. There are a wide range of optimization problems with similar structures and practitioners have a common interest in the same mathematical problem structures, each with different application in their chosen professions. A structural similarity is used to develop a framework or methodology within which any problem can be studied. Determining an optimum solution to a problem requires (a) considering the model representing the process and (b) choosing a suitable objective criterion to guide the decision making. Every optimization problem contains three essential categories [1]: 1. A  t least one objective function to be optimized (e.g., profit function, cost function, and so on). 2. Equality constraints (equations). 3. Inequality constraints (inequalities). Categories 2 and 3 constitute the model of the process or equipment and category 1 is referred to as the economic model. A feasible solution of the problem is obtained with a set of variables that satisfy categories 2 and 3 to the desired degree of precision. Figure 13.3 shows the feasible region or the region of feasible solutions defined by categories 2 and 3. Here, the feasible region consists of a line bounded by two inequality constraints. An optimal solution is a set of values of the variables that satisfy the components of categories 2 and 3 as this solution also provides an optimal value for the function in category 1. In most cases, the optimal solution is a unique one; and in some, it is not. If the optimization problem is formulated such that there are no residual degrees of freedom among the variables in categories 2 and 3, then optimization is not required to obtain a solution for a problem. Thus, if a unique solution exists, no optimization is needed to obtain a solution as one solves a set of equations and need not worry about optimization methods because the unique feasible solution is the optimal one.

Optimization in Chemical/Petroleum Engineering  1367 x2

Nonlinear inequality constraints

Linear equality constraint

Axis is linear ineaquality constraint

Feasible region is along the heavy line

Axis is linear inequality

x1

Figure 13.3  Feasible region for an optimization problem involving two independent variables. The dashed lines represent the side of the inequality constraints in the plane that form part of the infeasible region. The heavy line shows the feasible region [1].

If more process variables whose values are unknown exist in category 2 than there are independent equations, the process model is referred to as underdetermined; i.e., the model has an infinite number of feasible solutions such that the objective function in category 1 is the additional criterion used to reduce the number of solutions to one or a few by specifyingwhat is the “best” solution. However, if the equations in category 2 contain more independent equations than variables whose values are unknown, the process model is overdetermined and no solution satisfies all the constraints exactly. In resolving this difficulty, some of the constraints are relaxed; a typical example of an overdetermined model might be the reconciliation of process measurements for a material balance. A technique to obtain the desired material balance would be to resolve the inconsistent equations by minimizing the sum of the errors of the set of equations (e.g., by least squares procedure).

Objective Functions for Reactors Optimization in the design and operation of a reactor rely on formulating suitable objective functions and a mathematical description of the reactor with the latter forming a set of constraints. Reactors in chemical engineering are represented by one or a combination of 1. A  lgebraic equations. 2. Ordinary differential equations. 3. Partial differential equations. One extreme of representation of reactor operation is complete mixing in a continuous flow stirred tank reactor (CFSTR); the other extreme is no mixing (e.g., plug flow). Between these are various degrees of mixing within dispersion reactors. Single ideal reactor types can be combined in various configurations to represent intermediate types of mixing as well as nonideal mixing and fluid bypassing. Ideal reactors are classified in various ways and Table 13.1 shows the mathematical description of the reactor, as each of the reactors can be expressed in terms of integral equations, differential equations, or difference equations. Not all real reactors can fit neatly into the classification in Table 13.1; however, the accuracy and precision of the mathematical description depend not only on the character of the mixing and the heat and mass transfer coefficients

1368  Chemical Process Engineering Table 13.1  Classification of reactors [1]. Reactor type

Mathematical description (continuous variables)

Batch [well – mixed (CSTR), closed system]

Ordinary differential equations (unsteady state). Algebraic equation (steady state).

Semibatch [well-mixed (CSTR), open system]

Ordinary differential equations (unsteady state). Algebraic equations (steady state).

CFSTR*s, individual or in series.

Ordinary differential equations (unsteady state). Algebraic equations (steady state).

Plug flow reactor

Partial differential equations in one spatial variable (steady state).

Dispersion reactor

Partial differential equations (unsteady state and steady state). Ordinary differential equations in one spatial variable (steady state).

*CFSTR = continuous flow stirred tank reactor.

in the reactor, but also on the validity and analysis of the experimental data used to model the chemical reactions. Other factors often considered in the modeling of reactors, factors that influence the number of equations and their degree of nonlinearity, are: 1. R  eaction features (e.g., exothermic, endothermic, reversible, irreversible, number of species, parallel, consecutive, chain, selectivity, yield, and so on). 2. The geometric configuration (e.g., empty cylinder, packed bed, sphere). 3. The number and nature of the phases present in the reactor (e.g., gas, liquid, solid, and combinations). 4. The method of supplying and removing heat (adiabatic, heat exchange mechanism, and so on). 5. The catalyst characteristics. 6. Stability. Various questions that lead directly to the formulation of an objective function can be posed relating to reactors. Typical objective functions stated in terms of the adjustable variables are: 1. A  djust the temperature profile to specifications (via sum of squares) with respect to the independent variables. 2. Change the temperature from To to Tf in minimum time subject to heat transfer rate constants. 3. Design the optimal temperature sequence with respect to time per reactor length to obtain (a) a given fraction conversion, (b) a maximum rate of reaction, or (c) the minimum residence time. 4. Maximize production per batch. 5. Maximize conversion (yield) per volume with respect to time. 6. Maximize yield per number of moles of component per concentration with respect to time or operating conditions. 7. Maximize profit with respect to volume. 8. Maximize profit with respect to fraction conversion to get optimal recycle. 9. Minimize consumption of energy with respect to operating conditions. 10. Minimize total production costs per average production costs with respect to time per fraction conversion. 11. Minimize volume of the reactors(s) with respect to certain concentration(s).

Optimization in Chemical/Petroleum Engineering  1369

Cost

Cost of raw materials

Cost of the reactor

Cost of energy used Cost of the separator

0

Yield or selectivity

1

Figure 13.4  Costs of energy and raw materials for a reactor as a function of yield and selectivity (Adapted and modified from P. LeGoff., “The Energetic and Economic Optimization of Heterogeneous Reactors”, Chem. Eng. Sci., 35: 2089 [1980]).

12. Minimize production time for a fixed yield. 13. Optimize profit per volume per yield with respect to boundary per initial conditions in time. There are cases where a variable can be independent and in others the same variable can be dependent. However, the usual independent variables are pressure, temperature, flow rate or concentration of a feed. In considering a reactor by itself, we need to be mindful that a reactor will be one unit in a complete process and that at least a separator must be included in any economic analysis. Figure 13.4 shows the relation between the yield or selectivity of a reactor and costs. The optimization techniques can be applied to one or more types of reactor models. The reactor model forms a set of constraints so that more optimization problems involving reactors must accommodate steady-state algebraic equations or dynamic differential equations as well as inequality constraints.

Linear Programming (LP) For Blending Linear programming is an optimization modeling technique in which a linear function is maximized or minimized when subjected to various constraints. This technique has been useful for guiding quantitative decisions in business planning in industrial engineering, refineries, and chemical plants. Petroleum refining involving gasoline blending bears a different cost of manufacture; the proper allocation for each component into its optimal disposition is of major economic importance. In order to address this problem, most refiners employ LP that permits the rapid selection of an optimal solution from a multiplicity of feasible alternative solutions, as each component is characterized by its gasoline blending in petroleum refining. A few major areas where this technique is employed are [2]: 1. 2. 3. 4.

 lending gasolines. b refinery models. allocation of transportation facilities for shipping products from refineries to terminals. integrated operations – simultaneously consider the complete refinery models (item 2) along with the transportation models (item 3).

1370  Chemical Process Engineering 5. a llocation of transportation facilities for shipping products from the crude-oil field to refineries. 6. integrated operations which encompass items 1–5. The LP models in the areas listed are viewed as top-management planning tools, which can be used to balance various aspects of a company’s operations. However, progress has been made in using LP models for shorter- and longer-range problems. Figure 13.5 shows a schematic that indicates the material flow from the crude field to refinery to market. The arrows indicate the transportation links. Consider the cash-flow model within the framework of the Figure 13.5. If we keep an account and ask, at strategic check-points in the fluid flow model, whether cash flows into or out of it, we must know for each operating phase, whether the cash is generated and flows into the account and how much or vice versa. This constitutes the cash-flow model. The contention is that it will be feasible to construct a mathematical model that will observe all fluid flow requirements (or commitments) and at the same time, will keep track of all cash flows into and out the account. In a refinery, it will spell out in detail what crudes should go to what refinery, the throughput and product yields at each refinery, the complete allocation of product distribution all the way to the consumer and a summation of essential operating budgets broken down for each important facility [2]. It is essential that the proposed model as shown in Figure 13.5 can simulate and optimize with reasonable accuracy the fluid flow and cash flow of the corporation. Such a model could be used to determine the most economical means of selecting the type and source of the crude that is best suited for each refinery. Furthermore, it would help decide what products to make and how much of them to make for each market, resulting in a low-cost way to transport the product to the market. LP is an optimizing model that could be used to good advantage despite the highly nonlinear characteristics of the fluid flow-cash flow model. These non-linearities can be resolved within the framework of a linear program model by adding more constraints in order to make the model piece-wise linear. This results in the requirement of a very large computer to solve such linear program models. The structure of the linear program model follows very closely the schematic of Figure 13.5. For instance, each refinery is represented by a sublinear program model of 100 or more constraints. Furthermore, sublinear models are used to represent the movement of crude oil from the fields to the refineries, and transportation of finished products from the refineries to the markets.

Crude Oil Fields

C1

Markets

Refineries

M1

R1 T

Terminals M2

C2

R2

M100 C5

R3 M500

C10

R15 M1000

Figure 13.5  Fluid – flow model.

Optimization in Chemical/Petroleum Engineering  1371 The general linear programming problem is to find a vector (x1, x2, .........xn), where n is the independent variable, which minimizes or maximizes the linear form or the objective function, P as:



P = c1x1 + c2x2 + c3x3 + …………….cjxj + ……….. + cnxn

(13.1)

subject to the linear constraints

xj ≥ 0,j = 1,2,…………,n and

a11x1 + a12x2 + ………………….aijxj + ………… + a1nxn ≤ bi ai1x1 + ai2x2 + ......................aijxj + …………. + ainxn ≤ bi am1x1 + am2x2 + ......................amjxj + …………. + amnxn ≤ bm

(13.2)

where aij, bi and ci are given constants and m= R1 *(X11 + X21 + X31 + X41); X12*N1 + X22*N2 + X32*N3 + X42*N4 >= R2 *(X12 + X22 + X32 + X42); X13*N1 + X23*N2 + X33*N3 + X43*N4 >= R3* (X13 + X23 + X33 + X43); Output Variable

Value

ReducedCost

P1

3.500000

0.000000

P2

4.500000

0.000000

P3

6.000000

0.000000

S1

0.9000000

0.000000

S2

1.050000

0.000000

S3

1.250000

0.000000

S4

1.600000

0.000000

C1

13000.00

0.000000

C2

7000.000

0.000000

C3

25000.00

0.000000

C4

15000.00

0.000000

N1

82.00000

0.000000

N2

95.00000

0.000000

N3

102.0000

0.000000

N4

107.0000

0.000000

D1

13000.00

0.000000

D2

25000.00

0.000000

D3

18000.00

0.000000

R1

87.00000

0.000000

R2

89.00000

0.000000

R3

93.00000

0.000000

X11

409500.0

0.000000

X21

0.000000

0.1250000E-02

X31

136500.0

0.000000

Output (Continued)

Optimization in Chemical/Petroleum Engineering  1401 Table 13.5  LINGO Input and Output for the Case Study [16]. (Continued) Variable

Value

ReducedCost

X41

0.000000

0.1220238E-01

X12

682500.0

0.000000

X22

0.000000

0.1250000E-02

X32

367500.0

0.000000

X42

0.000000

0.1220238E-01

X13

340200.0

0.000000

X23

0.000000

0.1250000E-02

X33

415800.0

0.000000

X43

0.000000

0.1220238E-01

Row

Slack or Surplus

Dual Price

1

0.000000

546000.0

2

0.000000

1050000.

3

0.000000

756000.0

4

0.000000

-21100.00

5

0.000000

10100.00

6

0.000000

0.000000

7

0.000000

15000.00

8

0.000000

0.9000015

9

0.000000

1.050003

10

0.000000

1.050003

11

0.000000

1.599998

12

0.000000

255.7500

13

0.000000

0.000000

14

0.000000

164.2500

15

0.000000

0.000000

16

0.000000

146.0625

17

0.000000

188.0475

18

0.000000

251.0175

Row

Slack or Surplus

Dual Price

19

0.000000

-97.50000

20

0.000000

-187.5000 (Continued)

1402  Chemical Process Engineering Table 13.5  LINGO Input and Output for the Case Study [16]. (Continued) 21

0.000000

-135.0000

22

0.1118762E+08

1.000000

23

0.000000

3.477679

24

0.000000

4.477321

25

0.000000

5.976607

26

0.000000

-0.1785714E-03

27

0.000000

-0.1785714E-03

28

0.000000

-0.1785714E-03

Notation Parameters and variables estimate of property j PEj Wj property variable j P_Costj cost of property j ORj Off-spec ratio for property j feed flow rate of component i. Fi BVi j property j of feed component i C_Costi cost of component i P_Limj property j limit at which giveaway is minimized segregation flow for rundown k FSk TFb total flow of blender b *_Tgt target value of variable F(x) Non-linear objective function f Non-linear constraint function f linearized form of non-linear constraint function f x variables in non-linear objective/constraint function λ vector of estimated Langrangian multipliers ρ penalty parameter coefficients of nonlinear variables x in linear constraint A2 b1, b2 equality to the constraints l, u lower and upper bounds on constraints Indices b blenders i intermediate components j properties or qualities k rundown streams

Optimization in Chemical/Petroleum Engineering  1403

References 1. Edgar, Thomas, F., Himmelblau, David, M., and Leon S. Lasdon, Optimization of Chemical Processes, McGraw-Hill, 2nd ed., 2001. 2. Aronofsky, J. S., Linear Programming – A Problem Solving Tool for Petroleum Industry Management, Journ. of Petroleum Technology, pp. 729 – 736, SPE 315, July 1962. 3. Abadie, J., and J. Carpentier, “Generalization of the Wolfe Reduced Gradient Method to the Case of Nonlinear Constraints”, In Optimization, R. Fletcher, ed., Academic Press, New York, pp. 37-47, 1969. 4. Purohit, Amit, and Tukaram Suryawanshi, Integrated Product Blending Optimization for Oil Refinery Operations, 10th IFAC International Symp. On Dynamic and Control of Process Systems., Mumbai, India, pp. 343, Dec. 18-20, 2013. 5. Jia, Z., and M. Ieraptetritou., Mixed-integer linear programming model for gasoline blending and distribution scheduling. Ind. Eng. Chem. Res. 42, 825-835, 2003. 6. Moro, L., Zanin, A. and J. Pinto, A planning model for refinery diesel production. Computers & Chemical Engineering, 22, pp. 1039–1042, 1998. Available at: http://www.sciencedirect.com/sci​ence/article/pii/S0098135498002099 [Accessed September 6, 2013]. 7. Pinto, J. M., Joly, M. & Moro, L. F. L., Planning and scheduling models for refinery operations. Computers & Chemical Engineering, 24(9-10), pp. 2259–2276. 2000. Available at: http://linkinghub.elsevier.com/retrieve/pii/S0098135400005718. 8. Neiro, S. and J. Pinto, J. Multiperiod optimization for production planning of petroleum refineries. Chem. Eng. Comm., 192(1), pp. 62–88, 2005. Available at: http://www.tandfonline.com/doi/abs/10.1080/00986440590473155 [Accessed September 6, 2013]. 9. Hamisu, A. A., Petroleum Refinery Scheduling with Consideration for Uncertainty. Ph.D. Thesis, Cranfield University, 2015. 10. Riggs, J. A., Chemical Process Control. Lubbock, Texas: Ferret Publishing, 2001. 11. Healy, W. C., Maasen, C. W., and R. T. Peterson, Predicting Octane Numbers of Multicomponent Blends, Report Number RT-70, Ethyl Corporation, Detroit, 1959. 12. James H. Gary, Glenn E. Handwerk, and Mark J. Kaiser, Petroleum Refining Technology and Economics, 5th ed., CRC Press, Taylor & Francis Group, 2007. 13. Aronofsky, J. S., Linear Programming – A Problem Solving Tool for Petroleum Industry Management, Journ. of Petroleum Technology, pp. 729 – 736, SPE 315, July 1962. 14. Mendez, C. A., Grossman, I. E., Harjunkoski, I, and P. Kabor, A simultaneous optimization approach for offline blending and scheduling of oil-refinery operations. Computers & Chemical Engineering, 30, 614-634, 2006. 15. Gottfried, Byron S., Spreadsheet Tools for Engineers, Excel 5.0 Version, 1996. 16. Abdulrahman, S. Alsuhaibani, Texas A & M University. Private communications. 17. Coker, A. K., and A. AlSuhaibani, Optimize product blending using Excel spreadsheets and LINGO software Part 1, Hydrocarbon Processing, pp. 37–40, June 2021. Optimize product blending using Excel spreadsheets and LINGO software Part 2, Hydrocarbon Processing, pp 65–70, July 2021.

Further Reference Shixun Jiang, Optimisation of Diesel and Gasoline Blending Operations, Ph.D. Thesis, Centre for Process Integration, School of Chemical Engineering and Analytical Science, The University of Manchester, 2016.

Epilogue PROCESS SIMULATORS The field of chemical engineering is evolving with the development of new products and the resolving issues of global warming with carbon capture and storage. In these events, it is essential that chemical/process engineers are equipped with the correct tools for solving these intricate and sometimes complex problems. The different packages are applied to solve problems such as modeling and simulation of process plants involving mass and energy balance, fluid mechanics, computational fluid dynamics, process control, chemical kinetics and reactor design, and process plant operation. Figure 1 summarizes the most useful software packages in chemical/process engineering.

MS Excel Microsoft Office Excel is a spreadsheet application that features calculations via rows and columns, graphing tools, tables and a macro programming language with Visual Basic. The main advantage of Excel is that it is readily available and widely used in industry and academia. Thus, it is a perfect tool for calculations or interface with different software so that users can interact with Excel and behind the scenes, other software packages such as Chemcad, Polymath, Matlab, etc., are running and reporting the results back to Excel [1]. Its principal features are: Built-In-functions and formulas: There are a large number of built-in functions defined, such as statistics, (MEAN, AVERAGE, t-test), Algebraic, (SUM, ROUND, LOG, LOG10), logical (IF, FALSE, etc.), reference, database and information. • Operations with rows and columns: It is easy to find and sort data and use them in replicated formulas, etc. • Plotting: There is a large number of options depending on the requirements. • Solver: It is a tool to use within Excel to solve numerically a set of equations, problem optimization including fitting a set of data to a given linear and nonlinear equation and more. This is an add-in tool that needs to be activated when required. • Building functions in Visual Basic for Application: Excel has a built-in capability to generate customized functions using Visual Basic for Applications (VBA). This is a powerful tool that saves time for the user without becoming an expert in programming, since it allows the user to build large equations that are used in several areas of the worksheet (e.g., polynomials for the estimation of specific heat of components) and allows the user to read the calculations easily when looking at the formulas in the cells. • Link Excel with Other Software: Excel has become a standard package so that a number of other specialized software use it as a source of information to report data since it is more user-friendly. Therefore, we can use the information in Excel to be loaded in Matlab, Hysys, or Chemcad or transferred back to Excel.

Mathworks Matlab This is one of the most-used software packages in engineering and also in chemical engineering. It is a programming language, which can be divided into two classes; scripts and functions. A script is a number of operations that are A. Kayode Coker and Rahmat Sotudeh-Gharebagh. Chemical Process Engineering: Design, Analysis, Simulation and Integration, and Problem-Solving With Microsoft Excel – UniSim Design Software, Volume 2, (1405–1414) © 2022 Scrivener Publishing LLC

1405

1406  Chemical Process Engineering

General Mathematical Modeling

MS Excel Matlab Matcad Simulink Polymath

Process Simulation

Aspen Hysys Chemcad Aspen Plus UniSim Design SimSci Pro/II ProMax gPROMS

Computational Fluid Dynamics

Comsol Multiphysics Ansys Fluent

Figure 1  Most useful software packages in chemical/process engineering.

performed in a certain sequence. Functions are a particular type of scripts that must begin with the word “function” at the top of them. Functions can be user-friendly or typical operations such as equation solving or differential equations. This language has algebraic, statistical functions predefined along with plotting capabilities. Matlab has a number of functions that allow solving linear and nonlinear equations, optimizing a function and solving differential equations or partial differential equations. Some examples of the use of Matlab in chemical engineering include: • Momentum, Mass and Energy Transfer: There are a number of examples in the transport phenomena field that can be described using a partial differential equation. • Distillation Column Operation: McCabe Thiele Method – typical shortcut approach for the initial conceptual estimation of the operation of binary distillation columns. • Modeling of different kinds of process equipment: heat exchangers, pumps, valves, evaporators, columns, reactors, etc. • Reactor design: The models are based on explicit algebraic equations and differential equations. ODEXX function in Matlab is used to solve the concentration, temperature, and/or pressure profiles along the operation of such equipment. • Control loops analysis: control design and tuning.

Process Simulators The simulation, design, and optimization of a chemical process plant, which comprises of several processing units interconnected by process streams are the core activities in processing engineering. These tasks require performing material and energy balancing, equipment sizing, and cost estimation. A computer package that can accomplish these duties is known as a computer-aided-process design package or a process simulator. The process simulation market has undergone a transformation over two decades, and relatively few systems have survived, and these include: Chemcad, SimSci/Pro II, Aspen Plus, Aspen Hysys, ProSim Plus, SuperPro Designer, gPROMS, and UniSim Design. Generally, these simulation software packages provide the same features with modifications, and we shall review two of these simulation software packages.

Chemstations Chemcad Chemcad features include process development, equipment design, equipment sizing, thermophysical property calculations, dynamic simulations, process intensification studies, energy efficiency/optimization, data reconciliation, process economics, troubleshooting/process improvement, Microsoft Visual Basic, etc. The Chemcad suite includes six products that can be purchased individually or bundled as needed for specific industries, projects and processes.

Epilogue  1407 CC-steady state simulations of continuous chemical processes, features libraries of chemical components, thermodynamic methods, and unit operations. This allows the user to simulate processes from laboratory scale to full-scale plant. It is ideal for users who want to design processes or rate existing processes in the steady state. CC-dynamics is used to conduct dynamic flowsheet analysis, operability check-out, PID loop tuning, operator training, online process control and soft sensor functionality. It is ideal for users who want to design or rate dynamic processes. CC-Therm is used for sizing heat exchangers, covers shell-and-tube, plate and frame, air-cooled and double pipe exchangers. Rigorous designs are based on physical property and phase equilibria data. CC-Batch allows users to design or rate a batch distillation column. CC-Safety Net: Used for analysis of any pipe network with the piping and safety relief network simulation software. CC-Flash: Used to calculate physical properties and phase equilibria (VLE, LLE, VLLE) for pure components and mixtures with good accuracy.

Aspen Hysys and Aspen Plus Two similar software packages with all the functionalities that process simulator should have, are widely used by chemical engineers. AspenTech has a wide portfolio of modeling tools, and the suites of process simulation tools are Aspen Hysys and Aspen Plus. Aspen Hysys (or Hysys) is a chemical process simulator used to model chemical processes from unit operations to full-scale chemical plants and refineries. Hysys performs many of the core calculations of chemical engineering, including those concerned with mass balance, energy balance, vapor-liquid equilibrium, heat transfer, mass transfer, chemical kinetics, fractionation, and pressure drop. Hysys is used extensively in industry and academia for steady-state and dynamic simulation, process design, performance modeling and optimization. Aspen Plus is a process modeling tool for conceptual design, optimization, and performance monitoring for the chemical, polymer, speciality chemical, metals and minerals, and coal power industries. It can also be used for mass and energy balances, physical chemistry, thermodynamics, chemical reaction engineering, unit operations, process design and process control. UniSim Design (Honeywell) is a simulation software package that is used extensively in refinery and petrochemical industries, and has all the functionalities that a process simulator should have, and it is widely used by chemical/ process engineers.

Specialized Software Computational Fluid Dynamics Computational fluid dynamics, known as CFD is the numerical method of solving, mass momentum, energy and species conservation equations and related phenomena on computers by using programming languages. CFD and Multiphysics modeling and simulation can be applied to many science and engineering disciplines. The main areas in chemical engineering are: • • • • • •

Combustion processes. Food process engineering. Fuel cells, batteries, and supercapacitors. Microfluidic flows and devices. Pipe flows and mixing. Reaction engineering.

1408  Chemical Process Engineering The basics of CFD are partial differential equations, and the knowledge of numerical mathematics is essential to solve them with the appropriate numerical techniques. Since these conservation equations are designed and solved on computers, knowledge of programming languages such as FORTRAN, C++, Java or Matlab is important. The most widely used commercial software tools such as ANSYS Fluent, STAR-CD, and STAR-CCM+ are based on the finite volume method, whereas ANSYS CFX uses the finite element-based control volume method. Lukec [1, 2] has provided descriptions of commercial process simulation software with features and their applications.

Good Habits for Process Simulation [3] The following are essential habits that chemical/process engineers should adopt in carrying successful simulation problems.

Build a Simulation Model to Meet an Objective The objective of building a simulation model should be ascertained and well understood. The purpose of running a simulation should be clearly defined at the outset. If the designer were to perform mass and energy balances for a preliminary flowsheet, it may be acceptable to employ a simplified unit operation models available in the simulation software. An example is the use of a short-cut distillation model that uses the Fenske-Underwood-Gilliland method to provide a first-pass distillation model before constructing a rigorous tray-by-tray distillation model. This method requires some detailed information, such as the number of trays, top and bottom temperature, while the shortcut method would normally require the definition of the light and heavy keys, top and bottom column pressures, along with the reflux ratio to converge with the column model. The short-cut distillation computation often provides a useful information required for building a rigorous tray-by-tray distillation model.

Identify the System or Process and Draw and Envelope Around It It is essential to identify the system that is needed for simulation, as in some cases, not the entire flowsheet will be required. One reason may be the limitation of the simulation software. A typical example is where biomass is utilized as feedstock for a biorefinery. In the pretreatment section, biomass will go through some physical treatments for size reduction and moisture removal, before the biomass is fed into the gasification reactor and downstream separation system. Using commercial software such as Aspen Hysys, UniSim Design, dedicated for the refining and petrochemical industry to the simulation task, it would be best to leave out the treatment section, which is a very much a solid-based operation, which is not installed in such simulation, and would be best to focus on the gasification reactor and other separation systems.

Imagine What is Going on Physically Chemical/Process engineers who perform simulation tasks should incorporate some imagination. For example, the engineer can imagine the state and flow pattern/regime for an inlet stream heading to a reactor/flash unit or an effluent stream emitted from a reactor. For the latter case, if the reactor effluent stream contains compressed liquid with light gases, an adiabatic separator (i.e., flash unit) may be added once the reactor is converged to separate the light gases from the liquid components.

Translate the Physical Model to a Mathematical Model Designers should use their knowledge in chemical engineering principles such as reaction engineering, thermodynamics, separation processes, etc., to translate a physical process in the plant into an equivalent mathematical model. This ensures that the correct process simulation can be employed to perform the required tasks. Generally, commercial simulation software packages are for continuous processes. Thus, simulating a batch process

Epilogue  1409 (e.g., bio-fermentation, polymerization, etc.) using a commercial software that is meant for continuous process would be inappropriate and may present a challenging task. For a batch process, it would be more appropriate to use dedicated software packages such as SuperPro Designer (www.intelligent.com) or Aspen Batch Process Developer (www.aspentech.com).

Know Your Components It is important to know the chemicals that are present in the system that user is working on in order to successfully accomplish his or her simulation problem. Understanding the type of intermolecular interactions that may exist in the system will enable the user to choose the correct property estimation methods. In some cases, there may be some components that are not represented in the simulator’s component database. In this instance, it may be necessary to either find an equivalent component or create a user defined or “hypothetical” component as in refinery crude distillation unit of the hydrocarbon system. An awareness of the presence of water in a predominantly hydrocarbon process stream is essential, as some thermodynamic models may have to lump the organic and aqueous phases into a single liquid phase, even though water is immiscible with the hydrocarbon. Thus, the selection of a thermodynamic model is critical in this kind of system.

Know the Context of Your Feed Streams It is important to know the characteristics of the feed stream, e.g., its origin, composition, sampling conditions and the presence of impurities. In some instances, a composition for a gas stream that comes from a three-phase (gas, oil and water) separator may not contain any water. This is because the stream composition has been determined using gas chromatography (GC). In a GC analysis, a carrier gas typically, helium (He) transports the gas sample into a length of tubing (called a column), which is packed with a polymer or solid support. Water will damage this polymer and is removed before the gas enters the column. In this case, it is essential to saturate the gas with water prior to using it for any computations; otherwise, the contribution of water in the gas, particularly the heat of vaporization will not be accounted for and will result in an inaccurate heat and mass balance.

Know Your Components Boiling Points In performing simulation for a separation system (e.g., flash and distillation), it is important to know the boiling points and hence the relative volatility of the chemicals involved. It is good practice to have the chemicals arranged in ascending order of their boiling points (e.g., volatilities). An example is shown below. Chemicals arranged in the ascending order of their boiling points. Components

Boiling points (oC)

Ethane (C2H6)

-88.6

Propane (C3H8)

-42.1

n-Butane (nC4H10)

-0.5

n-Pentane (nC5H12)

36.2

n-Hexane (nC6H14)

68.8

A process stream consists of five hydrocarbon components was to be used for a distillation computation. It would be easy to draw a line between the light and heavy keys and perform a quick material balance to determine the distillate

1410  Chemical Process Engineering and bottom product flowrates. Furthermore, designers should be aware of polar molecules and chemicals that have hydrogen bonds that may give rise to azeotropic system where high boiling point components boil and vaporize before low boiling point components.

Keep Track of the Units of Measure in All Calculations Errors on units of measurement can be serious and costly, and should be avoided with some discipline. The best practice is always to keep track of the units of measurement in all computations or simulation exercises. Commercial simulation software packages are equipped with unit conversion functions for all unit operations and stream parameters. These packages allow for global units of measure profiles to be defined and saved. Prior to starting a simulation exercise, it is necessary to first define what units of measure are to be used for the analysis and reporting purposes and ensure that this is adopted by all personnel working on the project.

Always Do a Simple Material and Energy Balance First A good habit is to perform some manual calculations (or “hand calculations”). For example, performing a quick material and energy balances prior to executing a process simulation exercise enables the designer to have a better “feel” for the orders of magnitude in the numbers that may be encountered. Furthermore, these hand calculations can be employed as initial guesses for more complex types of computations. For an instance, in designing a depropanizer column, we can perform a quick material balance by assuming most (if not all) propane is recovered at the top stream of the column, and heavier components are recovered at the bottom stream. This will provide an estimate for overhead and bottom flows and can be used as an initial guess for a rigorous tray-by-tray distillation model.

Plot the Phase Envelope for Important Streams It is important to know the state of the fluid. For example, is it a subcooled or saturated liquid? For a process stream with a subcooled liquid, temperature rise is expected when sensible heat is added; the latter is the product of mass flowrate, heat capacity, and temperature rise. On the other hand, no temperature rise will be reported when a saturated liquid is heated, as latent heat is involved. Furthermore, it is necessary to check whether the fluid is near the critical point or is at the supercritical stage. Furthermore, it is important to know how close the process stream is to the dew point (either hydrocarbon or water). When adsorption beds or fuels gas systems were designed, liquid formed at the dew point may damage the adsorption bed or combustion chamber. Another practice is to identify the retrograde region of the fluid. In the retrograde region, compressing a fluid may result in its vaporization instead of liquefaction.

Caution in Using Process Simulators Process simulation software is a powerful and useful tool to model chemical process flowsheets of varying complexities and for sizing equipment that is associated with plants in all facilities. It is also employed in operators’ training after commissioning of the plants. Recent simulators incorporate comprehensive pure component databank, and exhaustive library of thermodynamic systems, physical property estimation methods and inbuilt algorithms for every unit operation/chemical process with user friendly graphical interface. Many commercial simulators are versatile, solve and optimize virtually any flowsheet synthesis problems. However, despite their sophistication, and rigorous modeling techniques, they fail to represent real-life plant data. In most cases, the user shows a blind faith in the inbuilt configurations and default selection of methods in the simulators, which can introduce erroneous results for specific systems. Since simulators generate multiple and at times conflicting solutions for the same set of external input data parameters, doubts about their effectiveness and reliability often occur.

Epilogue  1411 Advances in computer technology and the availability of modern tools have enabled commercial simulation software packages to be an integral part of process design practices. Process simulation is employed at all stages of process plants, from concept and feasibility study to basic design involving Front End Engineering Design (FEED) to detailed design, commissioning, training, and revamps. Process design heavily depends on software to model, simulate and optimize design alternatives. These process simulators are part of an integral computer-aided design package that contains computer-aided engineering software, computer-aided design systems, and process simulation software [4, 5]. Software manages flowsheet information, mass/energy balances, property data, equipment specification and cost data during the design phases from process development to plant operation. Process simulators consist of various building blocks: • Unit Operation Library. • Models for reactors (stirred tank, plug flow, fixed bed, membrane reactor, biochemical reactor, etc.) • Models for separators (distillation column, absorption column, Extractors, Chromatography, etc.) • Models of auxiliary equipment (pumps, compressors, pipes, splitter, etc.) • Reaction Kinetic Library • Models for different reactors types • Material Property Library • Material data (density, viscosity, thermal conductivity, boiling/melting points, etc.) • Mixture data (solubility, vapor-liquid equilibrium, etc.) • Cost Library • Equipment cost, raw material cost, utility cost • Mathematical Algorithms for mass balances, simulation, and optimization Process simulation generally follows a certain procedure: • • • • • • • • • • •

Use the most promising process structure to build a simulation model Select unit operations and equipment from software library Define streams and recycles between equipment Specify input data (feed rates, equipment size, tray number, heat exchanger, etc.) Define initial process parameters (temperature, split ratios, etc.) Validate simulation model Calculate conversion, selectivity, and yield Establish mass and energy balances Calculate manufacturing cost and capital investment Evaluate different process and equipment parameters Use to compare alternate process structure and optimizer parameters

Simulators serve a wide variety of unit operations in the refining, and chemical process industries, including the fine chemical and biochemical industries. This includes mathematical solver algorithms specific to every unit operation model. These mathematical models are supported with internal databases covering physical and thermodynamic property databanks. In a bid to enhance the capability of the software, these simulation packages present multiple choices for the user to configure and then to solve the flowsheet. As more options become available, it is expected and assumed that the user has adequate knowledge to select appropriate methods and employ correct choices to solve the flowsheet. Since simulation software uses advanced high-end computer hardware for such sophisticated and advanced simulation programs, there is no programming limit with respect to representing multiple choices to the user. In fact, they are increasingly interpreted falsely, as more choice, more capability products. Thus, the availability of many choices poses a challenge for process simulation engineers to

1412  Chemical Process Engineering Pure component database

Thermodynamic property database Physical property database

Circulation algorithms

Predefined unit operation mathematical models

Initial estimates

Multivariable controllers

Inbuilt calculation sequences

Data sheets

Stream data, heat and mass balances

Flowsheet tolerances

PFDs, heat release curves

Figure 2  General architecture of a typical commercial steady state simulator [4].

check the applicability and suitability of every choice to model a given process, verify the advantage or disadvantage of the selection, and determine its effectiveness over the operating range. Therefore, to utilize the capability of the simulation software, adequate knowledge and specific process experience become a prerequisite, as this basic and fundamental issue could affect the quality of simulation output results. Knowing how to configure a flowsheet in a simulation environment and familiarity in operating the simulator does necessarily confirm the availability of skills required to solve and analyze flowsheet synthesis results. Although simulator programs provide early warnings for missing input data or inadequate input data, there may be no warning if the user selects an inappropriate calculation method. This could occur in the application of various choices of selecting the thermodynamic system. Figure 2 shows a structure of modern simulators that carry a wide variety of unit operation libraries, expanded thermodynamic data libraries, comprehensive pure component and binary interaction parameter databases, initial estimate generators, etc. Reviewing these capabilities, the most chemical plant modeling problems or process design and optimization problems can be accurately resolved; however, this is not a reality. Accuracy of simulation output is critical, irrespective of the reputation of the simulation package deployed, or the speed to obtain the results. Unless the simulation model accurately describes the interaction of different components at varying temperatures or pressures using reliable methods, simulation results will not represent reality. Simulators are mainly automated mathematical model solvers based on inputs provided by the user. Therefore, simulation input parameters require skilful scrutiny, and the results must be carefully analyzed based on fundamental principles and the specific objectives of a simulation.

Conclusion A process simulator is one of the most powerful tools for modeling and simulating a process flowsheet. It is highly effective and flexible when applied to the design and analysis of complex systems, but at the same time its results can be misleading and prone to generate conflicting results if proper modeling techniques are not understood. The fundamental knowledge of thermodynamics, engineering principles and unit operations could cause and effect type of

Epilogue  1413 error analysis skills, the ability to understand, and gaps in input data; the degree of sensibility of performance parameters to the variable parameters and so on plays an essential role in the success of a simulation exercise. Furthermore, validation of a simulation model by mirroring actual operational performance in a laboratory scaled equipment, pilot plant, and scale-up plant unit can provide confidence of reliable results. The success of a simulation depends on the user’s ability to interpret input data and results.

References 1. Ivana Lukec, What is the Most Useful Software in Chemical Engineering, www.simulativelive.com, March 2019. 2. Ivana Lukec, Complete list of Process Simulators, (Part 1/2) Review of simulation software for industrial plants, www. simulativelive.com, April, 2017. 3. Dominic Chwan Yee Foo, et al. Chemical Engineering Process Simulation, Elsevier, 2017. 4. Atul Choudhari, Should you rely on your simulation results? Petroleum Technology Quarterly, (PTQ), pp. 47–52, Q4, 2020. 5. Agarwal, Rajeev, Yau-Kun Li, Oscar Santollani, Satyro, Marco and Andrew Viler, Uncovering the Realities of Simulation Part 1, pp. 42–52, CEP May 2001. Part 2, pp. 64–72, June 2001.

Index Absorber, 498, 625, 838 Absorption, 150, 386, 413, 425, 498 Activation, 681, 735, 815, 819 Adiabatic, xvi, 735, 765, 777, 827 Adsorption, 543, 756, 763, 803, 906 Agitation, 543, 759, 775, 882 Aircooled, 294, 315 Anaerobic, 758 Anerobic, 758 Annualized, 454, 525 Annular, 46 Antibiotics, 759 Arrhenius, 681, 795, 801, 875, 878 Axial, 365 Azeotrope, 422 Backpressure, 597, 633, 725 Baffle, 7, 30, 45, 47, 167 Biochemical, 751, 828 Biomass, 769, 771, 904 Bioreactor, 758–759, 769 Blanket, 640 Blenders, 834, 889, 898 Brackish, 405, 408 Bridgwater, 838, 858 Calorimeter, 683, 741 Cascades, 470–471, 578–579, 581 Catalysts, 750, 771 CFSTR, 778, 863–864 Channelling, 862 Chattering, 627 Chemostat, 760 Clapeyron, 712, 726 Combustion, 415, 419, 827–828, 903 Composites, 453, 465, 487, 539, 542, 578 Compositions, 635, 737, 768 Condensate, 126, 334, 439–441, 562 Condensers, 11, 42, 99, 392 Condensible, 688–689 Conduction, 25, 43, 45, 330, 332, 433 Conductivity, 258, 279–280 Convecton, 419 Cooler, ix, 285, 307, 392–393, 429, 441, 451 Cooler condenser, 393

Corrosion, 18, 133, 137, 139, 392 Crosby, 590–591, 637, 717 Crossflow, 23, 217, 232 Cryogenic, 2, 316, 542, 592 Crystallization, 136 CSTRs, 768, 797–798, 800 Danckwerts, 769, 828 Debottlenecking, 448, 554, 585 Depreciating, 845, 855 Depressurization, 741 Designs, 22, 446, 522, 583 Detonation, 737, 745, 777 Dispersion, 742, 864 Distillation, 334, 391, 491, 498, 621, 862, 870, 902 Distributor, 21, 752 Downcomer, 334 Downtherm, 161–162 Dryers, 834 Endothermic, 687, 756, 761, 813, 864 Equilibria, 903 Equilibrium, 698 Ergun, 808, 810, 820 Erosion, 1, 11, 29, 133 Erosion corrosion, 436 Evaporation, 11, 280, 464 Exchange, 2–3 Exchanger, 101 Exothermic, 680 Fenske, 904 Fermentation, 905 Financial, 842 Fintube, 26–28, 34, 252, 254–258, 260, 392 Flammability, 737 Flare, 79, 710 Flashing, 693, 722, 747 Flooding, 305, 862 Flowsheets, 444, 461, 765, 906 Fluidization, xxiii, 756 Fluidized, 752, 769, 827–828 Flux, xv, 331, 336, 713, 724, 726 Foam, 691, 781 Fouled, 134, 245

1415

1416  Index Fouling, viii–ix, 135, 280 Fractionating, 570 Friction, 123, 129–130, 185, 192, 209, 240, 250, 391 Furnace, 436, 563, 570 Gaseous, 49, 688–689, 752, 760 Gassy, 688, 693, 698, 705, 738 Greenhouse, 134, 445, 449, 543, 548, 858 Hairpins, 251–252 Hammer, 440 HAZAN, 741 Hazards, xvi, 679, 746–747, 774, 828 HAZID, 554 HAZOP, 738, 741 Helical, 37, 162, 164, 317 Hemisphere, 235, 390–391, 393 Hemispherical, 631, 669 Heterogeneous, 750, 763–764, 768, 801 Heuristic, 478–479, 487, 489 Homogeneous, 695, 699, 750 Hybrid, 688–689, 701–702 Immobilized, 759 Impeller, 749, 754 Incident, 676, 678, 751, 775–777 Inflation, 847 Inherently, 738, 778–781 Intensification, 445, 741, 756, 902 Intercooler, 248 Kirkpatrick, 845 Knockout, 702, 710 KuhnTucker, 869 Laminar, 235 Leakage, 36, 168 Lineweaver, 773, 825, 827 Lineweaver Burk, 823 Macromixing, 769 Macroscales, 770 Maldistribution, 314, 429–430 Maloperations, 677, 862 Management, 543, 585–586, 899 Michaelis, 772–773, 822, 824, 826, 828 Microbes, 759 Microorganisms, 543, 759, 771 Mist, 46, 439 Mixer, 768, 781, 882 Multicomponent, 1, 373, 549, 711–712, 723 Nucleate, 330–334, 336, 432–433 Nutrients, 759, 771

Omega, 711, 715–718, 720, 730, 732 Optimisation, 585, 899 Organisms, 137, 758–759, 771 Orifices, 43, 633 OSHA, 619, 675, 742 Overpressure, 646, 657–659 Oxygenates, 867 Packed, 4, 591 Packing, 10, 22, 753 Particulate, 136, 139 Pattern, 84, 235, 367 Payback, xvii, 448, 840 Payout, 554 Pfaudler, 146, 153 Pharmaceutical, xix, 675, 683, 774 Pipeline, 217, 365, 882 Plug, 288–289 Preflash, 569 Pressure relief, 624–625 Pretax, 845 Propeller, 290 Pulsation, 601 Pump, 429, 532–533, 570, 620–621 Pump around, 580 Purge, 405, 541, 640, 740 Quench, 406, 412 Radiative, 323 Reactors, xvi, 764, 768 Reboilers, 334, 390, 392 Recovery, 448, 456, 460, 465, 473, 526, 536, 584, 586 Recycled, 498, 530 Reflux, 365, 563, 620, 861–862 Refrigerant, 167 Refrigeration, 454, 464, 474, 498, 536 Reliefs, 607, 688, 702 Reseats, 590, 630 Residence, 543 Rohsenow, 247, 392–393 Runaways, 678, 680 Ruptured, 631, 645–646, 678 Safety, xiv, 596 Saturation, 543, 716–717, 719, 721 Scanning, 683, 777 Seal, 7, 601 Sealed, 20, 36, 42, 626, 708 Sealing, 216 Segregation, 898 Semibatch, 864 Separation, 755, 870 Simulators, 902, 906–909

Index  1417 Slug, 437 Slurry, 751–752 Solvers, 769, 867–869, 908 Sonic, 637–640, 736–737, 742, 744 Spheres, 668, 757 Spherical, xvi, 757–758, 815, 835 Spray, 294, 296, 405, 409, 429, 781 Stagnation, 740 Steady, 106, 366, 829 Steam, xiii–xiv, 164, 291 Stoichiometric, 766–767, 785, 790, 860 Storage, 287, 621, 745, 747, 882, 892 Strainer, 437 Stratified, 438 Subcooled, 711, 717, 720 Sublimation, 635 Subsonic, 742 Substrate, 750, 771–773, 822 Sucrose, 823–825 Super target, 528 Target, 461, 470, 506, 521, 526, 549, 581, 583 Tax, 845, 855, 858 Tempered, xv, 703 Tempering, 688–689, 695 Thermal, vii, xv, 137, 279–280, 323 Thermochemistry, 676, 775 Thermodynamic, 446, 460, 531, 740, 908 Thermosiphon, 441 Thicknesses, 76, 237, 669

Towers, 294, 296, 434, 553 Tracer, 322–323, 328–329 Transformer, 149, 385, 406, 412, 424 Traps, 334, 439, 549 Trays, 440, 670–671, 834, 904 Treating, 294, 336, 545, 870 Troubleshooting, 366, 393, 437–440 Tubesheet, 4 Tubeside, 157–158, 368 Tubular, 329 Turbine, 287, 620 Unbaffled, 366 Uncontrollable, 529, 688 Vacuums, 1 Vaporization, x, 86, 147, 329, 333, 436 Vaporizers, 23, 316, 332 Vent, xv, 694, 702 Venting, 699, 741, 745 Visualization, 544 Void, 700 Voidage, 810–811, 817 Wastewater, 544, 586 Watson, 42, 390, 858 Wavy, 440 Yield, 865

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