Ludwig's Applied Process Design for Chemical and Petrochemical Plants [3, 4 ed.] 0750685247, 9780750685245

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants Volume 3. Fourth Edition

A. Kayode Coker

AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW YORK • OXFORD • PARIS SAN DIEGO • SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Gulf Professional Publishing is an imprint of Elsevier

Gulf Professional Publishing is an imprint of Elsevier 225 Wyman Street, Waltham, MA 02451, USA The Boulevard, Langford Lane, Kidlington, Oxford, OX5 1GB, UK Copyright © 2015 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangement with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. ISBN: 978-0-7506-8524-5 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data A catalog record for this book is available from the Library of Congress For information on all Gulf Professional publications visit our website at http://store.elsevier.com/ Typeset by TNQ Books and Journals www.tnq.co.in Printed and bound in United States of America Last digit is the print number: 10 9 8 7 6 5 4

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To honor God in all things and to perform everything solely for the glory of God “In the Light of Truth” by Abd-ru-shin

Dedication In memory of Ernest E. Ludwig (A great chemical engineer) and In loving memory of my parents Mr. Gabriel Shodipo Coker and Mrs. Esther Modupe Ajibike Coker To my sons, Akintunde and Ebunoluwa To my wife, Victoria Omolara Coker Love and thanks

Crystal images (c) Office Masaru Emoto, LLC

Foreword Ernest Ludwig’s three-volume “Applied Process Design for Chemical and Petrochemical Plants” is one of the classic texts of chemical engineering. It is known for its blend of practical, scientifically-based design methods and realworld details of equipment and processes, and it has been a trusted resource for a generation of process engineers. The world of plant design has moved on since Ludwig’s first edition in the 1960s, and he authored two further editions to keep the material fresh and current. With his passing, it has fallen to A. Kayode Coker to handle the fourth edition. Dr. Coker brings a great breadth of experience to this undertaking, both from academia and industry, and this uniquely equips him to take on the task. His academic experience, including a period as Chairman of the Chemical & Process Engineering Department at Jubail

Industrial College, gives him deep insights into both the fundamental science of process design and the needs of the students who grapple with its concepts. His industrial experience, including his current role as engineering coordinator at Saudi Aramco Shell Refinery Company, together with his consulting work, have given him a broad understanding of the real-world aspects of process design and the requirements of its practitioners. The fourth edition reflects this balanced perspective, and it provides a resource of great value for readers at every stage of their engineering career. I heartily recommend it to you. Alan Rossiter, PhD, PE President, Rossiter & Associates Bellaire, Texas

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Preface to the Fourth Edition This complete revision of Applied Process Design for Chemical and Petrochemical Plants, Volume III, builds upon the late Ernest E. Ludwig’s classic text to enhance its use as a chemical engineering design manual of methods and proven fundamentals with supplemental mechanical and related data, nomographs and charts. Significantly expanded and thoroughly updated, this fourth edition contains new topics that will assist the engineer in examining and analyzing problems and finding design methods and mechanical specifications to secure the proper mechanical hardware to accomplish a process objective. This latest edition includes improved techniques and fundamental design methodologies to guide the engineer in designing process equipment, such as heat exchanger types, compressors, and applying chemical processes to the properly detailed hardware. Like its predecessor, this edition continues to present updated information for achieving optimum operational and process conditions and to avoid problems caused by inadequate sizing and lack of internally detailed hardware. The various derived and proven equations have been employed in actual plant equipment design, process control and operator’s training and they are some of the most indispensable available to both inexperienced and experienced engineers alike. This book further provides both fundamental theories where applicable and directs application of these theories to applied equations essential in the design effort. This approach in presenting design information serves well for troubleshooting heat exchangers, compressors equipment, and in executing system performance analysis. Chapter 15, “Heat Transfer”, has been thoroughly revised and updated, and now includes several important design techniques for difficult condensing situations and for the application of thermosiphon reboilers, designs of aircoolers, plate heat exchangers, double pipe heat exchanger, heat tracer requirements for pipelines and heat loss from insulated pipelines, batch heating and cooling of fluids, troubleshooting of heat exchangers and case studies of heat exchangers failures. The chapter provides a detailed review of fouling in heat exchangers and solutions in reducing this phenomenon. Computer programs have been developed for the design/rating of these exchanger types and Microsoft Excel spreadsheets have been developed to deal with batch heating and cooling of fluids.

Chapter 16, “Process Integration (PI)” is a new chapter. The chapter reviews PI in heat exchanger networks, involving a systematic and oriented approach to heating, cooling and power generation to process design, and optimization that exploits the interaction between different units, exchangers and utilities in order to employ resources effectively and minimize costs. The Excel spreadsheet program from Ian C. Kemp’s text [21] has been used to determine pinch temperature, cold and hot pinch temperatures, hot and cold composite curves, grand composite curve, hot and cold utility requirements. The program further produces graphical outputs of pinch temperatures, hot and cold utility requirements at varying DTmin. Chapter 17, “Refrigeration Systems,” has been improved with additional data and new systems designs for light hydrocarbon refrigeration. The chapter introduces the Carnot refrigeration cycle and its performance, mechanical refrigeration, types of refrigeration systems and a glossary. Chapter 18, “Compression Equipment,” has been generally updated with equations for the design of compressors, and it introduces other compressor types, such as the oil flooded screw compressor and integrally geared compressors. The chapter reviews compressor troubleshooting and applies Hysys simulation software on a case study. Chapter 19, “Reciprocating Compression Surge Drums,” presents several new techniques, as well as additional detailed examples. The chapter provides preliminary design methods and provides the reader with references for the most effective design approach. Further, the chapter reviews evaluation of the surge capacity and pulsation frequencies of the system, compressor, and discharge surge drums and discharge header in order to comprehend the performance of the compressor. Chapter 20, “Mechanical Drivers,” has been updated to include the latest code and standards of the National Electrical Manufacturer’s Association and information on new energy-efficient motors. The chapter describes the commonly used, general-purpose, alternating current motors and mechanical drive turbines that are used in the chemical and petrochemical industries. The chapter provides National Fire Codes for hazardous locations, and articles that recognize certain subjects that are pertinent to the process engineer. xiii

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Preface to the Fourth Edition

Chapter 21, “Industrial and Laboratory Reactors e Chemical Reaction Hazard and Process Integration of Reactors,” is a new chapter that reviews various reactor types and their advantages and disadvantages with respect to their individual applications and control. The chapter considers the design of a packed bed reactor by applying POLYMATH software in its design. Reviews of agitator types pertinent to various reaction systems are considered, as are catalysts and catalytic processes. Detailed analysis of chemical reaction hazards, hazard and operability (Hazop) studies of a batch process, hazard analysis (Hazan) and others such as Process Hazard Analysis (PHA), Failure Mode Effect Analysis (FMEA) and Fault Tree Analysis (FTA) are reviewed. A case study of a runaway reaction incident at T2 Laboratories, Jacksonville, Florida, USA is presented. Reaction System Screening Tools for classifying runaway chemical reactions, hazards of pyrophoric reactions and heat integration of reactors are described. Chapter 22, “Metallurgy e Corrosion,” is a new chapter that describes factors affecting the selection of materials, and reviews Stress Corrosion Cracking (SCC), providing a case study of a pressure vessel failure at NDK manufacturing company in Belvidere, Illinois, USA. The chapter describes corrosion types with illustrations, factors affecting the rate of corrosion and control. Finally, corrosion monitoring and common mistakes in chemical processing plants are considered.

Software/Programs/Excel Spreadsheets/ Charts ExcelTM spreadsheet programs as worked examples, and developed computer programs (Absoft FortranTM) that use the Microsoft Runtime Windows Environment (MRWE) are new additions to the fourth edition in various sections of the chapters. These programs are provided in executable format, and Appendix I provides an illustration of their use. Incorporated is Hysys simulation design software to perform case studies and some worked examples in the text. A program on Conversion Tables developed by Mr. Ahmed Mutuwa, formerly from SASREF Co., is

available. All the above can be accessed from the Elsevier companion website: http://booksite.elsevier.com/ 9780750685245 I assume that the reader is an undergraduate or graduate student in chemical or process engineering, or a chemical/ process, or other related engineer, having a sound knowledge of the fundamentals of the profession. With this assumption, I illustrate the techniques of design and mechanical details necessary for the construction of processes. The aim of the process engineer is to ensure that results of his or her process calculations for equipment are specified in terms of something that can be economically constructed or selected from special designs or manufacturers. This edition follows the format of previous editions, and the concept is stressed to a reasonable degree in the various chapters. The techniques of applied chemical plant process design continue to improve as the science of chemical engineering develops new and better interpretations of the fundamentals of chemistry, physics, metallurgy, mechanical engineering and polymer/plastics science. Accordingly, this fourth edition presents additional reliable design methods based on sound experimental data, proven techniques developed by companies and individuals and groups considered competent in their subjects and which are supported by pertinent data. In many chemical and petrochemical processes, the designer will find design techniques adaptable to 75 to 80% of his/her requirements. Thus, an effort has been made to place this book in a position of utilization somewhere between a handbook and an applied teaching text. The present work is considered suitable to provide a practical guide to chemical process design for undergraduate and graduate students in chemical engineering, practicing process engineers and chemical or process engineers working in process development. The text can readily be used, if a general course in plant design is available to fill in the broader factors associated with overall plant layout and planning. To access the additional material accompanying this book, please visit: http://booksite.elsevier.com/9780750685245 On this companion website there are many useful Excel spreadsheets, appendices, examples and software.

Biography A. Kayode Coker, Ph.D., is an engineering coordinator at Saudi Aramco Shell Refinery Company in Jubail, Saudi Arabia, and was Chairman of Chemical & Process Engineering Department at Jubail Industrial College, and is a consultant for AKC Technology in England. He has been both a chartered scientist and a chartered chemical engineer for more than 30 years. He is a Fellow of the Institution of Chemical Engineers, UK, (C.Eng., CSci, FIChemE). He is also a senior member of the American Institute of Chemical Engineers (MAIChE). 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, UK and a Teachers’ Certificate in Education at the University of London, UK. He has directed and conducted short courses in both the UK and for SABIC industries in Saudi Arabia. His articles have been published in several international journals, he is an author of four books in chemical engineering and a contributor to the encyclopedia of Chemical Processing and Design, vol. 61. He was named as one of the International Biographical Centre (Headquarters in Cambridge, UK) as LEADING ENGINEERS of the World 2008. Also, he is a member of International Who’s Who of ProfessionalsTM and Madison’s Who’s Who in the US.

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Acknowledgments This final project of Ludwig’s three-volume texts is a cul­ mination of four years of research, collating relevant and recent materials from organizations, institutions, companies and publishers. The three-volume texts took twelve years to complete, and soliciting for proofreaders has also been an important step in the editorial process. Emulating the incredible work of the late Ernest E. Ludwig is a formidable task, and without the help of various experts in their field of specializations and organizations, this project would have been impossible to achieve. My mentor, the late Dr. Clive Mumford, had provided constructive criticisms and inspiration in earlier works of the three-volume text for which I am deeply grateful. His views on various aspects in the earlier volumes and his attention to intricate details are greatly appreciated. Sincere appreciation and thanks to Mr. Dale Gulley and Mr. Manish Shah for their critical reviews and providing invaluable comments and suggestion for the various aspects of Chapter 15. In particular, Mr. Shah also gave permission to include his article “Good Practice for Heat Exchanger Selection and Design” in Appendix M of the text. Many thanks to Professors John R. Thome for providing figures relating to boiling and evaporation in Chapter 15, Mahmoud El-Halwagi, Robin Smith and Daniel R. Lewin for granting permission to incorporate exercises and examples from their texts in Chapter 16 and Professor Toyin Ashiru for providing figures for Chapter 22. Chapter 16, a new chapter on process integration, involved the participation of many experts, namely: Drs. Gavin Towler, Alan Rossiter and Uday V. Shenoy. I would like to record my appreciation and gratitude to these renowned people for their expert knowledge and help in providing suggestions and comments in the text. This chapter is greatly enhanced by comments and suggestions provided by these individuals and the review of case studies carried out by Dr. Alan Rossiter. Dr. James P. Burelbach has provided an invaluable help in reviewing aspects of Chapter 21 relating to two-phase flow in reactors, incorporating the new methodology and sizing equations, for which I am deeply grateful. Also, I would like to express my gratitude to Professor Micheal

B. Cutlip for granting permission to use the POLYMATH software. Many organizations, institutions and companies such as Gas Processors Supplier Associations (GPSA), USA, American Institute of Chemical Engineers (AIChE), The Institution of Chemical Engineers (IChemE), Absoft Corporation© USA, Chemical Engineering magazine by Access Intelligence, USA , Hydrocarbon Processing, Chemical Safety & Hazard Investigation Board (CSB), have readily given permission for the use of materials, and their release for publication. I greatly acknowledge and express my deepest gratitude to these organizations. I have been privileged to meet with wonderful indi­ viduals such as Tim Calk and Phil Carmical, former editors of Gulf Publishing Company and Elsevier respectively. Phil first suggested Ludwig’s classic work over twelve years ago and defended my proposals in the presence of Elsevier’s management to revise the three volumes of Ludwig. It has been an eventful and formidable task and I thank you for your trust and encouragement. To Tim, I am grateful for your friendship and help since my first book some nineteen years ago. Gratitude to the students of Chemical Engineering Technology major during my tenure as an instructor and as departmental chairman at Jubail Industrial College, Saudi Arabia. It has indeed been a privilege to have enriched the lives of these individuals in chemical engineering and to have learned from them also. I also wish to express my sincere thanks to the Elsevier team: Jonathan Simpson, Naomi Robertson, Pauline Wilkinson, Fiona Geraghty, and Cari Owen, and the pro­ duction staff for their patience and professionalism in the production of this final volume. Finally, Bow down in humility before the Greatness of God, whose Love is never ending, and who sends us his help at all times. He alone is Life and the Power and the Glory forever and ever. A. Kayode Coker

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Chapter 15

Heat Transfer 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, pinch technology (Chapter 16) have been employed in the energy integration of process plants and of heat exchangers, in particular. This has resulted in improved plant performance and 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 are 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 vacuum to ultra-high pressures of over 15,000 psig (100 MPa), from cryogenic conditions to high temperatures of w2000
F (1100
C), and any temperature and pressure differences between the fluids, limited only 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 1 ft2 (0.1 m2) 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 tubeside 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 noncompact exchangers, and the heat-transfer area per unit volume ranges from 15 to 30 ft2/ft3 (50e100 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 [5,22,36,40,61,70, 74,82,286,287,288 and 289] 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, and 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 [71] have proposed thermal concepts that may offer new approaches. The most popular and reliable software packages for the design or rating of shell and tube heat exchangers are: l l l

l

BJAC: USA 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

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants. http://dx.doi.org/10.1016/B978-0-7506-8524-5.00015-X Copyright © 2015 Elsevier Inc. All rights reserved.

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therefore, are not provided in the open literature. Tinker [290,291] 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 [292,293], using standard tolerances for commercial exchangers and only a limited number of baffle cuts. Devore has presented nomographs that facilitate the application of the method in manual calculations. Mueller [294] has further simplified Devore’s method and provides an illustrative example. Bell [295,296] has 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 (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 or 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, in pre-heat trains in the refining of crude oil. Detailed reviews are supplied with examples, employing developed Microsoft Excel programs for determining heat transfer coefficients in jacketed, agitated vessels and the time required for batch processing involving isothermal and non-isothermal heating and cooling conditions with coils and external heat exchangers, as experienced in various chemical process industries.

TYPES OF HEAT TRANSFER EQUIPMENT TERMINOLOGY The chemical process industries (CPIs) require heat exchangers 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 of the process. The optimal heat exchanger design should minimize operating costs and maximize product output. Shell and tube heat exchangers (Figures 15-1BeD) consist of a bundle of tubes inside a cylindrical shell. One fluid (the tube-side fluid) flows inside the tubes while 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’s stability, as they prevent the tube from sagging due to its structural weight 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 to check drawings of this equipment. The shell and tube exchanger consists of four major parts: l

l

l

l

Front header e this is where the fluid enters the tubeside of the exchanger. It is sometimes referred to as the stationary header. Rear header e 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 e this comprises of the tubes, tube sheets, baffles and tie rods etc. which hold the bundle together. Shell e this contains the tube bundle.

The standards of the Tubular Exchanger Manufacturers Association (TEMA) [107] is the only assembly of unfired mechanical standards, including selected design details and Recommended Good Practice and it is used by all reputable exchanger manufacturers in the US and many manufacturers in other countries who supply US 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 e 2007, 9th Ed] for mechanical design and fabrication are: RCB e 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  106 kPa); and maximum design pressure of 3,000 psi (20684 kPa). The intention of these parameters is to limit the maximum

Heat Transfer Chapter | 15

shell wall thickness to approximately 3 in. (76 mm), and the maximum stud diameter to approximately 4 in. (102 mm). R e Designates severe requirement of petroleum and other related processing applications. C e Indicates generally moderate requirements of commercial and general process applications. B e Specifies design and fabrication for chemical process service. RGP e 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

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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 15-1AeG and Table 15-1 from the Standards of Tubular Exchanger Manufacturers Association [107] give

FIGURE 15-1A Nomenclature for Heat Exchanger Components. Figures 15-1AeG used by permission: Standards of Tubular Exchanger Manufacturers Association, 7th Ed., Fig. Ne1.2, © 1988. Tubular Exchanger Manufacturers Association, Inc.

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FIGURE 15-1B Floating head. (© 1988 by Tubular Exchanger Manufacturers Association, Inc.)

FIGURE 15-1C Fixed tubesheet. (© 1988 by Tubular Exchanger Manufacturers Association, Inc.)

FIGURE 15-1D Floating headeoutside packed. (© 1988 by Tubular Exchanger Manufacturers Association, Inc.)

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 15-1 and Figures 15-1AeG. 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 15-1F and 15-1G). It is important to recognize that the components in Figures 15-1BeK are associated with the basic terminology regardless of the type of unit. Application and selection guides are shown

Heat Transfer Chapter | 15

FIGURE 15-1E Removable U-bundle. (© 1988 by Tubular Exchanger Manufactures Association, Inc.)

FIGURE 15-1F Kettle reboiler. (© 1988 by Tubular Exchanger Manufacturers Association, Inc.)

FIGURE 15-1G Divided flowdpacked tubesheet. (© 1988 by Tubular Exchanger Manufacturers Association, Inc.)

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6 Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-1 Standard TEMA Heat Exchanger Terminology/Nomenclature* 1. Stationary Heat e Channel 2. Stationary Heat e Bonnet 3. Stationary Heat Flange e Channel Bonnet 4. Channel Cover 5. Stationary Head Nozzle 6. Stationary Tubesheet 7. Tubes 8. Shell 9. Shell Cover 10. Shell Flange e Stationary Head End 11. Shell Flange e 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 e 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 15-1B-G. See Figure 15-1A 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.

in Table 15-2, Table 15-3 and Figure 15-2. Table 15-4 compares the attributes of these three classes of exchangers in order of decreasing cost and mechanical performance. Figures 15-1O and 1P show photographs of tube bundles with baffles, and Figure 15-1Q shows a typical shell of a shell and tube heat exchanger.

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 15-2, 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 [281].

FIGURE 15-1H Fixed tubesheet, single-tube pass vertical heater or reboiler. (Used by permission: Engineers & Fabricators, Inc., Houston.)

Construction Codes The ASME Unfired Pressure Vessel Code [119] is accepted by almost all states as a requirement by law and by most industrial insurance underwriters as a basic guide or requirement for the 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, ASME Boiler Code [6] applies, and many states and insurance companies require compliance with this. These classes are explained in the TEMA standards and in Rubin [99,100,133].

Thermal Rating Standards The TEMA Code [107] does not recommend a 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

Heat Transfer Chapter | 15

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FIGURE 15-1I Floating head, removable type. (Used by permission: Yuba Heat Transfer Division of Connell Limited Partnership.)

FIGURE 15-1J Split-ring removable floating head, four-pass tube-side and two-pass shell-side. (Used by permission: Engineers & Fabricators, Inc., Houston.)

FIGURE 15-1K U-tube exchanger. (Used by permission: Yuba Heat Transfer Division of Connell Limited Partnership.)

8 Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-2 Selection Guide Heat Exchangers Types Approximate Relative Cost In Carbon Steel Construction

Type Designation

Figure No.

Significant Feature

Best Suited Applications

Limitations

Fixes Tube Sheet

15-1C 15-1H

Both tubesheets Fixed to shell

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

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

1.0

Floating Heat or Tubesheet (removable and nonremovable bundles)

15-1B 15-1D 15-1G 15-1I 15-1J

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.

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

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

1.28

U-Tube; U-Bundel

15-1E 15-1K

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

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

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

0.9e1.1

Kettle

15-1F

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

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.

1.2e1.4

Double-Pipe

15-4A 15-4B 15-4C 15-4D

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

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

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

0.8e1.4

Pipe Coil

15-5A 15-5B

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

Condensing, or relatively low heat loads on sensible transfer.

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

0.5e0.7

Open Tube Sections (water cooled)

15-5A 15-5B

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.

Condensing, relatively low heat loads on sensible transfer.

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

0.8e1.1

Continued

Heat Transfer Chapter | 15

9

TABLE 15-2 Selection Guide Heat Exchangers Typesdcont’d

Type Designation

Figure No.

Open Tube Sections (aircooled); Plain or Finned Tubes

Significant Feature

Best Suited Applications

Limitations

15-6

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

Condensing, high-level heat transfer.

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

0.8e1.8

Plate and Frame

15-7A 15-7B 15-7C

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

Viscous fluids, corrosive fluids slurries, high heat transfer.

Not well suited for boiling or condensing; limit 350e500
F by gaskets. Used for liquid-liquid only; not gas-gas.

0.8e1.5

Small-Tube Teflon

15-8

Chemical resistance of tubes; no tube fouling.

Clean fluids, condensing, cross-exchange.

Low heat transfer coefficient.

2.0e4.0

Spiral

15-9A 15-9B 15-9C 15-9D

Compact, concentric plates; no bypassing, high turbulence.

Cross-flow, condensing, heating.

Process corrosion, suspended materials.

0.8e1.5

some tabulations of selected petroleum and chemical physical property data in the sixth (1978), seventh (1988), eight (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: l l l

Approximate Relative Cost In Carbon Steel Construction

Fixed tubesheet exchangers. U-tube exchangers. Floating header exchangers.

Fixed tubesheet exchangers: In a fixed tubesheet exchanger, the tubesheet is welded to the shell, resulting 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 a M type. The U-tubes permit unlimited thermal expansion, the tube bundle can be removed for cleaning, 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.

10

Tube O.D. Inches

Ft2 External Surface Per Ft Length

Ft2 Internal Surface Per Ft Length

Weight Per Ft Length Steel Lb*

Tube I.D. In.

Moment of Inertia In.4

Section Modulus In.3

Radius of Gyration In.

Constant C**

O.D. I.D.

Transverse Metal Area In.2

B.W.G. Gage

Thickness In.

Internal Area In2

1

/4

22 24 26 27

0.028 0.022 0.018 0.016

0.0296 0.0333 0.0360 0.0373

0.0654 0.0654 0.0654 0.0654

0.0508 0.0539 0.0560 0.0571

0.066 0.054 0.045 0.040

0.194 0.206 0.214 0.218

0.00012 0.00010 0.00071 0.00065

0.0791 0.0810 0.0823 0.0829

0.0791 0.0810 0.0823 0.0829

46 52 56 58

1.289 1.214 1.168 1.147

0.0195 0.0158 0.0131 0.0118

3/8

18 20 22 24

0.049 0.035 0.028 0.022

0.0603 0.0731 0.0799 0.0860

0.0982 0.0982 0.0982 0.0982

0.0725 0.0798 0.0835 0.0867

0.171 0.127 0.104 0.083

0.277 0.305 0.319 0.331

0.00068 0.00055 0.00046 0.00038

0.0036 0.0029 0.0025 0.0020

0.1166 0.1208 0.1231 0.1250

94 114 125 134

1.354 1.230 1.176 1.133

0.0502 0.0374 0.0305 0.0244

1

/2

16 18 20 22

0.065 0.049 0.035 0.028

0.1075 0.1269 0.1452 0.1548

0.1309 0.1309 0.1309 0.1309

0.0969 0.1052 0.1126 0.1162

0.302 0.236 0.174 0.141

0.370 0.402 0.430 0.444

0.0021 0.0018 0.0014 0.0012

0.0086 0.0071 0.0056 0.0046

0.1555 0.1604 0.1649 0.1672

168 198 227 241

1.351 1.244 1.163 1.126

0.0888 0.0694 0.0511 0.0415

5/8

12 13 14 15 16 17 18 19 20

0.109 0.095 0.083 0.072 0.065 0.058 0.049 0.042 0.035

0.1301 0.1486 0.1655 0.1817 0.1924 0.2035 0.2181 0.2299 0.2419

0.1636 0.1636 0.1636 0.1636 0.1636 0.1636 0.1636 0.1636 0.1636

0.1066 0.1139 0.1202 0.1259 0.1296 0.1333 0.1380 0.1416 0.1453

0.601 0.538 0.481 0.426 0.389 0.352 0.302 0.262 0.221

0.407 0.435 0.459 0.481 0.495 0.509 0.527 0.541 0.555

0.0061 0.0057 0.0053 0.0049 0.0045 0.0042 0.0037 0.0033 0.0028

0.0197 0.0183 0.0170 0.00156 0.0145 0.0134 0.0119 0.0105 0.0091

0.1865 0.1904 0.1939 0.1972 0.1993 0.2015 0.2044 0.2067 0.2090

203 232 258 283 300 317 340 359 377

1.536 1.437 1.362 1.299 1.263 1.228 1.186 1.155 1.126

0.177 0.158 0.141 0.125 0.114 0.103 0.089 0.077 0.065

3

10 11 12 13 14 15 16 17 18 20

0.134 0.120 0.109 0.095 0.083 0.072 0.065 0.058 0.049 0.035

0.1825 0.2043 0.2223 0.2463 0.2679 0.2884 0.3019 0.3157 0.3339 0.3632

0.1963 0.1963 0.1963 0.1963 0.1963 0.1963 0.1963 0.1963 0.1963 0.1963

0.1262 0.1335 0.1393 0.1466 0.1529 0.1587 0.1623 0.1660 0.1707 0.1780

0.833 0.808 0.747 0.665 0.592 0.522 0.476 0.429 0.367 0.268

0.482 0.510 0.532 0.560 0.584 0.606 0.620 0.634 0.652 0.680

0.0129 0.0122 0.0116 0.0107 0.0098 0.0089 0.0083 0.0076 0.0067 0.0050

0.0344 0.0326 0.0309 0.0285 0.0262 0.0238 0.0221 0.0203 0.0178 0.0134

0.2229 0.2267 0.2299 0.2340 0.2376 0.2411 0.2433 0.2455 0.2484 0.2531

285 319 347 384 418 450 471 492 521 567

1.556 1.471 1.410 1.339 1.284 1.238 1.210 1.183 1.150 1.103

0.259 0.238 0.219 0.195 0.174 0.153 0.140 0.126 0.108 0.079

/4

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-3 Characteristics of Tubing

10 11 12 13 14 15 16 17 18 20

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

0.2291 0.2291 0.2291 0.2291 0.2291 0.2291 0.2291 0.2291 0.2291 0.2291

0.1589 0.1662 0.1720 0.1793 0.1856 0.1914 0.1950 0.1987 0.2034 0.2107

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

0.0221 0.0208 0.0196 0.0180 0.0164 0.0148 0.137 0.0125 0.0109 0.0082

0.0505 0.0475 0.0449 0.0411 0.0374 0.0337 0.0312 0.0285 0.0249 0.0187

0.2662 0.2703 0.2736 0.2778 0.2815 0.2850 0.2873 0.289 0.2925 0.2972

451 494 529 575 616 655 680 706 740 794

1.442 1.378 1.332 1.277 1.234 1.197 1.174 1.153 1.126 1.087

0.312 0.285 0.262 0.233 0.207 0.182 0.165 0.149 0.127 0.092

1

8 10 11 12 13 14 15 16 18 20

0.165 0.134 0.120 0.109 0.095 0.083 0.072 0.065 0.049 0.035

0.3526 0.4208 0.4536 0.4803 0.5153 0.5463 0.5755 0.5945 0.6390 0.6793

0.2618 0.2618 0.2618 0.2618 0.2618 0.2618 0.2618 0.2618 0.2618 0.2618

0.1754 0.1916 0.1990 0.2047 0.2121 0.2183 0.2241 0.2278 0.2361 0.2435

1.473 1.241 1.129 1.038 0.919 0.814 0.714 0.650 0.498 0.361

0.670 0.732 0.760 0.782 0.810 0.834 0.856 0.870 0.902 0.930

0.0392 0.0350 0.0327 0.0307 0.0280 0.0253 0.0227 0.0210 0.0166 0.0124

0.0784 0.0700 0.0654 0.0615 0.0559 0.0507 0.0455 0.0419 0.0332 0.0247

0.3009 0.3098 0.3140 0.3174 0.3217 0.3255 0.3291 0.3314 0.3367 0.3414

550 656 708 749 804 852 898 927 997 1060

1.493 1.366 1.316 1.279 1.235 1.199 1.168 1.149 1.109 1.075

0.433 0.365 0.332 0.305 0.270 0.239 0.210 0.191 0.146 0.106

11/4

7 8 10 11 12 13 14 16 18 20

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

0.3272 0.3272 0.3272 0.3272 0.3272 0.3272 0.3272 0.3272 0.3272 0.3272

0.2330 0.2409 0.2571 0.2644 0.2702 0.2775 0.2838 0.2932 0.3016 0.3089

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

0.0890 0.0847 0.0742 0.0688 0.0642 0.0579 0.0521 0.0426 0.0334 0.0247

0.1425 0.1355 0.1187 0.110 0.1027 0.0926 0.0833 0.0682 0.0534 0.0395

0.3836 0.3880 0.3974 0.4018 0.4052 0.4097 0.4136 0.4196 0.4250 0.4297

970 1037 1182 1250 1305 1377 1440 1537 1626 1706

1.404 1.359 1.273 1.238 1.211 1.179 1.153 1.116 1.085 1.059

0.605 0.562 0.470 0.426 0.391 0.345 0.304 0.242 0.185 0.134

11/2

10 12 14 16

0.134 0.109 0.083 0.065

1.1921 1.2908 1.3977 1.4741

0.3927 0.3927 0.3927 0.3927

0.3225 0.3356 0.3492 0.3587

1.957 1.621 1.257 0.997

1.232 1.282 1.334 1.370

0.1354 0.1159 0.0931 0.0756

0.1806 0.1545 0.1241 0.1008

0.1853 0.4933 0.5018 0.5079

1860 2014 2180 2300

1.218 1.170 1.124 1.095

0.575 0.476 0.369 0.293

2

11 12 13 14

0.120 0.109 0.095 0.083

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

0.3144 0.2904 0.2586 0.2300

0.6660 0.6697 0.6744 0.6784

3795 3891 4014 4121

1.136 1.122 1.105 1.091

0.709 0.648 0.569 0.500 Continued

Heat Transfer Chapter | 15

7/8

11

12

Tube O.D. Inches

Ft2 External Surface Per Ft Length

Ft2 Internal Surface Per Ft Length

Weight Per Ft Length Steel Lb*

Tube I.D. In.

Moment of Inertia In.4

Section Modulus In.3

Radius of Gyration In.

Constant C**

O.D. I.D.

Transverse Metal Area In.2

B.W.G. Gage

Thickness In.

Internal Area In2

21/2

10 12 14

0.134 0.109 0.083

3.9127 4.0900 4.2785

0.6545 0.6545 0.6545

0.5843 0.5974 0.6110

3.3893 2.7861 2.1446

2.232 2.282 2.334

0.6992 0.5863 0.4608

0.5594 0.4690 0.3686

0.8378 0.8462 0.8550

6104 6380 6674

1.120 1.096 1.071

0.996 0.819 0.630

3

10 12 14

0.134 0.109 0.083

5.8621 6.0786 6.3080

0.7854 0.7854 0.7854

0.7152 0.7283 0.7419

4.1056 3.3687 2.5883

2.732 2.782 2.834

1.2415 1.0357 0.8096

0.8277 0.6905 0.5398

1.0144 1.0228 1.0317

9145 9483 9840

1.098 1.078 1.059

1.207 0.990 0.761

*Weights are based on low carbon steel with a density of 0.2836 lb/in.3 For other metals multiply by the following factors: Aluminum Titanium A.I.S.I. 400 Series S/Steels **Liquid Velocity ¼

0.35 0.58 0.99

lb:per tube hour C  Sp : gr : of liquid

A.I.S.I. 300 Series S/Steels Aluminum Bronze Aluminum Brass

1.02 1.04 1.06

Nickel-Chrome-Iron Admiralty Nickel

1.07 1.09 1.13

Nickel-Copper Copper and Cupro-Nickels

1.12 1.14

in. ft per see (sp. Gr. of water at 60
F ¼ 1.0)

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

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-3 Characteristics of Tubingdcont’d

Heat Transfer Chapter | 15

FIGURE 15-1L A shell and tube heat exchanger showing an inlet nozzle on the shell-side in preparation for pressure testing.

FIGURE 15-1N A shell and tube heat exchanger showing the nozzles on the shell- and tube-sides and nozzles at the rear end.

FIGURE 15-1O Heat exchanger tube bundles with baffles.

FIGURE 15-1M Reactor effluent vertical shell and tube heat exchangers in series of a hydrocracking unit.

13

FIGURE 15-1P A tube bundle with segmental baffles.

14

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-1Q Shell-side of a shell and tube heat exchanger.

Figure 15-1A 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 used for fixed tube sheet exchangers. Type C is not often used, other than for 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 manufacture and maintenance. Type D is a special enclosure for high pressure tubeside fluids, typically in excess of 2175 psi (150 bar). Type Y (not shown in Figure 15-1A) 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 tubeside or with suitable partitioning, any odd number of tubeside 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 15-1, 15-3 and 15-4 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 on, as shown in Figure 15-4. Figure 15-1L shows a shell and tube heat exchanger from a refinery unit in preparation for pressure testing, and Figure 15-1M shows vertical shell and tube heat exchangers in series in a hydrocracking unit. Many other arrangements may be found in references [37,38 and 61]. 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 one-half 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 its 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 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 [297]. 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.

No

Yes Yes No

Yes Yes Yes

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

LOW

No

HIGH

No No

Is chemical cleaning possible?

No

Yes

Yes Yes

No

Number of passes > 2

Is FT in unacceptable region?

Yes

No

Is there a high tube-side fouling factor (< 0.00035 W/m2.K) ? Yes

AES BES

No No

No

Yes AET

BET

No

No

Yes

Yes

No

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

BEW

BED

No

Yes

No

Yes AEU AFU

No

BEU BFU

No

Yes

No

Yes AEL AEM

No

BEM

FIGURE 15-2 Selection chart for choice of heat exchanger configuration. (See Figure 15-1 for definition of types.) Linnhoff, B., et al., User Guide on Process Integration for the efficient use of energy, IchemE., 1996.

Heat Transfer Chapter | 15

Yes No

Yes

No

15

TABLE 15-4 Comparison of TEMA class R, C and B heat exchangers (Cost decreases from left to right) [303] 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. (1.6 mm)

0.0625 in. (1.6 mm)

Tube diameters, OD

3

Tube pitch and minimum cleaning lane

1

1

/4, 1, 1 /4 , 1 /2 , and 2 in.

1

1

R + /4 , 3/8, /2 , and 5/8 in.

R +5/8 in.

1.25 x tube OD 1 /4 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 3/4 in tubes

Minimum shell diameter

8 inch, tabulated

6 inch, tabulated

6 inch tabulated

Longitudinal baffle thickness

1

Floating head cover cross-over area

1.3 x tube flow area

/4 inch minimum

o

1

1/8 inch alloy, /4 inch carbon steel

1/8 inch alloy, 1/4 inch carbon steel

Same as tube flow area

Same as tube flow area

Lantern ring construction

375 F 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

375 oF 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 11/4 OD 1 inch for 11/2 OD 1.25 inch for 2 OD

0.75 x tube OD for 1 inch and smaller 1/8 inch for 11/4 OD 1 inch for 11/2 OD 1.25 inch for 2 OD

Tube hole grooving

Two grooves

Above 300 psi design pressure or 350 oF 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

3

1 /2 inch recommended; smaller bolting may be used

5/8 inch

/4 inch

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Class R

16

Attribute

Heat Transfer Chapter | 15

17

FIGURE 15-3 Typical shell types.

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 shellside 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 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 [297]. 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 [411]. 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

18

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-4 Typical heads and closures.

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 vapors 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. (1500 mm) 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 > 10 ft. (3 m), since this would exceed the limit on maximum unsupported tube length specified by TEMA e typically 5 ft. (1.5 m.), though it varies with tube OD, thickness and material. The H shell is basically a double G shell. There are three full supports at the center of the tube length. G and H shells can be used where there is a temperature cross. This could be an attractive alternative 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 a kettle reboiler with a configuration that is different from the other shell types. The port where

Heat Transfer Chapter | 15

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 shellside 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. Crossflow, 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 Dp in the shell, and the only Dp is encountered in the nozzles), the configuration is used for cooling and condensing vapors at very low pressure, especially under vacuum. Full support plates can be located as required for structural equipment 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 Dp, while type K is used for kettle reboilers. Figure 15-1N shows a shell and tube heat exchanger with nozzles on the shell and tube-sides, and the rear end. Table 15-5 summarizes the features of the different shell types as illustrated in the TEMA notation of Figure 15-1A. Factors Affecting Shell Selection Several factors influence the selection of shell in a shell and tube heat exchanger. Among them are the following [298]. 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 3
C, any of the shell types can be used for the application. When the temperature approach is less than 3
C, 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

19

TABLE 15-5 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)

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 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 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 15-6 summarizes the advantages and disadvantages of these shell types.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-6 Each shell type has advantages and disadvantages that make it suitable for specific applications

TABLE 15-6 Each shell type has advantages and disadvantages that make it suitable for specific applicationsdcont’d

Shell type

Shell type

Advantages

Disadvantages

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.

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 epass 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 Gshells. Thermal conduction occurs across the longitudinal baffle. Temperature profile is not as good as with counter-and 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.

E

F

X

Advantages

Disadvantages

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).

Continued

Details of Rear End Heads The L type head is similar to an A type stationary head. It has the same flexibility in allowing cleaning of the tubes without disturbing the pipe work. The diagram shows a nozzle in broken lines. For an even number of tube passes, there is no nozzle in the channel. The M type head is similar to a B type stationary head. The pipe work must be detached to access the tubes, and it would only have a nozzle when there is an odd number of tube passes. The N type rear head is (not surprisingly) the same as the N type stationary head. The P and W types of the rear head are both inexpensive ways of accommodating thermal expansion/contraction of the tube bundle relative to the shell. However, they are susceptible to leakage and are therefore not normally used in the petrochemical industry. The S type rear head was developed to reduce the bundle/shell clearance for a removable bundle. It uses the split ring backing device, and the ring incorporates holes for bolts and a face for a gasket seal. The split ring is assembled on one side of the tube sheet and the floating head at the other. This enables the tube sheet diameter to be significantly reduced. Section 5 of TEMA shows four possible designs of split rings. For a 47.24 in. (1200 mm) shell, the bundle/shell diameter clearance would be about 2.76 in. (70 mm) e half the value of a T type. An advantage of the S type over the T type head is that more tubes can be fitted into a given shell size, and the C stream, which bypasses most of the heat transfer surface, is reduced so that the shell-side heat transfer coefficient is improved. Its disadvantages are that the increased complexity and the

Heat Transfer Chapter | 15

extra gasket make it more prone to leakage problems, therefore the diameters of the shell flange and the shell cover flange have to be increased [289]. The T type floating head is bolted to the floating tube sheet. The head for a normal T type is very simple, and the shell cover and floating head can be removed either to allow the tubes to be cleaned in situ or to allow the bundle to be removed to clean the outside of the tubes. The shell diameter to outer tube limit clearance is very high for a T type exchanger. For a 47.24 in. (1200 mm) shell with a design pressure of 391.58 psi (27 bar), the clearance would be about 5.5 in. (140 mm). This high clearance is essential to accommodate the nuts and bolts that attach the head to the tube sheet. When a U-tube bundle cannot be used for a kettle which requires a removable bundle, a T type head must be used. An advantage of the T type head is that there is only one simple gasket that minimizes potential leakage problems. The U-tube head has bends in the tubes, which facilitate the change in direction of the tube-side fluid. The majority of U-tube exchangers have two tube passes, which enable the bend to be in the vertical plane as shown in Figure 15-1A. However, any even number of tube-side passes could be used, and four tube-side passes are not uncommon. Except for the two-pass arrangement, the tube bends are always in the horizontal plane.

Common Combinations of Shell and Tube Heat Exchangers Yokell [299] 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 15-1BeG is given in the following sections.

21

AES The AES in Figure 15-1B is the most versatile of all the shell and tube exchanger types. The tubes can be mechanically cleaned in situ, or the whole unit can be dismantled to clean the shell-side mechanically, renew the bundle or take it 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.

The shell cover (Figure 15-1B (9)) is removed. 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.

Figure 15-5 shows a comparison between the pull through design and a split ring design, where the latter allows for a smaller shell diameter. BEM The BEM type in Figure 15-1C 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

FIGURE 15-5 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, McGraw-Hill.)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

one pass on the tube-side, where the channels at both ends would have a nozzle. The pressure drop on the tube-side 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 [287]: 1. Tube sheet and baffle holes are drilled. 2. The tubes are installed in one of the tubesheets. 3. The baffles and spacers are introduced through the tubes and tie rods. 4. The shell is placed in position. 5. The second tube sheet is installed. 6. The shell is welded to the tubesheets. 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 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 out 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. 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 15-1C (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. AEP The only difference between the AEP as shown in Figure 15-1D 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 spliton backing flange (20) is a loose flange that can be moved 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 involved. Leakage through a stuffing box is more likely than the failure of a gasketed 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 602.6
F (317
C). API Standard 660, which is used in the petroleum industry, does not permit this type of construction. CFU Figure 15-1E 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 shell-side-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 situations; 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 lower cost because it eliminates one head. The principal limitations are [287]: 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.

Heat Transfer Chapter | 15

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. AKT Figure 15-1F shows a kettle reboiler and kettles with a channel and removable cover at the front end, and a stationary head type to access the tubes for cleaning without disturbing the pipe work. The shell is a kettle type reboiler and has a pull-through 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 is steam. However, if the 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 over 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 22046e26455 lb (10e12 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. The advantages of the kettle type are that it can handle a wide range of percentage vaporization rates (10e100% vaporization e 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.

23

AJW Figure 15-1G 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 shellside 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 the J2-1 shell. Watson [289] has provided illustrations of other TEMA configurations, and Mukherjee [295] discusses the advantages of TEMA F shell compared to other shell types. The most common combinations for an E type shell are shown in Table 15-5.

Tubes The two basic types of tubes are (a) plain or bare, and (b) finned e external or internal, see Figures 15-6AeE, 15-12 and 15-13. The plain tube is used in the usual heat exchange applications. However, the advantages of the more common externally finned tube are becoming better identified. These tubes are performing exceptionally well in applications in which their best features can be used. Plain tubes (either as solid wall or duplex) are available in carbon steel, carbon alloy steels, stainless steels, copper, brass and alloys, cupro-nickel, monel, tantalum, carbon, glass and other special materials. Usually, there is no great problem in selecting an available tube material. However, when its assemblies into the tubesheet along with the resulting fabrication problems are considered, the selection

FIGURE 15-6A(1) Double-pipe longitudinal twin G-finned exchanger. (Used by permission: Griscom-Russell Co./Ecolaire Corp., Easton, PA, Bul. 7600.)

FIGURE 15-6A(2) Multitube hairpin fintube 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 31e6 in. (Used by permission: Brown Fintube Co., A Koch
Engineering Co., Bul. Be30e1.)

FIGURE 15-6A(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. 80e1.)

FIGURE 15-6B Cutaway view of finned double-pipe exchanger. (Used by permission: ALCO Products Co., Div. of NITRAM Energy, Inc.)

Heat Transfer Chapter | 15

25

FIGURE 15-6C High-pressure fixed-end closure and return-end closure. (Used by permission: ALCO Products Co., Div. of NITRAM Energy, Inc.)

FIGURE 15-6D Vertical longitudinal finned-tube tank heater, which is used in multiple assemblies when required. (Used by permission: Brown Fintube Co., A Koch
Engineering Co., Bul. 4e5.)

FIGURE 15-6E Longitudinal finned-tube tank suction direct line heater. (Used by permission: Brown Fintube Co., A Koch
Engineering Co., Bul. 4e5.)

of the tube alone is only part of a coordinated design. Plain tube mechanical data and dimensions and thermal conductivities are given in Tables 15-7, 15-8A and B and 15-9, respectively. The duplex tube (Figure 15-13) is a tube within a tube, snugly fitted by drawing the outer tube onto the inner or by other mechanical procedures. This tube is useful when the shell-side fluid is not compatible with the material needed for the tube-side fluid, or vice versa. The thicknesses of the two different wall materials do not have to be the same. As a general rule, 18 ga is about as thin as either tube should be, although thinner gages are available. In establishing the gage thickness for each component of the tube, the corrosion rate of the material should be about equal for the inside and outside, and the wall thickness should still withstand the pressure and temperature conditions after a reasonable service life. More than 100 material combinations exist for these tubes. A few materials suitable for the inside or outside of the tube include copper, steel, cupro-nickel, aluminum, lead, monel, nickel, stainless steel, alloy steels, various brasses, etc. From these combinations most process conditions can be satisfied. Combinations such as steel outside and admiralty or cupro-nickel inside are used in ammonia condensers cooled with water in the tubes. Tubes of steel outside and cupro-nickel inside are used in many process

26

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-6F(1) Single concentric corrugated tube in single corrugated shell. (Used by permission: APV Heat Transfer Technologies.)

FIGURE 15-6F(2) Multicorrugated tubes in single shell. (Used by permission: APV Heat Transfer Technologies.)

FIGURE 15-6G Twisted tubes with heat exchanger bundle arrangements. (Used by permission: Brown Fintube Co., A Koch
Engineering Co., Bul. Be100e2.)

Heat Transfer Chapter | 15

27

FIGURE 15-7 Plate and Frame heat exchanger basic components. (Used by permission: Alfa Laval Thermal, Inc., Bul. G101.)

FIGURE 15-7A Typical one side of Plate for Plate and Frame Exchanger. (Used by permission: Graham Manufacturing Company, Inc., Bul. PHE 96e1.)

FIGURE 15-7B 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. Ge101.)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-7C 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 15-8 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 is carbon steel shell plain or Teflon (LT)
lined. Heads are lined with Teflon
. Tube diameters range from 0.125e0.375 in. O.D.; the temperature range is 80e400
F; pressures range from 40e150 psig. (Used by permission: AMETEK, Inc., Chemical Products Div., Product Bulletin ”Heat Exchangers of Teflon
.”)

Heat Transfer Chapter | 15

29

FIGURE 15-9C Coil Assembly for bare tube Heliflow
exchanger. Tube sizes range from 1/4 d3/4 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.)

FIGURE 15-9A Spiral flow heat exchanger, cross-flow arrangement for liquids, gases, or liquid/gaseous (condensable) fluids. (Used by permission: Alfa Laval Thermal Inc., Bul. 1205 © 1993.)

condensers using sea water. These tubes can be bent for U-bundles without loss of effective heat transfer. However, care must be used, such as by bending while sand-filled, or on a mandrel. The usual minimum radius of the bend for copper-alloy-steel type duplex tube is three times the OD of the tube. Sharper bends can be made by localized heating; however, the tube should be specified at the time of purchase for these conditions. Finned tubes may have external or internal fins. The most common and perhaps most adaptable is the external fin. Several types of these use the fin: (a) as an integral part of the main tube wall; (b) attached to the outside of the tube by welding or brazing; or (c) attached to the outside of the tube by mechanical means. Figure 15-12 illustrates several different types. The fins do not have to be made of the same materials as the base tube (Figure 15-13). The usual applications for finned tubes are in heat transfer involving gases on the outside of the tube. Other applications also exist, such as condensers, and in fouling service where the finned tube has been shown to be beneficial. The total gross external surface in a finned exchanger is many times that of the same number of plain or bare tubes. A common fin tube used in shell and tube heat exchangers is a low fin tube with 19 fins/inch. Tube-side water velocities should be kept within reasonable limits, even though calculations indicated that improved tube-side film coefficients can be obtained if the water velocity is increased. Bending of Tubing

FIGURE 15-9B Spiral flow heat exchanger; vaporizer. (Used by permission: Alfa Laval Thermal Inc., Bul. 1205 © 1993.)

The recommended minimum radius of bend for various tubes is given in Table 15-10. These measurements are for

30

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

8 Coil* 1 Studs and nuts 2 Manifold nuts

9 Casing flange gasket

7 Manifold lower* 3 Manifold lock rings

4 5 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 15-9D Assembly of components of Heliflow
spiral heat exchanger. (Used by permission: Graham Manufacturing Company, Bul. “Operating and Maintenance Instructions for Heliflow
.”)

FIGURE 15-10 Cast iron sections; open coil cooler-coil and distribution pan.

FIGURE 15-11 Open tube sections. (Used by permission: GriscomRussel Co./Ecolaire Corp., Easton, PA.)

Heat Transfer Chapter | 15

31

FIGURE 15-12D Longitudinal fin tubes. (Used by permission: Brown Fintube Co., A Koch
Engineering Co.) FIGURE 15-12A Circular-type finned tubing. (Used by permission: Wolverine Tube, Inc.)

FIGURE 15-12B Low-finned integral tube details. (Used by permission: Wolverine Tube, Inc.)

FIGURE 15-12E 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 15-12C Bimetal high-finned tube. (Used by permission: Wolverine Tube, Inc.)

FIGURE 15-12F 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.)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-12G Tension wound fins.

180
U-bends and represent minimum values. TEMA, Par. RCB 2.31 recommends the minimum wall thinning of tubes for U-bends by the minimum wall thickness in the bent portion before bending, t1.


 do to ¼ t1 1 þ 4R

(15-1)

where: t0 ¼ original tube wall thickness, in. t1 ¼ minimum tube wall thickness calculated by code rules for straight tube subjected to the same pressure and metal temperature. do ¼ OD or tube in in. R ¼ mean radius of bend, in. See TEMA for more details.

Baffles Baffles are a very important part of the performance of a heat exchanger. Velocity conditions in the tubes as well as those in the shell are adjusted by design to provide the necessary arrangements for maintenance of proper heat transfer fluid velocities and film conditions. Consider the two classes of baffles described in the following sections. Tube-Side Baffles (TEMA Uses Pass Partition Plates)

FIGURE 15-12H 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.)

These baffles are built into the head and return ends of an exchanger to direct the fluid through the tubes at the proper relative position in the bundle for good heat transfer as well as for fixing velocity in the tubes; see Figures 15-1D and 15-4. Baffles in the head and return ends of exchangers are either welded or cast in place. The arrangement may take any of several reasonable designs, depending upon the number of tube-side passes required in the performance of

Heat Transfer Chapter | 15

33

Corrugation Pitch (P)

Prime Tube OD

Corrugated Section OD (do)

Prime Tube Wall

Wall at Corrugation Corrugation Depth

FIGURE 15-12I 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.)

Corrugation Pitch (P)

Corrugated Section OD (do)

Prime Tube OD

Wall at Corrugation Prime Tube Wall Corrugation Depth FIGURE 15-12J 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.)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-12K Type S/T Turbo-Chil
finned tube with internal surface enhancement by integral ridging. (Used by permission: Wolverine Tube, Inc.)

FIGURE 15-12L 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.)

Heat Transfer Chapter | 15

FIGURE 15-12L cont’d

35

36

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

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 15-12M 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.”)

FIGURE 15-13 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.)

the unit. The number of tubes per pass is usually arranged about equal. However, depending upon the physical changes in the fluid volume as it passes through the unit, the number of tubes may be significantly different in some of the passes. Practical construction limits the number of tube-side passes to 8e10, although a larger number of passes may be used on special designs. It is often better to arrange a second shell unit with fewer passes in each. The pass arrangements depend upon the location of entrance and exit nozzle connections to the head, and the position of the fluid paths on the shell-side. Every effort is usually made to visualize the physical flow and the accompanying temperature changes in orienting the passes. Figures 15-14 and 15-15 illustrate a few configurations. Single-pass tube-side. For these conditions, no baffle is present in either the head or the return end of the unit. The tube-side fluid enters one end of the exchanger and leaves from the opposite end. Generally, these baffles are not as convenient from a connecting pipe arrangement

viewpoint as units with an even number of passes, in which the tube-side fluid enters and leaves at the same end of the exchanger. See Figures 15-1C and 15-1G and Table 15-1. Two-pass tube-side. For these conditions one head end baffle is usually in the center, and no baffle is in the return end, as the fluid will return through the second pass of itself. See Figures 15-1A and B. Three-pass tube-side; five-pass tube-side. These are rare designs because they require baffles in both heads, and the outlet connection is at the end opposite the inlet. This provides the same poor piping arrangement as for a singlepass unit. Four-pass tube-side; even number of passes tube-side. These conditions are often necessary to provide fluid velocities that are high enough for good heat transfer, or to prevent the deposition of suspended particles in the tubes and end chambers. The higher the number of passes, the more expensive is the unit. The more passes in a head, the more difficult the problem of fluid bypassing through the gasketted partitions becomes, unless expensive construction is used. Seating of all partitions due to warping of the metals, even though machined, is a real problem. At pressures above about 500 psig (34 bar), multiple-pass units are only sparingly used. See Figure 15-1J. Shell-Side Baffles and Tube Supports Only a few popular, practical shell baffle arrangements exist, although special circumstances can and do require many unique baffling arrangements. The performance of the shell-side of the exchanger depends upon the designer’s understanding the effectiveness of fluid

TABLE 15-7 Characteristics of Tubing (S.I. units) B.W.G. Gage

Thickness mm.

Internal Area Sq. Cm

Sq. m External Surface Per m Length

Sq. m Internal Surface Per m Length

Weight Per Ft Length Steel kg*

Tube I.D. mm.

Moment of Inertia cm.4

Section Modulus cm.3

Radius of Gyration mm.

Constant C**

6.35

22 24 26 27

0.711 0.559 0.457 0.406

0.1910 0.2148 0.2323 0.2406

0.0199 0.0199 0.0199 0.0199

0.0155 0.0164 0.0171 0.0174

0.098 0.80 0.067 0.060

4.93 5.23 5.44 5.54

0.0050 0.0042 0.0037 0.0033

0.0161 0.0136 0.0116 0.0107

2.009 2.057 2.090 2.106

9.53

18 20 22 24

1.245 0.889 0.711 0.559

0.3890 0.4716 0.5155 0.5548

0.0299 0.0299 0.0299 0.0299

0.0221 0.0243 0.0255 0.0264

0.254 0.189 0.155 0.124

7.04 7.75 8.10 8.41

0.0283 0.0229 0.0191 0.0158

0.0590 0.0475 0.0410 0.0328

12.7

16 18 20 22

1.651 1.245 0.889 0.711

0.6935 0.8187 0.9368 0.9987

0.0399 0.0399 0.0399 0.0399

0.0295 0.0321 0.0343 0.0360

0.449 0.351 0.259 0.210

9.40 10.21 10.92 11.28

0.0874 0.0749 0.0583 0.0499

15.88

12 13 14 15 16 17 18 19 20

2.769 2.413 2.108 1.829 1.651 1.473 1.245 1.067 0.889

0.8394 0.9587 1.0677 1.1723 1.2413 1.3129 1.4071 1.4832 1.5606

0.0499 0.0499 0.0499 0.0499 0.0499 0.0499 0.0499 0.0499 0.0499

0.0325 0.0347 0.0366 0.0384 0.0395 0.0406 0.0421 0.0432 0.0443

0.894 0.801 0.716 0.634 0.579 0.524 0.449 0.390 0.329

10.34 11.05 11.66 12.22 12.57 12.93 13.39 13.74 14.10

Tube O.D. mm

B.W.G. Gage

Thickness mm.

Internal Area Sq. cm

Sq. m External Surface Per m Length

Sq. m Internal Surface Per m Length

Weight Per m Length Steel kg*

19.05

10 11 12 13 14 15 16 17 18 20

3.404 3.048 2.769 2.413 2.108 1.829 1.651 1.473 1.245 0.889

1.1774 1.3181 1.4342 1.5890 1.7284 1.8606 1.9477 2.0368 2.1542 2.3432

0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598

0.0385 0.0407 0.0425 0.0447 0.0466 0.0484 0.0495 0.0506 0.0520 0.0543

1.240 1.202 1.112 0.990 0.881 0.777 0.708 0.638 0.546 0.399

O:D: I:D:

Transverse Metal Area cm.2

69 77 84 87

1.289 1.214 1.168 1.147

0.1258 0.1019 0.8452 0.0761

2.962 3.068 3.127 3.175

140 170 185 200

1.354 1.230 1.176 1.133

0.3239 0.2413 0.1968 0.1574

0.1409 0.1163 0.0918 0.0787

3.950 4.074 4.188 4.247

250 295 337 359

1.351 1.244 1.163 1.126

0.5729 0.4477 0.3297 0.2677

0.2539 0.2373 0.2206 0.2040 0.1873 0.1748 0.1540 0.1374 0.1165

0.3228 0.2999 0.2786 0.2556 0.2376 0.2196 0.1950 0.1721 0.1491

4.737 4.836 4.925 5.009 5.062 5.118 5.192 5.250 5.309

302 345 384 422 447 472 506 534 562

1.536 1.437 1.362 1.299 1.263 1.228 1.186 1.155 1.126

1.1419 1.0194 0.9097 0.8065 0.7355 0.6645 0.5742 0.4968 0.4194

Tube I.D. mm

Moment of Inertia cm.4

Section Modulus cm.3

Radius of Gyration mm.

Constant C**

O:D: I:D:

Transverse Metal Area cm.2

12.24 12.95 13.51 14.22 14.83 15.39 15.75 16.10 16.56 17.27

0.5369 0.5078 0.4828 0.4454 0.4079 0.3704 0.3455 0.3163 0.2789 0.2081

0.5637 0.5342 0.5064 0.4670 0.4293 0.3900 0.3622 0.3327 0.2917 0.2196

5.662 5.758 5.839 5.944 6.035 6.124 6.180 6.236 6.309 6.429

424 474 516 572 622 670 701 733 775 843

1.556 1.471 1.410 1.339 1.284 1.238 1.210 1.183 1.150 1.103

1.6710 1.5355 1.4129 1.2581 1.1226 0.9871 0.9032 0.8129 0.6968 0.5097

37

Continued

Heat Transfer Chapter | 15

Tube O.D. mm

38

22.23

10 11 12 13 14 15 16 17 18 20

3.404 3.048 2.769 2.413 2.108 1.829 1.651 1.473 1.245 0.889

1.8671 2.0432 2.1871 2.3774 2.5471 2.7077 2.8123 2.9193 3.0593 3.2839

0.0698 0.0698 0.0698 0.0698 0.0698 0.0698 0.0698 0.0698 0.0698 0.0698

0.0484 0.0507 0.0524 0.0547 0.0566 0.0583 0.0594 0.0606 0.0620 0.0642

1.580 1.442 1.329 1.179 1.046 0.920 0.838 0.754 0.644 0.467

15.42 16.13 16.69 17.40 18.01 18.57 18.92 19.28 19.74 20.45

0.9199 0.8658 0.8158 0.7492 0.6826 0.6160 0.5702 0.5203 0.4537 0.3413

0.8276 0.7784 0.7358 0.6735 0.6129 0.5522 0.5113 0.4670 0.4080 0.3064

6.761 6.866 6.949 7.056 7.150 7.239 7.297 7.356 7.429 7.549

672 735 787 855 917 974 1012 1050 1101 1182

Tube O.D. mm

B.W.G. Gage

Thickness mm.

Internal Area Sq. cm

Sq. m External Surface Per m Length

Sq. m Internal Surface Per m Length

Weight Per m Length Steel kg*

Tube I.D. mm.

Moment of Inertia cm.4

Section Modulus cm.3

Radius of Gyration mm.

Constant C**

25.4

8 10 11 12 13 14 15 16 18 20

4.191 3.404 3.048 2.769 2.413 2.108 1.829 1.651 1.245 0.889

2.2748 2.7148 2.9264 3.0987 3.3245 3.5245 3.7129 3.8355 4.1226 4.3826

0.0798 0.0798 0.0798 0.0798 0.0798 0.0798 0.0798 0.0798 0.0798 0.0798

0.0535 0.0584 0.0607 0.0624 0.0646 0.0665 0.0683 0.0694 0.0720 0.0742

2.192 1.847 1.680 1.545 1.368 1.211 1.063 0.967 0.741 0.537

17.02 18.59 19.30 19.86 20.57 21.18 21.74 22.10 22.91 23.62

1.6316 1.4568 1.3611 1.2778 1.1655 1.0531 0.9449 0.8741 0.6909 0.5161

1.2848 1.1471 1.0717 1.0078 0.9160 0.8308 0.7456 0.6866 0.5441 0.4048

7.643 7.869 7.976 8.062 8.171 8.268 8.359 8.418 8.555 8.672

31.75

7 8 10 11 12 13 14 16 18 20

4.572 4.191 3.404 3.048 2.769 2.413 2.108 1.651 1.245 0.889

4.0135 4.2890 4.8864 5.1690 5.3968 5.6935 5.9542 6.3561 6.7245 7.0555

0.0997 0.0997 0.0997 0.0997 0.0997 0.0997 0.0997 0.0997 0.0997 0.0997

0.0710 0.0734 0.0784 0.0806 0.0824 0.0846 0.0865 0.0894 0.0919 0.0942

3.064 2.848 2.380 2.158 1.979 1.746 1.542 1.226 0.936 0.677

22.61 23.37 24.94 25.65 26.21 26.92 27.53 28.45 29.26 29.97

3.7045 3.5255 3.0885 2.8637 2.6722 2.4100 2.1686 1.7732 1.3902 1.0281

2.3352 2.2205 1.9452 1.8026 1.6830 1.5175 1.3651 1.1176 0.8751 0.6473

38.1

10 12 14 16

3.404 2.769 2.108 1.651

7.6910 8.3277 9.0174 9.5103

0.1197 0.1197 0.1197 0.1197

0.0983 0.1023 0.1064 0.1093

2.912 2.412 1.871 1.484

31.29 32.56 33.88 34.80

5.6358 4.8242 3.8751 3.1467

2.9595 2.5318 2.0336 1.6518

1.442 1.378 1.332 1.277 1.234 1.197 1.174 1.153 1.126 1.087

2.0129 1.8387 1.6903 1.5032 1.3355 1.1742 1.0645 0.9613 0.8194 0.5935

O:D: I:D:

Transverse Metal Sq. cm

819 977 1053 1115 1196 1268 1336 1380 1483 1577

1.493 1.366 1.316 1.279 1.235 1.199 1.168 1.149 1.109 1.075

2.7935 2.3548 2.1419 1.9677 1.7419 1.5419 1.3548 1.2323 0.9419 0.6839

9.743 9.855 10.094 10.206 10.292 10.406 10.505 10.658 10.795 10.914

1444 1543 1758 1860 1942 2049 2143 2287 2420 2539

1.404 1.359 1.273 1.238 1.211 1.179 1.153 1.116 1.085 1.059

3.9032 3.6258 3.0323 2.7484 2.5226 2.2258 1.9613 1.5613 1.1935 0.8645

12.327 12.530 12.746 12.901

2768 2997 3245 3422

1.218 1.170 1.124 1.095

3.7097 3.0710 2.3806 1.8903

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-7 Characteristics of Tubing (S.I. units)dcont’d

Tube O.D. mm

B.W.G. Gage

Thickness mm.

Internal Area Sq. cm

Sq. cm External Surface Per m Length

Sq. cm Internal Surface Per m Length

Weight Per m Length Steel kg*

Tube I.D. mm.

Moment of Inertia cm.4

Section Modulus cm.3

Radius of Gyration mm.

Constant C**

O:D: I:D:

Transverse Metal Sq. cm

50.8

11 12 13 14

3.404 2.769 2.108 1.651

15.6955 16.0909 16.6000 17.0432

0.1596 0.1596 0.1596 0.1596

0.1405 0.1422 0.1444 0.1463

3.589 3.280 2.880 2.531

44.70 45.26 45.97 46.58

13.0864 12.0874 10.7638 9.5734

5.1521 4.7588 4.2377 3.7690

16.916 17.010 17.130 17.231

5648 5790 5973 6133

1.136 1.122 1.105 1.091

4.5742 4.1806 3.6710 3.2258

63.5

10 12 14

3.404 2.769 2.108

25.2418 26.3854 27.6027

0.1995 0.1995 0.1995

0.1781 0.1821 0.1862

5.047 4.149 3.193

56.69 57.96 59.28

29.1022 24.4042 19.1746

9.1660 7.6864 6.0392

21.277 21.489 21.713

9087 9499 9937

1.120 1.096 1.071

6.4287 5.2847 4.0670

76.2

10 12 14

3.404 2.769 2.108

37.8178 39.2147 40.6957

0.2394 0.2394 0.2394

0.2180 0.2220 0.2261

6.113 5.016 3.853

69.39 70.66 71.98

51.6736 43.1108 33.6933

13.5626 11.3152 8.8434

25.760 25.975 26.200

13614 14117 14650

1.098 1.078 1.058

7.7873 6.3899 4.9083

Aluminum

0.35

Aluminum Bronze

1.04

Nickel

1.13

Titanium

0.58

Aluminum Brass

1.06

Nickel-Copper

1.12

A.I.S.I. 400 Series S/Steels

0.99

Nickel-Chrome-Iron

1.07

Copper and Cupro-Nickels

1.14

A.I.S.I 300 Series S/Steels

1.02

Admiralty

1.09

Used by permission: Standards of the Tubular Exchanger Manufacturers Association, 9th Ed., Table D-7M, © 2007. Tubular Exchanger Manufacturers Association, Inc. All rights reserved. *Weights are based on low carbon steel with a density of 7.85 gm/cu. Cm. For other metals multiply by the following factors: per tube hour **Liquid velocity ¼ C kg: x Sp: Gr: of liquid in meters per sec. (Sp. Gr. Of water at 15.6 deg. C ¼ 1.0)

Heat Transfer Chapter | 15 39

40

Btu/hr ft
F Temp.
F

70

100

200

300

400

500

600

700

800

900

1,000

1,100

1,200

1,300

1,400

1,500

30.0

29.9

29.2

28.4

27.6

26.6

25.6

24.6

23.5

22.5

21.4

20.2

19.0

17.6

16.2

15.6

24.8

25.0

25.2

25.1

24.8

24.3

23.7

23.0

22.2

21.4

20.4

19.5

18.4

16.7

15.3

15.0

21.3

21.5

21.9

22.0

21.9

21.7

21.3

20.8

20.2

19.7

19.1

18.5

17.7

16.5

15.0

14.8

Material Carbon Steel C 1/2 Moly Steel 1 Cr 1/2 Mo & 1 1/4 Cr 1/2 Mo 1

2 /4 Cr 1 Mo

20.9

21.0

21.3

21.5

21.5

21.4

21.1

20.7

20.2

19.7

19.1

18.5

18.0

17.2

15.6

15.3

1

16.9

17.3

18.1

18.7

19.1

19.2

19.2

19.0

18.7

18.4

18.0

17.6

17.1

16.6

16.0

15.8

1

7 Cr /2 Mo

14.1

14.4

15.3

16.0

16.5

16.9

17.1

17.2

17.3

17.2

17.1

16.8

16.6

16.2

15.6

15.5

9 Cr 1 Mo

5 Cr /2 Mo

12.8

13.1

14.0

14.7

15.2

15.6

15.9

16.0

16.1

16.1

16.1

16.0

15.8

15.6

15.2

15.0

1

3 /2 Nickel

22.9

23.2

23.8

24.1

23.9

23.4

22.9

22.3

21.6

20.9

20.1

19.2

18.2

16.9

15.5

15.3

13 Cr

15.2

15.3

15.5

15.6

15.8

15.8

15.9

15.9

15.9

15.9

15.8

15.6

15.3

15.1

15.0

15.0

15 Cr

14.2

14.2

14.4

14.5

14.6

14.7

14.7

14.8

14.8

14.8

14.8

14.8

14.8

14.5

14.8

14.8

17 Cr

12.6

12.7

12.8

13.0

13.1

13.2

13.3

13.4

13.5

13.6

13.7

13.8

13.9

14.1

14.3

14.5

17-19 Cr (TP 439) TP 304 Stn. Stl.

14.0 8.6

8.7

9.3

9.8

10.4

10.9

11.3

11.8

12.2

12.7

13.2

13.6

14.0

14.5

14.9

15.3

TP 316 & 317 Stn. Stl.

7.7

7.9

8.4

9.0

9.5

10.0

10.5

11.0

11.5

12.0

12.4

12.9

13.3

13.8

14.2

14.6

TP 321 & 347 Stn. Stl.

8.1

8.4

8.8

9.4

9.9

10.4

10.9

11.4

11.9

12.3

12.8

13.3

13.7

14.1

14.6

15.0

TP 310 Stn. Stl.

7.3

7.5

8.0

8.6

9.1

9.6

10.1

10.6

11.1

11.6

12.1

12.6

13.1

13.6

14.1

14.5

2205(31803)

8.0

8.5

9.0

9.5

10.0

10.5

11.0

11.5

12.0

3RE60(S31500)

8.4

8.5

9.0

9.4

9.8

10.2

10.6

11.0

11.3

Stn.Stl.

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-8A Thermal Conductivity of Metals

Nickel 200

38.8

37.2

35.4

34.1

32.5

31.8

32.5

33.1

33.8

Ni-Cu (N04400)

12.6

12.9

13.9

15.0

16.1

17.0

17.9

18.9

19.8

20.9

22.0

Ni-Cr-Fe (N06600)

8.6

8.7

9.1

9.6

10.1

10.6

11.1

11.6

12.1

12.6

13.2

13.8

14.3

14.9

15.5

16.0

Ni-Fe-Cr (N08800)

6.7

6.8

7.4

8.0

8.6

9.1

9.6

10.1

10.6

11.1

11.6

12.1

12.7

13.2

13.8

14.50

7.1

7.6

8.1

8.6

9.1

9.6

10.0

10.4

10.9

11.4

11.8

12.4

12.9

13.6

1,200

1,300

1,400

1,500

Ni-Fe-Cr-Mo-Cu (N08825)

Btu/hr ft
F Temp.
F

70

100

200

300

400

500

600

700

800

900

1,000

1,100

Ni-Mo Alloy B

6.1

6.4

6.7

7.0

7.4

7.7

8.2

8.7

9.3

10.0

10.7

Ni-Mo-Cr

5.9

6.4

7.0

7.5

8.1

8.7

9.2

9.8

10.4

11.0

11.5

102.3

102.8

104.2

105.2

106.1

96.1

96.9

99.0

100.6

101.9

12.7

12.5

12.0

11.7

11.5

11.3

11.2

11.1

11.2

11.3

11.4

11.6

Admiralty

70.0

75.0

79.0

84.0

89.0

Naval Brass

71.0

74.0

77.0

80.0

83.0

Copper

225.0

225.0

224.0

224.0

223.0

90-10 Cu-Ni

30.0

31.0

34.0

37.0

42.0

47.0

49.0

51.0

53.0

70-30 Cu-Ni (C71500)

18.0

19.0

21.0

23.0

25.0

27.0

30.0

33.0

37.0

12.1

13.2

Alloy C-276 Aluminum Alloy 3003 Aluminum Alloy 6061 Titanium

8.8

9.3

9.8

10.3

10.8

11.3

7 Mo Plus (S32950)

8.6

9.4

10.2

11.1

11.8

12.7

Muntz

71.0

Zirconium

12.0

Cr-Mo

11.3

Heat Transfer Chapter | 15

7 Mo (S32900)

Alloy XM-27 Cr-Ni-Fe-Mo-

7.6

41

Continued

42

dcont’d

Temp.
F

70

100

200

300

400

500

600

700

800

900

1,000

1,100

1,200

1,300

1,400

1,500

Ni-Cr-Mo-Cb (Alloy 625)

5.7

5.8

6.2

6.8

7.2

7.7

8.2

8.6

9.1

9.6

10.1

10.6

11.0

11.5

12.0

12.6

Al 29-4-2

8.8

SEA -CURE

9.4

12.9

13.7

Cu-Cb (Alloy 20Cb)

11.0 9.6

Al-6XN (N08367)

10.3

10.9

11.5

12.3

7.9

References

A.I.M.E. Tech. Publication Nos. 291, 360 & 648

Babcock & Wilcox Co.

Cabot-Stellite

ASME Sect. VIII, Div. 2, 1998 Edition

Teledyne Wah Chang Albany

American Brass Co.

Carpenter Technology

Huntington Alloy Inc. Bul. #15M1-76T-42

Trans. A.S.S.T. Vol. 21 pp. 1061-1078

Airco, Inc.

International Nickel Co.

Errata Note: k ¼ Btu/(hr) (ft) (
F) (Used by permission: Standards of the Tubular Exchanger Manufacturers Association, 8th Ed., Table D-12, © 1999 and 1991. All rights reserved.)

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Btu/hr ft
F

TABLE 15-8B Thermal Conductivity of Metals (S.I. units) W/m
C Temp.
C

21.10

37.8

93.3

148.9

204.4

260.0

315.6

371.1

426.7

482.2

537.8

593.3

648.9

704.4

760.0

815.6

51.9

51.7

50.5

49.2

47.8

46.0

44.3

42.6

40.7

38.9

37.0

35.0

32.9

30.5

28.0

27.0

42.9

43.3

43.6

43.4

42.9

42.1

41.0

39.8

38.4

37.0

35.3

33.7

31.8

28.9

26.5

26.0

36.9

37.2

37.9

38.1

37.9

37.6

36.9

36.0

35.0

34.1

33.1

32.0

30.6

28.6

26.0

25.6

Material Carbon Steel C 1/2 Moly Steel 1 Cr 1/2 Mo & 1 1/4 Cr 1/2 Mo 1

2 /4 Cr 1 Mo

36.2

36.3

36.9

37.2

37.2

37.0

38.5

35.8

35.0

34.1

33.1

32.0

31.2

29.8

27.0

26.5

1

29.2

29.9

31.3

32.4

33.1

33.2

33.2

32.9

32.4

31.8

31.2

30.5

29.6

28.7

27.7

27.3

1

7 Cr /2 Mo

24.4

24.9

26.5

27.7

28.6

29.2

29.6

29.8

29.9

29.8

29.6

29.1

28.7

28.0

27.0

26.8

9 Cr 1 Mo

5 Cr /2 Mo

22.2

22.7

24.2

25.4

26.3

27.0

27.5

27.7

27.9

27.9

27.9

27.7

27.3

27.0

26.3

26.0

1

3 /2 Nickel

39.6

40.2

41.2

41.7

41.4

40.5

39.6

38.6

37.4

36.2

34.8

33.2

31.5

29.2

26.8

26.5

13 Cr

26.3

26.5

26.8

27.0

27.3

27.3

27.5

27.5

27.5

27.5

27.3

27.0

26.5

26.1

26.0

26.1

15 Cr

24.6

24.6

24.9

25.1

25.3

25.4

25.4

25.6

25.6

25.6

25.6

25.6

25.6

25.6

25.6

25.6

17 Cr

21.8

22.0

22.2

22.5

22.7

22.8

23.0

23.2

23.4

23.5

23.7

23.9

24.1

24.4

24.7

25.1

TP 304 Stn. Stl.

24.2 14.9

15.1

16.1

17.0

18.0

18.9

19.6

20.4

21.1

22.0

22.8

23.5

24.2

25.1

25.8

26.5

TP 316 & 317 Stn. Stl.

13.3

13.7

14.5

15.6

16.4

17.3

18.2

19.0

19.9

20.6

21.5

22.3

23.0

23.9

24.6

25.3

TP 321 & 347 Stn. Stl.

14.0

14.5

15.2

16.3

17.1

18.0

18.9

19.7

20.6

21.3

22.2

23.0

23.7

24.4

25.3

26.0

TP 310 Stn. Stl.

12.6

13.0

13.8

14.9

15.7

16.6

17.5

18.4

19.2

20.1

20.9

21.8

22.7

23.5

24.4

25.1

Stn.Stl.

43

Continued

Heat Transfer Chapter | 15

17-19 Cr (TP 439)

44

W/m
C Temp.
C

21.10

37.8

93.3

148.9

204.4

260.0

315.6

371.1

426.7

2205(31803)

13.8

14.7

15.6

16.4

17.3

18.2

19.0

19.9

20.8

3RE60(S31500)

14.5

14.7

15.6

16.3

17.0

17.7

18.3

19.0

19.6

67.2

64.4

61.3

59.0

56.2

55.0

Nickel 200

482.2

537.8

56.2

57.3

58.5

593.3

648.9

704.4

760.0

815.6

Ni-Cu (N04400)

21.8

22.3

24.1

26.0

27.9

29.4

31.0

32.7

34.3

36.2

38.1

Ni-Cr-Fe (N06600)

14.9

15.1

15.7

16.6

17.5

18.4

19.2

20.1

20.9

21.8

22.8

23.9

24.7

25.8

26.8

27.7

Ni-Fe-Cr (N08800)

11.6

11.8

12.8

13.8

14.9

15.7

16.6

17.5

18.4

19.2

20.1

20.9

22.0

22.8

23.9

25.1

12.3

13.2

14.0

14.9

15.7

16.6

17.3

18.0

18.9

19.7

20.4

21.5

22.3

23.5

648.9

704.4

760.0

815.6

Ni-Fe-Cr-Mo-Cu (N08825)

W/m
C Temp.
C

37.8

93.3

148.9

204.4

260.0

315.6

371.1

426.7

482.2

537.8

593.3

Ni-Mo Alloy B

21.1

10.6

11.1

11.6

12.1

12.8

13.3

14.2

15.1

16.1

17.3

18.5

Ni-Mo-Cr

10.2

11.1

12.1

13.0

14.0

15.1

15.9

17.0

18.0

19.0

19.9

177.1

177.9

180.3

182.1

183.6

166.3

167.7

171.3

174.1

176.4

22.0

21.6

20.8

20.2

19.9

19.6

19.4

19.4

19.4

19.6

19.7

20.1

Admiralty

121.1

129.8

136.7

145.4

154.0

Naval Brass

122.9

128.1

133.3

138.5

143.6

Copper

389.4

389.4

387.7

387.7

385.9

90-10 Cu-Ni

51.9

53.7

58.8

64.0

72.7

81.3

84.8

88.3

91.7

Alloy C-276 Aluminum Alloy 3003 Aluminum Alloy 6061 Titanium

20.9

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-8B Thermal Conductivity of Metals (S.I. units)dcont’d

70-30 Cu-Ni (C71500)

31.2

32.9

36.3

39.8

43.3

46.7

51.9

57.1

64.0

15.7

16.6

17.5

7 Mo (S32900)

15.2

16.1

17.0

17.8

18.7

19.6

7 Mo Plus (S32950)

14.9

16.3

17.7

19.2

20.4

22.0

11.8

12.5

13.3

14.2

14.9

22.3

23.7

Muntz

122.9

Zirconium

20.8

Cr-Mo

19.6

Alloy XM-27 Cr-Ni-Fe-Mo-

13.2

Cu-Cb (Alloy 20Cb) Ni-Cr-Mo-Cb (Alloy 625)

9.9

Al 29-4-2

15.2

SEA -CURE

16.3

10.0

10.7

18.3

19.0

19.9

20.8

21.8

19.0 16.6

Al-6XN (N08367)

References ASME Sect. VIII, Div. 2, 1998 Edition Huntington Alloy Inc. Bul. #15M1-76T-42

17.8

18.9

20.1

21.3

13.7

A.I.M.E. Tech. Publication Nos. 291, 360 & 648 Babcock & Wilcox Co. American Brass Co. Teledyne Wah Chang Albany Airco, Inc. Trans. A.S.S.T. Vol. 21 pp. 1061-1078

Cabot-Stellite Carpenter Technology International Nickel Co.

Errata Note: k ¼ Btu/(hr) (ft) (
F) (Used by permission: Standards of the Tubular Exchanger Manufacturers Association, 8th Ed., Table D-12, © 1999 and 1991. All rights reserved.)

Heat Transfer Chapter | 15 45

46

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-9 Thermal conductivity of metals used in heat exchangers Heat Exchanger Tube Material

k, W/m-K

Aluminum

147

Brass, Admiralty

111

Brass, Red

159

Carbon steel (0.5% C)

54 @ 20oC

Carbon steel (1.5% C)

36 @ 20oC 33 @ 400

Copper

386

Hastelloy C

8.7

Inconel

14.5

Monel

26

Nickel

90

Tantalum

54

Titanium

21

Type 316 stainless steel

16.3

Type 410 stainless steel

24.9 FIGURE 15-14 Tube-side pass arrangements.

TABLE 15-10 Manufacturers’ Suggested Minimum Radius of Bend for Tubes Tube O.D., In.

Bend Radius, In.

Center-to Center Distance

Duplex, all sizes *Plain: 5/8 in. 3 /4 in. 1 in.

3 X tube O.D. 13 /16 in. 1 in. 13/16 in.

6 1 2 3

X tube O.D. 5 /8 in. in. 3 /8 in.

d0 ¼ O.D. or tube in in. R ¼ mean radius of bend, in. See TEMA for more details. *For bends this sharp, the tube wall on the outer circumference of the tube may thin down 11/2 - 2 gage thicknesses, depending on the condition and specific tube material. More generous radii will reduce this thinning. TEMA107 presents a formula for calculating the minimum wall thickness.

contact with the tubes as a direct result of the baffle pattern used. The baffle cut determines the fluid velocity between the baffle and the shell wall, and the baffle spacing determines the parallel and cross-flow velocities that affect heat transfer and pressure drop. Often the shell-side of an exchanger is subject to low pressure drop limitations, and the baffle patterns must be arranged to meet these specified conditions, and at the same time provide maximum effectiveness for heat transfer. The plate material used for these supports, and baffles should not be too thin and is usually 3/16 in. minimum thickness to 1/2 in. for large units. TEMA

gives recommendations. Figure 15-16 summarizes the usual arrangements for baffles. a. Tube Supports. Tube supports for horizontal exchangers are usually segmental baffle plates cut off in a vertical plane to a maximum position of one tube past the centerline of the exchanger and at a minimum position of the centerline. The cut-out portion allows for fluid passage. It takes at least two tube supports to properly support all the tubes in an exchanger when placed at maximum spacing. A tube will sag and often vibrate to destruction if not properly supported. However, because only half of the tubes can be supported by one support; the support plate must be alternated in orientation in the shell. The approximate maximum unsupported tube length and maximum suggested tube support spacing are given in Table 15-11. Although detailed calculations might indicate that for varying materials with different strengths the spacing could be different, it is usually satisfactory to follow the guides in Table 15-11 for any material commonly used in heat exchangers. Practice allows reasonable deviation without risking trouble in the unit. The tube support acts as a baffle at its point of installation and should be so considered, particularly in pressure drop calculations. Tube supports are often ignored in heat transfer coefficient design. They should also be provided with openings in the lower portion at the shell to allow liquid drainage to the outlet. Holes for tubes are drilled 1 /64 in. larger than the tube OD when an unsupported length

Heat Transfer Chapter | 15

47

FIGURE 15-15 Tube-side baffles.

standard segmental baffle designed for side to side flow

standard segmental baffle designed for up and down flow

standard single flow design

standard double split flow design

standard split flow design with horizontal baffle

standard double split flow design with horizontal beffles

standard segmental two shell baffle design

standard segmental three shell pass baffle design

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

FIGURE 15-16 Shell baffle arrangements. (Used by permission: Patterson-Kelley Div., a Harsco Company, “Manual No. 700A.”)

48

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-11 Maximum Unsupported Straight Tube SpansDimensions in Inches (mm) Tube Materials and Temperature Limits oF (oC) Carbon Steel & High Alloy Steel , 750 (399) Low Alloy Steel 850 (454) Nickel-Cooper 600 (316) Nickel 850 (454) Nickel-Chromium-Iron 1000 (538)

Aluminum & Aluminum alloys, Copper & Copper Alloys, Titanium Alloys at Code Maximum Allowable Temperature

1

26 (660)

22 (559)

3

35 (889)

30 (762)

1

44 (1118)

38 (965)

5

52 (1321)

45 (1143)

3

/4 (19.1)

60 (1524)

52 (1321)

7/8 (22.2)

69 (1753)

60 (1524)

1 (25.4)

Tube O.D. /4 (6.4) /8 (9.5) /2 (12.7 /8 (15.9)

74 (1880)

64 (1626)

1

88 (2235)

76 (1930)

1

1 /2 (38.1)

100 (2540)

87 (2210)

2 (50.8)

125 (3175)

110 (2794)

2 /2 (63.5)

125 (3175)

110 (2794)

3 (76.2)

125 (3175)

110 (2794)

1 /4 (31.8)

1

Notes: (1) Above the metal temperature limits shown, maximum spans shall be reduced in direct proportion to the fourth root of the ratio of elastic modulus at temperature to elastic modulus at tabulated limit temperature. (2) In the case of circumferentially finned tubes, the tube O.D. shall be the diameter at the roof of the fins and the corresponding tabulated or interpolated span shall be reduced in direct proportion to the fourth root of the ration of the weight per unit length of the tube, if stripped of fins to that of the actual finned tube. (3) The maximum unsupported tube spans in Table 15-11 do not consider potential flow-induced vibration problems. Refer to Section 6 for vibration criteria. (Used by permission: Standards of the Tubular Exchanger Manufacturers Association, 9th Ed., Table RCB 4.52, © 2007. Tubular Exchanger Manufacturers Association, Inc. All rights reserved.)

is greater than 36 in. (914.4mm) and are drilled 1/32 in. larger when the unsupported tube length is 36 in. (914.4 mm) or less, per TEMA standards, and are free from burrs. If there is much clearance, the natural flow vibration will cause the edge of the support to cut the tube. Pulsating conditions require special attention, and holes are usually drilled tight to tube OD. b. Segmental Baffles. This type of baffle is probably the most popular. It is shown in Figures 15-17 and 15-18 for horizontal and vertical cuts, respectively. A segmental baffle is a circle near the shell diameter from which a horizontal or vertical portion has been cut. The cut out portion, which represents the free-flow areas for shell-side fluid, is usually from 20 to near 50% of the open shell area. The net flow area in this space must recognize the loss of flow area covered by tubes in the area. Tube holes are drilled as for tube supports. The baffle edge is usually vertical for service in horizontal condensers, reboilers, vaporizers and heat exchangers carrying suspended matter or with heavy fouling fluids. In this arrangement, non-condensable vapors and

inert gases can escape or flow along the top of the unit. Thus, they prevent vapor binding or vapor lock causing a blanking to heat transfer of the upper portion of the shell. As important as vapor passage is liquid released from the lower portion of the shell as it is produced. Although provision should be made in the portion of the baffle that rests on the lower portion of the shell for openings to allow liquid passage, it is good practice to use the vertical baffle cut to allow excess liquid to flow around the edge of the baffle without building up and blanking the tubes in the lower portion of the exchanger, Figure 15-19. The horizontal cut baffles are good for all gas phase or all liquid phase service in the shell. However, if dissolved gases in the liquid can be released in the exchanger, this baffling should not be used, or notches should be cut at the top for gas passage. Notches will not serve for any significant gas flow, just for traces of released gas. Liquids should be clean; otherwise sediment will collect at the base of every other baffle segment and blank off part of the lower tubes to heat transfer.

Heat Transfer Chapter | 15

FIGURE 15-17 Horizontal cut segmental baffles. (Used by permission: B.G.A. Skrotzki, B.G.A. Power, © June 1954. McGraw-Hill, Inc. All rights reserved.)

49

c. Disc and Doughnut Baffles. The flow pattern through these baffles is uniform throughout the length of the exchanger. This is not the case for segmental baffles. The disc and the doughnut are cut from the same circular plate and are placed alternately along the length of the tube bundle, as shown in Figure 15-20. Although these baffles can be as effective as the segmental ones for singlephase heat transfer, they are not used as often. The fluid must be clean; otherwise, sediment will deposit behind the doughnut and blank off the heat transfer area. Furthermore, if inert or dissolved gases can be released, they cannot be vented effectively through the top of the doughnut. If condensables exist, the liquid cannot be drained without large ports or areas at the base of the doughnut. d. Orifice Baffles. This baffle is seldom used except in special designs, as it is composed of a full circular plate with holes drilled for all tubes about 1/16 in. to 1/8 in. larger than the outside diameter of the tube (see Figure 15-21). The clean fluid (and it must be very clean) passes through the annulus between the outside of the tube and the drilled

FIGURE 15-18 Vertical cut segmental baffles. (Used by permission: B.G.A. Skrotzki, B.G.A. Power, © June 1954, by McGraw-Hill, Inc. All rights reserved.)

FIGURE 15-20 Disc and doughnut baffles. (Used bytrun-1 permission: B.G.A. Skrotzki, B.G.A. Power, © June 1954, by McGraw-Hill, Inc. All rights reserved.)

FIGURE 15-19 Baffle details.

FIGURE 15-21 Baffles with annular orifices. (Used by permission: B.G.A. Skrotzki, B.G.A. Power, © June 1954, by McGraw-Hill, Inc. All rights reserved.)

50

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-22A RODbaffle
exchanger cross-section showing assembly, using TEMA E, F, H, J, K, and X shells. (Used by permission: © Phillips Petroleum Company, Licensing Div., Bul. 1114e94-Ae01.)

hole in the baffle. Considerable turbulence exists at the orifice, but very little cross-flow exists between baffles. Usually condensables can be drained through these baffles unless the flow is high, and non-condensables can be vented across the top. For any performance, the pressure drop is usually high, and it is mainly for this and the cleanliness of fluid requirements that these baffles find few industrial applications. e. RODbaffles
. These baffles are rods set throughout the shell-side of the tube bundle (see Figures 15-22AeD). The primary objective in using this style of baffle is to reduce tube failure from the vibrational damage that can be caused by the various metal baffles versus metal tube designs. The RODbaffles
are designed to overcome the tube vibration mechanisms of (a) vortex shedding, (b) turbulence and (c) fluid elastic vibration. For proper application

FIGURE 15-22B RODbaffle
Intercooler in fabrication, 67 in. 40 ft, 2,232e3/4-in. O.D. copper-nickel tubes, 1.00 in. pitch. TEMA AHL. (Used by permission: © Phillips Petroleum Company, Licensing Div., Bul. 1114e94-Ae01.)

and design, the engineer should contact Phillips Petroleum Company Licensing Division for names of qualified design/ manufacturing fabricators. This unique design has many varied applications, but they can only be handled by licensed organizations. f. Impingement Baffles. These baffles are located at inlet flow areas to the shell-side of tube bundles to prevent suspended solid particles or high velocity liquid droplets in gas streams from cutting, pitting or otherwise eroding portions of the tubes. Several arrangements exist for effectively placing these baffles, as is shown in Figures 15-23AeC. Besides preventing destruction of the tubes, impingement plates serve to spread out and distribute the incoming fluid

FIGURE 15-22C RODbaffle
tube-baffle details. (Used by permission: © Phillips Petroleum Company, Licensing Div., Bul. 1114e94-Ae01.)

Heat Transfer Chapter | 15

51

FIGURE 15-22D 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.,1114e94eAe01.)

FIGURE 15-23A Impingement baffles and fluid-flow patterns. (Used by permission: Brown & Root, Inc.) FIGURE 15-23B Impingement fluid-flow pattern with annular inlet distributor. (Used by permission: Brown & Root, Inc.)

52

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-23C Impingement baffle located in inlet nozzle neck.

into the tube bundle. If they are used in proper relation to the bundle cross-flow baffles, the fluid can be effectively spread across the bundle near the inlet end. If this is not accomplished, part of the tube area will be stagnant, and its heat transfer will be less than the other parts of the exchanger. Some indications are that these stagnant partially effective areas may be 10e20% of the total exchanger surface in a 16 ft (5 m) long bundle [55]. It is apparent that this portion of the design requires a close visualization of what will occur as the fluid enters the unit. Braun [17] suggests flow patterns as shown in Figures 15-23A and B. Some exchanger designs require that the inlet nozzles be placed close to the tubesheet to obtain the best use of the surface in that immediate area.

Fabrication problems limit this dimension. Therefore, internal baffling must be used to force the incoming fluid across the potentially stagnant areas. g. Longitudinal Baffles. Longitudinal baffles are used on the shell-side of a unit to divide it into two or more parts, giving higher velocities for better heat transfer, or to provide a divided area of the bundle for the subcooling of liquid or the cooling of non-condensable vapors as they leave the shell. The baffle must be effectively sealed at the shell to prevent bypassing. Depending upon the shell diameter, the usual sealing methods are (a) welding, (b) sliding slot and (c) special packing. Figure 15-24 illustrates some of these techniques. Longitudinal baffles must also be compatible with the shell-side fluid, so they normally will be of the same material as tubes or baffles. This baffle never extends the full inside length of the shell, because fluid must flow by its far end to the return pass in reaching the exchanger outlet. Figure 15-24E is a photograph of a heat exchanger showing the tube bundles with segmental baffles. Generally, a basic understanding of the various baffle types with advantages and disadvantages is essential for choosing an effective baffle configuration, as shown in Table 15-12 [298].

Tie Rods Tie rods are used to keep the baffles and the tube support plates at their appropriate locations as determined during the process design of the heat exchanger. Tie rods with

FIGURE 15-24A Construction details of two-pass expanding shell-side baffle. (Used by permission: Struthers-Wells Corp., Bul. Ae22.)

Heat Transfer Chapter | 15

53

FIGURE 15-24B Assembled two-pass shell baffle for installation in shell of exchanger. (Used by permission: Struthers-Wells Corp. Bul. Ae22.).

concentric tube spacers are used to space the baffles and tube supports along the tube bundle. The baffles or supports must be held fixed in position, because any chattering or vibration with respect to the tubes may wear and eventually destroy the tube at the baffle location. The number of tie rods used depends upon the size and construction of the exchanger bundle. The material of the rods and spacers must be the same or equivalent to that of the baffles or bundle tubes. Provision must be made in the tube sheet layout for these rods, which is usually accomplished by omitting a tube (or more) at selected

FIGURE 15-24D Longitudinal baffle, sliding slot detail.

locations on the outer periphery of the tube bundle. The rod is usually threaded into the back of only one of the tube sheets, being free at the other end, terminating with the last baffle or support by means of lock washers or similar fool-proof fastening. See the upper portion of Figure 15-24A for tie rod spacers.

FIGURE 15-24C Longitudinal shell-pass baffle. (Used by permission: Henry Vogt Machine Co., Patent No. 2,482,335.)

54

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Table 15-13 shows suggested tie rod count and diameter for various sizes of heat exchangers, as recommended by TEMA [107]. Other combinations of tie rod number and diameter with equivalent metal area are permissible; however, no fewer than four tie rods, and no diameter less than 3 /8 in., should be used. Any baffle segment requires a minimum of three points of support. Without the tie rods and spacers, the baffles and the support plates can move along the tubes thereby adversely affecting the performance of the exchanger.

Tubesheets

FIGURE 15-24E A series of shell and tube heat exchangers.

Tubesheets form the end barriers to separate the shell-side and tube-side fluids. Most exchangers use single plates for tubesheets. However, for hazardous or corrosive materials such as chlorine, hydrogen chloride, sulfur dioxide, etc., where the intermixing due to leakage from shell to

TABLE 15-12 Each Baffle Type has Advantages and Disadvantages that Make it Suitable for Different Applications Baffle Type

Advantages

Disadvantages/Limitations

TEMA

SingleSegmental

Highest potential heat transfer rates Easiest to fabricate Least expensive

Highest potential pressure drop Cannot be used for very viscous fluids

Type

DoubleSegmental

Lower pressure drop than with singlesegmental baffles

Lower heat transfer rates than with single segmental baffles

TripleSegmental

Lower pressure drop than with doublesegmental baffles

Lower heat transfer rates than with double segmental baffles

Baffles

No-Tubes-inWindow Configuration

All tubes are supported, eliminating tube vibration Higher conversion of pressure drop to shell-side heat transfer than singlesegmental baffles

Requires a smaller tube bundle and/or larger shell; a larger shell makes this configuration more expensive

Non

Helical

Less shell-side fouling Moderate heat transfer rates and pressure drops Minimizes or eliminates areas of stagnant flow Minimizes or eliminates tube vibration

Difficult fabrication, design methods are not standardized Significant bundle-to-shell bypass at high mass flowrates

TEMA Type

Disc and Donut

Radially symmetric flow distribution Minimizes bypass flow Same pressure drop as with doublesegmental baffles, with better heat transfer Well suited for gas-gas applications

More expensive than traditional double-segmental baffles Preferred radial tube layout requires a less-common fabrication method than triangular and square layouts In a radial tube layout, the angular gaps between tubes near the shell are larger than those between tubes near the center; this requires the addition of an improved, nonradial (e.g. triangular or rotated square) layout between the radial tube rows

Baffles

Grid

Provides tube support Uniform flow distribution Relatively low pressure drops High conversion ratio of pressure drop to heat transfer

Relatively low heat-transfer rates, unless the tubes are long Specific tube layouts are required

(Source: Salem Bouhairie, Selecting Baffles for Shell-and-Tube Heat Exchangers, CEP, pp 27e33, Feb. 2012).

Heat Transfer Chapter | 15

55

TABLE 15-13 Tie Rod StandardsdDimensions in Inches (mm) Nominal Shell Diameter

Tie Rod Diameter

Minimum Number of Tie Rods

6e15 (152-381)

3

4

16e27 (406e686)

3

6

28e33 (711e838)

1

6

34e48 (864e1219)

1

8

46e60 (1245e1524)

1

10

61e100 (1549e2540)

5

12

/8 (9.5) /8 (9.5) /2 (12.7) /2 (12.7) /2 (12.7) /8 (15.9)

Used by permission: Standards of Tubular Exchanger Manufacturers Association, 8th Ed., Table R 4 71, © 1999. Tubular Exchanger Manufacturers Association, Inc., All rights reserved.

FIGURE 15-26 A U-tube bundle with tie rods, spacers attached to the baffles.

Figure 15-26 illustrates stationary tube sheet with tie rods and spacers attached to the baffles.

Tube Joints in Tubesheets tube-side or vice versa would present a serious problem, the double tubesheet is used, as shown in Figure 15-25. This is considerably more expensive for fabrication, not only due to the plate costs, but also for the extra grooving of these sheets and rolling of the tubes into them. Because they must be aligned, the machining must be carefully handled; otherwise assembly of the unit will be troublesome. The number of tubes in an exchanger, also referred to as the tube count, is reduced because of the space occupied by the tie rods and spacers. Normally, each set of a tie rod and spacer requires the removal of four to six tubes around it. Therefore, the total number of tubes removed is dependent upon the shell diameter.

FIGURE 15-25 Tube-to-double tubesheet assembly detail.

The quality of the connection between the tube and tubesheet is extremely important. A poor joint here means leakage of shell-side fluid into the tube-side or vice versa. This joint can be one of several designs, depending upon the service and type of exchanger. In general, it is good to standardize on some type of grooved joint as compared to the less expensive plain joint. In Figures 15-25 and 15-27, these joints are indicated, as well as special types for the duplex-type tube. The plain joint is used in low pressure services where the differential pressure across the tubesheet is 5e50 psi (0.3e3.4 bar), and the differential expansion of tubes with respect to shell is very low, as gaged by a rule of thumb. The maximum temperature differential anywhere in the unit between fluids is no more than 200
F (93.3
C) for steel or copper alloy construction. Serrated and grooved joints are used for high pressure differentials but usually not in services exceeding 200
F (93.3
C) as a rule. Actually these joints will withstand more than twice the push or pull on the tube as a plain joint. The serrations or grooves provide points of strength and affect a better seal against fluid leakage. The welded joint is used only for high system pressures above 1,000 psig (69 barg), or high temperatures, greater than 300
F (150
C), where the properties of the fluid make it impossible to hold a seal with grooved or serrated joints due to temperature stresses or where extra precautions must be taken against cross-contamination of the fluids. If a weld is used, it must be considered as the only sealing and strength part of the connection, because tubes cannot be safely rolled into the tubesheet after welding for fear of cracking a weld. The rolls made prior to welding are usually separated by the heat of the welding operation. This means that the weld cannot be a seal weld, but must truly be a strength weld and must be so designed. Tubes to be

FIGURE 15-27 Tube to tubesheet joint details.

TABLE 15-14 Recommended Diameter of Flared Inlet Holes in Tubesheets for Copper and Copper Alloys O.D. of Tube, In.

Flare Diameter, In.

Radius of Flare, In.

Tangent Point to Tubesheet, In.

1

0.60 0.75 0.90 1.20

0.38 0.47 0.56 0.75

0.21 0.26 0.31 0.42

/2 5/8 3 /4 1

Used by permission: Condenser and Heat Exchanger Tube Handbook, Bridgeport Brass Co., Bridgeport, Conn. © 1954, p. 148. See TEMA [107], Par, RCB 7.4 and 7.5. All rights reserved.

welded into the tubesheet should be spaced farther apart to allow for the weld, without the welds of adjacent tubes touching. The details will depend upon the materials of construction. Tubes may be inserted into a tubesheet, and packing may be added between them and the tubesheet. A threaded ferrule is inserted to tighten the packing. This type of joint is used only for special expansion problems. If conditions are such as to require a duplex tube, it is quite likely that a plain end detail for the tube will not be satisfactory. Grooved or serrated joints are recommended for this type of tube, and the ends should be flared or beaded. Table 15-14 gives recommended flare or bell radii for copperbased alloys. Also see Tables 15-14A and B. In services where galvanic corrosion or other corrosive action may

TABLE 15-14A TEMA Standard Tube Hole Diameters and Tolerances (All Dimensions in inches) Nominal Tube Hole Diameter and Under Tolerance Standard Fit (a)

Special Close Fit (b)

Nominal Tube O.D.

Nominal Diameter

Under Tolerance

Nominal Diameter

Under Tolerance

1

0.259

0.004

0.257

3

0.384

0.004

1

0.510

5 3 7

/4 /8 /2 /8 /4 /8

1

Over Tolerance: 96% of Tube Holes Must Meet Value in Column (c). Remainder may not Exceed Value in Column (d) (c)

(d)

0.002

0.002

0.007

0.382

0.002

0.002

0.007

0.004

0.508

0.002

0.002

0.008

0.635

0.004

0.633

0.002

0.002

0.010

0.760

0.004

0.758

0.002

0.002

0.010

0.885

0.004

0.883

0.002

0.002

0.010

1.012

0.004

1.010

0.002

0.002

0.010

1

1 /4

1.264

0.006

1.261

0.003

0.003

0.010

1

1 /2

1.518

0.007

1.514

0.003

0.003

0.010

2

2.022

0.007

2.018

0.003

0.003

0.010

Used by permission: Standards of Tubular Exchanger Manufacturers Association, 7th Ed., Table RCB 7.41, © 1988. Tubular Exchanger Manufacturers Association, Inc. all rights reserved.

TABLE 15-14B TEMA Standard Tube Hole Diameters and Tolerances (All Dimensions in mm) Nominal Tube Hole Diameter and Under Tolerance Standard Fit (a)

Over Tolerance: 96% of Tube Holes Must Meet Value in Column (c). Remainder May not Exceed Value in Column

Special Close Fit (b)

Nominal Tube O.D.

Nominal Diameter

Under Tolerance

Nominal Diameter

Under Tolerance

(c)

(d)

6.4

6.58

0.10

6.53

0.05

0.05

0.18

9.5

9.75

0.10

9.70

0.05

0.05

0.18

12.7

12.95

0.10

12.90

0.05

0.05

0.20

15.9

16.13

0.10

16.08

0.05

0.05

0.25

19.1

19.3

0.10

19.25

0.05

0.05

0.25

22.2

22.48

0.10

22.43

0.05

0.05

0.25

25.4

25.70

0.10

25.65

0.05

0.05

0.25

31.8

32.11

0.15

32.03

0.08

0.08

0.25

38.1

38.56

0.18

38.46

0.08

0.08

0.25

50.8

51.36

0.18

51.26

0.08

0.08

0.25

Used by permission: Standards of Tubular Exchanger Manufacturers Association, 8th Ed., Table RCB 7.41, © 1999. Tubular Exchanger Manufacturers Association, Inc. All rights reserved.

take place on the outside material used in the tube, a ferrule of inside tube materials should be used on the outside in the tubesheet only to avoid this contact, as shown in Figure 15-27. As an added sealing feature, the end of the duplex tube may be beaded over to seal against surface tension effects. As a precaution, the rolling of tubes into their tubesheets is a very special job that requires experience and “feel,” even though today there are electronically controlled rolling and expanding tools. The tubes must be just right; i.e., not over or under expanded, to give a good joint and seal.

Shell Baffles

Seal strips

Shell

Seal strips

Baffles

Seal Strips These are strips of metal used to reduce the amount of fluid bypassing the tube bundle in a floating head heat exchanger where the clearance between the shell and the outer tube limit (OTL) is large. Seal rods are used in tube pass partition lanes to reduce the bypass stream. The seal strips are installed in pairs on the baffles, usually by welding as shown in Figure 15-28. The strips seal off the space between the shell and the OTL, thus forcing the bypassing liquid to flow over the tube bundle. Generally, one pair of seal strips is used for every five to seven tube rows in crossflow. Seal strips are not applicable in the fixed tubesheet or U-tube bundle units where the clearance between the shell and the OTL is not large. Further, these are not applicable where a phase change is occurring (e.g. boiling, condensation) even if the clearance is large, because the seal strips might adversely affect the phase separation. For fluids with sensible heat and tubes removed due to impingement protection, a seal strip is added to prevent bypassing over the bundle. Also a rear end head type T bundle should always have seal strips for sensible heat services.

FIGURE 15-28 Seal strips.

EXAMPLE 15-1 Determine Outside Heat Transfer Area of Heat Exchanger Bundle

To determine the outside heat transfer area of a heat exchanger bundle consisting of 100 tubes, 3/4 in. OD tubing, 18 BWG (gage thickness)  16 ft long. For fixed tubesheets (2), thickness is 1.0 in. each. From Table 15-7, read: External surface area/foot length for these tubes ¼ 0.1963 ft2. Note: 1/8 ¼ projection of tubes past exterior face of two tube sheets

58

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Total external tube surface for this bundle: Interior face-to-face of the two tube sheets ¼ 16 ft  21/4 in. ¼ 15 ft, 9.75 in. Net tube surface per tube ¼ (15.8125 ft length net) (0.1963 ft2/ft) ¼ 3.1039 ft2/tube. For 100 tubes, total heat exchanger NET outside tube surface area: ¼ (100) (3.1039) ¼ 310.39 ft2 Tubesheet Layouts The layout of the heat exchanger tubesheet determines the number of tubes of a selected size and pitch that will fit into a given diameter of shell. The number of tubes that will fit into the shell varies depending upon the number of

(2) Square pitch   2 ðDs  K1 Þ p=4 þ K2  pðDs  K1 Þ½K3 ðnÞ þ K4  Nt ¼ ðpÞ2 (15-3) where Nt ¼ Number tubes in shell Ds ¼ Inside diameter of shell, in. p ¼ Tube pitch, in. n ¼ Number of tube passes K1, K2, K3, K4 ¼ Constants depending on the tube size and layout. Use the following table.

Table of K values Tube Size Inch

Arrangement

Pitch Inch

K1

K2

K3

K4

3

Triangular

15

1.080

0.900

0.690

0.800

3

Triangular

1

1.080

0.900

0.690

0.800

3

Square

1

1.040

0.100

0.430

0.250

/4 /4 /4

/16

1

1

Triangular

1 /4

1.080

0.900

0.690

0.800

1

Square

1 1/4

1.040

0.100

0.430

0.250

tube-side passes and even upon whether there is a shell-side pass baffle that divides the shell itself into two or more parts. The usual tube sizes for most exchangers are 3/4 in. OD and 1 in. OD. The 5/8 in. and 1/2 in. OD tubes are used in package exchangers with refrigeration and other systems. However, they present problems in both internal and external cleaning as well as fabrication. Tubes of 11/4 in. and 11/2 in. OD and sometimes larger are used in boilers, evaporators, reboilers and special designs, Tubes of 3 in., 31/2 in. and 4 in. are used in direct fired furnaces and a few special process exchanger designs.

Tube Counts in Shells Although there are several equations for numerically calculating the number of tubes in a shell, the counts presented in Table 15-15 have been carefully prepared. Errors in tube count can cause recalculation in expected exchanger performances [125]. Number of tubes/shell: (1) Triangular pitch   ðDs  K1 Þ2 p=4 þ K2  pðDs  K1 Þ½K3 ðnÞ þ K4  Nt ¼ 2 1:223ðpÞ (15-2)

The tube layouts given in Figures 15-29AeK are samples of the convenient form for modifying standard layouts to fit special needs, such as the removal of certain tubes. Figures 15-29AeE are for U-bundle tubes and require a wide blank space across the center of the tubesheet to recognize the U-bend requirement at the far end of the tube bundle; see Figures 15-1E, 15-1A item U and 15-1K. Figures 15-29FeK are for fixed tubesheet layouts. Before fabrication, an exact layout of the tubes, clearances, etc., must be made; however, for most design purposes, the tube counts for fixed tubesheets and floating heads as given in Tables 15-15 and 15-16 AeF are quite accurate. A comparison with tube counts in other references [19,70] indicates an agreement of 3% in the small diameters up to about 231/4 in. ID shell and graduating up to about 10% for the larger shells. The counts as presented have checked manufacturers’ shop layouts  one tube for 8 in. to 171/4 in. I.D. shell; 5 tubes for 211/4 in. to 27 in. ID; and 10e20 tubes for the larger shells. No allowances for impingement baffles are made in these layouts, although channel and head baffle lanes have been considered. A standard manufacturing tolerance of 3/8 in. has been maintained between the specified inside diameter of the shell to the nearest point on any tube (tube clearance).

TABLE 15-15 Heat Exchanger Tubesheet Layout Tube Count Table Note the Right Column for Tubesheet and Number of Passes Per Configuration 37

35

33

31

29

27

25

23 1/4

21 1/4

19 1/4

17 1/4

15 1/4

13 1/4

12

10

8

I.D. of Shell (in.) 3

15

1,019 889 765 551 477

881 765 665 481 413

763 667 587 427 359

663 577 495 361 303

553 493 419 307 255

481 423 355 247 215

391 343 287 205 179

307 277 235 163 139

247 217 183 133 111

193 157 139 103 83

135 117 101 73 65

105 91 85 57 45

69 57 53 33 33

33 33 33 15 17

/4 in. on /16 in. D /4 in. on 1in. D 3 /4 in. on 1in. , 1 in. on 1/4 in. D 1 in. on 11/4 in.,

Fixed Tubes

OnePass

1,242 1,088 946 688 584

1,088 972 840 608 522

964 858 746 530 460

846 746 644 462 402

734 646 560 410 348

626 556 486 346 298

528 468 408 292 248

452 398 346 244 218

370 326 280 204 172

300 264 222 162 136

228 208 172 126 106

166 154 126 92 76

124 110 94 62 56

94 90 78 52 40

58 56 48 32 26

32 28 26 16 12

3

/4 in. 15/16 in D /4 in. on 1in. D 3 /4 in. on 1in , 1 in. on 11/4 in D 1 in. on 11/4 in,

Fixed Tubes

TwoPass

1,126 1,000 884 610 526

1,008 882 778 532 464

882 772 688 466 406

768 674 586 396 356

648 566 506 340 304

558 484 436 284 256

460 406 362 234 214

398 336 304 192 180

304 270 242 154 134

234 212 188 120 100

180 158 142 84 76

134 108 100 58 58

94 72 72 42 38

64 60 52 26 22

34 26 30 8 12

8 8 12 XX XX

3

/4 in. on 15/16 in D /4 in. on 1in. D 3 /4 in. on 1in , 1 in. on 11/4 in D 1 in. on 11/4 in,

U Tubes2

1,072 1,024 880 638 534

1,024 912 778 560 476

904 802 688 486 414

788 692 590 422 360

680 596 510 368 310

576 508 440 308 260

484 424 366 258 214

412 360 308 212 188

332 292 242 176 142

266 232 192 138 110

196 180 142 104 84

154 134 126 78 74

108 96 88 60 48

84 72 72 44 40

48 44 48 24 24

XX XX XX XX XX

3

/4 in. on 15/16 in D /4 in. on 1in. D 3 /4 in. on 1in , 1 in. on 11/4 in D 1 in. on 11/4 in,

Fixed Tubes

1,092 968 852 584 500

976 852 748 508 440

852 744 660 444 384

740 648 560 376 336

622 542 482 322 286

534 462 414 266 238

438 386 342 218 198

378 318 286 178 166

286 254 226 142 122

218 198 174 110 90

166 146 130 74 66

122 98 90 50 50

84 64 64 36 32

56 52 44 20 16

28 20 24 XX XX

XX XX XX XX XX

3

U Tubes2

3

3

3

3

/4 in. on 15/16 in D /4 in. on 1in. D 3 /4 in. on 1in , 1 in. on 11/4 in D 1 in. on 11/4 in, 3

FourPass

Continued

59

1,143 1,007 865 633 545

Heat Transfer Chapter | 15

1,269 1,127 965 699 595

60

Note the Right Column for Tubesheet and Number of Passes Per Configuration 37

35

33

31

29

27

25

23 1/4

21 1/4

19 1/4

17 1/4

15 1/4

13 1/4

12

10

8

I.D. of Shell (in.) 3

15

1,106 964 818 586 484

964 852 224 514 430

844 744 634 442 368

732 640 536 382 318

632 548 460 338 268

532 464 394 274 226

440 388 324 226 184

372 322 266 182 154

294 258 212 150 116

230 202 158 112 88

174 156 116 82 66

116 104 78 56 44

80 66 54 34 XX

XX XX XX XX XX

XX XX XX XX XX

XX XX XX XX XX

/4 in.on /16 in D /4 in. on 1in. D 3 /4 in. on 1in , 1 in. on 11/4 in D 1 in. on 11/4 in,

Fixed Tubes

1,058 940 820 562 478

944 826 718 488 420

826 720 632 426 362

716 626 534 356 316

596 518 458 304 268

510 440 392 252 224

416 366 322 206 182

358 300 268 168 152

272 238 210 130 110

206 184 160 100 80

156 134 118 68 60

110 88 80 42 42

74 56 56 30 XX

XX XX XX XX XX

XX XX XX XX XX

XX XX XX XX XX

3

/4 in. on 15/16 in D /4 in. on 1in. D 3 /4 in. on 1in , 1 in. on 11/4 in D 1 in. on 11/4 in,

U Tubes2

1,040 902 760 542 438

902 798 662 466 388

790 694 576 400 334

682 588 490 342 280

576 496 414 298 230

484 422 352 240 192

398 344 286 190 150

332 286 228 154 128

258 224 174 120 94

198 170 132 90 74

140 124 94 66 XX

94 82 XX XX XX

XX XX XX XX XX

XX XX XX XX XX

XX XX XX XX XX

XX XX XX XX XX

3

/4 in. on 15/16 in D /4 in. on 1in. D 3 /4 in. on 1in , 1 in. on 11/4 in D 1 in. on 11/4 in,

Fixed Tubes

1,032 908 792 540 456

916 796 692 464 396

796 692 608 404 344

688 600 512 340 300

578 498 438 290 254

490 422 374 238 206

398 350 306 190 170

342 286 254 154 142

254 226 194 118 98

190 170 146 90 70

142 122 106 58 50

102 82 70 38 34

68 52 48 24 XX

XX XX XX XX XX

XX XX XX XX XX

XX XX XX XX XX

3

/4 in. on 15/16 in D /4 in. on 1in. D 3 /4 in. on 1in , 1 in. on 11/4 in D 1 in. on 11/4 in,

U Tubes2

37

35

33

31

29

27

25

23 1/4

21 1/4

19 1/4

17 1/4

15 1/4

13 1/4

12

10

8

I.D. of Shell (in.)

1 2

Allowance made for tie rods. R.O.B. ¼ 21/2  Tube diameter. Actual number of “U” tubes is one-half the figure shown in the table.

3

3

3

3

Six Pass

Eight Pass

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-15 Heat Exchanger Tubesheet Layout Tube Count Tabledcont’d

Heat Transfer Chapter | 15

61

FIGURE 15-29A Tubesheet layout for U-tube exchanger. Tube passes: two or four. Tube sizes and pitch: 3/4 in. on 15/16 in. Radius of bend: 2 1/2 tube diameter.

Tube spacing arrangements are shown in Figure 15-30 for the usual designs. Countless special configurations exist for special purposes, such as wide pitch dimensions to give larger ligaments to provide access for cleaning tools to clean scale and fouling films from the outside of tubes by mechanical means. Often chemical cleaning is satisfactory, and wide lanes are not justified. Wide spaces also give low pressure drops but require special care to avoid low transfer coefficients, or at least recognition of these conditions. Special directional tube lanes, as in steam surface condensers for power plants, allow the fluid to penetrate the large bundle and, thereby, give good access to the surface. Method of Figuring Tube Counts e Use With Table 15-15 A. Fixed Tubes: Pass: One: Two: Four:

Six: Eight:

All pitches and tube sizes Straight through Half-circle per pass 151/4 in. shell I.D. and smaller, used pie shape baffle layout 171/4 in. shell I.D. and larger, used ribbon baffle layout Ribbon baffle layout for all shell I.D. Ribbon baffle layout for all shell I.D.

Radius of Bend ¼ 21/2 times tube OD for all pitches and tube sizes Pass: Two: Pie shaped layout Four: Pie shaped layout Six: Vertical baffle layout Eight: Vertical baffle layout C. Allowances: For tie rods: 8e131/4 in. shell ID, removed 4 tubes 151/4 e29 in. shell ID, removed 6 tubes 31e37 in. shell ID, removed 8 tubes B. U-Tubes:

1 6 1 6

1 6 1 6

Six Pass

1 6 1 6

1 8

1 8

1 8

1 8

1 8

1 8

1 8

1 8

Eight Pass

62

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-29B Tubesheet layout for U-tube exchanger. Tube passes: two or four. Tube size and pitch: 3/4 in. on 15/16 in. Radius of bend: 1 1/2 tube diameter.

Applications of Tube Pitch Arrangements, Figure 15-30. Triangular Pitch, Apex Vertical or Facing Oncoming Flow. Most popular, generally suitable for non-fouling or fouling services handled by chemical treatment, mediumto-high pressure drop, gives better coefficients than inline square pitch. In-Line Triangular Pitch, Apex Horizontal or at Right Angle to Oncoming Flow. Not as popular as the staggered triangular pitch; coefficients not as high, but better than in-line square pitch; pressure drop about medium to high; generally suitable for fouling conditions same as preceding. In-Line Square Pitch. Popular for conditions requiring low pressure drop and/or cleaning lanes for mechanical cleaning of outside of tubes; coefficient lower than triangular pitch. Diamond Square Pitch. Popular arrangements for reasonable low pressure drop (not as low as in-line square), mechanical cleaning requirements and better coefficient than in-line square pitch.

Exchanger Surface Area The actual surface area available for heat transfer is determined from the fabricator’s shop drawings. From these details, the following are fixed:

Number of Tubes The actual number of tubes to be installed in the unit. Manufacturing tolerances may require elimination of some tubes that preliminary design layouts and tables indicated might be installed in the unit. Figures 15-29AeK and Table 15-15 have considered known fabrication tolerances. Sometimes extra tie rods for baffles must be added, or in some cases, eliminated. The outer tube circle limit for each exchanger is determined by the type of shell to be used. That is, (1) if commercial pipe, greater out-of-round tolerances might be required or (2) if formed on shop rolls, the out-of-round tolerance will be known, but not necessarily be the same for each diameter shell.

Heat Transfer Chapter | 15

63

FIGURE 15-29C Tubesheet layout for U-tube exchanger. Tube passes: two or four. Tube size and pitch: 3/4 in. O.D. on 1 in. Radius of bend: 2 1/2 tube diameter.

Exact Distance between Faces of Tubesheets Tubes are usually ordered in even lengths, such as 8, 10, 12, 16, 24 or 32 ft, and the tubesheets are from 1/4 in. to 1/2 in.

Net Effective Tube Length This is the net length of tube exposed inside the shell and available for contact by the shell-side fluid. This length accounts for the thickness of each tubesheet (and for the double tubesheets when used). For design purposes, it is usually estimated from experience, allowing the following (approx.): 1. 11/2 in. per tubesheet for low pressure units. 2. 2e3 in. per tubesheet for high pressure exchangers, 200e400 psi (14e28 bar).

Exact Baffle Spacing In some instances, the baffle spacing must be rearranged to allow for a nozzle or coupling connection. It is important

that changes in baffle location be reviewed, as performance or pressure drop can be seriously affected. This is of particular importance in vacuum units. Baffle orientation is sometimes misinterpreted by the fabricator, and this can cause serious problems where liquid drainage is concerned, or the revised vapor flow path can allow for bypassing the tube surface.

Impingement Baffle Location When scale drawings are made, the effectiveness of impingement baffles can be evaluated easily. Sometimes it is necessary to relocate or make slight size changes in order to properly protect the tubes and direct the vapor flow. Tables 15-17AeF serve as a help in preliminary heat exchanger design for determining the number of tubes that is permitted in a certain shell diameter. These tables indicate only the maximum number of tubes for each shell diameter, because no allowance was made to install impingement plates or to satisfy TEMA requirements in relation to the maximum bundle entrance and shell

64

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-29D Tubesheet layout for U-tube exchanger. Tube passes: two or four. Size and pitch: 3/4 in. on 1 in. Radius of bend: 2 1/2 tube diameter.

entrance velocities. Since most removable bundles are constructed with square tube patterns to allow mechanical cleaning of the tube exteriors, tables for triangular arrays are only included in fixed tubesheet designs (TEMA type L). The pass partition arrangements on which these tables are based are shown in Figure 15-31. Some of the tube distributions resulting from these tables are shown in Figures 15-32 Ae32N.

Net effective outside area for finned tube is:  Anf ¼ ft2 external finned surface per ft length from  Table 15-50 ðLe; net effective tube lengthÞ ðNt; number of tubesÞ (15-5)

Effective Tube Length for U-Tube Heat Exchangers

Effective Tube Surface The effective tube surface is usually evaluated on the outside tube surface. Use net tube length. Net effective outside area for plain or bare tube is:  An ¼ ft2 external surface per ft length from Table 15-7  ðLe; net effective tube lengthÞ  ðNt; number of tubesÞ (15-4)

One challenge in the design of U-tube heat exchangers is determining the effective length of the tubes. For example, when U-tube bundles are fabricated from 12 ft tubes, the maximum length tube in the bundle is 12 ft, which is in the outside tube row. The inside tube is the shortest and is less than 12 ft long. The effective tube length, Le of the bundle for surface area calculations is the mean of the tube lengths between

Heat Transfer Chapter | 15

65

FIGURE 15-29E Tubesheet layout for U-tube exchanger. Tube passes: two or four. Tube size and pitch: 1 in. on 1 1/4 in. Radius of bend: 1 1/2 tube diameter.

the outside tubes and the inside tubes. See Figure15-33A. In calculating the optimum U-tube heat exchanger design, most designers estimate the effective tube length for each of the various heat exchangers. After a specific heat exchanger design is selected, the effective tube length is determined accurately by the fabricator. If the estimated length differs significantly from the actual length, additional design calculations may be necessary. To more easily determine effective tube lengths for U-tubes, the correction chart shown in Figure 15-33B [124] is convenient. The chart is based on many actual U-tube bundle layouts. Values read from the chart are not more than 1% lower than those obtained by calculation, except

No. of U-Tubes

Tube Size

where the curve is extrapolated to lower tube counts. Such extrapolations result in errors of 3%, 4% and higher, giving larger values than those calculated. This does not apply to higher tube count extrapolations. The chart is limited to 3 /4 in. and 1 in. OD tubes. The accuracy of extrapolation to other diameters has not been determined. The chart is applicable to low-finned tubes, as well as to plain tubes. However, it is restricted to either two or four tube passes. For arrangements other than those used in the chart preparation, the chart may be used at the designer’s discretion. As an example of those “beyond limits,” the following is a comparison of calculated areas with actual areas for various U-tube bundles installed in a chemical plant.

Inside Tube Pitch

Calc’d* Tube ROB

Area Ft2

Act. Area

% Error

66

3

1 in.

2 in.

400.0

405.7

þ1.43

88

3

1 in.

2 in.

534

533

0.19

1

3 in.

439

448

þ2.05

54

/4 in. OD  32 ft /4 in. OD  32 ft

1 in. OD  32 ft

1 /4 in.

Note: ROB ¼ Radius of bend. * The calculated areas were based on Figure 15-33B using only the respective tube size and number of tubes.

66

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-29F Fixed tubesheet layout (also nonremovable floating head). Tube passes: two. Tube size and pitch: 3/4 in. on 15/16 in.

TUBE VIBRATION The tubes of an exchanger are supported at both ends by the tubesheets and in intermediate positions by baffles (see Figure 15-26). Fluid flow interrelates with the heat exchanger geometry, as each tube section between two consecutive supports is a flexible element that can vibrate. The vibration that occurs depends on the mass (i.e., both that of the tube and the fluid that flows through it), on its moment of inertia, the way it is supported and the distance between supports. The natural frequency of vibration depends on the density of the shell-side and the tensile strength at which the tube is submitted, as the flow of the shell-side fluid past the tubes can produce certain periodic unbalanced forces over the tubes. When the frequency of these forces coincides with the natural frequency of the tubes, resonance occurs, and the tubes may commence to vibrate with large amplitude. Under certain conditions, the vibrational amplitude could be large enough to cause severe damage to the tubes. Mechanical failure of tubes resulting from flow-induced vibration may occur in various

situations, and damage can result from any of the following independent conditions or combinations of these: Collision damage: This is caused by the impact of the tubes against each other or against the shell-side wall, due to the large amplitudes of the vibrating tube. The impacted area of the tube develops the characteristic flattened, boat shaped spot, generally at the mid-span of the unsupported length. The tube wall eventually wears thin, causing failure. Baffle damage: Baffle tube holes require a manufacturing clearance over the tube outer diameter to facilitate fabrication. When large fluid forces are present, the tube can impact the baffle hole, causing thinning of the tube wall in a circumferential, uneven manner, usually the width of the baffle thickness. Continuous thinning over a period of time results in tube failure. Tubesheet clamping effect: Tubes are generally expanded into the tubesheet to minimize the crevice between the outer tube wall and the tubesheet hole. The natural frequency of the tube span adjacent to the tubesheet is increased by the clamping effect. However, the stresses

Heat Transfer Chapter | 15

67

FIGURE 15-29G Fixed tubesheet layout (also nonremovable floating head). Tube passes: two. Tube size and pitch: 3/4 in. on 1 in. 6.

due to any lateral deflection of the tube are also maximum at the location where the tube emerges from the tubesheet, contributing to possible tube breakage. Material defect propagation: Some designs determined to be free of harmful vibrations contain tubes that vibrate with very minimal amplitude because of the baffle tube hole clearances and the flexibility of the tube span. If a material contains flaws oriented with respect to the stress field, they can readily propagate and increase tube failure. Also, corrosion and erosion can add to such failure mechanisms. Acoustic vibration: This phenomenon is due to gas column oscillation, which is excited by phased vortex shedding. The oscillation creates an acoustic vibration of a standing wave. The generated sound wave will not affect the tube bundle unless the acoustic resonant frequency approaches the tube’s natural frequency, however the heat exchanger and the associated piping may vibrate with loud noise. When the acoustic resonant frequency approaches the tube’s natural frequency, any tendency

toward tube vibration will be accentuated with possible tube failure. Tube failures have appeared in various locations within a heat exchanger. Those of primary concerns are locations of relatively flexible tube spans and/or high flow velocities. U-tubes bends: Outer rows of U-bends have a lower natural frequency of vibration, and therefore are more susceptible to flow-induced vibration failures than the inner rows (Figure 15-26). Nozzle entrance and exit area: In these regions, impingement plates, large outer tube limits and small nozzle diameters can contribute to restricted entrance and exit areas. These restricted areas normally create high local velocities that can result in damaging flow-induced vibration. Tubesheet region: Unsupported tube spans adjacent to the tubesheet are frequently longer than those in the baffled region of the heat exchanger, and result in lower natural frequencies. Entrance and exit areas are common to this

68

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-29H Fixed tubesheet layout (also nonremovable floating head). Tube passes: two. Tube size and pitch: 3/4 in. on 1 in. ,.

region. The possible high local velocities, in conjunction with the lower natural frequency, make this a region of primary concern in preventing damaging vibrations. Baffle window region: Tubes located in the baffle windows have unsupported spans equal to multiples of the baffle spacing. Long unsupported tube spans result in reduced natural frequency of vibration and have a greater tendency to vibrate. Obstructions: This can happen where any obstruction to flow such as tie rods, sealing strips and impingement plates may cause high localized velocities which can initiate vibration in the immediate vicinity of the obstruction.

Vibration Mechanisms There are four flow-induced vibration mechanisms that can occur: Fluidelastic whirling: This occurs when a displacement of a tube in a tube bundle causes a shift of the flow field and a subsequent change of fluid forces on the tubes. This

mechanism is associated with high fluid velocities, as this change can induce instabilities and the tube will start vibrating in oval orbits. These vibrations are referred to as fluidelastic whirling (or the fluidelastic instability). This phenomenon is recognized as the major cause of tube vibrations in tubular heat exchangers. Vortex shedding: A tube exposed to an incident cross-flow above critical Reynolds numbers provokes an instability in the flow and a simultaneous shedding of discrete vortices alternately from both sides of the tube. This phenomenon is known as vortex shedding or Von Karman turbulence. Alternate shedding of the vortices produces harmonically varying lift and drag forces that may cause movement of the tube. When the tube oscillation frequency approaches within about 20% of the tube’s natural frequency, the tube starts vibrating at its natural frequency. Vortex shedding occurs for Reynolds number greater than 100 (Re > 100). The Reynolds number is based on the upstream fluid velocity and tube outside diameter. In the region 105 < Re < 2106 , vortex shedding has a broad band of shedding frequencies. Consequently, the regular vortex shedding does not exist in this region.

Heat Transfer Chapter | 15

69

FIGURE 15-29I Fixed tubesheet layout (also nonremovable floating head). Tube passes: two. Tube size and pitch: 1 in. on 1 1/4 in. ,.

Turbulent buffeting: This refers to unsteady forces developed on a body exposed to a highly turbulent flow. The turbulence has a wide range of frequencies around a dominating frequency which increases as the cross-flow increases. This effect is observed only in heat exchangers handling high velocity gases. The oscillatory phenomenon in turbulent flow on the shell-side (i.e. when the shell-side fluid is gas) is characterized by fluctuating forces with a dominant frequency. Acoustic vibration: As explained previously, this mechanism produces noise but generally does not produce tube vibration. It is one of the most common forms of flow-induced vibration in shell-and-tube exchangers for high velocity shell-side gas flows in large exchangers, which can be excited by any of the preceding mechanism and provokes the appearance of sound waves.

Treatment of Vibration Problems The determination of potential flow-induced vibration problems in heat exchanger design is not an integral

part of the process design. However, in many cases, to solve vibration problems, it is essential to make changes to the exchanger geometry as this affects the thermal design. TEMA standards provide a methodology to predict vibration damage, however as the phenomenon is rather complex, TEMA does not guarantee prevention of vibration damage [352]. Commercial heat exchanger design software usually includes a vibration evaluation model based on this methodology, which alerts the designer(s) when vibration may be expected in a certain design. The method by TEMA consists of determining the natural frequency of vibration for each tube section within the exchanger. This frequency depends on the unsupported span, type of support, tensile or compression stress and physical properties of tube material and fluids. This method incorporates criteria to avoid tube vibration caused by all the mechanisms described. For vortex shedding vibration, the TEMA standards include equations and graphs that allow calculation of the vibration frequency resulting from this mechanism. If the tube natural frequency is less than double the vortex

70

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-29J Fixed tubesheet layout (also nonremovable floating head). Tube passes: one. Tube size and pitch: 1 in. on 1 1/4 in 6.

shedding frequency, there is a possibility of vibrational damage. In such a case, it is essential to determine the amplitude of the tube vibration, which must not exceed 2% of the tube’s diameter. In the case of fluidelastic whirling (instability), vibration is avoided if the fluid velocity at each section of the heat exchanger is below a certain critical velocity. This critical velocity is dependent on the tube geometry, its natural frequency of vibration and the viscous damping effect of the shell-side fluid. If the fluid velocity at any location is higher than the critical velocity determined for that location, tube damage can result. The velocity in this instance is calculated point by point at every location in the shell. This requires noting internal bypass streams, leakage streams between tubes and baffles and between baffles and the shell, the effect of impingement plates, pass partition lanes sealing strips, etc. These calculations can be found in the TEMA standards [252]. In the case of acoustic vibration, the vibration frequency of the shell, which depends on the physical

properties of the circulating fluids is determined. The TEMA standards then define criteria to compare this frequency with the vortex shedding and turbulent buffeting frequencies and decide if the acoustic resonance effect is present.

Corrective Measures When there is the conclusion of a vibration analysis with a potential risk of tube damage, then the designer(s) should modify/alter the design by [287]: l

l

Reducing the unsupported tube span. This can be achieved by using baffles with no tubes in the window area (NTIW type ¼ no tube in window baffles). Reducing the fluid velocity in the critical regions. By changing the tube patterns, increasing the baffle spacing (this increases the unsupported span), increasing the nozzle diameters, or by eliminating some tubes.

Heat Transfer Chapter | 15

71

FIGURE 15-29K Fixed tubesheet layout (also nonremovable floating head). Tube passes: one. Tube size and pitch: 1 1/4 in 6.

EXAMPLES 15-2 Use of U-Tube Area Chart [124]

Case 1 Given: Number of U-Tubes: 168 Tubes: 0.75 in. O.D.  16 ft (nominal) plain tubes Required: Total effective exposed area. From Figure 15-33B: Effective tube length ¼ 14.5 ft  0:75 Total effective exposed area ¼ ð14:5Þð168Þp 12 ¼ 478:3ft2 Case 2 Given: Tubes: 1 in.  12 ft (nominal) low-finned tubes (19 fins/in.). 2 Outside area of tubes ¼ 0.678 linft f t Exposed area of bundle ¼ 2,142 ft2 Required: Number of tubes required. A brief trial and error procedure is necessary. Assume effective tube length ¼ 11 ft.

2;142 ¼ 288 Thus, the number of tubes required ¼ ð11Þð0:678Þ From Figure 15-33B: Effective tube length for 288 tubes ¼ 9.6 ft. 2;142 ¼ 330 Calculate new number of tubes ¼ ð9:6Þð0:678Þ Effective tube length ¼ 9.42 ft. 2;142 Calculate new number of tubes ¼ ð9:42Þð0:678Þ ¼ 336 Effective tube length for 336 tubes ¼ 9.4 ft. Thus, required number of tubes ¼ 336 The equations of Figure 15-33B correlations are as follows:

Le ¼ Effective tube length, ft. Nt ¼ Number of U-tubes L ¼ Nominal tube length, ft. For 3/4 in. U-tubes:     Le ¼ ðL  0:5Þ  7:4007  103 ðNt Þ þ 8:5791  106 ðNt Þ2  3 ð3:7873  109 ðNt Þ (15-6) For 1 in. U-tubes:     2 Le ¼ ðL  0:5Þ  9:2722  103 ðNt Þ þ 1:1895  105 ðNt Þ  3 ð8:4977  109 ðNt Þ (15-7)

TABLE 15-16A Full Circle Tube Layouts Floating Heat Exchanger 3/4ein. O.D. Tubes on

15

/16ein. 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

TABLE 15-16B Full Circle Tube Layouts Floating Heat Exchanger 3/4ein. O.D. Tubes on 1ein. 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

TABLE 15-16C Full Circle Tube Layouts Floating Heat Exchanger 3/4ein. O.D. Tubes on 1ein. 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

TABLE 15-16D Full Circle Tube Layouts Floating Heat Exchanger, 1ein. O.D. Tubes on 11/4 ein. 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

74

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-16E Full Circle Tube Layouts Floating Heat Exchanger, 1ein. O.D. Tubes on 1 1/4 -in. Triangular Pitch Number of Passes

Size (In.)

1

2

4

6

8

Net Free Distance 2 passes

Rows Across

8

22

20

18

16

12

4.13

9

10

38

36

32

32

28

4.50

13

12

60

52

48

46

44

4.63

15

14

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

NOZZLE CONNECTIONS TO SHELL AND HEADS

FIGURE 15-30 Tube spacing layouts for tubesheets.

Inlet and outlet liquid nozzles are sized by conventional pressure drop evaluations or by the more common velocity guides. For low pressure vacuum services, velocities should not be used to establish any critical connection size. (Figure 15-93 is a useful guide for the usual case.) Safety valves are often required on the shell-side of heat exchangers and sometimes on the tube-side. These valves may require sizing based upon process reaction, over pressure, abnormal conditions or on external fire, etc. For details, see Chapter 9, Vol. 1, 4th ed. of this series on safety-relieving devices. Drains are necessary on the shell and on the bottom of most heads. Sometimes several drains are necessary on the shell-side to facilitate drainage between baffles when flushing is a part of the operation.

Heat Transfer Chapter | 15

TABLE 15-17A Tube Count 3/4-in. (19.05 mm) Tubes on Triangular (30 Degrees) Array, Pitch 1 in (25.4 mm) TEMA Type L Internal Shell Diameter

TABLE 15-17B Tube Count 3/4-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

Number of Tube Passes

in

mm

1

2

4

6

in

mm

2

4

6

8

203.2

38

36

32

24

8

203.2

22

20

18

10

254

69

62

56

48

10

254

40

40

36

304.8

105

94

88

76

12

12 1

13 /4 1

15 /4 1

336.5 387.3

129 181

120 166

108 154

104 148

304.8

70

64

70

1

336.5

90

84

84

1

387.3

126

114

114

1

13 /4 15 /4

17 /4

438.15

235

218

206

198

17 /4

438.15

164

158

156

19 1/4

488.9

295

280

262

252

19 1/4

488.9

218

210

198

21 1/4

539.7

356

344

330

314

21 1/4

539.7

268

262

260

23 1/4

590.5

431

418

398

388

23 1/4

590.5

334

326

314

25

635

504

492

462

446

25

635

392

378

364

27

685.8

597

578

550

538

27

685.8

462

450

426

29

736.6

694

674

646

634

29

736.6

544

534

510

31

787.4

799

778

750

732

31

787.4

634

610

594

33

838.2

919

888

854

834

33

838.2

716

702

674

35

889

1031

1004

968

946

35

889

816

796

780

37

939.8

1149

1128

1084

1052

37

939.8

914

896

882

39

990.6

1284

1258

1216

1202

39

990.6

1028

1012

988

42

1066.8

1499

1452

1416

1382

42

1066.8

1194

1168

1156

45

1143

1727

1686

1640

1616

45

1143

1390

1364

1336

Vents are usually placed on the shell and on the tubeside heads to allow venting of inert gases or other material. A 1 in.e6,000 lb. half of full-coupling is recommended for both vent and drain, unless other sizes are indicated. Couplings are handy to have on the process inlet and outlet nozzles of both the tube and shell-sides. These may be used for flushing, sampling or thermometer wells, thermocouple bulbs or pressure gages.

TYPES OF HEAT EXCHANGE OPERATIONS The process engineer identifies heat exchange equipment in a process by the operation or function it serves at a particular location in the flow cycle. For example, the bottom vaporizer on a product finishing distillation column

75

is usually termed Finishing Column Reboiler E-16, or Reboiler E-16; the overhead vapor condenser on this column is termed Condenser E-17; etc. The usual operations involved in developing a process flowsheet are described in Table 15-18 or in Chapter 1, Volume 1, 4th ed. of this series.

Thermal Design The engineering thermal design of heat transfer equipment is concerned with heat flow mechanisms of the following three types e either 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.

76

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-17C Tube Count 3/4-in. (19.05 mm) Tubes on Square (90 Degrees) Array, Pitch 1 in (25.4 mm) TEMA Type U Internal Shell Diameter

TABLE 15-17D 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

Number of Tube Passes

in

mm

2

4

6

in

mm

1

2

4

6

8

203.2

26

20

20

8

203.2

22

22

12

12

10

254

48

44

40

10

254

40

36

32

28

304.8

74

68

68

12

12 1

13 /4 1

15 /4 1

336.5 387.3

94 126

88 122

84 114

304.8

61

58

48

48

1

336.5

81

72

68

58

1

387.3

104

100

94

82

1

13 /4 15 /4

17 /4

438.15

172

170

160

17 /4

438.15

145

132

122

114

19 1/4

488.9

218

218

218

19 1/4

488.9

181

174

162

152

21 1/4

539.7

280

278

268

21 1/4

539.7

224

218

202

198

23 1/4

590.5

346

338

330

23 1/4

590.5

270

264

246

242

25

635

408

390

386

25

635

317

306

286

280

27

685.8

478

470

454

27

685.8

376

362

338

328

29

736.6

560

546

534

29

7366

431

414

398

388

31

787.4

646

634

618

31

787.4

500

492

462

458

33

838.2

744

730

716

33

838.2

571

556

530

510

35

889

840

820

816

35

889

641

630

604

582

37

939.8

946

932

918

37

939.8

737

708

680

664

39

990.6

1060

1048

1032

39

990.6

813

796

764

748

42

1066.8

1240

1220

1192

42

1066.8

941

918

888

868

45

1143

1430

1404

1388

45

1143

1091

1068

1028

1008

Radiation is not generally considered in conventional heat transfer equipment except for direct gas/oilfired heaters and cracking units. These latter types are not a part of this chapter, because they are specialty items of their own as far as design considerations are concerned. Conduction is heat transfer through a solid, non-porous 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 ¼ 

ka ka Aðt2  t1 Þ ¼  A Dt Lc Lc

(15-8)

Referring to Figure 15-34, conduction occurs through the tube wall and is represented by a temperature drop t4 e t5 and through the scale of fouling by the drops t3 e t4 and t5 e 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, or rapid for forced convection when artificial means are used to mix or agitate the fluid. The basic equation for designing heat exchangers is: Q ¼ UAðt2  t1 Þ ¼ UA Dt

(15-9)

where: (t2  t1) represents the temperature difference across a single fluid film. Referring to Figure 15-34, convection occurs through the fluid t1  t3 and also t6  t8. where: A ¼ net external surface areas of tubes exposed to fluid heat transfer (not just the length of the individual tubes), ft2 (m2). Q ¼ heat load, Btu/h (kW).

Heat Transfer Chapter | 15

TABLE 15-17E 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 mm

2

4

8

203.2

12

8

10

254

26

20

304.8

40

36

12 1

13 /4 1

15 /4 1

336.5 387.3

TABLE 15-17F 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

56 76

48 70

6

Number of Tube Passes

in

mm

2

4

8

203.2

12

8

20

10

254

26

24

22

28

12

48 66

6

304.8

40

40

36

1

336.5

56

48

48

1

387.3

76

70

66

1

13 /4 15 /4

17 /4

438.15

102

98

94

17 /4

438.15

102

98

94

19 1/4

488.9

126

130

118

19 1/4

488.9

126

130

118

21 1/4

539.7

164

166

156

21 1/4

539.7

164

166

156

23 1/4

590.5

206

202

198

23 1/4

590.5

206

202

198

25

635

248

242

232

25

635

248

242

232

27

685.8

294

282

274

27

685.8

294

282

274

29

736.6

346

334

322

29

736.6

346

334

322

31

787.4

400

390

382

31

787.4

400

390

382

33

838.2

458

446

438

33

838.2

458

446

438

35

889

522

508

496

35

889

522

508

496

37

939.8

584

576

548

37

939.8

584

576

548

39

990.6

648

648

628

39

990.6

648

648

628

42

1066.8

758

744

742

42

1066.8

758

744

742

45

1143

898

880

854

45

1143

898

880

854

U ¼ overall heat transfer coefficient, Btu/(h-ft2-
F) (kW/m2.
C). Dt ¼ mean temperature difference,
F, (
C) corrected. An important step in accurately establishing the required net surface area of an exchanger is to determine the true Dt. For example, the simplest temperature difference involves a constant temperature on each side of the tube, such as steam condensing on one side at about 410
F (210
C) and an organic hydrocarbon compound boiling at constant temperature of about 250
F (121
C). Use this simple temperature difference for Equation 15-9. DT ¼ 410  250 ¼ 160
F (89
C) This applies regardless of the fluid flow pattern in the unit [129]. Such a unit could be like the one shown in Figure 15-1C; also see Figure 15-35B.

77

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 15-35: Hot: 200
F / 100
F Cold: 80
F / 150
F Note that the log mean temperature difference (DTLMTD) is somewhat less than the arithmetic mean, represented by the following: ½ðT1  t2 Þ þ ðT2  t1 ÞO2; or; ðhot  cold terminal temperature differenceÞO2 (15-10)

The DTLMTD for this flow is given by Reference [129], Equation 15-11, using end conditions of exchanger. Thus: DTLMTD ¼

ðT2  t1 Þ  ðT1  t2 Þ ðGTD  LTDÞ   ¼ T2 t1 In T1 t2 In GTD LTD (15-11)

where:

FIGURE 15-31 Pass partition arrangements for Tables 15-17Ae17D.

GTD ¼ Greater Terminal Temperature Difference,
F (
C) LTD ¼ Lesser Terminal Temperature Difference,
F (
C) DTLMTD ¼ Logarithmic Mean Temperature Difference,
F (
C) T1 ¼ Inlet temperature of hot fluid,
F (
C) T2 ¼ Outlet temperature of hot fluid,
F (
C) t1 ¼ Inlet temperature of cold fluid,
F (
C) t2 ¼ Outlet temperature of cold fluid,
F (
C)

FIGURE 15-32A 3/4 in. tube distribution in 1-in. triangular patttern, one-pass configuration. Rear head type L.

Heat Transfer Chapter | 15

79

FIGURE 15-32B 3/4 in. tube distribution in 1-in. triangular patttern, two-pass configuration. Rear head type L.

Note that the logarithmic mean temperature difference should be used when the following conditions generally apply [107]; for conditions of true counter current or cocurrent flow: l l

l l l l l

Constant overall heat transfer coefficient. Complete mixing within any shell cross pass or tube pass. The number of cross baffles is large (more than 4). Constant flow rate and specific heat. Enthalpy is a linear function of temperature. Equal surfaces in each shell pass or tube pass. Negligible heat loss to surroundings or internally between passes.

For co-current flow (see Figure 15-35B), the temperature difference will be (T1  t1), and the opposite end of the unit will be (T2  t2). This pattern is not often used, because it is not efficient and will not give as good a transfer as counter-current flow [129] flow. Because the

temperature cannot cross internally, this limits the cooling and heating of the respective fluids. For certain temperature controls related to the fluids, this flow pattern proves beneficial. For one shell and multipass on the tube-side, it is obvious that the fluids are not in true counter current flow (nor co-current). Most exchangers have the shell-side flowing through the unit as in Figure 15-35C (although some designs have no more than two shell-side passes as in Figures 15-1J and 15-24, and the tube-side fluid may make two or more passes as in Figure 15-1J); however, more than two passes complicates the mechanical construction.

TEMPERATURE DIFFERENCE: TWO FLUID TRANSFER The temperature difference, Dt,
F (
C), required to satisfy the basic heat transfer relationship Q ¼ UA Dt is the logarithmic mean of the differences in temperatures at the

80

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-32C 3/4 in. tube distribution in 1-in. triangular patttern, four-pass configuration. Rear head type L.

opposite ends of the paths of flow of the two fluids. The temperature flow paths can be represented as shown in Figures 15-36 and 15-37. In true counter flow operation (sensible heat transfer), the one fluid, A, being cooled is flowing at all times in a near 180
direction to the fluid being heated, B (Figure 1536). Note that because A is being cooled, it comes into the exchanger at a temperature, T1, which is hotter than the inlet, t1, of the fluid being heated. In this case the fluid B can leave at a temperature, t2 which is greater than the outlet temperature T2 of fluid A. the vertical distance between the two curves at any point along the travel length of the fluid is the temperature difference ðT0  t0 Þ (or D, Figure 15-36) at that point. In parallel operation (sensible heat transfer), fluids A and B (Figure 15-36) flow in the same direction along the length of travel. They enter at the same general position in the exchanger, and their temperatures rise and fall

respectively as they approach the outlet of the unit and as their temperatures approach each other as a limit. In this case the outlet temperature, t2, of fluid B, Figure 15-36, cannot exceed the outlet temperature, T2, of fluid A, as was the case for counter flow. In general, parallel flow is not as efficient in its use of available surface area as is counter flow. In condensation, one fluid remains at constant temperature throughout the length of the exchanger while the fluid B that is absorbing the latent heat of condensation is rising in temperature to an outlet temperature of t2. Note that as fluid A condenses, it does not flow the length of the travel path. Fluid A drops to the bottom of the exchanger and flows out the outlet at temperature T2, which is the same as T1, the temperature of condensation, providing no subcooling occurs to lower the temperature of the liquid to less than T2. In this case, t2 approaches but never reaches T2.

Heat Transfer Chapter | 15

81

FIGURE 15-32D 3/4 in. tube distribution in 1-in. square patttern, two-pass configuration. Rear head type S.

When viewed from the condensation operation, the unit is termed a condenser, however, if the main process operation is the heating of a fluid with the latent heat of another stream, such as steam, then the unit is termed a heater. If boiling follows sensible heating, the unit is a reboiler. Temperature crosses in an exchanger can prevent the unit from operating. Figure 15-38 indicates two situations, one involving desuperheating and condensing a vapor, and the second requiring the heating and vaporizing of a fluid. In the first instance, note that it is not simply the desire to remove a fluid t2 at a temperature greater than T2, but more fundamentally involves the shape of the temperature profile curves. To be certain of performance, the heating, cooling, condensing or vaporizing curves for the fluids should be established. Although calculations may give a unit a performance based on end limits of temperature, if a cross exists inside between

these limits, the expected heat exchange will not be accomplished. For the average fluid temperature and/or true caloric temperature see Temperature for Fluid Properties Evaluation e Caloric Temperature later in this chapter. Counter current or co-current flow of the two (usual) fluids in a heat transfer operation is the most efficient of the several alternate design combinations. The most efficient heat transfer occurs in a straight through, singlepass operation, such as shown in Figures 15-2 and 15-35, and design-wise Figure 15-1H (but not as a reboiler). Usually for these cases the logarithmic mean temperature difference may be applied. Murty [132] discusses a calculation method for establishing the maximum possible cross in a parallel counter flow exchanger (Figure 15-37). This technique is outlined in the following example.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-32E 3/4 in. tube distribution in 1-in. square patttern, four-pass configuration. Rear head type S.

EXAMPLE 15-3 One Shell Pass, 2 Tube Passes ParallelCounterflow Exchanger Cross, After Murty [132]

Find the minimum temperature to which a hot fluid at 410
F can be cooled if the cold fluid is heated from an inlet temperature of 167
F to 257
F. Also find the theoretical temperature cross and theoretical minimum hot fluid shellside outlet temperature T2. Using equations from Reference [132]: T2min  t1 ¼

ðT1  t1 Þ 1  ½2ðTðDtÞ 1 t1 Þ

 ðT1  t1 Þ

(15-12)

where:

  ðt2  T2 Þmax ¼ 0:1715 410  167 ¼ 41:7
F Theoretical T2min ¼ 257  41:7 ¼ 215:3
F or; when, T1  t1 > DT, then the following approximation applies:
  T2min  t1 y T1  t1 1 þ

Dt ¼ t2  t1 Substituting : T2min  167 ¼

The theoretical maximum possible temperature cross in this exchanger type is: (t2  T2min) ¼ 0.1715 Theoretical (t2  T2)max ¼ 0.1715 (T1  t1) Then, theoretical T2min ¼ t2  (t2  T2)max Then, for the example: the theoretical maximum possible temperature cross:

½ð410  167Þ ð257167Þ 1  2ð410167Þ

 ð410  167Þ

T2min  167 ¼ 55.23
F (actual) T2min ¼ 222.23
F Maximum temperature cross:    2  21=2 21=2  1 ½t2  T2  ¼ ¼ 0:1715 21=2 ½T1  t1 

 Dt  ðT1  t1 ÞÞ y Dt=2 2ðT1  t1 Þ

Use the preceding equation when (T1  t1)  50
F T ¼ Shell side fluid,
F t ¼ Tube-side fluid,
F T2min ¼ Minimum hot fluid exit temperature achievable,
F 1 ¼ Inlet (hot) 2 ¼ Outlet (cool)

Heat Transfer Chapter | 15

83

FIGURE 15-32F 3/4 in. tube distribution in 1-in. square patttern, two-pass configuration. Rear head type U.

In vaporization, one fluid, B, vaporizes at constant temperature, while the second fluid, A, is cooled from T1 to T2. When a refrigerant such as propylene is being vaporized to condense ethylene vapors, the unit actually operates at a fixed temperature difference for the entire length of the exchanger. In this latter situation, t1 equals t2 and T1 equals T2. In an evaporator, one fluid is vaporized as the heating fluid is cooled to T2.

Mean Temperature Difference or Log Mean Temperature Difference Figure 15-39 shows a counter current heat exchanger. At the section where the axial coordinate is x, the temperature of the hot fluid is T and the temperature of the cold fluid is t. At the section corresponding to coordinate x þ dx, these

temperatures are T þ dT and t þ dt. Here, both increments are positive because both temperatures increase with coordinate x. A heat balance involving both cold and hot fluid streams is: dQ ¼ Wh Cph dT ¼ wc Cpc dt

(15-13)

However, the heat flow in terms of the overall heat transfer coefficient U, pipe outside diameter and an incremental length of pipe, dx is: dQ ¼ UdAðT  tÞ ¼ UpDo dxðT  tÞ

(15-14)

From Equation 15-13, we have: dQ ¼ dT Wh Cph

(15-15)

84

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-32G 3/4 in. tube distribution in 1-in. square patttern, four-pass configuration. Rear head type U.

and: dQ ¼ dt wc Cpc

(15-16)

Subtracting Equation 15-16 from 15-15, we have:  1 1 ¼ dðT  tÞ (15-17)  dQ Wh Cph wc Cpc

Equation 15-19 is a differential equation that can be integrated along the length of the heat exchanger with the following limits: For x ¼ 0, T  t ¼ T2  t1 For x ¼ L, T  t ¼ T1  t2 we have:  pDo U

Considering Equation 15-14, we have: dQ ¼ ðT  tÞ UpDo dx

1 1  Wh Cph wc Cpc

ZL

TZ1 t2

dx ¼ T2 t1

0



1 1 pDo LU  Wh Cph wc Cpc

(15-18)

Dividing Equation 15-17 by Equation 15-18 gives:  1 1 dðT  tÞ pDo dxU ¼  (15-19) Wh Cph wc Cpc Tt





dðT  tÞ (15-20) Tt

T1  t2 ¼ ln T2  t1

(15-21)

The total heat exchanged in the unit can be expressed as: Q ¼ Wh Cph ðT1  T2 Þ

(15-22)

Heat Transfer Chapter | 15

85

FIGURE 15-32H 3/4 in. tube distribution in 1.25-in. triangular patttern, one-pass configuration. Rear head type L.

or: Q ¼ wc Cpc ðt2  t1 Þ

(15-23)

Rearranging Equations 15-22 and 15-23 gives: 1 T1  T2 ¼ Q Wh Cph

(15-24)

and: 1 t2  t1 ¼ Q wc Cpc

(15-25)

Substituting Equations 15-24 and 15-25 into Equation 15-21 gives:  pUDo L T1  t2 (15-26) ½ðT1  T2 Þ  ðt2  t1 Þ ¼ ln T2  t1 Q

Further rearrangement of Equation 15-26 gives: 2 3 6ðT1  t2 Þ  ðT2  t1 Þ7 7  Q ¼ ðpDo LÞU6 4 5 T1 t2 ln T2 t1

(15-27)

Equation 15-27 shows that the mean temperature difference that must be used to establish a relationship between the total area of the unit and the total heat transferred is the logarithmic mean temperature difference, DTLMTD as expressed by: DTLMTD ¼

ðT1  t2 Þ  ðT2  t1 Þ  T1 t2 ln T2 t1

(15-28)

86

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-32I 1-in. tube distribution in 1.25-in. triangular patttern, two-pass configuration. Rear head type L.

Equation 15-28 is applicable for counter current flow heat exchanger, but is also valid for a concurrent configuration, where the expression is: DtLMTD ¼

ðT1  t1 Þ  ðT2  t2 Þ  T1 t1 ln T2 t2

Dt1 ¼ Temperature difference at one end of exchanger (smaller value), see Figure 15-35. Dt2 ¼ Temperature difference at other end of exchanger (larger value) ln ¼ Natural logarithm to base e MTD ¼ Mean Temperature Difference,
F, see Figure 15-40. ¼ Log mean temperature difference LTD ¼ Dt1 ¼ Lesser terminal temperature difference GTD ¼ Dt2 ¼ Greater terminal temperature difference

(15-29)

For these cases, the logarithmic mean temperature difference may be applied as: DtLMTD ¼ MTD ¼

ðDt2  Dt1 Þ ðDt2  Dt1 Þ   ¼ Dt2 2 In Dt 2:3log 10 Dt2 Dt1 (15-30)

where: DtLMTD ¼ Log mean Temperature difference ¼ LMTD

Figure 15-40 is a useful means of solving the LMTD calculation. Equations 15-29 and 15-30 are applicable for the heat exchanger unit as long as: l l

The overall heat transfer coefficient U is constant. The fluid heat capacities of the streams are constant.

Heat Transfer Chapter | 15

87

FIGURE 15-32J 1-in. tube distribution in 1.25-in. triangular patttern, four-pass configuration. Rear head type L.

Log Mean Temperature Difference Correction Factor, F Correction factors are given in Figures 15-41AeF to modify the true counter current LMTD for the multipass exchanger actual flow paths and accompanying temperature deviations. Note that where Figures 15-41AeJ represent corrections to the LMTD for the physical configuration of the exchanger, Figures 15-42AeC represent the temperature efficiency of the unit and are not the same as the LMTD correction. Often, a reasonable and convenient way to understand the heat transfer process in a heat exchanger unit is to break down the types of heat transfer that must occur: such as, vapor subcooling to dew point, condensation and liquid subcooling. Each of these demands heat transfers of a different type, using different DT values, film coefficients and fouling factors. This is illustrated in Figure 15-43. It is possible to properly

determine a weighted overall temperature difference and to calculate the total heat transfer area directly: Qtotal

DT ðlong mean weightedÞ ¼  Q1 DT1

(15-31)

Q3 Q2 þ DT þ DT 2 3

where: Q ¼ Heat transferred is specific section of the exchanger, Btu/h (kW). DT ¼ Corresponding LMTD for the respective heat transfer area,
F (
C). Subscripts 1, 2 and 3 ¼ segments of heat exchanger corresponding to the Q and DT values. These MTD (or DTLMTD) correction factors are read from the appropriate chart, which describes the exchanger’s mechanical and temperature terminal operational conditions. The P and R ratios must be calculated as represented

88

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-32K 1-in. tube distribution in 1.25-in. square patttern, two-pass configuration. Rear head type S.

in the diagrams, otherwise the factor read will have no meaning. A true counterflow or parallel flow exchanger does not require any correction to the LMTD. The equations used to calculate F are based on the following assumptions: l

l l l

l l l

The overall heat transfer coefficient, U, is constant throughout the heat exchanger. The rate of flow of each fluid is constant. The specific heat of each fluid is constant. There is no condensation of vapor or boiling of liquid in that part of the exchanger considered. Heat losses are negligible. There is equal heat transfer surface in each pass. The temperature of the shell-side fluid in any shell-side pass is uniform over any cross-section. P ¼

t2  t1 T1  t1

R ¼

(15-33)

For an exchanger with N shell passes, Bowman et al. [8] developed a general solution for the correction factor. pffiffiffiffiffiffiffiffi!  R2 þ1 ð1Px Þ ln ð1RPx Þ R1 F ¼

pffiffiffiffiffiffiffiffi) 2 þ1 pRffiffiffiffiffiffiffiffi

( ln

(15-34)

ð2=Px Þ1Rþ ð2=Px Þ1R

where: P ¼

(15-32)

T1  T2 t2  t1

1 R

h

R2 þ1

i1=N

RP1 P1

h

i1=N

RP1 P1

(15-35)

Heat Transfer Chapter | 15

89

FIGURE 15-32L 1-in. tube distribution in 1.25-in. square patttern, four-pass configuration. Rear head type S.

N is the total number of shell passes, that is the product of shell passes per shell and the number of units in series. Solving for N by repetitive trial and error with a minimum desired F, the minimum required number of shell passes can be determined. If R ¼ 1, Equation (15-35) becomes indeterminate, which reduces to: P Px ¼ ðN  NP þ PÞ

(15-36)

Equation (15-34) then becomes: pffiffiffiffiffiffiffiffi Px

(

F ¼ ln

R2 þ1 1Px

ð2=Px Þ1Rþ ð2=Px Þ1R

pffiffiffiffiffiffiffiffi) 2 þ1 pRffiffiffiffiffiffiffiffi

(15-37)

R2 þ1

The corrected mean temperature difference (CMTD) becomes: CMTD ¼ ðFÞðLMTDÞ

(15-38)

90

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-32M 1-in. tube distribution in 1.25-in. square patttern, two-pass configuration. Rear head type U.

where: F ¼ correction factor DTLMTD ¼ log mean temperature difference,
F, (
C) N ¼ number of series exchanger shells required. T1 ¼ hot fluid inlet temperature,
F, (
C) T2 ¼ hot fluid outlet temperature,
F, (
C) t1 ¼ cold fluid inlet temperature,
F, (
C) t2 ¼ cold fluid outlet temperature,
F, (
C)

Correction for Multipass Flow Through Heat Exchangers In most multipass exchangers, a combination of counter current and co-current flow exists as the fluid flows through alternate passes (see Figure 15-35). The mean temperature is less than the logarithmic mean calculated for counter current flow, and greater than that based on cocurrent flow.

The corrected calculated:

mean

temperature

ðCMTDÞ ¼ ðLMTDÞcalc ðFÞ

difference

is

(15-39)

F ¼ Correction factor to LMTD for counter current flow for various mechanical pass configurations, see Figures 1541AeL. Use (CMTD) in determining exchanger area requirements. Ao ¼

Q ¼ ðQ=UDTm Þ UðCMTDÞ

(15-40)

Ao ¼ Required effective outside heat transfer surface area based on net exposed tube area. Note: Later in text Ao ¼ A. D Tm ¼ Corrected mean temperature difference. U ¼ Overall heat transfer (fouled) coefficient, Equations 15-161 or 161A.

Heat Transfer Chapter | 15

91

FIGURE 15-32N 1-in. tube distribution in 1.25-in. square patttern, four-pass configuration. Rear head type U.

To determine the true overall temperature difference, the correction factors, F, shown in Figure 15-41 are used to correct for the deviations involved in the construction of multi-passes on the shell and tube-sides of the exchanger. Note that R of the charts represents the heat capacity rate ratio [107], and P is the temperature efficiency of the exchanger. MTDcor ¼ DTc ¼ ðFÞðLMTDÞ

(15-41)

where: DTLMTD¼ defined by Equation 15-29 F ¼ Correction factor as defined by the charts of Figure 15-41

Equation 15-40 allows the heat transfer in any heat exchanger to be determined, if the value of F is known. Figures 15-44A and B show F against P1 and different heat capacity rates R1 with the number of transfer units (NTU) represented by dashed lines for parallel flow and pure cross-flow heat exchangers. As illustrated in these figures, the curves fall off very rapidly for F below 0.75, which indicates a considerable sensitivity with respect to the temperature efficiency, P. Although the steepness varies with the heat capacity rates ratio R, a generally accepted rule is to take F > 0.75 so that the effectiveness does not become too sensitive to the F values [299]. Computer programs (PROG151 and PROG15A) have been developed

92

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-33A U-tube bundle.

to determine the value of F for known inlet and outlet temperatures of the fluids in both the shell and tube-sides of the heat exchanger. A default value of 1 is provided for the number of shells, and the program then calculates the

dimensionless parameters, P and R, the number of tube passes and the required number of shells as well as the corrected value of F. Calculations are shown in the examples later in the text. Note: F ¼ 1.0 for pure counter current flow. As cocurrent flow increases in design arrangement (not flow rate), the F is reduced, and the exchanger efficiency falls, to a usual practical lower limit of 0.750.80 [131]. Ratnam and Patwardhan [134] present graphs to aid in analyzing multipass exchangers, based on equations developed. Turton, et al. [135] also present performance and design charts based on TEMA charts (Figure 15-41J) and combining these with Temperature Efficiency Charts [107] from TEMA (Figures 15-42AeC). MTD (c) ¼ DTc ¼ corrected LMTD for specific exchanger design/style

FIGURE 15-33B Effective tube length correlations for calculating outside surface areas of U-tube bundles (two or four passes). (Used by permission: D. L. Whitley and E. E. Ludwig, Chemical Engineering. V. 67, No. 6 © 1960. McGraw-Hill, Inc. All rights reserved.)

Heat Transfer Chapter | 15

TABLE 15-18 Heat Exchange Operations Equipment Designation

Process Operation

Condenser

(a) Condenses all vapors (pure or mixed) entering. (b) Condenses all condensable vapor, cools the gases e 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 (a) Forced Circulation (b) Natural Circulation or Thermosyphon

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 “Thermosyphon Reboiler.”

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 it’s 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 (b) Heat 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.

EXAMPLE 15-4 Performance Examination for Exit Temperature of Fluids

In this example, we use the method of Turton [135], which incorporates combined working charts not included in this text. A 1-2 (one shell, two tube passes) shell and tube exchanger is described as follows: For shell-side: W ¼ 65,000 lb/h Cps ¼ 0.58 Btu/lb (
F) T1 ¼ 210
F For tube-side: w ¼ 155,000 lb/h Cpt ¼ 0.55 Btu/lb (
F) t1 ¼ 135
F; t2 ¼ 168
F

Estimate the exchanger performance if the hot fluid (shell-side) is to be increased 35% greater than the original design: A ¼ 187 ft2. Note that the method does not specifically incorporate fouling, but it should be acknowledged. Determine the outlet temperature when U is established. 1. On the shell-side: W ¼ 1.35 (65,000) ¼ 87,750 lb/h; the Cps and T1 are kept the same. 2. On the tube-side: w, Cpt, t1, U and A remain the same. 3. Now calculate the ratio of the heat capacities of tubeside to shell-side fluid, R as: R ¼

wCpt T1  T2 ¼ t 2  t1 WCps

¼ ð155; 000Þð0:55Þ=ð87; 750Þð0:58Þ ¼ 1:675

93

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-34 Tube wall conditions affecting overall heat transfer and associated temperature profile.

FIGURE 15-36 Temperature paths in heat exchangers.

6. Now using Figure 15-41A, at P ¼ 0.25 and R ¼ 1.675, read F ¼ 0.954. 7. Using P and R to find exit temperatures: t2 ¼ PðT1  t1 Þ þ t1 ¼ 0:25ð210  133Þ þ 133 ¼ 152
F T2 ¼ T1  Rðt2  t1 Þ ¼ 210  1:675 ð152  133Þ ¼ 178
F

FIGURE 15-35 Three flow patterns for examiningT and LMTD. Note: T1 shell-side fluid inlet, and t1 tube-side fluid inlet.

4. UA/(wc) ¼ (170) (187) / (155,000) (0.55) ¼ 0.37, see Figure 15-42. 5. Using Figure 15-42, at UA/wc ¼ 0.37 and R ¼ 1.675, read P ¼ 0.25.

This rating concept incorporating the TEMA charts can be used to: (1) determine the heat transfer area, ft2 required for an exchanger; and (2) determine flow rate and outlet temperature of the fluids of the (shell or tube-side) [135]. where: A ¼ Heat exchanger surface area, ft2 (m2). Cpt ¼ Specific heat capacity (tube or cold side), Btu/(lb) (
F) [kJ/kg.
C] Cps ¼ Specific heat capacity (shell or hot side), Btu/(lb) (
F) [kJ/kg.
C] F ¼ MTD correction factor, Figure 15-41 F ¼ Heat exchanger efficiency, dimensionless

Heat Transfer Chapter | 15

FIGURE 15-37 Fluid flows through two passes in tubes: part of flow is parallel to shell-side fluid, and part is counterflow.

w ¼ Mass flow rate (tube or cold side), lb/h [kg/h] W ¼ Mass flow rate (shell or hot side), lb/h [kg/h] P ¼ Temperature efficiency factor, (t2  t1) / (T1  t1), Figure 15-41 (Equation 15-32) q ¼ Rate of heat transfer, Btu/h [W] R ¼ Ratio of the heat capacities of tube-side to shell-side fluid/heat capacity rate ratio, Dimensionless 2Þ ¼ ðTðt12 T ; Figure 15  41ðEquation 15-33Þ: t1 Þ t ¼ Temperature of tube-side fluid,
F [
C] T ¼ Temperature of shell-side fluid,
F [
C] D TLMTD ¼ Log mean temperature difference for counter current flow,
F [
C] U ¼ Overall heat transfer coefficient in exchanger, Btu/(ft2) (h) (
F) [W/m2.
C] Subscripts: 1 ¼ Inlet 2 ¼ Outlet Weighted MTD applies to the more complicated shell and tube heat exchangers. Gulley [59] discusses several important cases in which the conventional LMTD for fluid temperature change and the corresponding MTD correction factors (Figure 15-41AeJ) do not adequately represent the design requirements (see Figure 15-45). From the sample listing that follows, recognize that the heat release for each section of an exchanger is necessary to properly analyze the condition. It can be misleading if the end point conditions previously cited are used to describe some of the special cases. It is necessary to break the heat transfer calculations into zones and calculate the weighted MTD. Typical services requiring the use of weighted MTD’s are [59,70]. 1. Overhead condensers with steam and hydrocarbon condensing. 2. Exchangers with change of phase. 3. Amine overhead condensers. 4. Pure component condensers with subcooling. 5. Condensers with large desuperheating zones such as for refrigerants, chemicals and steam. 6. Pure component vaporizing with superheating. 7. Vertical reboilers in vacuum service. 8. Desuperheating-condensing-subcooling. 9. Condensing in presence of non-condensable gases.

EXAMPLE 15-5 Calculation of Weighted MTD [59]

A gas is to be cooled from 190
F to 105
F with partial condensation taking place. The dew points is 120
F. The cooling water enters at 90
F and leaves at 110
F. Figure 15-45 illustrates the basic exchanger functions. 1. The heat load is FIGURE 15-38 Typical temperature situations that contain cross-over points, preventing exchanger operation. (Adapted and used by permission: Brown and Root, Inc.)

Q (desuperheat) Q (condensation)

¼ 420,000 Btu/h ¼ 1,260,000 Btu/h 1,680,000 Btu/h

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

T2

t t1

t +dt T

t2

T + dT

T1 T1 Temperature t2 T2

t1 Length of the heat exchanger x x +dx FIGURE 15-39 Temperature profiles in a counter current shell and tube heat exchanger

2. The cooling water temperature rise in each zone is


Desuperheating: DT; F ¼ ð110  90Þð420; 000Þ=1; 680; 000 ¼ 5
F

For shells in series, it is necessary to develop a weighted MTD correction factor, and a graphical technique is presented by Gulley [59].

Condensation: DT;
F ¼ ð110  90Þð1; 260; 000Þ=1; 680; 000 ¼ 15
F 3. For desuperheating, the DTLMTD is 190 / 105 110 ) 90 80 15 Reading Figure 15-40: DTLMTD¼ 38.8
F 4. For condensation, the DTLMTD is 120 / 105 105 ) 90 15 15

EXAMPLE 15-6 Calculation of LMTD and Correction

An oil cooler is to operate with an inlet temperature of 138
F and an outlet temperature of 103
F, and the cooling water enters at 88
F and is to be allowed to rise to 98
F. What is the corrected MTD for this unit, if it is considered as (a) a concentric pipe, counter flow unit, (b) a single-pass shell-two-pass tube unit and (c) a parallel flow unit? 1. (a) Counterflow T1 ¼ 138
F / 103
F ¼ T2 t2 ¼ 98
F ) 88
F ¼ t1 Dt2 ¼ 40
F Dt1 ¼ 15
F

DTLMTD¼ 15
F 5. The weighted LMTD for calculations is: Wt: LMTD ¼ 

¼ 

Qtotal Qdes Qcond þ ðLMTDÞdes ðLMTDÞcond

1; 680; 000 ¼ 17:7
F 420; 000 1; 260; 000 þ 38:8 15

DTLMTD ¼

ð40  15Þ  ¼ 25:5
F ln 40 15

(Calculate or read from Figure 15-41) (b) Shell and tube 1-2 (1 pass shell-2 pass tubes) T1 ¼138
F / 103
F ¼ T2 t2 ¼ 98
F ) 88
F ¼ t1 Dt2 ¼ 40
F Dt1 ¼ 15
F

Heat Transfer Chapter | 15

FIGURE 15-40 Mean temperature difference chart. (Used by permission: The Griscom-Russell/Ecolaire Corporation.)

DTLMTD ¼

ð40  15Þ


 ¼ 25:5 F ln 40 15

(c) Parallel flow T1 ¼138
F / 103
F ¼ T2 t1 ¼ 88
F / 98
F ¼ t2 Dt2 ¼ 50
F Dt1 ¼ 5
F DTLMTD ¼

ð50  5Þ


 ¼ 19:5 F In 50 5

t2  t1 T1  t1

98  88 10 ¼ ¼ 0:2 138  88 50 138  103 35 ¼ ¼ 3:5 R ¼ 98  88 10 P ¼

2. Corrections to DTLMTD (See Figure 15-41.) P ¼

(a) Counterflow No correction factor, F ¼ 1.0 corrected DTLMTD¼ 25.5
F (b) Shell and tube, 1-2 (This is part parallel, part counterflow.)

R ¼

T1  T2 t 2  t1

F read from Figure 15-41A ¼ 0.905 Corrected LMTD ¼ (0.905) (25.5) ¼ 23.1
F (c) Parallel flow Correction factor does not apply, DTLMTD ¼ 19:5
F

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-41A MTD correction factor, 1 shell pass, even number of tube passes. (Figures 15-34Ae15-34J used by permission: Standards of Tubular Exchanger Manufacturers Association, 7th Ed., Figure T-32, ©1988. Tubular Exchanger Manufacturers Association, Inc.)

3. For an exchanger design, the unit requiring the smallest area will be the counter flow having the largest corrected DTLMTD¼ 25.5
F for this example. Table 15-19 shows the computed results, with a calculated corrected mean temperature difference of 22.9
F. This gives a percentage deviation of 0.87% from the result of Figure 15-41A. Correction factors should seldom be used when they fall below a value that lies on a curved portion of the P-R curves, Figure 15-41. In other words, values on the straight portions of the curves have little or no accuracy in most cases. For the “single shell pass-two or more than two passes” unit chart, an F of less than about 0.8 would indicate consideration of a two shell pass unit. As a general guide, F factors less than 0.75 are not used. To raise the F factor, the unit flow system, temperature levels or both must be changed.

available at 25
C with a specific heat of 4.18 kJ/kg.
C. Calculate the DTLMTD using: a. A counter current heat exchanger b. A co-current flow heat exchanger. Solution The heat exchanged between the shell and tube-sides from the heat balance is:

Q = WhCps(T1–t2) = wcCpt (t2–t1) Q = WhCps(T1–t2) = 20 x 1960 x (110-50) kJ/s The cold water outlet temperature is: t2 ¼ t1 þ

EXAMPLE 15-7 Calculate the LMTD

It is desired to cool 20 kg/s of oil having a heat capacity of 1960 kJ/kg.
C from an inlet temperature of 110
C to 50
C. The operation will be performed using 60 kg/s of cold water

Q 2:35  106 ¼ 34:37o C ¼ 25 þ ð60  4:18  103 Þ wc Cpt

This value is independent on the heat exchanger configuration. For a counter current heat exchanger: DTLMTD ¼

ðT1  t2 Þ  ðT2  t1 Þ  2 ln TT12 t t1

(15-28)

Heat Transfer Chapter | 15

FIGURE 15-41B MTD correction factor, 2 shell passes, 4 or a multiple of 4 tube passes.

FIGURE 15-41C MTD correction factor, 3 shell passes, 6 or more even number of tube passes.

99

FIGURE 15-41D MTD correction factor, 4 shell passes, 8 or a multiple of 8 tube passes.

FIGURE 15-41E MTD correction factor, 5 shell passes, 10 or more even number of tube passes.

MTD correction factor, 6 shell passes, 12 or more even number of tube passes.

Heat Transfer Chapter | 15

FIGURE 15-41F

101

102 Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-41G MTD correction factor, 1 shell pass, 3 tube passes (2 counter and 1 co-current).

Heat Transfer Chapter | 15

FIGURE 15-41H MTD correction factor, crossflow shell, 1 tube pass.

103

104 Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-41I

MTD correction factor, 1 divided flow shell pass, even number of tube passes.

Heat Transfer Chapter | 15

FIGURE 15-41J MTD correction factor, split flow shell, 2 tube passes.

105

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-42A Temperature efficiency for counterflow exchangers. (Used by permission: Standards of Tubular Exchanger Manufacturers Association, 7th Ed., Figure Te3.3, ©1988. Tubular Exchanger Manufacturers Association, Inc. All rights reserved.)

Heat Transfer Chapter | 15

107

FIGURE 15-42B Temperature efficiency, 1 shell pass, even number of tube passes. (Used by permission: Standards of Tubular Exchanger Manufacturers Association, 7th Ed., Figure Te3.3A, ©1988. Tubular Exchanger Manufacturers Association, Inc. All rights reserved.)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-42C Temperature efficiency, 2 shell passes, 4 or a multiple of 4 tube passes. (Used by permission: Standards of Tubular Exchanger Manufacturers Association, 7th Ed., Figure Te3.3B, ©1988. Tubular Exchanger Manufacturers Association, Inc. All rights reserved.)

Heat Transfer Chapter | 15

109

will be required. The ratio of the required areas for both cases is: Apc ðDTLMTD Þcc 45:74 ¼ 1:17 ¼ ¼ Acc ðDTLMTD Þpc 40:96

T2 T3

ΔT1 t1

ΔT2

T4

t2

ΔT3 t4

t3 Q1 or A1

Q2 or A2

Q3 or A3

Total Heat Transfer, Btu

FIGURE 15-43 Breakdown of heat transfer zones in an exchanger.

counter current flow heat exchanger.

DTLMTD ¼

ðT1  t2 Þ  ðT2  t1 Þ ð75:63  25Þ   ¼ 2 ln TT12 t ln 75:63 25 t1

¼ 45:74o C

co-current heat exchanger. The log mean temperature difference is: DTLMTD ¼

DTLMTD ¼

ðT1  t1 Þ  ðT2  t2 Þ  1 ln TT12 t t2

(15-29)

TEMPERATURE FOR FLUID PROPERTIES EVALUATION e CALORIC TEMPERATURE For most exchanger conditions, the arithmetic mean temperatures of the shell-side and tube-side, respectively, are satisfactory to evaluate the properties of the fluids, which in turn can be used to determine the overall heat transfer coefficient, U. This means that the DTLMTD as determined is correct. When it is determined that the overall heat transfer coefficient U or fluid properties vary markedly from the inlet to the exit conditions of the unit, the arith-

metic mean is no longer satisfactory for fluid property evaluation. For this case, the proper temperature of each stream is termed the caloric temperature for each fluid. The F fraction is the smallest of the values calculated and applied to both streams. Although the caloric temperature applies to counter current and parallel flow only, it can be used with reasonable accuracy for multipass flow [107].

The caloric value of hot fluid (from Kern [70], by permission): th ¼ th2 þ Fe ðth1  th2 Þ The caloric value of the cold fluid: tc ¼ tc1 þ Fc ðtc2  tc1 Þ

ðT1  t1 Þ  ðT2  t2 Þ ð85  15:63Þ   ¼ 85 1 ln TT12 t ln 15:63 t2

Fc ¼

o

¼ 40:96 C We see that DTLMTD for counter current configuration is higher than in concurrent configuration. This means that if a co-current heat exchanger is used, a larger heat transfer area

(15-42)

tc  t1 t2  t1

or

Fc ¼

th  th1 th2  th1

where: th ¼ caloric value or hot fluid,
F th1 ¼ inlet hot fluid temperature,
F

(15-43) (15-44)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-44 a) LMTD correction factor for parallel flow heat exchanger b) LMTD correction factor for pure cross-flow heat exchanger

th2 ¼ outlet hot fluid temperature,
F tc ¼ caloric value of cold fluid,
F tc1 ¼ inlet cold fluid temperature,
F tc2 ¼ outlet cold fluid temperature,
F Fc ¼ correction factor, F, (see Reference [70] for details),

Figure 15-46. The insert allows for more rapid calculation for petroleum fractions. For heat exchangers in true counter current (fluids flowing in opposite directions or outside a tube) or true cocurrent (fluids flowing inside and outside of a tube, parallel to each other in direction) conditions, with essentially

Heat Transfer Chapter | 15

190

T1

180 170 TEMPERATURE °F

160 150 140 130

DEWPOINT 120°F.

120 110

t2 T2 (105°F)

100 105°F (110 – 5)

90 80

0

t1 (90°F)

0.5 1.0 1.5 HEAT LOAD, BTU/HR. (MM)

2.0

FIGURE 15-45 Finding a counterflow weighted MTD. (Reprinted with permission: Gulley, Dale E., Heat Exchanger Design Handbook, © 1968 by Gulf Publishing Company, Houston, Texas. All rights reserved.)

TABLE 15-19 Input Data and Computer Results for Example 15-6 DATA151.DAT 138.0

103.0

88.0

98.0

111

constant heat capacities of the respective fluids and constant heat transfer coefficients, the long mean temperature difference may be appropriately applied (see Figure 15-40 [107]). For a variation in heat transfer coefficient from one end of the exchanger to the other where the average fluid temperature is considered approximately linear, the physical properties of the fluids can be approximated by evaluating them using Figure 15-46. To use this figure, the temperature change of each fluid multiplied by the F factor from the chart is added to its respective cold terminal temperature to obtain the average temperature. The Dtc and D th from the figure represent the cold and hot terminal temperature differences, and C of the chart represents the fractional change in heat transfer coefficient as a parameter of the chart. For hydrocarbon fluids, C may be simplified using the insert in Figure 15-46 [107]. Other, less frequently used, exchanger arrangements are discussed by Gulley [129]. Note that the F factor for Figure 15-46 is not the same F factor as given in Figures 15-41AeJ. The C ratio (disregard sign if negative) is evaluated from the estimated overall coefficients based on the temperatures at the cold and hot ends, respectively. For Figure 15-46, the hot terminal difference is th ¼ th1  tc2; the cold terminal temperature difference is tc ¼ th2  tc1.

Tube Wall Temperature Refer to Figure 15-34. The temperature of the outside of the tube wall is based on the hot fluid being on the outside of the tubes:

1

tw ¼ th 

hio ðth  tc Þ hio þ ho

(15-45)

t w ¼ tc þ

ho ðth  tc Þ hio þ ho

(15-46)

or:

Computer Results THE CORRECTED LMTD IN A SHELL AND TUBE HEAT EXCHANGER HOT FLUID INLET TEMPERATURE,
F:


138.000

HOT FLUID OUTLET TEMPERATURE, F:

103.000

COLD FLUID INLET TEMPERATURE,
F:

88.000

COLD FLUID OUTLET TEMPERATURE,
F:

98.000

NUMBER OF SERIES EXCHANGER SHELLS:

1.

THE PARAMETER P VALUE IS:

0.2000

THE PARAMETER R VALUE IS:

3.5000

THE NUMBER OF SHELLS REQUIRED:

1.

THE F-FACTOR:

0.8970

THE LOG MEAN TEMPERATURE DIFFERENCE,
F:

25.4886

THE CORRECTED LMTD,
F:

22.8629

where: hio ¼ inside film coefficient referred to outside of tube, Btu/h (ft2) (
F) ho ¼ outside film coefficient referred to outside of tube, Btu/h (ft2) (
F) tw ¼ temperature of outside wall of tube,
F The outside tube wall temperature for hot fluid on the inside of the tube is: t w ¼ tc þ

hio ðth  tc Þ hio þ ho

(15-47)

tw ¼ th þ

ho ðth  tc Þ hio þ ho

(15-48)

or:

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-46 Caloric or true average fluid temperature. (Used by permission: Standards of Tubular Exchanger Manufacturers Association, ©1959 and 1968. Tubular Exchanger Manufacturers Association, Inc. All rights reserved.)

An alternativee and possibly less accurate calculation (but not requiring the calculation of caloric temperature) using reasonably assumed or calculated film coefficients and bulk rather than caloric temperature is as follows: For hot fluid on the shell-side:  ho ðth  tc Þ (15-49) tw ¼ tc þ hi þ ho tw ¼ the outside surface temperature of the wall For hot fluid on the tube-side:  h1 ðth  tc Þ tw ¼ tc þ hi þ ho

(15-50)

where: tw ¼ tube wall temperature, neglecting fouling and metal wall drop,
F tc ¼ cold fluid bulk temperature,
F th ¼ hot fluid bulk temperature,
F Often this may be assumed based upon the temperature of the fluids flowing on each side of the tube wall. For a more accurate estimate, and one that requires a trial and

error solution, neglecting the drop-through tube metal wall (usually small): tw ¼

hi t i þ ho t o hi þ ho

(15-51)

where: ti ¼ bulk temperature of fluid inside tube to ¼ bulk temperature of fluid outside tube hi ¼ heat transfer film coefficient for fluid inside tube ho ¼ heat transfer film coefficient of fluid outside tube To determine a reasonably good value for tw, either tw must be estimated and used to calculate hi and ho, or hi and ho must be assumed and a tw calculated. In either case, if the calculated values are not reasonably close to the assumed values, the new calculated results should be used to recalculate better values. Film temperatures are generally taken as the arithmetic average of the tube wall, tw, and the bulk temperature, ti or to. This approach neglects the effect of tube wall fouling (i.e. it is applicable for clean tube conditions). Corrections can be made to account for the fouling if this is considered necessary.

Heat Transfer Chapter | 15

Usually this fouling is accounted for in the overall heat transfer coefficient U. The temperature for calculating film properties is as follows: For stream line: tf ¼ tav þ 1=4ðtw  tav Þ

(15-52)

For turbulent flow: tf ¼ tav þ 1=2ðtw  tav Þ

(15-53)

Ganapathy [161] presents a shortcut technique for estimating heat exchanger tube wall temperature, which so often is needed in establishing the fluid film temperature at the tube wall: tw ¼ ðhi ti þ ho to Þ=hi þ ho Þ

(15-54)

where: hi ¼ inside tube heat transfer film coefficient, Btu/(h) (ft2) (
F) ho ¼ outside tube heat transfer film coefficient, Btu/(h) (ft2) (
F) ti ¼ temperature of inside fluid entering tubes,
F to ¼ temperature of outside fluid on tubes
F For example, a hot flue gas flows outside a tube and shell exchanger at 900
F (to) while a hot liquid is flowing into the tubes at 325
F (ti). The heat transfer film coefficients have been estimated to be hi ¼ 225 Btu/(h) (ft2) (
F) and ho ¼ 16 Btu/(h) (ft2) (
F) respectively. Estimate the tube wall temperature using hi as hio corrected to the outside surface for the inside coefficient. tw ¼ ½ð225Þð325Þ þ ð16Þð900Þ=ð225 þ 16Þ ¼ 363
F This calculation neglects the temperature drop across the metal tube wall and considers the entire tube to be at the temperature of the outside surface of the wall, tw. Kern [70] for the same equation suggests using the caloric temperature for ti and to. Edmister and Marchello [165] present a tube wall temperature equation: t2 ¼

Di hi ti þ Do ho t4
;F D i hi þ D o ho

(15-55)

This relationship can be used for estimating surface temperature and back-checking estimation assumptions. For many situations involving liquids and their tube walls, the temperature difference (t2  t3) across the wall is small and equals t2  t3 for practical purposes. Example 15-8. Heating Glycerin in a Multipass Heat Exchanger

A multipass heat exchanger is used to heat glycerin from 20
C to 50
C by hot water, which enters the thin-walled 20 mm diameter tubes at 80
C and leaves at 40
C (Figure 15-47). The total length of the tubes in the heat exchanger is 80 m. The convection heat transfer coefficient is 25 W/m2.
C on the glycerin (shell) side and 160 W/m2.
C on the water (tube) side. Determine the rate of heat transfer in the heat exchanger: (a) before any fouling and (b) after fouling with a fouling factor of 0.0006 m2.
C/W occurring on the outer surfaces of the tubes. Solution Glycerin is heated in a multipass heat exchanger by hot water. The rate of heat transfer for the cases of fouling and no fouling are determined as follows: Assumptions: The following assumptions are made: 1. Steady state operating conditions exist. 2. Changes in kinetic and potential energies of fluid streams are negligible. 3. Heat transfer coefficients and fouling factors are constant and uniform. 4. The thermal resistance of the inner tube is negligible since the tube is thin-walled and highly conductive. 5. The heat exchanger is well insulated so that heat loss to the surroundings is negligible. Since the tubes are thin-walled, then it can be assumed that the inner and outer surface area of the tubes to be equal; the heat transfer surface area is: As ¼ pDo L ¼ pð0:02 mÞð80 mÞ ¼ 5:03 m2 Cold glycerin

20oC

40oC

where t1 ¼ fluid No. 1 mean fluid temperature,
F t4 ¼ fluid No. 2 mean fluid temperature,
F t2 ¼ fluid No. 1 fluid film tube wall temperature,
F t3 ¼ fluid No. 3 fluid film tube wall temperature,
F Do ¼ tube outside diameter, in. Di ¼ tube inside diameter, in hi ¼ inside tube heat transfer film (surface) coefficient, Btu/(h) (ft2) (
F) ho ¼ outside tube heat transfer film (surface) coefficient, Btu/(h) (ft2) (
F)

113

Hot water

80oC

50oC

FIGURE 15-47 Schematic for Example 15.8.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

The rate of heat transfer in this heat exchanger is: Q ¼ UAs FDTLMTD where F is the correction factor and DTLMTD is the log mean temperature difference for the counter current flow arrangement. The counter current flow DTLMTD is: DTLMTD ¼

ðT1  t2 Þ  ðT2  t1 Þ ð80  50Þ  ð40  20Þ 

 ¼ T1 t2 ln T2 t1 ln 30 20

¼ 24:7o C (15-28) A computer program PROG15A has been developed to determine the corrected LMTD and the required number of shells for given hot and cold stream inlet and outlet temperatures. The results indicate that the corrected factor F ¼ 0.9113, and the corrected mean temperature difference is 22.48
C. The results show that the exchanger is classified as 2e4, i.e. having two shell passes and four tube passes. Table 15-20 shows the input data and results of the program for Example 15-8. CMTD ¼ FðLMTDÞ ¼ ð0:9113Þð24:663Þ ¼ 22:48
C (a) For no fouling, the overall heat transfer coefficient U is: 1 ¼ 1 1 ¼ þ hi ho

1 W ¼ 21:6 2 o 1 1 C m þ 160 W=m2 C 25 W=m2 C

TABLE 15.20 DATA15S.DAT 80.0

40.0

20.0

50.0

1 THE CORRECTED LMTD IN A SHELL AND TUBE HEAT EXCHANGER HOT FLUID INLET TEMPERATURE,
C:


80.000

HOT FLUID OUTLET TEMPERATURE, C:

40.000

COLD FLUID INLET TEMPERATURE,
C:

20.000

COLD FLUID OUTLET TEMPERATURE,
C:

50.000

NUMBER OF SERIES EXCHANGER SHELLS:

1.

THE PARAMETER P VALUE IS:

0.5000

THE PARAMETER R VALUE IS:

1.3333

THE NUMBER OF SHELLS REQUIRED:

2.

THE F-LMTD CORRECTION FACTOR:

0.9113

THE LOG MEAN TEMPERATURE DIFFERENCE,
C:

24.6630

THE CORRECTED LMTD,
C:

22.4766

Then the rate of heat transfer is: ⎧ W ⎫ Q = UAs CMTD = (21.6) (5.03) (22.48) ⎨ 2 o ⋅ m 2 ⋅ o C ⎬ ⎩m . C ⎭ = 2442.4W

(b) When there is fouling on one of the surface, the overall heat transfer coefficient U is: ¼

1 hi

1 ¼ þ h1o þ Rf

1 1 160W=m2 C

¼ 21:3

þ

1 25W=m2 C

 2 o þ 0:0006 m W: C

W m2 o C

Then the rate of heat transfer is: ⎧ W ⎫ Q = UAs CMTD = (21.6) (5.03) (22.48) ⎨ 2 o ⋅ m 2 ⋅ o C ⎬ ⎩m . C ⎭ = 2442.4W

The results show that the rate of heat transfer decreases because of fouling e as expected. The decrease is not dramatic, however, because of the relatively low convection heat transfer coefficients involved.

The Effectiveness-NTU Method The log mean temperature difference (DTLMTD) method discussed earlier is employed in heat exchanger analysis when the inlet and outlet temperatures of the hot and cold fluids are known or can be determined from an energy balance. Once DTLMTD, the mass flow rates and the overall heat transfer coefficient are available, the heat transfer surface area of the heat exchanger can be determined from Q ¼ UAs FDTLMTD

(15-56)

Therefore, the DtLMTD method is very suitable for determining the size of a heat exchanger to realize prescribed outlet temperature when the mass flow rates and the inlet and outlet temperatures of the hot and cold fluids are known. With the DTLMTD method, the task is to select a heat exchanger that will meet the prescribed heat transfer requirements. The procedure for the selection process is: 1. Select the type of heat exchanger suitable for the application. 2. Determine any unknown inlet or outlet temperature and the heat transfer rate using an energy balance. 3. Calculate the DTLMTD and the correction F factor. 4. Obtain (select or calculate) the value of the overall heat transfer coefficient U. 5. Calculate the heat transfer surface area, As. The procedure is completed by selecting a heat exchanger that has a heat transfer surface area equal to or larger than As.

Heat Transfer Chapter | 15

The other type of problem encountered in heat exchanger analysis is the determination of the heat transfer rate and the outlet temperatures of the hot and cold fluids for known fluid mass flow rates and inlet temperatures when the type and size of exchanger are specified. The heat transfer surface area of the heat exchanger is specified, but the outlet temperatures are not known. The task is to determine the heat transfer performance of a specified heat exchanger, or to determine if a heat exchanger available is suitable for the job. The DTLMTD method can still be applied for this alternative problem, but it is tedious and iterative, making it impractical. The effectiveness-NTU method is applied, and is based on a dimensionless parameter referred to as the heat transfer effectiveness, ε, defined as: ε ¼

Actual heat transfer rate Q_ ¼ Maximum possible heat transfer rate Q_ max (15-57)

The actual heat transfer rate in a heat exchanger can be determined from an energy balance on the hot or cold fluids, and can be expressed as: Q_ ¼ CPh ðT1  T2 Þ ¼ CPc ðt2  t1 Þ

(15-58)

where: CPh ¼ WhCph and CPc ¼ wcCpc are the heat capacity rates of the hot and cold fluids respectively. To determine the maximum possible heat transfer rate in a heat exchanger, the maximum temperature difference in a heat exchanger is the difference between the inlet temperatures of the hot and cold fluids. That is, DTmax ¼ T1  t1

(15-59)

The heat transfer in a heat exchanger will reach its maximum value when: (1) The cold fluid is heated to the inlet temperature of the hot fluid; or (2) The hot fluid is cooled to the inlet temperature of the cold fluid. These two limiting conditions will not be reached simultaneously unless the heat capacity rates of the hot and cold fluids are identical (i.e. CPh ¼ CPc). When CPc sCPh , which is usually the case, the fluid with the smaller heat capacity flow rate will experience a larger temperature change, and therefore it will be the first to experience the maximum temperature, at which point the heat transfer will come to a halt. Therefore, the maximum possible heat transfer rate in a heat exchanger is: Q_ max ¼ CPmin ðT1  t1 Þ

(15-60)

115

where: CPmin is the smaller of CPh and CPc and thus, the actual heat transfer rate Q_ can be expressed by: Q_ ¼ εQ_ max ¼ εCPmin ðT1  t1 Þ

(15-61)

The effectiveness of a heat exchanger allows the evaluation of the heat transfer rate without knowing the outlet temperatures of the fluids. The effectiveness of a heat exchanger depends on the geometry of the heat exchangers as well as the flow arrangement. Thus, different heat exchanger types have different effectiveness relations. Effectiveness relations of the heat exchangers generally involve the dimensionless group UAs =CPmin . This quantity is called the number of transfer units NTU and is expressed as: NTU ¼

UA UAs  ¼  CPmin WCp min

(15-62)

where U is the overall heat transfer coefficient and As is the heat transfer surface area of the heat exchanger. The NTU is proportional to As. Therefore, for specified values of U and CPmin, the value of NTU is a measure of the heat transfer surface area, As. Thus, the larger the NTU, the larger the heat exchanger. In heat exchanger analysis, another dimensionless quantity called the capacity ratio is: c ¼

CPmin CP

(15-63)

The effectiveness of a heat exchanger is a function of the number of transfer units, NTU and the capacity ratio, c. as: ε ¼ fðUAs =CPmin ; CPmin =CPmax Þ ¼ fðNTU; cÞ (15-64) Effectiveness relations have been developed for a large number of heat exchangers, and the results are given in Table 15-21. The following observations from the effectiveness relations and charts are: 1. The value of the effectiveness ranges from 0 to 1. It increases rapidly with NTU for small values (up to wNTU ¼ 1.5) but rather slowly for larger values. Therefore, the use of a heat exchanger with a large NTU (usually larger than 3) and thus a large size cannot be justified economically. This is because a large increase in NTU corresponds to a small increase in effectiveness. Therefore, a heat exchanger type with a very high effectiveness may be desirable from a heat transfer point of view, but undesirable from an economical view point. 2. For a given NTU and capacity ratio, c ¼ CPmin/CPmax, the counter current flow heat exchanger has the highest

TABLE 15-21 Effectiveness relations for heat exchangers: NTU [ UAs =CPmin and c [ CPmin =CPmax [ ðWCp Þmin =ðWCp Þmax Heat exchanger type

Effectiveness relation

1. Double pipe Parallel-flow Counter-flow

ε ¼

1  exp½NTU ð1 þ cÞ 1 þc

ε ¼

1  exp½NTU ð1 þ cÞ 1  c exp½NTUð1  cÞ

(

2. Shell and tube: One-shell pass 2, 4, .. tube passes

ε ¼ 2

1 þ c þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ c2

0:22

ε ¼ 1  expfNTUc

)1

½exp ðc NTU0:78 Þ  1g

3. Cross-flow (single-pass) Both fluids unmixed Cmax mixed, Cmin unmixed Cmin mixed, Cmax unmixed

ε ¼

4. All heat exchangers with c ¼ 0

ε ¼ 1  expðNTUÞ

1 c

pffiffiffiffiffiffiffiffiffiffiffi 1 þ exp ½NTU pffiffiffiffiffiffiffiffiffiffi 1 þ c 2ffi  1  exp ½NTU 1 þ c 2 

ð1  expf1  c ½1  expðNTUÞgÞ

ε ¼ 1  exp f 

1 c

½1  exp ðc NTUÞg

(Source: W. M. Kays and A. L. London. Compact Heat Exchangers, 3rd. ed., McGraw-Hill, 1984).

effectiveness, followed closely by cross-flow heat exchangers with both fluids unmixed. The lowest effectiveness values are encountered in parallel flow heat exchangers. 3. The effectiveness of a heat exchanger is independent of the capacity ratio, c for NTU values of less than about 0.3. 4. The value of the capacity ratio, c ranges between 0 and 1. For a given NTU, the effectiveness becomes a maximum for c ¼ 0 and a minimum for c ¼ 1. The case c ¼ CPmin/CPmax/0 corresponds to CPmax/N, which is realized during a phase change process in a condenser or reboiler. All effectiveness relations in this case reduce to: ε ¼ εmax ¼ 1  expðNTUÞ

(15-65)

Regardless of the heat exchanger type, the temperature of the condensing or boiling fluid remains constant in this instance. The effectiveness is the lowest in the other limiting case of c ¼ CPmin/CPmax ¼1, which is realized when the heat capacity rates of the two fluids are equal. Once the dimensionless parameters are determined, c and NTU, the effectiveness ε can be determined from either the charts or the effectiveness relationship for the specified type of heat exchanger (Table 15-21). Then the actual rate of _ the outlet temperatures T2 and t2 can be heat transfer Q, determined from Equations 15-58 and 15-61 respectively. The analysis of heat exchangers with unknown outlet temperatures can be easily determined with the effectiveness-NTU method, but requires rather tedious iterations with the DtLMTD method. As discussed earlier, when all the inlet and outlet temperatures are known, the

heat exchanger size can be determined from the DtLMTD method. Alternatively, the NTU method can also be used by first evaluating the effectiveness ε from its definition and then the NTU from the appropriate NTU relations as shown in Table 15-21. Figures 15-48AeF show the ε-NTU charts for parallel, counter flow and some more commonly based configurations.

EXAMPLE 15-9 Heating Water in a Counter Current Flow Heat Exchanger

A counter current double-pipe heat exchanger, as shown in Figure 15-49, is to heat water from 30
C to 90
C at a rate of 1.5 kg/s. The heating is to be accomplished by geothermal water available at 170
C 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.
C, determine the length of the heat exchanger required to achieve the desired heating using the log mean temperature difference method, DtLMTD and the effectiveness-NTU methods. Take: The specific heat of water and geothermal fluid to be 4.18 and 4.31 kJ/kg.
C respectively. Solution Using the Log Mean Temperature Difference DTLMTD From the heat balance involving the tube-side and shellside of the exchanger, we have: Q ¼ Wh Cph ðT1  T2 Þ ¼ wc Cpc ðt2  t1 Þ 2:5  4:31ð170  T2 Þ ¼ 1:5  4:18  ð90  30Þ 170  T2 ¼ 376:2=10:775 T2 ¼ 135:1
C

Heat Transfer Chapter | 15

FIGURE 15-48AeF

Shows the ε e NTU charts for parallel, counter flow and some more commonly based configurations.

117

118

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Hot geothermal water 170oC 2.5 kg/s T1

Cold water t1

90oC

t2

30oC 1.5 kg/s D = 15mm T2

FIGURE 15-49 Schematic for Example 15-9.

The log mean temperature difference, DTLMTD: DTLMTD ¼

Dt2  Dt1  Dt2 ln Dt1

 ð90  30Þo C ¼ 376:2 kW

105:1  80 ¼  105:1 ln 80

Therefore, the effectiveness of the heat exchanger is:

¼ 91:97
C

ε ¼

The log mean temperature difference correction factor, F ¼ 0.9571 The corrected mean temperature difference ¼ 88.03
C The head load, Q ¼ UAs FDTLMTD 376200 ¼ 650  As  88:03 As ¼ 6:57 m2 The length of the tube is: As ¼ pD L 6:57 ¼ pð0:015ÞL L ¼ 140 m

Therefore, CPmin ¼ 6.27 kW/
C and the capacity ratio, c ¼ CPmin/CPmax ¼ 6.27/10.775 ¼ 0.582 The maximum heat transfer rate is determined from Equation 15-60: Q_ max ¼ CPmin ðT1  t1 Þ


¼ ð6:27 kW= CÞð170  30Þ C ¼ 877:8 kW

Actual heat transfer rate Q_ ¼ _ Maximum possible heat transfer rate Qmax ¼

376:2 kW ¼ 0:429 877:8 kW

Knowing the effectiveness, the NTU of this counter current flow heat exchanger can be determined from Table 15-21 as:  1 ε1 NTU ¼ ln ðc  1Þ cε  1  1 0:429  1 ¼ ¼ 0:653 ln ð0:582  1Þ 0:582  0:429  1 Then the heat transfer surface area becomes:

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 ¼ Wh Cph ¼ ð2:5 kg=sÞð4:31 kJ=kg:
CÞ ¼ 10:775 kW C 
CPc ¼ wc :Cpc ¼ ð1:5 kg=sÞð4:18 kJ=kg:
CÞ ¼ 6:27 kW C




That is, the maximum possible heat transfer rate in this heat exchanger is 877.8 kW. The actual rate of heat transfer is:   Q ¼ wc Cpc ðt2  t1 Þ cold water ¼ ð1:5 kg=sÞ ð4:18 kJ=kg:o CÞ

NTU ¼

UAs CPmin




As ¼

NTU$CPmin ð0:653Þð6270W= CÞ ¼ U 650 W=m2 :o C

¼ 6:30 m2 To provide this much heat transfer surface area, the length of the tube is: As ¼ pDL and L ¼

As 6:3m2 ¼ ¼ 134 m pD pð0:015 mÞ

EXAMPLE 15-10 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 200
C to heat water also flowing at 0.1 kg/s from 35.0
C to 95
C. Determine the

Heat Transfer Chapter | 15

product of heat transfer coefficient and area using LMTD method and ε-NTU Method. The specific heat of oil ¼ 2.1 kJ/kg.
C and water ¼ 4.18 kJ/kg.
C Solution From the heat balance:

119

 1 ε1 ln ðc  1Þ cε  1  1 0:72  1 ¼ ln ð0:5024  1Þ 0:5024  0:72  1

NTU ¼

¼ 1:655

Q ¼ Wh Cph ðT1  T2 Þ ¼ wc Cpc ðt2  t1 Þ ¼ 0:1  2:1  ð200  T2 Þ ¼ 0:1  4:18  ð95  35Þ ð200  T2 Þ ¼ 25:08=0:21 ¼ 119:43 T2 ¼ 80:53
C Q ¼ 25:08 kW

The number of transfer units, NTU can be expressed by: NTU ¼ 

UA  WCp min


The log mean temperature difference, DTLMTD is determined as follows:

UA ¼ 1:655  0:21 ¼ 0:347 kW= C

Percentage deviation % is: DTLMTD

ð105  45:57Þ ¼  105  ln 45:57

ð0:352  0:347Þ  100 0:347 ¼ 1:4%:

¼

¼ 71:2
C The product of heat transfer and area, UA is: UA ¼

Q 25:08 ¼ DTLMTD 71:2

EXAMPLE 15-11




¼ 0:352 kW= C Using the ε-NTU Method The heat capacity flow rates of the hot and cold fluids are:


CPh ¼ 0:1  2:1 ¼ 0:21 kW= C
CPc ¼ 0:1  4:18 ¼ 0:418 kW= C Therefore, the minimum heat capacity flow rate, CPmin ¼ 0.21 kW/
C. The maximum flow rate is: _ ¼ CPmin ðT1  t1 Þ ¼ 0:21  ð200  35Þ ¼ 34:65 kW Q max (15-60) Therefore, the effectiveness of the heat exchanger is: ε ¼

_ Q _ Q max

¼

Actual heat transfer rate Maximum possible heat transfer rate

¼

25:08 ¼ 0:72 34:65

and the capacity ratio, c ¼ CPmin/CPmax ¼ 0.21/0.418 ¼ 0.5024 The number of transfer units, NTU is:

In a one shell, two tube pass heat exchanger, water at 15
C 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 15 m2. The overall heat transfer coefficient is 200 W/m2
C. Determine the exit temperature of the two fluids, if oil enters at 150
C. Take Cp of oil ¼ 2.6 kJ/kg.
C and Cp of water ¼ 4.18 kJ/kg.
C. Solution From the heat balance: Q ¼ Wh Cph ðT1  T2 Þ ¼ wc Cpc ðt2  t1 Þ
CPh ¼ 2500:0  2:6=3600 ¼ 1:806 kW= C
CPc ¼ 5000:0  4:18=3600 ¼ 3:61 kW= C Therefore, the minimum heat capacity flow rate, CPmin ¼ 1.806 kW/
C. The maximum flow rate is: _ ¼ CPmin ðT1  t1 Þ ¼ 1:806  ð150  15Þ Q max ¼ 243:81kW The capacity ratio, c ¼ CPmin/CPmax ¼ 1.806/3.61 ¼ 0.5 Therefore, the effectiveness of the heat exchanger is:

120

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Q_ ε ¼ Q_

max

Actual heat transfer rate ¼ Maximum possible heat transfer rate

For a one shell two tube passes, Table 15-21 gives the effectiveness ε: 8 h 1 pffiffiffiffiffiffiffiffiffiffiffiffiffii9 > > < pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ exp NTU 1 þ c2 = h ε ¼ 2 1 þ c þ 1 þ c2 pffiffiffiffiffiffiffiffiffiffiffiffiffii > ; : 1  exp NTU 1 þ c2 > where: pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ c2 ¼ 1 þ 0:52 ¼ 1:118 and the number of transfer units:

8 h pffiffiffiffiffiffiffiffiffiffiffiffiffii91 > < = pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ exp NTU 1 þ c2 > h ε ¼ 2 1 þ c þ 1 þ c2 pffiffiffiffiffiffiffiffiffiffiffiffiffii 2 > : ; 1  exp NTU 1 þ c >  1 1 þ exp½1:66  1:118 ¼ 2 ð1 þ 0:5 þ 1:118Þ 1  exp½1:66  1:118 ¼ 0:557 _ The actual heat transfer rate, Q: _ _ ¼ εQ Q max ¼ εðCPÞmin ðT1  t1 Þ ¼ ð0:557Þð1:806Þð150  15Þ ¼ 135:9 kW

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: pR2 pz ¼ pR2 pzþDz þ 2pRDzsr¼R  Dp 2  ¼ $sr¼R Dz R and the shear stress at the tube wall is:  vvz sr¼R ¼ m vr r¼R

dG ¼ vz rdA Integrating in the entire section Z Z G ¼ dG ¼ vz rdA

Re ¼

t2 ¼ t1 þ 37:65 ¼ 15 þ 37:65 ¼ 52:65
C

PRESSURE DROP, DP 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 15-50 and 15-51.

rvD < 2100 m

v ¼

¼ 74:8 C Q 135:9 ¼ ¼ 37:65o C ðCPÞwater 3:61

(15-71)

(15-72)

where v is a mean velocity defined as:




t2  t1 ¼

(15-70)

For the boundary layer to remain in laminar flow:

T2 ¼ 150  75:2 ðCPÞwater ðt2  t1 Þ ¼ Q

(15-68)

wherevz;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:

ðCPÞoil ðT1  T2 Þ ¼ Q Q 135:9 ¼ 75:2o C ¼ ðCPÞoil 1:806

(15-67)

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 15-68 can be calculated from the velocity distribution.


r 2  (15-69) vz ¼ vz;max 1  R

The outlet temperatures of oil and water are:

T1  T2 ¼

(15-66)

G ra

(15-73)

where: G ¼ mass flow rate r ¼ fluid density at ¼ flow cross-sectional area of the tube Combining Equations 15-71 and 15-73 and rearranging gives: R R vz rdA vz dA ¼ (15-74) v ¼ rat at
Z R

r 2  2prdr vz;max 1  R ¼ 0 (15-75) pR2

Heat Transfer Chapter | 15

2vz;max ¼ R2

ZR h

r i 1 rdr R

or: (15-76)

0

v ¼ 

vz;max 2

(15-77)

Dp 2  ¼ $sr¼R Dz R  2 dv m ¼ R dr r¼R

Dp ¼

(15-78) (15-79)

2 $mvz;max Dz R

¼ m

4v dz R2 =2

dp ¼ 32m

(15-82)

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 15-68 cannot be calculated and analytical solution is not possible, therefore the usual approach is to define the friction factor, f. From Equation 15-67, 2 dp ¼ $sr¼R dz R

(15-83)

The friction factor, f is defined as the ratio of the shear stress to the kinetic energy as: s rv2 =2 ! 2 s rv2 dz dp ¼ $ R r v22 2 f ¼

2 rv2 dz $f R 2

(15-84)

(15-85)

(15-86)

Integrating Equation 15-86 between p ¼ p1 and p2 and the pipe length z ¼ 0 and L gives: 

2 rv2 dp ¼ f R 2

ZL dz

(15-87)

  2 rv2 L  p2  p 1 ¼ f R 2

(15-88)

p1

 2    L rv 1 ; lbf in2  p2  p1 ¼ 4f D 2gc 144

(15-90)

Pressure drop in an exchanger with number of tubes is:  2   L rv 1 (15-91)  p2  p1 ¼ 4f D 2gc 144

v ¼ G=r and r ¼ sr Dpf ¼

(15-81)

  v  p2  p1 ¼ 32m 2 dz D

Zp2

In Imperial units:

(15-80)

v dz D2

(15-89)

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

or:

dp ¼

 2    L rv ; N m2  p2  p1 ¼ 4f D 2

121

0

f LG2 2gc rwater Di s

(15-92)

The specific gravity of liquids is usually referenced to water at 4
C, which has a density of 62.43 lbm/ft3. The petroleum industry uses a reference temperature of 60
F, at which rwater ¼ 62.37 lbm/ft3, the difference in reference densities is significant. gc ¼ 32:174

lbm ft lbm ft ¼ 4:16975  108 lbf s2 lbf h2

(15-93)

With these numerical values, Equation 15-92 becomes: Dpf ¼

f LG2 lbf ; 2 10 5:206  10 Di s ft

(15-94)

When L and Di are expressed in ft and G in lbm/h.ft2, the units of DPf are lbf/ft2. Or: Dpf ¼

f LG2 lbf ; 7:50  1012 Di sf in2

(15-95)

where: f ¼ ðm=mw Þ0:14 for turbulent flow f ¼ ðm=mw Þ0:25 for laminar flow The viscosity correction factor accounts for the effect of variable fluid properties on the friction factor in nonisothermal flow, while the factor of 144 converts the pressure drop from lbf/ft2 to lbf/in2 (psi). where: L ¼ Pipe length, ft, m D ¼ Pipe diameter, ft, m  lbm ft gc ¼ 32.174 lbf s2 f ¼ friction factor (dimensionless) v ¼ fluid velocity, ft/s2, m/s2 r ¼ fluid density, lbm/ft3, kg/m3

122

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

dz

|r =R

. 2πr

R

r

πR2p|z

z

πR2p|z + Δz

Flow of fluid L FIGURE 15-50 Forces acting on a segment of fluid. Direction of fluid flow through a pipe.

p1 ¼ inlet pressure, lbf/in2, N/m2 p2 ¼ outlet pressure, lbf/in2, N/m2 s, f ¼ dimensionless The friction factor f is a function of the Reynolds number and the roughness of the tube surface ðε=DÞ. A well-known graph representing the friction factor as a function of the Reynolds number was produced by Moody [302]. The curves parameter is the relative roughness, defined as the quotient between the tube surface roughness and the pipe diameter ðε=DÞ. For laminar flow, the friction factor is defined by: f ¼

16 Re

(15-96)

At a 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 ¼ fðRe; ε=DÞ fy

0:079 Re1=4

3  103  Re  105

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: Dpt ¼

f G2 Ln0 5:22ð10Þ ðDi ÞðsÞðm=mw Þ0:14 10

; psi

(15-100)

Figure 15-52 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: Dps ¼

fG2 Di ðN þ 1Þ 5:22ð10Þ10 ðDe ÞðsÞðm=mw Þ0:14

; psi

(15-101)

(15-97)

Figure 15-53 shows the shell-side friction factors for bundles with 25 percent cut segmental baffles.

(15-98)

Frictional Pressure Drop

(15-99)

The frictional pressure drop for fluids circulating in the tube-side of a heat exchanger can be considered as the sum of two effects:

Implicit and various explicit equations for the friction factor, f are well illustrated in Volume 1, 4th ed. of this series (page 155).

1. The pressure drop along the tubes 2. The pressure drop due to the change in direction in the exchanger heads

and fy

0:046 Re1=5

Re  2  104

vz (r)

R r

dA = 2 π r dr FIGURE 15-51 Parabolic velocity distribution in laminar flow.

Heat Transfer Chapter | 15

FIGURE 15-52 Tube-side friction factors by Kern.

FIGURE 15-53 Shell-side friction factors for bundles with 25% cut segmental baffles.

123

124

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

The pressure drop along the tubes can be determined with the Fanning equation:  2  m L Gt m (15-102) Dp ¼ 4f Nt Di 2r mw where: m ¼ 0.25 for laminar flow, Re < 2100 ¼ 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 ¼

16 Re

(15-96)

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 3/4 or 1 in. smooth tubes, a recommended expression by Drew, Koo and McAdams within  5% is [302]: f ¼ 0:0014 þ

0:125 Re0:32

(15-103)

Some authors suggest increasing them by 20% for commercial steel heat exchanger tubes. In addition, for clean commercial iron and steel heat exchanger tubes, an equation given by Wilson, McAdams and Seltzer within  10% is [305]: f ¼ 0:0035 þ

0:264 Re0:42

(15-103A)

0:4137 Re0:2585

(15-103B)

Equation 15-103B is analogous to the friction factor equation given for the pipe and annulus by: f ¼

0:3673 Re0:2314

(15-103C)

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: G2t 2r 2  4Nt v 62:5 ; psi ¼ s 2g0 144 Dpr ¼ 4Nt

where g0 ¼ conversion factor, 32:174

Figure 15-54 shows the tube-side return pressure drop for varying mass velocity. The pressure losses due to contraction at the tube inlets, expansion at the exists 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 [70] suggested adding four velocity heads per pass. Butterworth [306] 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, 180
bend 1.5; so for two passes the maximum loss is [307]: 2  0:5 þ 2:  1:0 þ 1:5 ¼ 4:5 velocity heads ¼ 2:25 per pass Frank’s recommended value of 2.5 velocity heads per pass is the most value to use [308]: # "   m L m ru2t  2 Dpt ¼ Nt 8Jf ; N m ðPaÞ þ 2:5 2 Di mw (15-105)

For turbulent flow in commercial heat exchanger tubes for Re  3000 [288]: f ¼

Nt ¼ number of tube passes. s ¼ specific gravity v ¼ fluid velocity, ft/s.

lbm ft lbf s2

(15-104)

where: Di ¼ inside diameter of the tube, m jf ¼ tube-side friction factor (Figure 15-55) L ¼ length of one tube, m m ¼ 0.25 for Re  2,100 and m ¼ 0.14 for Re  2100 Nt ¼ number of tube-side passes ut ¼ tube-side fluid velocity, m/s r ¼ density of tube-side fluid, kg/m3 Dpt ¼ tube-side pressure drop, N/m2 (Pa) Dpt calculated by Equation 15-105 is an actually permanent pressure loss. The calculated pressure drop should be less than the maximum allowable pressure drop. In some applications, the maximum allowable pressure drop is decided by process conditions, while in other applications, the 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 þ operating cost).

Heat Transfer Chapter | 15

125

FIGURE 15-54 Tube-side return pressure loss

Table 15-22 shows the optimum pressure drop based on economic considerations. Kern [70] 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 Dp0 t using Equation 15-106 for inlet vapor flow rate and conditions and multiply it by a factor of 0.5. Dpt ¼ 0:5 Dp0 t

(15-106)

The total pressure drop is: DpT ¼ Dpt þ Dpr

(15-107)

Pressure drops from Dowtherm A heat transfer media flowing in pipes may be calculated from Figure 15-52. The

effective lengths of fittings, etc. are shown in Chapter 4 of Vol. 1, 4th ed. of this volume series. 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 100e700
F 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

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FIGURE 15-55 Tube-side friction factors by Sinnott and Towler.

TABLE 15-22 Optimum Pressure Drop (Maximum Allowable Pressure Drop) Based on Economic Considerations Fluid

Optimum, Dpt or Dps , kPa

Liquids of mL < 1 cP

35

Liquids of mL ¼ 1 to 10 cP

50e70

Gas or vapor at 1 to 2 atm

13.8

Gas or vapor at high vacuum (up to 60 torr absolute pressure)

0.4e0.3 (3e6 torr)

Gas or vapor at high pressure > 10 atm

0.1 times operating pressure

Chemical Co., (g) Calfo division of Petro Canada and (h) others with qualified products. Gulley [417] 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 þ 9% when compared with available literature. He defined the total shell-side pressure drop as the sum of the cross-flow Dpc, total cross-flow pressure drop in baffle end zones Dpends,

total nozzle zone pressure drops Dpnoz and the total baffle window pressure drops Dpw. He inferred that the improved accuracy of Dpw 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.

Factors Affecting Pressure Drop (Dp) 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 the 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 needs 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 (Dp), and then the required pumps can be specified to overcome this pressure drop. Where these cases occur, the designer decides by balancing a higher heat exchanger cost against a higher pumping power, and thus adopts the most cost effective solution.

Heat Transfer Chapter | 15

Tube-Side Pressure Drop, Dpf

Also,

The frictional pressure drop Dpf loss on the tube-side is given by:

G ¼

f np L G2 Dpf w Di

127

pT p m_ m_  ¼  T  ¼
¼ 0 ds C Bs as ds Bs pT  Do ds C0 Bs 144 pT

(15-108)

(15-118)

Further, the mass flux G is the mass flow rate per tube ðm_ np =nt Þ divided by the flow area per tube ðpD2i =4Þ. Substituting yields:

The equivalent diameter, de depends on the tube-side and pitch. For a square pitch,    de ¼ 4 p2t  p D2o 4 pDo (15-119)

Dpf w

f Ln3p n2t D5i

(15-109)

The friction factor is inversely proportional to Reynolds number in laminar flow (Equation 15-96) and proportional to the 0.2585 power of Reynolds number in turbulent flow (Equation 15-103B). Since: Re ¼

4 m_ per tube np w p Di m nt D i

(15-110)

Combining Equations 15-116 to 15-119 gives: Dpf w

Dpf w

L n2p nt D4i

ðturbulent flowÞ

ðlaminar flowÞ

 (15-111)

(15-112)

For a given amount of heat transfer surface and a specified tube Birmingham Wire Gage (BWG), Ai ¼ nt p Di L ¼ constant

(15-113)

If the tube diameter is also specified, then nt is inversely proportional to the tube length and the proportionalities of Equations (15-111) and (15-112) become: L2:74 ðturbulent flowÞ Dpf wn2:74 p

(15-114)

Dpf wn2p L2 ðlaminar flowÞ

(15-115)

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

Shell-Side Pressure Drop (Dpf) The shell-side pressure drop is: Dpf w

f G2 ds ðnb þ 1Þ de

(15-116)

The number of baffles is approximately equal to the tube length divided by the baffle spacing in consistent units, i.e. nb þ 1wL=Bs

(15-117)

(15-120)

For a given tube and shell diameter, the relation simplifies to: f L P2t (15-121) Dpf w  2 B3s ðPt  Do Þ2 P2t  p 4Do

Proportionality, Equation 15-109 becomes: L n2:74 p Dpf w 1:74 4:74 nt Di

f L p2t D2o   2 p D2o 3 2 2 Bs ds pt  Do pt  4

Dps ¼ 8jf

Ds de

 2  0:14  L rus m ; N m2 ðPaÞ 2 Bs mw (15-122)

where Bs ¼ baffles spacing, m de ¼ equivalent diameter, m. ds ¼ internal diameter of shell, m jf ¼ shell-side friction factor (Figure 15-56) L ¼ length of one tube, m us ¼ shell-side fluid velocity, m/s. r ¼ density of shell-side fluid, kg/m3 Dps ¼ shell-side pressure drop, N/m2 (Pa) 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 Dpf. 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 [416]. Figures 15-55 and 15-56 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

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-56 Shell-side friction factor by Sinnott and Towler.

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 the 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 Dpf 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 [288].

Shell Nozzle Pressure Drop (Dpnoz) 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 tube matrix, bundle bypassing and recirculation. 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 ¼ 0.8, maximum ¼ 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.   (15-122A) DPnoz ¼ 0:000108 Kn v2s ðrÞ where: DPnoz ¼ Total nozzle pressure drop, lbf/in2 Kn ¼ Pressure loss coefficient for total shell nozzle pressure drop, dimensionless. ¼ (0.7 < Kn < 1.8)

Heat Transfer Chapter | 15

vs ¼ Velocity in the shell nozzle entrance and exit areas, ft/s. r ¼ shell fluid density, lb/ft3

Total Shell-Side Pressure Drop, Dptotal The total pressure drop on the shell-side is expressed by: Dptotal ¼ Dpc þ Dpends þ Dpw þ Dpnoz

(15-122B)

The terms Dpc for the interior cross-flow sections and Dpends for the end nozzles are determined by Taborek [418]. Dpw is the baffle window pressure drop and Dpnoz is the pressure drop for the nozzles and entrance effects. The baffle window pressure drop Dpw is expressed by [417]:   Kp ð0:000108Þ G2w ðNb Þ (15-122C) Dpw ¼ r and Kp is

"



Kp ¼ f i ðCl Ncw

Sl DÞ2 Sw

2 # (15-122D)

Equations for the distortion factor, D are [417]: Below a baffle cut of 24% : D ¼ 1:0 þ 2:35ð0:24  Bc Þ (15-122E) Above 29% baffle cut :

D ¼ 1:0 þ 1:9ðBc  0:29Þ (15-122F)

129

There are no published charts for 60
triangular tube pattern friction factors. The above constant was derived from using 0.78 of the square rotated friction factor. The 45
square rotated tube layout gives higher pressure drops than the 30
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 15-122D is good above a Reynolds number of 800. Below 800, it calculates low pressure drops. Gulley [417] reported that the minimum number of tube rows effective in the baffle window investigated was 4.

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 [130] 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 or are otherwise considered.

where: Bc ¼ Baffle cut as a fraction of the shell I.D. Cl ¼ Constant in Kp Equation (15-122D) D ¼ Distortion factor of the shell fluid profile, dimensionless Kp ¼ pressure loss coefficient for baffle window pressure drop, dimensionless fi ¼ friction factor for an ideal tube bank gc ¼ gravitational conversion factor, 32.174 lbm/lbf (ft/s2) Gw ¼ mass velocity in baffle window, lb/(s) (ft2) Nb ¼ number of baffles Ncw ¼ number of effective tube rows crossed in baffle window. Sl ¼ total of leakage areas, in2 Sw ¼ net flow area in baffle window, in2. r ¼ density of shell fluid, lbm/ft3 The constant Cl depends on the tube layout pattern. The values are: 30
90
45
60


triangular square square rotated triangular

2.2 3.64 2.29 1.79 estimate

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 require for the cooling.   (15-123) q ¼ W cp t2  t1 for latent heat changes: q ¼ W 1v

(15-124)

For cooling (or heating) and latent heat change (condense or boil):   (15-125) Q ¼ q0 ¼ Wcp t2  t1 þ W1v 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

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

known for the design of an exchanger, although it may be determined on existing equipment from operating data. This latter is termed performance evaluation.

FOULING OF TUBE SURFACE

EXAMPLE 15-12 Heat Duty of a Condenser with Liquid Subcooling

The overhead condenser on a distillation column is required to subcool the condensed vapors from the condensation temperature of 46.4
F down to 35
F. the specific heat of the liquid is 0.3 Btu/lb (
F) and the latent heat of vaporization at 46.4
F is 265 Btu/lb. the vapor rate to the condenser is 740.3 lb/h. What is the total heat load on the condenser? Latent duty: q1 ¼ 740.3 (265) ¼ 196,180 Btu/h Sensible duty: q2 ¼ 740.03 (0.3) (46.4  35) ¼ 2532 Btu/h Total heat duty: Q ¼ q1 þ q2 ¼ 198,712 Btu/h

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 [287]: % over  surface ¼

A  Ac  100 Ac

(typically about 10% or less) is considered acceptable and often desirable, since it provides an additional safety margin in the final design.

(15-126)

where: A ¼ actual heat transfer surface area in the exchanger Ac ¼ 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 20e40% are considered typical, higher values are not unusual. Equation 15-126 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

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 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 (Dp). 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 the environment that they are in contact with. Fouling and corrosion represent heat exchanger operation induced effects, and require consideration in 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 it may result in eventual failures of some heat exchangers and an increase in Dp. For example, in the refining 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 the production of additional carbon dioxide (CO2) emissions, with the associated environmental impact. Figure 15-57 shows the effect of corrosion-erosion on the shell-side of a shell and tube exchanger. 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 15-28). These deposits may vary in nature (brittle, gummy), texture, thickness, thermal conductivity, ease of removal, etc. Although there are no deposits 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

Heat Transfer Chapter | 15

131

TABLE 15-23 Devices for Fouling Measurements Measurement Principle

Typical Reference

Jet fouling Test Oxidation Tester (JFTOT)

Mass collection of solid by a filter

Hazlett et al. [314]

Thermal fouling test

Change in fluid temperature for given heat rate

Dickakian [315]

Closed-flow loop

Change in heat transfer coefficient measured by a fouling probe

Panchal and Watkinson [316], Crittenden [317]

Laboratory fouling test apparatus (LFTA)

Autoclave with rotating cylinder around a heating probe

Eaton and Lux [318]

Fouling Unit

FIGURE 15-57 Corrosion and erosion on the shell-side of a shell and tube heat exchanger.

can be 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. Fouling is very expensive (costing over a billion US dollars in the world refineries) and accounts for 0.2 percent of the gross national products (GNP) since it [310]: 1. Increases capital costs due to the need to over surface the heat exchanger and for cleaning. 2. Increases maintenance costs resulting from cleaning, chemical additives or troubleshooting. 3. Results in loss of production due to shut down or reduced capacity. 4. Increases energy losses due to reduced heat transfer. 5. Increases Dp and dumping of dirty streams present. 6. Enhances heating costs with the associated increase in greenhouse-gas emissions (e.g. CO2, SO2, NOx, H2S). 7. Increases capital expenditure for over-designed units. Fouling is commonly measured as the change in the overall heat transfer coefficient, but other measurements are used. Knudsen [311] and Melo et al. [312] reviewed commercial and laboratory monitors used to measure the rate of fouling for low-temperature applications. Marner and Henslee [313] investigated available fouling probes for high temperature gas streams. However, since fouling in the refining industry occurs at high temperature > 480
F (250
C) and high pressure conditions > 20 atm (> 20.23 bar), these fouling units cannot be used. Table 15-23 summarizes fouling units used for high temperature organic fluid fouling experiments.

Kuru and Panchal [319] improved the above fouling units by modifying the installation of a helical impeller in a flow tube and a fouling probe in the autoclave to simulate the fluid dynamics and heat transfer of typical heat exchanger equipment for high temperature 930
F (500
C) and high pressure of 70 atmospheres. They were able to determine the threshold fouling conditions, the effectiveness of new and improved mitigation methods and changes in the fouling characteristics due to different chemical composition and or operating conditions. Liquid-side fouling occurs on the heat exchanger side where liquid is being heated, and gas-side fouling occurs on the gas cooling side, although reverse examples can be found. Gas-side fouling can be a potential fire hazard in a fossil-fuel fired exhaust environment, resulting in catastrophic lost production and repair costs. In certain applications, increased Dp due to fouling may reduce gas flows that adversely affect the heat transfer and increase solvent concentration (such as during waste heat recovery from paint oven exhausts), which pose an environmental problem. For systems with low heat transfer coefficients, such as gases, fouling significantly increases the fluid pumping power with some reduction in heat transfer. Fouling factors have become increasingly controversial recently, because they can result in significant over design, resulting in the specification of an expensive heat exchanger with unnecessary area. For many applications, fouling factors should not account for more than 20% excess area in the heat exchanger design. Excessive use of design margin has several drawbacks; superfluous heat transfer area leads directly to unnecessary capital cost, a

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

larger and heavier exchanger, weight and footprint, which are essential for offshore applications, and excessive design margin can result in accelerated fouling. Designers often incorporate excess margin by increasing the shell diameter, which invariably increases the cross-sectional area available for flow, resulting in lower shell-side velocities for a given flow rate. Further, the number of tubes increases, which reduces tube-side velocity, which again increases the rate of fouling. Additionally, over performance caused by excess heat transfer area can also accelerate fouling, because the process stream temperature change will be greater than the desired value, thus requiring the flow rate of utility stream to be reduced. Figures 15-58A, B and C show fouling by flakes, fouled tubes on the rear tube-side and a fouled floating head of shell and tube heat exchangers respectively. Published fouling resistances often do not reflect true heat exchanger performance for some services because they are either too high or too low. Fouling factors are generally static, but for some fouling mechanisms they are dynamic. Temperature and velocity often greatly affect fouling, but published fouling factors that account for these effects are limited. Furthermore, fouling factors often implicitly account for uncertainty in the heat transfer methods that often

FIGURE 15-58A Rusty flakes and corroded tubes of a tube bundle of a shell and tube heat exchanger.

FIGURE 15-58B Fouled and corroded tubes and segmental baffle of a shell and tube heat exchanger.

FIGURE 15-58C A shell and tube heat exchanger with fouling of sediments at the rear end showing the floating head.

result in the duplication of uncertainty effects. Nesta and Bennett [319] and Bennett et al. [320] and have provided design algorithms for fouling mitigation and excess margin reduction. A heat exchanger represents a relatively small portion of the total capital investment in a facility; however, the global cost of heat exchanger fouling is enormous in terms of additional capital, as well as the costs of additional energy, mitigation, cleaning, increased maintenance and lost production. Cost data are not made public, as the true cost is engrained in operating costs (e.g. maintenance and steam costs), but from studies carried out, the cost of heat exchanger fouling runs into millions of US dollars per annum [322]. For example, in a refinery, crude oil from storage tanks is fed to the heat exchangers of the crude preheat train, initially at an ambient temperature. The crude oil is then heated at around 480
F (250
C) at entry to the furnace. From the furnace, the crude is fed to a distillation column where valuable product streams, such as kerosene, gasoline and gases are separated and collected. The most damaging fouling occurs from asphaltene deposition from the crude oil onto the metal surfaces of the pre-heat train hot end heat exchangers. This fouling results to a reduction in furnace inlet temperature by as much as 54
F (30
C) and a subsequent requirement to burn extra fuel in the furnace to make up the temperature necessary for efficient distillation. Additionally, fouling causes a significant decrease in the crude unit throughput resulting in reduced production. Generally, studies have shown that the cost associated with refinery pre-heat fouling worldwide is in the order of $4.5 billion. Fouling in refineries and petrochemical plants is dependent on many variables. Factors affecting fouling in pre-heat exchangers include process conditions (e.g. temperature, pressure, flow rate), and exchanger piping configuration, crude oil composition, corrosion and inorganic contaminants. Effective control of these variables may reduce fouling in crude oil units. Studies have shown

Heat Transfer Chapter | 15

the existence of fouling thresholds for chemical reaction (asphaltene) fouling in particular crudes and crude blends, and that these thresholds are function of both temperature and velocity. Fouling mitigation in the hot end of the preheat train is influenced by chemical reactions which are triggered by the high temperatures. Further, it has been established that critical velocities occur, above which fouling does not occur due to deposit removal by shear forces from the flow [323]. 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

133

unfouled coefficient than for one of the low value. For example, a unit with a clean overall heat transfer coefficient of 400 Btu/h.ft2 .
F 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 15-59 and Table 15-24). The traditional method of accommodating fouling is to assign an individual fouling resistance (i.e. fouling factor) to each stream. This fouling resistance is the expected resistance due to fouling at the end of run, based upon user experience. The sum of the fouling, fluid and metal

FIGURE 15-59 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 þ ro), as hr-ft2-o F/Btu. (Used by permission: Standards of Tubular Exchanger Manufacturers Association ©1959 and 1968. Tubular Exchanger Manufacturers Association, Inc. All rights reserved.)

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resistances provides a total design resistance to determine the required surface for the exchanger. Although the TEMA has published fouling resistances (see Tables 15-24e29), these values have been the subject of considerable debate [234]. This is because the fouling resistance is dynamic, as fouling depends on many factors, such as velocity, surface temperature and chemistry of the fluids, as it is most noticeable in exchanger performance where the fouling margin is large. Difficult services or frequent foulers can attain their performance limit in few days, rather than the full run cycle, thus implying that the user must clean the exchanger intermittently, or live with the reduced performance. It appears that fouling factors in the literature do not, in fact, represent the true dynamic nature of fouling in shell and tube heat exchangers [309]. However, the fouling factors suggested by TEMA [107] and shown in Tables 15-25e29 are estimates which can be used in preliminary design calculations. These values are predominantly for petroleum operations, although portions of the table are applicable to general use and to petrochemical processes. In general, some experience in petrochemical mixtures indicates that the values for certain waters, organic materials and a few others are too low but not as high as suggested by Fair [44]. High values for some materials do not seem justified in the light of normal process economics. Tables 15-26, 27 and 28 represent a selected group of materials with suggested fouling factors. Other references dealing with various types of conditions of heat exchanger fouling include [145,146, 147,148,149,150,151,152,153,154,155, 156,157 and 158]. Nelson [89] presents data in Figure 15-59A on some fluids showing the effects of velocity and temperature. Also see Figure 15-59B. The fouling factors are applied as part of the overall heat transfer coefficient to both the inside and outside of the heat transfer surface using the factor that applies to the appropriate material or fluid. As a rule, the fouling factors are applied without correcting for the inside diameter to the outside diameter, because these differences are not known to any great degree of accuracy. For fouling resistances of significant magnitude, a correction is usually made to convert all values to the outside surface of the tube; see Equation 15-161 or 161A. Sometimes only one factor is selected to represent both sides of the transfer fouling films or scales. In the tables, the representative or typical fouling resistances are referenced to the surface of the exchanger on which the fouling occurs e that is, the inside or outside tubes. Unless specific plant/equipment data represent the fouling in question, the estimates in the listed tables are a reasonable starting point. It is not wise to keep adjusting the estimated (or other) fouling to achieve a specific overall heat transfer coefficient, U. Fouling generally can be kept

TABLE 15-24 Devices for Fouling Measurements Measurement Principle

Typical Reference

Jet fouling Test Oxidation Tester (JFTOT)

Mass collection of solid by a filter.

Hazlett et al. [314]

Thermal fouling test

Change in fluid temperature for given heat rate

Dickakian [315]

Closed-flow loop

Change in heat transfer coefficient measured by a fouling probe

Panchal and Watkinson [316], Crittenden [317].

Laboratory fouling test apparatus (LFTA)

Autoclave with rotating cylinder around a heating probe

Eaton and Lux [318]

Fouling Unit

to a minimum provided that proper and consistent cleaning of the surface takes place. Kern [269] discusses fouling limits. Inside tubes may be rodded, brushed or chemically cleaned, but most outside tube surfaces in a shell can only be cleaned by chemical means, or by hydraulic/corncob external cleaning or rodding/brushing between tube lanes provided that the shell is removable (as in Figures 15-1A, B, DeF, I and K). 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 [107] as follows: ro ¼ fouling resistance on outside of tube; ðhÞð
FÞ ðft2 outside surface Þ ðBtuÞ ri ¼ fouling resistance on inside of tube; ðhÞð
FÞ ðft2 inside surface Þ ðBtuÞ 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

TABLE 15-25 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

0.001e0.002

Fuel oil #6

0.005

Overhead products

0.001e0.002

Transformer oil

0.001

Engine lube oil

0.001

Liquids

Quench oil

0.004

Lean oil

0.002

Rich oil

0.001e0.002

Natural gasoline and liquefied petroleum gases

0.001e0.002

Gases and Vapors 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)

0.0015e0.002

Atmospheric tower overhead vapors

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 0 to 250
F velocity ft/sec

Liquids

250 to 350
F velocity ft/sec

4

4

Molten heat transfer salts

0.0005

DRY

0.003

0.002

0.002

0.003

0.002

0.002

Refrigerant liquids

0.001

SALT*

0.003

0.002

0.002

0.005

0.004

0.004

135

Continued

Heat Transfer Chapter | 15

Manufactured gas

136

RGP-T2.4 Design Fouling Resistance (hr-ft2-
F/Btu) Hydraulic fluid

0.001

Industrial organic heat transfer media

0.002

Ammonia liquid

0.001

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

0.002e0.003

Kerosene

0.002e0.003

Light gas oil

0.002e0.003

Heavy gas oil

0.003e0.005

Heavy fuel oils

0.005e0.007

Fouling Resistance for Chemical Processing Streams

Gases and Vapors

350 to 405
F velocity ft/sec

450
F and more velocity ft/sec

Acid gases

0.002e0.003

Solvent vapors

0.001

Asphalt and Residuum

Stable overhead products

0.001

Vacuum tower bottoms

0.010

Atmosphere tower bottoms

0.007

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

0.001e0.002

Light cycle oil

0.002e0.003

Caustic solutions

0.002

Heavy cycle oil

0.003e0.004

Vegetable oils

0.003

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-25 Guide to Fouling Resistancedcont’d

Catalytic Hydro Desulfurizer: Charge

0.004e0.005

Effluent

0.002

Light coker gas oil

0.003e0.004

H.T. sep. Overhead

0.002

Heavy coker gas oil

0.004e0.005

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. feed

Reformer charge

0.0015

All other process streams

Reformer effluent

0.0015

Hydrocracker charge and effluent*

0.002

Recycle gas

0.001

Fouling resistances for Water

Hydrodesulfurization charge and effluent*

0.002

Temperature of Heating Medium

Overhead vapors




Liquid product 30-50 A.P.I.

0.002

Up to 240
F

240 to 400
F

125

More than 125


0.001

Water Velocity Ft/Sec

Water Velocity Ft/Sec

0.002

3 and Less

More Than 3

3 and Less

More Than 3

0.001

Liquid product greater than 50
A.P.I.

0.003

Temperature of water




*Depending on charge, characteristics and storage history, charge resistance may be many times this value.

Sea Water

0.0005

0.0005

0.001

0.001

Light Ends Processing Streams:

Brackish Water

0.002

0.001

0.003

0.002

0.001

Cooling tower and artificial spray pond:

Liquid products

0.001

Treated makeup

0.001

0.001

0.002

0.002

Alkylation trace acid streams

0.002

Untreated

0.003

0.003

0.005

0.004

Absorption oils

0.002e0.003

City or well water

0.001

0.001

0.002

0.002

Alkylation trace acid streams

0.002

Reboiler streams

0.002e0.003

Lube Oil Processing Streams Feed stock

0.002

137

Continued

Heat Transfer Chapter | 15

Overhead vapors and gases

138

TABLE 15-25 Guide to Fouling Resistancedcont’d

Solvent feed mix

0.002

Solvent

0.001

River Water:

Extract*

0.003

Minimum

0.002

0.001

0.003

0.002

Raffinate

0.001

Average

0.003

0.002

0.004

0.003

Asphalt

0.005

Muddy or silty

0.003

0.002

0.004

0.003

Wax slurries*

0.003

Hard (more than 15 grains/gal)

0.003

0.003

0.005

0.005

Refined lube oil

0.001

Engine jacket Distilled or closed cycle

0.001

0.001

0.001

0.001

Condensate

0.0005

0.0005

0.0005

0.0005

0.0005

0.001

0.001

0.002

0.002

0.002

*Precautions must be taken to prevent wax deposition on could tube walls. Visbreaker Overhead vapor

0.003

Treated boiler feedwater

0.001

Visbreaker bottoms

0.010

Boiler blowdown

0.002


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.)

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

RGP-T2.4 Design Fouling Resistance (hr-ft2-
F/Btu)

Heat Transfer Chapter | 15

139

TABLE 15-26 Suggested Fouling Factors in Petrochemical Processes r [ (hr) (ft2) (
F)/Btu Temperature Range Fluid




Velocity, ft/s.

100
F

7

0.0015

0.002

4

0.0005e 0.0015

0.001e0.0025

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





Condensate (100 e300 F)

0.001 4

0.0005

0.001

Steam (saturated) oil free with traces oil

0.0005e0.0015 0.001e0.002

Light hydrocarbon liquids (methane, ethane, propane, ethylene, propylene, butane-clean)

0.001

Light hydrocarbon vapors: (clean) 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)

3e8

0.0005

50% (nickel tube)

6e9

0.001

73% (nickel tube)

6e9

0.001

Gases (industrial clean) Air (atmos.)

0.0005e0.001

Air (compressed)

0.001

Flue gases

0.001e0.003

Nitrogen

0.0005

Hydrogen

0.0005

Hydrogen (saturated with water)

0.002 Continued

140

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-26 Suggested Fouling Factors in Petrochemical Processes r [ (hr) (ft2) (
F)/Btudcont’d Temperature Range Fluid

Velocity, ft/s.




100
F

Polymerizable vapors with inhibitor

0.003e0.03

High temperature cracking or coking, polymer buildup

0.02e0.06




Salt brines (125 F max.)

4

0.002

0.003

Carbon dioxide [93] (sublimed at low temp.)

0.2e0.3

TABLE 15e27 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 e 0.0004

Lean oil

0.0004

Column overhead products

0.0002

Natural gasoline and LPG

0.0002 Continued

Heat Transfer Chapter | 15

141

TABLE 15e27 Fouling Resistances for Industrial Fluids (m2 K/W)dcont’d Oils

Gases and vapors

Fouling Resistances for Oil Refinery Streams Crude Oil Temp. 0 e 120oC

120 e 180oC

180 e 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

< 0.60 1.20 > 1.20

< 0.60 1.20 > 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

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 e 50o API

Light gas oil

0.0005

Heavy gas oil

0.0005 e 0.0008

Heavy fuel oil

0.0008 e 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

Cracking and coking unit streams

Alkylation trace acid streams

Overhead vapors

0.0004

Light-cycle oil

0.0004

Heavy-cycle oil

0.0005 e 0.0007

Lube oil processing streams

Light coker gas oil

0.0005 e 0.0007

Feed stock

Heavy coker gas oil

0.0007 e 0.0009

Solvent feed mix

Bottom slurry oil (minimum 4.5 ft/s)

0.0005

Solvent

Light liquid products

0.0005

Extract Continued

142

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15e27 Fouling Resistances for Industrial Fluids (m2 K/W)dcont’d Oils

Gases and vapors 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

TABLE 15-28 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 e 1248

Jet fuels

100 e 150

0.0015

Cutback asphalt

Water

10 e 20

0.01

Demineralized water

Water

300 e500

0.001

Ethanol amine (MEA or DEA) 10 e 25% solutions

Water or DEA, or MEA solutions

140 e200

0.003

Fuel oil

Water

15 e 25

0.007

Fuel oil

Oil

10 e 15

0.008

Gasoline

Water

60 e 100

0.003

Heavy oils

Heavy oils

10 e 40

0.004

Heavy oils

Water

15 e 50

0.005

Hydrogen-rich reformer stream

Hydrogen-rich reformer stream

90 e 120

0.002

Kerosene or gas oil

Water

25 e 50

0.005

Kerosene or gas oil

Oil

20 e 35

0.005

Kerosene or jet fuels

Trichloroethylene

40 e 50

0.0015

Jacket water

Water

230 e 300

0.002

Lube oil (low viscosity)

Water

25 e 50

0.002

Lube oil (high viscosity)

Water

40 e 80

0.003

Lube oil

Oil

11 e 20

0.006

Naphtha

Water

50 e 70

0.005

Naphtha

Oil

25 e 35

0.005

Organic solvents

Water

50 e 150

0.003

Liquid-liquid media

Continued

Heat Transfer Chapter | 15

143

TABLE 15-28 Typical Values of Overall Heat Transfer Coefficients in Tubular Heat Exchangers U [ Btu/h.ft2.oFdcont’d Shell-side

Tube-side

Design U

Includes total dirt

Organic solvents

Brine

35 e 90

0.003

Organic solvents

Organic solvents

20 e 60

0.002

Tall oil derivatives, Vegetable oil, etc

Water

20 e 50

0.004

Water

Caustic soda solutions (10e30%)

100 e 250

0.003

Water

Water

200 e 250

0.003

Wax distillate

Water

15 e 25

0.005

Wax distillate

Oil

13 e 23

0.005

Alcohol vapor

Water

100 e 200

0.002

Asphalt (450 oF)

Dowtherm vapor

40 e 60

0.006

Dowtherm vapor

Tall oil and derivatives

60 e 80

0.004

Dowtherm vapor

Dowtherm liquid

80 e 120

0.0015

Gas-plant tar

Steam

40 e 50

0.0055

High-boiling hydrocarbons V

Water

20 e 50

0.003

Low-boiling hydrocarbons A

Water

80 e 200

0.003

Hydrocarbon vapors (partial condenser)

Oil

25 e 40

0.004

Organic solvents A

Water

100 e 200

0.003

Organic solvents high NC, A

Water

20 e 60

0.003

Organic solvents low NC, V

Water or brine

50 e 120

0.003

Kerosene

Water

30 e 65

0.004

Kerosene

Oil

20 e 30

0.005

Naphtha

Water

50 e 75

0.005

Naphtha

Oil

20 e 30

0.005

Stabilizer reflux vapors

Water

80 e 120

0.003

Steam

Feed water

400 e 1000

0.0005

Steam

No. 6 fuel oil

15 e 25

0.0055

Steam

No. 2 fuel oil

60 e 90

0.0025

Sulfur dioxide

Water

150 e 200

0.003

Tall-oil derivatives, vegetable oil (vapor)

Water

20 e 50

0.004

Water

Aromatic vapor-stream azeotrope

40 e 80

0.005

Air, N2, etc. (compressed)

Water or brine

40 e 80

0.005

Air, N2, etc. A

Water or brine

10 e 50

0.005

Condensing vapor e liquid media

Gas e liquid media

Continued

144

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-28 Typical Values of Overall Heat Transfer Coefficients in Tubular Heat Exchangers U [ Btu/h.ft2.oFdcont’d Shell-side

Tube-side

Design U

Includes total dirt

Water or brine

Air, N2 (compressed)

20 e 40

0.005

Water or brine

Air, N2, etc., A

5 e 20

0.005

Water

Hydrogen containing natural e gas mixtures

80 e 125

0.003

Anhydrous ammonia

Steam condensing

150 e 300

0.0015

Chlorine

Steam condensing

150 e 300

0.0015

Chlorine

Light heat transfer oil

40 e 60

0.0015

Propane, butane, etc.

Steam condensing

200 e 300

0.0015

Water

Steam condensing

250 e 400

0.0015

Vaporizers

NC: non e condensable gas present; V: vacuum; A: atmospheric pressure. Dirt (or fouling factor) units are (h) (ft2) (oF)/Btu.

TABLE 15-29 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 ¼ 10,000 Btu/(hr)(ft2)(
F) Convecton zone q/A ¼ 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.

density of the fouling material. Some authors [137] suggest the need to specify 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 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 [145,146] lists six types of fouling: l

l

l

l

categorized by the following characteristics [107]. Note that biological fouling is not included. l l l

Linear Falling-rate Asymptotic

Essentially, all three of these types are time-dependent in terms of the buildup or increase in the thickness and/or

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, typically occurring at high temperatures 400
F < T < 450
F bulk [204
C < T < 232
C] in the crude and middle distillate service. The foulant materials are characterized by their high organic content and appear as black oily deposits. In severe coking situations, the effect is usually a 50e80% loss in heat transfer effectiveness. The rate of coking and the loss

Heat Transfer Chapter | 15

145

FIGURE 15-59A 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.)

FIGURE 15-59B 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 bulidup 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.)

146

l

l

l

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

in effectiveness are a function of the tube wall temperature and the amount of fouling precursors, such as 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.

Many cooling waters have inverse solubility characteristics due to dissolved salt compounds (organic and inorganic); others carry suspended solids that deposit on the tube at low-flowing velocities (< 2 ft/s). Biological fouling usually does not occur and is not a serious problem in most plant waters that are treated with biocides. Inverse solubility of dissolved salts in water occurs when the water contacts warm surfaces, and the salts deposit on the tube surfaces [140]. Do not design an exchanger by selecting a fouling resistance that has not fully developed, but rather select a value that has been stabilized over a period of time, see Figure 15-60. It is also quite important to appreciate that the fluid velocity often affects the fouling material’s thickness and hence its ultimate value for exchanger design; note Tables 15-25e28 and Figure 15-61 as examples for some waters [140]. Although TEMA [107] presents suggested fouling resistances, r, these are average values to

FIGURE 15-60 For many cooling waters, the fouling resistance increases rapidly, then decreases, and finally approaches an asymptotic value. (Used by permission: Knudsen, J. G., Chemical Engineering Progress. V. 87, No. 4, ©1991. American Institute of Chemical Engineers. All rights reserved.)

FIGURE 15-61 It is important to understand the relationships among velocity, surface temperature, and fouling resistance for a given exchanger. (Used by permission: Knudsen, J. G., Chemical Engineering Progress. V. 87, No. 4, ©1991. American Institute of Chemical gEngineers. All rights reserved.)

consider and do not identify the actual effects of hot surfaces, fluid velocity or composition of the deposited film, solid suspension or other scale. Thus, the designer must establish from usually meager data (if any) the fouling resistances to use in an actual design, and often this can only be done through experience. Some field plant operation performance can aid in establishing the ultimate magnitude of the fouling. Knudsen [140] reports useful data in Chenoweth [142] and Koenigs [141]. Zanker [143] has presented a graphical technique for determining the fouling resistance (factor) for process or water fluid systems based on selected or plant data measurements, as shown in Figures 15-62A, B and C. The design determination procedure presented by Zanker [143] is quoted here and used by permission from Hydrocarbon Processing© 1978 by Gulf Publishing Company, all rights reserved. It is based on: Rt ¼ R* (1  eBT). The asymptotic R*, is the expected fouling resistance after operating at time q2 and is the value proposed for the use in design. In order to use these nomographs, two sets of data have to be known: t1, R1 and t2, R2. Prior to using these nomographs, the auxiliary values have to be computed: q ¼ t1/t2 and a ¼ R1/R2 The following steps are used with the Nomograph Part 1, Figure 15-62A. Find the intersecting point of the curves of known values of q and a on the grid in the center of the nomograph. Interpolate if necessary; mark this point A. 1. Connect Point A, with a ruler, to the known value of q on the ‘primary scale.’ Extend this line up to the intersecting point with the Y scale. (Read the Y value as an intermediate result).

Heat Transfer Chapter | 15

147

FIGURE 15-62A Predict fouling by nomograph, Part 1. Calculation of R* value for fouling factor; use in conjunction with Figures 15-43B and 15-43C. (Used by permission: Zanker, A., Hydrocarbon Processing. March 1978, p. 146. ©Gulf Publishing Company, Houston, Texas. All rights reserved.)

2. Connect the Y value, with a ruler, to the known value of R1 on the appropriate scale. Read the final result, R*, at the intersection point of the line with the oblique R* scale. The following steps are used with Nomograph Part 2 (Figure 15-62B). 1. Connect with a ruler, the known values of Y (found by Nomograph, Part 1) and t1 2. Read the final result, B, at the intersection point with the central B scale.

FIGURE 15-62B Fouling Nomograph, Part 2. Calculation of B Value for fouling factor; use with Figures 15-43A and 15-43C. (Used by permission: Zanker, A., Hydrocarbon Processing. March 1978, p. 147. ©Gulf Publishing Company, Houston, Texas., All rights reserved.)

After using both nomographs, the constants R* and B are known, and equation can be solved with R1 as the unknown. It has to be emphasized that the units of t and B are opposite (reciprocals). If t is in days, then B is the days1. The Nomograph Part 3 (Figure 15-62C) may be used in a number of ways. For example, what will the fouling resistance, Rt, be after an arbitrarily chosen time, t, or it can calculate the thickness of a fouling deposit after an arbitrarily chosen time t, providing the thermal conductivity of the deposited material is known. It can calculate thermal conductivity of a deposit, providing thickness is known, or estimated.

148

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-62C Fouling Nomograph, Part 3. Final and practical calculation for fouling factor; use in conjunction with Figures 15-43A and 15-43B. (Used by permission: Zanker, A., Hydrocarbon Processing. March 1978, p. 148. ©Gulf Publishing Company, Houston, Texas. All rights reserved.)

And, finally, it can answer: after how much time will the fouling resistance achieve a desired percentage of the asymptotic fouling value, R*? The simplest calculation is to find the unknown fouling resistance after a time t. For this purpose, the nomograph is used as follows: 1. Connect, with a ruler, the known values of B and t on the appropriate scales. Extend this line up to the intersection point with Reference Line 1. Mark this as Point A. 2. Transfer Point A from Reference Line 1 to Reference Line 2, using the oblique tie-lines as a guide. Mark as A1 the transferred point. 3. Connect Point A1,with a ruler, to the known value of R* on the appropriate scale. Extend this line up to the intersection with the Rt scale. Read the final result, Rt, at this intersecting point. 4. If the thickness of deposit Xt is the desired value, and the conductivity, K is known, connect with a ruler the value of Rt to the known value of K on the appropriate scale and read the thickness Xt at the intersection point of this line with the Xt scale. Conversely, if the thickness Xt is known and the value of conductivity is desired, it can be easily found. The Nomograph Part 3 may also be used to predict when the fouling resistance will reach an appropriate percentage of the asymptotic R*, or any desired R value.

The procedure for this purpose is as follows: 1. Find the desired or calculated R value on the Rt scale and connect it with the known value of R* on the R* scale; extend this line up to the intersection with Reference Line 2. Mark this Point A1. 2. Transfer Point A1 from Reference Line 2 to Reference Line 1 using the oblique tie-lines as a guide. Mark the transferred Point A. 3. Connect Point A to the known value of B on the appropriate scale. Read the final result, t, at the intersection point of this line with the t scale. where: Rt ¼ Fouling resistance at time T, (h) (ft2) (
F)/Btu R* ¼ Asymptotic value of fouling resistance, (h) (ft2) (
F)/Btu t ¼ time, corresponding to the fouling resistance, Rt, (any units) B ¼ Constant, describing the rate of fouling, (any time units)1 (the constant B, is measured in the reciprocals of the same time units, as t) e ¼ Base of natural logarithms, (2.71821). As a simplification it is assumed that: Rt ¼ Xt/K Xt ¼ Thickness or deposit formed at time t (ft) K ¼ thermal conductivity of deposited material, (Btu/(h) (ft) (
F)

Heat Transfer Chapter | 15

Ganapathy [141] presents a working chart, Figure 15-63, to plot actual operating Ua values to allow projection back to infinity and to establish the “base” fouling factor after the operating elapsed time. Note that the flow rate inside or outside the tubes is plotted against the overall heat transfer coefficient, U. For a heat exchanger in which gas flows inside the tubes [144].  (15-127) 1 U ¼ A W0:8 þ B

149

and for gas flowing over or outside plain or finned tubes:  1 U ¼ A W0:6 þ B (15-128)

upon historical performance data or real time data, can ensure improvement in the design procedures of heat exchangers, and Waters et al. [325] have employed such a monitoring technique using KBC proprietary software at the Irving Oil refinery in Canada. Figure 15-64 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:   (15-129) Rt ¼ RN 1  ebt

where:

where:

U ¼ overall heat transfer coefficient, Btu/(h) (ft ) (
F) W ¼ flow rate of the fluid controlling the heat transfer, lb/h B ¼ constant, equal to fouling factor at infinity flow rate F or ff ¼ fouling factor 2

As the value of B or the fouling factor increases with time, the engineer can determine when the condition will indicate that cleaning of the exchanger is required. Gas flows are used because usually the gas film controls in a gas-liquid exchanger. Bott [324] proposed that good fouling management, such as the use of continuous and reliable monitoring based

Rt ¼ fouling resistance at time t, m2.K/W RN ¼ asymptotic fouling resistance, m2.K/W b ¼ undetermined constants t ¼ time, s. Considerable interest in fouling crude oil pre-heat trains (PHT) has resulted in the setting up of a consortium of researchers from institutions, oil companies and industrial partnership via The Engineering Science Data Unit (HIS ESDU), with the sole aim of providing a platform to investigate the fundamental parameters leading to deposition, to provide a framework for predicting deposition and avoiding it by design and to formulate methods of

FIGURE 15-63 Keep track of fouling by monitoring the overall heat transfer coefficient as a function of flow rate. (Used by permission: Ganapathy, V., Chemical Engineering, Aug. 6, 1984, p. 94. ©McGraw-Hill, Inc. All rights reserved.)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

naphthenes, aromatic hydrocarbons and asphaltenes. The crude oils can be classified to its measured API gravity (see Vol. 2, 4th ed. of this series). Heavy oils contain much higher proportions of asphaltenes and sulfur than medium or light oils and they tend to foul at a faster rate.

Crude Blending

FIGURE 15-64 Typical fouling trend chart for a refinery shell and tube exchanger.

mitigation [326]. Fouling in service is often a combination of two or more mechanisms. Also, one mechanism may be an initiator of another mechanism. Fluids can be categorized into three groups according to their potential for fouling [327]: 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 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, the flow area is reduced and the 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.

Crude Oil Fouling in Pre-heat Train Exchangers Crude Type The crude oil is a mixture of a large number of hydrocarbons. The most commonly found molecules are paraffins,

An important factor that influences fouling is crude blending. This can cause unstable mixes which precipitate species such as asphaltenes and result in rapid fouling. The crude oil incompatibility and the precipitation of asphaltenes on blending of crude oils can result in significant fouling and coking in the crude pre-heat train. Wiehe et al. [328] have developed a crude oil compatibility model, and tests to predict the proportions and order of blending of oils that will avoid incompatibility. Saleh et al. [329] further studied the effect of mixing and blending crude oils under certain operating conditions with the intention of using the results to guide a fouling mitigation strategy. Crude oil refining takes place in the distillation unit, where the incoming crude is first heated up and split into its main fractions. This uses a large amount of energy. Attempts have been made to recover as much as possible of the energy from the product streams of the crude distillation unit (CDU) and other refinery units by means of a network of heat exchangers, often referred to as the PHT. Figure 1565 shows a schematic of a typical CDU with pumparounds. Crude oil contains many organic substances that deposit as fouling layers in the heat exchangers when heated. The material deposited ranges from gel-like to solid-like and often changes its properties over time. The fouling deposit growth that occurs over a period of time reduces the energy recovery and invariably increases the energy demand (e.g. via the furnace prior to the CDU in Figure 15-65), incurring an extra cost of fuel and carbon dioxide (CO2) emissions. Fouling of tubes in the heat exchangers requires extra pumping power to overcome the pressure drops (Dps), and as the furnace reaches its maximum capacity (firing limit), the crude oil throughput must be throttled back, with serious economic impact. Periodically, an individual heat exchanger is then taken out of service and cleaned, thus affecting production and raising health and safety concerns. The economic cost of crude oil fouling in the refinery worldwide is enormous, estimated to be of the order of US$4.5 billion [330]. In the US it has been estimated around US$1.2.billion per annum e this figure being estimated at a time when CO2 emissions were not costed. Further, the cost of pre-heat train fouling in one 160,000 bbl/day Total Refinery Co., plant was estimated to be US$1.5 million. Other estimates state that the energy equivalent of some 0.25% of all oil production is lost to fouling in the pre-heat train. This is equivalent to one day’s production loss per annum (85 million barrels on a

Heat Transfer Chapter | 15

151

Desalter

Heavy gas oil

Light gas oil

Bottom pump around Gases Top pump around

Naphtha Kerosene

Bottom pump around

Light gas oil

Residue Heavy gas oil

Kerosene

Furnace

Top pump around

Residue

Storage

FIGURE 15-65 Schematic diagram of typical crude distillation unit.

worldwide basis). The main benefits to refiners of reducing fouling is the increased capacity of their products and massive savings due to reduced fouling and cleaning. Preheat train exchanger performance is essential in reducing the fuel consumption in the downstream furnace, and supplying uniform crude flow rates to the furnace over a run cycle. The second important process unit in a refinery is the naphtha hydrotreater. The process stream in a hydrotreater reacts with hydrogen in the presence of a catalyst at elevated temperatures and pressures to remove sulfur and nitrogen. The major fouling in this unit occurs in the feedeffluent heat exchangers. In these heat exchangers, cold naphtha feed is preheated using the hot product effluent (Figure 15-66). Fouling in the feed-effluent heat exchangers can decrease the outlet pre-heat temperature of naphtha, leading to greater fuel consumption in the furnace, and/or possibly a reduction in the naphtha flow rate. The last process unit in which heat exchangers are used as feed-effluent heat exchangers is the reformer unit (Figure 15-67). Here, a catalytic process is designed to increase the anti-knock quality of the naphtha streams. The dehydrogenation process in this unit converts the napthenes to aromatics. Again, fouling in the pre-heat exchangers plays a vital role in reducing the heat transfer coefficient, by 25e30% in the first quarter, and to as low 50% in the second quarter after start-up. Extra fuel costs in the downstream furnace, as well as maintenance and cleaning costs of heat exchangers, affect the overall plant operating costs. Companies often employ anti-fouling agents in the process streams to reduce

the fouling tendencies and improve the overall plant economics. Further, the impact of crude oil fouling is starting to affect all oil companies, as heavier crudes, which are more difficult to process, are being used to a greater extent, as compared to the lighter crudes that are today becoming scarcer. Further, the worldwide shortage of middle distillates means that heavier, dirtier crudes are being processed, resulting in greater fouling problems. In order to mitigate crude oil fouling in PHT, Engineering Sciences Data Unit (IHS ESDU, UK) has set up an international Oil Industry Fouling Working Party of oil companies and their suppliers with collaboration with the Universities of Bath, Imperial College and Cambridge. In the US, similar groups include those at Heat Transfer Research Inc., where a pilot-scale facility has been constructed, and at the Argonne National Laboratory (ANL). Experiments have considered the effects of surface temperature, velocity and heat flux, and the effectiveness of in-tube inserts. Others have considered physical measurement methods, and modeled the influence of fouling rates on the film temperature, fluid velocity, wall shear stress, etc. The mechanisms by which fouling occurs vary across the temperature span of the train. Upstream of the desalter, the deposition of waxes and salts is important. At the high temperature end of the train, fouling is usually caused by chemical reactions. Considering the heat recovery performance, a reduction in recovery at the lower temperature part of the train is partially compensated by increased temperature driving force, and therefore increased recovery

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

550 – 800oF Reactor 550 – 800oF

Preheat Furnace

300-500oF

To reformer or product blending Naphtha feed from storage or Crude distillation unit

75 – 300oF Feed / Effluent exchangers

FIGURE 15-66 Schematic diagram of a Hydrotreater.

in the downstream exchangers. Therefore, in terms of energy efficiency, heat transfer at the hot end of the train is most important and investigation in developing mitigation is concentrated on the high temperature end of the process. There are a number of excellent reviews of fouling in heat exchangers and heat exchanger networks [331]. In crude oil pre-heat service, Heat Transfer Research, Inc. (HTRI) has inferred that fouling depends primarily on velocity, surface temperature and the relative amounts of saturates, asphaltenes, resins and aromatics [332]. Nesta and Bennett [333] have suggested that, provided the crude oil being processed is at a temperature below 570
F (300
C), the shear stress generated by using a tube-side velocity of 6.6 ft/s (2 m/s) will be sufficient to suppress fouling. However, Polley et al. [334] have discounted this suggestion and reported that measurements in compact heat exchangers found that fouling was not fully suppressed under shear stress conditions, but were greater than this recommended value [335]. Further, Polley et al. [336] showed that crude oil fouling at the hot end of a pre-heat train is dependent on both wall temperature and shear stress. They reported cases where at higher flow velocities (i.e., > 2 m/s), high fouling rates occur because of high wall temperatures. These inferences illustrate the importance of considering fouling rates in both individual exchanger design and pre-heat train structure, as the designer needs to

consider the velocities within an individual exchanger; the use of high flow velocities throughput in a pre-heat train could result in excessive pumping power requirements [337]. HTRI concluded that depending on conditions, crude oil fouling can be either much greater or much less than the TEMA recommended fouling factors [332]. The conceptual approach in Pinch analysis assumes that the system operates in a steady state, and incorporates fouling by oversizing heat exchangers on the basis of fouling factors (such as the fouling factors of TEMA). Rigorous numerical design methods have generally omitted fouling behavior considerations, as both techniques give fouling as a later consideration with something that requires to be reviewed when performance decreases and immediate actions are required. Traditional energy integration techniques favor an exchange of heat between the hot streams or hot utilities and cold streams at the highest temperature in order to construct vertical alignment of the matches in the composite curve. In CDU, the method employs the splitting of a cold stream, i.e. the crude oil stream, which is required to be in contact with multiple hot streams from the outlet of the distillation column (Figure 15-65). Where pumparound streams are used as a source of heat, exchanger by-passes on the crude side are necessary to maintain a fixed duty, resulting in lower crude flow rates in the heat exchangers. As a result, the use of Pinch analysis

Heat Transfer Chapter | 15

153

Reactors 880 – 960oF

200 – 300oF

880 – 960oF

Reheat Furnace

Reheat Furnace

o

Preheat Furnace

300-500 F

Naphtha feed from Hydrotreater

200 – 300oF Feed / Effluent exchangers

FIGURE 15-67 Schematic diagram of a Reformer Unit

results in the heat exchanger network (HEN) with the highest heat exchanger surface temperature and low flow velocity, both increasing the fouling rate. Pinch analysis provides the HEN that has the highest heat recovery in clean conditions, but it does not provide a network that mitigates fouling. Therefore the subsequent deposition of fouling on pre-heat train exchangers results in a less efficient network over time [338,339]. Pinch technology is reviewed in Chapter 16. Experimental studies by Knudsen et al. [340] have demonstrated that the temperatures encountered at the hot end of crude pre-heat trains resulted in fouling, which once established can rapidly develop. The fouling rate increases as the extent to which the wall temperature exceeds that require for initiating fouling increases.

Crude Oil Fouling Models Mathematical models have been developed to predict the fouling rates as a function of key design and operational

parameters. A large number of semi-empirical models for crude oil fouling have been reported in the literature [341,342,343,344,345,346,347], developed using experimental data from laboratory test rigs. The models describing fouling are usually based on the concept proposed by Kern and Seaton [341], where the net fouling rate is the difference between the rates of deposition and removal. Fouling rate ¼ Rate of deposition  Rate of removal. Crittenden and Kolaczkowski [342] developed a transport-reaction model by considering chemical reactions as well as the transport of fouling precursors to and from the heated surface. They modified their model to include a back diffusion term [343]. Epstein [344] observed that at time zero, it is fundamentally difficult to justify the finite concentration of foulant at the surface which would be required for back diffusion to occur. He developed a model for the initial chemical reaction fouling rate at a surface in which the surface attachment is proportional to the

154

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

residence time of the fluid at the surface. The greater the residence time, the greater is the opportunity for chemical reaction to occur. The relationship between the initial fouling rate and the mass flux is given by:
 dRf mf ¼ (15-130) dt t¼0 k f rf where, m is the stoichiometric factor, rf the foulant density, kf the thermal conductivity of foulant and f is the deposition mass flux. The driving force for the mass transfer from the bulk fluid to the heater surface of foulant precursor was expressed as the difference between its bulk and surface concentrations, Cb and Cs respectively. The deposition mass flux is given by: f ¼ 

Cb    1=2   00  n1  2 f m exp E=RT r u k0 S2=3 u f þ k s Cs c (15-131) 0

00

where k and k are constants, Sc is the Schmidt number, f is the friction factor, r is the fluid density, m is fluid viscosity and n is the order of the reaction plus attachment process. Epsteins’s model showed an excellent fit to Crittenden’s data for initial fouling rates of polymerization of styrene, as it was able to explain the effects of temperature and velocity. However, the model could not be used for describing crude oil fouling due to the order of the reaction, and also because the attachment terms, n and Sc are unknown for crude oil fouling. Further, it was difficult to isolate the key precursors of fouling, as crude oil has a complex composition, and this creates difficulty in finding out the concentration of exact precursor and its role in fouling. Yeap et al. [339] reduced Epstein’s model to a functional group of dimensional parameters, A, B, C and E for turbulent flow conditions, with mean velocity u, and a mass transfer related removal term by: dRf A Cf u Ts2=3 r2=3 m4=3 ¼  Cu0:8 dt 1 þ B u3 C2f r1=3 m1=3 T2=3 exp ðE=RTs Þ s (15-132) The form of the denominator in Equation 15-132 enables the model to describe data sets where mass transfer dominates and fouling increases with flow rate, which arise in a small number of situations. They estimated the parameters of the above model using plant data from a UK refinery that processes mainly light to medium North Sea crudes. Various models have been proposed in the concept of threshold fouling conditions for crude oils, including Ebert and Panchal’s model for predicting the linear rate of fouling as a function of film temperature and fluid velocity [345]. The concept suggests that chemical reaction fouling in crude oil heat exchangers is the result of two opposing mechanisms: formation and removal. The formation or

deposition rate depends on the temperature of the heat transfer surface. Foulants are formed by chemical reaction of the crude oil near heat transfer surfaces. The removal or suppression mechanism is related to the transport of foulants away from the surface before deposition occurs. The removal rate depends on the flow velocity, such that when the rate of formation is higher than the rate of removal, significant fouling occurs. However, if the removal mechanism dominates, fouling deposition is negligible. The onset of the fouling process or fouling threshold occurs when both mechanisms are balanced. Ebert and Panchal’s model is represented by: Fouling rate ¼ deposition rate  suppression rate zfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflffl{  z}|{ dRf E  g sw ¼ a Reb exp (15-133) dt RTf where Rf is the thermal fouling resistance, Re the Reynolds number of the fluid, R is the gas constant, Tf the film temperature and sw, the wall shear stress; a; b, E and g are constants to be determined from the experimental data. This model was originally developed using the Exxon crude oil slip stream coking data obtained by Scarborough et al. [346]. This model assumes that foulant forming reactions occur in the thermal boundary layer at a mean film temperature, Tf, foulant is transported by diffusion and turbulent eddies from the boundary layer to the bulk flow and the net rate of deposition is the difference between the rate of formation and rate of removal. This model allowed users to estimate operating conditions where the fouling rate would be close to zero, termed the threshold fouling conditions. The threshold fouling curve is determined by setting Equation 15-133 to zero, and calculating the film temperatures for a wide range of wall shear stresses. However, the model ignores the effect of crude oil thermal conductivity and specific heat, and only considered the effect of crude oil density and viscosity through Reynolds number. Panchal et al. [347] modified the Ebert and Panchal model by incorporating the Prandtl number.  dRf E 0:66 0:33 ¼ a Re  g sw Pr exp (15-134) dt RTf and: Tf ¼ Tb þ 0:55ðTs  Tb Þ where: E ¼ activation energy, J/kg R ¼ universal gas constant ¼ 8.314 kJ/mol.K Re ¼ Reynolds number Rf ¼ fouling resistance, m2.K/W Pr ¼ Prandtl number Tf ¼ film temperature, K Ts ¼ surface temperature, K.

(15-135)

Heat Transfer Chapter | 15

Tb ¼ bulk temperature, K t ¼ time, h a, g ¼ undetermined constants with units (m2.K/kW.h) and (m2.K/kW.h.Pa)

 2 sw ¼ wall shear stress, N/m2. f$r u2 f ¼ friction factor u ¼ tube-side fluid velocity r ¼ fluid density. Equation 15-134 considers fouling resistance, Rf as the sum of two terms. A deposition term represents a chemical reaction whose rate is given by an Arrhenius type expression with activation energy E and pre-exponential factor, a. A suppression term, which antagonizes deposition, depends on the wall shear stress sw (hence fluid velocity) according to a proportionality constant g. These constants are typically fitted to operating data. The first term on the righthand side of Equation 15-134, which is related to chemical reaction, promotes fouling. The second term acts to mitigate fouling. However, if the first mechanism dominates the second, deposition will occur. The threshold where the net rate is zero occurs where these mechanisms are balanced ði:e: dRf =dt ¼ 0Þ. Below this threshold, no significant fouling will occur. The parameters in these models are obtained by regression of pilot plant or operating data to yield the threshold conditions. Therefore, for a given velocity, once the film temperature exceeds the threshold value, the deposition term dominates and fouling will occur, becoming more severe as the surface temperature increases. This is in contrast to the asymptotic fouling concept described quantitatively by Kern and Seaton [341], which describes limiting conditions where the thickness of a deposit results in a zero net growth rate. Asymptotic fouling provides a suggested extent of fouling as described by a fouling factor such as the TEMA values that do not change over time and results in an exchanger being oversized. The Ebert-Panchal model cannot be directly used for modeling and predicting fouling within exchanger shells. This is because it assumes that the suppression mechanism is controlled by wall friction, which cannot be estimated from shell-side pressure drop, as this includes a significant contribution from drag. One approach is to apply the heat and mass transfer analogy and thereby employ the shellside heat transfer coefficient as a measure of the wall friction and shear stress. This approach has been used in assessing the use of a helical baffle with crude oil flowing on the shell-side of the exchanger. The existing exchanger models suffer from several limitations, such as the underlying thermal model and thermophysical properties of the oil, including density, viscosity and heat capacity. Further, the heat transfer coefficient is assumed to be constant, and the models include many other approximations, which severely limit their overall accuracy and thus their applicability. Coletti and

155

Macchietto [338] recently proposed a novel model for heat exchangers undergoing crude oil fouling, which overcomes several limitations of previous models. They combined Equation 15-134 with a detailed dynamic and distributed thermal model for a multipass shell and tube unit developed from first principles. Their model accounts for exchanger geometry and configuration, the variation in fluid temperature, velocity, physical properties and fouling rate along the length of each unit, the distinct growth of the deposit layer at different points and it also captures the interactions between the fouling layer growth and the fluid dynamics. This model has been validated against refinery data over a wide range of operating conditions with excellent results. Polley et al. [348] have provided a new design approach for shell and tube heat exchangers in refinery pre-heat trains which uses dynamic crude oil fouling models rather than conventional fouling factors to yield designs that are capable of achieving a specified operating period between cleaning operations. Polley et al. made modifications to the Ebert and Panchal model incorporating the tube wall temperature in the fouling formation as:  dRf E ¼ a Re0:8 Pr0:33 exp  gRe0:8 (15-136) dt RTw where: E ¼ fouling activation energy, kJ/mol R ¼ gas constant, kJ/mol.K Re ¼ Reynolds number Rf ¼ fouling resistance, m2.K/W Pr ¼ Prandtl number Tw ¼ wall temperature,
C. a ¼ deposition constant, m2K kWh1 g ¼ removal constant, m2 K/kW-h-Pa t ¼ time, h Saleh et al. [349] proposed a model as follows:  dRf E (15-137) ¼ a Prb ug exp dq RTf However, this model is only able to predict fouling without considering the effect of fluid velocity on the fouling removal. Nars et al. [350] provided an improved model in the form of the following equation:  dRf E b ¼ a Re exp  g Re0:4 (15-138) dq RTf Equation 15-138 includes two parts; the first contains a term for fouling formation and the second has a term for fouling removal due to chemical and tube wall shear stress respectively. They implied that since the heat capacity and thermal conductivity of the crude do not show remarkable differences; the proposed model does not show any severe dependence on the Prandtl number. Further, the viscosities

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

of the various crude oils tested are different and have a strong impact on their model, as the viscosity term is included in the Reynolds number. Nasr et al.’s model could identify whether or not a heat exchanger is located in the fouling zone. Additionally, these authors determined the fouling formation rate and the threshold curve, which reveal that by increasing the film temperature, a heat exchanger can be located in the fouling zone area or alternatively by increasing the fluid velocity, the heat exchanger can be expelled from the fouling zone and located in the no fouling zone area. Shell and tube exchangers remain a common design for many heat transfer duties, and it is essential to review the opportunities offered by these exchangers in operations that involve potential fouling problems. The principal disadvantage of shell and tube heat exchangers with respect to fouling is on the shell-side, where fouling is pronounced. It is essential that the tube bundle be removable, and that the tubes are arranged on a square pitch to facilitate cleaning. Baffles are included to provide support for the tubes, but principally to redirect the fluid across the tubes. The flow pattern developed on the shell-side can leave stagnant areas where deposition can occur. Further, regions of recirculation can occur thus resulting in extended residence times, with an opportunity for chemical reactions to take place, and cold or hot spots that may influence the occurrence of fouling. Therefore, careful conceptual design of the shell-side may reduce or even eliminate fouling, e.g., through the use of helical baffles, rod baffles or twisted tubes. Also, improvements to the tube-side may be made by using vibrating or fixed inserts to promote turbulence and to increase heat transfer thereby reducing the occurrence of fouling. Another approach to heat exchanger design, referred to as “envelope method,” aims to provide the required heat duty within the performance constraints of the system. The envelope method is a simplified design method for shell and tube heat exchangers that takes the problem of fouling into account [324]. The aim is to design an exchanger that achieves the required heat duty within the constraints of the stream pressure drop and other constraints that are required. For a given number of tubes and tube passes, one determines the tube-side velocity, v (m/s) that provides the allowable pressure drop (Dp). Further, a set of points relating the allowable Dp to the number and length of tubes and another set for the desired heat transfer are also calculated, as shown in Figure 15-68. All exchangers in the shaded area satisfy the criteria and are therefore valid designs. The fouling resistance, Rf can be related to the velocity v by: Rf f

1 vn

where n varies between 0.2 and 2.0 [351]

(15-139)

Valid Design Area “Envelope”

Pressure Drop

Number of Tubes

156

Exchanger with the least tubes

FIGURE 15-68 Envelope curve for a clean exchanger.

A similar graphical technique was developed to provide guidance on the allowable Dp and the geometry of the heat exchanger. The technique was extended to allow for fouling by taking into account the effects of the velocity and wall temperature Tw on the design. For a given flow rate, as the number of tubes increases, the fluid velocity decreases resulting in an increase in fouling. A relationship between fouling and velocity and to the tube count at which fouling commences can be ascertained. This is shown in Figure 15-69. All heat exchangers with tube counts above this fouling threshold line are declared to be impracticable. Thus, heat exchanger designs that are bound by certain thermal and pressure drop constraints and that consider the influence of wall temperature, Tw and velocity on fouling propensity must have tube counts below the threshold. In crude oil processing, the oil usually flows through the tubes of the exchanger. An increase in the number of tubes results in a decrease in the velocity of the crude and possibly forces the geometry above the fouling threshold line. The designer can reduce the incidence of fouling by altering the position of the threshold line to bring the exchanger back into a valid design area by modifying the baffle cut and spacing on the shell-side and altering the number of passes on the tube-side. Proper selection of construction materials can mitigate heat exchanger fouling. For example, copper alloys provide high thermal conductivity and are a popular choice for construction materials. However, in the processing of crude oil, copper tubes are highly susceptible to coking, resulting in the formation of solids that accumulate in the tubes and

Heat Transfer Chapter | 15

157

TABLE 15-30 Comparison of Fouling Resistance of No. 6 Fuel Oil

Fouling Threshold

Number of Tubes

Valid Design Area “Envelope”

Exchanger with the least tubes

Copper

Stainless Steel

Thermal conductivity, k, Btu/h.ft.
F

225.0

8.4

Heat transfer resistance, t/k, (h.ft2.
F)/Btu

0.000081

0.0004861

Fouling resistance per TEMA, Rf (h.ft2.
F)/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%

(Source: A. Corp, CEP, pp. 14, February 2006.)

FIGURE 15-69 Envelope curve with fouling in mind.

cause a loss in heat transfer efficiency. Table 15-30 summarizes the effect of accumulated coke hardcrust deposit fouling on the thermal resistance (t/k) of copper and stainless steel tubing (wall thickness t ¼ 0.049 in.). The results indicate that type 316 stainless steels, although considerably less thermally conductive than copper, have a lower fouling resistance, Rf , meaning that tubes made from them are less likely to foul, resulting in less cleaning and maintenance. Hydrocarbon coking occurs more rapidly at higher tube operating temperatures; therefore additional measures are required to ensure that fouling is minimized. It is recommended that the heating medium temperature of the hydrocarbon stream is maintained at no more than 120
F (48.9
C) above the exit temperature of hydrocarbon stream. This recommendation is also valid for asphalt and other highly viscous liquid applications. Additionally, because type 316 stainless steel contains 2% molybdenum, the tubes are immune to stress corrosion that can damage tubes when the liquid contains chlorides [352]. The complexity of the crude oil fouling mechanism and heat exchanger model are such that several attempts have been made to employ neural networks to predict fouling behavior and optimize the maintenance scheduling of preheat trains. Xie et al. [353] applied Artificial Neural Networks (ANN) to predict the temperature difference at the inlet and outlet of a shell and tube heat exchanger. Their model yielded < 2% error using 30 sets of data from 8 variables to train the model, which is equivalent to 77% of all data gathered. Radhakrishnan et al. [354] and Aminian et al. [355] applied statistical and neural networks methods to predict deposition behavior by entering historical data of

a particular heat exchanger, such as operational and maintenance data including fluid properties. These models require a lot of data, both in terms of variety and amount, to achieve a high predictive accuracy, which is normally not practical in industry. Further, the prediction period of the models seems limited compared to the amount of data used in the training step.

Tubular Exchanger Manufacturers’ Association (TEMA) and Model Approach for Fouling Resistance, Rf of Crude Oil Pre-Heat Trains The design of heat exchangers has always incorporated the thermal resistance or factors from Tables 15-25e28 recommended by TEMA to determine the area of the exchanger. This involves selecting the value of the thermal resistance due to fouling for both the hot and cold sides of the exchanger. These thermal resistances are then added to the overall heat transfer coefficient in clean conditions to calculate the overall heat transfer coefficient, and this is used to determine the area of the exchanger. However, the values from TEMA for crude oil pre-heat trains heat exchangers have been criticized by researchers as being either too high or too low. The TEMA recommended values treat fouling as a transient process, as if it reaches a steady state instantaneously with a fixed value of the thermal resistance, Rf. The heat exchanger surfaces are clean when initially put into service, so TEMA’s approach results in lower initial fluid velocities and a higher initial surface temperature due to the oversizing of the heat exchanger from the additional fouling resistance and excess heat transfer area. These two conditions have been found to accelerate fouling formation.

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It has also been established that fouling of pre-heat trains in the refinery is very costly in terms of energy recovery and maintenance, coupled with release of greenhouse gases into the atmosphere. Results from threshold modeling of crude oil have shown that the fouling resistance gives a more realistic value than the static value of TEMA. Figure 15-70 shows a comparison between the TEMA recommendation (dry crude at bulk temperature > 232
C and velocity > 1.2 m/s) and the fouling threshold model of Equation 15-134 with the fouling resistance predicted for a velocity of 1 m/s after 4000 hours of operation. From Figure 15-70, for a film temperature below 240
C, the TEMA value is far too high, so that the exchanger will be effectively oversized for considerable period of time. For film temperatures above 280
C, the TEMA value is far too low [356]. Jones et al. [357] showed from the audit of refinery performance data that some units exhibited fouling that was less than 30% of the TEMA value, while others showed values over four times greater than the TEMA value. Therefore, reasonable knowledge of expected fouling behavior is required for good exchanger design and to obtain pre-heat trains with good operability characteristics. For a preliminary design, the TEMA recommended values are still being used, however the challenge is now to employ a more effective approach to supersede the TEMA method, since their first publication in 1941. HTRI’s Exchanger Design Margin Task Force is currently involved in producing a practical supplement to the TEMA fouling factors known as the “resistance factor method.” This method aims to combine fluid design based margins with good design practice [358].

Fouling Mitigation and Monitoring The enormous costs attributed to fouling in heat exchangers have resulted in a number of preventive and control

strategies being developed. Generally, fouling is dependent on many variables; for example, in crude oil heat exchangers, it is affected by crude oil composition, inorganic contaminants, process conditions (e.g., pressure, temperature and flow rate), piping configuration and surface temperature. Therefore, effective control of these variables may minimize fouling. Effective control methods should involve: l

l

l

Preventing foulants from adhering to themselves and to heat transfer surfaces: This is attained by increasing the shear force on the heat exchanger surface, thus preventing deposits from forming. If the wall shear stress is above the threshold value of the wall temperature, little or no fouling will occur. Preventing foulant from forming: This is achievable by filtering the crude oil from the well to remove sediments as well as by improving the crude desalting process. Removal of deposits from the surfaces: This basically involves heat exchanger cleaning, achievable through mechanical, chemical or supersonic cleaning methods.

Figure 15-71A shows a fouled visbreaker shell and tube heat exchanger in a cleaning yard, Figure 15-71B shows jet cleaning of the tube bundles and Figure 15-71C shows machining of the surface of the exchanger and also indicates plugging of some of the tubes. Table 15-25 summarizes cleaning considerations for different types of heat exchangers. Figure 15-72 shows the different fouling patterns known to occur in heat exchangers. If a change in operation changes the fouling behavior of an exchanger, or re-enforces the upward trend of the saw tooth type of fouling, it is important that such a change be discovered and resolved. Master et al. [359] have discussed various mitigation techniques for fouling, and in particular the use of Helixchanger type heat exchanger. This structure

FIGURE 15-70 Comparison of fouling resistances predicted by Equation 15-133.

Heat Transfer Chapter | 15

FIGURE 15-71A A fouled visbreaker tube bundle of shell and tube heat exchanger at a cleaning yard.

consists of quadrant shaped baffles positioned at an angle to the tube axis, creating a uniform velocity helical flow through the tube bundle. They reported that near plug flow conditions are realized with little back-flow and eddies, exchanger run lengths are increased to two to three times those achieved using the conventional segmented baffles, as these are largely responsible for higher fouling rates. They further reported that heat exchanger performance is maintained at a higher level for longer periods of time, giving savings in total fuel cycle costs for owning and operating Helixchanger heat exchanger banks. Ebert and Panchal [345] have reported that there is a fouling threshold velocity, whereby operating at velocities beyond the threshold value eliminates fouling in the exchanger. Other methods of reducing online fouling are: 1. 2. 3. 4. 5.

FIGURE 15-71B Tube jet cleaning of tube bundle of a shell and tube heat exchanger.

FIGURE 15-71C Machining the surface of a shell and tube heat exchanger.

159

Treatment by adding chemicals. Use of jets of air or steam to dislodge mineral deposits. Sonic vibrations. Tube inserts. Circulation of polymer fibers.

The last three are considered for the reduction of biofouling in water systems because of their non-toxicity. The inserts which have proved effective in reducing fouling are wire mesh inserts (HiTRANTM), rotating coils (TurbotalTM) and spring inserts (SpirelfTM). For Reynolds numbers < 4,000, HiTRAN inserts provide the better enhancement, and above this value, Turbotal and Spirelf provide similar enhancement levels at significantly lower pressure drops [360,361]. In particular, laboratory studies of fouling within tubes fitted with HiTRAN inserts have been conducted by Crittenden et al. [362], and have shown that the use of such inserts can reduce fouling in crude oil systems. However, they are not recommended if the fouling is due to the precipitation of asphaltenes, as the formation of coke could reduce the effectiveness of the inserts and lead to fusion of the insert to the deposit. HiTRAN inserts can be used to reduce or eliminate sedimentation within tubes, and therefore can be used to reduce fouling in exchangers handling column residues. Both Turbotal and Spirelf inserts have been found to significantly reduce fouling in exchangers that are positioned at the hot end of operational pre-heat trains. The higher the heat recovery in a pre-heat train, the higher the bulk temperature of the crude oil and the greater the wall temperatures encountered in the heat recovery exchanger. At the highest bulk temperatures the fouling rate can be so high that regular cleaning of an exchanger is required in order to maintain production rates. TurbotalTM has successfully been applied to reduce the rate at which fouling occurs, which subsequently controls the thickness of the deposit formed and maintaining a constant fouling resistance. Aquino et al. [363] presented a modified form

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Asymptotic

Saw tooth Fouling Resistance

Delay time

Time

FIGURE 15-72 Various fouling mechanisms observed in crude refining exchangers.

of the Ebert-Panchal model for predicting the initial fouling rates in tubes fitted inserts as:  dRd hplain a E ¼ exp Rg Tf dt henhanced Re0:66 Pr0:33 DPenhanced  0:7 gsw (15-140) DPplain The deposition term in Equation 15-140 has been multiplied by the ratio of the plain tube heat transfer coefficient to the enhanced coefficient. This modification quantifies the reduced thickness of the thermal film and hence the reduction in ‘reaction volume’ assumed by Ebert and Panchal. The removal term is multiplied by the ratio of the pressure drop encountered in the enhanced tube to that in the plain tube. The 0.7 in the equation reflects that only 70% of the pressure drop encountered during flow through tubes fitted with inserts is associated with wall friction and the remainder is due to form drag. Once the deposit has filled the space between the tube wall and the rotating insert, the fouling resistance is maintained at a constant value. Materials that deposit on the surface are removed by mechanical action of the insert, and the limiting fouling resistance is determined from the insert clearance divided by the thermal conductivity of the deposit [364].

Figure 15-73 shows an idealized representation of the fouling process, in which the final asymptotic level of the curve may be regarded as the equilibrium between the rate of deposition and the rate of removal. However, in many practical situations, the actual shape of the curve differs from the ideal because of the operating conditions under which the fouling accumulates. Table 15-31 summarizes cleaning considerations for various types of heat exchangers. Note: There is an ongoing discussion among researchers and engineers in industry as to whether either fouling resistance or fouling rate concepts should be applied as the most appropriate tool in resolving design problems incurred by fouling. One suggestion in resolving this problem would be that the design fouling resistance values used for sizing heat exchangers be based on fouling rate data and estimated cleaning time intervals.

HIS smartPM Software ESDU, UK, which is technology transfer partner of the UK Government funded Crude Oil Fouling (CROF) research program with its oil company members, working closely with a research team at Cambridge University, have developed network thermo-hydraulic simulation methods

Heat Transfer Chapter | 15

161

Deposit Thickness

Asymptotic or Equilibrium Fouling

Exponential Deposition

Initiation or Conditioning

Time FIGURE 15-73 Idealized fouling curve.

TABLE 15-31 Some Considerations for the Choice of Heat Exchanger Design [324] 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 heattransfer 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 for slurries and fouling conditions

Graphite Block

Graphite

Impossible to clean mechanically, chemical cleaning possible

Useful for corrosive conditions

Scraped-Surface

Most materials

Self-cleaning generally

Incorporates moving parts

Plate-Fin

Aluminum, stainless steel, titanium

Only chemical cleaning possible

Highly compact

Air-Cooled

Aluminum fins on carbon steel tubes common, other combinations possible

Inside tubes relatively easy, finned surface more difficult

Large plot area required.

that include fouling models, and are incorporated into the EXPRESS plus software. The software has eight main modes of operation, namely: network construction, monitoring data reconciliation, fouling analysis mode, fixed rate crude fouling simulation, dynamic crude fouling simulation, cleaning schedule e optimum for maximum profit, cleaning schedule, network redesign for improve performance.

The various models described earlier have reinforced the notion that the use of a fixed set of fouling factors for the design of shell and tube heat exchangers for crude pre-heat trains is no longer an acceptable practice. In some cases, their use results in designs that yield fouling unnecessarily, while in others they under predict fouling by a very large margin. Use of heuristics such as the minimum velocity is used to overcome the fixed set of fouling factors,

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TABLE 15-31A Thermal Conductivity of Metals Used in Heat Exchangers Heat Exchanger Tube Material

k, W/m-K

k, Btu/hr-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

otherwise fouling models would be a rational way forward. Wilson et al. [360] have provided examples using ESDU’s ExpressTM software.

Effect of Fouling on Exchanger Heat Transfer Performance The influence of fouling on heat exchanger performance can be determined in terms of: 1. Required increased surface area for the same heat transfer rate, q and mean temperature difference, DTmin . 2. Required increased mean temperature difference for the same q and surface area A. 3. Reduced heat transfer rate for the same A and DTmin . The following expressions used in these approaches are Af =A; DTm;f =DTm;c ; and qf =qc . In the first two cases, the heat transfer rate in a heat exchanger under clean and fouled conditions are the same. Therefore, q ¼ Uc Ac DTm ¼ Uf Af DTm

for constant DTmin (15-141)

Thus: Af Uc ¼ Ac Uf

(15-142)

where: c ¼ clean surface f ¼ fouled surface The relationships between the overall heat transfer coefficients (based on the tube outside surface area) and thermal resistances for clean and fouled conditions are defined as follows. For a clean heat transfer surface: 1 1 b w Ao þ 1 Ao ¼ þR Aw hi;c Ai Uc ho;c

(15-143)

For a fouled heat transfer surface: 1 1 bf þ R bw ¼ þR Uf ho;f 1 bf þ R bw ¼ þR ho;c

Ao 1 þ Aw hi;f Ao 1 þ Aw hi;c

Ao Ai Ao Ai

(15-144)

Note the expressions ho;f ¼ ho;c ; hi;f ¼ hi;c ; Ai;f ¼ Ai;c ¼ Ai and Ao;f ¼ Ao;c ¼ Ao . Here, Ao represents the tube outside surface area, and not the free-flow area in the exchanger. The difference between Equation 15-143 and 15-144 is: bf ¼ 1  1 R Uf Uc

(15-145)

Equation 15-145 is valid as long as clean overall heat transfer coefficients are constant. If this assumption is not satisfied, the right-hand side of Equation 15-145 does not represent only the overall fouling resistance, but a quantity that includes other influences on overall heat transfer coefficients in addition to fouling. In such a case, the fouling assessment will be incorrect. Rearranging Equation 15-145 gives: Uc bf þ 1 ¼ Uc R Uf

(15-146)

Substituting Equation 15-142 in Equation 15-146 gives: Af bf þ 1 ¼ Uc R Ac

(15-147)

Similarly, when q and A are the same and DTmin is different for clean and fouled exchangers, we have: q ¼ Uc Ac DTm;c ¼ Uf Ac DTm;f

for constant A (15-148)

Heat Transfer Chapter | 15

163

FIGURE 15-74 Percent change in heat transfer area, mean temperature difference, or heat duty vs. fouling unit thermal resistance for a fouled exchanger.

Hence:

DTm;f Uc ¼ DTm;c Uf

(15-149)

Substituting Equation 15-149 into Equation 15-146 gives: DTm;f bf þ 1 ¼ Uc R DTm;c

Uf ¼ CF:Uc

(15-154)

(15-155)

Substituting Equation 15-155 into Equation 15-145 gives: bf ¼ R

(15-151)

1 1  Uc CF Uc

or: 1 Rf ¼ Uc



1 1 CF

(15-156)

(15-157)

(15-152)

Alternatively, Equation 15-152 can be expressed by: qf 1 ¼ bf þ 1 qc Uc R

Uf 1 ¼ b f Uc Uc 1þR

or:

Again, substituting Equating 15-151 into Equation 15-146 gives: qc bf þ 1 ¼ Uc R qf

CF ¼

(15-150)

For the final condition, if one assumes that heat transfer area and mean temperature differences are fixed, heat transfer rates for the same heat exchanger under clean and fouled conditions are given by qc ¼ Uc A DTm and qf ¼ Uf A DTm respectively. Then, qc Uc ¼ qf Uf

Figure 15-74, it is obvious that fouling has a significant bf impact on the exchanger performance for high values of R and/or Uc. A factor referred to as the cleanliness factor, CF, b f as: relates to the fouling resistance R

(15-153)

We notice that the right-hand sides of Equation 15-147, 15-150 and 15-152 are the same. Equations 15-147, 15-150 and 15-153 are shown in Figure 15-74 in terms of the percentage increase in A and DTmin and the percentage reduction in the heat transfer rate q, for the fouled exchanger over that for the clean exchanger. From

Effect of Heat Transfer Area for a Change in Fouling Resistance For a given heat transfer rate, overall clean heat transfer coefficient, constant mean temperature differences under clean and fouled conditions, but a change in the fouling b f;2 , the corresponding change b f;1 to R resistance from R in surface area due to fouling can be determined from Equation 15-147 as follows: Af bf þ 1 ¼ Uc R Ac

(15-147)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

b f;1 However, a change in total fouling resistance from R b f;2 causes a change in heat transfer area from Af;1 to to R Af;2 . For this condition, Equation 15-147 becomes: Af;1 b f;1 þ 1 ¼ Uc R Ac

and

Af;2 b f;2 þ 1 (15-158) ¼ Uc R Ac

From Equation 15-158, we have: Af;2 Uc Rf;2 þ 1 ¼ Af;1 Uc Rf;1 þ 1

(15-159)

Equation 15-159 shows the factor by which the surface area can be increased or decreased due to a corresponding increase on decrease in the fouling resistance.

EXAMPLE 15-13

The overall heat transfer coefficient of a heat exchanger operating under clean conditions is calculated as 900 W/ m2.
C. Following industrial experience, the cleanliness factor, CF for this exchanger is found to be 0.8. Determine the magnitude of the corresponding fouling resistance. Solution b f of Given: Uc ¼ 900 W/m2.
C and CF ¼ 0.8 Determine R the deposit formed by this exchanger. Assumptions: The convective heat transfer coefficients on the cold and hot sides are the same for both fouled and clean heat transfer surfaces. The thermal resistance of the wall is unchanged under fouled conditions. The change in heat transfer surface areas due to fouling deposit formation is negligible; fin efficiency is equal to 1.0, and all idealized conditions for the heat exchanger design theory are valid. The relationship between fouling resistances and overall heat transfer coefficients for clean and fouled conditions is given by Equation 15-145 as: bf ¼ 1  1 : R Uf Uc Uf 1 ¼ From the definition of CF as: CF ¼ b f Uc Uc 1þR 1 1 bf ¼ Uf ¼ CF  Uc and R  CF  Uc Uc  1 1 1 (15-157) ¼ Uc CF  1 1 m2 :o C  1 ¼ 2:78  104 ; ¼ 900 0:8 W Comments: In some industries such as the power industry, use of the cleanliness factor is common for assessing the influence of fouling. The reason is the difficulties associated with experimental determination of fouling thermal resistances. Equation 15-157 can be used to calculate fouling resistance or unit thermal resistance if the

cleanliness factor is known or vice versa under the conditions governed by the above-mentioned assumptions.

EXAMPLE 15-14

Determine how much will the required heat transfer area of an exchanger change under fouling conditions if the fouling resistance changes from 104 m2.
C/W to 103 m2.
C/W. The heat transfer rate and mean temperature differences remain the same, and Uc ¼ 1800 W/m2
C. Consider no extended surfaces on either fluid side of the exchanger.  Given: Uc ¼ 1800 W m2 :
C  b f;1 ¼ 104 ; m2 :
C W R  b f;2 ¼ 103 m2 :
C W R qc ¼ qf ; DTm;c ¼ DTm;f h0;1 ¼ h0;2 ¼ 1 Solution Assumptions: The convective heat transfer coefficients are the same for fouled and clean heat transfer surfaces. The thermal resistance of the wall is unchanged under fouled conditions. The change in heat transfer surface areas due to deposit formation is negligible. All assumptions that were adopted for heat exchanger design theory are valid. The heat transfer rate and mean temperature differences in this exchanger under clean and fouled conditions are the same. Hence, from Equation 15-147, we have: Af bf þ 1 ¼ Uc R Ac

(15-147)

This shows that the change in total fouling resistance b f;2 causes a change in heat transfer area from b f;1 to R from R Af;1 to Af;2 Af;1 b f;1 þ 1 ¼ Uc R Ac

and

Af;2 b f;2 þ 1 ¼ Uc R Ac

(15-158)

From Equation 15-158, we have: Af;2 Uc Rf;2 þ 1 ¼ Af;1 Uc Rf;1 þ 1 1800  103 þ 1 ¼ ¼ 2:37 1800  104 þ 1

(15-159)

Thus an increase in the fouling resistance by a factor of 10 requires that the surface area increases by a factor of 2.37. This shows a significant increase in the surface area requirement for the exchanger when the total fouling resistance is increased by an order of magnitude. Correspondingly, a significant reduction in surface area can be achieved if the total fouling resistance is reduced by an

Heat Transfer Chapter | 15

order of magnitude. The case of a reduction of fouling resistance to 105 m2.
C/W requires that the surface area decreases by a factor of 0.86. This result provides direct information on how large a factor change in heat transfer area would be, compared to a clean heat exchanger for a given fouling resistance, as shown in Figure 15-74.

Prevention and Control of Liquid-Side Fouling A heat exchanger should be designed to minimize or eliminate fouling. An example is heavy fouling liquids, which can be handled in a direct contact heat exchanger since heat and mass transfer takes place due to direct contact of the fluids over the surface or “fill” in such an exchanger. The fill can be fouled without affecting the energy transfer between the fluids in direct contact [327]. Gasketed plate and frame heat exchangers can be easily disassembled for cleaning. Compact heat exchangers are unsuitable for fouling service unless chemical cleaning or thermal baking is possible. For a shell and tube heat exchanger, the following considerations are essential for reducing fouling. The heavy fouling fluid should be placed in the tube-side for cleanability; horizontal heat exchangers are easier to clean than vertical ones. Geometric configurations on the shell-side should be such to minimize or eliminate stagnant and low velocity regions. Additionally, it is easier to clean square or rotated square tube layouts mechanically on the shell-side [with a minimum cleaning lane of 1/4 in. (6.35 mm)] than it is to clean other types of tube layouts. Measures taken to control fouling phenomena are: Particulate fouling: use a filter or similar device to capture all particles greater than about 25% of the smallest gap size in the flow path. Eliminate any dead zones and low velocity zones. Chemical reaction fouling: Chemical cleaning is the most effective cleaning method. Corrosion fouling: Select a suitable corrosion-resistant material. For example, use proper aluminum alloy to prevent mercury corrosion in a plate-fin exchanger. Reduced fouling rates have been observed with noncorrosive alloys and a smooth surface is obtained by surface treatments, such as chrome plating [363]. Copper and its alloys also reduce organic growth since the material is toxic to the organisms. Biofouling: This is best controlled with biocides, but compatibility with the exchanger construction materials must be checked. Chlorination, aided by flow-induced

165

removal of disintegrated biofilm, is the most common mitigation method. Crystallization fouling: This is controlled or prevented by preheating the stream so that crystallization does not occur. The most frequently used techniques for control of liquid-side fouling is the application of chemical inhibitors/ additives. The list of additives includes: (a) dispersants to maintain particles in suspension; (b) various compounds to prevent polymerization and chemical reactions; (c) corrosion inhibitors or passivators to minimize corrosion; (d) chlorine and other biocide/germicides to prevent biofouling; (d) softeners, polycarboxylic acid and polyphosphates, to prevent crystal growth. Finally, filtration can be used as an effluent method of mechanical removal of particles. Heat transfer surface mitigation methods can be applied either on or offline. Online methods, usually for tube-side applications, include mechanical techniques such as flowdriven or power driven rotating brushes, scrapers, drills, acoustic/mechanical vibration, air or steam lancing on the outside of tubes, chemical feeds and flow reversal. In certain instances flows are diverted in a bypass exchanger and the fouled exchanger is cleaned offline. Other offline techniques with the heat exchanger being opened or removed from the site are: high pressure steam or water spray for a shell and tube heat exchanger; baking compact heat exchanger modules in an oven (to burn the deposits) and then rinsing. Where fouling is severe, a combination of these techniques could be applied.

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 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,

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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 fuelair 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 300
F (150
C) for sulfuric acid or hydrochloric acid condensation or below 400
F (200
C) 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 [364]. 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 < 500
F (260
C)], stainless steel and super alloys to medium- temperature corrosion [500
F (260
C) < Tgas < 1500
F (815
C)] and super alloys and ceramic materials to high temperature corrosion [Tgas > 1500
F (815
C)]. 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. Details regarding various techniques for gas-side fouling prevention, mitigation and accommodation are provided by Shah and Sekulic [327] and by Marner and Suitor [365].

Selecting Tube Pass Arrangement Analysis of refinery monitoring data shows that crude oil fouling at the hot end of a pre-heat train is a function of

both wall temperature and shear stress, as shown in Equation 15-136. Cases have been identified where even at higher flow velocities > 2 m/s, high fouling rates occur because of high wall temperatures. These have highlighted the importance of fouling rates in both individual exchanger design and pre-heat train structure. It is essential to give careful consideration to the velocities within individual exchangers, as the use of high flow velocities throughout a pre-heat train yields excessive pumping power requirements and additional Dp. Shell and tube exchangers generally use more than a single tube pass. Using a multipass exchanger, the designer can choose to have the first pass co-current with the shell-side flow or counter current to the shell-side flow. The choice does not affect the “effective mean temperature difference” used for the design. For heat exchangers used for “clean” duties this choice has no effect on heat exchanger performance. Where fouling occurs, the choice of the heat exchanger is important, as the designer needs to know the relationship between the wall temperature and fouling rate. For example, if the fouling rate increases significantly with increasing wall temperature, then a pass arrangement that minimizes the wall temperature is chosen. Wall temperature is maximized when the entering hot fluid is matched against the exiting cold fluid. Where the hot fluid is on the shell-side of a heat exchanger unit, this situation is avoided if the hot fluid enters the exchanger at the opposite end of the shell to the inlet-outlet header. Therefore, the better arrangement is the first pass in counter flow to the shellside fluid [360].

Exchanger Design It is most preferable to use a dynamic calculation for the fouling resistance/factor based on velocity, rather than a static fouling factor. Like hydrocarbons fouling, water fouling depends on velocity, temperature and composition. Tube metallurgy is also an essential contribution for untreated water where biological growth and corrosion are part of the fouling mechanism. Fouling resistance for treated cooling tower water inside carbon steel tubes can be defined by [366]: Rf ¼

0:025 v1:65

(15-160)

where Rf is the fouling factor in ft2 h.
F/Btu and v is velocity in ft/s. The actual fouling resistance can vary significantly from the static value of 0.002 ft2 h.
F/Btu that is typically stated, and it is preferable to design for high velocity 6e7 ft/s (1.8e2.1 m/s) in order to minimize fouling, instead of allowing low velocity with a large fouling resistance. Pressure drops (Dps) for the shell and tube-sides should not exceed the allowable values, and would require

Heat Transfer Chapter | 15

monitoring in all pre-heat train exchangers as these result in reduced efficiency, greater pumping costs due to the buildup of fouling resistance. Some refineries often initiate cleaning of the exchangers once Dps reach prescribed limits. If a longitudinal baffle is used in fouling service, the baffle should be welded to the shell. For removable bundles, this requires the use of U-tubes with the U-bends in a horizontal plane (normally four or more tube passes). The designer should investigate differential thermal stresses across the shell. Generally, a welded longitudinal baffle is acceptable where the shell-side temperature difference across the shell does not exceed 160
F (89
C), and the provision of bundle slide rails in both top and bottom parts of the bundle is required. In pre-heat train design, the threshold concept has been used to identify the maximum heat recovery level at which fouling can be eliminated through good design, and operating beyond this level would require either employing tube inserts or the provision of regular cleaning schedules. The threshold fouling model can be used to identify which strategy should be adopted. Identifying the heat recovery level, the fouling threshold can then be used to develop “field plots” that guide the engineer in developing an efficient pre-heat train structure. Further, the threshold concept can be used to identify geometries that are unlikely to foul and also the sensitivity of the design to changes in operating conditions. Operating below the fouling threshold is not advisable, as the model gives a useful tool for identifying better shell and tube exchanger designs from the wide range available. Great care must be exercised in the design

167

of exchangers situated at the hot end of crude oil pre-heat trains for there is a strong interaction between geometry and fouling, and energy losses associated with exchanger fouling can be very high. Studies have shown the use of inserts in reducing fouling in crude oil systems. HiTRAN inserts have been observed to reduce or eliminate sedimentation within tubes, and can therefore be used to reduce fouling in exchangers that handle column residues. Both Turbotal and Spirelf inserts have been found to significantly reduce fouling in exchangers that are positioned at the hot end of operational pre-heat trains. However, the use of inserts is not recommended if the fouling is due to precipitation or asphaltenes, as the formation of coke could further reduce the effectiveness of the inserts and result to fusion of the inserts to the deposit [361]. Photographs of heat exchangers’ fouling and cleaning are illustrated in Elsevier companion website.

OVERALL HEAT TRANSFER COEFFICIENTS FOR PLAIN OR BARE TUBES The overall heat transfer coefficient as used in the relationship Q ¼ UA Dt is the sum of the individual coefficients 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 making a new design, or they may be grouped together as U when obtaining data on an existing unit (see Tables 15-28, 29 and 32).

TABLE 15-32 Overall Heat Transfer Coefficients in Typical Petrochemical Applications U, Overall Heat Transfer Coefficient, Btu/(h) (ft2) (
F) Estimated Fouling Outside Tubes

Type Equipment

Velocities Tube

ft/s. Shell

Overall Coefficient

Temp. Range,
F

Tube

Shell

Overall

Butadiene mix. (superheating

Stream

H

25-35

.

12

400-100

.

.

0.04

Solvent

Solvent

H

.

1.01.8

35-40

110-30

.

.

0.0065

Solvent

Propylene (vaporization)

K

1-2

.

30-40

40-0

.

.

0.006

C4 unsaturates

Propylene (vaporization)

K

20-40

.

13-18

100-35

.

.

.005

Solvent

Chilled water

H

.

.

35-75

115-40

.003

.001

.

Oil

Oil

H

.

.

60-85

150-100

0.0015

.0015

.

In Tubes A. Heating

Continued

168

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-32 Overall Heat Transfer Coefficients in Typical Petrochemical Applicationsdcont’d U, Overall Heat Transfer Coefficient, Btu/(h) (ft2) (
F) Ethylenevapor

Condensate and vapor

K

.

.

90-125

600-200

0.002

.001

.

Ethylene vapor

Chilled water

H

.

.

50-80

270-100

.001

.001

.

Condensate

Propylene (refrigerant)

K-U

.

.

60-135

60-30

0.001

0.001

.

Chilled water

Transformer oil

H

.

.

40-75

75-50

0.001

0.001

.

Calcium brine-25%

Chlorinated Ci

H

1-2

0.51.0

40-60

-20-+20

0.002

0.005

.

Ethylene liquid

Ethylene vapor

K-U

.

.

10-20

-170-(100)

.

.

0.002

Propane vapor

Propane liquid

H

.

.

6-15

-25-100

.

.

0.002

Lights and choir. HC

Steam

U

.

.

12-30

-30-260

0.001

0.001

.

Unsat. Light HC, CO, CO2,HI2

Steam

H

.

.

10-2

400-100

.

.

0.3

Ethanolamine

Steam

H

.

.

15-25

400-40

0.001

0.001

.

Steam

Air mixture

U

.

.

10-20

-30-220

0.005

0.0015

.

Steam

Styrene and tars

U (in tank)

.

.

50-60

190-230

0.001

0.002

.

U, Overall Heat Transfer Coefficient, Btu/(h) (ft2) (
F) Estimated Fouling In Tubes

Outside Tubes

Type Equipment

Velocities Tube

ft./sc Shell

Overall Coefficient

Temp. Range,
F

Tube

Shell

Overall

Chilled Water

Freon-12

H

4-7

.

100-130

90-25

0.001

0.001

.

Water*

Lean copper solvent

H

4-5

.

100-120

180-90

.

.

0.004

Water

Treated water

H

3-5

1-2

100-125

90-110

.

.

0.005

Water

C2-chlor Hc, lights

H

2-3

.

6-10

360-100

0.002

0.001

.

Water

Hydrogen chloride

H

.

.

7-15

230-90

0.002

0.001

.

Water

Heavy C2-chlor.

H

.

.

45-30

300-90

0.001

0.001

.

Water

Perchlorethylene

H

.

.

55-35

150-90

0.001

0.001

.

Water

Air and water vapor

H

.

.

20-35

370-90

0.0015

0.0015

.

Continued

Heat Transfer Chapter | 15

169

dcont’d U, Overall Heat Transfer Coefficient, Btu/(h) (ft2) (
F) Water

Engine jacket water

H

.

.

230-160

175-90

0.0015

0.001

.

Water

Absorption oil

H

.

.

80-115

130-90

0.0015

0.001

.

Water

Air-chlorine

U

4-7

.

8-18

250-90

.

.

0.005

Water

Treated water

H

5-7

.

170-225

200-90

0.001

0.001

.

C4, unsat

Propylene refrig.

K

v

.

58-68

60-35

.

.

0.005

HC unsat. lights

Propylene refrig.

K

v

.

50-60

45-3

.

.

0.0055

Butadiene

Propylene refrig.

K

v

.

65-80

20-35

.

.

0.004

Hydrogen chloride

Propylene refrig.

H

.

.

110-60

0-15

0.012

0.001

.

Lights and chloriethanes

Propylene refirg.

KU

.

.

15-25

130-(-20)

0.002

0.001

.

Ethylene

Propylene refrig.

KU

.

.

60-90

120-(-10)

0.001

0.001

.

B. Condensing

U, Overall Heat Transfer Coefficient, Btu/(h) (ft2) (
F) Estimated Fouling In Tubes

Outside Tubes

Type Equipment

Velocities Tube

ft/s. Shell

Overall Coefficient

Temp. Range,
F

Tube

Shell

Over-all

Unsat. Chloro HG

Water

H

7-8

.

90-120

145-90

0.002

0.001

.

Unsat Chloro HG

Water

H

3-8

.

180-140

110-90

0.001

0.001

.

Unsat Chloro HG

Water

H

6

.

15-25

130-(-20)

0.002

0.001

.

Chloro HG

Water

KU

.

.

20-30

110-(-10)

0.001

0.001

.

Solvent and noncond.

Water

H

.

.

25-15

260-90

0.0015

0.004

.

Water

Propylene vapor

H

2-3

.

130-150

200-90

.

.

0.003

Water

Propylene

H

.

.

60-100

130-90

0.0015

0.001

.

Water

Steam

H

.

.

225-110

300-90

0.002

0.0001

.

Water

Steam

H

.

.

190-235

230-130

0.0015

0.001

.

Treated water

Steam (exhaust)

H

.

.

20-30

220-130

0.0001

0.0001

.

Continued

170

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

dcont’d U, Overall Heat Transfer Coefficient, Btu/(h) (ft2) (
F) Oil

Steam

H

.

.

70-110

375-130

0.003

0.001

.

Water

Propylene cooling and cond.

H

.

.

25-50

30-45 (C)

0.0015

0.001

.

110-150

15-20 (Co)

U, Overall Heat Transfer Coefficient, Btu/(h) (ft2) (
F) Estimated Fouling In Tubes

Outside Tubes

Type Equipment

Velocities Tube

ft/s. Shell

Overall Coefficient

Temp. Range,
F

Tube

Shell

Overall

Chilled water

Air-chlorine (part.cond.)

U

.

.

8-15

8-15 (C)

0.0015

0.005

.

20-30

10-15 (Co)

Water

Light HC, cool and cond.

H

.

.

35-90

270-90

0.0015

0.003

.

Water

Ammonia

H

.

.

140-165

120-90

0.001

0.001

.

Water

Ammonia

U

.

.

280-300

110-90

0.001

0.001

.

Air-Water vapor

Freon

KU

.

.

10-50

60-10

.

.

0.01

10-20 C. Reboiling Solvent, Copper-NH3

Steam

H

7-8

.

130-150

180-160

.

.

0.005

C4 Unsat.

Steam

H

.

.

95-115

95-150

.

.

0.0065

Chloro HC

Steam

VT

.

.

35-25

300-350

0.001

0.001

.

Chloro, unsat HC

Steam

VT

.

.

100-140

230-130

0.001

0.001

.

Chloro ethane

Steam

VT

.

.

90-135

300-350

0.001

0.001

.

Chloro ethane

Steam

U

.

.

50-70

30-190

0.002

0.001

.

Solvent (heavy)

Steam

H

.

.

70-115

375-300

0.004

0.0005

.

Mono-diethanolamines

Steam

VT

.

.

210-155

450-350

0.002

0.001

.

Organics, acid, water

Steam

VT

.

.

60-100

450-300

0.003

0.0005

.

Amines and water

Steam

VT

.

.

120-140

360-250

0.002

0.0015

.

Heat Transfer Chapter | 15

171

U, Overall Heat Transfer Coefficient, Btu/(h) (ft2) (
F) Estimated Fouling In Tubes

Outside Tubes

Type Equipment

Velocities Tube

ft/s. Shell

Overall Coefficient

Temp. Range,
F

Tube

Shell

Overall

Steam

Naphtha frac.

Annulus, long F.N.

.

.

15-20

270-220

0.0035

0.0005

.

Propylene

C2, C2

KU

.

.

120-140

-150-40

0.001

0.001

.

Propylenebutadiene

Butadiene, unsat

H

.

2535

15-18

400-100

.

.

0.02

Notes: H ¼ horizontal, fixes or floating tube sheet T ¼ thermosiphon V ¼ Vertical U ¼ U-tube horizontal bundle v ¼ variable r ¼ reboiler (C) ¼ cooling range Dt K ¼ kettle type HC ¼ hydrocarbon (Co) ¼ condensing range Dt Data/results based on actual and specific industrial equipment. *Unless specified, all water is untreated, brackish, bay or sea.

Najjar, Bell, and Maddow [162] 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 15-34 illustrates the factors affecting the overall heat transfer expressed in equation form: Uo ¼

1 r ho o

þ rw

Ao Aavg



or:

1 þ ri

 Ao Ai

 1 1 1 ¼ þ þ Uo ho hod

do ln 2kw

do di

þ

1 hi

þ h1i

 Ao Ai

(15-161)

  do 1 do þ di hid di (15-161A)

where: Uo ¼ Overall heat transfer coefficient corrected for fouling conditions, Btu/h (ft2) (
F), (W/m2.
C), and referenced to outside tube surface area ho ¼ Film coefficient of fluid on outside of tube, Btu/h (ft2) (
F), (W/m2.
C) hod ¼ Fouling factor for shell-side fluid, (W/m2.
C) hi ¼ Film coefficient of fluid on inside of tube, Btu/h (ft2) (
F), (W/m2.
C) hid ¼ Fouling factor for tube-side fluid, (W/m2.
C) ro ¼ Fouling resistance (factor) associated with fluid on outside of tube, h (ft2) (
F)/Btu [m2
C/W]

ri ¼ Fouling resistance (factor) associated with fluid on inside of tube, h (ft2) (
F)/Btu [m2
C/W] *rw ¼ Resistance of tube wall Lw/kw, h (ft2) (
F)/Btu [m2
C/W] t ¼ Lw ¼ Thickness of tube wall, in or ft (mm), as consistent **kw ¼ Thermal conductivity of material of tube wall, (Btu-ft)/[(h) (ft2) (
F)], (W/m.
C) Ao ¼ Outside area of unit length of tube, ft2/ft, Table 15-8 Ai ¼ Inside area of unit length of tube, ft2/ft, Table 15-8 Aavg ¼ Average of inside and outside tube area for unit length, ft2/ft DT ¼ Corrected mean temperature difference,
F (
C) Ao ¼ A ¼ Total required net effective outside heat transfer surface referenced to tube length measured between inside dimensions between tubesheets. rw ¼ Resistance of tube wall referred to outside surface of tube wall, including extended h surface, i if present [107] ðdÞ d In ðd2fÞ reference; [107]: *rw ¼ Also for bare tubes 24k

(h) (
F) (ft2 outside surface)/Btu d ¼ O.D. bare tube (or, root diameter of fin tube), in. (mm) di ¼ Tube inside diameter, in. (mm) do ¼ tube outside diameter, in. (mm) t ¼ Tube wall thickness, in. (mm) N ¼ Number of fins/in. **K ¼ k ¼ Thermal conductivity, Btu-ft/(h) (ft2) (
F), [W/m
C] (Note the difference in units.) for conversion, see Table 15-33A

172

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

w ¼ Fin height, in. ln ¼ Natural logarithm ** ¼ must be consistent units, also * Note: Btu/(h) (ft2) (
F/ft) ¼ 12 Btu/(h) (ft2) (
F/in.) For integral circumferentially finned tubes [107]. rw ¼

t ½d þ 2Nwðd þ wÞ 12k ðd  tÞ

(15-162)

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 (18e12 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 Tables 15-33A and B 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 ¼ (15-163)

ðhÞðft2 Þð F=in:Þ ðhÞðft2 Þð F=ftÞ and Btu/(h) (ft) (
F) ¼ Btu-ft/ (h) (ft2) (
F) Table 15-34 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 Ao 1 Ao þ ri þ (15-164) þ ro þ rw ¼ Aavg U ho hi Ai 1/ho ¼ resistance of outside fluid film 1/hi ¼ 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   Ai dit ¼ hi (15-165) hio ¼ hi Ao do This value is the used to represent the film coefficient equivalent to the converted inside coefficient, as hio. Figure 15-75 is convenient for solving for a clean U using known or estimated film coefficients only.

EXAMPLE 15-15 Calculation of Overall Heat Transfer Coefficient from Individual Components

An exchanger has been examined, and the following individual coefficients and resistances 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 Film coefficient inside tube, hi Fouling factor outside tube, ro Fouling factor inside tube, ri

¼ ¼ ¼ ¼

175 Btu/h ft2
F 600 Btu/h ft2
F 0.001 h ft2
F/Btu 0.0025 h ft2
F/Btu

Tube wall 1 in. e16 ga, Admiralty, 0.065 in. thick, kw ¼ 768 Btu/(ft2) (h)/(
F)/(in.) Inside area/ft ¼ Ai ¼ 0.2278 ft2/ft Outside area/ft ¼ Ao ¼ 0.2618 ft2/ft Uo ¼

1  1 0:065 1 0:2618 þ 0:001 þ þ 0:0025 þ 175 768 600 0:2278

1 0:00571 þ :001 þ 0:0000846 þ 0:0025 þ 0:00192     Uo ¼ 1 0:01121 ¼ 89:17 Btu h ft2 ð
FÞ

Uo ¼

Note the relative effects of the tube wall resistance when compared to the fouling factors in this case.

TABLE 15-33A Metal Resistance of Tubes and Pipes Value of rw

Thermal Conductivity, K

25

OD Tube 5

/8 in.

3

/4 in.

1 in.

1

1 /4 in.

63

89

21

17

14.6

238

1

4-6% Chrome /2 % Moly Steel 80-20 CU-NI

70-30 CU-NI

34.4

85

10

57.7 Yarkalbro, Alum, Brass

Gauge

Factor

Carbon Steel

Admiralty

Red Brass 45% Ars. Copper

Monel

Copper 99.9DCU

Nickel

Aluminum

Stainless AISI Type 302 & -304

18

.00443

.000177

.000070

.000050

.000211

.000261

.000303

.000019

.000129

.000052

.000443

.000077

16

.00605

.000424

.000096

.000068

.000288

.000356

.000414

.000025

.000176

.000071

.000605

.000105

14

.00798

.000319

.000127

.000090

.000380

.000469

.000547

.000034

.000232

.000094

.000798

.000138

18

.00437

.000175

.000069

.000049

.000208

.000257

.000299

.000018

.000127

.000051

.000437

.000076

16

.00593

.000237

.000094

.000067

.000282

.000349

.000406

.000025

.000172

.000070

.000593

.000103

14

.00778

.000311

.000123

.000087

.000370

.000458

.000533

.000033

.000226

.000092

.000778

.000135

13

.00907

.000363

.000144

.000102

.000432

.000534

.000621

.000038

.000264

.000107

.000907

.000157

12

.01063

.000425

.000169

.000119

.000506

.000625

.000728

.000045

.000309

.000125

.001063

.000184

18

.00429

.000172

.000068

.000048

.000204

.000252

.000294

.000018

.000125

.000050

.000429

.000074

16

.00579

.000232

.000092

.000065

.000276

.000341

.000397

.000024

.000168

.000068

.000579

.000100

14

.00754

.000302

.000120

.000085

.000359

.000444

.000516

.000032

.000219

.000089

.000754

.000100

13

.00875

.000350

.000139

.000098

.000417

.000515

.000599

.000037

.000254

.000103

.000875

.000152

12

.01019

.000408

.000162

.000114

.000485

.000599

.000698

.000043

.000296

.000120

.001019

.000177

10

.01289

.000516

.000205

.000145

.000614

.000758

.000883

.000054

.000375

.000152

.001289

.000223

8

.01647

.000659

.000261

.000185

.000784

.000967

.001128

.000069

.000479

.000194

.001647

.000285

18

.00425

.000170

.000067

.000048

.000202

.000250

.000291

.000018

.000124

.000050

.000425

.000074

16

.00571

.000228

.000091

.000064

.000272

.000336

.000391

.000024

.000166

.000067

.000571

.000099

14

.00741

.000296

.000118

.000083

.000353

.000436

.000508

.000031

.000215

.000087

.000741

.000128

13

.00857

.000343

.000136

.000096

.000408

.000504

.000587

.000036

.000249

.000101

.000857

.000149

12

.00995

.000398

.000158

.000112

.000474

.000585

.000682

.00042

.000289

.000117

.000995

.000172

10

.01251

.000500

.000199

.000141

.000596

.000736

.000857

.000053

.000364

.000147

.001251

.000217

8

.01584

.000634

.000251

.000178

.000754

.000932

.001085

.000067

.000460

.000186

.001584

.00275 Continued

TABLE 15-33A Metal Resistance of Tubes and Pipesdcont’d Value of rw

Thermal Conductivity, K

25

OD Tube

Gauge

1 1/2 in.

18

2 in.

3

Pipe /4 in. IPS

3

Pipe /4 in. IPS

63

89

21

17

14.6

238

Factor

Carbon Steel

Admiralty

Red Brass 45% Ars. Copper

1

4-6% Chrome /2 % Moly Steel 80-20 CU-NI

70-30 CU-NI

Monel

Copper 99.9DCU

.00422

.000169

.000067

.000047

.000201

.000248

.000289

.000018

16

.00566

.000226

.000090

.000064

.000270

.000333

.000388

.000024

14

.00732

.000293

.000116

.000082

.000349

.000431

.000501

13

.00845

.000338

.00134

.000095

.000402

.000497

12

.00979

.000392

.000155

.000110

.000466

10

.01226

.000490

.000195

.000138

8

.01545

.000618

.000245

18

.00419

.000168

16

.00560

14

34.4

85

10

57.7

Nickel

Aluminum

Stainless AISI Type 302 & -304

Yarkalbro, Alum, Brass

.000123

.000050

.000422

.000073

.000165

.000067

.000566

.000098

.000031

.000213

.000086

.000732

.000127

.000579

.000036

.000246

.000099

.000845

.000146

.000576

.000671

.000041

.000285

.000115

.000979

.000170

.000584

.000721

.000840

.000052

.000356

.000144

.001226

.000212

.000174

.000736

.000909

.001058

.000065

.000449

.000182

.001545

.000268

.000067

.000047

.000200

.00246

.000287

.000018

.000122

.000049

.000419

.000073

000224

.000089

.000063

.000267

.000329

.000384

.000024

.000163

.000066

.000560

.000097

.00722

.000289

.000115

.000081

.000344

.000124

.000495

.000030

.000210

.000085

.000722

.000125

13

.00831

.000332

.000132

.000093

.000396

.000489

.000569

.000035

.000242

.000098

.000832

.000144

12

.00961

.000384

.000153

.000108

.000458

.000565

.000658

.000040

.000279

.000113

.000961

.000167

10

.01197

.000479

.000190

.000134

.000570

.000704

.000820

.000050

.000348

.000141

.001197

.000207

8

.01499

.000600

.000238

.000168

.000714

.000882

.001027

.000063

.000436

.000176

.001499

.000260

St’d

.01055

.000422

.000167

.000119

.000502

.000621

.000723

.000044

.000307

.000124

.001055

.000183

X Hvy

.01504

.000602

.000239

.000169

.000716

.000885

.001030

.000063

.000437

.000177

.001504

.000261

Sch. 160

.0299

.000916

.000363

.000257

.001090

.001347

.00157

.000096

.000666

.000269

.00229

.000397

XX Hvy

.0363

.00145

.000576

.000408

.00173

.00214

.00249

.000153

.001055

.000427

.00363

.000629

in. St’d

.01308

.000523

.000208

.000147

.000623

.000769

.000896

.000055

.000380

.000154

.001308

.000227

X Hvy

.01863

.000745

.000296

.000209

.000887

.001096

.001276

.000078

.000542

.00029

.001863

.000323

Sch. 160

.0275

.00110

.000437

.000309

.00131

.00162

.00188

.000166

.000799

.000324

.00275

.000477

XX Hvy

.0422

.00169

.000670

.000474

.00201

.00248

.00289

.000177

.001227

.000496

.00422

.000731

rw for 1 in. O.D. 16 BWG steel tube with 18 BWG admiralty liner ¼ .00031 For other materials, divide factor number by the thermal conductivity of various materials: 60-40 Brass Zinc

K in Btu/(hr)(ft2)(
F/ft) rw in

55 64 1 Btu=ðhrÞðft2 Þð
FÞ

Chrome Vanadium Steel SAE 6120

23.2

Tin Lead

Used by permission: Griscom-Russell/Ecolaire Corporation.

35 20

Everdur #50 Wrought Iron

19 40

Heat Transfer Chapter | 15

TABLE 15-33B Preliminary Design Resistances Basis: Pressures used in Commercial Fractionations Heating Side, r0p

Clean

Service

Condensing steam

0.0005

0.0010

Cooling hot water

0.0025

0.0045

Cooling hot oil

0.0080

0.0100

Combustion gases

*

*

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

Boiling Side,

r0h

*For direct-fired reboilers, estimate area on basis of heat flux: Radiant zone q/A ¼ 10,000 Btu/(hr)(ft2)(
F) Convecton zone q/A ¼ 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.

TABLE 15-34 Thermal Conductivity e 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

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 15-35, 36, 37 and 37A give general estimating overall coefficients; Table 15-38 gives the range of a few common film heat transfer coefficients. Table 15-39 illustrates the effect of tube wall resistance for some special construction materials. Table 15-39A lists estimating coefficients for glass lined vessels. For steam jacketed, agitated closed reactor kettles, the overall U usually will range from 40e60 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 20e30 Btu/h ft2
F. For DuPont’s Telfon
tube (1/4 in. diameter) heat exchangers (Figure 15-10) for condensing, heating and cooling service, the U values range from 15e35 Btu/h ft2
F. 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, m; 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:

Various fluid heat transfer operations can be characterized in a general way by values of the overall coefficient, U. The values given in Perry [94] 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. Table 15-28, 29 and 32 list a variety of applications and the corresponding overall heat transfer coefficient (U) values and fouling factors. In general, these units have performed

Nu ¼ 0:027 Re0:8 Pr0:33

(15-166)

 0:8  hD DG cm 0:33 ¼ 0:027 k m k

(15-167)

or:

Rearranging Equation 15-167 gives:  0:8 0:33  DG cm k h ¼ 0:027 m k D

* To convert to Btu/(h) (ft2) (
F)/(in.), multiply by 12. To convert to gram calories/(sec) (cm2) (
C)/(cm), multiply by 0.004134.

APPROXIMATE VALUES FOR OVERALL HEAT TRANSFER COEFFICIENTS

175

(15-168)

In Equation 15-166, viscosity influences the heat transfer coefficient as parameters of both the Reynolds and Prandtl numbers. From Equation 15-168, hfm0:330:8

(15-169)

hfm0:47

(15-170)

or:

In Equation 15-170, the heat transfer coefficient is inversely proportional to the viscosity raised to the power of 0.47. 1 hf 0:47 m

(15-171)

176

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-75 Chart for determining U-clean from tube-side and shell-side fluid film coefficients; no fouling included. Note: s ¼ shell-side, t ¼ tube-side. (Used by permission: Elements of Heat Transfer, ©1957. Brown and Root, Inc.)

Similarly, the heat transfer coefficient is directly proportional to the thermal conductivity raised to the power of 0.67. hfk0:67

(15-172)

These two facts account for the heat transfer coefficient such that a high thermal conductivity promotes a high heat transfer coefficient. Table 15-40 shows the thermal conductivity and heat transfer coefficient for some components. 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 (Dp) is directly proportional to G2 and inversely proportional to the density, r. Thus, for the same Dp, 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 15-59 presents the effect of total fouling on the overall heat transfer coefficient. For example, if a clean non-fouled 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 15-75 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 15-59, and reading the dirty or fouled U valued or by using Equation 15-173 developed by Hedrick [159], 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 i 1=3 0:14 (15-173) hio ¼ ð16:1=do Þ BI kðcm=kÞ ðm=mw Þ

Heat Transfer Chapter | 15

TABLE 15-35 General Evaporator Overall Coefficient, U

TABLE 15-36 Approximate Overall Heat Transfer Coefficient, U*dcont’d

U, Btu/hr (ft2) (
F) Long-tube vertical evaporator Natural circulation Forced circulation

200-600 400-2,000

Short-tube evaporators Horizontal Calandria (vertical, thermosyphon)

200-400 150-500

Coil evaporators

200-400

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

400 300 120

Low boiling atmospheric

Water

80-200

High boiling hydrocarbon, vacuum

Water

10-30

Heaters

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

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

TABLE 15-36 Approximate Overall Heat Transfer Coefficient, U*

Evaporators Steam

Water

350-750

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.

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

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

Organic solvents, atmospheric and high noncondensable

Water, brine

Aromatic vapors, atmospheric with noncondensables

Water

Organic solvents, vacuum and high noncondensables

Water, brine

Heat Exchangers (No Change of Phase)

50-120

20-80

5-30

10-50

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.

Continued

177

178

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-37 Approximate Overall Heat Transfer Coefficient, U (Btu/h.ft2 oF)

TABLE 15-37 Approximate Overall Heat Transfer Coefficient, U (Btu/h.ft2 oF)dcont’d

Condensing

Condensing

Process Side (Hot)

Condensing Fluid (Cold)

Hydrocarbons (light)

Water

Hydrocarbons w/ inerts (traces)

Process Side (Hot)

Condensing Fluid (Cold)

100-160

Hot Water

Water (agitation)

90-150

Water

30-75

Hot Water

Oil-heavy (no agitation)

6-25

Organic vapors

Water

70-160

Heat transfer oil

25-50

Water vapor

Water

150-340

Organics (agitation)

Water vapor

Hydrocarbons

60-150

Salt brine

Water (agitation)

50-110

Exhaust steam

Water

280-450

Water (cooling)

Glycerine (agitation)

50-75

Hydrocarbons (light)

Refrigerant

45-110

Organics (light)

Cooling brine

50-120

Gasoline

Water

65-130

Useful dimensionless groups for heat transfer calculation are [70].

Ammonia

Water

135-260

Symbol

Name

Function

Hydrocarbons (heavy)

Water

40-75

Gz

Graetz number

wc/kL

Gr

Grashof number

D3 r2 gbDt=m2

Dowtherm vapor

Liquid organic

75-115

Nu

Nusselt number

h D/k

Pe

Peclet number

DG c/k

Hydrocarbons, light

Steam

90-210

Pr

Prandtl number

c m=k

Hydrocarbons, C4C8

Steam

75-150

Re

Reynolds number

DG=m; or; D u r=m

Hydrocarbons, C3C4 (vac)

Steam

45-175

Sc

Schmidt number

m=rkd

Chlorinated HC

Steam

90-210

St

Stanton number

h/cG

HCI solution (1822%)

Steam

120-240

Chlorine

Steam

130-220

Vaporization

Coils in Tank Coil Fluid

Tank Fluid

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

Continued

Film Coefficients with Fluid Inside Tubes, Forced Convection

where:   B ¼ 3:08 þ 3:075X þ 0:32567X2  0:02185X3 h i  ð10 di =LÞ 1  ðX=10Þ0:256 X ¼ Re=1; 000 (15-174) Re ¼ Reynolds number di ¼ inside tube diameter, in. do ¼ outside tube diameter, in. k ¼ thermal conductivity, Btu/h-ft-
F c ¼ specific heat of fluid, Btu/lb-
F m ¼ viscosity of fluid, centipoise mw ¼ viscosity at the wall, centipoise L ¼ tube length, ft hio ¼ inside film coefficient based on the outside tube diameter, Btu/(h) (ft2) (
F)

Heat Transfer Chapter | 15

179

TABLE 15-37A Miscellaneous Heating Overall Heat Transfer Coefficient,1 U (Btu/h ft2 oF) Heating Surface

Overall Coeff. Btu/h/(ft2) (
F)

Controlling Resistance

Paper

Cast iron

20-58

Paper film*

Yankee drying rolls

Paper

Cast iron

100

Metal wall*

Steam

Jacketed kettle

Paraffin wax

None

Copper

27.4

Product

d

Steam

Jacketed kettle

Paraffin wax

Scraper

Cast iron

107

Product

d

Steam

Jacketed kettle

Boiling water

None

Steel

187

Product

d

DOWTHERM A (vapor phase)

Jacketed kettle

Varnish

None

Steel

20-50

Product

DOWTHERM A (vapor phase)

Jacketed kettle

Asphalt

None

Steel

8-20

Product

DOWTHERM A (vapor phase)

Heat exchanger

Fatty acids

Forced circn.

Steel

45-50

Product

DOWTHERM A (vapor phase)

Heat exchanger

Rosin

Forced circn.

Steel

40

Product

DOWTHERM A (vapor phase)

Reboiler

Asphalt

Forced circn.

Steel

25-50

Product

DOWTHERM A (vapor phase)

Jacketed kettle

Fatty acids

None

80

Product

DOWTHERM A (liquid phase)

Heat exchanger

Varnish

Forced circn.

Steel

15-40

Product

DOWTHERM A (vapor phase)

Heat exchanger

Edible oil

Forced circn.

Steel

124-150

Product

DOWTHERM A (vapor phase)

Heat exchanger

Cocoa butter

Forced circn.

Steel

70-75

Product

Mercury vapor

Heat exchanger

DOWTHERM A MEDIUM

Forced circn.

Steel

220-350

Product

Equipment

Material Treated

Steam

Paper dying rolls

Steam

Agitation

Approximate Overall Design Coefficient1 Hot Fluid

Cold Fluid

Overall U

Coolers

Light organic

Water

75-150

Heaters

Steam

Light organic

100-200

Exchangers

Light organic

Light organic

40-75

Heavy organic

Light organic

30-60

Light organic

Heavy organic

10-40

1

Values include dirt factors of 0.003 and allowable pressure drops at 5e10 psi on the controlling steam. DOWTHERM fluid would be included as light organic. (Kern. Process Heat Transfer, 1st Ed., p.840 ©1950.) *Montgomery, A.E. “ Heat Transfer Calens. In Paper Machine.” Paper Trade Journal, Oct. 3, 1946, p.29. d Perry. Chemical engineers Handbook, 3rd Ed., p.482, ©1950.

180

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

where: C or c ¼ specific heat of fluid, Btu/(lb) (
F) D ¼ inside diameter of tube, ft G ¼ mass velocity, lb/h (ft2)

TABLE 15-38 Approximate Film Heat Transfer Coefficients, hi or ho Film Coefficient, Btu/h. (ft2) (
F) No Change of Phase Water

300-2000

Gases

3-50

Organic solvents

60-500

Oils

10-120

Gas and liquid heat transfer inside tubes has been studied by Sieder and Tate [101] and is represented by Figure 15-76 and 76A. Also see References [270] and [271]. The equations representing portions of the graph are as follows:

Condensing Steam

1000-3000

Organic solvents

150-500

Light oils

200-400

Heavy oils (vacuum)

20-50

Ammonia

500-1000

A. For viscous streamline flow of organic liquids, water solutions (not water) and gases with DG/m< 2,100 in horizontal or vertical tubes: deviation 6 12% [70]:
   1=3  0:14 hi D DG cm D m ¼ 1:86 (15-175) ka m ka L mw 1=3  0:14  hi D 4Wc m ¼ 1:86 (15-176) ka pka L mw

m 2=3  k 2=3 D 1=3  m 0:14 hi a ¼ 1:86 (15-177) cG mc DG L mw

Evaporation Water

800-2000

Organic solvents

100-300

Ammonia

200-400

Light oils

150-300

Heavy oils

10-50

g ¼ acceleration of gravity, ft/(h2), or ft/s2, depends on the system of units h ¼ heat transfer film coefficient, Btu/(h) (ft2) (
F) jH ¼ factor for heat transfer, dimensionless k ¼ thermal conductivity, Btu/(h) (ft2) (
F/ft) L ¼ length, ft Dt ¼ temperature difference for heat transfer,
F v ¼ velocity, ft/h m ¼ viscosity, absolute, lb/(h) (ft) r ¼ density, lb/ft3 kd ¼ diffusivity (volumetric), ft2/h b ¼ thermal coefficient of expansion, 1/
F

B. For turbulent flow of viscous fluids as organic liquids, water solutions (not water) and gases with

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

TABLE 15-39 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 Heating Water with Steam

Condensing Organic Vapor with Water

Cooling Organic Liquid with Water

Cooling Viscous Organic Liquid with Water

Stainless steel, 30416BWG

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 þ ho

300

100

50

20

Tube

*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.

Heat Transfer Chapter | 15

181

TABLE 15-39A 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. walld

90.2

62.2

35.1

16.7

Glasteel reactor, 0.05 in. glass 0.688 in. steeld

77.0

55.6

32.6

16.5

Combined film conduci ho tance, hhi þh o

300

137

50

20

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

TABLE 15-40 Heat Transfer Coefficients of Certain Components

m ¼ viscosity of fluid, lb/(h) (ft) m w ¼ viscosity of fluid at wall temperature, lb/(h) (ft)

Thermal Conductivity k, W/m
C (Btu/h ft
F)

Heat Transfer Coefficient h, W/m2.
C (Btu/h ft
F)

Figures 15-77, 15-78 and 15-79 are useful in solving the equivalent of Equation 15-178 for turbulent as well as streamline flow of gases and vapors inside tubes. To use the charts, proceed as follows.

Cooling water

w64 (111)

7000 (39746)

Hydrocarbon liquids

0.09e0.14 (0.16e0.20)

291e1512 (1652e8585)

Hydrocarbon gases

0.02e0.03 (0.03e0.05)

58e582 (329e3305)

A. for turbulent flow: 1. Determine fp using fluid properties (Figure 15-77). 2. Determine tube-side film coefficient, hi, based on inside tube surface (Figure 15-78). 3. Correct hi for the effect of tube size by multiplying by the accompanying factor shown in Figure 15-78. B. For streamline flow: 1. Determine fp (Figure 15-77). 2. Determine hi (Figure 15-79). 3. Correct hi by multiplying by the tube size and heated length factors accompanying Figure 15-79. C. For water, the inside film coefficient is represented by Figure 15-80A. Furman [49] presents charts that reduce the expected deviation of the film coefficient from the 20% of Figures 15-80A, B, C and D. D. For heating and cooling turbulent gases and other low viscosity fluids at DG/m > 8,000; the Dittus-Boelter relation in used. See Figures 15-76, 15-81 and 15-82.  0:8  0:4  0:14 hi D DG cm m ¼ 0:0243 (15-179) ka m ka mw

Component

DG/m > 10,000 in horizontal or vertical tubes: deviation 115% to 210% [70]:  0:8  1=3  0:14 hi D DG cm m ¼ 0:023 (15-178) ka m ka mw C. For transition region between streamline and turbulent flow, use Figure 15-76. where: c ¼ specific heat of fluid at constant pressure, Btu/(lb) (
F) D ¼ inside diameter of tube, ft G ¼ fluid mass velocity, lb/(h) (ft2 tube cross-section flow area) hi ¼ film heat transfer coefficient inside tube, Btu/(h) (ft2) (
F) ka ¼ thermal conductivity of fluid at average bulk temperature of fluid, Btu/h (ft2)/(
F/ft) L ¼ total heated or cooled length of heat transfer path, ft w ¼ mass flow rate of fluid flow per tube, lb/h

For cooling, DG/m > 8,000, the following is sometimes used in place of the preceding relation, Figure 15-81:  0:8  0:4  0:14 hi D DG cm m ¼ 0:023 (15-180) ka m ka mw

182 Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-76 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.)

Heat Transfer Chapter | 15

183

FIGURE 15-77 Flow inside tubes 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.)

When the Prandtl number (cm/ka) can be used at 0.74, as is the case for 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: 0:8  hi D DGC ¼ 0:026 (15-181) ka ka 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 15-178 can be simplified to give the following approximate equations:

hi ¼

0:014 Cp G0:8 D0:2

(15-182)

Similarly, for water at ordinary temperatures and pressures, hi ¼

150 ð1 þ 0:011tb Þ ðV0 Þ0:8 ðD0 Þ0:2

(15-183)

where: Cp ¼ heat capacity of fluid, Btu/lb.
F D ¼ diameter, ft. D0 ¼ diameter, in. G ¼ mass velocity inside tube, lb/h ft2 hi ¼ heat transfer film coefficient, Btu/h.ft2
F tb ¼ average (i.e. bulk) temperature of water,
F V0 ¼ velocity of water, ft/s.

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-78 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.)

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

184

Mass velocity G , lb/sec-ft2 Tube Size Correction Factors for Turbulent Flow 3 /4" × 14 BWG 1.011 1" × 14 BWG 0.942 0.912 16 1.000 11/4" × 10 1" × 10 0.967 12 0.903 12 0.955 14 0.894

Equations 15-182 and 15-183 are dimensional, and a value of hi is obtained only if the units are employed for the indicated variables. Pierce [164] 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: 31=12 2 6 ! 6 6 1 J4 ¼ 6 6 N9:36 " 6 Re 4

7 7 7 7 8 #3=2 7 7 1:6 NRe 6Þ 5 þ 1:969ð10 NRe 7:831ð1014 Þ 1 

ð4Þ

(15-184) Colburn Factor, J: J ¼ J4 ðmb =mw Þ0:14 Then, convective heat transfer coefficient: .

 2=3 h ¼ J Cp rv NPr where: Cp ¼ specific heat, J/kg K ¼ J/kg-Kelvin

(15-185)

(15-186)

D ¼ diameter, m, meter J ¼ Colburn factor J4 ¼ Colburn factor given by equation proposed by Pierce L ¼ length of tube, m NPr (Pr) ¼ Prandtl number NRe (Re) ¼ Reynolds number v ¼ velocity, m/sec m ¼ dynamic viscosity, Pa-s (pascal-sec) r ¼ density, kg/m3 b ¼ evaluate at bulk temperature w ¼ evaluate at wall temperature kg ¼ kilogram Buthod [22] presents Figure 15-82 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: cm=ka ¼ 0:78 and m ¼ 0:435 (Reference [81]) h ¼ 0:0144

cG0:8 D0:2

(15-187)

Note that below G ¼ 1,200P2/3, results may be too conservative. Gases in turbulent flow in circular helical coils [81].

Heat Transfer Chapter | 15

185

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

Mass velocity G , lb/sec-ft2 Heated Length Correction Factors, Streamline Flow 08 ft 1.26 16 ft 1.00 10 1.17 18 0.96 12 1.10 20 0.96 14 1.05

Tube Size Correction Factors for Streamline Flow 3 /4 in. 14 BWG 1.060 1 in. 14 BWG 16 1.000 1 1/4 in. 10 BWG 1 in. 10 0.846 12 12 0.793 14

0.744 0.631 0.600 0.571

FIGURE 15-79 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.)

Multiply hi for straight tubes by [1 þ 3.5dit/DH] where: c ¼ specific heat capacity of the gas, Btu/lb
F dit ¼ inside tube diameter, in. DH ¼ diameter of helix of coil, in. P ¼ absolute pressure, atm. (this equation only) Ganapathy [263] developed nomograms for solving for film heat transfer coefficients for superheated steam, gases, liquids and vapor refrigerants flowing inside exchanger tubes. See Figures 15-83A, B, C and D. Also see Rubin, Reference 280. Liquids in turbulent flow in circular helical coils [80,81] should be handled in the same way as gases, or use 1.2  h1 for straight tubes.

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 [5,70]: 0:55  1=3  0:14  ho De De Gs cm m ¼ 0:36 (15-188) ka m ka mw and as represented in Figure 15-84 (S.I. units), deviation: 0 to þ20%. The Gs is correlated for both cross and parallel flow through the bundle by using the hydraulic radius along the tubes only [70]. Figure 15-85 is helpful in visualizing shell-side fluid flow.

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where: de ¼ equivalent tube diameter for the shell-side ¼ 4 (flow area/wetted perimeter), in. Do ¼ outside diameter of tube, ft Gw ¼ weighted mass velocity ¼ w/Se ¼ w/(GcGb)0.5 in lb/(h) (ft2) Se ¼ weighted flow area ¼ [(cross-flow area) (baffle window area)]0.5, ft2 Gc ¼ cross-flow mass velocity, lb/h (ft2) Gb ¼ mass velocity through baffle window opening, based on the area of the opening Less the area of tubes passing through it, lb/h (ft2) m ¼ viscosity, lb/h (ft)

Viscosity Correction Factor ðm=mw Þ0:14 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 ðtw  t Þ ¼ UðT  tÞ

(15-190)

where: FIGURE 15-80A 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.)

t ¼ tube-side bulk temperature (mean) tw ¼ estimated wall temperature T ¼ shell-side bulk temperature (mean)

Heat Transfer Coefficient for Water, Hi where: ho ¼ film heat transfer coefficient outside of tubes in bundle, Btu/h (ft2) (
F) ka ¼ thermal conductivity, Btu/h (ft2) (
F/ft) Gs ¼ mass flow rate, lb/h (ft2) De ¼ equivalent tube diameter, ft de ¼ equivalent tube diameter, in as ¼ flow area across the tube bundle, ft2 Bs ¼ baffle spacing, in c ¼ specific heat of fluid, Btu/lb (
F) m ¼ viscosity at the caloric temperature, lb/ft (h) mw ¼ viscosity at the tube wall temperature, lb/ft (h) Kern’s [70] correlation checks well with the data of Short [102], Bowman [7] and Tinker [116] for a wide variety of baffle cuts and spacing for segmental baffles, with and without leakage as summarized by Donohue [36]. Short’s data for disc and doughnut baffles are better calculated by [36]:  0:6  0:33 hD cm 0:6 Do Gw ¼ 0:23ðde Þ (15-189) m ka ka

Equations 15-174, 15-176 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 adapted from data given by Eagle and Ferguson [367] as: hi ¼

4200ð1:35 þ 0:02tÞ u0:8 t d0:2 i

(15-191)

where: di ¼ tube inside diameter, mm hi ¼ inside heat transfer coefficient for water, W/m2
C ut ¼ water velocity, m/s t ¼ water temperature,
C.

Shell-Side Equivalent Tube Diameter [70] See Figure 15-86 and Table 15-41. Best results are obtained when baffle pitch or spacing between baffles is between one-fifth to one shell diameter.

Heat Transfer Chapter | 15

187

FIGURE 15-80B Heat transfer film coefficient for water flowing inside 1 in.  18 BWG tubes referred to outside tube surface area for plain tubes. Note the corrections for tubes of wall gauges other than 18 BWG. (Used by permission: J. B. Co., Inc., Western Supply Div., Tulsa, Okla.)

FIGURE 15-80C Tube-side (inside tubes) liquid film heat transfer coefficient for Dowtherm
. A fluid inside pipes/tubes, turbulent flow only. Note: h ¼ average film coefficient, Btu/hr-ft2 -
F; di inside tube diameter, in.; G0 ¼ mass velocity, lb/sec/ft2; v ¼ fluid velocity, ft/sec; k ¼ thermal conductivity, Btu/ hr (ft2)(
F/ft); m ¼ viscosity, lb/(hr)(ft); Cp ¼ specific heat, Btu/(lb)(
F). (Used by permission: Engineering Manual for Dowtherm Heat Transfer Fluids, ©1991. The Dow Chemical Co.)

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FIGURE 15-82 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.)

FIGURE 15-80D 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 Heat Transfer Fluids,©1991. The Dow Chemical Co.)

FIGURE 15-81 Convection inside film coefficient for gases and low viscosity fluids inside tubeseheating and cooling. (Used by permission: McAdams, W. H. Heat Transmission, 2nd Ed., ©1942. McGraw-Hill, Inc. All rights reserved.)

Heat Transfer Chapter | 15

FIGURE 15-83A 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.)

189

FIGURE 15-83C 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.)

For 60
triangular equilateral pitch tubes:  4  12 pt  pt sin 60o  p8 d2o de ¼ pdo

(15-194)

2

de ¼ ¼

     4 0:5 pt 0:866pt  0:5 pd2o 4 pdo 2

 1:094  2 pt  0:913d2o do

; in: (15-195)

where: de ¼ equivalent diameter, in., shell-side for cross-flow pt ¼ tube pitch, in do ¼ outside diameter of tube, in. FIGURE 15-83B 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.)

Cross-flow area for Figure 15-84 is based upon the maximum flow area at the nearest tube row to the centerline of the shell [70]. The length of the flow areas is the baffle spacing. as ¼

For square pitch tubes, the shell-side equivalent diameter is: de ¼

4  cross-sectional area wetted perimeter    4 p2t  pd20 4 ; in de ¼ pdo

 1:273  2 ¼ pt  0:785d2o do

(15-192)

Gs ¼

Ds ðc0 Bs Þ 2   ; ft pt 144

(15-196)

W ; lb=ðhÞðft2 Þ as

(15-197)

where: (15-193)

Ds ¼ shell inside diameter, in. c0 ¼ clearance between tubes measured along the tube pitch, in.

190

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-83D 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.)

Bs ¼ baffle spacing, in W ¼ weight flow of fluid, lb/h pt ¼ 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 15-42. 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-sectional 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 15-87). Figure 15-88 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 15-89 is useful for this equalization. Shell-side film coefficients can be conveniently obtained from the charts of Chen [25], Figures 15-90,

Heat Transfer Chapter | 15

FIGURE 15-84 Shell-side heat transfer curve for segmental baffles. (Used by permission: Engineering Data Book Section II, ©1959. Wolverine Tube, Inc.)

191

192

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-85 Shell-side baffles and cross-flow area.

FIGURE 15-86 Equivalent diameter for tubes on shell-side of exchanger taken along the tube axis. (a) Square pitch, (b) triangular pitch on 60
equilateral angles. (Used by permission: Kern, D. Q. Process Heat Transfer, 1st Ed., ©1959. McGraw-Hill, Inc. All rights reserved.)

Heat Transfer Chapter | 15

TABLE 15-41 Shell-Side Equivalent Tube Diameters for Various Tube Arrangements Equivalent Diameter, de0 , In.

Tube O.D. In.

Pitch

1

5

0.36

1

3

0.74

3

15

3

1 triangular

/2 /2 /4 /4

/8 triangular

/4 triangular /16 triangular

1

0.72

9

0.91

1 /4

1 /16 triangular

1

5

0.48

1

3

0.88

3

15

0.72

3

1 square

0.95

1

1 1/4 square

0.99

11/4

1 9/16 square

1.23

/2 /2 /4 /4

/8 square

/4 square /16 square

De ¼

0.73

Tolerance

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

1 Ds  16 in:ð1:6 mmÞ

1 þ32 in: ð0:8 mmÞ

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

Ds  18 in:ð3:2 mmÞ

1 þ0; 32 in: ð0:8 mmÞ

27 to 42 in. (686 to 1067 mm)

3 Ds  16 in:ð4:8 mmÞ

1 þ0; 16 in: ð1:6 mmÞ

15-91 and 15-92. These are based on Donohue’s equation [38]: 0:6  0:333  0:14  ho D o Do Gw cp m m ¼ 0:22 ka m ka mw

D22  D21 4ðflow areaÞ ¼ 4rh ¼ D1 ðwetted perimeterÞ (15-192A)

 2  4p2t  p de 0 4 de ¼ pde 0 where pt is the tube pitch, in. (c) Triangular Pitch

TABLE 15-42 Typical Baffle Clearances and Tolerances Baffle Diameter

(15-192)

where: D1 ¼ outside diameter of inner tube, ft D2 ¼ inside diameter of outer pipe, ft rh ¼ hydraulic radius, ft ¼ (radius of a pipe equivalent to the annulus cross-section) (b) Square Pitch and Rotated Square Pitch

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.

Shell Diameter, Ds

4  free area ; in: wetted perimeter

(a) Equivalent Diameter, De, for Annulus

0.55

1

1 /4 triangular

1

de ¼

193

(15-198)

Equivalent tube diameter for shell-side heat transfer calculations is used by permission from Kern and Kraus [206]. The volumetric equivalent diameter, de in., is again calculated on the basis of 4 times the hydraulic radius; see Figure 15-86.

de ¼

h    2  i 4 0:5pt 0:866pt  0:5p de 0 4 0:5pde 0

(15-199)

(15-200)

For plain tubing, the nominal OD replaced de0 . The volumetric equivalent diameter does not distinguish between square pitch and square pitch rotated by 45
. where: dé ¼ 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 [206]. See Figure 15-11H de ¼ equivalent diameter, in. For use in the equivalent diameter equations, the following volumetric dé, in. values are taken from Reference [206]. Plain Tube Second Tube OD in.

19 Fins/in. 3 1 /16 in. High Equivalent Diameter de0 , in.

16 Fins/in. 3 /16 in. High Equivalent Diameter de0 , 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

1

Used by permission: Based on data from Kern and Kraus, pp. 512e513, ©1972. McGraw-Hill, Inc.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Example: If the shell-side coefficient of a unit is 25 Btu/hr (ft2)( ºF) and velocity in the shell is doubled, read the new shell-side coefficient, ha, as 36 (line a). If the tube-side 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 15-87 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. Putnam Publishing Co., Itasca, Ill. All rights reserved.)

Heat Transfer Chapter | 15

195

FIGURE 15-88 Baffling for low pressure drop shell-side designs.

FIGURE 15-90 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.)

FIGURE 15-89 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.)

The charts are used as follows: 1. Determine geometric mean mass velocity, Ge0 using Figure 15-90. (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 Ge0 , lb/sec (ft2) by dividing the shell-side flow rate by the cross-flow area. (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 Gb0 , as lb/s (ft2) by dividing the flow rate of the shellside by this new baffle opening flow area. (c) Read Ge0 , lb/s (ft2), from Figure 15-90 at the intersection of Gc0 and Gb0 .

FIGURE 15-91 Shell-side physical property factor forp fp0 . (Used with permission: Ning Hsing Chen, Chemical Engineering, V 65, Oct. 1958. ©McGraw-Hill, Inc. All rights reserved.)

2. Determine the physical property factor, fp0 , using Figure 15-91. 3. Read the outside film coefficient, ho, using Figure 15-92. Note: This has the viscosity correction (ðm=mw Þ0:14 , included. A correction multiplier must be used to

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-92 Shell-side film coefficient. (Used with permission: Ning Hsing Chen, Chemical Engineering, V. 65, Oct. 1958. ©McGraw-Hill, Inc.All rights reserved.)

correct the results of Figure 15-92 for tubes different than 5 /8 in. OD. The charts of Rubin [98] are somewhat similar and also useful for solving the equation by graph rather than by calculator.

Shell-Side Velocities Figure 15-93 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 15-43 presents suggested maximum velocities for fluids flowing through exchanger nozzles. The effect of entrance and exit losses on pressure losses should be checked, as they become important in low pressure systems. Figure 15-94 is convenient in selecting pipe or nozzle sizes.

DESIGN AND RATING OF HEAT EXCHANGERS Two main types of problem can exist in relation to 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 15-95. 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 and 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 15-95). Therefore, an exchanger can be rejected in step 3 of the algorithm before the fouling factors enter the calculation. The rating procedure in Figure 15-95 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

Heat Transfer Chapter | 15

197

FIGURE 15-93 Maximum velocity for gases and vapors through heat exchangers on shell-side.

TABLE 15-43 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.

More than 1500

2

Very heavy oils

1000 e 500

2.5

Heavy oils

500 e 100

2.5

Medium oils

100 e 35

5

Light oils

35 e 1

6

Light oils

Less than 1

8

.

Remarks

Vapors and Gasses Use 1.2 to 1.4 of the value shown on Figure 15-93 for velocity through exchangers.

compared with the specified maximum allowable pressure drops as described earlier. The steps for rating an exchanger are as follows: 1. Write the heat balance for the cold and hot streams: Q ¼ Wh Cph ðT1  T2 Þ ¼ wc Cpc ðt2  t1 Þ

(15-201)

and then calculate Q and the remaining unknown, flow rate or temperature.

FIGURE 15-94 Nozzle sizes for fluid flow. (Used by permission: ITT Technologies, ITT Standard. All rights reserved.)

2. With the four temperatures known, determine DTLMTD as: DTLMTD ¼

ðT1  t2 Þ  ðT2  t1 Þ  T1 t2 ln T2 t1

(15-28)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

1. Calculate the required overall coefficient Q U req = (A ⋅ F ΔTLMTD ) 2. Calculate the clean overall coefficient 1 1 1 1 = + + h o D o ln (D o D i ) Uc Do hi 2k Di

or Uc =

1 Do h i Di

+

3.

D ln (D o D i ) 1 + o ho 2k

−1

Is Uc > Ureq ?

Yes Continue

No Exchanger is not suitable

4. Obtain required fouling factors, RDi and RDo from Tables 15-24, 25 and 26 then compute Do R D = R Di + R Do Di 5. Calculate the design overall heat transfer coefficient, UDes 1 1 = + RD U Des U c Or U Des =

1 + RD Uc

−1

6. Is Uc > Ureq ?

Yes Exchanger is suitable

No Exchanger is not suitable

FIGURE 15-95 Thermal rating procedure for a shell and tube heat exchanger. (Source: R.W. Serth, Process Heat Transfer - Principles and Applications, Elsevier, 2007.)

3. Calculate the P and R parameters:

R ¼

t2  t1 P ¼ T1  t1

(15-32)

T1  T2 wc Cpc ¼ t2  t1 Wh Cph

(15-33)

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 (T1þT2)/2 and (t1þt2)/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 (m/mw) for each fluid, where m is the viscosity at the mean temperature, and mw 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 (m/mw) is used, as this factor is not very high and the first guess is a reasonable value.

Heat Transfer Chapter | 15

6. The flow area of the fluid flowing into the tubes is determined: at ¼

Nt a0 t n

(15-202)

where: (15-203)

Nt ¼ number of tubes n ¼ number of tube passes The mass velocity of the tube-side fluid is calculated: wt at

(15-204)

7. Calculate the Reynolds number for the tube-side fluid: Ret ¼

Dt Gt m

(15-205)

8. Calculate hi, Equations 15-176 through 15-181 based on the Reynolds number. 9. Correct the external diameter: hio ¼ hi

Di Do

(15-206)

10. Calculate the shell-side heat transfer coefficient, ho. 11. With the calculated values of hio and ho, the tube wall temperature assumed in step 5 can be checked. This is done by equating the heat transfer rates at both sides of the wall: hio ðTw  tÞ ¼ ho ðT  Tw Þ

(15-207)

If the shell-side fluid is the hot fluid, or: hio ðT  Tw Þ ¼ ho ðTw  tÞ

(15-208)

If the tube-side fluid is the hot fluid, Equation 15-207 or 15-208 is solved for Tw. 12. The clean heat transfer coefficient can be calculated as:  1 1 1 (15-209) ¼ þ Uc hio ho 13. The total heat transfer coefficient can be determined as:  1 1 (15-210) ¼ þ Rf U Uc 14. The calculated area is: Acalc ¼

Q U Ft DTLMTD

(15-211)

15. The real area of the heat exchanger is determined with its geometric dimensions:

(15-212)

16. If Areal > Acalc , the exchanger is suitable for use. The excess area is: Percent excess ¼

pD2i a0 t ¼ 4

G t ¼ r vt ¼

Areal ¼ Nt p Do L

199

Areal  Acalc  100 Acalc

(15-213)

The tube-side pressure drop calculation is as follows: Using the Ret calculated in step 7, obtain the friction factor from Equations 15-103 and 15-103A (see Vol. 1, Chapter 4, 4th ed. of this series) and determine the straight tube pressure drop from Equation 15-105. Then calculate the pressure drops in the headers from Equation 15-104. The total pressure drop will be the sum of both effects. 17. The 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 Dp values must be less than the allowable values.

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 of the increase in heat transfer coefficients is the allowable Dp for both fluids. The design will be optimal when Dp 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. Determine the unknown process variable (e.g., flow rate or temperature) of one of the streams from the heat balance. Then calculate the DTLMTD. 2. Select 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 counter current configuration provides the highest DT because Ft ¼ 1. On many occasions, a pure counter current configuration is

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

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 2n0 tube passes, with n0 being any integer number. Calculate Ft. 3. Choose as a first guess the overall heat transfer coefficient, U from Tables 15-28, 29, 35, 36, 37 and 37A. 4. With the assumed U, determine an approximate value of the heat transfer area: A0 ¼

Q U Ft DTLMTD

(15-214)

5. Choose 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 ¼

Wt r a0 t ð1 m=sÞ

(15-215)

7. Select 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 that satisfies the value of A0 ¼ Nt p Do L

(15-216)

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 ¼ Nt =np

(15-217)

Adjust 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 Table 15-16. 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 ¼ Nt p Do L

(15-218)

10. Select the baffle separation Bs a first guess, determine the Reynolds number that gives a reasonably high shellside 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.

Design Procedure for Forced Convection Heat Transfer in Exchanger Design 1. Establish the 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 DTLMTD. 4. Determine the DTLMTD with correction if needed from Figures 15-40 and 15-41. 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 15-80A or 15-80B. For other liquids and gases, use Figure 15-76A. Correct hi to the outside tube surface by:  I:D: (15-219) hio ¼ hi O:D: 7. Determine the shell-side film coefficient for an assumed baffle spacing. (a) Establish Gs from Equation 15-197. (b) Calculate the Reynolds number, Re, expressed as: Re ¼

De Gs m

(15-220)

(c) Read jH from Figure 15-84. Note that 25% is a good average value for many designs using segmental baffles. (d) Calculate ho from:  0:14 ho De cm1=3 m (15-221) jH ¼ k k mw Let m=mw ¼ 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 tubeside and shell-side fouling (Tables 15-25 and 15-26, Figures 15-59, 15-59A, 15-60e15-62).

Heat Transfer Chapter | 15

9. Calculate the overall heat transfer coefficient using Equation 15-161/161A. Neglect the tube wall resistance, unless special situations indicate that is should be included. 10. Calculate the area required using Equation 15-9. 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 units 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 10e20%. 14. Calculate the shell-side pressure drop. (Refer to the later section on “Pressure Drop Relations” and Figure 15-100. If Dp is too high, reassume unit (step 3).) 15. Calculate the tube-side pressure drop. (Use Figure 15-99 for the end return losses. For water in tubes, use Figure 15-98 for tube losses. For other liquids and gases in tubes, use Figure 15-97.)

201

Total pressure drop ¼ (end return þ 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 15-95A illustrates the influence of various geometrical parameters on heat exchanger heat transfer and pressure drop.

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

Need to increase heat transfer

Increase heat Transfer coefficient

Increase surface area

Increase tube length

Shell-side

Tube-side

Increase number of tubes, decrease tube outside diameter

Decrease the baffle spacing or baffle cut

Increase shell diameter with appropriate number of tubes

Employ multiple shells in series or parallel

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

Shell-side

Tube-side

Decrease number of tube passes

Increase tube diameter

Decrease tube length and increase shell diameter and number of tubes

Increase the baffle cut

Increase the baffle spacing

Increase tube pitch

FIGURE 15-95A Influence of various geometrical parameters of a shell and tube exchanger on heat.

Use double or triple segmental baffles

202

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

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 on 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 Dps 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 15-44 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 15-95B 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. Determine 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. 4. Evaluate the log mean temperature difference driving force. 5. Determine the necessary area of heat transfer and the exchanger dimensions. 6. Analyze the results to see if all dimensions, costs, pressure drops and other design details are satisfactory. 7. If the results of step 6 show that the exchanger is unsatisfactory, the specifications given in step 2 are

TABLE 15-44 Process and Mechanical Information for a Quotation/Price Estimate on a Proposed Heat Exchanger Process Information

Mechanical Information

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.

Flow rates or amounts of fluids.

2. Tube layout and pitch a. Horizontal tubes b. Vertical tubes.

Entrance and exit temperatures.

3. Maximum and minimum temperatures and pressures.

Amount of vaporization and condensation.

4. Necessary corrosion allowances.

Operating pressures and allowable pressure drops.

5. Special codes involved.

Fouling factors.

6. Recommended materials of construction.

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).

inadequate. Choose new specifications and repeat steps 3 through 7 until a satisfactory design is achieved. In general, when the designer selects 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 or triangular pattern. The square pitch has the advantage of easier external cleaning, but the triangular pitch is 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

Heat Transfer Chapter | 15

203

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

Collect physical properties

Step 11 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 ∆TLMTD, correction factor, F and ∆Tm.

0
4000, then the tube-side heat transfer coefficient is determined by Dittus-Bolter equation:

Nu ¼

 0:14 hi di m ¼ C Re0:8 Pr0:33 kf mw

(15-227)

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:   pt  do Ds Bs (15-229) As ¼ pt where: pt ¼ tube pitch. do ¼ tube outside diameter, m Ds ¼ shell inside diameter, m Bs ¼ 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 as:

where Nu ¼ Nusselt number (dimensionless) ¼

hi di kf Re ¼ Reynolds number (dimensionless) ¼ r umt di C m Pr ¼ Prandtl number (dimensionless) ¼ pk 2


¼

di G t m

hi ¼ Tube-side heat transfer coefficient, W/m C di ¼ Tube inside diameter, m. L ¼ Length of tube, m k ¼ Thermal conductivity of fluid, W/m
C Cp ¼ Specific heat of fluid, kJ/kg.
C m ¼ Viscosity of fluid at the bulk fluid temperature, (N.s)/m2, (Pa.s) mw ¼ Viscosity of fluid at the tube wall temperature, (N.s)/m2 , (Pa.s) C ¼ Constant ¼ 0.021 for gases ¼ 0.023 for non-viscous liquid ¼ 0.027 for viscous liquid Gt ¼ Tube-side mass velocity, kg/(s.m2) _ Gt ¼ m at at ¼ Tube-side flow area ¼ NNpt  p4 d2t Nt ¼ Number of tubes Np ¼ Number of tube-side passes ut ¼ Tube-side fluid velocity ¼ Gt/r, m/s r ¼ 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 numbers (from Re ¼ 10e106) for different values of L/di from: Nu ¼ hi

di ¼ Jh Re:Pr0:33 k



m mw

0:14 (15-228)

211

Gs ¼

Ws As

(15-230)

us ¼

Gs r

(15-231)

where: Ws ¼ fluid flow rate on the shell-side, kg/s r ¼ shell-side fluid density, kg/m3 3. Calculate the shell-side equivalent diameter (hydraulic diameter) For a square pitch arrangement:

de ¼

 2 4 p2t  pd4 o pdo

¼

 1:273  2 pt  0:785d2o do

(15-190)

For an equilateral triangular pitch arrangement:

 2 4 p2t  0:86 pt  12 p d4o  1:094  2 ¼ de ¼ pt  0:913d2o pdo d o 2 (15-192) where de ¼ equivalent diameter, m 4. Calculate the shell-side Reynolds number, Re, and Prandtl number, Pr, given by: Re ¼

G s de rus de ¼ m m

(15-232)

Cp m k

(15-233)

Pr ¼

where m ¼ viscosity of shell-side fluid at average temperature, kg/m.s (Pa.s) Cp ¼ specific heat capacity of shell-side fluid at average temperature, W/m
C k ¼ thermal conductivity of shell-side fluid at average temperature, kJ/kg.
C

212

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

5. For the calculated Reynolds number, read the value of jh from Figure 15-84A, for the selected baffle cut and tube arrangement, and calculate the shell-side heat transfer coefficient hs from:  0:14 ho de m ¼ jh Re Pr0:33 (15-234) Nu ¼ kf mw or: Alternatively, calculate the shell-side heat transfer coefficient by the following correlation  0:14 ho de m 0:55 0:33 ¼ 0:36 Re Pr (15-235) Nu ¼ k mw 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. 6. For the calculated shell-side Reynolds number, read the friction factor from Figure 15-56 and calculate the shellside pressure drop from:   2  0:14 Ds L rvs m ; N=m2 ðpaÞ Dps ¼ 8jf de 2 Bs mw (15-236) where: L ¼ tube length. Bs ¼ baffle spacing The term (L/Bs) is the number of times the flow crosses the tube bundle ¼ (Nb þ 1), where Nb is the number of baffles. Example 15-17. Design of a Shell and Tube Heat Exchanger (SI Units) by Kern’s Method

Design a shell and tube exchanger for the following duty. Kerosene, 25,000 kg/h (42
API) leaves the base of a sidestripping column at 200
C and is to be cooled to 90
C by exchange with 85,000 kg/h light crude oil (34
API) coming from a storage at 40
C. 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/m2
C on the crude stream and 0.0002 W/m2
C 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 ¼ 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 15-95B, where the procedure set out in this figure is followed in the solution. Step 1. Hot Fluid: Kerosene: 25,000 kg/h (42
API) at 200
C cooled to 90
C by exchange with 85,000 kg/h light crude oil (34
API) at 40
C.

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.
C/W, and light crude oil 0.00035 m2.
C/W The outlet temperature of the crude oil is determined from the energy balance:     Q ¼ UA:DTLMTD ¼ Wh Cph T1  T2 ¼ wc Cpc t2  t1 The mean temperature of kerosene ¼ (200 þ 90) / 2 ¼ 145
C. At this temperature, the specific heat capacity of 42
API kerosene ¼ 2.47 kJ/kg.
C The heat duty: Q ¼

25; 000  2:47ð200  90Þ ¼ 1886:8 kW 3600

As a first trial, take the mean temperature of the crude oil as equal to the inlet temperature, 40
C. The specific heat capacity at this temperature ¼ 2.01 kJ/kg.
C. The energy balance between kerosene and the crude oil gives: 1886:8 ¼

85; 000  2:01 ðt2  40Þ 3600

t2 ¼ 79.8
C and the crude oil stream mean temperature ¼ (79.8 þ 40) / 2 ¼ 59.9
C. The specific heat capacity at this temperature is 2.05 kJ/ kg.
C. Using this value for the second trial to determine the outlet temperature of the crude oil stream. 1886:8 ¼

85; 000  2:05 ðt2  40Þ 3600

t2 ¼ 78.98
C, and the new mean temperature ¼ (78.98 þ 40) / 2 ¼ 59.49
C 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 ¼ 78.98
C (say 79
C). Step 2: Physical Properties Kerosene temperature specific heat thermal conductivity

inlet 200 2.72 0.130

mean 145 2.47 0.132

outlet 90 2.26 0.135


C kJ/kg
C W/m
C

density

690

730

770

kg/m3

viscosity Crude oil temperature specific heat thermal conductivity

0.22 outlet 79 2.09 0.133

0.43 mean 59.5 2.05 0.134

0.80 Inlet 40 2.01 0.135

mNsm2

density

800

820

840

kg/m3

viscosity

2.4

3.2

4.3

mNsm2




C kJ/kg
C W/m
C

Step 3: Overall Heat Transfer Coefficient, U. The overall heat transfer coefficient is in the range 300 e500 W/m2.
C. From Table 15-32, choose U ¼ 350 W/ m 2 .
C 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:

Heat Transfer Chapter | 15

Calculation of LMTD,

Shell

200°C

tube

79°C 121°C

90°C



1 Nt n l Kl  1 260 2:207 ¼ 19:05 0:249

40°C

Db ¼ D o

ð121  50Þ o 121 ¼ 80:34 C ln 50

Correction to LMTD read Figure 15-41A, 79  40 ¼ 0:2437 200  40 200  90 ¼ 2:82 R ¼ 79  40 Computed correction factor, F from Equations 15-34-37 gives F ¼ 0.8673 Corrected LMTD, DTCMTD ¼ (0.8673) (80.34) ¼ 69.43
C Step 5: Heat transfer area, A is: P ¼

Q ¼ U Ao DTCMTD Q 1886:8 x 103 ¼ 77:64 m2 Ao ¼ ¼ 350 x 69:43 U DTCMTD 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 ¼ 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: ATotal ¼ p Do L Nt Nt ¼

Step 8: Bundle and Shell Diameter From Table 15-46, for two tube passes, Kl ¼ 0.249 and nl ¼ 2.207

50°C

DTLMTD ¼

Ao 77:64 ¼ ¼ 259:46 ATotal ðpÞð0:01905Þð5Þ

Say 260 tubes. For two passes, the number of tubes per pass ¼ 260/2 ¼ 130 Check the tube-side fluid velocity, ut. p d2i p  ð0:01483Þ2 ¼ 4 4 ¼ 0:0001727 m2

Tube cross-sectional area ¼

Area per pass ¼ 130  0.0001727 ¼ 0.02246 m2 Volumetric flow rate, Q is:

¼ 444 mm Clearance is between 50 to 80 mm for split ring floating head Choose C ¼ 56 mm, so the shell inside diameter, Ds is Ds ¼ 444 þ 56 ¼ 500 mm. Step 9: Tube-Side Heat Transfer Coefficient, hi Re ¼

rut di 820  1:28  0:01483 ¼ ¼ 4864 m 3:2  103

Cp m 2:05  103  3:2  103 ¼ ¼ 48:96 k 0:134 Re ¼ 4864 and L/di ¼ (5000/14.84) ¼ 337 Pr ¼

jh ¼ 3:5  103 The heat transfer factor, jh correlation is: 

0:14 m mw  0:14 hi di m ¼ jh Re Pr kf mw   Assuming mmw is negligible, Nu ¼ jh Re Pr0:33

 hi ¼ 3:5  103

0:134 ð4864Þð48:96Þ0:33 0:01483

¼ 555:48 W=m2 :
C The tube-side velocity is low, if Uo ¼ 350 W/m2.
C. So, increase the number of tube passes to four. This will reduce the cross-sectional are by 1/2 and double the fluid velocity. ut ¼ 2  1:28 ¼ 2:56 m=s Re ¼ 2  4864 ¼ 9728 jh ¼ 3.9  103  hi ¼ 3:9  103

0:134 ð9728Þ ð48:96Þ0:33 0:01483


¼ 1237 W m2 C

Step 10. Shell-Side Heat Transfer Coefficient, Ho With four tube passes, the shell diameter will be larger, therefore from Table 15-46, Kl ¼ 0.175, nl ¼ 2.285 

1 Nt nl Kl  1 260 2:285 ¼ 19:05 0:175

Db ¼ Do The tube-side velocity, ut is: 0:02879 m ¼ 1:28 0:02246 s This velocity is satisfactory, but may a little low. ut ¼

213

¼ 465:6 mm The bundle shell clearance is still 56 mm

214

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Ds ¼ 465:6 þ 56 ¼ 521:6 mm ð522 mmÞ Ds 5

As a first trial, take the baffle ¼ 521:6 ¼ 104:32 mm 5 The shell-side flow area is:   p  d o D s Bs As ¼ t pt

spacing

¼

This value is above the initial estimate for Uo ¼ 350 W/m2.
C. Percentage difference between Uo and Uocal is: 0
2,100), the friction factor depends on the roughness of the tube material. From Figure 15-55, at Re ¼ 9728, the tube-side friction factor, Jf is: Jf ¼ 4.8  103

Volumetric flow rate is: Q ¼

25; 000 1 m  ¼ 0:00951 s 3600 730

L 5 ¼ ¼ 337:15 di 0:01483

3

Nt ¼ 4, r ¼ 820 kg/m3, ut ¼ 2.56 m/s The pressure drop for the tube-side is:

The shell-side fluid velocity, us: us ¼

Q 0:00951 m ¼ 0:51 ¼ As 0:01853 s

Re ¼

rus de 730  0:51  0:01353 ¼ ¼ 11; 714 m 0:43  103

Pr ¼

Cp m 2:47  103  0:43  103 ¼ 8:17 ¼ 0:13 k

Use a segmental baffle cut with 25% cut, from Figure 15-84A, the heat transfer factor, jh is: jh ¼ 5.8  103  0:14 ho de m ¼ Jh Re Pr0:33 Nu ¼ k mw

 Assuming mmw is negligible,  0:132 0:33 ð11; 714Þ ð8:17Þ ho ¼ 5:8  10 3 0:01353 
¼ 1325:69 W m2 C Step 11. Overall Heat Transfer Coefficient, Uocal  d   do ln o 1 1 do 1 do 1 di ¼ þ þ Rdi þ þ Uo;cal hi di hio di ho 2kw   1 1 19:05 ¼ þ 0:00035 Uo;cal 1237 14:83  19:05 19:05  103 ln 1 14:83 þ þ þ 0:0002 ð2  55Þ 1325:69 ¼ 402:3 W=m2 :
C

Uocal  Uo:ass < 30% Uo;ass

"





m

#

rv2t ; N=m2 ðPaÞ 2   ¼ 4½8  4:8  103  337:15 þ 2:5  820  2:562 2 Dpt ¼ Nt 8Jf

L Di

m mw

þ 2:5

¼ 96443:9 N=m2 ð0:96 barÞ This pressure drop is slightly higher than the allowable Dpt ¼ 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 (w15% of the total); which leaves 0.8 bar across the tubes. DPt fu2t 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, Dps With four tube passes, the shell diameter will be larger, therefore from Table 15-46, Kl ¼ 0.175, nl ¼ 2.285  Db ¼ D o

Ds 5

 1 1 Nt nl 260 2:285 ¼ 19:05 ¼ 465:6 mm 0:175 Kl

The bundle shell clearance is still 56 mm Ds ¼ 465.6 þ 56 ¼ 521.6 mm (522 mm) As a first trial, take the baffle ¼ 521:6 ¼ 104:32 mm 5

spacing

¼

Heat Transfer Chapter | 15

ð23:81  19:05Þ  522  104 ¼ 10853:04 mm2 23:81 ¼ 0:01853 m2 1:094  2 2 pt  0:913do de ¼ do  1:094  23:812  0:913  19:052 ¼ 13:53 mm ¼ 19:05 Volumetric flow rate is: As ¼

25; 000 1 m3  ¼ 0:00951 s 3600 730 The shell-side fluid velocity, us: Q ¼

Q 0:00951 m us ¼ ¼ 0:51 ¼ As 0:01853 s Re ¼

rus de 730  0:51  0:01353 ¼ ¼ 11; 714 m 0:43  103

At Re ¼ 11,714 and at 25% baffle cut, From Figure 15-56, the shell-side friction factor, Jf is: Jf ¼ 4.8  102 The pressure drop, Dps is:    0:14 Ds L ru2s m ; N=m2 ðPaÞ de 2 Bs mw   
522 5000 730  0:512 ¼ 8 4:8  102 2 13:75 104

Dps ¼ 8jf

tw ¼ 27.16 þ 59.5 ¼ 86.66
C The crude oil viscosity at this temperature ¼ 2.1  103 Ns/m2 0:14

The viscosity factor ðm=mw Þ

Viscosity Correction Factor ðm=mw Þ0:14 The viscosity correction factor ðm=mw Þ0:14 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. The inside area of the tubes ¼ p  13:75  103  5  260 ¼ 56:2 m2 Heat flux ¼ Q/A ¼ 1886.8  103 / 56.2 ¼ 33,599.2 W/m2 The heat balance on the tube wall is: (tw  t) hi ¼ 33,559.2 where hi ¼ 1237 W/m2
C, t is the mean temperature and tw is the wall temperature. tw  t ¼ 33,559.2 / 1237 ¼ 27.16

 ¼

3:2  103 2:1  103

0:14 ¼ 1:06

This value shows the viscosity factor can be neglected.

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 [70]: fG2t Ln fG2t Ln ¼ ; psi (15-237) 10 2grDi ft 5:22ð10Þ Di sft The friction factor, f, ft2/in.2, must be obtained from Figure 15-97. Because it is not a dimensional factor, the Dpt relations take this into account. Dpt ¼

 ft ¼

¼ 66537:87 N=m2 ð0:7 barÞ 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. 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 what is required. However, Kern’s method is only an approximation and a detailed design will require the use of simulation software as described earlier.

215

 ft ¼

m mw m mw

0:14 for Re > 2; 100

(15-238)

for Re < 2; 100

(15-239)

0:25

For non-condensing gases and vapors in Equation 15-237, use the average of the 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 15-98. In SI units:   2  a L Gt m (15-240) Dpt ¼ 4 f n 2r mw Di where: a ¼ 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 [36]: For streamline flow, Re < 2,100: 16 ðsee note below regarding fÞ Di Gt =m and this can be used in Equation 15-248 The turbulent flow [38], Re > 2,100: ff ¼

0:2  Di Gt f f ¼ 0:048 m

(15-241)

(15-242)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-97 Heating and cooling in tube bundlesetube-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.)

Divide this f by 144 in order to use an Dpt Equation 15-237. Stoever [108,109] 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 [70]. y

4nv2 2g0 c

Dpr ¼

4nðG00 Þ 2g0 s

2



1 ð62:5Þð144Þ

(15-245)

G00 ¼ mass velocity for tube-side flow, lb/(s) (ft2 crosssection of tube) In SI units: Dpr ¼ 4n

rv2 ; N=m2 2

(15-246)

or: (15-243) This is given in Figure 15-99. Where: Dpr ¼ return end pressure loss, including entrance losses, psi n ¼ number of tubes passes per exchanger g0 c ¼ gravitational constant 32.174 lbm/lbf . ft/s2 rH2 O ¼ density of water (62.5 lbm/ft3) s ¼ specific gravity of fluid (vapor or liquid) referred to water v ¼ tube velocity, ft/s

Dpr ¼ 4n

G2t 2r

where: G ¼ mass fluid velocity, kg/m2 s n ¼ number of tube passes r ¼ fluid density, (kg/m3) v ¼ fluid tube velocity, m/s Total Tube-Side Pressure Drop ¼ Dpt þ Dpr ; psi

(15-247)

Heat Transfer Chapter | 15

217

FIGURE 15-98 Pressure drop for water in smooth tubes at 68
F. (Used by permission: Scovill Heat Exchanger Tube Manual, 3rd Ed. Scovill Manufacturing Co.)

Tube-Side Condensation Pressure Drop Kern [70] recommends the following conservative relation: Dpt ¼

9:56ð10Þ12 fðGt Þ2 Ln ; psi Di s

(15-248)

This is one-half the values calculated for straight fluid drop, based on inlet flows; f is from Figure 15-97.

Shell-Side Pressure losses through the shell-side of exchangers are subject to much more uncertainty in evaluation than the 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 aboveatmospheric 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 [279]. Unbaffled Shells For short exchangers with no shell-side baffles, the pressure drop is usually negligible. Allowances should be made for nozzle entrances and exits if the pressure level of the system warrants this level of detail. For longer units requiring support plates for the tubes, the pressure drop will still be very small or negligible, and can be estimated by Figure 15-100 using the appropriate

218

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-99 Tube-side end return pressure drop per tube pass; viscosity close to water.

baffle cut curve to match the tube support cut-out of about 50%. Kern [70] recommends that the flow be considered similar to an annulus of a double pipe and treated accordingly. Equivalent shell-side diameter for pressure drop, D0 e : ¼

4ðflow area of space between shell and tubesÞ wetted perimeter of tubes þ wetted perimeter of shell I:D: (15-249)


D0 e ¼

pD2s =4  Npdo =4



þ p D12s

Dps ¼

f s G2s LNc 5:22ð10Þ10 D0 e sfs

; psi

(15-251)

where Nc ¼ 1 for single-pass shell, no baffles

144 Npdo 12

The friction factor, fs, is determined using Figure 15-100 for shell-side pressure drop with De, used in determining Re. For bundles with bare tubes (plain tubes), fs ¼ f/1.2 (see Figure 15-100), calculate pressure drop:

(15-250)

where: D0 e ¼ equivalent diameter for pressure drop of bundle in shell, ft Ds ¼ shell I.D. in. N ¼ number of tubes do ¼ tube OD, in.

fs ¼ ðm=mw Þ

0:14

Dps ¼ shell-side pressure drop with no baffles, psi Segmental Baffles in Shell Figure 15-100 is used for determining the friction factor (dimensional) for segmental type baffles. The loss across the tube bundle and through the baffle ‘window’ is represented in the combined factor, f, which is to be used with the equation for pressure drop [70].

Heat Transfer Chapter | 15

FIGURE 15-100 Shell-side friction factors for low-finned and plain tubes. (Used by permission: Engineering Data Book, © 1960. Wolverine Tube, Inc.)

219

220

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Dps ¼

f s G2s D0 s ðNc þ 1Þ 5:22ð10Þ De s fs

Dps ¼

also

10

; psi

f s G2s D0 s ðNc þ 1Þ 2grDe fs

(15-252)

(15-253)

In SI units Dps ¼

f G2s D0 s ðNc þ 1Þ 2 rDe

 0:14 mw ; N=m2 m

(15-254)

The friction factor can be correlated as a function of the shell Reynolds number. The correlations are presented graphically in the original source. A numerical regression of the curves gives the following [287]: For Res < 500  2 f ¼ exp 5:1858  1:7645 lnðRes Þ þ 0:13357 ½ln ðRes Þ (15-255) For Res > 500 f ¼ 1:728 Re0:188

(15-256)

where: fs ¼ friction factor from Figure 15-100 for plain bare tubes, fs ¼ f/1.2 (from Figure 15-100), shell-side: Gs ¼ mass velocity, lb/h (ft2 of flow area), [kg/m2.s] De ¼ equivalent diameter of tubes, ft. See Figure 15-86 or Table 15-41. Ds0 ¼ I.D. of shell, ft [m] Nc ¼ number of baffles (Nc þ 1) ¼ number of times fluid crosses bundle from inlet to outlet g ¼ 4.17  108 ft/h2 s ¼ specific gravity of gas or liquid referenced to water fs ¼ ðm=mw Þ0:14 , subscript w refers to wall condition m ¼ viscosity, lb/h (ft) ¼ (centipose) (2.42)

Donohue [36] reports agreement of  36% in turbulent flow conditions. where: Dps ¼ total shell-side pressure drop, psi Dpb ¼ pressure drop across window opening of segmental baffles, total for all baffles, psi Dpc ¼ pressure drop across the bundle in cross-flow, psi s ¼ specific gravity of gas or liquid referenced to water Nc ¼ number of baffles Gb ¼ flow rate, lb fluid/(h) (ft2 of flow cross-section area through window opening in baffle) b. Bundle Cross-flow Pressure Drop, Dpc, psi, Williams [126] ! cb f f ðGc Þ2 (15-259) ðnc ÞðNc þ 1Þ Dpc ¼ 109 grðm=mw Þ0:14 ff ¼ (f, from Figure 15-100) (144) Note: f from Figure 15-100 must be divided by 1.2 when plain bare tubes are used. cb ¼ 1.07 for bare tubes ¼ 1.2 for low-finned tubes

For values of specific gravity for non-condensing gases and vapors use the average density at the inlet and outlet conditions referenced to water at 62.4 lb/ft3.

Alternate: Segmental Baffles Pressure Drop Dps ¼ Dpb þ Dpc

(15-257)

a. Baffle Window Pressure Drop Dpb, psi This drop is usually very small unless the baffle cut has been limited to a low value [36]. Dpb ¼

2:9ð10Þ

13

ðGb Þ ðNc Þ ; psi s 2

(15-258)

FIGURE 15-101 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.)

Heat Transfer Chapter | 15

As an alternative, consider the equation of Chilton and Generaux [28,82]:  (15-260) Dpc ¼ 4 f 00 s nc G2max ð2g0 rÞð144Þ For triangular pitch [57,58,82]: rt from 1.5 to 4.0 " # 1:16 0:1175 Do Gmax 00 f s ¼ 0:25 þ 1:08 m0 f ðrt  1Þ For square or in-line pitch [57,58,82]. rt from 1.5 to 4.0  0:15
0:08r1 Do Gmax f 00 s ¼ 0:044 þ ðrt  1Þa m0 f a ¼ 0:43 þ

1:13 r1

(15-261)

(15-263)

cb ¼ constant ff ¼ dimensionless friction factor for shell-side crossflow Gc ¼ mass flow, lb/(h) (ft2 of cross-section at minimum free area in cross-flow) Gmax ¼ mass flow, lb/s (ft2 of cross-section at minimum free area in cross-flow) r ¼ fluid density, lb/ft3 g0 ¼ acceleration constant 32.2 ft/s2 m=mw ¼ viscosity ratio of fluid at bulk temperature to that at wall temperature m0f ¼ absolute viscosity, lb/(ft-s), m0t ¼ (centipoises) (0.000672) nc ¼ minimum number of tube rows fluid crosses in flowing from one baffle window to one adjacent. Nc ¼ number of baffles Dpc ¼ bundle cross-flow pressure drop, psi

rl ¼

Tube pitch; in: Tube O:D:; in:

Tube pitch; in: Tube O:D:; in:

transverse to fluid flow; dimensionless

longitudinal value in direction of fluid flow; dimensionless

McAdams [82] points out that at rt of 1.25, the pressure drop may deviate high as much as 50% and is high for rt < 1.5 and > 4. Streamline flow shell-side cross-flow; modified Donohue [38]. 5

Dpc ¼ 3:02ð10Þ

ðnc ÞGc m0 ; psi sðp  do Þ

s ¼ specific gravity of fluid referenced to water p ¼ tube pitch, in. do ¼ tube O.D., in. m0 ¼ viscosity, centipoise, at average temperature Shell-Side Pressure Drop in Condensers Kern [70] recommends Equation 15-265 as being conservative: 12

where:

rt ¼

where:

Dps ¼ (15-262)

(15-264)

221

9:56ð10Þ

ðf s ÞG2s D0s ðNc þ 1Þ ; psi D0 e s

(15-265)

This equation gives values that are half of those calculated as total gas flow for the shell-side by using friction factors from Figure 15-100. (Note that fs for plain or bare tubes ¼ f/1.2 (from Figure 15-100)). The method of Buthod [22] has given unusually good checks with data from industrial units. In general, this method appears to give results that are slightly higher than field data but not as high as the other methods presented previously. For shell-side pressure drop: Dps ðtotalÞ ¼ Dplong: þ Dpc

(15-266)

1. Calculate loss due to longitudinal flow through tube bundle; use Figure 15-101. G ðlongitudinalÞ ¼

p 4



  0:04Ws  ; lb=s ft2 (15-267)  Ndo Bca

D2s

where: Ws ¼ shell-side flow, lb/h Ds ¼ shell I.D. in. do ¼ tube O.D. in. N ¼ number of tubes in bundle Bca ¼ baffle cut area, expressed as fraction, representing opening as percent of shell cross- section area. From the chart, read Dplong per baffle, as psi. To obtain total longitudinal drop, multiply by the number of baffles. 2. Calculate loss due to cross-flow through the tube bundle, use Figure 15-102    G ðcross-flowÞ ¼ ð0:04 WÞ ðBÞðMÞ; lb s ft2 (15-268) where: B ¼ baffle pitch or spacing in. M ¼ net free distance (sum) of spaces between tubes from wall to wall at center of shell circle, in.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-102 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.)

B is held to a 2 in. minimum or 1/5 shell diameter (I.D.) and is 26 in. maximum for 3/4 in tubes and 30 in. for 1 in. tubes. Refer to TEMA for tube support and baffle spacing recommendations. Read pressure drop factor, Fp, from Figure 15-102.   ðFt Þ Fp ðNc þ 1Þðnc Þ ; psi (15-269) Dpc ðcross-flowÞ ¼ r where: Ft ¼ tube size factor, from table on Figure 15-102 Fp ¼ pressure drop factor, Figure 15-102 Nc ¼ number of baffles nc ¼ number of rows of tubes in cross-flow r ¼ density of fluid, lb/ft3 The number of tube rows that will be crossed as the fluid flows around the edge of one baffle and then crosses over to the next baffle is used as for conventional designs. nc ¼ 0.9 (total tube rows in shell at center line). Manish V. Shah [374] has presented an excellent article on good practice for heat exchanger selection and design and his article is in Appendix O of this volume.

Shell and Tube Heat Exchangers: Single Phase The shell-side fluid enters the shell through one or more nozzles, and, after passing through the shell one or more times depending on the number of shell passes, exits from it through one or more nozzles. In the shell, the fluid flows over the tube bundle several times depending upon the

number of baffles, except in the X-type shell or when rod baffles are used. The flow over the tube bundle is crossflow between consecutive baffles and parallel flow in the baffle window. In the X-type shell, fluid is distributed in each baffled zone by a manifold and flows over the tube bundle only once. For ease in threading the tubes through the baffles, a slight clearance is allowed between the tube holes in the baffles and the tube outside diameter (OD). Similarly, for ease in pushing a tube bundle into the shell, a slight clearance is again allowed between the shell internal diameter (ID) and the baffle. These clearances are referred to as manufacturing clearances. The clearance between the baffle holes and the tube OD depends upon the tube OD and the unsupported tube length (baffle spacing). It is governed by the TEMA Standards paragraphs R, C. B-4.2. It is generally 1/32 in. (0.8 mm) in diameter, when the unsupported tube length is 36 in. (910 mm) or less, and 1/64 in. (0.4 mm) when the unsupported tube length is longer. The clearance between the shell ID and the baffles depends upon the shell diameter. It is governed by the TEMA Standards, paragraphs, R, C, B-4.3, RGP.RCB-4.3 and varies from a minimum of 0.1 in. (2.5 mm) for a shell of 6 in. (150 mm) diameter to a maximum of 0.438 in. (11 mm) for a shell of 100 in. (2500 mm) diameter.

Effect of Manufacturing Clearances on the Shell-Side Flow Tinker [290,291] was the first to show the effects of the manufacturing clearances on the shell-side flow. He divided the flow into four streams, namely: A, B, C and E as

Heat Transfer Chapter | 15

illustrated in Figures 15-103e107. These streams are briefly described as: 1. Stream A (Figure 15-103). Since the fluid loses pressure as it flows through the exchanger, there is a net pressure difference between any two consecutive baffled zones. This forces a part of the fluid to leak through the annular space between the tube OD and the tube holes in the baffle. This is referred to as a leakage stream. 2. Stream B (Figure 15-104). This is the stream in crossflow over the tube bundle between any two baffles. It comes closest to the theoretical analysis of flow over an ideal tube bank. The main effort in the design should be to maximize the amount of the B-stream within the

223

allowable pressure drop. This is known as the crossflow stream. 3. Stream C (Figure 15-105). The resistance to fluid flow is the maximum in cross-flow over the tube bundle and the least in the space between the shell ID and the outer tube limit (OTL) (i.e., a contour around the outermost tubes in the tube layout by replacing a few tube for each set of a tie-rod and spacer). Since any fluid prefers to take the path of least resistance, a part of the total stream flows through this space. This is referred to as a bypass stream, since it bypasses the tube bundle. This stream is very small in fixed tubesheet designs and in U-tube bundles, but is significant in floating head designs, because the space between the shell ID

FIGURE 15-103 Tube-to-baffle hole leakage stream, A-stream.

FIGURE 15-104 Shell-side flow streams in a typical unit. B-stream is cross-flow (Source: TInker)

224

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

5. Stream F (Figure 15-107). This stream was introduced by Palen and Taborek [91] as the pass partition stream, where the fluid flows through the gap in the tube arrangement due to the pass partition plates. Where the gap is vertical, it provides a low-pressure drop path for fluid flow.

FIGURE 15-105 Shell-to-tube bundle by pass stream, C-stream.

The complex flow pattern on the shell-side and the large number of variables involved make it difficult to predict the shell-side heat transfer coefficient and pressure drop with certainty. In the methods used for the design of exchangers illustrated earlier, no attempt was made to account for the leakage and bypass streams. Generally, correlations were based on the total stream flow, and empirical methods were used to account for the performance of real exchangers compared with that for cross-flow over ideal tube banks. The methods of Kern [70] and Donohue [36,37,38] are typical, and reliable predictions can only be achieved by comprehensive analysis of the contribution to heat transfer and pressure drop made by the individual streams shown in Figures 15-103e107.

Bell-Delaware Method

FIGURE 15-106 Shell-to-to baffle leakage stream, E-stream.

Accurate sizing of the shell and tube heat exchanger requires the Bell-Delaware method to determine the shellside film heat transfer coefficient, as described by Bejan and Kraus [368] 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.

Ideal Shell-Side Film Heat Transfer Coefficient The heat transfer film coefficient on the outside of the tube is defined by: ho ¼ hideal Jc Jl Jb Js Jr FIGURE 15-107 Pass partition by pass stream, F-stream.

and the OTL is large. To reduce the amount of the Cstream in the floating head, seal strips or dummy tubes are used. 4. Stream E (Figure 15-106). There is a leakage through the annular space between the shell ID and the baffle due to the difference in the pressure of the fluid on either side of a baffle. This is referred to as a leakage stream.

(15-270)

where: hideal ¼ ideal heat transfer coefficient for pure crossflow in an ideal tube bank. Jc ¼ Factor due to baffle cut and spacing. Jl ¼ Factor due to baffle leakage effects. Jb ¼ Factor due to flow that bypasses the tube bundle and partition effects. Js ¼ Factor that accounts for the variations in baffle spacing. Jr ¼ Factor that accounts for the temperature gradient for laminar flow regime.

Heat Transfer Chapter | 15

Due to the nature of the correction factors, many geometrical properties of the shell, such as baffle cut, baffle spacing, shell diameter and outside diameter of the tube bundle, must be known or estimated. The procedure uses geometrical properties to calculate each factor, and where these properties are unknown, then a total correction of 0.6 may be used (i.e. ho¼ 0.6 hideal) as a rule of thumb [372]. The procedure involves the following steps: Calculate the ideal heat transfer coefficient for pure crossflow in an ideal tube bank [369].   2=3  0:14 ws ks ms (15-271) hideal ¼ Jideal cps As cps ms ms;w The subscript s stands for physical properties at the average temperature of the shell-side fluid; subscript w is at the wall temperature. where: As ¼ bundle crossflow area at the centerline of the shell between two baffles. Jideal ¼ the Colburn factor for an ideal tube bank. Ws ¼ mass flow rate of shell-side fluid across the tube bank. For 30
and 90
tube layout bundles, 45
layout with pt/do  1.707 and 60
layout with pt/do  3.732:
  p  do (15-272) As ¼ Bs Ds  Dotl þ ðDotl  do Þ n pn For 45
and 60
layouts with ratios less than 1.707 and 3.732, respectively, the equation is:
  pt  do (15-273) As ¼ Bs Ds  Dotl þ ðDotl  do Þ pn where: Bs ¼ baffles spacing do ¼ Tube outside diameter Ds ¼ Shell inside diameter Dotl ¼ outside diameter of the tube bundle pt ¼ tube pitch, (PR  do), which is the Pitch Ratio  tube OD pn ¼ pitch normal to the flow direction (Table 15-46A) The Colburn factor is a function of the shell-side Reynolds number: Res ¼

do W s ms As

TABLE 15-46A Tube Geometry as a Function of Tube Pitch, pt Pitch Normal to Flow, pn

Tube Layout 30
Triangular Staggered Array

90
Square Inline Array 45
Rotated Square Staggered Array

Pitch Parallel to Flow, pp

pffiffiffi 3 pt

pffiffiffi 3 pt 2 pt 2

pt

pt

pffiffiffi 2 pt

pt pffiffiffi 2

pt

60
Rotated Triangular Staggered Array

where: a ¼

a3 1 þ 0:14 Reas 4

(15-276)

The coefficients of a1, a2, a3, a4 shown in Table 15-47 depend on the tube pitch layout and Reynolds number.

Shell-Side Film Heat Transfer Coefficient Correction Factors This section describes the five Bell-Delaware correction factors where the equations require additional information about the construction of the heat exchanger. Baffle Cut and Spacing, Jc This factor accounts for the heat transfer rate that occurs in the baffle window where the shell-side fluid flows more longitudinally, deviating from the ideal cross-flow arrangement. It is related to the shell diameter, tube diameter and baffle cut. The value ranges from w0.53 for a large baffle cut, up to 1.15 for small windows with a high window velocity. If there are no tubes in the window, Jc ¼ 1.0 [369]. It is expressed as a fraction of the number of tubes in cross-flow, Fc [368]. The equation assumes single segmental baffles: Jc ¼ 0:55 þ 0:72 Fc

(15-277)

where: Fc ¼

(15-274)

Calculate Jideal from the following relationship:  a 1:33 Reas 2 (15-275) Jideal ¼ a1 PR=do

225

1 ½p þ 2f sin ðarc cos fÞ  2 arccos f (15-278) p f ¼

Ds  2 lc Dotl

(15-279)

where Dotl ¼ outside diameter of the tube bundle, in. (mm). Ds ¼ shell inside diameter, in. (mm).

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-47 Correlation Coefficients for Jideal and fideal [369] Pitch Layout

Reynolds Number

a1

a2

a3

a4

b1

b2

b3

b4

30

0e10

1.4

0.667

1.45

0.519

48

1

7

0.5

30

10e100

1.36

0.657

1.45

0.519

45.1

0.973

7

0.5

30

100e1000

0.593

0.477

1.45

0.519

4.57

0.476

7

0.5

30

1000e10000

0.321

0.388

1.45

0.519

0.486

0.152

7

0.5

30

10000þ

0.321

0.388

1.45

0.519

0.372

0.123

7

0.5

45

0e10

1.55

0.667

1.93

0.5

32

1

6.59

0.52

45

10e100

0.498

0.656

1.93

0.5

26.2

0.913

6.59

0.52

45

100e1000

0.73

0.5

1.93

0.5

3.5

0.476

6.59

0.52

45

1000e10000

0.37

0.396

1.93

0.5

0.333

0.136

6.59

0.52

45

10000þ

0.37

0.396

1.93

0.5

0.303

0.126

6.59

0.52

60

0e10

1.4

0.667

1.45

0.519

48

1

7

0.5

60

10e100

1.36

0.657

1.45

0.519

45.1

0.973

7

0.5

60

100e1000

0.593

0.477

1.45

0.519

4.57

0.476

7

0.5

60

1000e10000

0.321

0.388

1.45

0.519

0.486

0.152

7

0.5

60

10000þ

0.321

0.388

1.45

0.519

0.372

0.123

7

0.5

90

0e10

0.97

0.667

1.187

0.37

35

1

6.3

0.378

90

10e100

0.9

0.631

1.187

0.37

32.1

0.0963

6.3

0.378

90

100e1000

0.408

0.46

1.187

0.37

6.09

0.602

6.3

0.378

90

1000e10000

0.107

0.266

1.187

0.37

0.0815

0.022

6.3

0.378

90

10000þ

0.37

0.395

1.187

0.37

0.391

0.148

6.3

0.378

lc ¼ baffle cut ¼ distance from the baffle to the inside of the shell, in. (mm). f ¼ angle in radians

Asb, Atb and Aw are determined by the following expressions: The shell to baffle leakage area is: 1 ðp  q1 Þ Ds dsb 2

(15-283)

 2 lc q1 ¼ arc cos 1  Ds

(15-284)

Asb ¼

Baffle Leakage Effects, JL This factor includes tube-to-shell and tube-to-baffle leakage, where the shell fluid bypasses the normal flow path. If baffles are too closely spaced, the fraction of flow in the leakage stream increases compared with cross-flow. It is typically between 0.7 and 0.8 [369]. JL is expressed by: JL ¼ 0:44ð1  ra Þ þ ½1  0:044 ð1  ra Þ expð2:2rb Þ (15-280) where: Asb ra ¼ Asb þ Atb

(15-281)

Asb þ Atb rb ¼ Aw

(15-282)

where:

dsb ¼ Ds  Db , shell-to-baffle spacing from Table 15-48. Db ¼ baffle diameter. The tube-to-baffle leakage area, Atb is: Atb ¼

p do ð1  Fw Þ Nt dtb 4

(15-285)

where: q3 Fw ¼ q3 sin 2 p , fraction of the total number of tubes in one window

Heat Transfer Chapter | 15

TABLE 15-48 Diametric Shell-to Baffle Clearance, Based on TEMA Class R [352]

Nominal Shell DN

Inches

200 to 325

8 to 13

350 to 425

Diameter Shell

Type Difference in Shell-to-Baffle Diameter Millimeters

Inches

Pipe

2.540

0.100

14 to 17

Pipe

3.175

0.125

450 to 575

18 to 23

Pipe

3.810

0.150

600 to 975

24 to 39

Rolled

4.445

0.175

1000 to 1350

40 to 54

Rolled

5.715

0.225

1375 to 1500

55 to 60

Rolled

7.620

0.300

This parameter strongly influences the calculation of Jl. The clearance may be reduced to 0.00035 to 0.004 times the shell diameter limit the baffle to-shell leak stream, but only for rolled shells and only if necessary since it is hard to guarantee compliance [333].

 D s  2 lc q3 ¼ 2 arc cos Ds  C1

The shell to outer tube limit distance, C1 is expressed by: (15-287) C1 ¼ Ds  Dotl dtb ¼ baffle hole diameter  tube OD (usually 0.8 mm or 0.03125 in., but may be reduced to 0.4 mm or 0.0156 in. to reduce the leak stream between the tube and baffle hole [320]). The free area for fluid flow in one window section is: Aw ¼ Awg  Awt

(15-288)

Where the gross window area, Awg is: Ds ðq2  sin q2 Þ 8  l  2 lc q2 ¼ arc cos Ds Awg ¼

(15-289) (15-290)

The area occupied by tubes in one window, Awt is: p ntw do 4 and the number of tubes in the window, ntw is: Awt ¼

ntw ¼ Fw nt

Bundle and Partition Bypass Effects, Jb This factor corrects for flow that bypasses the tube bundle due to clearance between the outermost tubes and the shell and pass dividers. For exchangers with very small clearances the factor is about 0.9, but larger clearances are required for a pull-through floating head where the factor is about 0.7. Sealing strips can increase the value [369], and a rule of thumb is to use one pair of sealing strips for approximately every six tube rows. The expression for Jb is:    1 Jb ¼ exp Crc 1  221=3 for 2 < (15-293) 2 or Jb ¼ 1 for 2  12 where C ¼ 1.35 for Res  100 or 1.25 for Res > 100 Abp (15-294) As ss (API Standard 660 requires a seal device from 2 ¼ nnr;cc 1 in. to 3 in. (25 mm to 75 mm) from the baffle tips and for every 5 to 7 tube pitches thereafter [320], resulting to the rule of thumb of 0.17 for this parameter). nss ¼ number of sealing strip pairs. The effective tube rows crossed through one cross-flow section, nr, cc is: rc ¼

nr;cc ¼ (15-286)

(15-291)

(15-292)

227

Ds  2 lc Pp

(15-295)

where: Ds ¼ inside diameter of the shell. lc ¼ baffle cut ¼ distance from the baffle to the inside of the shell, in. (mm). Pp ¼ longitudinal tube pitch. The tube bundle bypass area, Abp is:   Abp ¼ Lbc Ds  Dotl þ 0:5ndp wp

(15-296)

Lbc ¼ central baffle spacing in. (mm). ndp ¼ number of bypass divider lanes that are parallel to the crossflow stream. wp ¼ width of the bypass divider lane (if unknown, assume 2  Tube OD). Variations in Baffle Spacing, Js When the baffle spacing is increased at the ends of the exchanger to accommodate the nozzles, local decreases in the flow velocity are observed. This factor accounts for the subsequent decrease in heat transfer, and typically ranges from 0.85 to 1.0 [369]. Js is determined by: Js ¼

 ð1nÞ  ð1nÞ nb  1 þ L i þ L    o nb  1 þ L i þ L o

(15-297)

228

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

where:

where:

nb ¼ number of baffles in the exchanger

L i ¼

Lbi Lbc

L o ¼

Lbo Lbc

Uo ¼ overall heat transfer coefficient based on the outside area of the tubes. di, do ¼ inside and outside tube diameters respectively. hi, ho ¼ inside and outside film heat transfer coefficients. kw ¼ thermal conductivity of the tube material Rf,i, Rf,o ¼ fouling factors on the tube and shell-sides respectively.

where: Lbc ¼ central baffle spacing. Lbi ¼ baffle spacing at inlet. Lbo ¼ baffle spacing at outlet. n ¼ 1/3 for laminar flow or 3/5 for turbulent flow. Temperature Gradient for Laminar Flow Regime, Jr The final correction factor, Jr accounts for the temperature gradient when the Reynolds number on the shell-side is less than 100 (i.e., Re < 100). It is equal to 1.0 for Res  100. If Res  20, 0:18  10 (15-298) Jr ¼ nr;cc where: nr,cc ¼ the number of effective tube rows crossed through one crossflow section. For 20 < Res < 100, the line interpolation between the two extreme values is used [368].

Overall Heat Transfer Coefficient, U

1

Bd Bo @ di

  1 hi

þ

do ln

do di

2kw

1

(15-299)

C þ h1o C A

For fouled condition, the overall heat transfer coefficient is: 1

Uo;clean ¼ 0 Bd Bo @ di

1

  1 hi

þ

do Rf;i di

þ

do ln

do di

2kw

þ Rf;o þ

Shell-Side Pressure (Dp) The Bell-Delaware method accounts for tube bundle bypass and baffle leakage effects. It calculates a Dp 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 15-47 to determine the friction factor for an ideal tube bank, which depends on the tube layout and Reynolds number as:  b 1:33 Rebs 2 (15-301) f ideal ¼ b1 PR=do where:

The overall heat transfer coefficient, U, can be determined using the known parameters such as the tube (inside) and shell (outside) film heat transfer coefficients, fouling factors and the tube wall thermal conductivity, by use of: Uo;clean ¼ 0

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.

C

1C ho A

(15-300)

b ¼

b3 1 þ 0:14 Rebs 4

Dp for one ideal cross-flow section is:  0:14 4f ideal W2s nr;cc mw Dpb;ideal ¼ 2 rs g c A s m s

(15-302)

(15-303)

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 [369]. For a Reynolds number Res  100, Cbp ¼ 4:5. For Res > 100, Cbp ¼ 3:7. The limit of Rb is 1.0 for: 2  0:5 where 2 is the ratio of sealing strip pairs to tube rows in cross-flow section. pffiffiffiffiffi   (15-304) Rb ¼ exp Cbp rc 1  3 22

Heat Transfer Chapter | 15

The baffle leakage correction factor is a function of ra and rb, and it typically ranges from 0.4 to 0.5.   Rl ¼ exp 1:33 ð1 þ ra Þ rcb (15-305) c ¼ 0:15 ð1 þ ra Þ þ 0:8

(15-306)

2. The Baffle Windows For an ideal window, determine the Dp using the equation corresponding to the flow regime as: For Res  100: Dpw;ideal ¼ ð2 þ 0:6ntw Þ

rv2z 2

(15-307)

where vz is defined as the geometric mean between the cross-flow velocity and the window velocity and is determined by: pffiffiffiffiffiffiffiffiffiffi (15-308) v z ¼ vm vw vm ¼ cross-flow fluid velocity ¼ Gm/r vw ¼ fluid velocity through window ¼ Gw/r or Dpw;ideal ¼

ð2 þ 0:6ntw Þ 2rs gc As Aw

W2s

(15-309)

229

SIMSCI-ESSCOR using Bell-Delaware’s method in his examples.

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 15-193 and 15-194 are used to calculate de. However, this approach has been refuted by other authors for the following reasons [287]: 1. The equivalent diameter is defined for a flow direction parallel to the tubes, whereas the shell-side flow is normal to the tubes. 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 a 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.

If Res < 100

 ms W s nr;tw Lbc Ws þ 2 þ Dpw;ideal ¼ 26 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r As Aw r As Aw pt  do Dw (15-310) Dw ¼ nr;tw ¼

4 Aw p do ntw þ Ds2q2

0:8 ½lc  0:5ðDs  Dotl þ do Þ Pp

(15-311)

(15-312)

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: h i   Dps ¼ ðnb  1Þ Dpb;ideal Rb þ nb Dpw;ideal Rl  nr;tw þ 2 Dpb;ideal Rb 1 þ nr;cc (15-313) Cao Eduardo [287] and Hall [373] have presented Excel spreadsheet programs for the design of a shell and tube heat exchanger using the Bell-Delaware method, and Serth [288] has employed HEXTRAN software from Invensys

Accuracy of Correlations Between Kern’s Method and the Bell-Delaware Method Heat exchanger designs have been arrived at using the Kern’s, Tinker’s or Bell’s 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 [136] presented a study of the errors found in heat transfer coefficient and pressure drop predictions obtained with the Kern and Bell methods. Palen and Taborek [370] show that the Bell-Delaware method allows the prediction of shellside film coefficients in the range from 50% lower to 100% higher than the real values. Table 15-49 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 15-108 is an example of such a template (see also Figure 15-96).

230

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-49 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.

Dplam 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. Dp 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. [286]).

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

Heat Transfer Chapter | 15

FIGURE 15-108 Specification Process Data Sheet of Shell and Tube Heat Exchanger.

231

232

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Film

%

%

50

Viscosity

cP

lb/ft hr

51

Temps for Phase Change Start/Finish LMTD weighting Factor 'F'

-

55

PART 3 Number of Points in Table Below % Heat Load

%

%

56

Hot Fluid Temperature

C

F

57

59

Cold Fluid Temperature C PART 4 - CODE NUMBERS TO BE FILLED IN COMPLETELY Code Material for Description No.

60

Tubes

Yes/No

61

Shell

Yes/No

62

Floating Head

52 53 54

58

63 64

C

F -

1

2

3

O.D.

Thickness

4

5

6

7

8

9

10

Number

Contents Lethal?

F

Length

Passes

Tube Pitch = mm/in.

o

∆

Date

5

Channel Tube Sheets NOTES

Issue No.

1

Date

2

Date

3

Date

4

Date

Made/Revised by Checked by Approved- Process Approved by

FIGURE 15-108 cont’d

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. 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.

Rapid Design Algorithms for Shell and Tube and Compact Heat Exchangers: Polley et al. [371] Polley et al. [371] 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 crossflow 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.

Heat Transfer Chapter | 15

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 shellside velocity being determined from the shell-side 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 (Dp) 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 the 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). A

Input data E Solve:

Initialize: Shell-side friction factor Heat transfer j-factor

A=

F

Q 1 1 + R fs + + R ft ΔTLMTD FT h s ht

do di

Δp t = K t A h 3.5 t

Δps = ( K s1 A + K s2 ) h s2

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: Tube-side and shell-side constants

233

Estimate: Shell diameter

C

Update: shell diameter

Yes

Ds Changed?

No B

A

FIGURE 15-109 New algorithm for shell and tube exchanger design. (Source: G.T. Polley et al. Ref [371].)

234

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

E

B

D

Calculate Δps

Change: No. of tube pass

Search for: Baffle cut

Yes

Search fails?

Yes

Δps changed?

No No Estimate: Friction factor Heat transfer j-factor Δps

F

Update: Friction factor J -factor

Yes

Δps changed?

No Output: Performance specifications Geometrical specifications

FIGURE 15-109 cont’d

For compact heat exchangers, the approach can be extended to duties involving isothermal two-phase flows. Figure 15-109 shows the algorithm of the rapid design of the shell and tube heat exchanger, and the notations used in this figure are: A ¼ area (m2) d ¼ tube diameter (m) Ds ¼ shell diameter (m) FT ¼ DTLMTD correction factor (non-counter current flow) h ¼ film heat transfer coefficient (W/m2 K) K ¼ dimensional constant, solely dependent on physical properties, volumetric flow rate, and a single characteristic dimension. R ¼ fouling resistance (m2 K/W) Dp ¼ pressure drop (kPa)

Subscripts: i ¼ inside surface o ¼ outside surface s ¼ shell-side t ¼ tube-side 1 ¼ side 1 of compact exchanger 2 ¼ side 2 of compact exchanger

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 15-110. One fluid flows in the annulus between the

Heat Transfer Chapter | 15

235

D2 Tube (A)

D1

Tube (B)

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 15-110 Double-pipe tube arrangement showing annulus area.

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 15-76e82, 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.
F), 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 suitable for ‘dirty’ service, because it is easy to dismantle and clean. In addition, a double pipe exchanger can be considered in the following situations: l

l

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. At duties requiring 100e200 ft2 of the surface, which make it more economical when a true counter current 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 15-193), 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 (Figures 15-11A and B) are uniquely adaptable to the conventional shell and tube exchanger [16,127] (see Table 15-50) 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 15-11A, E, G and H and represent increased external finning possibilities. Internal ribs, shown in Figures 15-11K 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 [203] present the use of finned titanium in corrosive services. One of the outstanding books by Kern and Kraus [206] 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 those of Hashizume [208] and Webb [209].

236

19 Fins Per In. Nominal Size

Plain Section Dimensions

O.D.

O.D.

Wall Thk.

Rood Dia.

Wall Thickness

I.D.

dc

Outside Area ft2 per lin ft

Surface Area Ratio ao/ai

I.D. Cross Sectional Area, in.2

Approx. wt/ft lb (Copper)

5

.625

.042

.500

.028

.444

.535

.405

3.48

.155

.275

.049

.035

.430

3.60

.145

.316

.058

.042

.416

3.72

.136

.368

.065

.049

.402

3.85

.127

.408

.072

.065

.370

4.18

.108

.444

.028

.569

3.33

.254

.344

.049

.035

.555

3.41

.242

.376

.058

.042

.541

3.50

.230

.449

.065

.049

.527

3.60

.218

.490

.082

.065

.495

3.84

.192

.612

.095

.083

.459

4.13

.166

.695

.035

.680

3.30

.363

.483

.058

.042

.666

3.37

.349

.530

.065

.049

.652

3.44

.334

.589

.082

.065

.620

3.62

.302

.727

.095

.083

.584

3.85

.268

.829

.042

.791

3.27

.492

.612

.065

.049

.777

3.33

.474

.680

.082

.065

.745

3.48

.436

.841

.095

.083

.709

3.65

.395

.965

/8

3

/4

7

/8

1

.750

.875

1.000

.049

.054

.058

Finned Section Dimensions

.625

.750

.875

.660

.785

.910

.496

.588

.678

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-50 Approximate Estimating Physical Data for Low-Finned Tubing for Use in Design Calculations

16 Fins per in. 5

.625

.082

.500

.065

.370

.540

.368

3.80

.108

.497

3

.750

.082

.625

.065

.495

.665

.438

3.38

.192

.612

.083

.459

3.63

.166

.695

.065

.620

3.20

.302

.727

.083

.584

3.40

.268

.829

.065

.745

3.07

.436

.841

.083

.709

3.22

.395

.965

/8

/4

.095 7

/8

.875

.082

.750

.095 1

1.00

.082 .095

ALLOY

.875

.790

.917

.520

.598

wt/ft Conversion Factor (wt/ft of Copper 3 Conv. Factor wt/ft of Alloy) 1

Admiralty (type C)

.9531

Admiralty (types of B & D)

.9531

85/15 red brass

.9780

Aluminum brass (type B)

.9319

1100 aluminum

.3032

3003 aluminum

.3065

Nickel

1

70/30 cupro-nickel

1

90/10 cupo-nickel

1

Monel

1

Low carbon steel

.8761

Stainless steel

.8978

Note: Units are in., except as noted. Used by permission: Engineering Data Book, Section 2, ©1959. Wolverine Tube, Inc.

Heat Transfer Chapter | 15

Copper

237

238

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Low Finned Tubes, 16 and 19 Fins/In.

where: hfo ¼ mean outside finned surface heat transfer (usually gas) coefficient, Btu/(h) (
F) (ft2 external) Dr ¼ root diameter of tube (external), ft dn ¼ root diameter of tube, external, in. k ¼ thermal conductivity of gas, Btu/(h) (ft2) (
F/ft) Gmax ¼ gas mass velocity at minimum cross-section, through a row or tubes normal to flow, lb/(h) (ft2) Gm ¼ mass velocity at minimum cross-section through a row of tubes normal to flow, lb/(h) (ft2) g ¼ acceleration of gravity, 4.18  108, ft/(h) (h) n ¼ number of rows in direction of flow m ¼ gas/vapor viscosity at bulk temperature, lb/(h) (ft) cp ¼ specific heat, Btu/(lb) (
F) s ¼ distance between adjacent fins, in. l ¼ fin height, in. t ¼ fin thickness, in. Pt ¼ transverse pitch between adjacent tubes in same row, in. Pl ¼ longitudinal pitch between adjacent tubes in different rows measured on the diagonal, in. DP ¼ static pressure drop, lbf/ft2 r ¼ density of gas, lb/ft3 f ¼ mean friction factor, this is the “small” or fanning friction factor.

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.

Finned Surface Heat Transfer Rohsenow and Hartnett [166] recommend the Briggs and Young [205] convection film coefficient relation for externally finned tubes.  1=3 0:681 0:2 0:113 cp m hfo Dr ðDr Gmax Þ ðsÞ ðsÞ ¼ 0:134 k ðmÞ ðkÞ l t (15-314)

TABLE 15-51 Comparison of Calculated, Designed, and Operating Uo Values; 3/4-in., 19 Fins/in. Finned Tubes Calc’d. Uo

Designed Uo

Operating Uo

Comments

Propane condenser (66 F H2O)

0

35

47.4

0

Ethylene cross exchanger (liquid to gas)

9.9

9.5

14.8

0

Ethylene compressor intercooler (67
F H2O)

21

18

28.7

0

Ethylene compressor aftercooler (67
F H2O)

21

18.3

16.3

Possibly fouled by oil.

Propane compressor intercooler (67
F H2O)

21.6

20

23.8

0

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

0

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.

Service


Heat Transfer Chapter | 15

239

Note: f ¼ DP gc r/(nG2m)

Pressure Drop Across Finned Tubes [166] 0:316

ðGm Dr Þ Dp ¼ 18:93 ðmÞ

0:927

ðPt Þ ðDr Þ

ðPt Þ ðPl Þ

0:515

 2  G n  m  gc r (15-315)

These equations provide reasonable estimates per Rohsenow [166], who suggests using it with caution, only when performance on the system is not available. Ganapathy [204] offers simplified equations and nomographs to solve these relationships. Table 15-51 provides a suggested range of overall heat transfer coefficients, Uo, for actual finned heat exchangers.

Economics of Finned Tubes Figure 15-111 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 5-112 and 113 [126] also indicate the relative advantage regions for the finned unit, for the average

FIGURE 15-112 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.)

FIGURE 15-111 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.)

FIGURE 15-113 Generalized design evaluation of low-finned tubes and fluid heat exchangers. (Used by permission: “An Opportunity.” Wolverine Tube, Inc.)

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water cooled exchanger of 150 psi design. 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. Again, these are not to be used for specific exchanger design, but merely in deciding the region of applicability. Wolverine [21] has presented evaluations of the cost comparisons for various types of exchangers and tube materials. Figure 15-114 gives a rough indication of the possible advantages of a finned tube unit when referenced to a specific design. If the film heat transfer coefficients and fouling factors based on plain tubes are known, the reduction in the number of finned tubes for the same length and service can be approximated roughly. A significant saving arises when a reduction in shell diameter can be effected, based on the estimated reduction in the number of tubes. The results of this graph should indicate whether a detailed comparison in design is justified; keep in mind that the curve is based on an average set of conditions.

Tubing Dimensions, Table 15-50 For finned tube efficiencies, see Figure 15-115. The fin efficiency is defined by Kern and Kraus [206] as the “ratio of the actual heat dissipation of a fin to its ideal heat dissipation if the entire fin surface were at the same temperature at its base.” Figure 15-115 provides weighted fin efficiency. Weighted fin efficiency is expressed by Kern and Kraus [206] as: hw ¼

hf s00f þ s00o s00f þ s00o

(15-316)

where: sf00 ¼ fin surface per ft of pipe length so00 ¼ plain pipe surface per ft length hw ¼ weighted fin efficiency, fraction, from Figure 15-115 hf ¼ fin efficiency, fraction ¼ [(tanh) (mb)]/(mb) tanh ¼ hyperbolic tangent m ¼ fin performance factor ¼ ½ð2hÞ=km do 1=2 ; ft1 b ¼ fin height, ft h ¼ heat transfer coefficient, Btu/(h) (ft2) (
F) km ¼ metal thermal conductivity, Btu/(ft) (h) (
F) do ¼ fin width, ft, at fin base

FIGURE 15-114 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 Chapter | 15

Design for Heat Transfer Coefficients by Forced Convection Using Radial Low Fin Tubes in Heat Exchanger Bundles Kern and Kraus [206] reference the ASME-University of Delaware Cooperative Research Program on Heat Exchangers by Bell [207] and later work by Bell and Tinker. The Kern [206] recommendation is based on the Delaware work and the TEMA details of construction. Heat Transfer Coefficient, Shell-Side
  0:14 k cp m1=3 m (15-317) ho ¼ j H De k mw See Figure 15-115. where: De ¼ shell-side equivalent diameter outside tubes, ft, see Figure 15-86 cp ¼ specific heat of shell-side fluid, Btu/(lb-
F) k ¼ thermal conductivity of fluid, Btu/(ft) (h) (
F) m ¼ viscosity of shell-side fluid (at bulk temperature) lb/(ft) (h) mw ¼ viscosity of shell-side fluid at tube wall temperature, lb/(ft) (h) jH ¼ heat transfer factor, dimensionless

241

ho ¼ heat transfer coefficient for fluid outside tubes based on tube external surface, Btu/(h) (ft2) (
F) Res ¼ Reynolds Number, shell-side, dimensionless Gs ¼ mass velocity (cross-flow), lb/(h) (ft2) The baffle used in the preceding equation has 20% segmental cuts. Shell-side cross-flow velocity [206]. Cross-flow area; as ¼

ds C 0 B 144p

(15-318)

where: as ¼ cross-flow area in a tube bundle, ft2 ds ¼ shell-side ID, in. p ¼ tube pitch, in., see Figures 15-86 and 15-116. C0 ¼ clearance between low fin tubes, ðp  d0 e Þ, or for plain tubes, (p  d), in., see Figure 15-116 B ¼ baffle pitch, in. Figure 15-115 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 15-84. Referring to Figure 15-115, the marking “low fin limit” [206] at Re ¼ 500 is explained by Kern [206]; 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

FIGURE 15-115 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.)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

where:

FIGURE 15-116 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, ©1960. Wolverine Tube, Inc. Used by permission: Kern, D. Q., and Kraus, A. D. External Surface Heat Transfer, p. 511, ©1972. McGraw-Hill Book Co., Inc. All rights reserved.)

result of a high mass velocity and high viscosity as compared to a low mass velocity at low viscosity, caution is suggested [206].

Pressure Drop in Exchanger Shells Using Bundles of Low Fin Tubes The Delaware [207] work is considered [206] to be 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 total exchanger operation. Figure 15-116 presents a recommended pressure drop correlation [206] 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 [206] state that this University of Delaware correlation has some factors built in that limit the deviations to a relatively small range. Figure 15-116 has allowances built in for entrance and exit losses to the shell and leakage at baffles [206]. The suggested pressure drop for shell-side heating or cooling, including entrance and exit losses is: f G2c Ds ðnb þ 1Þ ; psi Dps ¼ ð5:22  1010 ÞðDe s fs Þ

(15-319)

f ¼ friction factor, dimensionless, ft2/in.2 Dps ¼ shell-side pressure drop, psi Gc ¼ cross-flow mass velocity, lb/(h) (ft2) Ds ¼ shell ID, ft nb ¼ number of baffles De ¼ Des ¼ equivalent OD of tubes, ft, see earlier discussion on this topic. de ¼ des ¼ equivalent OD of tubes, in., see Figure 15-115 for numerical values. s ¼ specific gravity, dimensionless. Dps ¼ pressure drop of fluid, heated or cooled, including entrance and exit losses, lbf/in.2 fs ¼ viscosity correction ¼ ðm=mw Þ, dimensionless mw ¼ viscosity of fluid at wall of tube, lb/(ft-h) m ¼ viscosity of fluid in bulk at caloric temperature, lb/(ft-h) r ¼ fluid density, lb/ft3 ds ¼ shell diameter, in. Bs ¼ baffle spacing, in. Res ¼ 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 [206].

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.

Design Procedure for Shell-Side Condensers and Shell-Side Condensation With Gas Cooling of Condensables, FluidFluid Convection Heat Exchange Follow the procedures outlined for bare tube equipment, substituting the characteristics of finned tubes where appropriate. The presentation of Wolverine [41] recommends this technique over previous methods [16]. The methods of Reference [16] have proven acceptable in a wide number of petrochemical hydrocarbon systems. Figure 15-117 is an example unit in summary form.

Vertical Condensation on Low Fin Tubes Follow the same procedure as for horizontal tubes but multiply outside film heat transfer coefficient, ho, by a factor of 0.7 and try for balance as previously outlined.

Heat Transfer Chapter | 15

243

FIGURE 15-117 Exchanger rating for intercooler, using low-fin tubes. Note: specifications here are for illustration purposes. The design as developed represents more conservative surface area than substantiated by current data.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Nucleate Boiling Outside Horizontal or Vertical Tubes Nucleate boiling is boiling at the tube surface at a temperature difference between outside tube surface temperature and the fluid body, less than the critical temperature difference. At and beyond the critical temperature difference, metastable and film boiling take place. These produce lower heat transfer coefficients as the temperature difference increases. The nucleating region is the one of interest in most plant design as previously described for plain tube boiling. The critical temperature difference curves have been determined experimentally for a reasonable number of fluids and should be used whenever possible. This phenomenon is reviewed later in the chapter.

Design Procedure for Boiling, Using Experimental Data The method suggested by Katz, et al. [69] is logical when using experimental data: 1. Determine the heat duty by the usual procedures and define the boiling temperature on the shell-side. 2. Determine the arithmetic average of tube-side temperature, ta. 3. Determine overall temperature drop, Dto, from average tube-side temperature, ta, to shell-side boiling temperature, ts. Dtoa ¼ ta  ts

1 Ao Ao ¼ þ ri þ ro A i ht A i hb

9. Substitute the graph value of hb in:

(15-320)

4. Calculate the tube-side film coefficient for finned tube, ht. If water, use Figure 15-80A or B; if other fluid, use Equation 15-175 or 15-178. Use an assumed or process determined tube-side velocity or other “film fixing” characteristic. 5. Assume fouling resistances for shell-side and tube-side. 6. Calculate the overall resistance, less shell-side film resistance: B ¼ Rt 

FIGURE 15-118 Boiling coefficients for low-finned tubes. (Used by permission: Katz, D. L., Meyers, J. E., Young, E. H., and Balekjian, G. Petroleum Refiner, V. 34, No. 2, ©1955. Gulf Publishing Company. All rights reserved.)

(15-321)

Note: Subscripts s and t represent shell and tubeside respectively; b and i represent boiling outside and inside tube. 7. Assume a temperature drop across the boiling film, Dtb. Neglect tube wall resistance. 8. From Figure 15-118, read an expected film coefficient, hb, at the value of Dtb. The shell-side boiling temperature should be within 15e20
F of the values given on the graph in order to be reasonably close. Calculate 1/hb from the chart.

Rt  1=h ¼ B b

(15-322)

Then, Rt Rt ¼ B þ 1=hb 10. Calculate Dtb:    1 1 rb ¼ Dto Dtb ¼ Dto Rt hb Rt

(15-323)

If the calculated value agrees with the assumed value, proceed to finish the design; if not, reassume the Dtb in Step 7 and repeat until an acceptable check is obtained. 11. Calculate the overall heat transfer coefficient, Uo. Uo ¼

1
; Btu=ðhÞðft2 Þð FÞ Rt

(15-324)

12. Determine the length of tubing required: UL ¼ Uc ðAo Þ; Btu=h ðlin ftÞð
FÞ

(15-325)

Q ¼ UL Lt Dtoa ; Btu=h

(15-326)

Heat Transfer Chapter | 15

Lt ¼

Q ; ft: ðtotal for exchangerÞ UL Dto

(15-327)

13. Check that the maximum flux, Q/A, and critical temperature difference, Dto, are not exceeded, or even approached too closely. This is to avoid a film boiling condition, rather than nucleate boiling. 14. Determine the number of tubes: No: tubes ¼

LT 1

(15-328)

where 1 ¼ assumed length of tube, ft. Remember to keep a standard length if possible and maintain a tube-side pass condition to realize the film conditions established in Step 4. U-tubes are a good selection for this type of service, and a kettle-type shell is usually used. 15. Determine the pressure drops in the usual manner. In general, at low boiling temperature film drops, the finned tubes give considerably higher coefficients than plain tubes, but in the general region of a 10e12
F boiling film temperature difference, the two tubes become about the same. where: l ¼ assume length of one tube, ft Lt ¼ total tube length, ft Lf ¼ total finned tube length, ft Lp ¼ total plain tube length, ft Rt ¼ total resistance to heat transfer, (h) (
F) (ft2) / Btu rb ¼ ro ¼ outside (tube) fouling factor, (h) (
F) (ft2) / Btu ri ¼ inside (tube) fouling factor, (h) (
F) (ft2) / Btu Ao ¼ outside tube surface area, ft2/ft Ai ¼ inside tube surface area, ft2/ft Dto ¼ overall Dt between average tube-side bulk temperature,
F and evaporating (boiling) side fluid. Dtb ¼ temperature drop across boiling film,
F Uo ¼ overall coefficient of heat transfer, Btu/(h) (ft2) (
F) UL ¼ overall coefficient of heat transfer per ft of tube length, Btu/(h) (ft of tubing) (
F) hb ¼ boiling heat transfer film coefficient, Btu/(h) (ft2) (
F) ht ¼ hw ¼ inside water heat transfer film coefficient, Btu/(h) (ft2) (
F) Ao ¼ outside tube surface area, ft2/ft Q ¼ total heat duty, Btu/h EXAMPLE 15-18 Boiling with Finned Tubes

See Figures 15-119 and 119A. A direct evaporation water chiller is to use Freon 12 on the shell-side, cooling 187 gpm of water for a closed system

245

from 82
F to 40
F. Because the Freon is to come from an already existing system, operating at 30
F evaporator temperature, this same condition will be used to avoid compressor suction pressure problems. Note: Care must be given to avoid water freezing on the tubes. Keep the evaporating temperature slightly above the freezing point of the fluid. Tubes are steel, ASTM A-179, 1 in. nominal OD  14 BWG (0.083 in. thick at finned section)  19 fins/in. Wolverine Trufin
(standard tube (unfinned) wall thickness ¼ 0.095 in.). Finned surface area/ft length ¼ 0.678 ft2/ft. Plain tubes are 0.5463 ft2/ft. The shell is steel, ASTM A e 185, Gr. C. 1. Heat duty Q ¼ ð187Þð8:33Þð60Þð82  40Þ ¼ 3; 935; 000 Btu=h Shell-side boiling temperature ¼ 30
F 2. Arithmetic average tube-side temperature, ta ¼

82 þ 40 ¼ 61
F 2

3. Overall shell temperature drop:


Dto ¼ ta  ts ¼ 61  30 ¼ 31 F 4. Tube-side film coefficient. Assume minimum water velocity of 5 ft/s, using 1 in.  14 BWG tubes. From Figures 15-80A and B, hi ¼ 1,215 Btu/h (ft2) (
F) Correction ¼ 0.925 In terms of outside surface: 1 hio ¼ ht ¼ 1; 215 ð0:925 Þ 3:66   ¼ 307 Btu=ðhÞ ft2 ð
FÞ 5. Assumed fouling resistances: Tube-side ¼ 0.002, ft2 h
F/Btu Shell-side ¼ 0.001, ft2 h
F/Btu 1 þ ð3:66Þð0:002Þ þ ð0:001Þ 6. B ¼ Roa  h1s ¼ 307 ¼ 0:01158 7. Assume temperature drop across film, Dtb ¼ 5
F 8. From Figure 15-118, hs ¼ 620 Btu/h (ft2) (
F) 9. Roa ¼ 0.01158 þ 1/620 ¼ 0.01158 þ 0.00162 ¼ 0.0132 10. Calculate:  1=620 ¼ 3:79
F Dtb ¼ 31 0:0132 Not a check. 7a. Reassume: Dtb ¼ 4.5
F. 8a. hs ¼ 550 1 9a. Roa ¼ 0:01158 þ 550 ¼ 0:01340 10a. Calculated, 1=550 ¼ 4:21
F 0:01340

 Dtb ¼ 31

This is close enough.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-119 Exchanger rating for refrigerant vaporizerewater chiller.

Heat Transfer Chapter | 15

FIGURE 15-119A

247

248

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

11. Overall heat transfer coefficient, Uo: Uo ¼

1 1 ¼ 74:6 ¼ Roa 0:01340

  Btu=h ft2 ð
FÞ ðoutsideÞ

Total tubing length: Ao ¼ 0.675 ft2/ft

Volumetric flow rate in gpm :

UL ¼ Uo ðAo ; finned tubesÞ

¼

¼ ð74:6Þð0:688; updated Table 15-50Þ 2

¼ 51:3 Btu=ðhÞð
FÞðft Þ tubingÞ Lt ¼

Q 3; 935; 000 ¼ ¼ 2; 474 ft finned tubing UL ðDto Þ ð51:3Þð31Þ

Water flow, lb/min. 1 ft3 ¼ 7.48 US gal, water density ¼ 62.3 lb/ft3 Therefore,

Water flow in lb/min

ð187 gpmÞð0:00288Þ      ð0:519 in tube I:D: 1 144 in2 ft2 ð3:9 ft=sÞ 2

¼ 38:3 tubes=pass; use 38 tubes Number of 12 ft tubes required, total ¼ 2,474/12 ¼ 206.2 use 206 tubes Number of tube passes ¼ 206/38 ¼ 5.43 passes, use 6 passes 13. Number of tubes: Tube velocity ¼ 5 ¼

74; 035ð0:0123Þð7:48Þ ¼ 113:5 gpm ð60Þ

Design volumetric flow rate ¼ (113.5)(1.25) ¼ 141.9 gpm Use 3-in. nozzle, velocity ¼ 6.2 ft/s Vapor Freon 12, Out: From Figure 15-93, max. allowable vapor Velocity ¼ (28)(1.3) ¼ 36 ft/s To reduce entrainment, use 25e30 ft/s At 30
F, vapor ¼ 0.939 ft3/lb

Total flow

12. Number of tubes to give 5 ft/s water velocity ¼

Enthalpy of the vapor ¼ 81.61 Btu/lb Enthalpy change ¼ 81.61  28.46 ¼ 53.15 Btu/lb Freon flow ¼ 3,935,000/53.15 ¼ 74,035 lb/h At 80
F and 84 psig, specific volume ¼ 0.0123 ft3/lb

ð187Þð0:813Þ No: tubes=pass

No. tubes/pass ¼ 30.4, say 30 Number of 12 ft tubes, total ¼ 2,470/12 ¼ 206 Number tube passes ¼ 206/30 ¼ 6.87, use 6 passes 14. For 6 passes: Use 226 tubes on 11/4 in. triangular pitch Shell I.D. ¼ 25 in. (Table 15-15) No. tubes/pass ¼ 226/6 ¼ 37.7 Use a larger shell diameter in order to have vapor disengaging space; a diameter of 29 in. or 31 in. ID will be satisfactory e the latter being the better choice. Outside surface area; net ðfinnedÞ : 2

¼ ð226Þð0:688Þð12 ft:  4 in:=12Þ ¼ 1; 814 ft  2 3; 935; 000 Actual U ¼ ¼ 69:9 Btu=h ft ð
FÞ ð31Þð1; 814Þ Nozzles for water inlet and outlet: Flow ¼ 187 gpm Use 4 in. nozzle, velocity ¼ 4.79 ft/s (Cameron Table, Fluid Flow Chapter) Liquid Freon 12, In: 80
F and 84 psig (from condenser) Enthalpy of liquid ¼ 26.28 Btu/lb At 30
F and 28.46 psig evaporation condition

For 12 in. nozzle area of cross-section ¼ 0.777 ft2 Capacity at 25 ft/s ¼ (0.777)(25) ¼ 19.4 ft3/s This nozzle is O.K. Shah [374] employed the HTRI software package to simulate the shell and tube exchanger involving Freon 12 on the shell-side and cooling water on the tube-side. The latent heat of Freon 12 is 67.4094 Btu/lb (Freon 12 vendor data), and the flow rate of 75400.0 lb/h give the heat duty ¼ 5,082,669.0 Btu/h. Figure 15-119A shows the results of Example 15-17 on the heat exchanger specification sheet. The exchanger type is BXL, but BKU is recommended for vapor-liquid separation.

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 15-120 shows a hairpin heat exchanger, formed by two sets of concentric tubes and 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 15-121. 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

Heat Transfer Chapter | 15

249

FIGURE 15-120 Hairpin heat exchanger.

FIGURE 15-121 Hairpin heat exchanger in series.

FIGURE 15-123A Typical longitudinal finned tubes. Uninterrupted and Interrupted G-Fin
Tubes. (Used by permission: Griscom-Russell, Ecolaire Corp.) (Also see Figure 15-4A(3).)

FIGURE 15-122 Photograph of a double pipe heat exchanger for liquefied petroleum gas product rundown in a LPG unit.

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 large number of hairpins for most industrial applications. The unit is not compact, and thus involves a high labor cost. Figure 15-122 shows a 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 15-5A, B, C and D illustrate the usual

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-123B Typical longitudinal finned tubes. Relative pipe sizes and number of longitudinal fins. (Used by permission: Griscom-Russell, Ecolaire Corp.) (Also see Figure 15-4A(3).)

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 15-123. The tube may be fabricated with fins attached by resistance welding rather than imbedding in the tube as shown in Figure 15-123B. The ID of the internal finned pipe usually ranges from 3/4e11/2 in., and the outside surrounding pipe shell can be 21/2 in., 3 in. and 31/2 in. nominal standard pipe size. The number of fins ranges from 18 for the 3/4 in. pipe, 24 or 32 for the 1 1/2 in. pipe, and 16 or 32 for the 11/2 in. pipe with 1/2 in. fin height, per manufacturer Griscom-Russell/Ecolaire Corp. The fins of Figure 15-123B 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 possible 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 crossexchange, kettle-type reboilers, chillers and condensers. The rating/design of longitudinal finned tubes is presented by Brown Fintube Co. in an unnumbered bulletin, Reference [211]. The double pipe finned tube, Figure 15-5A, is often applicable for gases, viscous liquids or small volumes, and the economics favor high operating pressure due

to the small diameter shell [211]. They operate well in dirty or somewhat fouling conditions due to their ease of cleaning. Units can be fabricated with more than one finned tube in a larger 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 15-5A, the heat flow resistances are [211]: 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. 1=Uo ¼ 1=ho þ 1=hi þ Rm

(15-329)




where Uo, ho, hi ¼ Btu/(h) (ft ) ( F)   Rm ¼ ðhÞ ft2 ð
FÞ=btu 2

e. See Table 15-76 for suggested overall heat transfer coefficients (U) and Table 15-53 for mechanical data Figure 15-46 gives the usual Sieder-Tate chart and equation for tube-side, bare tube heat transfer. For the finned shell-side heat transfer, see Figures 15-124A, B, C [211] or the recommendation of Kern and Kraus [206], Figure 15-125.

Heat Transfer Chapter | 15

The needed equivalent diameter, De, is determined [211] from the following:

TABLE 15-52 Estimating Overall Heat Transfer Rates, U0, for Longitudinal Finned Heat Exchangers

De ¼

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 pipedcut & twist fins Multitube bare tubes

12 15

Medium HC viscosity 3d15 cp avg. Heatingddouble pipe w/fins Multitube bare tube Coolingddouble pipe w/fins Multitube bare tube

15 25 12 20

Light HC viscosity < 1 cp Double-pipe w/fins Multitube w/fins Multitube bare tube

25 40 75

Condensing & vaporizingdbare tube

150

Very light HCdbare tubes

150

Gases 0 psig w/1/2 psi DP bare tube 100 psig w/1 psi DP fin tube

25 15

Water to waterdbare tubes

200

Glycol to glycol Double pipe w/fins Multitube bare tube w/turbulators

10 30

251

4NFA pðDs þ Dt Þ þ 2NðlÞ

(15-330)

where NFA ¼ net free, in.2 from typical manufacturer’s data as Table 15-53. The denominator is the wetted perimeter. Ds ¼ shell ID, in. Dt ¼ tube OD, in. N ¼ number of fins per tube l ¼ fin height, in. After determining ho from the preceding figures, the film coefficient must be corrected for fin efficiency using Figure 15-125. where: E ¼ 100 (Tanh X)/X X ¼ L(HF/6KT)0.50 L ¼ fin height, in. HF ¼ fin film coefficient K ¼ conductivity of fin material, Btu/(h) (ft2) (
F/ft) E ¼ % fin efficiency T ¼ fin thickness, in. Conductivity values*

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.

Material

K

Monel

15.0

18e8 st.stl

9.5**

C.steel

25.0

Low chrom stl

17.0

Nickel

35.0

TABLE 15-53 Brown Fintube’s Typical Mechanical Design Data for Fintube Sections As Needed for Design Calculations

BFT Section Type

No. Tubes

No. Fins

Tube O.D. & Wall thick (in.)

X51

1

24

1.900 x

36

.145

X53

1

24

1.900 x

36

.145

Shell Size Sch. 40 IPS 3 in.

4 in.

Fin Height in. 1

/2

1

Nominal Surface, Ft2 Ao Nominal Length of Section

Net Free Area in.2

De Equiv. Dia., in.

Af, Ao

AAo, Ai

5 ft

10 ft

15 ft

20 ft

25 ft

4.11

.415

.801

5.93

25

50

76

101

126

3.89

.301

.858

8.3

35

71

106

141

177

9.03

.542

.889

10.67

45

91

136

182

227

8.60

.379

.923

15.42

66

131

197

262

328

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.

252

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-124A For determination of ho, shell-side (finned side) film coefficient hoK0.667C0.333 for longitudinal fins, flow laminar. ho must be corrected for fin efficiency using Figure 15-154 and mechanical data as Table 15-42. (Used by permission: Bul. “How to Design Double-Pipe Finned Tube Heat Exchangers.” © Brown Fintube Company, A Koch
Engineering Company, Houston, Texas.)

Adm.% brass

65.0

Al

100

Cu

FIGURE 15-124B Shell-side film coefficient for longitudinal fins, transition flow. See Figure 15-153A for applicable details. (Used by permission: Brown Fintube Company, A Koch
Engineering Company, Houston, Texas.)

200


*Average K values for temperatures 100e600 F. For temperatures beyond this range, see literature. **Use E chart ¼ 0.70 for design efficiency for this material.

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, hw ; ef or E, from Figure 15-125 is corrected for the percent surface that is finned. The corrected value, hw is the effective surface efficiency. hw ¼ ðE=100ÞðAf =Ao Þ þ ð1  Af =Ao Þ

(15-331)

where: Af/Ao ¼ fraction finned area (l  Af/Ao) ¼ 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 [211], fouling is excluded:

  (15-332) hbare ¼ ho K0:667 cp0:333 K0:667 c0:333 p using Figure 15-124A, B or C. with ro ¼ shell-side fouling resistance hf ¼

  1 ; Btu=ðhÞ ft2 ð
FÞ ð1=hbare Þ þ ro

(15-333)

FIGURE 15-124C Shell-side film coefficient, ho, for longitudinal fins, flow turbulent. See Figure 15-153A and mechanical data from Table 15-42 for applicable details. The value of ho must be corrected using Figure 15-125 and data of Table 15-42. (Used by permission: Brown Fintube Co., A Koch
Engineering Company, Houston, Texas.)

hof ¼ hw ðhf Þ, outside film coefficient with fouling, Btu/(h) (ft2) (
F)

Tube Wall Resistance The pipe wall resistance to heat transfer is [211]: 
  O:D:tube O:D:tube ln (15-334) Rm ¼ 2Km I:D:tube

Heat Transfer Chapter | 15

253

Finned Side Pressure Drop Brown [211] recommends: ð0:000432Þðf o ÞðG0 Þ L 2

DP ¼

ðDe ÞðZ=Zw Þ

0:14

ðrÞ

(15-335)

Use Figure 15-126 to determine fo. Re ¼

De G ðZÞð2:42Þ

(15-336)

where: De ¼ equivalent annulus diameter, ft; (see earlier calculation) G ¼ mass velocity flow rate, lb/ (h) (ft2) ¼ 3,600 (G0 ) G0 ¼ mass velocity flow rate, lb/(s) (ft2) Z ¼ average viscosity, centipoise r ¼ fluid density, lb/ft3 L ¼ equivalent length of travel, including bend factor, ft. D ¼ tube ID, ft. Figure 15-127 shows the heat transfer profiles for annuli and longitudinal fins. After designing an approximate unit area requirement, it is important to review the final design performance details with a qualified exchanger manufacturer. See Table 15-53. FIGURE 15-125 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.)

where Km ¼ thermal conductivity of tube metal, Btu/(h) (ft2) (
F/ft) Rm ¼ wall resistance, (h) (ft2) (
F)/Btu

Tube-Side Heat Transfer and Pressure Drop Refer to the earlier section in this chapter, because tubeside 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. The double pipe longitudinal finned exchanger is designed by adding the fouling factor to each respective film coefficient before calculating the overall Uo [211].

Design Equations for the Rating of a DoublePipe 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, ma, ka, Dpa, Rd, sa or ra Cold fluid: t1, t2, w, Cpc, mt, kt, Dpt, Rd, st or rt The diameter of the pipe must be given or assumed. The fluids’ velocities must be in the range 3e10 ft/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 15-54. The following assumes that the cold fluid is in the inner pipe. 1. The heat duty, Q, Btu/h is:     Q ¼ WCph T1  T2 ¼ wCpc t2  t1

(15-337)

2. The log mean temperature difference, DTLMTD is: DTLMTD ¼

Inner Pipe

ðT1  t2 Þ  ðT2  t1 Þ  2 ln TT12 t t1

254

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-126 Shell-side friction facgtor, fo for pressure drop calculation is determined from plot vs. Reynolds number, z ¼ viscosity at average flowing temperature, centipoise. (Used by permission: Brown Fintube Company, A Koch
Engineering Company, Houston, Texas.)

TABLE 15-54 Flow Areas and Equivalent Diameters in Double-Pipe Exchangers [70] Exchanger, Iron Pipe Size (IPS)

Flow Area, in.2

Annulus, in.

Annulus

Pipe

de

d0 e

1.19

1.50

0.915

0.40

2 /2  1 /4

2.63

1.50

2.02

0.81

32

2.93

3.35

1.57

0.69

43

3.14

7.38

1.14

0.53

1

2  1 /4 1

FIGURE 15-127 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 Mechnical Engineers) (Used by permission: Kern, D. Q., and Kraus, A. D. Extended Surface Heat Transfer, p. 464, ©1972. McGraw-Hill, Inc. All rights reserved.)

3. The flow area, ap is: ap ¼

pD ; ft2 4 2

(15-338)

4. The mass velocity, Gp: w lb Gp ¼ ; ap h ft2

(15-339)

5. The Reynolds number, Ret: Ret ¼

DGp mt

(15-340)

1

7. The heat transfer film coefficient, hi, Btu/h ft2
F: 0:8  0:33  0:14  hi D DGp Cpc mt mt ¼ C mt kt mw kt (15-342) hi can be expressed by:  kt 0:33 Re0:8 hi ¼ C t Pr t D

where mt =mw ¼ 1:0 C ¼ 0.021 for gases. C ¼ 0.023 for non-viscous fluids. C ¼ 0.027 for viscous fluids. Converting hi to hio, the heat transfer film coefficient referred to the pipe outside diameter, Btu/h ft2
F is:

6. The Prandtl number, Prt: Cpc mt Prt ¼ kt

hio ¼ hi (15-341)

(15-343)

Annulus

ID OD

(15-344)

Heat Transfer Chapter | 15

8. The flow area of the annulus is:   p D2o  D2i aa ¼ ; ft2 4

Shell-Side Bare Tube (15-345)

¼

4  flow area wetted perimeter D2o

 Di

D2i

hi is calculated using Equations 15-342 and 343 and hif is calculated using Equation 15-355. 17. The equivalent diameter, De is:

9. The equivalent diameter, De: De ¼

De ¼ Ds;i  Dt;o (15-346)

; ft

10. The mass velocity, Ga: (15-347)

11. The Reynolds number, Rea: De Ga Rea ¼ ma

18. The overall heat transfer coefficient, Uo, Btu/h ft2
F  1 Dw 1 1 ¼ þ  þ (15-357) Þshell Uo kt tube wall ðh if Ai hi A o where the tube wall thickness, Dw is:

Cph ma ka

13. The heat transfer film coefficient, ho is: If Rea < 2100  0:33 ka 0:33 0:33 De Rea Pra ho ¼ 1:86 Do L

Dw ¼ Dt;o  Dt;i ; ft

(15-358)

Ai Dt;i ¼ Ao Dt;o

(15-359)

and: (15-348)

12. The Prandtl number, Pra: (15-349)

Shell-Side (Finned Tube) 19. The equivalent diameter, De, ft, is: De ¼

(15-350)

If Rea > 2100

4 NFA pðDs;i þ Di;o Þ  Nq þ 2HN

(15-360)

20. The net free cross-sectional area, NFA, shell-side, ft2: NFA ¼ CSA  NHq

ka 0:33 ho ¼ C Re0:8 a Pra Do

(15-351)

14. The overall heat transfer coefficient, Uo. Btu/h ft2
F: 1 1 1 ¼ þ þ Rd þ Rw Uo hio ho

(15-352)

A ¼

Q Uo DTLMTD

(15-353)

(15-354)

and: 1 1 ¼ þ Fol ðhi is corrected for foulingÞ hif hi

21. The cross-sectional area without fins, CSA, ft2:  p 2 (15-362) CSA ¼ Ds;i  D2i;o 4 22. Finned surface area, ft2: Af ¼ 2HN

(15-363)

23. Outside heat transfer area of tube, ft /ft (for finned tubes includes fin area):

Vapor Service 16. The heat transfer film coefficient, hi, Btu/h ft2
F: 0:0144 Cph G0:8 D0:2 e

(15-361)

2

15. The heat transfer area, A ft2:

hi ¼

(15-356)

tube

W lb Ga ¼ ; aa h ft2

Pra ¼

255

(15-355)

Ao ¼ pDt;o þ Af

(15-364)

24. Parameter for fin efficiency, X:  X ¼ H

hif 6Ki q

0:5 (15-365)

25. The fin efficiency, e:
 tanh X 1 expðXÞ  expðXÞ ¼ e ¼ X X expðXÞ þ expðXÞ

(15-366)

256

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

The Reynolds number, Rea is:

26. The effective surface efficiency for fins, eff: 

Af eff ¼ e Ao





Af þ 1 Ao

(15-367)

(15-368)

28. The overall heat transfer coefficient, Uo, Btu/h ft2
F:  1 Dw 1 1 ¼ þ  þ (15-369) Uo kt tube wall ðhifd Þshell hi AAoi

Dha ¼

Dhr ¼

v2 ; ft=hair pin 2g

(15-379)

(15-380)

(15-370)

Tube-Side Pressure Drop, Dpt 29. The pressure drop in the tube-side is, the frictional head, Dh, ft: 4f G2 L ; ft 2g r2 D

(15-378)

The total annulus pressure drop Dpa is: 
ðDha þ Dhr Þr ; psi Dpa ¼ 144

where:

Dh ¼

4f G2a L ; ft 2g r2 D0 e

The pressure drop due to the reversal of flow in the annulus for each hairpin is:

tube

Ai p Dt;i ¼ Ao pDt;o þ 2HN

(15-377)

Head loss, Dha , ft:

27. The corrected film heat transfer coefficient, hifd, Btu/h ft2
F: hifd ¼ ðhif Þðeff Þ

D0 e Ga ma

Rea ¼



(15-371)

where:

Calculation of the Pressure Drop The friction factors for both streams can be determined and the pressure drop for each fluid will be:  a L rv2 m (15-381) Dpt ¼ 4f D 2 mw or:

16 f ¼ for Re < 2; 100 Re

(15-372)

Using the Wilson et al. [367] correlation for commercial pipe: f ¼ 0:0035 þ

0:264 for Re > 2; 100 Re0:42

The pressure drop, Dpt is:  Dh r ; psi Dpt ¼ 144

(15-373)

(15-374)

(15-382) Where a ¼ 0.14 for Re > 2,100 and a ¼ 0.25 for Re < 2,100. In Equation 15-382, 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:

Or in terms of static height Dh, ft.: Dh ¼ 2:31

Dpt ; ft Sp Gr

Dpr ¼ (15-375)

where Sp Gr ¼ specific gravity of liquid.

Annulus For an annulus, the equivalent diameter, D0 e is:   4p D2o  D2i 0 De ¼ 4pðDo þ Di Þ (15-376) ¼ Do  Di

or:

nt rv2 2 2

 nt rv2 1 Dpr ¼ ; psi 2 2gc 144

(15-383)

(15-384)

Kern’s equation for tube-side return pressure drop is shown in Figure 15-122 and is expressed by [70].

(15-385)

Heat Transfer Chapter | 15

where: v ¼ velocity, ft/s gc ¼ conversion factor (32.174 lbm/lbf. ft/s2) s ¼ specific gravity nt ¼ number of tube passes The total pressure drop is: Dp ¼ Dpt þ Dpr

(15-386)

Effect of Pressure Drop (Dp) 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 Dp. If the heat exchanger must be installed in an existing process, the designer must adhere to the maximum allowable Dp. 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 this Dp. 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 Dp 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 Dp is smaller than that allowed, 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 Dp 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 tube thicknesses, selecting materials, rating the nozzles, choosing gaskets and reviewing the mechanical drawings. This work falls within the mechanical engineering discipline. Nomenclature: A ¼ cross-sectional area, ft2. Ai ¼ inside heat transfer area-tube, ft2/ft. Ao ¼ outside heat transfer area-tube, ft2/ft (for finned tubes includes fin area). Ai ¼ finned transfer area, ft2. ap ¼ flow area, ft2. Cp ¼ specific heat capacity of hot fluid, Btu/lb
F. cp ¼ specific heat capacity of cold fluid, Btu/lb
F.

257

CSA ¼ cross-sectional area, shell-side without fins, ft2. D ¼ inside diameter, ft. Di, Do ¼ for annuli, Di is the outside diameter of inner pipe, Do is the inside diameter of the outer pipe, inch. Dt,i ¼ tube inside diameter, inch. Dt,o ¼ tube outside diameter, inch. Ds,i ¼ shell inside diameter, inch. De ¼ equivalent diameter for heat transfer, ft. D0 e ¼ equivalent diameter for pressure drop, ft. e ¼ fin efficiency. e0 ¼ effective surface efficiency for fins. FOL ¼ fouling factor, ft2 h
F/Btu. f ¼ friction factor, dimensionless. Dh ¼ pressure drop, ft. Dha ¼ annulus pressure drop, ft. Dhr ¼ pressure drop due to reversal of flow in the annulus, ft. G ¼ mass velocity, lb/h-ft2. Ga ¼ mass velocity in annulus, lb/h-ft2. Gp ¼ mass velocity of inner pipe, lb/h-ft2. g ¼ acceleration due to gravity, 32.2 ft/s2 (4.18  108 ft/h2).

 gc ¼ Conversion factor 32:174 lbm =lbf :sft2 H ¼ fin height, inch. hi, ho ¼ heat transfer film coefficient for inside fluid and outside fluid respectively, Btu/h ft2
F. hio ¼ value of hi, when referred to the pipe outside diameter, Btu/h ft2
F. ID ¼ inside diameter, inch or ft. jH ¼ heat transfer factor, dimensionless. k ¼ fluid thermal conductivity, Btu/h ft
F. Kt ¼ thermal conductivity of tube material, Btu/h ft
F. L ¼ pipe length, ft. NFA ¼ net free cross-sectional area, shell-side, ft2. N ¼ number of fins. OD ¼ outside diameter, inch or ft. Pr ¼ Prandtl number, dimensionless. Dp ¼ pressure drop, psi. Q ¼ exchanger duty, Btu/h. Rd ¼ fouling resistance, ft2 h
F/Btu. Re ¼ Reynolds number, dimensionless. Rw ¼ wall resistance, ft. s ¼ specific gravity. T1, T2 ¼ temperature of hot fluid, inlet and outlet respectively,
F. t1, t2 ¼ temperature of cold fluid, inlet and outlet respectively,
F. DTLMTD ¼ log mean temperature difference,
F. U ¼ overall heat transfer coefficient, Btu/h ft2
F. v ¼ fluid velocity, ft/s. W ¼ mass flow rate of hot fluid, lb/h. w ¼ mass flow rate of cold fluid, lb/h. X ¼ parameter used in fin efficiency. r ¼ fluid density, lb/ft3. m, mw ¼ fluid viscosity (flowing and at wall), cP.

258

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Conversion: m ðlb=ft:hÞ ¼ cP  2:42 Heat Balance: Heat lost by oil ¼ heat gained by water That is:

q ¼ fin thickness (normally 0.035 inch). p ¼ 3.1415927. a ¼ annulus. p ¼ pipe.

Q ¼ W Cp ðT1  T2 Þ ¼ w cp ðt2  t1 Þ Q ¼ ð180; 000Þ ð0:518Þ ð250 e 150Þ ¼ w ð1Þ ð120 e 80Þ 932400 ¼ 40 w

Example 15-19

Petroleum distillate oil of 18,000 lb/h, 28
API is to be cooled from 250
F to 150
F in a double pipe finned tube heat exchanger consisting of 3 in. Internal Pipe Size (IPS) shells with 11/2 in. IPS inner pipes on which are mounted 24 fins 1/2 in. high by 0.035 in. (20 BWG) wide. Water from 80
F to 120
F will be the cooling medium. Allowable pressure drops of 10 psi are allowable on both streams, and the following 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:

Type of Fluid Flow rate, lb/h Inlet temperature,
F Outlet temperature,
F Thermal conductivity, Btu/h.ft
F Viscosity, cP Specific heat capacity, Btu/lb
F Density, lb/ft3 Number of passes Fouling factor, h ft2
F/Btu

Tube-Side Inner Pipe Cooling-tower water 23,310 80 120 0.366

Shell-Side Annulus Petroleum distillate 18,000 250 150 0.074

0.72 1

2.45 0.518

62.3 5 0.002

45 1 0.002

¼

ðT1  t2 Þ  ðT1  t1 Þ 

2 ln TT11 t t1 ð250  120Þ  ð150  80Þ ¼ 96:9
F

 250120 ln 15080

3. The flow area, ap is: ID pipe in ft. ¼ 1.610/12 ¼ 0.13417 ft. 2

ap ¼

pð0:13417Þ 4 2

¼ 0:0141 ft 4. The mass fluid velocity, Gp is:

Ret ¼

Cold Fluid (Water) Tube-side ID ¼ 1.61 in., OD ¼ 1.91 in. Passes ¼ 5

w 23310 lb ¼ ¼ 1648514:85 ap 0:01414 h:ft2

D Gp ð0:13417  1648514:85Þ ¼ ð0:72  2:42Þ m ¼ 126941

6. The Prandtl number Prt: Prt ¼

cm 2:42  1:0  0:72 ¼ ¼ 4:7607 k 0:366

7. Heat transfer film coefficient, hi:  0:14 hi D m 0:33 Pr ¼ CRe0:8 t t k mw

 where for non-viscous fluid, C ¼ 0.023 and mmw ¼ 1:0  0:366 0:8 0:33 ð126941Þ ð4:7607Þ hi ¼ 0:023 0:13417 
¼ 1270:3 Btu h ft2 F The heat transfer film coefficient corrected for fouling:

Physical Property data: Oil 2.45 45.0 0.518 0.074

DTLMTD ¼

5. The fluid’s Reynolds number in the tube is Ret:

Solution: Exchanger

Physical Property Viscosity, cP Density, lb/ft3 Specific heat, Btu/lb
F Thermal conductivity, Btu/h ft
F

Assuming counter current flow, The Log Mean Temperature Difference DTLMTD is:

Gp ¼

Exchanger size: Shell-side: 3 in (3.068 in. ID, 3.5 in. OD). Tube-side: 11/2 in. (1.61 in. ID, 1.9 in. OD). Tube length: 12 ft. Fins: 24, 0.5 in. high  0.035 in. wide. Thermal conductivity of the tube material: K ¼ 25 Btu/ h ft
F.

Hot Fluid (Oil) Shell-side ID ¼ 3.068 in., OD ¼ 3.5 in. Passes ¼ 1

W ¼ 23310 lb=h:

Water 0.72 62.3 1.0 0.366

1 1 ¼ þ FOL hif hi ¼

1 2
þ 0:002 ¼ 358:78 Btu=h ft F 1270:3

Shell-side (Finned Tube)

Heat Transfer Chapter | 15

The Prandtl number, Pra:

The equivalent diameter, De is:

cm k 0:518  2:45  2:42 ¼ 0:074 ¼ 41:5

4 NFA pðDs;i þ Di;o Þ  Nq þ 2HN  ¼ 3:068 12 ¼ 0:2556 ft  ¼ 1:9 12 ¼ 0:1583 ft

Pra ¼

De ¼ Ds;i Dt;o

Nq ¼ 24  0:035=12 ¼ 0:07 ft:

The film heat transfer film coefficient on the shell-side:  0:14 hif De m ¼ C Re0:8 Pr0:33 t t ka mw  where for non-viscous fluid, C ¼ 0.023 and mmw ¼ 1:0

Finned transfer area, Af: Af ¼ 2HN 2 ¼ 2  24  0:5=12 ¼ 2 ðft ftÞ NHq ¼ 24  0:5  0:035=144 ¼ 2:917  103 ft

2



2

Cross-sectional area, shell-side without fins, CSA, ft :  p 2 CSA ¼ Ds;i  D2t;o 4  p 0:25562  0:15832 ¼ 4

0:074 0:8 0:33 ð3755Þ ð41:5Þ 0:0355 
¼ 118:68 Btu h ft2 F

hif ¼ 0:023

The heat transfer film coefficient corrected for fouling: 1 1 ¼ þ FOL hif hi

¼ 0:03163 ft2 Net free cross-sectional area, NFA, ft2: NFA ¼ CSA  NHq ¼ 0:03163  0:002917 ¼ 0:0287 ft

2

Outside heat transfer area-tube including fin area, Ao, ft2/ft: Ao ¼ pDt;o þ 2HN ¼ Lpð0:1583Þ þ 2 2 ¼ 2:497 ðft ftÞ

4  0:0287 pð0:2556 þ 0:1583Þ  0:07 þ 2 ¼ 0:0355 ft:

Mass fluid velocity in the annulus, Ga: Ga ¼

W 18000 ¼ NFA 0:0287 2

¼ 627178 lb=h ft Fluid velocity, vF is: vF ¼ ¼

Ga ð3600rÞ

627178 ð3600  45Þ

¼ 3:87 ft=s: The Reynolds number, Rea is: Rea ¼ ¼

¼

1
þ 0:002 ¼ 95:91 Btu=h ft2 F 118:68

Parameter X for fin efficiency, e is: 0:5  hif shell X ¼ H 6Kt q !0:5  0:5 95:91 ¼ 12 6  25  0:035 12 ¼ 0:6169 Fin efficiency, e:

Equivalent diameter, De is: De ¼

Ga De m

627178  0:0355 ð2:45  2:42Þ ¼ 3755:0

259


 tanh ðXÞ 1 eX  eX ¼ X X eX þ eX # " 1 e0:6169  e0:6169 ¼ 0:6169 e0:6169 þ e0:6169

e ¼

e ¼ 0:8898 ð89%Þ Effective surface efficiency for fins, e0 :   Af Af e0 ¼ e þ 1 Ao Ao   2 2 ¼ 0:8898 þ 1 2:497 2:497 ¼ 0:9117 ð91:2%Þ Corrected film heat transfer rate, hifd: hifd ¼ ðhif Þ ðe0 Þ ¼ 95:91  0:9117  2
¼ 87:45 Btu h ft F Tube wall thickness, DW: DW ¼ Dt;o  Dt;i ¼ 1:90  1:61 ¼ 0:29 in=12 ¼ 0:02417 ft

260

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Ai pðDt;i Þ ¼ Ao pðDt;o Þ þ 2HN ¼

p  0:13417 p ð0:1583Þ þ 2:0 ¼ 0:1688

Overall heat transfer coefficient, Uo:  1 DW 1 1 ¼ þ þ Ai ðhifd Þshell Uo Kt tube wall hif  Ao tube 0:02417 1 1 ¼ þ þ 25 ð358:78  0:1688Þ 87:45 
¼ 34:59 Btu h ft2 F

G rA

Dp ¼

2

pD2i p ð0:134Þ ¼ ¼ 0:01413 ft2 4 4 G ¼ 23310 lb=h ¼ 23310=3600 ¼ 6:475 lb=s

A ¼

r ¼ 62:3 lb=ft3 G 6:475 ¼ rA ð62:3  0:01413Þ

¼ 7:36 ft=s:

0:264 Re0:42 0:264 ¼ 0:0035 þ ð126941Þ0:42 f ¼ 0:0035 þ

The tube-side Dp is:

(15-381)

 L rv2 1 D 2gc 144   12 62:3  7:362 ¼ 4 ð0:005397Þ 0:134 2  32:174  144 ¼ 0:704 lbf =in2

where: Nc ¼ 1.0 for single-pass shell, no baffles. Assuming that fs ¼ ðm=mw Þ0:14 ¼ 1:0. Specific gravity of the liquid, s ¼ 45.0/62.3 ¼ 0.72. Equivalent diameter, D0 e ¼ 0.0355 ft. Pipe length, L ¼ 12 ft. f ¼ 0.000355. Ga ¼ 627178 lb/h ft2. 0:00036  6271782  1:0  12 ð5:22  1010 Þ  0:0355  0:72  1:0  ¼ 1:27 lbf in2

A computer program PROG153 rates the double pipe heat exchanger using either the fin tubes or bare tubes. Table 15-55 lists the input data and the computer results. The fin efficiency is 89%, the heat transfer surface is 278 ft2 and the computed overall heat transfer coefficient is 34.64 Btu/h ft2
F. The pressure drops have not been exceeded, and the double pipe exchanger will be suitable for the required service.

¼ 0:005397

Dpt ¼ 4f

f G2a L Nc ð5:22  1010 Þ  D0 e s fs

Dp ¼

The friction factor, f is:

where ðm=mw Þ ¼ 1:0; L ¼ 12 ft; D ¼ 0:134ft;  lbm ft gc ¼ 32:174

2 ; v ¼ 7:36 ft=s:; lbf s

(15-386)

Shell-side Dp

where, A is the area of tube of inside diameter ¼ 1.61 in. (0.134 ft) is:

r ¼ 62:3 lb=ft3

Dp ¼ Dpt þ Dpr

Shell-side: Fluid velocity, vF ¼ 3.87 ft/s The friction factor for longitudinal fin, f at Re ¼ 37550 is: f ¼ 0.00036 (From Figure 15-123)

G ¼ rvA

Fluid velocity; v ¼

For the annulus fluid, the total pressure drop is: ¼ 0:704 þ 7:30  ¼ 8:0 lbf in2

Pressure Drop Calculations Tube-side: Fluid velocity, v from the mass flow rate G is:

v ¼

Dpr on the return side of the tube with the number of tubes nt ¼ 5 using Kern’s equation (15-385) is:  4nt v2 62:5 Dpr ¼ ; psi (15-385) s 2gc 144  45 7:362 62:5  ¼ ð2  32:174 Þ 144 1:0  ¼ 7:30 lbf in2

PLATE AND FRAME HEAT EXCHANGERS Figures 15-8, 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.

Heat Transfer Chapter | 15

TABLE 15-55 Input Data and Computer Results for Example 15-19

TABLE 15-55 Input Data and Computer Results for Example 15-19dcont’d

Input data

Input data

WATER

TUBE LENGTH, ft.:

12.000

LIQUID

NUMBER OF FINS:

24

261

1.61

1.9

23310.0

FIN HEIGHT, inch:

0.500

1.0

0.72

0.366

FIN THICKNESS, inch:

0.035

80.0

120.0

0.002

THERMAL COND.

62.3

12.0

5

TUBE MATERIAL, Btu/hr.ft.
F:

25.000

0.722

FLUID VELOCITY, ft/sec.:

7.351

3.867

OIL

REYNOLDS NUMBER:

126958.

3759.

FINS

PRANDTL NUMBER:

4.7607

41.503 0.011819

2

2

LIQUID

FRICTION FACTOR (ft /in ):

0.005397

24

PRESSURE DROP, psi.:

0.702

RETURN LOSSES PRESSURE DROP, psi:

7.267

TOTAL PRESSURE DROP, psi:

7.969

FIN MODULUS:

0.619

FIN EFFICIENCY, %:

88.910

EFFECTIVE SURFACE EFFICIENCY, %:

89.135

LOG MEAN TEMP. DIFF.,
F:

96.92

3.068

3.5

18000.0

0.518

2.45

0.074

250.0

150.0

0.002

0.5

0.035

25.0

45.0

1

DOUBLE PIPE HEAT EXCHANGER RATING USING BARE-TUBES/LONGITUDINAL FINNED TUBES FORCED CONVECTION WITH NO CHANGE OF PHASE TUBESIDE

SHELLSIDE

FLUID NAME:

WATER

OIL

TYPE OF PHASE FLOW:

LIQUID

LIQUID

HEAT TRANSFER FILM COEFF. CORRECTED

FLUID FLOW RATE, lb/hr.:

23310.

18000.

FOR FOULING:, Btu/hr.ft2.
F:

SPECIFIC HEAT CAPACITY, Btu/Ib.
F:

1.000

0.518

OVERALL HEAT

FLUID DENSITY, lb/ft^3.:

62.300

45.000

SPECIFIC GRAVITY:

0.722

FLUID VISCOSITY, cP:

0.720

2.450

FLUID THERMAL COND., Btu/Ib.
F:

0.366

0.074

FLUID INLET TEMPERATURE,
F:

80.000

250.000

FLUID OUTLET TEMPERATURE,
F:

120.000

150.000

INSIDE DIAMETER, inch:

1.610

3.068

OUTSIDE DIAMETER, inch:

1.900

3.500

FOULING FACTOR:

0.002

0.002

NUMBER OF PASSES:

5

1

HEAT TRANSFER FILM COEFF., Btu/h.ft2
F:

119.87

359.31

96.69

TRANSFER COEFF., Btu/hr.ft2.

34.64

HEAT LOAD ON UNIT, Btu/hr.:

932400.0

2

HEAT TRANSFER SURFACE ft .:

Continued

1276.90

277.680

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 15-128, Figures 15-128AeF illustrate the general description and operating principles of plate heat exchangers (PHEs), and detailed descriptions of these figures are provided by Cao [287].

262

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-128 Convection heat transfer comparison for shell and tube and plate and frame exchangers. (Used by permission: Bul. PHE 96-1 6/96. ©Graham Manufacturing Company, Inc.)

The plate and frame designs are used in convection, condensing and some evaporation/boiling applications. Table 15-56 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 their performance and capabilities is presented by Carlson [210]. 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. Plate heat exchangers have overall heat transfer coefficients (U) that are superior to those of 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
F; much lower than the 1,000 Btu/h ft2
F 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
F/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

TABLE 15-56 Typical Gasket Materials for Plated Heat Exchangers Approximate Temperature Limit,
C

Fluids

Styrene-butane rubber

85

Aqueous systems

Acrylonitrilebutane rubber

140

Aqueous system, fats, Aliphatic hydrocarbons

Ethylenepropylene rubber

150

Wide range of chemicals

Fluorocarbon rubber

175

Oils

Compressed asbestos

250

General resistance to organic chemicals

Material

them an ideal choice for many services. Table 15-57 shows fouling coefficients for PHEs. The following design equations for sizing PHE are as follows: 1. Log mean temperature difference (DTLMTD) correction factor, Ft for PHE is determined from the value of number of transfer units (NTU). Ft ¼ fðNTUÞ where: NTU ¼ number of transfer units ¼

(15-387) Dt DTLMTD

Heat Transfer Chapter | 15

1.00

Fluid

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 e20,000

0.0002 e0.00005

Correction Factor, Ft

TABLE 15-57 Fouling Coefficients for Plate Heat Exchangers Coefficient (W/m2 oC)

0.95 1-1

Reported values of constant and exponents are in the range of: C ¼ 0.15 to 0.4 a ¼ 0.65 to 0.85 b ¼ 0.3 to 0.45 x ¼ 0.05 to 0.2 Typical values are C ¼ 0.26, a ¼ 0.65, b ¼ 0.4 and  ¼ 0.14, which are expressed by:  0:14 h p de m ¼ 0:26 Re0:65 Pr0:4 (15-389) kf mw where: hp ¼ plate film heat transfer coefficient, W/m2
C de ¼ equivalent diameter, m de ¼ 2y y ¼ Gap between the plates, m 

d G Re ¼ Reynolds number ¼ e m p

4-

4

0.90

3-3 2-2

0.85

0.80

Dt ¼ Temperature change required in the process stream,
C DTLMTD ¼ Logarithmic mean temperature difference,
C For series flow, Ft can be taken as 0.95. For 1e1 pass and higher passes (2e2, 3e3, 4e4) curves of Ft vs. NTU are shown in Figure 15-129. 2. If there is no phase change in the fluid, then forced convective heat transfer coefficient in conduits or plate film coefficient:  x hp de m ¼ C Rea Prb (15-388) kf mw

263

0

1

2

3

4

5

6

NTU FIGURE 15-129 Log Mean Temperature correction Factor for Plate Heat Exchanger.

Gp ¼ Mass velocity of fluid, kg/s m2 _ f ¼ m=A m_ ¼ Mass flow rate of fluid per channel, kg/s Af ¼ Cross-sectional area of channel or gap (i.e. flow area), m2 up ¼ Channel velocity, m/s 3. Fouling coefficients for PHE are shown in Table 15-57. 4. Pressure drop in plate heat exchanger can be determined by the following equations: Dp ¼ Dpp þ Dppo

(15-390)

where: Dp ¼ Total pressure drop, Pa Dpp ¼ Conduit or channel pressure drop, Pa Dppo ¼ Port pressure drop, Pa Pressure drop occurs when the fluid is flowing through a conduit or channel:  Lp ru2p (15-391) Dpp ¼ 8J2 de 2 where: de ¼ Equivalent diameter for conduit, m. de ¼ 2y ¼ 2  gap between plate, m r ¼ Density of fluid, kg/m3 Lp ¼ Path length, m Jf ¼ Friction factor ¼ f(Re) The value of Jf depends on the design of plate used. For turbulent flow, Jf ¼ 0:6 Re0:3

(15-392)

The transition from laminar to turbulent flow normally occurs at a Reynolds number of 100 to 400, depending on the plate design. In some designs, turbulence can be achieved at very low Reynolds numbers, thus making PHEs very suitable for use with viscous fluids.

264

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

The pressure drop due to contraction and expansion losses through the ports in the plates must be added to the friction loss. Kumar [375] suggests adding 1.3 velocity heads per pass, based on the velocity through the holes. The pressure drop ðDppo Þ that occurs due to the flow of fluid through the ports is: Dppo ¼ 1:3

ru2h  Np ; Pa 2

(15-393)

where: _ Ah , m/s uh ¼ velocity of fluid through the ports m=r Ah ¼ Area of port ¼ p4 d2h , m2 dh ¼ Diameter of port, m Np ¼ Number of passes.

Design Charts for Plate and Frame Heat Exchangers Haslego and Pulley [376] have provided a series of charts (Figures 15-130e135) for a preliminary sizing of a PHE. The following points are applied when using these charts: 1. The heat transfer correlations apply to single-phase, liquid-liquid designs. 2. These charts are valid for single-pass units with 0.50 mm thick plates. The accuracy of the charts will not be compromised for most materials of construction. 3. Wetted-material thermal conductivity is taken as 8.67 Btu/h ft
F (which is the value for stainless steel). 4. The following physical properties for hydrocarbonbased fluids were used for the calculations: thermal conductivity, k ¼ 0.06 Btu/h ft
F, density, r ¼ 55.0 lb/ft3, heat capacity, Cp ¼ 0.85 Btu/lb
F. The following physical properties for water-based fluids were used for the calculations: thermal conductivity, k ¼ 0.33 Btu/h

ft
F, density, r ¼ 62.3 lb/ft3, heat capacity, Cp ¼ 0.85 Btu/lb
F. 5. Accuracy should be within 15% of the service value for the overall heat transfer coefficient, assuming a nominal 10% excess heat transfer area. 6. For fluids with viscosities between 100 and 500 cP, use the 100 cP line on the graphs. For fluids in excess of 500 cP, consult the equipment manufacturers. The stream flows can be arranged in series or parallel or a combination of series and parallel. Each stream can be sub-divided into a number of passes, analogous to the passes used in shell and tube heat exchangers. Figure 15-8 shows plate heat exchanger flow arrangements. The Log mean temperature difference, DTLMTD is: DTLMTD ¼

ðThot;in  Tcold;out Þ  ðThot;out  Tcold;in Þ  Thot;in  Tcold;out ln Thot;out  Tcold;in (15-394)

The number of transfer units for hot stream, NTUhot is: NTUhot ¼

Thot;in  Thot;out DTLMTD

(15-395)

The number of transfer units for cold stream, NTUcold is: NTUcold ¼

Tcold;out  Tcold;in DTLMTD

(15-396)

Typically, the NTU ranges from 0.5 to 4.0, and for most applications will lie between 2.0 and 3.0. After the local heat transfer coefficients h are read from the charts, the overall heat transfer coefficient, U is: 1 1 Dx 1 ¼ þ þ U hhot k hcold

FIGURE 15-130 Heat-transfer correlations for water-based fluids 0.25.

(15-397)

Heat Transfer Chapter | 15

FIGURE 15-131 Heat-transfer correlations for water-based fluids 2.0.

FIGURE 15-132 Heat-transfer correlations for water-based fluids 4.0.

FIGURE 15-133 Heat-transfer correlations for hydrocarbons 0.25.

265

266

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-134 Heat-transfer correlations for hydrocarbons 2.0.

FIGURE 15-135 Heat-transfer correlations for hydrocarbons 4.0.

Selection The advantages and disadvantages of gasketted plate heat exchangers as compared with conventional shell and tube heat exchangers are: Advantages [377] 1. Plates 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 1
C, compared with 5 to 10
C 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 15-57). 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 15-56). 3. The maximum operating temperature is limited to about 250
C, 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

Heat Transfer Chapter | 15

chemical industry, as this depends on the relative cost for the particular application compared with a conventional shell and tube heat exchanger.

Selecting an effective plate of width, W ¼ 0.5 m and effective length ¼ 1.5 m gives: Effective area of one plate ¼0.5  1.5 ¼ 0.75 m2 Area provided ¼ 82.5 m2 z number of plates  0.75 m2 total heat transfer area effective area of one plate

The number of plates ¼

Example 15-20

150,000 kg/h of ethanol is to be cooled from 80
C to 40
C in a gasketted plate heat exchanger using cooling water available in the plant at 25
C and outlet temperature 40
C. Design a suitable plate heat exchanger. Physical properties of ethanol and water at average temperatures of 60
C and 32.5
C respectively (see Volume 1, Appendix C) are: Specific heat capacity, kJ/kg
C Viscosity, cP Thermal conductivity, W/m
C Density, kg/m3

Ethanol 2.435 0.5872 0.1594 753.3

Water 4.188 0.77725 0.6164 995.0

Solution The heat duty, Q is:

82:5 ¼ 110 0:75 ðNumber of plates  1Þ Number of channels per pass ¼ 2 ¼ ð110  1Þ=2 ¼ 54:5 z 55 ¼

Take plate spacing (i.e., gap between successive plate) as 3 mm apart. i.e., y¼ 3 mm Equivalent diameter, de ¼ 2y ¼ 6 mm ¼ 6  103 m. Flow area (i.e., cross-sectional area of gap), Af is: Af ¼ y W ¼ 0.003  0.5 ¼ 1.5  103 m2 Ethanol side: Heat transfer coefficient  x hp de m ¼ C Rea Prb k mw where C ¼ 0.26, a ¼ 0.65, b ¼ 0.4 and m=mw z1:0  k hp ¼ 0:26 Re0:65 Pr0:4 de The Reynolds number, Re is: Re ¼

Q ¼ 4058.66 kW The cooling water flow rate w is: w ¼

Total gap area ¼ ðNumber of channelsÞðFlow areaÞ  ¼ ð55Þ ð1:5  103 ¼ 0:0825 m2

¼ 64:62 kg=s: The log mean temperature difference; DTLMTD ¼

DTLMTD ¼

ðDt1  Dt2 Þ  Dt1 ln Dt2

ð40  15Þ lnð40=15Þ

¼ 25:5
C Number of transfer unit (NTU) based on the maximum temperature difference is: DT 40 ¼ 1:569 ¼ NTU ¼ DTLMTD 25:5 For 1:1 pass arrangement from Figure 15-129. FT ¼ 0:965, and the corrected mean temperature difference is: DTCMTD ¼ ð0:965Þ ð25:5Þ ¼ 24:6o C Assuming the overall heat transfer coefficient, U ¼ 2000 W/m2
C Area required, Areq is: Areq ¼

de WpE m

The mass velocity, WpE is:

4058:66 ð4:187Þ ð15Þ

Q 4058:658  103 ¼ 82:5m2 ¼ 2000  24:61 U DTCMTD

267

WpE ¼ ¼

W Total gap area 41:67 kg ¼ 505:05 2 0:0825 m s

Channel velocity, v is: v ¼

W 41:67 ¼ r A ð753:3Þ ð0:0825Þ

¼ 0:67 m=s: Reynolds number, Re:

¼ 5161 Prandtl number, Pr is:

268

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Film heat transfer coefficient, hpE is:  0:1594 0:65 0:4 ð8:97Þ hpE ¼ 0:26 ð5161Þ 3 6  10 
¼ 4302:87 W m2 C Cooling water side heat transfer coefficient: Mass velocity of water, wpW: wpW ¼

Area required Areq is: Areq ¼ ¼

Q U FT DTLMTD

4058:3  103 ð1869:12Þ ð0:965Þ ð25:5Þ ¼ 88:23 m2

w Total gap area

The cooling water flow rate w is: w ¼ 64.62 kg/s. Total gap area ¼ 0.0825 m2 wpW ¼ 64.62/0.0825 ¼ 783.27 kg/s m2 Density of water at 32.5
C ¼ 995 kg/m3 Velocity, v ¼ wpW/r ¼ 783.27/995 ¼ 0.787 m/s. Reynolds number, Re:

Area required > Area provided. For the second trial: Increase the number of channels per pass to 60 giving (2  60) þ 1 ¼ 121 plates with 2 e 2 pass arrangement. Number of channels per pass ¼

121  1 ¼ 30 22

Area provided, Apro ¼ number of plates  effective area of one plate Apro ¼ 121  0:75 m2 ¼ 90:75 m2 For NTU ¼ 1.57, FT ¼ 0.96 (Figure 15-129) DTCMTD ¼ 0:96  25:5 ¼ 24:48
C Total gap area ¼ ðNumber of channelsÞ ðFlow areaÞ  ¼ ð30Þð1:5  103 ¼ 0:045 m2

Prandtl number, Pr is:

Mass velocity WpE WpE ¼

W 41:67 ¼ Total gap area 0:045

¼ 926 kg=s m2 Channel velocity, v is: v ¼ Film heat transfer coefficient, hpW is:  0:6164 0:65 0:4 hpW ¼ 0:26 ð6103Þ ð5:23Þ 6  103 
¼ 14949:33 W m2 C

WpE 926 W ¼ r 753:3 r A

¼ 1:229 m=s: Reynolds number, Re:

The overall heat transfer coefficient, U is: tp 1 1 1 1 1 ¼ þ þ þ þ U hpE hfE kp hpW hfW

(15-398)

where: hpE ¼ 4302.87 W/m2
C hfE ¼ Fouling coefficient of ethanol ¼ 10,000 W/m2
C (Table 15-57) tp ¼ Plate thickness ¼ 0.75 mm kp ¼ Thermal conductivity of plate material, for titanium ¼ kp ¼ 21 W/m
C. hpW ¼ 14949.33 W/m2
C hfW ¼ Fouling coefficient of cooling water in PHE ¼ 10,000 W/m2
C (Table 15-57). 1 1 1 0:75  103 1 þ ¼ þ þ 21 U 4302:87 10; 000 14949:33 1 þ 10000 2


U ¼ 1869.12 W/m C

Prandtl number, Pr is:

Film heat transfer coefficient, hpE is:  0:1594 ð9461Þ0:65 ð8:97Þ0:4 hpE ¼ 0:26 6  103 
¼ 6379:49 W m2 C Cooling water side heat transfer coefficient: Total gap area ¼ ðNumber of channelsÞ ðFlow areaÞ  ¼ ð30Þð1:5  103 ¼ 0:045 m2

Heat Transfer Chapter | 15



Mass velocity of water, wpW: wpW ¼

Percent excess area ¼

w Total gap area

The cooling water flow rate w is: w ¼ 64.62 kg/s. The mass velocity, wpW:   wpW ¼ 64:62 0:045 ¼ 1436:0 kg m2 s Density of water at 32.5
C ¼ 995 kg/m3 Velocity, v ¼ wpW/r ¼ 1436/995 ¼ 1.44 m/s. Reynolds number, Re:

Apro  1  100 Areq

269

(15-399)

 90:75  1  100 ¼ 25:7% 72:16

¼

Pressure Drop Calculations Ethanol side pressure drop consists of the channel pressure and the port pressure drop: Dp ¼ Dpc þ Dpp

(15-400)

The channel pressure drop, Dpc is: Dpc ¼ 8Jf

  Lp ru2p N de 2 m2

(15-401)

Jf ¼ 0:6 Re0:3 0:3 ¼ 0:6 ð9461Þ ¼ 0:03849 Prandtl number, Pr is:

The path length, Lp ¼ plate length  number of passes. ¼ 1:5  2 ¼ 3:0 m: The channel pressure drop, Dpc is:  2 Lp rup N de 2 m2   3 1:2292 ¼ 8 ð0:03849Þ ð753:3Þ 0:006 2

Dpc ¼ 8Jf Film heat transfer coefficient, hpW is:  0:6164 0:65 0:4 ð5:23Þ hpW ¼ 0:26 ð11190Þ 6  103 
¼ 22169:83 W m2 C The overall heat transfer coefficient, U is: tp 1 1 1 1 1 ¼ þ þ þ þ U hpE hfE kp hpW hfW where hpE ¼ 6380.28 W/m2
C hfE ¼ Fouling coefficient of ethanol ¼ 10,000 W/m2
C tp ¼ Plate thickness ¼ 0.75 mm kp ¼ Thermal conductivity of plate material, for titanium ¼ kp ¼ 21 W/m
C. hpW ¼ 22169.83 W/m2
C hfW ¼ Fouling coefficient of cooling water in PHE ¼ 10,000 W/m2
C (Table 15-57). 3

1 1 1 0:75  10 ¼ þ þ 21 U 6380:28 10; 000  2
U ¼ 2285 W m C

þ

1 1 þ 22169:83 10000

¼ 87625:78 N=m2 ð0:876 barÞ Port pressure drop: Take port diameter (i.e., hole diameter) ¼ 100 mm. Port area, Ap is: 2

Ap ¼

ue ¼  ue ¼

Area provided, Apro ¼ 90.75 m2

150000 ð3600Þð753:3Þð0:00785Þ

¼ 7:05 m=s: Port pressure drop, Dpp is: Dpp ¼ 1:3

 ru2e N  Np 2 m2

ð753:3Þ ð7:05Þ2 2 2

¼ 48619:84 N=m2 ð0:48barÞ

3

4058:3  10 ð2285Þð0:965Þð25:5Þ

¼ 72:16 m2

p ð0:1Þ2 ¼ 0:00785 m2 4

w  3600 r Ap

¼ 1:3

Q ¼ U FT DTLMTD ¼

4

¼

Velocity of ethanol through the port, ue is:

Area required, Areq is: Areq

p dp

Ethanol side pressure drop Dp is: Dp ¼ 0.87 þ 0.48 ¼ 1.35 bar. Increasing the port diameter to 120 mm. Port area, Ap is: Ap ¼

p d2p 4

2

¼

p ð0:12Þ ¼ 0:01131 m2 4

(15-402)

270

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Velocity of ethanol through the port, ue is: ue ¼  ue ¼

Velocity of water through the port, uw is:

w  3600 r Ap

uw ¼ 

150000 ð3600Þ ð753:3Þ ð0:01131Þ

uw ¼

Port pressure drop, Dpp is:

Port pressure drop, Dpp is: Dpp ¼ 1:3

2

  Np ;

N m2

Dpp ¼ 1:3

ð753:3Þ ð4:89Þ 2 2

¼ 1:3

Dp ¼ 1:259 þ 0:44 ¼ 1:699 bar:

Dp ¼ 0:87 þ 0:234 ¼ 1:10 bar: Increasing the port diameter reduces the fluid velocity through the port and subsequently reduces the pressure drop. The port pressure drop is 21.3 % of the total pressure drop which is significant. Cooling Water Side Pressure Drop Cooling water side pressure drop consists of the channel pressure and the port pressure drop: (15-400)

To decrease the cooling water Dp, let the number of cooling water side passes ¼ 1, i.e., 2:1 arrangement. Re ¼ 11190

(15-401)

¼ 1:5  1 ¼ 1:5 m: The channel pressure drop, Dpc is;  2 Lp rup N de 2 m2   3 1:442 ¼ 8 ð0:0610Þ ð995:0Þ 2 0:006 Dpc ¼ 8Jf

¼ 125857:15 N=m2 ð1:259 barÞ Port pressure drop: Take port diameter (i.e., hole diameter) ¼ 100 mm. Port area, Ap is: 4

2

¼

p ð0:1Þ ¼ 0:00785 m2 4

uw ¼

64:62 w_ ¼ ¼ 5:74 m=s ð995Þ ð0:01131Þ r Apo

Port pressure drop, Dpp is: Dpp ¼ 1:3 ¼ 1:3

 ru2w N  Np ; 2 m2

ð995Þ ð5:74Þ2 1 2

Water side pressure drop Dp is:

The path length, Lp ¼ plate length  number of passes.

p d2p

Increasing the port diameter ¼ 120 mm Port area, Apo ¼ 0.01131 m2 Velocity of water through the port, uw

¼ 21325:48 N=m2 ð0:21 barÞ

Jf ¼ 0:6 Re0:3 e0:3 ¼ 0:6 ð11190Þ ¼ 0:0610

Ap ¼

ð995Þ ð8:27Þ 1 2

Water side pressure drop Dp is:

Ethanol side pressure drop Dp is:

The channel pressure drop, Dpc is:   Lp ru2p N Dpc ¼ 8Jf de 2 m2

(15-402)

¼ 44233:11 N=m2 ð0:44 barÞ

¼ 23416:88 N=m2 ð0:234 barÞ

Dp ¼ Dpc þ Dpp

 ru2w N  Np ; 2 m2 2

2

¼ 1:3

232632 ð3600Þ ð995Þ ð0:00785Þ

¼ 8:27 m=s:

¼ 74:89 m=s:

ru2e

w  3600 r Ap

Dp ¼ 1:259 þ 0:21 ¼ 1:469 bar: The port pressure drop is 14.3% of the total pressure drop as compared to 25.9% with the port diameter of 100 mm.

SPIRAL HEAT EXCHANGERS 1. The spiral design heat exchangers, are conveniently adaptable to many process applications. The true spiral units are usually large and suitable for higher flow rates, and the Heliflow
-style, 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 vacuums as low as 3 mm Hg, because the pressure drops can be quite low. Bailey [214] identifies temperature limits of 30 to þ1,500
F, pressure limits of 0 to 350 psia, maximum flow rate per

Heat Transfer Chapter | 15

271

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 exchanger 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, interchangers, steam generators, process condensers, pump seal coolers, high temperature and high pressure exchangers and others [212]. The heat transfer design and pressure drop should be referred to the manufacturer to obtain proper unit surface and casing size selection. The company has a bulletin providing charts to aid in preliminary size selection by the engineer. Also, see Minton [268] for heat transfer calculations. This unit can be fabricated from a wide range of ferrous stainless steels, and nonferrous corrosion resistant metals and alloys. Figure 15-136 shows a spiral flow in both channels. Flow channels are closed by welding alternate channels at both sides of the spiral plate. This arrangement type is suitable for liquid-liquid services, where the unit is covered by flat heads on both sides. In this arrangement, two liquids flow counter currently, with the cold liquid entering at the periphery and flowing toward the core, and the hot liquid entering at the core and flowing toward the periphery. This arrangement type is used in cooling hot hydrogenated edible oil from deodorizers, as it offers good heat transfer coefficient for viscous oil. Figure 15-137 shows flow in a spiral in one channel and axial in the other. One channel is completely open on both ends and the other is closed at both sides of the plate. Here, this arrangement type is used for condensing or boiling, as the heat exchanger is covered by conical heads

FIGURE 15-137 Spiral Flow in One Channel, axial in another.

on one or both sides. Condensation or boiling takes place in the axial direction. This arrangement is suitable where there is a large difference in the volumes of two fluids. Where there is condensation, the difference between volumetric flow rates of the condensing vapor and cooling medium is always large. In the case of boiling where hot oil is used as a heating medium, the difference between the volumetric flow rate of boiling liquid and of the hot oil can be large. Figure 15-138 shows a spiral heat exchanger with a combination of flow. This arrangement is used to condense vapors. The condensing vapor flows axially and the condensate flows spirally. This type of spiral heat exchanger is adaptable for condensing with subcooling. Part of the open spiral is kept closed at the top. Entering fluid (condensing vapor) flows axially through the center part of the assembly in a downward direction. Condensate at the bottom flows spirally and exits from the side bottom. This arrangement is equipped with a conical head at the top and a flat cover at the bottom. Table 15-58 shows the advantages and disadvantages of spiral flow heat exchangers and the shell and tube heat exchangers.

Process Design for a Spiral Plate Heat Exchanger The steps in the design of a spiral flow heat exchanger are:

FIGURE 15-136 Spiral flow in both channels.

1. Calculate the heat duty. 2. Select the cooling or heating medium. 3. Based on the energy balance, determine the mass flow rate of heating or cooling medium. 4. Calculate the DTLMTD. 5. Assume the value of the overall heat transfer coefficient, U, for the first trial calculation. 6. Determine the heat transfer area required based on the assumed value of the overall heat transfer coefficient.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

The diameter of the heat exchanger or that of the outside spiral can be calculated from the following equation: Ds ¼ ½1:28  Lðdc þ dh þ 2tÞ þ c2 

The heat transfer area is provided for the first trial calculation. Q A ¼ (15-403) U  DTLMTD 7. Determine the heat transfer area for spiral plate heat exchanger:

De ¼

4  flow area 4 ðspacing  widthÞ ¼ wetted perimeter 2ðspacing þ widthÞ (15-407)

For hot fluid: Deh ¼

(15-404)

where: A ¼ Heat transfer area, m2 L ¼ Length of plate, m H ¼ Width of plate ¼ Height or length of heat exchanger, m Fix the value of H and find the value of L: L ¼ A=ð2  HÞ

(15-406)

where: Ds ¼ outside spiral diameter, m L ¼ length of plate, m dc ¼ channel spacing of cold side, m dh ¼ channel spacing of hot side, m t ¼ plate thickness, m c ¼ core diameter, m 8. Calculate the equivalent diameter of the flow channel from the following equation:

FIGURE 15-138 Combination flow.

A ¼ 2ðLÞðHÞ

1=2

4 ðdh  HÞ 2 ðdh þ HÞ

(15-408)

4 ðdc  HÞ 2 ðdc þ HÞ

(15-409)

For cold fluid: Dec ¼

9. Calculate the Reynolds number from the following equation: Re ¼

(15-405)

2m_ Hm

(15-410)

TABLE 15-58 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.

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.

Heat Transfer Chapter | 15

273

TABLE 15-59 Comparison of Bayonet, U-Tube, and Fixed Tubesheet Heat Exchangers Design

Advantages

Limitations

Applications and Notes

Bayonet

Removable tube bundle permits easy internal cleaning. Design allows free expansion of tubes in hightemperatures service. Needs no expansion joint if shell is used.

Double tubesheet increases initial cost.

Commonly used for heating or cooling very corrosive fluids that require expensive corrosion-resistant materials. Less economical than U-tube design for in-tank heating.

U-tube

Elimination of one tubesheet reduces initial cost. Tube bundle is removable for inspection and cleaning. Full tube bundle minimizes shellside bypassing. U-bends permit each tube to expand and contract individually. Tube bundle expansion is independent of shell; no expansion diaphragm is required.

Bends make mechanical cleaning of tube interiors difficult. Also, only a few outer bends can be replaced, so retubing usually involves replacement of all tubes.

Recommended for high-pressure (>600 psi), high-temperature applications. Tube shape allows extreme temperature differences (DT>250
F) across the bundle. Often used as integral column bottom reboiler and as tank suction heater to preheat product before pumping. Tube-side cannot be made single-pass.

FixedTubesheet

Lower cost per ft2 of heat transfer surface. Replaceable straight tubes allow for easy internal cleaning. Full tube bundle minimizes shell-side bypassing. No packed joints or internal gaskets, so hot and cold fluids cannot mix due to gasket failure.

Differential expansion must be accommodated by an expansion joint. Gasket failure can allow tube-side fluid to escape to the atmosphere.

Almost universal application unless a removable tube bundle is required for exterior inspection and cleaning, which may be avoided by running the fouling fluid on the accessible tube-side. Completely closed shellside eliminates gasket leakage. Excellent for high-vacuum work. Also available in double-tubesheet design to eliminate crosscontamination.

Used by permission: Corsi, R. Chemical Engineering Progress, V. 88, No. 7, p. 32, ©1992. American Institute of Chemical Engineers, Inc. All rights reserved.

where: m_ ¼ mass flow rate of fluid, kg/s H ¼ width of plate, m m ¼ viscosity of fluid, (kg/m s) 10. Calculate the critical Reynolds number Rec. This is the value of Reynolds number above which turbulent flow is achieved.  0:32 De (15-411) Rec ¼ 20000 Ds where: Rec ¼ critical Reynolds number De ¼ equivalent diameter of flow channel, m Ds ¼ outside diameter of spiral, m 11. Calculate the cold fluid side and the hot fluid side heat transfer coefficients by using suitable correlations as follows: (a) For spiral flow with no phase change and Re > Rec (i.e., turbulent flow):
    h De ¼ 1 þ 3:5 0:023 Re0:2 Pr2=3 Cp G Ds (15-412)

(b) For spiral flow with no phase change and Re < Rec (i.e., laminar flow):  1=6  0:14 h d mf ¼ 1:86 Re2=3 Pr2=3 mb Cp G Ds (15-413) (c) For axial flow with no phase change and Re > 10000: h ¼ 0:023 Re0:2 Pr2=3 Cp G where: d ¼ channel spacing, dc or dh, m Ds ¼ outside spiral diameter, m Cp ¼ specific heat of fluid, J/(kg
C) G ¼ mass velocity of fluid, kg/(m2 s) h ¼ heat transfer coefficient, W/(m2
C) k ¼ thermal conductivity, W/(m
C) Re ¼ Reynolds number (dimensionless) C m Pr ¼ Prandtl number pk , dimensionless m ¼ viscosity, (kg/m s)

(15-414)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Mass velocity, G, is calculated by: m_ ðd  HÞ

G ¼

(15-415)

where: m_ ¼ mass flow rate, kg/s d ¼ dc or dh, m H ¼ width of plate, m 12. Calculate the overall heat transfer coefficient, U, from: 1 1 1 1 1 t þ þ þ þ ¼ U hc hh hcd hhd km where: U ¼ overall heat transfer coefficient, W/(m2
C) hc ¼ cold fluid side heat transfer coefficient, W/(m2
C) hh ¼ hot fluid side heat transfer coefficient, W/(m2
C) hcd ¼ cold fluid side fouling coefficient, W/(m2
C) hhd ¼ hot fluid side fouling coefficient W/(m2
C) t ¼ thickness of plate, m km ¼ thermal conductivity of plate material, W/(m
C) 13. Calculate the heat transfer area required Areq ¼

Q U  DTLMTD

(d) Axial flow with no phase change and Re > 10000:  1:8  W 0:2 H 0:0115 m þ 1 þ 0:03H Dp ¼ 253:85 H ds (15-421) The calculated pressure drop must be less than or equal to the maximum allowable pressure drop or optimum pressure drop. where: Dp ¼ pressure drop, Pa L ¼ total length of plate, m r ¼ density of fluid, kg/m3 W ¼ m_ ¼ mass flow rate of fluid, kg/s ds ¼ channel spacing (dc or dh), m H ¼ width of plate, m m ¼ viscosity of fluid, kg/(m s) mb ¼ bulk fluid viscosity, kg/(m s) Example 15-21

Design a spiral flow plate heat exchanger for cooling a suspension of an organic liquid from 50
C to 35
C by using cooling water based on the following data. Cooling water is available at 30
C.

(15-417)

14. Calculate the percent excess heat transfer area; ideally it should be in the range 10 to 20%. 15. Calculate the cold fluid side and the hot fluid side pressure drops by using the following correlations. (a) Spiral flow with no phase change and Re > Rec: 2
L W Dp ¼ 0:0789 r ds H " #  1=3 1:3m1=3 H 16  þ 1:5 þ ðds þ 0:0032Þ W L (15-418) (b) Spiral flow with no phase change and 100 < Re < Rec: 
L W Dp ¼ 36:84 r ds H " #  1=2  1:035 m1=2 H mf 16  þ 1:5 þ ðds þ 0:0032Þ W mb L (15-419) (c) Spiral flow with no phase change and Re < 100: " #  0:17 Lrm mf W 5 Dp ¼ 5:5256  10 (15-420) 2:75 mb H ds

Component Water Carbon dioxide Ammonia Urea Organic liquid Total

Molecular Weight kg/h 18.0 17,000 44.0 3500

mol/h 944.44 79.55

mole % 74.89 6.31

mass % 57.63 11.86

17.0 60.06 126.12

3000 1500 4500

176.47 24.98 35.68

13.99 1.98 2.83

10.17 5.08 15.25

29500

1261.12 100.00

100.0

Physical properties of suspension liquid are: Specific heat, CpL, kJ/(kg
C) Thermal conductivity, W/(m
C) Viscosity at 50
C, cP Viscosity at 35
C, cP Density at 50
C, kg/m3 Density at 35
C, kg/m3

3.349 0.4935 1.6928 2.228 1118.71 1125.14

Specific heat capacity of water, kJ/(kg
C) ¼ 4.187 Suitable material of construction: SA 240 Gr. 316 L Maximum allowable pressure drops: For organic liquid suspension ¼ 1.0 bar For cooling water ¼ 1.0 bar Solution The heat balance between organic suspension liquid and cooling water is: Q ¼ W CpL ðT1  T2 Þ ¼ wcp ðt2  t1 Þ

Heat Transfer Chapter | 15

Let the outlet temperature of water ¼ 38
C 29500 Q ¼ ð3:349Þ ð50  35Þ ¼ wð4:187Þ ð38  30Þ 3600 Q ¼ 411:65 kW 411:65 ¼ 33:49 w w ¼ 12:29 kg=s The mass flow rate of organic solution suspension is: _ ¼ 29500 ¼ 8:19 kg W 3600 s

The log mean temperature difference, DTLMTD is: DTLMTD ¼ ¼

ðDt1  Dt2 Þ lnðDt1 =Dt2 Þ ð12  5Þ lnð12=5Þ

¼ 7:99
C Assuming the overall heat transfer coefficient, U ¼ 1500 W/(m2
C) The heat transfer area provided for the first trial calculation, Apr is: Q 411:65  103 A ¼ ¼ ð1500Þð7:99Þ U DTLMTD ¼ 34:32 m2 Let H ¼ 24 in. ¼ 609.6 mm ¼ 0.6096 m Area ¼ 2 (L) (H)

L ¼

275

34:32 ¼ 28:15 m ð2Þ ð0:6096Þ

To get the most compact design of spiral plate heat exchanger, width of plate (or length of heat exchanger) should be approximately equal to the outsides spiral diameter (or outside diameter of heat exchanger). Dimensions of the spiral heat exchanger: dc ¼ channel spacing for the cold side fluid ¼ 1/2 in. (12.7 mm) dh ¼ channel spacing for the hot side fluid ¼ 1/4 in. (6.35 mm)

c ¼ core diameter ¼ 8 in. (203.2 mm) t ¼ plate thickness ¼ 1/8 in. (3.175 mm) outside spiral diameter, Ds: Ds ¼ Ds ¼

 

1:28  Lðdc þ dh þ 2tÞ þ c2

1=2

1:28  28:15 ð0:0127 þ 0:00635 1=2 þ 2  0:003175Þ þ 0:20322

¼ ½0:95651=2 ¼ 0:978 m H s Ds Second trial, increase H ¼ 36 in. ¼ 914.4 mm (0.914 m) L ¼

34:32 ¼ 18:766 m ð2Þ ð0:9144Þ

Ds ¼ ½1:28  18:766 ð0:0127 þ 0:00635 þ 2  0:003175Þ þ 0:20321=2 ¼ 0:807 m

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Increase H ¼ 48 in. ¼ 1219.2 mm ¼ 1.2192 m 34:32 ¼ 14:075 m ð2Þ ð1:2192Þ  ¼ 1:28  14:075 ð0:0127 þ 0:00635 1=2 þ 2  0:003175Þ þ 0:20322

L ¼ Ds

¼ 0:706 m H y Ds H ¼ 914.4 mm dc ¼ 12.7 mm t ¼ 3.175 mm

Ds ¼ 807 mm dh ¼ 6.35 mm km ¼ 16.26 W/(m
C)

L ¼ 18766 mm C ¼ 203.2 mm

Hot fluid side heat transfer coefficient calculation: Equivalent diameter; Deh Deh ¼

4 ð6:35  914:4Þ 2 ð6:35 þ 914:4Þ

4 ðdh  HÞ ¼ 2 ðdh þ HÞ ¼ 12:612 mm

Mass velocity, G: G ¼

_ W 8:194 ¼ ð0:00635  0:9144Þ ðdh  HÞ

¼ 1411:19 kg=ðm2 sÞ
    Deh hh ¼ Cp G 1 þ 3:5 0:023 Re0:2 Pr2=3 Ds 
 0:0126 ¼ 4726:08  103  1411:19 1 þ 3:5 0:807 h i  0:023 ð9142Þ0:2 ð13:3Þ2=3 
 ¼ 3295:14 W m2 C The cold fluid heat transfer coefficient, hc is as follows: Equivalent diameter; Dec ¼ Dec ¼

¼ 0:0126 m:

The Reynolds number:

_ 2W Re ¼ Hm 2  8:194  103 ð0:9144Þ ð1:9604Þ

¼ 25:052 mm

¼ 0:02505 m:

Reynolds number:

¼

4 ð12:7  914:4Þ 2 ð12:7 þ 914:4Þ

4 ðdc  HÞ 2 ðdc þ HÞ

Re ¼ ¼ 9142

Critical Reynolds number, Rec:  0:32 Deh Rec ¼ 20; 000 Ds  0:32 0:0126 ¼ 20; 000 0:807 ¼ 5283:8 ¼ 5284 Since Re > Rec, the process fluid is turbulent. For spiral flow with no phase change and Re > Rec. The heat transfer film coefficient correlation on the hot side, hh:
    hh Deh ¼ 1 þ 3:5 0:023 Re0:2 Pr2=3 Cp G Ds Viscosity at average temperature ¼ 1.9604 cP ¼ 1.9604  103 kg/(m s) k ¼ 0.4935 W/(m
C) Cp ¼ 3.349 kJ/(kg
C) The Prandtl number, Pr:

¼

2 w_ Hm

2  12:29  103 ð0:9144Þ ð0:7486Þ

¼ 35924

The critical Reynolds number for the hot side fluid, Rec:  0:32 Dec Rec ¼ 20; 000 Ds 0:32  0:02505 ¼ 20; 000 0:807 ¼ 6583 Since Re > Rec, the process fluid is turbulent. For spiral flow with no phase change and Re > Rec. The heat transfer film coefficient correlation on the hot side, hc:
    hc Dec ¼ 1 þ 3:5 0:023 Re0:2 Pr2=3 Cp G Ds  Cp ¼ 4:187 kJ ðkg
CÞ The mass velocity of cooling water: G ¼

w_ 12:29 ¼ ðdh  HÞ ð0:0127  0:9144Þ

¼ 1058:3 kg=ðm2 sÞ

Pr ¼ 13:3

The heat transfer film coefficient correlation on the cold side, hc:
   hc Dec  ¼ 1 þ 3:5 0:023 Re0:2 Pr2=3 Cp G Ds

Heat Transfer Chapter | 15

Viscosity at average temperature ¼ 0.7486 cP ¼ 1.9604  103 kg/(m s) Cp ¼ 4.187 kJ/(kg
C) k ¼ 0.62 W/(m
C) The Prandtl number, Pr:

277

The revised calculated parameters are as follows: Revised outside diameter of the spiral, Dsr: 1=2  Dsr ¼ 1:28  Lðdc þ dh þ 2tÞ þ c2  Dsr ¼ 1:28  26:18 ð0:0127 þ 0:00635 þ 2  0:003175Þ 1=2 þ 0:20322 1=2

¼ ½0:8925 Pr ¼ 5:055 hc ¼ Cp G

¼ 0:9447 m


 1 þ 3:5

Dec Ds





0:023 Re0:2 Pr2=3




  0:02505 ¼ 4:187  103  1058:3 1 þ 3:5 0:807 i h 0:2 2=3 ð5:055Þ  0:023 ð35924Þ  2
 ¼ 4707:49 W m C The fouling coefficients on both the cold and hot sides are: hcd ¼ 15000 W/(m2
C) hhd ¼ 15000 W/(m2
C) The overall heat transfer coefficient, U: 1 1 1 1 1 t þ þ þ þ ¼ U hc hh hcd hhd km ¼

1 1 1 1 0:003175 þ þ þ þ 4707:49 3295:14 15000 15000 16:26 U ¼ 1183.96 W/(m2
C) Heat transfer area required, Areq: Areq ¼

Q 411:65  103 ¼ ð1183:96Þ ð7:99Þ U DTLMTD

¼ 43:52 m2 The heat transfer area required > the heat transfer area provided, i.e.:   Areq > Apr 43:5 2 m2 > 34:32 m2 This is unacceptable in the design; therefore recalculate the length, L by increasing the area by a factor 1.1. The length, L: L ¼

Areq  1:1 43:52  1:1 ¼ 2 ðHÞ 2  0:9144

¼ 26:18 m Therefore, the new area, Apr provided is: Apr ¼ 2 ðLÞ ðHÞ ¼ 2 ð26:18Þð0:9144Þ ¼ 47:88 m2

The critical Reynolds number for the hot side fluid, Rec:  0:32 Deh Rec ¼ 20; 000 Dsr  0:32 0:0126 ¼ 20; 000 0:9447 ¼ 5024 Since Re > Rec, the process fluid is turbulent. For spiral flow with no phase change and Re > Rec. The revised heat transfer film coefficient correlation on the hot side, hhr:
    hhr Deh ¼ 1 þ 3:5 0:023 Re0:2 Pr2=3 Cp G Dsr
    Deh 0:023 Re0:2 Pr2=3 hhr ¼ Cp G 1 þ 3:5 Dsr and the heat transfer coefficient for the hot fluid, hh:
    Deh hh ¼ Cp G 1 þ 3:5 0:023 Re0:2 Pr2=3 Ds Dividing hhr by hh gives:
  Deh 1 þ 3:5 h D  sr  ¼
D hh 1 þ 3:5 Ds hhr ¼ ¼

½1 þ 3:5 ðD=Dsr Þ  hh ½1 þ 3:5 ðDeh =Ds Þ ½1 þ 3:5 ð0:0126=0:9447Þ  3295:14 ½1 þ 3:5 ð0:0126=0:807Þ


¼ 3270:24 W=ðm2 CÞ Critical Reynolds number, Rec for cold fluid is:  0:32 Dec Rec ¼ 20; 000 Dsr 0:32  0:02505 ¼ 20; 000 0:9447 ¼ 6259:7

278

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

The revised value for the cold fluid heat transfer coefficient, hcr:
  Dec 1 þ 3:5 h D  sr  ¼
D hc 1 þ 3:5 Ds hcr ¼ ¼

½1 þ 3:5 ðD=Dsr Þ  hc ½1 þ 3:5 ðDec =Ds Þ

½1 þ 3:5 ð0:02505=0:9447Þ  4707:49 ½1 þ 3:5 ð0:0505=0:807Þ

Cooling water side with no phase change and Re > Rec, Dp is: 2 "  1=3  L w 1:3 m1=3 H Dp ¼ 0:0789 ðds þ 0:0032Þ W r ds H # 16   2  ; N m þ 1:5 þ L L ¼ 26.18 m H ¼ 0.9144 m




¼ 4640:22 W=ðm2 CÞ



The overall heat transfer coefficient, U:

Dp ¼ 0:0789

1 1 1 1 1 t ¼ þ þ þ þ U hc hh hcd hhd km ¼

"

1 1 1 1 0:003175 þ þ þ þ 4640:22 3270:24 15000 15000 16:26


U ¼ 1176:62 W=ðm2 CÞ Heat transfer area required, Areq: Areq ¼

r ¼ 994 kg=m3 w ¼ 12.29kg/s ds ¼ dc ¼ 0.0127 m m ¼ 0:7486 cP 3 ¼ 0:7486 x 10 kg=ðm sÞ 26:18 994



1=3

2 12:29 0:0127  0:9144  1=3 0:9144 þ 1:5 12:29

1:3 ð0:7486  103 Þ ð0:0127 þ 0:0032Þ # 16 þ 11174:99 N=m2 26:18

¼ 0:112 bar < 1 bar ðacceptableÞ 3

Q 411:65  10 ¼ ð1176:62Þ ð7:99Þ U DTLMTD

¼ 43:79 m2 The heat transfer area provided > the heat transfer area required, i.e.:   Apr > Areq 47:88 m2 > 43:79 m2

It is necessary to work with the manufacturer to size and rate these special units, because sufficient public data/correlations of heat transfer do not exist to allow the design engineer to handle the final and detailed design with confidence.

The percentage excess heat transfer area:  47:88  43:79 ¼  100 43:79 ¼ 9:3% ðacceptableÞ Pressure Drop Calculations Organic liquid suspension side with no phase change and Re > Rec, Dp is: 2 "  1=3  L W 1:3 m1=3 H Dp ¼ 0:0789 ðds þ 0:0032Þ W r ds H # 16   2  þ 1:5 þ ; N m L L ¼ 26.18 m H ¼ 0.9144 m

r ¼ 1121:93 kg=m3 ds ¼ dh ¼ 0.00635 m 



MISCELLANEOUS SPECIAL APPLICATION HEAT TRANSFER EQUIPMENT

W ¼ 8.194 kg/s m ¼ 1:9604 cP ¼ 1:9604 x 103 kg=ðm sÞ 2

26:18 8:194 1121:93 0:00635  0:9144 " # 1=3 1=3  1:3 ð1:9604  103 Þ 0:9144 16  þ 1:5 þ ð0:00635 þ 0:0032Þ 8:194 26:18 Dp ¼ 0:0789

¼ 37814:37 N=m2 ¼ 0:38 bar < 1 bar ðacceptableÞ

Corrugated Tube Heat Exchangers Figures 15-12I, J and K indicate the process flow patterns for single tube units for multiple corrugated tubes in a single plain shell. These units are suitable for heating or cooling process fluids containing high pulp or fiber content suspended particulates. The heat transfer coefficients are better than plain tubes, as the turbulence improves the performance. The units can be arranged in multiple shells for parallel or series flow. The manufacturers should be contacted for details.

Heat Transfer Flat (or Shaped) Panels Heat transfer panels are generally used to fit to a process vessel shape and to transfer heat from the panel through good heat transfer cement and into the wall of the process vessel, or they can be used to create a physically tight fit without the cement. Then the fluid in the vessel is heated, cooled or “held at temperature” by the heat/cooling

Heat Transfer Chapter | 15

279

from/into the panel. The shapes of these panels are versatile and can be used individually to submerge in tanks or vessels and to wrap around cylindrical vessels to serve a wide range of applications. Generally, two styles and techniques of fabrication are used, but this may vary between manufacturers, see Figures 15-139A and B. Note the importance of good flow distribution in between the heat transfer plates/panels, which suggests a specific style, depending on whether the heat is to be transferred to only one side of the plate pair or to both sides, as in submerged applications. Note that to improve heat transfer (internally), the fluid velocity may be designed to increase the film coefficient by use of series of parallel zones. A few application arrangements are given in Figures 15-140A,B, 15-141, 15-142 and 15-143. Heat transfer calculations are presented by the relevant manufacturers, and due to the proprietary nature of the surface areas, are available for various arrangements. It is advisable to obtain specific help. It is important to recognize any galvanic corrosion between the heat transfer surface and any metal to which it is attached or connected. This can depend on many factors, which must be recognized in the selection of construction materials as well as pure corrosion of the metal by the chemical environment. Likewise, the thermal expansion of the heat transfer surface must be accounted for by the manner in which is is attached, fastened or connected to the equipment to be heated or cooled.

Direct Steam Injection Heating This system is used for heating liquids for process and utility services [217]. Using proper controls, the temperature of the resulting mixture can be set for the desired temperature for direct mixing, heating jackets of vessels and similar requirements, see Figures 15-144 and 15-145.

Bayonet Heat Exchangers Bayonet heat exchangers are modified shell and tube types. The tubes are concentric within the outer tube, being sealed closed at one end, although the shell in its entirety is not always used or needed (see Figure 15-146). A helpful article describing this type of unit is that of Corsi [216]. A useful application is for tank and vessel heating, with the heater protruding into the vessel. Bayonet heat exchangers are used in place of reactor jackets when the vessel is large and the heat transfer of a large mass of fluid through the wall would be difficult or slow; because the bayonet can have a considerably greater surface area than the vessel wall for transfer. Table 15-60 compares bayonet, U-tube and fixed tubesheet exchangers [216].

FIGURE 15-139A Styles of Mueller Temp-Plate
heat transfer plates. (1) Double-embossed surface, inflated both sides. Used in immersion applications, using both sides of the heat transfer plate. (2) Single embossed surface, inflated one side, used for interior tank walls, conveyor beds. (3) Dimpled surface (one side), available MIG plugwelded or resistance spot welded. Used for interior tank walls, conveyor belts. (Used by permission: Bul. TP-108-9, ©1994. Paul Mueller
Company.)

The outer and inner tubes extend from separate stationary tube sheets. The process fluid is heated or cooled by heat transfer to/from the outer tube’s outside surface. The overall heat transfer coefficient for the OD of the

280

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-139B Platecoil
double- and single-embossing designs for standard units. The Platecoil
is fabricated using resistance, spot, seam, and Tungsten Inert Gas (TIG) and/or Metal Inert Gas (MIG) welding techniques in order to hold and seal the two plates together. (Used by permission: Cat. 5-63, ©1994. Tranter
, Inc.)

FIGURE 15-140B Typical styles of Platecoil
. Other styles include vertical and serpentine. (Used by permission: Cat. PCC-1-25M-RLB-1290, ©1990. Tranter
, Inc.)

Heat Loss Tracing for Process Piping

FIGURE 15-140A Used as an immersion plate with liquids, the serpentine flow path increases the heat transfer rate. (Used by permission: Cat. “Heat Transfer Equipment.” DEC International, Engineered Products Group.)

inner tube is found in the same manner as for the doublepipe exchanger [70]. The equivalent diameter of the annulus uses the perimeter of the OD of the inner tube and the ID of the inner tube. Kern [70] presents calculation details.

Many industrial processes require the transfer and storage of process fluids through pipelines and equipment. These fluids are liquids, gases, vapors, slurries or suspensions, and have temperature characteristics that allow them to freeze, become viscous or condense at normal ambient temperatures. In order to solve 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 the 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 [377]: 1. The lowest ambient site temperature will be below the freezing point of the liquid carried in the pipes. An

Heat Transfer Chapter | 15

281

FIGURE 15-141 Platecoils
on tank walls and cone bottoms. Note: See Figure 15-163 for use of heat transfer mastic between vessel and heat transfer coils/plates. (Used by permission: Bul. 5-63, ©1994. Tranter
, Inc.)

exception must be made 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, pxylene 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 freeze control valves or even the whole system; compressor suction lines (liquid is harmful to compressors); and H2S/water vapor (causes corrosion on condensation).

FIGURE 15-142 This figure illustrates an individual multizone Platecoil
as typically installed in agitated vessels. The stress pads, hemmed edges, and manifolds are omitted for clarity. Installation may be completed by welding or bolting. (Used by permission: Cat. 5-63,Sept. 1994. ©Tranter
, Inc.)

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 of 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 configuration of turns as well as elevations and drops. A tube or small diameter pipe attached to the process pipe that carries a heating medium for the addition of heat

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-143 Typical heat transfer cement/mastic sealing between vessel and heat transfer plates/coils/Temp-Plates
using spring-loaded assembly. (Used by permission: Cat. TP-108-9, ©1994. Paul Mueller
Co.)

FIGURE 15-144 Constant flow direct steam heater (variable flow also available.) (Used by permission: Cat. CF-5924 P. Pick Heaters, Inc.)

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 in 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. Steam also has a high film heat transfer coefficient, condenses at constant temperature and flows to the point of use without pumps. Lam and Samberg [378] have provided a comprehensive checklist and criteria for steam and electric tracing, and Table 15-61 lists a typical checklist for a petroleum refinery plant. The two basic types of system for maintaining and/or heating process piping temperature conditioning are (1) steam tracing or jacketing and (2) electric tracing. For most systems requiring extensive pipe lengths of heat maintenance, it is advisable to make an economic cost comparison for both capital and operating costs between the two applicable systems.

Heat Transfer Chapter | 15

283

Steam Tracing

FIGURE 15-145 Direct steam heating of liquids with internal temperature control using variable orifice steam nozzle. (Used by permission: Bul. H 150. Hydro-Thermal Corp.)

See Figures 15-147A and B. To maintain a desired temperature in the process pipe, it may be necessary to use one, two or three tracer tubes (small pipes) located symmetrically around the pipe and running parallel to the it; however, at valves and fittings, the tracing needs to be placed so as to provide protection uniformly to the surface. Some designers recommend arranging the tracing in the lower half of the pipe. Steam tracing has always been an easy heat tracing option for the plant engineer. This is because the steam distribution and return system is usually an integral part of the plant energy system, as steam is used in the turbines to turn generators for the production of electricity, as a prime mover for pumps and other equipment and for process heat in heat exchangers and reactors. There have been articles [379] regarding the inefficiency of steam tracing, where these assertions may be a result of comparisons with uncontrolled and less than optimally selected steam tracing systems, or a lack of knowledge of currently available high efficient steam tracing products and design technology. However, new steam tracing products exist that offer the design engineer a range of heat transfer capabilities to cover the range from freeze protection to high temperature tracing requirements. Additionally, design methodologies for steam tracing systems have become much more sophisticated and are based upon a combination of extensive empirical data, mathematical analysis and simulation techniques. Pitzer et al. [379] have provided a table in which the steam

FIGURE 15-146 Typical bayonet type heat exchanger, showing the key sparger arrangement internally as a part of each tube. (Used by permission: Corsi, R. Chemical Engineering Progress, V. 88, No. 7, ©1992. American Institute of Chemical Engineers. All rights reserved.)

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TABLE 15-60 Comparison of Bayonet, U-Tube, and Fixed Tubesheet Heat Exchangers Design

Advantages

Limitations

Applications and Notes

Bayonet

Removable tube bundle permits easy internal cleaning. Design allows free expansion of tubes in high-temperatures service. Needs no expansion joint if shell is used.

Double tubesheet increases initial cost.

Commonly used for heating or cooling very corrosive fluids that require expensive corrosionresistant materials. Less economical than U-tube design for in-tank heating.

U-tube

Elimination of one tubesheet reduces initial cost. Tube bundle is removable for inspection and cleaning. Full tube bundle minimizes shell-side bypassing. U-bends permit each tube to expand and contract individually. Tube bundle expansion is independent of shell; no expansion diaphragm is required.

Bends make mechanical cleaning of tube interiors difficult. Also, only a few outer bends can be replaced, so retubing usually involves replacement of all tubes.

Recommended for high-pressure (>600 psi), high-temperature applications. Tube shape allows extreme temperature differences (DT>250
F) across the bundle. Often used as integral column bottom reboiler and as tank suction heater to preheat product before pumping. Tube-side cannot be made single-pass.

FixedTubesheet

Lower cost per ft2 of heat transfer surface. Replaceable straight tubes allow for easy internal cleaning. Full tube bundle minimizes shell-side bypassing. No packed joints or internal gaskets, so hot and cold fluids cannot mix due to gasket failure.

Differential expansion must be accommodated by an expansion joint. Gasket failure can allow tube-side fluid to escape to the atmosphere.

Almost universal application unless a removable tube bundle is required for exterior inspection and cleaning, which may be avoided by running the fouling fluid on the accessible tubeside. Completely closed shell-side eliminates gasket leakage. Excellent for high-vacuum work. Also available in double-tubesheet design to eliminate cross-contamination.

Used by permission: Corsi, R. Chemical Engineering Progress, V. 88, No. 7, p. 32, ©1992. American Institute of Chemical Engineers, Inc. All rights reserved.

TABLE 15-61 Checklist to Decide Between Steam and Electric Heat Tracing Electric

Steam

Heat tracing recommended in company (Yes/No) engineering practices

Yes

Yes

Plant preferences

e

Yes

Total feet of traced pipe

4,700

Cost of electricity ($/kWh) and steam energy ($/1,000 lb)

TABLE 15-61 Checklist to Decide Between Steam and Electric Heat Tracingdcont’d Electric

Steam

Low

e

Labor cost to install tracing and accessories ($/ft.)

$30.00

$40.00

4.700

Training time per plant laborer (h)

20

20

$0.067

Consider free

Labor and overhead costs ($/h)

$23.50

$23.50

Estimated annual maintenance cost per foot of tracing ($/ft.)

$1.67

$1.33

Total installed heat-tracing costs ($/ft.)

$62.00

$74.00

Number of heat-tracing circuits required

50

65

Needed accuracy of temperature control (degrees)

 50
F

 50
F

Annual maintenance required (h/ft.)

0.03

0.05 $0.80

No extra

No extra

Annual cost for replacement parts ($/ft.)

$1.00

Temperature control cost per circuit for needed accuracy ($)

Total annual maintenance cost ($)

$6,182

$6,807

Cost of monitoring one circuit in distributed control system ($)

NA*

NA*

Total annual operating cost ($)

$7,179

$6,807

Design time per circuit (h)

0.5

0.5

Design tools available for engineers (Good, Fair, Poor, None)

Good

Good

Pre-Existing Project Constraints

Capital cost of required electrical power ($) Other

Project Design Phase Criteria

Project Installation Criteria

Other Project Operation Criteria

Continued

Other *NA ¼ 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.

Heat Transfer Chapter | 15

285

Bare Tracer See Figure 15-147A. The bare tracer is usually copper tubing, or sometimes carbon or stainless steel tubing, usually of 3/8 in., 1/2 in., or 3 /4 in. nominal size. a. From reference Foo [223], heat loss through the insulation to the ambient air is: Qia ¼ Uo

pDo ðTm  Ta Þ 12

(15-422)

The overall heat transfer coefficient for the insulation and the ambient air is [223]:

FIGURE 15-147A 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 circumference, then insulated. (Used by permission: Foo, K. W. Hydrocarbon Processing, V. 73, No. 1, Part 1, ©1994. Gulf Publishing Company.)

1 ðDo =2Þ lnðDo =Di Þ 1Do 1 ¼ þ þ hc D i f o Uo ko

(15-423)

The overall transfer coefficient for the tracer annulus space is: 1 1 1 ¼ þ Ut hc hs

(15-424)

For condensing steam, the heat transfer coefficient, hs, is approximately 2,000 Btu/(h) (ft2) (
F), and the preceding equation approximates to: 

Ts  Tap Ut ¼ hc ¼ 0:45 Dt

2 (15-425)

b. Heat loss when the tracer is surrounded by thermally conducting cement and insulated (otherwise same as (a), see Figure 15-148):   Qia ¼ Uo pðDo =12Þ Tap  Ta

(15-426)

Annulus space temperature, Tap ¼ Tm  FIGURE 15-147B 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

tracer heat output can be closely matched with the specified temperature maintenance requirements of a particular tracing project. They point out the energy savings in freeze protection service that can be achieved by selecting the optimal convection tracer design versus using a traditional convection tracer as shown in Table 15-62. Table 15-63 shows some of the common pitfalls to avoid when insulating steam-traced lines.

nqt Acc ðTs  Tm Þ
 ; F hc Ap  nAcc

(15-427)

Pipe temperature, [223]
Tm ¼



a Ta ðaþbþcÞ

þ

c Ts ðaþbþcÞ

b 1 þ d  ðaþbþcÞ

where: a ¼ UoAo b ¼ hc(Ap e nAcc) c ¼ hcAcp d ¼ nqtAcc




þd

(15-428)

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TABLE 15-62 Tracer Selection and Energy Saving [378]

Pipe Size

Traditional 13mm (1/2 in.) Conventional Tube Maintain Temperature


Today’s Optimal Conventional Tube Maintain Temperature










Resultant Energy Savings (%)

50 mm (2 inch)

89 C (193 F)

48 C (118 F) 10 mm (3/ 8 inch) (Extra light heat)

24

100 mm (4 inch)

71
C (159
F)

31
C (87
F) 10 mm (3/ 8 inch) (Extra light heat)

35

150 mm (6 inch)

49
C (120
F)

21
C (70
F) 10 mm (3/ 8 inch) (Extra light heat)

42

200 mm (8 inch)

38
C (101
F)

19
C (67
F) 10mm (3/8 inch) (Extra light heat)

34

250 mm (10 inch)

33
C (92
F)

16
C (60
F) 100 mm (3/ 8 inch) Type (Light heat)

35

300 mm (12 inch)

26
C (79
F)

10
C (50
F) 10 mm (3/ 8 inch) (Light heat)

36

Ap ¼ pDp/12, superficial area of pipe, ft2/ft Acp ¼ 0.23357 Dt, cement channel superficial area, ft2/ft Acc ¼ 2 Dt/12, cement contact area, ft2/ft Ao ¼ p Do/12, external superficial area of insulation, ft2/ft Qia ¼ Qpa þ Qta Qtp ¼ Qpa Do ¼ OD of insulation, in. Dt ¼ OD of tracer, in. Ts ¼ steam temperature,
F Ta ¼ ambient temperature,
F hc ¼ average of the horizontal and vertical transfer film coefficients by convection in still air. 

Ts  Tap Ut ¼ hc ¼ 0:45 Dt

2 (15-429)

TABLE 15-63 Insulation Installation Pitfalls to Avoid [378] Pitfalls

Possible Causes

Longitudinal gaps in insulation and fishmounting

Improper over-sizing of insulation does not allow room for steam tracer. Gaps in the insulation result in increased heat loss.

Longitudinal and circumferential gaps in rigid insulation

Many rigid insulants experience shrinkage due to high pipe temperature exposure. Good design practice (GDP) includes provision for compressible insulation expansion joints when using these types of materials. Where thicker layers are specified, using a double layer approach with staggered joints can reduce the effects of open joints/ gapping.

Wet insulation

Many times, the insulation materials used in conjunction with steam traced lines are hygroscopic (absorb and wick water). The insulation should be weather protected during installation and after the installation is completed. All weather barriers should be installed in a water shedding manner and should be sealed at fixed surface interfaces with water resistant flexible sealants. A wet insulation can increase its thermal conductivity by a factor of 12 over its normal dry state and must be avoided.

Insulation type changes

Thermal conductivity values of today’s insulation types can vary by a factor of two in a dry state. If the hygroscopic of the materials are compared, the installed thermal conductivity difference can be enormous. Avoid changing insulation type specifications because of availability or cost without an extensive design review.

Insulation thickness changes

Sometimes poor planning results in pipe interferences with a resulting need to reduce the insulation thickness at the time of installation. Avoid changing insulation thickness without reviewing (and changing where necessary) the steam tracer design.

Removable insulation covers on valves, pumps and equipment

While removable insulation covers are desirable from an ease of service viewpoint, they can be an uncontrolled source of heat leaks due to improper closure (and resultant gaps) at the many seam and joint surfaces. Whenever possible, avoid their use on critical steam traced piping.

Cracked insulation

Due to over sizing requirements necessary with steam traced piping/equipment, rigid insulants are more vulnerable to cracking when walked upon. Cracks when open can result in increased heat leaks from the insulation envelope. Provide adequate walkways whenever possible to discourage foot traffic on insulation steam traced pipes.

Heat Transfer Chapter | 15

287

TABLE 15-64 Insulation Material and Thickness Temp. Ranges,
F and Recommended Insulation Thicknesses, in. Mineral Wool & Calcium Silicate

Foam Glass 100e390

Up to 390

Pipe Size NPS

100e199

200e399

400e599

600e699

700e799

Normal

Fire protn.

1

1

11/2

2

2

21/2

11/2

3

1

1

2

1

1

1 /2

3

3

1

1 /2

3

3

1

1 /2

3

4

1

1 /2

3

1

1

1 /2

1 /2

2

2

1 /2

1

1 /2

2 /2

3

1

1 /2

1

1 /2

1

2 /2

4

1

1 /2

1

1 /2

1

2 /2

6

1

1

1

2 /2

3

4

1 /2

3

2

1

2 /2

3

4

2

3

1

1 /2

8

2

1 /2

1

2 /2

1

1

2 /2 3 3

10

2

2

2 /2

3

5

2

3

12

2

2

3

3

5

14 16 18 20 24 30 36

2 2 2 2 2 2 2

2 2 2 2 2 2 2

3 3 3 3 3 3 3

2

3

4

1

5 /2

2

3

4

1

5 /2

2

3

4

1

5 /2

2

3

4

1

5 /2

2

3

4

1

5 /2

2

3

4

1

5 /2

2

3

4

1

2

3

5 /2

(Used by permission: Foo, K.W. Hydrocarbon Processing, V. 73, No. 1, ©1994. Gulf Publishing Company. All rights reserved.)

Qtp ¼ heat transfer from tracer to process pipe, Btu/h/ft pipe Qap ¼ heat transfer from annulus space to pipe, Btu/h/ft pipe n ¼ number of tracers

Assume Tap ¼ Tm, annulus space temperature ¼ pipe temperature,
F. Annulus space temperature, Tap; Tap ¼ Tm 

nqt Acc ðTs  Tm Þ   hc Ap  nAcc

Then the pipe temperature, Tm is [223] i h i h a c Ta ðaþbþcÞ þd þ Ts ðaþbþcÞ Tm ¼ b a þ d  aþbþc

(15-430) Qia ¼ Uo

(15-431)

The heat transfer from annulus space through insulation to air: Qia ¼ heat transfer from annulus space through insulation to air, Btu/h/ft pipe Qpa ¼ heat transfer from process pipe to annulus space, Btu/h/ft pipe Qta ¼ heat transfer from tracer to annulus space, Btu/h/ ft pipe

 nDo  Tap  Ta 12

(15-432)

Table 15-64 presents types of insulation material. Foo [233] gives insulation thermal conductivity, k, at 100
F mean as: Calcium silicate 0.38 Btu/(h)(ft)(F) Foam glass 0.40 Mineral wool 0.28 The length of a traced line varies from a few feet (m) in a process area to a few thousand feet between offsites and the process area, and even to hundreds of miles when involving underground pipelines conveying crude oil. The most common steam tracing lines are 3/8 inch and 1/2 inch

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TABLE 15-65 Wind Velocity Factor, fo @ dT [ 150
F Mean Wing velocity, mph

fo

0

2.5

5

3.8

10

4.8

15

5.5

20

6

25

6.5

30

7

35

7.3

40

7.7

45

8

Note: dT ¼ Twall e Ta (Used by permission: Foo, K.W. Hydrocarbon Processing, V. 73, No. 1, ©1994. Gulf Publishing Company, Inc. Houston, Texas. All rights reserved.)

OD copper or stainless steel tubing. Larger tubing of 5/ 8 inch and 3/4 inch. OD can be used, but is more expensive. The 3/8 inch tube is more easily plugged by debris or sediment and is therefore used less than 1/2 inch tubing. Copper is preferred for its heat transfer characteristics, but stainless steel generally provides better resistance in corrosive situations. The length of a single trace tube (e.g., from steam supply valve to steam trap) is limited by the pressure drop in the trace. Additionally, the trap should be a condensate drainage capacity to match the heating load. At steam pressure of 100 psig or higher, Kohli [380] recommends that the length of a single trace should not exceed 200 ft. Conversely, if the steam pressure is lower, a tracer length of 100 ft is recommended. The trace tube is wired to the pipeline to provide greater contact. The conductive heat transfer rate is often low, but this may be increased by putting a layer of heat conducting cement (graphite mixed with sodium silicate or other binders) between the trace and the pipeline. This results in better surface for conductive heat transfer. Figure 15-147C shows various configurations of tracer and lagging and Figure 15-147D shows how various pipe fittings, pumps, instruments are treated with steam tracing.

Heat transfer cements are quite useful for transferring the heat from an external tracing when attached outside of the process pipe (Figures 15-148 and 15-149). To determine the number of heat transfer steam tracers, it is important to contact the manufacturer of the heat transfer cement. The illustrations here should be considered as preliminaries for approximating purposes. The information/data that follows is used with permission from Thermon
Manufacturing Co./Cellex Div. Except for specific conditions, most applications represent the requirements to maintain a pipe (or vessel) at system temperature, not to raise or lower the temperatures. In design considerations for Thermonized
process lines, temperatures may be determined by the “Stagnation Method.” The calculations involved in this method are based on static conditions where process fluid flow is not present, and are independent of the viscosity, density and thermal conductivity of the process fluid. The process temperature is calculated from the following relationship: R ¼

Tp  ta Ts  Tp

(15-433)

Tp ¼

RTs þ ta 1þR

(15-434)

where: Tp ¼ process temperature,
F ta ¼ ambient temperature,
F Ts ¼ steam temperature,
F R ¼ factor from Table 15-66 EXAMPLE 15-22. Determine the Number of Thermonized
Tracers to Maintain a Process Line Temperature

Used by permission of Thermon
Manufacturing Co./Cellex Div. Assume a 3 in. line. Design process temperature: 320
F (Tp). Insulation 11/2 in. thick calcium silicate. Steam temperature: 366
F (Ts). Ambient temperature: 0
F (ta). Required: The number (N) and size of Thermonized
tracers required to maintain 320
F process temperature (Tp) under the preceding conditions. Solution Calculate the R factor and determine the tracer requirements from Table 15-66. R ¼

T p  ta 320  0 ¼ 6:96 ¼ Ts  Tp 366  320

Heat Transfer Chapter | 15

289

Dt ¼ O.D. of tracer, in. fo ¼ wind velocity factor, Btu/h-ft2-
F hc ¼ convective heat transfer coefficient, Btu/h-ft2-
F hs ¼ steam, heat transfer coefficient , Btu/h-ft2-
F ko ¼ thermal conductivity of insulation, Btu/h-ft-
F L ¼ length of pipe, ft n ¼ number of tracers qt ¼ overall heat transmittance from tracer through cement to process pipe, Btu/h-ft2-
F Qap ¼ heat transfer from annulus space to pipe, Btu/h/ft pipe Qta ¼ heat transfer from tracer to annulus space, Btu/h/ft pipe Qtp ¼ heat transfer from tracer to process pipe, Btu/h/ft pipe Qia ¼ heat transfer from annulus space through insulation to air, Btu/h/ft pipe Ta ¼ ambient temperature,
F Tap ¼ annulus space temperature,
F Td ¼ desired holding temperature,
F Tm ¼ pipe temperature,
F Ts ¼ steam temperature,
F Uo ¼ overall outside heat transfer coefficient, insulation to air, Btu/h-ft2-
F Ut ¼ overall heat transfer coefficient from tracer to annulus space, Btu/h-ft2-
F Other useful references to steam and electrical tracing include [232e240]. The electric heat tracer systems require good temperature control, and Figure 15-150 shows a self-regulating system. The manufacturers should be consulted to prepare proper temperature control systems. FIGURE 15-147C Various configurations of tracer and lagging.

From Table 15-66, it can be determined that the calculated R factor of 6.96 is less than of 7 shown for one 3/8 in. OD tracer on a 3 in. line using 11/2 in. insulation. Thus, a single 3/8 in. OD tracer is satisfactory. The overall heat transmittance from the tracer through heat transfer cement to process pipe, qt, in Btu/(h) (ft2) (
F) is given in Table 15-67 [223]. From the detailed articles of Foo [233], the following nomenclature applies. Acc ¼ cement contact area, ft2/ft Acp ¼ cement channel superficial area, ft2/ft Ao ¼ external superficial area of insulation, ft2/ft Ap ¼ superficial area of pipe, ft2/ft Di ¼ I.D. of insulation, in. Do ¼ O.D. of insulation, in. Dp ¼ O.D. of pipe, in.

HEAT LOSS FOR BARE PROCESS PIPE Table 15-68 presents a tabulation of heat loss from the outside surface of bare standard pipe. Heat loss through wall of uninsulated pipe [70]. q ¼

2pkðti  to Þ ; Btu=lin ft 2:3 logðDo =Di Þ

(15-435)

where: D ¼ pipe diameter, in. t ¼ temperature,
F q ¼ heat loss through wall, Btu/lin ft k ¼ thermal conductivity of pipe wall, Btu/(h) (ft2) (
F/ft) i ¼ inside wall pipe o ¼ outside wall surface of pipe

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FIGURE 15-147D How various pipe fittings, pumps, instruments are treated with steam tracing.

FIGURE 15-148 Tracer placement on pipe using heat transfer cement. (Used by permission: Bul T-109M ©1994. Thermon
Manuifacturing Co./Cellex Div.)

FIGURE 15-149 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.)

TABLE 15-66 R-Factors for Thermonized
Process Lines TRACER TUBING SIZE Number of Parallel Tracers or Ft. of Tracing Per Ft. of Pipe 1" 2" 3" 4"

Process Line Size I.P.S. (Schedule 40)

6" 8" 10" 12" 14" 16" 18" 20" 24"

3/8” O.D. Tubing 1

2

3

4

5

29 – – – – 32 – – – – 9.5 29 – – – 32 10.6 – – – 6.3 13.2 9.5 – – 7.0 14.7 32 – – 4.7 9.5 17.6 29 – 5.3 32 – 10.6 19.6 3.1 6.3 9.5 13.2 18.9 3.5 7.0 21 10.6 14.7 – – – – – 2.7 5.3 8.2 10.6 13.9 – – – – – 2.1 4.2 6.4 8.9 10.6 – – – – – 1.7 3.5 5.3 7.0 8.9 – – – – – 1.5 3.1 4.6 6.2 7.9 – – – – – 1.3 2.7 3.9 5.3 6.9 – – – – – 1.1 2.3 3.5 4.8 6.1 – – – – – 1.0 2.1 3.1 4.2 5.3 – – – – – .8 1.7 2.6 3.5 4.5

1/2” O.D. Tubing 6

– – – –

7

– – –

– 29 32 – 18.7 – 13.1 – 10.6 – 9.4 – 8.2 – 7.3 – 6.4 – 5.3

– – – – – – –

8

– – – – – –

– – 12.4 – 10.6 – 9.3 – 8.4 – 7.6 – 6.3

–

1

32 36 10.9 – – 12.1 7.3 – 8.1 – 5.4 – 6.0 – 3.6 – 4.0 – – – 3.1 – – – 2.4 – – – 14.7 1.9 – – 12.6 1.7 – – 10.6 1.5 – – 9.4 1.2 – – 8.6 1.1 – – 7.4 .9 –

2 –

3

–

–

4

–

32 – 36 – 15.1 32 16.8 36 10.9 19.8 12.1 22 7.3 10.9 8.1 12.1 – – 6.0 9.3 – – 4.8 7.3 – – 4.0 6.0 – – 3.5 5.2 – – 3.0 4.4 – – 2.6 4.0 – – 2.4 3.5 – – 1.9 2.9

– – –

5

– –

– 32 36 15.1 16.8 – 12.1 – 10.1 – 8.1 – 7.1 – 6.0 – 5.5 – 4.8 – 3.9

– – – –

6

– – –

– 21 24 – 15.9 – 12.1 – 10.1 – 9.0 – 7.8 – 7.0 – 6.1 – 5.1

– – – –

7

– – –

– 32 36 – 21 – 15.0 – 12.1 – 10.7 – 9.7 – 8.3 – 7.3 – 6.0

Note: the upper figure is based on 1-in. insulation, the lower on 1 1/2 -inch. These data are to be used for temperature maintenance only. (Used by permission: “Engineering Data and Calculations, Part A,” Sect. 11, p. 12, ©1994. Thermon
Manufacturing Co./Cellex Division.)

– – – – – – –

8

– – – – – –

– – 14.1 – 12.1 – 10.6 – 9.6 – 8.7 – 7.2

– – – – – – –

– – – – – –

– – 16.8 – 14.4 – 12.1 – 10.7 – 9.8 – 8.4

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TABLE 15-67 Heat Transmittance from Tracers through Heat Transfer Cement to Process Pipe4

Heat loss from fluid inside pipe though exterior insulation to outside air [70]. Combined convection and radiation: q ¼

pðts  ta Þ    ; Btu=ðhÞðlin ftÞ ð2:3=2kc Þlog Dl D00s þ 1=ðha Dl Þ

NPC

qt

1

34.3

1.5

34.3

2

32.6

2.5

32.6

3

29.1

4

26.9

6

23.8

8

21.5

10

18.4

12

14.6

14

12.2

16

9.8

18

9.8

Material

k, Btu/(h) (ft2) (
F/ft)

20

9.8

Mineral wool

0.28

Foam glass

0.43

Calcium silicate

0.38

Magnesia, 85%

0.38

Glass

0.59e0.79

Glass wool

0.022

* Note: Reference 4 is to Foo’s article’s literature citation. Symbols: NPS ¼ nominal pipe size, in.; qt ¼ Btu/ (hr) (ft2) (
F). (Used by permission: Foo, K.W. Hydrocarbon Processing, V. 73, No. 1, ©1994. Gulf Publishing Company: All rights reserved.)

(15-436) where: s ¼ inside surface of pipe ha ¼ surface coefficient of heat transfer, Btu/(h) (ft2) (
F/ft.) k ¼ thermal conductivity of insulation, Btu/(h) (ft2) (
F/ft) D ¼ pipe OD, ft Dl ¼ insulation OD, ft a ¼ bulk fluid outside insulated pipe q ¼ heat loss per linear foot of pipe, Btu/(h) (lin ft) Selected Value of k, Thermal Conductivity of Insulation*

*Compiled from references [284] and [223].

Heat loss through the walls of the insulation is [221]. q ¼ k Dti =X ¼ h Dto

(15-437)

For heat loss from bare standard NPS pipe, see Table 15-68 [220]. For pipe insulation, heat flow between the inside surface of pipe insulation and the outside air at outside surface of pipe insulation [248]. Rate of heat transfer: qs ¼ 

to  ta    rs loge ðrl =ro Þ kl þ rs loge ðrs =rl Þ k2 þ Rs (15-438)

FIGURE 15-150 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.)

where: qs ¼ rate of heat transfer per ft2 of outer surface of insulation, Btu/(h) (ft2)

TABLE 15-68 “Q” Heat Loss from Bare NPS Pipe, Btu/(lin ft) (hr) Ambient Air Temperature 70
F, Natural Circulation Pipe Temperature,
F (English Units) NPS Pipe

100

200

300

400

500

600

700

800

900

1,000

1,100

1,200

Pipe dia. mm

1

13

75

165

287

444

649

901

1,218

1,602

2,075

2,644

3,317

21.3

3

16

93

204

353

547

801

1,113

1,508

1,984

2,576

3,282

4,122

26.7

/2 /4

1

114

250

433

674

989

1,379

1,865

2,462

3,194

4,080

5,123

33.4

1 /4

24

141

312

541

843

1,237

1,728

2,342

3,091

4,010

5,123

6,433

42.2

1

1 /2

27

159

352

613

955

1,403

1,960

2,661

3,514

4,568

5,841

7,345

48.2

2

33

196

432

753

1,176

1,732

2,423

3,295

4,355

5,665

7,251

9,133

60.3

2 /2

40

233

516

899

1,408

2,077

2,907

3,956

5,235

6,817

8,732

11,005

73.0

3

48

280

620

1,083

1,695

2,505

3,511

4,784

6,337

8,259

10,582

13,344

88.9

3 /2

55

317

701

1,226

1,922

2,841

3,987

5,434

7,201

9,390

12,039

15,189

101.6

4

61

354

784

1,370

2,149

3,179

4,467

6,094

8,079

10,545

13,513

17,049

114.3

6

87

503

1,122

1,976

3,105

4,604

6,479

8,858

11,769

15,366

19,740

24,909

168.3

8

111

644

1,436

2,530

3,988

5,927

8,356

11,433

15,211

19,895

25,568

32,293

219.1

10

136

791

1,769

3,114

4,918

7,312

10,325

14,147

18,812

24,621

31,679

40,051

273.0

12

159

930

2,076

3,664

5,809

8,627

12,194

16,721

22,248

29,133

37,501

47,429

323.3

14

174

1,009

2,258

3,989

6,316

9,404

13,301

18,236

24,279

31,844

40,965

51,856

355.6

16

197

1,142

2,560

4,529

7,160

10,697

15,124

20,769

27,663

36,257

46,689

59,089

406.4

18

221

1,282

2,873

5,074

8,032

12,010

16,992

23,346

31,109

40,788

52,539

66,456

457.2

20

244

1,416

3,168

5,618

8,897

13,270

18,777

25,810

34,432

45,147

58,159

73,691

500.8

24

289

1,683

3,772

6,679

10,593

15,825

22,375

30,836

41,112

53,958

69,536

88,221

609.6

30

351

2,042

4,642

8,242

13,103

19,606

27,758

38,299

51,107

67,125

86,558

109,872

762.0

36

421

2,450

5,570

9,890

15,724

23,527

33,309

45,959

61,328

80,550

103,860

131,846

914.4

38

93

149

205

260

315

371

423

482

539

593

649

1

1




Pipe Temperature, C (Metric Units)

293

(Used by permission: Turner, W. C., and Malloy, J. F., Handbook of Thermal Insulation Design Economics for Pipe and Equipment, © 1980, R. E., Krieger Publishing Company, Joint edition with McGrawHill Book Company, Inc. All rights reserved).

Heat Transfer Chapter | 15

20 1

294

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

k ¼ thermal conductivity of insulation at mean temperature, Btu/(h) (ft2) (
F/in.) ro ¼ inside radius of pipe insulation, in. rs ¼ outside radius of pipe insulation, in. rl ¼ outside radius of any (if used) intermediate layer of insulation, in. Rs ¼ outside surface resistance, (
F) (h) (ft2)/Btu Dt ¼ temperature difference (tl  tave) between inside surface of pipe insulation and average outside air temperature,
F L ¼ thickness of insulation, in. ta ¼ temperature of ambient air,
F to ¼ temperature of inner surface of insulation,
F ts ¼ temperature of outer surface of insulation,
F X ¼ insulation thickness, ft Note: For k, subscript 1 ¼ first (inner) layer of insulation. If more than one has a different k value, subscript 2 ¼ second layer of insulation if different from first year. Heat flow per ft2 of pipe surface qo ¼ qs(rs/ro) Btu/ (h) (ft2)

Heat Loss Through Insulation for Process Pipe An alternate presentation of Chapman and Holland [227] is useful. Heat transfer from the surface of an insulated or uninsulated pipe in air involves convection and radiation. In still air, more heat is lost by radiation than through convection. The heat loss from an insulated or bare pipe is, in Btu/h:   (15-439) Q ¼ h0a Aa Ts  Ta where: Ts ¼ surface temperature of insulated or bare pipe in contact with air,
F ha0 ¼ heat transfer film coefficient between the insulated or bare pipe and air. See Figure 15-151, assume ˛¼ 0.90 and ambient air temperature ¼ 70
F h0 a ¼ hc þ ˛ hr, Btu/(h) (ft2) (
F) hc ¼ convection heat transfer film coefficient, Btu/(h) (ft2) (
F) hr ¼ radiation heat transfer film coefficient, Btu/(h) (ft2) (
F) ˛ ¼ emissivity of the outside surface of insulated or bare pipe Ta ¼ ambient temperature,
F D ¼ OD of the insulated or bare pipe, whichever is being studied. Aa ¼ area of heat transfer between the insulation or bare pipe and air, ft2 T0 ¼
R (degrees Rankine)

The authors [227] point out that the emissivity, ˛, for many pipe surfaces ranges from 0.87e0.92 at approximately 70
F. For highly polished aluminum, ˛¼ 0.23e0.28. For pipe exposed to wind velocities other than “calm,” use Figure 15-152 to determine a value for hc, which can be much greater than the “calm” values of 1.8e2.1 Btu/(h) (ft2) (
F) To calculate hr as per Kern [70].    Q ¼ ð˛Þðarea=lin ftÞ T0s 100 4 4     (15-440)  T0s 100 ; Btu hðlin ftÞ s ¼ Stefan-Boltzmann constant     ¼ 0:173  108 ; Btu ðhÞ ft2 R4        hr ¼ q A; ft2 lin ft Ts  Tr ; Btu ðhrÞ ft2 ð
FÞ (15-441) Because pipe heat loss can be an expensive cost for many process plants, Figure 15-153 illustrates a rapid solution applicable to many situations. Ganapathy [218] summarizes his analysis by use of this figure. Example 15-23. Determine Pipe Insulation Thickness [218]

Used by permission of Ganapathy [218]. (Follow dotted line on Figure 15-153.) Determine the thickness of insulation to limit heat loss to 60 Btu/ft2-h in a 3 in. NPS pipe. Pipe temperature tl is 580
F; ta, the ambient temperature, is 80
F. Insulation K value is 0.5 Btu/ft2-h-
F/in., and outside film coefficient is 2.0 Btu/ ft2-h-
F. (See table that follows.) What is the surface temperature of the insulation? Solution Using Figure 15-153, connect (tl  ta) ¼ 500 with Q ¼ 60 and extend to cut line 1 (dashed lines) at A. Connect f ¼ 2.0 with point A and extend to cut line 2 at B. Connect B with K ¼ 0.5 to cut line 3 at C. The horizontal from C and the vertical from pipe size 3 intersect the curve corresponding to t ¼ 25 in. Therefore, the solution is 2.5 or the next standard size of insulation. From the equation, (ts  ta) ¼ Q/f, (ts  ta) ¼ 60/2 ¼ 30. Therefore, ts ¼ 30 þ 80 ¼ 110
F. The effect of using a different thickness of insulation and the corresponding heat loss can easily be calculated. For example, using 2 in. thick insulation, we see that (solid lines) Q ¼ 78 Btu/ft2-h, and surface temperature increases to (78/2 þ 80) ¼ 119
F. Values of f* Still air 7.5 mph wind 15 mph wind

1.2e1.8 2.0e4.0 3.5e5.0

*Btu/(ft2) (h) (
F); for preliminary estimates, use. 2.0

Heat Transfer Chapter | 15

295

FIGURE 15-151 Outside heat-transfer film coefficient as function of pipe temperature and O.D. (Used by permission: Chapman, F. S., and Holland, F. A. Chemical Engineering, Dec. 20, 1965, p. 79. ©McGraw-Hill, Inc. All rights reserved.)

where f ¼ outside film coefficient, Btu/(h) (ft2) (
F) Q ¼ heat loss, Btu/(ft2) (h), from pipe insulation ta, ts, tl ¼ ambient, surface and pipe temperatures,
F K ¼ thermal conductivity of insulation Btu/(ft2) (h) (
F/in.) Heilman [219] presents a thorough discussion of heat loss from bare and insulated surfaces. 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: l l l l l

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.

296

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-152 How air velocity over heated pipe increases heat transfer through forced convection. (Used by permission: Chapman, F. S., and Holland, F. A. Chemical Engineering, Dec. 20, 1965, p. 79. ©McGraw-Hill, Inc. All rights reserved.)

FIGURE 15-153 Heat loss through process pipes and insulation. (Used by permission: Ganapathy, V. Oil and Gas Journal, Apr. 25,1983, p. 75. ©PennWell Publishing Company. All rights reserved.)

Heat Transfer Chapter | 15

1. 2. 3. 4.

The film resistance on the inside wall of the pipe. Heat resistance through the pipewall. Heat resistance through the insulation. Air film resistance on the outside of the insulation.

That is, Ta  Ts ¼ CðTs  Tair Þ where:

The Equations

C ¼ ðha Þ

1. The average temperature of the hot medium,
F. Tm;avg ¼ 0:5ðTmi þ Tmo Þ

(15-442)

2. The average temperature of pipe and tracer,
F.   Tavg ¼ 0:5 Tm;avg þ Tp (15-443)

Ts ð1 þ CÞ ¼ Ta þ CTair

(15-451)

Ta þ CTair 1þC

(15-452)

and:

(15-444)

Do ¼ Di þ 2Tk

(15-445)

5. Heat lost per foot of pipe, Q, Btu/h.ft. Q ¼

2pKi ðTa  Ts Þ

 ln DDoi

(15-446)

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
F ha p Do ðTa  Tair Þ Q ¼ 12

(15-447)

Using Equations 15-446 and 15-447 and rearranging the terms gives: 2pKi ðTa  Ts Þ ha pDo ðTs  Tair Þ ¼ Q ¼

 12 ln DDoi

(15-448)

(15-450)

Equation 15-449 can be expressed in terms of Ts as follows:

Ts ¼

4. The outside diameter of insulation, inches.

(15-449)

   Do 1 Do ln 12 Di 2Ki

3. The inside diameter of insulation, inches. Di ¼ OD þ TAL

297

Equations 15-450 and 15-452 involve two unknowns, ha and Ts. An initial value of ha is assumed and Ts is calculated. McAdams [82] 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 15-69 gives values of ha for pipes in still air, and Table 15-70 lists the correction factor for ha at different wind velocities. 6. The combined convective and radiative heat transfer coefficient (hc þ hr) is given by: hc þ hr ¼

564 ½273  ðTs  Tair Þ  D0:19 o

(15-453)

7. The wind factor, WF: WF ¼ C0 þ C1 ðTs  Tair Þ þ C2 ðTs  Tair Þ (15-454) 2

where: C0 ¼ 2.814 C1 ¼ 0.00038857 C2 ¼ 0.0000012857

TABLE 15-69 Values of ha for Pipes in Still Air (ts L ta)
F (For an Unlagged Pipe, ts [ tw) Nominal Pipe dia., inch

50

100

150

200

250

300

400

500

1

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

/2

(Source: McAdams [82]).

298

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-70 Correction Factor for ha at Different Wind Velocities (ts L ta)
F

TABLE 15-71 Thermal Conductance Tracer to Pipe Tube Size, inch.

a

b

Wind Velocity, m/h

3/8

0.295

3.44

100

200

300

400

500

2.5

1.46

1.43

1.40

1.36

1.32

1/2

0.393

4.58

5.0

1.76

1.69

1.64

1.59

1.53

5/8

0.490

5.73

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 ¼ tw) (Source: McAdams [82]).

8. The new film heat transfer coefficient to air corrected for wind, ha (Btu/h.ft2
F): ha ¼ ðhc þ hr Þ ðWFÞ

(15-455)

9. The total heat lost from pipeline, Qt, Btu/h: Qt ¼ ðQÞ ðLTotal Þ

(15-456)

where LTotal ¼ total length of pipe, ft. 10. The flow rate of hot medium, W, lb/h: W ¼

Qt Cp ðTmi  Tmo Þ

(15-457)

11. The number of tracers required without heat transfer cement is; Q  NTWOC ¼  a Tm;avg  Tp

(15-458)

where: a ¼ thermal conductance tracer to pipe without cement, Btu/h
F (ft of pipe) 12. The number of tracers required with heat transfer cement: Q  NTWC ¼  b Tm;avg  Tp

(15-458a)

where b ¼ thermal conductance tracer to pipe with cement, Btu/h
F (ft of pipe) Table 15-71 lists the values of a and b. where: a ¼ thermal conductance, tracer to pipe without heat transfer cement, Btu/h
F (ft of pipe, Table 15-71)

(Source: Kohli [380]).

b ¼ thermal conductance, tracer to pipe with heat transfer cement, Btu/h
F (ft of pipe, Table 15-71) C0, C1, C2 ¼ constants for wind factor equation. Cp ¼ specific heat of hot medium, Btu/lb
F Di ¼ inside diameter of insulation, inch. Do ¼ outside diameter of insulation, inch. ha ¼ film heat transfer coefficient to air (corrected for wind, Btu/h ft2
F) hc þ hr ¼ combined convective and radiative heat transfer coefficients, (Btu/h ft2
F) Ki ¼ thermal conductivity of insulation, Btu/h ft2 (
F/ft) LTOTAL ¼ total pipe line length, ft NTWC ¼ number of tracers required with heat transfer cement. NTWOC ¼ number of tracers required without heat transfer cement. Q ¼ heat lost per ft of pipe, Btu/h ft. Qt ¼ total heat lost from pipeline, Btu/h Ta ¼ average temperature of pipe and tracer,
F Tair ¼ air temperature,
F TAL ¼ allowance for tracer diameter, inch. Tm,avg ¼ average temperature of hot medium,
F. Tmi ¼ inlet temperature of hot medium,
F Tmo ¼ outlet temperature of hot medium,
F Tp ¼ temperature in pipe,
F Ts ¼ outside surface temperature of insulation,
F W ¼ flow rate of hot medium, lb/h WF ¼ Wind factor. Blackwell [381] recommends approximately 11/4 inch between pipe and insulation to accommodate a 1/2 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 15-24

Determine the number of tracers required to maintain 100 ft of 8 inch (Schedule 40) process line (ID ¼ 7.981 inch)

Heat Transfer Chapter | 15

at 500
F. Hot tracing medium is available at 630
F and has a heat capacity of 0.53 Btu/lb
F. The process line is covered with 2.5 in. of insulation, and this insulation has a thermal conductivity of 0.033 Btu/h ft2 (
F/ft). Design for 0
F air temperature and 20 mph winds. Use 1/2 inch tracers, the hot medium outlet temperature is 550
F. Allow approximately, 11/4 inch. between pipe and insulation to accommodate a 1 /2 inch in tracer line and heat transfer cement. Assuming the trial film heat transfer coefficient is 4.0 Btu/h ft2
F, and the thermal conductances tracer to 1/2 inch pipe are a ¼ 0.393 and b ¼ 4.58 Btu/h
F (ft of pipe), respectively. Solution The computer program PROG154 calculates the heat tracer requirements and heat loss for an insulated pipe line, either with or without tracing. Table 15-72 lists the

TABLE 15-72 Input Data and Computer Results for Example 15-24 Input Data 100.0

500.0

630.0

550.0

0.0

7.981

1.25

2.5

0.037

0.53

4.0

0.393 4.58

HEAT TRACER REQUIREMENTS FOR PIPELINES AND HEAT LOSS FROM AN INSULATED PIPELINE WITH TRACING

TABLE 15-72 Input Data and Computer Results for Example 15-24dcont’d WITHOUT CEMENT, Btu/h.
F. ft of pipe:

0.393

THERMAL CONDUCTANCE TRACER TO PIPE WITH CEMENT, Btu/h.
F.ft of pipe:

4.580

OUTSIDE SURFACE TEMPERATURE OF INSULATION,
F:

18.958

THE COMBINED CONVECTIVE AND RADIATIVE HEAT TRANSFER COEFFICIENT, Btu/h.
F.ft^2:

1.340

WIND FACTOR:

2.806

HEAT TRANSFER COEFFICIENT TO AIR CORRECTED FOR THE WIND, Btu/h.ft2.
F:

3.762

HEAT LOSS PER FOOT OF PIPE, Btu/h.ft:

282.526

TOTAL HEAT LOSS FROM PIPELINE, Btu/h.:

28252.650

FLOW RATE OF HOT MEDIUM, lb/h.:

666.336

THE NUMBER OF TRACERS

TOTAL PIPELINE LENGTH, ft.:

100.0

TEMPERATURE IN PIPE,
F:

500.0

WITHOUT HEAT TRANSFER CEMENT:

HOT-MEDIUM INLET TEMPERATURE,
F:

630.0

THE NUMBER OF TRACERS

HOT MEDIUM OUTLET TEMPERATURE,
F:

550.0

AIR TEMPERATURE,
F:

0.0

OUTSIDE DIAMETER OF PIPE, in.:

7.981

ALLOWANCE FOR TRACER DIAMETER, in.:

1.25

THE COMBINED CONVECTIVE AND RADIATIVE

INSULATION THICKNESS, in.:

2.50

1.354

THERMAL CONDUCTIVITY OF INSULATION, Btu/h.ft2 (
F/ft)

0.037

HEAT TRANSFER COEFFICIENT, Btu/h.
F.ft2: WIND FACTOR:

2.807

SPECIFIC HEAT OF HOT MEDIUM, Btu/Ib.
F:

0.530

WITH HEAT TRANSFER CEMENT:

0.69

HEAT LOSS FROM AN INSULATED PIPE WITHOUT TRACING OUTSIDE SURFACE TEMPERATURE OF INSULATION,
F:

16.982

HEAT TRANSFER COEFFICIENT TO AIR

FILM HEAT TRANSFER COEFFICIENT TO AIR CORRECTED FOR WIND, Btu/ ft2.h.
F:

7.99

4.000

THERMAL CONDUCTANCE TRACER TO PIPE Continued

CORRECTED FOR THE WIND, Btu/h.ft2.
F:

3.800

HEAT LOSS PER FOOT OF PIPE, Btu/h.ft:

230.850

TOTAL HEAT LOSS FROM PIPELINE, Btu/h.:

23085.040

299

300

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

input data and computer results of Example 15-24. 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 666.3 lb/h, and the heat lost from 100 ft of pipe line is 23,085 Btu/h. In SI Units

The following equations are used for designing bare and cement heat tracers respectively [382]: Q ¼ UADT

For cemented tracing, the equations are: Lact ¼



r1  r2 r1 þ r2

(15-459)

(15-460)

(15-474)

Qca þ Qcp ¼ Qal þ Qpl

(15-475)

Qca ¼ ð0:992257866nLÞ ð0:4714r2  2aðr1 þ ct ÞÞ # " 1:25 ðTs  Tann Þ  ðr2 þ ct Þ0:25   Qcp ¼ 4qt nLr2 Ts  Tp Qal ¼

Equations for determining the different areas across which heat transfer occurs: a ¼ cos1

ðtan aÞ ðr1  r2 Þ 
 sin tan1 ðtan aÞc1ðr1 r2 Þ

Qpl

(15-461)

Qta ¼ Qal þ Q

(15-462)

2 n L ðTann  Tamb Þ ðr1  r2 Þ ðtan aÞ 
t 1 þ kins ho

Qpl ¼

L Tp  Tamb ð2 p  ð1:25 þ 0:75nÞðtan aÞÞ
 lnðr1 =rpinn Þ þ lnðrkinsins=r1 Þ þ ho1 ri kins  Tann ¼

Ts þ Tp þ Tins 3



Tin ¼ 0:5Tsurf þ 0:45Tp þ 0:05Ts k1 ¼ Qta  Qal ð2 p  ð1:25 þ 0:75nÞ aÞ k2 ¼
 lnðr1 =rpinn Þ lnðrins =r1 Þ 1 þ þ kins ho r i kins k1 Tp ¼ Tamb þ k2

(15-465) (15-466) (15-467) (15-468) (15-469)

q ¼

" 0:548ε

(15-470)

4  4 #! Tsurf Tamb  55:55 55:55

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i þðð1:957ðjTsurf  Tamb jÞ5=4 Þð 2:85Vm þ 1ÞÞ

Tsurf

2

3 r2 þtins ðr þ t Þ ln s ins r2 6 7 7 ðqÞ ¼ Ts  6 4 5 kins ho ¼

q ðTsurf  Tamb Þ

Tp ¼

c3 ¼ 4nqt r2 c1 þ c3 Ts þ c2 Tamb c2 þ c3



(15-481)

(15-482) (15-483)

Equation (15-484) determines the hottest surface temperature for cemented tracing:  3 2 ðrs þ ct þ tins Þ ln r2 þcrt2þtins 6 7 7 ðqÞ (15-484) Tsurf ¼ Ts  6 4 5 kins where: " q ¼

" 0:548ε

4  4 #! Tsurf Tamb  55:55 55:55

#  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

5=4 2:85Vm þ 1 þ 1:957ðjTsurf  Tamb jÞ (15-485)

Equation (15-472) determines the hottest surface temperature for bare tracing, where q is the overall heat transmittance from cemented tracer to process fluid pipe: "



(15-464)



(15-480)

½2p  ð1:25 þ 0:75nÞ a c2 ¼
 lnðr1 =rpinn Þ lnðrins =r1 Þ 1 þ þ h k kw o ins

Qta ¼ 1:98451554 nL ðp  aÞ ðTs  Tann Þ1:25 r0:75 2 (15-463)



(15-478)

c1 ¼ Qca  Qal

Lai ¼ ðr1  r2 Þ ðtan aÞ

(15-477)

  L Tp  Tamb ð2 p  ð1:25 þ 0:75nÞ aÞ ¼ (15-479)
 lnðr1 =rpinn Þ lnðrins =r1 Þ 1 þ þ ho kins kw

For bare tracing:

Qal ¼

2 n L ðTann  Tamb Þ
 t 1 þ kins ho

(15-476)

(15-472)

(15-473)

where: Ata ¼ effective area of tracer exposure to annulus, m2 Aal ¼ effective area of annulus exposed to air, m2 Aca ¼ effective area of cement exposed to air, m2 Acp ¼ effective area of cement exposed to process fluid pipe, m2 Atl ¼ effective area of tracer exposed to air, m2 Acl ¼ effective area of cement exposed to air, m2 Dt ¼ diameter of tracer pipe, m Tins ¼ insulation thickness, m ct ¼ cement thickness, m hc ¼ heat transfer coefficient in still air, W/m2 K ho ¼ heat transfer coefficient at surface, W/m2 K kw ¼ thermal conductivity of pipe wall, W/m K kins ¼ thermal conductivity of insulation, W/mK L ¼ length of tracer connected to pipe, m Lai ¼ length of insulation between annulus and air for bare tracer, m

Heat Transfer Chapter | 15

Lact ¼ length of insulation between annulus and air for cemented tracer, m m ¼ mass flow rate of steam, kg/h n ¼ amount of bare or cemented tracers, tracers Ps ¼ saturated steam pressure, kPa q ¼ overall heat transmittance from cemented tracer to process fluid pipe, W/m2K Qta ¼ energy transfer between tracer and annulus, J Qal ¼ energy transfer between annulus and air, J Qpl ¼ energy transfer between process pipe and air, J Qca ¼ energy transfer between cement and annulus, J Qcp ¼ energy transfer between cement and process fluid pipe, J Qtl ¼ energy transfer between cement and air, J Qcl ¼ energy transfer between cement and air, J r1 ¼ outer radius of steam tracer pipe, m r2 ¼ inner radius of process fluid pipe, m rpinn ¼ inner radius of process fluid pipe, m Ts ¼ saturated steam temperature, K Tp ¼ process fluid temperature, K Tann ¼ annulus temperature, K Tamb ¼ ambient design temperature, K Tsurf ¼ outer surface temperature, K Tins ¼ average insulation temperature, K Vm ¼ wind velocity, m/s a ¼ angle used in determining area, radians ε ¼ emissivity of insulation lagging de Lange [382] has developed an Excel spreadsheet program based upon the above equations for bare and cemented tracers and this can be accessed from www. cheresources.com

Direct Contact Gas-Liquid Heat Transfer

301

where: Zsp ¼ height of a single zone of spray contact, which most likely in the space between spray nozzles when the full area coverage is achieved, ft G ¼ superficial gas mass velocity, lb/(h) (ft2) L ¼ superficial liquid mass velocity, lb/(h) (ft2) hga ¼ gas phase volumetric heat transfer coefficient, Btu/(h) (ft3) (
F) The liquid phase resistance, hla, is considered low when compared to the overall resistance, therefore, the hga should give a reasonable approximation to the overall resistance for the system [242,247], because 1/Ua ¼ 1/hga þ 1/hla.

Random Packed Columns Fair [242] recommends the correlating relations from Huang [250], as shown in Table 15-73, which satisfy the relationship: Coefficient ¼ hga, or hla, or Ua ¼ Cl Gm Ln where: hga ¼ volumetric gas phase heat transfer coefficient, Btu/(h) (ft3) (
F) hla ¼ liquid phase heat transfer coefficient, Btu/(h) (ft3) (
F) Ua ¼ volumetric overall heat transfer coefficient, Btu/ (h) (ft3) (
F) G ¼ superficial gas mass velocity, lb/(h) (ft2) L ¼ superficial liquid mass velocity, lb/(h) (ft2) a ¼ Ackerman correction factor, dimensionless, source unknown.

The direct counter-current contact of a hot gas with a cool immiscible liquid is used effectively in certain hydrocarbon cracking processes for quenching hot gases/vapors. Sometimes the liquid used is oil and is followed by a water quench, as is typical in ethylene plants, cracking naphtha or other hydrocarbon as feedstock. The three primary devices used in this service are (a) open spray columns [242,245], (b) packed columns [242,243,244,245], and (c) tray columns, which are perforated plates, baffle trays, etc. [242,245,246,247, 248,249]. Fair [242] reports that the data for mass transfer in spray, packed and tray columns can be used for heat transfer calculations for these columns. The pressure drop in these types of columns is usually quite low.

where:

Spray Columns

Sieve Tray Columns

Data correlated by Fair [242] provides an empirical relationship for heat transfer:

The thesis of Stewart [249] indicates that the overall liquid film and mass transfer coefficients were functions of the gas flow rate and the column pressure, and are independent of the liquid flow rate and inlet air temperature. The gas film

hga ¼

0:015G0:82 L0:47 Z0:38 sp

(15-486)

For little or no condensation in the system:    1 Ua ¼ 1 hg a þ 1 hi a For condensation:   1 Ua ¼ 1 ahg a þ ð1=hl aÞ ðQs =QT Þ Sc ¼ Schmidt number, dimensionless Pr ¼ Prandtl number, dimensionless cpg ¼ gas specific heat, Btu/lb-
F a ¼ interfacial area, ft2/ft3 Qs ¼ sensible heat transfer duty, Btu/h QT ¼ total heat transfer duty, Btu/h

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TABLE 15-73 Heat Transfer Coefficients for Packed Columns Coefficient* [ ClGmLn Packing

System

Coefficient

Cl

m

n

RR-I in.

Air/Water

hla

0.774

0.51

0.63

Air/Water

hga

0.230

1.10

0.02

Air/Oil

Ua

0.00026

1.69

0.51

Air/Water

hla

0.738

0.48

0.75

Air/Water

Hga

0.008

1.45

0.16

Air/Oil

Ua

0.0016

1.49

0.38

Air/Water

hla

2.075

0.20

0.84

Air/Water

hga

0.095

1.01

0.25

Air/Oil

Ua

0.0045

1.32

0.43

Air/Water

hla

6.430

0.20

0.69

Air/Water

hga

0.019

1.38

0.10

Air/Oil

Ua

0.003

1.44

0.36

Air/Water

hla

0.296

0.45

0.87

Air/Water

hga

0.019

1.12

0.33

Air/Oil

Ua

0.0013

1.47

0.46

Air/Water

hla

1.164

0.31

0.80

Air/Water

hga

0.011

1.28

0.26

Air/Oil

Ua

0.027

1.07

0.36

RR-1.5 in.

IS-1 in.

IS-1.5 in.

RP-1 in.

PR-1.5 in.

Symbols RR 1 in. Ceramic Raschig rings, 1-in and 1.5 in. nominal size RR 1.5 in. IS 1 in. Ceramic Intalox saddles, 1-in. and 1.5-in. nominal size IS 1.5 in. PR 1 in. Metal Pall rings, 1-in. and 1.5-in. normal size PR1.5 in *hga or hia or Ua, Btu/(hr-ft2-
F) Used by permission: Fair, J.R. ASME Solar Energy Division Conference, April 1989. ©American Society of Mechanical Engineers, San Diego, CA.

heat transfer coefficient was found to be a function only of the air flow rate. From Fair [242], the gas phase coefficient is: hg a ¼

 2=3 cpg G Scg   Hg;d Prg

(15-487)

and the heat transfer efficiencies range from 60e100%. Based on the gas phase, the height of a transfer unit, Hg, is [242]: Hgd ¼

G kg a M g P

For nitrogen data [242], Ua ¼ 0.213 G1.0

(15-488)

For helium data [242], Ua ¼ 1.05 G1.0

Baffle Tray Column [242] The contacting counterflow action provides a dependence on the liquid rate, similar in concept for packed columns: Hg a ¼ Gl Gm Ln

(15-488A)

where: Cl ¼ coefficient which depends on the system used, for example, Cl ¼ 2.058 for nitrogen/absorption oil hg ¼ heat transfer coefficient, J/sm2K a ¼ interfacial area, n2/m3, or ft2/ft3 cp ¼ specific heat, Btu/(lb) (
F)

Heat Transfer Chapter | 15

G ¼ superficial gas mass velocity, lb/(h) (ft2) H ¼ heat transfer coefficient, Btu/(h) (ft2) (
F) hga ¼ volumetric gas phase coefficient, Btu/(h) (ft3) (
F) Hgd ¼ height of a gas phase mass transfer unit, ft Hl,d ¼ height of a liquid phase mass transfer coefficient, ft kg ¼ gas phase mass transfer coefficient, lb-mol/(h) (ft2) (atm) L ¼ superficial liquid mass velocity, lb/(h) (ft2) M ¼ molecular weight m ¼ exponent in baffle tray columns n ¼ exponent in baffle tray columns ¼ 1.18 experimental values for system studied n ¼ exponent in baffle tray columns ¼ 0.44 P ¼ pressure, atm Pr ¼ Prandtl number, dimensionless Q ¼ heat transfer duty, Btu/h Sc ¼ Schmidt number, dimensionless Ua ¼ volumetric overall heat transfer coefficient, Btu/(h) (ft2) (
F) U ¼ overall heat transfer coefficient, Btu/(h) (ft2) (
F) Z ¼ height, ft Zsp ¼ height of individual spray zone, ft r ¼ density, lb/ft3

303

ΔT V

L CL

V CV

ΔT L FIGURE 15-154 Direct contact tray column for heat transfer. This could be a baffle tray, sieve type tray, bubble or other contact device, or open spray or random packed column. (Symbols only used by permission: Smith, J. H. Hydrocarbon Processing, Jan. 1979, p. 147. ©Gulf Publishing Company. All rights reserved.)

Subscripts d ¼ diffusional g ¼ gas l ¼ liquid Smith [248] presents a design for this type of tray direct contact column, summarized as shown in Figure 15-154. Also see Vol. 2, 4th Ed., Chapter 10 of this series for design details. When vapor stream has lower heat capacity than liquid stream (DTv > DTL), use [248]: (15-489) Hv ¼ DTv =DTL    Hv ¼ Hvnþ1  Hv Hvnþ1  1 ¼ DTv DTv;max 

(15-490) 





Hv ¼ Hv nþ1  Hv Hnþ1  1:0 ; solve for n number v of equilibrium states (15-491) When liquid stream has lower heat capacity than vapor stream (DTL > DTv) use [248]: HL ¼ DTL =DTv (15-492)     HL HL ¼ Hnþ1 HLnþ1  1 ¼ DTL DTL;max L 



 HL HL ¼ Hnþ1 L



(15-493)  Hnþ1  1:0 ; solve for n (15-494) L

Example 15-25. Determine Contact Stages Actually Required for Direct Contact Heat Transfer in Plate Type Columns

Used by permission: Smith, J. H. Hydrocarbon Processing, V. 58, No. 1, ©1979. How many theoretical contact stages are required for a side reflux system on an atmospheric crude tower? The vapor is to be cooled from 500
F to 440
F; the circulating distillate is to be heated from 325
F to 475
F. Because DTL > DTv, use Equations 15-492 and 15-493. HL ¼ ð475  325Þ=ð500  440Þ ¼ 2:50 HL ¼ ð475  325Þ=ð500  325Þ ¼ 0:857   0:857 ¼ ð2:5nþ1  2:5 2:5nþ1  1:0 n ¼ 1:665 About 65% efficiency is to be expected in this service, requiring three actual trays. where: Hv ¼ heat transfer factor, vapor limiting HL ¼ heat transfer factor, liquid limiting HL* ¼ heat transfer efficiency, equals ration of actual liquid temperature decrease to maximum possible decrease Hv* ¼ heat transfer efficiency, equals ratio of actual vapor temperature decrease to maximum possible decrease

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

n ¼ number of equilibrium contact stages DTv ¼ actual vapor temperature decrease ATv,max ¼ maximum possible vapor temperature decrease (to liquid inlet temperature) DTL ¼ actual liquid temperature rise DTL,max ¼ maximum possible liquid temperature rise (to vapor inlet temperature) E Baffle Tray Column (or, Termed Shower Deck, No Holes, Caps or Other Contact Devices) For counter flow, gas flowing up a column through a falling shower film of liquid, Fair’s correlation [242] of collected data is to be used as guide: Ua ¼ 0:011 G1:04 L0:3

(15-495)

See Fair’s reference, given previously, for nomenclature. For baffle trays, the coefficient equation given under packed columns, the values of m ¼ 1.18 and n ¼ 0.44 with Cl depending on the system. For example, for a nitrogen/ absorption oil system, Cl ¼ 0.00250. See the reference and Table 15-68 for more details.

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 costs. 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 applications, but not to provide methods for preparing final fabrication designs [106,206,251,252,253,254,255,256, 257,258,259,260,261,262,263,264,265]. 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 [251]. To be effective, the air must flow in forced convection to develop acceptable transfer coefficients. Figures 15-155, 15-156 and 15-157 illustrate the two types, designated by the type of air movement, induced draft or forced draft.

FIGURE 15-155 Two types of air-cooled heat exchangers. (Used by permission: © Hudson Products Corporation.)

FIGURE 15-156 Typical forced draft air-cooled exchanger showing two exchanger sections and one fan. (Used by permission: Yuba Heat Transfer Division of Connell Limited Partnership.)

Heat Transfer Chapter | 15

305

Forced Draft Advantages: 1. Possibly lower horsepower requirements if the affluent 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: FIGURE 15-157 Typical induced draft air-cooled exchanger showing two exchanger sections and two fans. (Used by permission: GriscomRussell/Ecolaire Corporation, Easton, PA.)

The advantages and disadvantages of forced and induced draft fan operation on the performance of the unit as presented by Hudson Products Corp [251] are used by permission in the following discussions.

Induced Draft Advantages: 1. Better 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. Possibly higher horsepower requirements if the effluent air is very hot. 2. Effluent air temperatures should be limited to 220
F to prevent damage to fan blades, bearings or other mechanical equipment in the hot air stream. When the process inlet temperature exceeds 350
F, 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.

1. Less 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. Hudson [251] states that the advantages of the induced draft design outweigh the disadvantages. Although most units are installed horizontally, inclined (Figure 15-158) and vertical units are also in service. Figures 15-159 and 15-160 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 15-156, 15157, 15-159, 15-160 and 15-161. The usual headers are plug and cover plate, but U-bend types can be accommodated if the design so dictates. The headers may be: 1. Cast 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). 3. Cover 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 [16,18]. 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 Temperature Difference is better with the

306

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-158 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.)

horizontal pass plates. The fan drive may be operated by any of the available means, including: 1. Direct electric motor or with belts. 2. Two-speed electric motor with belts or gears, gear or fluid coupling. 3. Steam turbine, direct or with gear or fluid coupling. 4. Gasoline engine with belt, gear or fluid coupling. 5. Hydraulic drive (see Figure 15-162). 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 [88]. 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 e usually three. B-sections are most common. V-belts are not considered for drives over about 50e60 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 2e20 blades per fan, which force or induce the air across the bundle. Four blades are considered minimum, and an even number of blades (2e20) are preferable to an

Heat Transfer Chapter | 15

307

FIGURE 15-159 Typical tube bundle using fabricated or cast end headers. (Used by permission: Yuba Heat Transfer Division of Connell Limited Partnership.)

FIGURE 15-160 Typical tube bundle using flanged end cover plates. (Used by permission: Yuba Heat Transfer Division of Connell Limited Partnership.)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-161 Typical construction of tube bundles with plug and cover plate headers. (Used by permission: Bul. M92-3003MC 10/94. ©Hudson Products Corporation.)

Heat Transfer Chapter | 15

309

FIGURE 15-162 Typical drive arrangements for air coolers. (Used by permission: Griscom-Russell/Ecolaire Corporation.)

odd number (for emergency removal of blades to obtain balance for continued partial operation). Fan diameters range from 3e60 ft. The blades may be of solid or hollow construction [251], 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

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

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, and plastic is limited to about 160e180
F 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 nonpenetrating. 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 11,000e12,000 ft. per min (¼ p  blade dia. ln ft  rpm). This may run higher for units below 48 in. dia. Figure 15-160 illustrates the assembly of a typical forced draft unit with electric motor and gera 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 hailsusceptible areas. If damaged just slightly, the performance is not impaired. 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 recommended to keep unauthorized individuals away from all the equipment; however, a close fan guard, Figure 15-163, will prevent blade contact by the operators. Figures 15-164A 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

FIGURE 15-163 Fan blade guard mounted directly below blades. Note that drive shaft connects through the opening. (Used by permission: Bul. 107. SMITHCO Engineering, Inc.)

FIGURE 15-164A Fin designs for use with air-cooled exchangers.

FIGURE 15-164B Illustrations of actual fin construction. (Used by permission: Bul. B589-455, 6/89. ©Hudson Products Corporation.)

Heat Transfer Chapter | 15

finned to bare tube surface of 15:1e20:1. Common sizes are 3/4 in. and 1 in. OD with 1/2 in. to 5/8 in. high fins, although 11/2 in. OD as well as small sizes are available for a specific design. The minimum number of tube rows recommended to establish a proper air flow pattern is four, although three rows can be used [265]. The typical unit has 4e6 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 in transverse or longitudinal patterns, however, the transverse arrangement is usually used due to the improved performance related to pressure drop and heat transfer [256]. 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 [256]. 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 2.125e2.5. For a 1 in./2.25 in. tube, the pitch range would be 2.375e2.75. Reference [265] 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 14e24 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 7e11, 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 1 /2 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 1/2 in. triangular (60
) spacing. Fin thickness usually varies from 0.016e0.014 in. The effect of mechanical bond on heat transfer resistance is discussed by Gardner [50]. 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: 1. Preferred bare tube OD and gage, giving minimum average wall thickness.

311

2. Seamless or resistance welded base tube. 3. 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, etc. and also in condensing service for steam, high boiling organic vapors, petroleum still vapors, gasoline, ammonia, etc. In general, the economics of application favors service allowing a 30e40
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 20e25
F of the dry bulb air temperature, if this is the desired endpoint, rather than adding a small trim cooler. Kern [72] has studied optimum trim cooler conditions. As the 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 2e5 hp per 106 Btu/h [63]. First costs range from 25e150% of cooling tower systems, with an average indicated at greater than 30% [115]. 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 15-165). Economic comparisons should include such items as tower costs, basin, make-up facilities, water treatment, pumps for circulation, power supply, blow down, piping, etc. 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: 1. Quantity and quality of available water. 2. Ambient air and water temperature. 3. Fluid inlet as well as exit temperatures.

312

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-165 Combined system using cooling tower and air cooler units. (Used by permission: Hudson Products Corporation.)

4. 5. 6. 7.

Operating pressure. Fixed costs. Maintenance and operating costs. Physical location and space requirements.

Mukherjee [265] presents an interesting examination of factors that can influence operating problems with air-cooled heat exchangers. Advantages e 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, etc. 3. Excellent for removing high level temperatures, particularly greater than 200
F. 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.

Disadvantages 1. Rather 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. Fixed capital costs may range from only 25e125% 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 they are used in such applications. Chase [24] lists these factors affecting the overall costs: 1. Exchanger 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.).

Heat Transfer Chapter | 15

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 [24]. 1. Induced Draft a. Recirculation of air is less (exit air velocity 2e3 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.

Bid Evaluation Manufacturer’s specification sheets, Figure 15-166 are important for proper bid evaluation, and purchaser’s specifications may be offered on a form, as in Figure 15-167. Optimum design is not often achieved in all respects; however, the fundamentals and application cost factors of Nakayama [87] are of real value in selecting goals and design features. In addition to the items listed on the specification sheets and in other paragraphs of this section, it is important for the process engineer to evaluate the manufacturer’s bids for air-cooled units with the following points in mind [88]. 1. The dollars/ft2 of finned or dollars/ft2 of bare tube surface in a finned unit do not necessarily give the only important factor.

313

2. Determine whether parallel or counter flow exists inside tubes. 3. For condensing problems, determine whether apparent weighted mean temperature difference is used, and which is applicable. 4. Determine fouling factors. 5. Determine tube metal resistance. 6. Determine net free flow area for air across bundle, and determine air linear velocity. Compare air- side coefficients for same linear velocities. 7. Determine required fan horsepower (bhp) per million Btu transferred. 8. Determine total dollars per ft2 of finned surface including standard (or specified) support structure, ladders, etc. From such items and others pertinent to a specific situation, will emerge the conclusions: 1. The lowest dollar value based on complete structure, including the important finned surface. 2. The best dollar value considering amount of basic surface, type of fans, etc. These two may not be the same. In some instances, high finned surface area but low bare tube surface mean that a lot of tall (sometimes less efficient) fins are crowded onto the tube. In this case, horsepower might be expected to be higher. Bid evaluations must include a study of the peculiar costs expected to be associated with a given unit, and these include first cost of equipment, power (or driver) operating costs, maintenance for entire unit, foundations, special structural limitations, pipe layout, and perhaps others. To simplify the evaluation, it is to the advantage of the purchaser to advise the manufacturer of the dollar cost per installed horsepower in his plant and the operating costs for power. The manufacturer can select, from a wide combination of units, the size and number that are the most economical. Otherwise, the bids should be requested as based on “lowest operating cost” or “lowest capital cost,” neither being the best in itself except for certain purposes. Table 15-74 provides some useful correlations for air-cooled heat exchanger design [383].

Design Considerations (Continuous Service) The air-cooled heat transfer exchanger is like other exchangers in that the basic heat transfer equation must be satisfied [265]. A ¼

Q ðUÞðMTDÞ

(15-496)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-166 Specification sheet for air-cooled exchangers. (Used by permission: Air-Cooled Exchangers Manufacturers Association, New York (no longer in existence, 1999); Hudson Engineering Corporation, now Hudson Products Corporation.)

Heat Transfer Chapter | 15

315

FIGURE 15-167 Air-cooled equipment specifications form. (Used by permission: Segel, K. D. Chemical Engineering Progress, V. 55, ©1959. American Insistute of Chemical Engineers. All rights reserved.)

where:

or [251], Q ¼ ðUÞðAÞðT e tÞmean 1 1 1 ¼ þ þ rf;t þ rf;a þ rw U htca htct

(15-497)

A ¼ total bare tube heat transfer area, ft2 htca ¼ airside heat transfer coefficient, Btu/(ft2) (h) (
F) htct ¼ tube-side heat transfer coefficient, Btu/(ft2) (h) (
F) MTD ¼ mean temperature difference,
F

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-74 Correlations for Air-cooled Heat Exchanger Design Correlation Ha ¼ 0:295

Where Used G0:681 a

d0:319 o

S

0:313

0:2

h

0:113

b

Air-side heat transfer coefficient

b

Tube-side heat transfer coefficient (for mass velocities between 15 and 1000  103 lb/h ft2

G0:8 d0:2 ml0:4 c0:4 Hl ¼ 0:276 K0:6 i l l pl 0:19 ðPe Nu ¼ 3:66 þ 1þ0:117ðPe

 f 2

Nu ¼ NuDh

1:07þ12:7

d=LÞ0:8 d=LÞ0:46

Tube-side heat transfer coefficient for laminar flow. Tube-side heat transfer coefficient in turbulent flow.

ReDh Pr

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2=3 f 2 ðPr

1Þ


 1:25 0:5m ¼ 5:172 1 þ 5:484 x 103 Pr0:7 Re y

Tube-side heat transfer coefficient with twisted tapes.

The correlations need to be augmented with fin efficiency and fouling factors. H ¼ heat transfer coefficient, W/m2 K G ¼ mass velocity, kg/m2 s d ¼ diameter of tube, m S ¼ fin surface area, m2 h ¼ fin height, m b ¼ fin thickness, m b ¼ equivalence function m ¼ viscosity of fluid kg/m s cp ¼ specific heat, J/kg K Nu ¼ Nusselt number Re ¼ Reynolds number Pe ¼ Peclet number f ¼ friction factor Pr ¼ Prandtl number L ¼ length, m k ¼ thermal conductivity, W/m K y ¼ twist ratio Subscripts a ¼ air l ¼ liquid i ¼ inner o ¼ outer Dh ¼ hydraulic diameter

Q ¼ heat transfer duty, Btu/h rf,t ¼ tube-side fouling resistance, (h-ft2-
F)/Btu rf,a ¼ air side fouling resistance, (h-ft2-
F)/Btu rw ¼ wall resistance, (h-ft2-
F)/Btu t ¼ air temperature,
F T ¼ hot fluid temperature,
F U ¼ overall heat transfer coefficient, Btu/(h-ft2-
F) CMTD ¼ corrected mean temperature difference,
F LMTD ¼ log mean temperature difference,
F and: ðT  tÞmean ¼ CMTD ¼ ðLMTDÞðFÞ ¼

½ðT1  t2 Þ  ðT2  t1 Þ½F ½ðT1 t2 Þ In ½ðT 2 t1 Þ

(15-498)

F ¼ MTD correction factor, dimensionless, corrects log mean temperature difference for any deviation from true counter-current flow. In air-cooled heat exchangers, the air flows upward unmixed across the finned tubes/bundle, and the tube-side process fluid can flow back and forth and downward as established by the pass arrangements. At four or more passes, the flow is considered counter-current, and the “F” factor ¼ 1.0 [215]. The other fewer-passes correction factors are given in Figures 15-168A, B, C. Referring to Hudson Products Corporation [251], used by permission: 1: Hot fluid heat capacity rate ¼ Ch ¼ Ctube     ¼ Mcp tube ¼ Q T1  T2 (15-499)

Heat Transfer Chapter | 15

317

FIGURE 15-168A MTD correction factors/1 pass, cross-flow. (Used by permission: Bul. M92-300-3M C (10/94). ©Hudson Product Corporation.)

2: Cold fluid heat capacity rate ¼ Cc ¼ Cair     ¼ Mcp air ¼ Q t2  t1

W ¼ width of exchangers; ft ¼

(15-500) 3:

Number of heat transfer units ¼ Ntu ¼ ðAÞ ðUÞ=Cmin

(15-501)

4: Heat capacity rate ratio ¼ R ¼ Cmin =Cmax (15-502)

Ch ðT1  T2 Þ Cc ðt2  t1 Þ ¼ Cmin ðT1  t1 Þ Cmin ðT1  t1 Þ E ¼

R ¼

1  eNTUð1RÞ 1  ReNTUð1RÞ

Cmin Cair ðscfmÞð1:08Þ ¼ ¼ Cmax Chot ½Q=ðT1  T2 Þ ¼ ðFVÞ L Wð1:08ÞðT1  T2 Þ=Q

AU AU nNaWLU ¼ ¼ Cmin Cair 1:08WLFV

nNa ¼ 1:08ðFVÞðr1 þ rair þ rf þ rm Þ t2 ¼

5: Heat transfer effectiveness ¼ E E ¼

Nta ¼

(15-503)

(15-504) (15-505)

QR 1:08ðFVÞLðT1  T2 Þ (15-506)

T1  T2 þ t1 R

(15-507)

(15-508)

Air flow is expressed as standard ft3 per min (scfm). It is determined by the effective width of the exchanger, W, times the length, L, times the face velocity, FV, in standard ft per min (sfm). Taken from reference [251]. Studies have been conducted to further understand the flow and heat transfer characteristics on the air side, involving the effect of structure on the air flow and heat transfer. Meyer and Kr€oger [384] reviewed the flow losses in the plenum that diminish the performance of forced draft air coolers,

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-168B MTD correction factors/2 pass, cross-flow. (Used by permission: Bul. M92-300-3M C (10/94). ©Hudson Product Corporation.)

where such information can be applied to define the critical distance between the fan and heat exchanger bundle. Manufacturers have stated that such a distance should be one fan diameter, while process guidelines recommend half the fan diameter (API 661). Experimental and theoretical studies have confirmed that there must be a minimum distance of one fan diameter between the fan and tube bundles. Various fan types have been reviewed, and the main conclusion is that the performance of an air cooler is affected if the plenum depth is less than a critical value, and the only guideline is that it should not be less than half a fan diameter. Another essential design parameter is the wind velocity e reviewed by Duvenhage and Kr€ oger [385]. The effect of wind has been divided into two categories; plume circulation and influence of the wind on fan performance. Plume circulation occurs when a part of the exit air stream is sucked into the inlet, which reduces the fan performance. Wind velocity and direction can affect both plume recirculation as well as fan performance, and the authors implied that a

cross-flow wind could produce a maldistribution of the air at the fan inlet with a corresponding reduction in fan performance. They showed that for a cross wind velocity of 3 m/s, the performance of the upward fan is drastically reduced. When there is a strong cross wind, it distorts the streamlines of air entering the fan. Additionally, the flow profile is distorted and eventually affects the intake to the upward fan, thus reducing the performance of ACHEs. The fan downwind reveals little performance change, and in some cases can exceed 100% of design specified performance. Plume circulation occurs when there is no wind, and with a little cross wind, the chances of plume circulation would actually be reduced. Although some cross wind can be beneficial, too high a cross wind could increase the plume circulation, and thus there is a critical velocity below which crosswind is beneficial. Further, the performance of an ACHE is dependent on the height of the fan platform. Where it is lower than the standard height of 5.7 m, the chances of the wind affecting the intake are high, as is that of plume

Heat Transfer Chapter | 15

319

FIGURE 15-168C MTD correction factors/3 pass, cross-flow. (Used by permission: Bul. M92-300-3M C (10/94). ©Hudson Product Corporation.)

recirculation. A higher platform actually improves the performance, since the space beneath the upwind fan is now increased, and the crosswind can flow with fewer problems. Longitudinal flow of the wind increases the plume circulation, which subsequently reduces the heat exchanger performance. FV (ft/min)

Rows of Tubes

650

4

600

5

550

6

400e450

8e10

Because it is not practical for the design engineer to expect to specify all fabrication features (including size, number of tubes, etc.) the foregoing provides an exposure to the topic, but relies on contact with a competent design/ manufacturing firm for the final details. where (from reference [251] by permission) a ¼ heat transfer surface area per unit length of tube, ft2/ft A ¼ total exchanger bare tube heat transfer surface, ft2 cp ¼ specific heat Btu/(lb) (
F)

t ¼ air temperature,
F T ¼ hot fluid temperature,
F U ¼ overall heat transfer coefficient (rate), Btu/(hr) (ft2) (
F) Subscripts air ¼ air-side cold ¼ cold fluid ¼ air f ¼ tube-side fouling hot ¼ hot fluid ¼ tube-side fluid i ¼ inside tube max ¼ maximum min ¼ minimum m ¼ tube metal 1 ¼ inlet 2 ¼ outlet The lower outside film coefficient (air-side) makes use of finned tubes beneficially, while the inside (usually liquid) film coefficient is greater, thus “approaching” a balance for the two sides. The film coefficients on the tube-side are calculated in the same manner as described in an earlier topic for conventional exchangers. Mukherjee [265] suggests pressure drop ranges in tubes.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

a. For gases and condensers, the allowable pressure drop is 0.7e2.84 psi. Lower pressure systems require lower pressure drops. b. For liquids, allowable pressure drop is 7.11e9.95 psi, except when the viscosity is high, when higher pressure drops are required. The airside calculations require specific manufacturer’s data and can only be estimated or approximated by published data. Cair ¼ Ccold ¼ Q=Dt ¼ Q=ðt2  t1 Þ ¼ air side heat capacity; rate; Btu=ðhÞ ð
FÞ ¼ 1:08ðFVÞ ðLÞ ðWÞ

(15-509)

Mean Temperature Difference

Ctube ¼ Chot ¼ Q=DT ¼ Q=ðT1  T2 Þ ¼ tube-side heat capacity rate ¼ Btu=ðhÞ ð
FÞ (15-510) ¼ Mcp Cmin ¼ minimum heat capacity rate; Btu=ðhÞ ð
FÞ Cmax ¼ maximum heat capacity rate; Btu=ðhÞ ð
FÞ CMTD ¼ corrected mean temperature difference ¼
F ðLMTDÞ;
F E ¼ exchanger thermal effectiveness, dimensionless ¼

Chot ðT1  T2 Þ ; Cmin ðT1  t1 Þ

Note, see previous information; Chot ¼ Ctube ¼

Ccold ðt2  t1 Þ Cmin ðT1  t1 Þ

FV ¼ standard air face velocity, sfm G ¼ mass velocity, lb/(s) (ft2) h ¼ individual heat transfer coefficient, Btu/(h) (ft2) (
F) k ¼ parameter ¼ nNa/[(1.08) (FV) (1/U)] LMTD ¼ log mean temperature difference,
F M ¼ mass flow rate, lb/h NTU ¼ number of heat transfer units, dimensionless N ¼ number tubes/row in direction of air flow n ¼ number tubes/row, per ft or exchanger width, 1/ft Q ¼ total exchanger heat load (duty), Btu/hr R ¼ Cmin/Cmax ¼ heat capacity ratio, dimensionless

(15-511) (15-512)

F ¼ MTD correction factor, dimensionless FA ¼ face area, ft2

These units are pure cross-flow and require the use of specific data not found in the TEMA Standards [266], but are available in references [251] and [206]. See Figures 15-168A, B and C. 1. Design maximum ambient air temperature should be selected so that it will not be exceeded more than 2e5% of the time. Lower figures mean a smaller exchanger, but they also indicate a question on performance during the hottest weather. Daily temperature charts as well as curves showing the number of hours and time of year any given temperature is exceeded are valuable, and often necessary in establishing an economical design air temperature. Collins and Mathews discuss this in detail [32]. Also see Table 15-75. 2. Units should preferably be placed in the open, and at least 75e100 ft from any large building or obstruction to normal wind flow. If closer, the recirculation from down drafts may require raising the effective inlet air temperature 2e3
F or more above the ambient selected for unobstructed locations. If wind velocities are high around congested areas, the allowance for recirculation should be raised to greater than 3
F.

TABLE 15-75 Typical Temperature Study for Design Air Temperature Determination Dry Bulb Temp.
F; % of Annual Hr Stated Temp. Is Exceeded 3%

Annual Average Dry Bulb Temp.
F

Suggested Design Temp.
F

91

90

69

91

89

96

95

71

96

106

90

87

86

55

87

102

92

91

89

70

91

Location

Maximum Dry Bulb Temp.
F

1%

2%

Beaumont, Texas

102

93

Victoria, Texas

110

Parkersburg, W. Va. New Orleans, La. Wilmington, Del.

106

88

85

84

55

85

Grand Rapids, Mich.

99

83

80

78

47

80

Note: 1% ¼ 88 hr; 2% ¼ 175 hr; 3% ¼ 263 hr. Used by permission: Mathews, R. T. Chemical Engineering Progress, V. 55, No. 5, p. 68., ©1959. American Institute of Chemical Engineers, Inc. All rights reserved.

Heat Transfer Chapter | 15

3. Units should not be located near heat sources. Cook [33] cautions that units near exhaust gases from engines can raise the inlet air temperature by 15
F or more above the expected ambient. 4. The effect of cold weather on the freezing of tube-side fluids and increasing horsepower due to increased air density cannot be overlooked. Usual practice is to reduce fan output by using a two-speed motor, louvers on variable pitch fans, or drivers [33]. 5. Fouling on the outside of finned surfaces is usually rather small, but must be recognized. Values of 0.0001e0.0015 usually satisfy most fin-side conditions. Finned surfaces should be cleaned

¼

321

use in the detailed design of film coefficients and pressured drop. 10. In general, tube-side pressure drops less than one psi per pass should not be specified for economical designs [80]. Drops as low as 15 mm Hg. have been specified, and designs obtained which were competitive with cooling tower installations. For viscous materials, pressure drop limitations can markedly influence a design and its economics. Required fan driver horsepower based on material from Hudson Products Corp., [251] motor shaft horsepower output to fan is:

½Actual ft3 =minðat fan nletÞ½Total pressure loss ðin: waterÞ through air-cooled outside fins 6; 356½fanðsystemÞ efficiency½speed reducer efficiency

(15-513)

ðstandard volume of air; scfm Þ½Air Std: density 0:075 lb=ft  3

Volume of fan ¼

6.

7.

8.

9.

½density of air at fan inlet; lb=ft 

periodically to avoid excessive buildup of dust, oil films, bugs, etc. When inquiring or designing, the range of expected temperature operations should be stated as well as maximums only. If any particular temperature is “key” or critical to the system, it should be so identified. When processing (tube-side) coefficients referred to the bare outside tube are less than 200 Btu/h (ft2) (
F), the total surface of the air-cooled unit usually compares favorably cost-wise with a water-cooled unit [80]. For a specific service of desuperheating Freon 11 (180
F) and condensing at 115
F ambient air at 70
F, total Q ¼ 31.6  106 Btu/h, Smith [106] points out that for three comparative designs with a threefold reduction in fan horsepower, a 35% increase occurs in first cost, a 30% increase in surface and a 75% increase in plan area. In general, this trend will apply to all comparisons on design parameters. Of course, it is influenced to a greater or lesser degree by specific conditions, which reflect the sensitivity of changes in flow quantities on heat transfer coefficients. Nakayama [87] suggests essentially the same procedure except recommends that specific manufacturers’ data for various units be assembled and correlated for

3

Total pressure difference across fan ¼ velocity pressure for fan diameter þ static pressure loss through air-cooled bundle (from manufacturer’s data for a specific exchanger) þ other losses in the air system Fans usually result in velocity pressure of approximately 0.1-in. water. The system’s efficiency is influenced by the air plenum chamber and fan housing. Industrial axial flow fans in proper system design will have efficiency of approximately 75% based on total pressure. Poor designs can run at 40% [251]. Speed reducers are about 75% mechanically efficient. Then, motor (driver) input power ¼

motor shaft hp to fan motor efficiency; fraction

(15-514)

*See the chapter on Drivers, this volume.

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

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

specification sheet is shown in Figure 15-167. This serves to define the known factor at the time of inquiry and then to summarize the exact specifications as proposed by a specific vendor.

TABLE 15-76 Typical Overall Heat Transfer Coefficients for Air-Cooled Exchangers Based on Bare Tube Surface Condensing Service

U

Amine reactivator

100e120

Ammonia

105e125

Refrigerant 12

75e90

Heavy naphtha

70e90

Light gasoline

95

Light hydrocarbons

95e105

Light naphtha

80e100

Reactor effluent Platformers, Hydroformers, Rexformers

80e100

Steam (0e20 psig)

135e200

Gas Cooling Service Air or flue gas @ 50 psig (DP ¼ 1 psi)

10

Air or flue gas @ 100 psig (DP ¼ 2 psi)

20

Air or flue gas @ 100 psig (DP ¼ 5 psi)

30

Ammonia reactor stream

90e110

Hydrocarbon gases @ 15e50 psig (DP ¼ 1 psi)

30e40

Hydrocarbon gases @ 50e250 psig (DP ¼ 3 psi)

50e60

Hydrocarbon gases @ 250e1500 psig (DP ¼ 5 psi)

70e90

Light Cooling Service

The method summarized is essentially that of Smith [106]: 1. Determine heat duty for the exchanger from process fluid temperatures. 2. Select design ambient air temperature, t1. 3. Select design pressure on tube-side, tube-side, tube material, tube size and gage. 4. From Table 15-76 select overall U for exchanger service. Note that Table 15-77 gives transfer rates based on outside finned surface. 5. Calculate: T 1  t1 Uðbare tubeÞ

(15-515)

and from Figure 15-169, read optimum bundle tube row depth. 6. From Table 15-78, select (a) typical standard air face velocity, (b) ratio of surface area to face area and (c) ratio of weight to face area.

TABLE 15-77 Overall Heat Transfer Rates for AirCooled Heat Exchangers *Stab Transfer Rate

**Suggested No. of Tube Layers

Engine jacket water

6e7

4

Light hydrocarbons

4e5

4 or 6

Light gas oil

3e4

4 or 6

Heavy gas oil

2.5e3

4 or 6

Lube oil

1e2

4 or 6

Bottoms

0.75e1.5

6 or more

2e2.5

4

Service Cooling Service

Engine jacket water

130e155

Fuel oil

20e30

Flue gas @ 100 psig & 5 psi DP

Hydroformer and Platformer liquids

85

Condensing Service

Light gas oil

70e90

Steam

7e8

4

Light hydrocarbons

90e120

Light hydrocarbon

4e5

4 or 6

Light naphtha

90

Reactor effluent

3e4

6

Process water

120e145

Still overhead

2.75e3.5

4 or 6

Residuum

10e20

Tar

5e10

*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.

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.

Heat Transfer Chapter | 15

(f) (g)

FIGURE 15-169 Optimum bundle depth. (Used by permission: Smith, E. C. Chemical Engineering, V. 65, Nov. ©1958. McGraw-Hill, Inc. All rights reserved.)

(h)

TABLE 15-78 Estimating Heat Factors, 1-in. O.D. Tube 3 2 3/8-in. D Spacing

(i)

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 ¼ face velocity

where subscript 2 refers to second or check calculation, and 1 refers to original trial. If FA2 ¼ FA1, proceed with detailed design. If FA2 s FA1, reassume new air outlet temperature and repeat from (a) For a 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 15-170 may be used directly to obtain the 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. Calculate tube-side pressure drop in usual manner, including loss in headers. Determine unit plant size: face area assumed tube length ðusually 4 ft; 6 in: min: through 30 ftÞ (15-518)

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 15-171; read surface area/hp or read Figure 15-170 for pressure drop for certain tube arrangements. total surface; A (15-519) surface area=hp   ðACFMÞ pt (15-520) Also : HP ¼ ð6; 356Þðef Þðed Þ pv ¼ 0.1 in. water, usually ps ¼ 0.2 to 0.25 in. water at y 500 ft/min FV for each three rows of tubes pt ¼ pv þ ps, in. water er ¼ 0.65 usually ed ¼ 0.95 usually HP ¼

**Used by permission: Smith, E. C. Chemical Engineering, V. 65, p. 145, ©1958. McGraw-Hill, Inc. All rights reserved.

7. Determine surface requirements by trial and error: (a) Assume a temperature rise, t2  t1. (b) Solve for total face area required: FA ¼

Width ¼

323

Q ðt2  t1 ÞðFVÞð1:08Þ

(15-516)

(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 ¼

Q UðLMTDÞ

This can be converted to finned surface by ratio of finned/bare surface areas. (e) Calculate face area, FA2: FA2 ¼ 

A

  ¼ FA1 ; Table 15-78

surface area face area

(15-517)

ðkÞ Approximate weight : ¼ ðface areaÞ ðweight=face areaÞ

(15-521)

pv ¼ velocity pressure, in. water ps ¼ static pressure, in. water pt ¼ total pressure, in. water ACFM ¼ actual CFM at fan intake FA ¼ face area of air-cooled exchanger tube bundle, length  width, ft2 t1, t2 ¼ inlet and outlet air temperature of fin unit T1, T2 ¼ inlet and outlet tube-side fluid temperature of fin unit FV ¼ face velocity, ft/min, entering face area of air-cooled unit U ¼ overall heat transfer rate based on bare tube OD, Btu/h (ft2) (
F)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-170 Outside fin film, coefficient for air-fin exchangers. (Used by permission: Hajek, J. D. Compiled from manufacturer’s data, private communications, now deceased.)

Tube-Side Fluid Temperature Control

FIGURE 15-171 Surface per fan hp. (Used by permission: Smith, E. C. Chemical Engineering, V. 65, Nov. 1958. ©McGraw-Hill, Inc. All rights reserved.)

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 can 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.

Heat Transfer Chapter | 15

325

Depending upon the extent of control considered necessary, the following systems are used (Figures 15-172 and 15-173): 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). 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.

FIGURE 15-172 Temperature control and horsepower savings with automatic variable pitch fans. (Used by permission: Hudson Products Corporation.)

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.

When only one fan and/or exchanger exists per process service, it may 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 15-174. If single fans are used per cell, see Figure 15-175. If several cells are used per process service, some of the fans should be

PNEUMATIC TEMPERATURE CONTROLLER PRESSURE REGULATOR AND FILTER

PNEUMATIC SHUTTER OPERATOR WITH POSITIONER

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 temperatures with appreciable power savings under low load conditions. 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 adjustable shutters. The arrangement lends itself to many cooling services while effecting a horsepower savings through the use of the two-speed motor.

PNEUMATIC TEMPERATURE CONTROLLER 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 15-173 Schemes for temperature control of air coolers. (Used by permission: Griscom-Russell/Ecolaire Corporation.)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

No.Cells

B C A Sections Nom. Lg. Fan Tubes Dia. Per Cell 240" 288" 288" 360" 240" 288" 360"

8'-0" 8'-0" 10'-0" 10'-0" 10'-0" 10'-0" 10'-0"

E Width CL to CL Col’s. per Cell

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"

(A) No. Sections per Cell

2 2 2 2 2 1/2 2 1/2 2 1/2

D Length

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. For winter operation, it is important to consider the effect of cold temperatures on process fluid (gelling, freezing, etc.), as 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.

Total Width

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"

Fan Dia. (C) (B) Nominal Tube Length PLAN

6'-7"

Ladder and Walkway Optional

Galv. Chain Link Fence & Gate (Optional)

END ELEVATION

10'-0"

6'-5"

13'-0"

Fan Ring

D C Fan Length Dia. CL to CL Col’s. 8'-0" 10'-0" 10'-0" 10'-0" 12'-0"

120" 180" 240" 180" 240"

(A) No. Sections per Cell

2 2 2 2 1/2 2 1/2

B Nom. Lg. Tubes

E Width CL to CL Col’s. per Cell

8'-3 1/2" 13'-3 1/2" 18'-3 1/2" 13'-3 1/2" 18'-3 1/2"

A C ¼ C3 ðRÞ 4 FA

Fan Dia. (C)

6'-7" 6'-5"

13'-0"

(15-522)

(15-523)

where C3 ¼ 1.2557 C4 ¼ 1.0031 3. The face velocity of air, FV, ft/min.

(B) Nominal Tube Length Ladder and Walkway Optional

Fan Ring

This Column in 240 Length only

1. The number of tube rows, R is: 
T2  t2 R ¼ C1 þ C2 ln U where: C1 ¼ 3.1679 C2 ¼ 3.7948 2. The area ratio is:

10'- 8 1/4" 10'- 8 1/4" 10'- 8 1/4" 13'- 4 5/16" 13'- 4 5/16"

PLAN

END ELEVATION

Total Width

Galv. Chain Link Fence & Gate (Optional)

10'-0"

A Sections Per Cell

The rating methods for air-cooled exchangers are outlined by Cook [386] and Ganapathy [387]. Here, the preliminary design of air coolers is based upon correlations, tables and graphs presented by Smith [106] and Brown [388] and fitted to a series of equations developed by Blackwell [381].

The Equations

LEFT ELEVATION

FIGURE 15-174 Typical dimensions for air coolers with two fans. (Used by permission: Griscom-Russell/Ecolaire Corporation.)

No.Cells

RATING METHOD FOR AIR-COOLED EXCHANGERS

LEFT ELEVATION

FIGURE 15-175 Typical dimensions for air coolers with one fan. (Used by permission: Griscom-Russell/Ecolaire Corporation.)

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

FV ¼ C5 ðC6 Þ

R

(15-524) where C5 ¼ 720.8542 C6 ¼ 0.9530 Typical face velocities (FVs) used for design are shown in Table 15-79. These values result in air-cooled heat exchangers that approach an optimum cost [389]. This takes into account the purchase cost, the cost of installation and the cost of power to drive the fans. Table 15-80 lists an estimate of the outlet air temperature, based on 90e95
F design ambient air temperature. 4. Estimated air outlet temperature, t1,
F 
 T1 þ T2  t2 þ t2 t1 ¼ 0:005U (15-525) 2

Heat Transfer Chapter | 15

TABLE 15-79 Design Face Velocities for Air-Cooled Exchangers Face Velocity, ft/min (m/s.)

327

8. The face area of bundle FA, ft2: FA ¼

A C ðRÞC4 3

(15-529)

9. The calculated outlet air temperature, t0 1 ,
F:

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 [389]).

TABLE 15-80 Estimated Outlet Air Temperature for Air-Cooled Exchangers Outlet Air Temperature,
C

t0 1 ¼

Q þ t2 ð1:08Þ ðFAÞ ðFVÞ

(15-530)

10. The air flow over tubes, F std. ft3/min: F ¼ ðFAÞ ðFVÞ (15-531) 11. The ratio of the bare tube surface area based on the tube OD to the fan horsepower: A ¼ C7 þ C8 ðRÞ Bhp

(15-532)

where: C7 ¼ 7.4212 C8 ¼ 12.5342 12. The ratio of air cooler weight to the face area of bundle Wt ¼ C9 þ C10 ðRÞ FA

Process Inlet Temperature,
C

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

Av ¼ p Nr Nt Do L

60

45

48

50

50

40

41

42

where Nr ¼ number of rows Nt ¼ number of tubes per row ¼ (tube bundle width)/ (tube spacing) ¼ W/s L ¼ tube length, ft Do ¼ 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 DTLMTD, the new required area, and the new available area. 15. The air side heat transfer coefficient, ha, Btu/h. ft2
F. The air side coefficient is determined on the basis of the outside surface of a bare tube, ha is expressed as:

FA L 2 14. The area available, Av, ft :

5. The effective log mean temperature difference, DTLMTD
F DTLMTD ¼

ðT1  t2 Þ  ðT2  t1 Þ  T1 t2 ln T2 t1

(15-526)

6. The heat duty Q, Btu/h.: Q ¼ w c Dt

(15-527)

where: w ¼ fluid flow rate, lb/h c ¼ specific heat capacity, Btu/lb
F Dt ¼ temperature difference,
F 7. The bare tube surface area based on the tube, OD, ft2: A ¼

Q ðUÞðDTLMTD Þ

where: C9 ¼ 36.4 C10 ¼ 9.35 13. The tube bundle width, W ft: W ¼

(Source: Chopey and Hicks [389]).

(15-528)

(15-533)

ha ¼ 8ðFVÞ

0:5

for 10 fins per inch:

(15-534)

(15-535)

(15-536)

ha ¼ 6:75ðFVÞ for 8 fins per inch: (15-537) 16. The tube wall heat transfer coefficient, hw, Btu/h ft2
F: 0:5

hw ¼

2k Do  D

(15-538)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

where: k ¼ thermal conductivity, Btu/h ft
F Do ¼ outside diameter of tube, ft. Di ¼ inside diameter of tube, ft 17. The overall heat transfer coefficient, U, Btu/h ft2
F 1 1 1 1 1 þ þ þ ¼ U ha hi ðD=Do Þ hw hs

(15-539)

where: hi ¼ inside of tube heat transfer coefficient, Btu/h ft2
F hs ¼ fouling coefficient, Btu/h ft2
F

The Air Side Pressure Drop, Dpa (inch H2O) The following equations are used to calculate the pressure drop on the air side [389]: Dpa ¼ 0:0047Nr ðFV=100Þ 2:375 inch spacing

1:8

for 10 fins per inch: (15-540)

Dpa ¼ 0:0044Nr ðFV=100Þ1:8 for 8 fins per inch: 2:375inch spacing (15-541) Dpa ¼ 0:0037Nr ðFV=100Þ1:8 for 10 fins per inch; where:

2:5 inch spacing

R ¼ number of tube rows T1 ¼ outlet process fluid temperature,
F T2 ¼ inlet process fluid temperature,
F t1 ¼ estimated air outlet temperature,
F t0 1 ¼ calculated outlet air temperature,
F t2 ¼ inlet air temperature,
F Dt ¼ temperature difference,
F U ¼ overall heat transfer coefficient (based on bare tube, OD), Btu/h ft2
F W ¼ tube bundle width, ft w ¼ Fluid flow rate, lb/h Wt ¼ air cooler weight, lb Example 15-26

Calculate a preliminary air cooler design using the following data. A light hydrocarbon liquid is to be cooled from 170
F to 135
F 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
F. The design dry bulb air temperature is 85
F and the tube length is 40 ft. Solution Computer program PROG155 has been developed for a preliminary air cooler exchanger and Table 15-81 shows the input data and computer results.

TABLE 15-81 Input Data and Computer Results for Example 15-26 Input Data

Nr ¼ the number of tube rows FV ¼ face velocity, ft/min Dpa ¼ inch H2O

160.0

125.0

95.0

where

55.0

4550000.0

40.0

A ¼ bare tube surface, area ft2 Av ¼ available area, ft2 Bhp ¼ fan horsepower c ¼ specific heat of fluid, Btu/lb
F C1, C2, C3 ¼ constants C4, C5, C6 ¼ constants C7, C8, C9 ¼ constants C10 ¼ constant Di ¼ inside diameter of tube, ft Do ¼ outside diameter of tube, ft F ¼ air flow over tubes, std ft3/min FA ¼ face area of bundle, ft2 FV ¼ face velocity of air, ft/min. ha ¼ air side heat transfer coefficient, Btu/h ft2
F hi ¼ inside of tube heat transfer coefficient, Btu/h ft2
F hs ¼ fouling coefficient, Btu/h ft2
F hw ¼ tube wall heat transfer coefficient, Btu/h ft2
F k ¼ thermal conductivity, Btu/h ft
F L ¼ pipe length, ft DTLMTD ¼ log mean temperature difference,
F Nr ¼ number of rows Nt ¼ number of tubes per row Dpa ¼ air side pressure drop, inch (H2O) Q ¼ exchanger duty, Btu/h

An Air-Cooled Heat Exchanger Design INLET PROCESS FLUID TEMPERATURE,
F:

160.0 125.0

OUTLET PROCESS FLUID TEMPERATURE,
F: INLET AIR TEMPERATURE,
F:

95.0

OVERALL HEAT-TRANSFER COEFFICEINT, Btu/h.ft^2.
F:

55.0

HEAT LOAD, Btu/h.: TUBE LENGTH, ft.:

4550000. 40.0

NUMBER OF TUBE ROWS:

3.8

RATIO OF BARE-TUBE SURFACE TO FACE AREA OF BUNDLE:

4.8

FACE VELOCITY OF AIR, ft./min.:

600.291

ESTIMATED AIR OUTLET TEMPERATURE,
F:

108.062

EFFECTIVE LOG MEAN TEMPERATURE DIFFERENCE,
F: BARE-TUBE SURFACE AREA BASED ON TUBE OD, ft^2:

39.970 2069.7

Continued

Heat Transfer Chapter | 15

TABLE 15-81 Input Data and Computer Results for Example 15-26dcont’d Input Data FACE AREA OF BUNDLE, ft 2:

431.8

CALCULATED OUTLET AIR TEMPERATURE,
F:

111.255

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,
F:

38.617

BARE-TUBE SURFACE AREA BASED ON TUBE OD, ft 2:

2142.2

FACE AREA OF BUNDLE, ft^2:

446.9

CALCULATED OUTLET AIR TEMPERATURE,
F:

110.705

CALCULATED BARE-TUBE SURFACE AREA 2142.2

BASED ON TUBE OUTSIDE DIAMETER, ft 2: FACE AREA OF BUNDLE, ft 2:

446.9 3

AIR FLOW OVER TUBES, std.ft / min.:

268258.

FAN HORSEPOWER, bhp:

38.9

AIR COOLER WEIGHT, lb:

32151.8

TUBE BUNDLE WIDTH, ft.:

11.2

Operation 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 [265]: 1. Tube-side flow maldistribution is particularly relevant when two-phase flow is encountered. At lower temperatures, the performance reduction for a fixed maldistribution is higher. 2. Inadequate cooling e this often results from other problems (such as fans not operating properly, tube blockage, property changes, etc.) 3. Excessive fouling e congealing is the main reason cited for fouling inside ACHE tubes. Streams that

329

have high pour points (greater than 6e10
C) should normally not be cooled in ACHEs. (Most crude oils have a pour point less than 0
C.) Depending on location, significant fouling on the air side could occur as well. 4. High inlet air temperature. 5. Insufficient air side flow rate e generally, this is a problem if the existing ACHE is used for higher flow rates or different operating conditions. Berryman [390] provides a report on the condition monitoring of air-cooled heat exchangers, and Table 15-82 gives a useful troubleshooting chart for air-cooled heat exchangers. Studies have 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 air-cooled heat exchanger 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.

TWO-PHASE FLOW PATTERNS The distribution of the liquid and vapor phases in the flow channel is an essential aspect of two-phase flow patterns. These distributions take on commonly observed flow structures, which are referred to as two-phase patterns. They have particular identifying characteristics, which are related to heat transfer coefficients and pressure drops. Thus, two-phase flow pattern prediction forms an important aspect of modeling evaporation and condensation. Heat transfer models for predicting in-tube boiling and condensation rely upon the reliable flow pattern maps to identify what type of flow pattern exists at the local flow conditions. Analogous to predicting the transition from laminar to turbulent flow in single-phase flows, twophase flow pattern maps are employed for predicting the transition from one type of two-phase flow pattern to another.

330

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-82 Fault-Finding Chart for Air-Cooled Heat Exchangers

TABLE 15-82 Fault-Finding Chart for Air-Cooled Heat Exchangersdcont’d

Symptom

Possible Faults

Solution

Symptom

1. High tube-side outlet temperature

A. Cooler may be undersized.

Perform design calculations, and if possible use commercially tested software.

2. High tube-side outlet pressure drop.

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 Continued

Possible Faults

Solution require a trim cooler in some cases.

3. High air outlet temperature.

4. Low air outlet temperature.

5. Unequal exit temperatures from bundles for same flow.

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 tube-side configuration.

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

B. Strong crosswinds

.

C. Fans may differ in efficiency

Check fan operation, pitch, speed, etc.

Flow Patterns in Vertical Tubes Figure 15-176 shows the flow patterns for cocurrent upflow of gas and liquid in a vertical tube. The liquid and gas phases distribute themselves into various flow structures and are described as follows: Bubbly flow: In this flow type, the gas and vapor are distributed as discrete bubbles in a continuous liquid phase.

Heat Transfer Chapter | 15

331

FIGURE 15-176 Two-phase flow patterns in vertical concurrent flow.

The bubbles vary widely in size and shape, from small and spherical, to large with a spherical cap and a flat tail. The bubbles are typically much smaller than the diameter of the tube. Slug flow: At moderate vapor fractions and relatively low flow rates, large bullet-shaped vapor bubbles flow through the tube separated by slugs of liquid in which smaller bubbles may be dispersed. Churn flow: Formed by the breakdown of the large vapor bubbles in slug flow. The large vapor bubbles present in slug flow become unstable and break apart, resulting in an oscillatory or churning motion of the liquid upward and downward in the tube. This flow pattern is an intermediate regime between the slug flow and annular flow regimes. Annular flow: At high vapor fractions, and high flow rates, the liquid flows as a film along the tube wall while the vapor flows at a higher velocity in the central region of the tube. Small liquid droplets are usually entrained in the vapor phase, and vapor bubbles may also be dispersed in the liquid film. At sufficiently high liquid flow rates, the droplet coalesce to form large streaks or wisps of liquid entrained in the vapor phase. Wispy annular flow: When the flow rate is further increased, the entrained droplets may form transient coherent structures as clouds or wisps of liquid in the central vapor core. The liquid in the film is aerated by small gas bubbles, and the entrained liquid phase appears as large droplets that have agglomerated into long irregular filaments or wisps.

Vertical Heated Channel Upward Flow Heat flux through the channel wall alters the flow pattern from that which occurs in a long unheated channel at the same local flow conditions. These changes occur due to: 1. The departure from thermodynamic equilibrium coupled with the presence of radial temperature profiles in the channel. 2. The departure from local hydrodynamic equilibrium throughout the channel. Figure 15-177 illustrates a vertical tubular channel heated by a uniform low heat flux and fed with liquid just below the saturation temperature. In the initial single-phase region, the liquid is heated to the saturation temperature. A thermal boundary layer forms at the wall and a radial temperature profile forms. At some distance from the inlet, the wall temperature and the conditions for the formation of vapor (nucleation) at the wall are satisfied. Vapor forms at preferred positions on the tube surface. Vapor bubbles grow from these sites, finally detaching to form a bubbly flow. As more vapors are formed, the bubble population increases with length and coalescence occurs, forming slug flow, which in turn gives way to annular flow further along the channel. At this point, the formation of vapor at sites on the wall may cease, and further vapor formation will result from evaporation at the liquid film vapor core interface. Increasing velocities in the vapor core causes entrainment of liquid in the form of droplets. The depletion of the liquid

332

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

2

2 G G momentum fluxes of the liquid rll and vapor rgg phases, respectively. The mass flux rates for the gas and liquid are defined by: Gg ¼ m_ G ¼ mass flux of gas ¼

 gas mass flow rate kg tube cross-sectional area m2 s

(15-542)

Gl ¼ m_ L ¼ mass flux of liquid ¼

 liquid mass flow rate kg tube cross-sectional area m2 s

(15-543)

where: rg ¼ gas density, kg/m3 rl ¼ liquid density, kg/m3

Horizontal Cocurrent Flow

FIGURE 15-177 Flow patterns in a vertical evaporator tube.

from the film by this entrainment and by evaporation finally causes the film to dry out completely. However, droplets continue to exist and are slowly evaporated until only single-phase vapor is present. Figure 15-178 shows shell-side two-phase flow patterns in heat flux controlled systems. When the film is completely dried out, the wall temperature rises very quickly and can exceed the melting temperature of the wall (called dry out). Figure 15-179 shows a flow pattern map by Hewitt and Roberts [391] for vertical up-flow in a tube. The axes are the superficial

In horizontal tubes, the situation is somewhat different due to stratification of the flow resulting from the gravitational force. Figure 15-180 illustrates the flow regimes, which are described as follows: Bubbly (froth) flow: The gas bubbles are dispersed in the liquid with a high concentration of bubbles in the upper half of the tube. At moderate gas and liquid velocities, the entire pipe cross-section contains bubbles. At higher velocities, a flow pattern equivalent to the wispy annular pattern exists. Plug flow: The flow pattern is similar to slug flow in vertical tubes and the gas bubbles tend to travel in the upper half of the tube. Stratified flow: The two phases are completely stratified, with the liquid flowing along the bottom of the tube and the vapor flowing along the top. Wavy flow: As the vapor velocity increases, the interface becomes disturbed by waves traveling in the direction of flow. Slug flow: Intermittent slugs of liquid pass through the tube, where the slugs occupy the entire tube cross-section and contain a large number of entrained vapor bubbles that impart a frothy character to the liquid. Annular flow: At higher vapor velocities, a gas core forms with a liquid film around the periphery of the tube. Flow patterns formed during the generation of vapor in horizontal tubular channels are influenced by departures from thermodynamic and hydrodynamic equilibrium. Figure 15-181 shows a horizontal tubular channel heated by a uniform low heat flux and fed with liquid just below the saturation temperature. The sequence of flow patterns corresponds to a relatively low inlet velocity (< 1 m/s). There is intermittent drying and rewetting of the upper surfaces of the tube in wavy flow, and

Heat Transfer Chapter | 15

FIGURE 15-178 Shell-side two-phase flow patterns.

FIGURE 15-179 Hewitt and Robertson map for vertical upflow in a tube.

333

334

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-180 Two-phase flow regimes in a circular horizontal tube.

FIGURE 15-181 Flow patterns in a horizontal evaporator tube.

progressive drying out over long tube lengths of the upper circumference of the tube wall in annular flow. At higher inlet liquid velocities, the influence of gravity is less obvious, the phase distribution becomes more symmetrical, and the flow patterns become closer to those seen in vertical flow. The well-known Baker map for horizontal flow, shown in Figure 15-182, consists of a plot of Gg =l and Gl j, where Gg and Gl are the superficial mass velocities of the vapor and liquid phases, respectively. The Baker map [392] for horizontal two-phase in tubes as shown in Figure 15-182 is represented by: Gg ¼ m_ G ¼ mass flux of gas

 gas mass flow rate kg ; ¼ tube cross-sectional area m2 s

Gl ¼ m_ L ¼ mass flux of liquid  liquid mass flow rate kg ¼ ; tube cross-sectional area m2 s The factors l and j are:
  1=2 rg rl l ¼ rair rw

(15-544)

and:  "  2 #1=3 sw ml rw j ¼ sl mw rl where:

(15-542)

(15-543)

rl ¼ liquid density, kg/m3 rg ¼ gas density, kg/m3

(15-545)

Heat Transfer Chapter | 15

335

FIGURE 15-182 Baker map for horizontal flow in a tube.

rw ¼ water density, (1000 kg/m ) rair ¼ air density, (1.23 kg/m3) ml ¼ liquid viscosity, (Ns/m2) mw ¼ water viscosity, (103 Ns/m2) sw ¼ water surface tension of air-water ¼ 0.072 N/m rl ¼ liquid density, kg/m3 3

The Taitel and Dukler [397] map for horizontal flow in the tubes shown in Figure 15-183 is based on their analytical analysis of the flow transition mechanisms, together with empirical selection of various parameters. The map uses the Martinelli parameter, X, the gas Froude number, Frg, and the parameters T and K, and is composed of three graphs. The Martinelli parameter, X, is: #1=2 " ðdp=dzÞl (15-546) X ¼ ðdp=dzÞg The gas phase Froude number, Frg, is: Frg ¼ h

Gg

i1=2  rg rl  rg d g 

The T and K parameters are: 2  31=2 ðdp=dzÞ  l 5 T ¼ 4 g rl  r g

(15-548)

The modulus sign in Equation 15-548 ensures that T is always positive.
1=2 Gl d (15-549) K ¼ Frg ml where: d ¼ tube diameter, m g ¼ acceleration due to gravity, 9.81 m/s2 The pressure gradient of the flow for phase k (where k is either l or g) is:  dp 2f k G2k (15-550) ¼  rk d dz k For Rek < 2000, The laminar flow friction factor equation is used:

(15-547) fk ¼

16 Rek

(15-551)

336

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-183 Taitel and Kukler method for flow pattern determination in horizontal flow in a tube.

For Rek > 2000, the turbulent flow friction factor equation is used (even for the transition region from 2000 to 10,000). fk ¼

0:079 Re0:25 k

(15-552)

ðdp=dzÞl ¼ the frictional pressure gradient if the liquid in the two-phase flow were flowing alone in the tube (N/m3) ðdp=dzÞg ¼ the frictional pressure gradient if the gas in the two-phase flow were flowing alone in the tube (N/m3). Implementing Figure 15-183, first determine the Martinelli parameter, X, and Frg. Using these two

parameters on the top graph, if their coordinates fall in the annular flow regime, then the flow pattern is annular. If the coordinates of X and Frg fall in the lower left zone of the top graph, then K is calculated from Equation 15-549. Using X and K in the middle graph, the flow regime is identified as either stratifiedwavy or a fully stratified. If the coordinates of X and Frg fall in the right zone on the top graph, then T is calculated. Using T and X in the bottom graph, the flow regime is identified as either bubbly flow or intermittent (plug or slug) flow. These flow pattern maps were all developed for adiabatic two-phase flows, but are often extrapolated for use with the adiabatic processes or evaporation or condensation.

Heat Transfer Chapter | 15

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 are almost useless in a stagnant or non-circulating tank; therefore, the best arrangement is to use the coil in an agitated/mixing tank. Batch heating and cooling are reviewed later in the text.

Tube-Side Coefficient Kern [70] reports that tube-side coefficients can be approximately 20% greater in a spiral coil than in a straight pipe or tube using the same velocities. The Sieder-Tate correlation is shown in Equations 15-175 and 15-176, and for streamlined flow is DG/m < 2,100. For transition and turbulent flow, see Equation 15-176 and Figure 15-176 or Figure 15-180A and B for straight pipes and tubes. McAdams [81] suggests multiplying the h value obtained by (1 þ 3.5 (D/DH)), when D is the inside diameter of the tube and DH is the diameter of the helix, in ft [70].

337

where: (use conventional units for symbols) m ¼ 0.1 (m 8.621  105) 0.21 Cp ¼ heat capacity, Btu/(lb) (
F) D ¼ impeller diameter, ft do ¼ tube diameter, ft dt ¼ tube OD, ft ho ¼ outside (process fluid side) heat transfer coefficient k ¼ thermal conductivity of liquid, Btu/(h) (ft2) (
F/ft) m ¼ experimental exponent, usually 0.14 N ¼ impeller speed, rev/h T ¼ tank diameter, ft m ¼ viscosity, bulk fluid, lb/(ft) (h) ms ¼ viscosity of fluid at film temperature at heat transfer surface, lb/(ft) (h) r ¼ liquid density, lb/ft3 Uo ¼ overall heat transfer coefficient based on outside tube area, Btu/(h)(ft2) (
F)

Outside Tube Coefficients

MODES OF CONDENSATION

This design is not well adapted to free convection heat transfer outside a tube or coil; therefore, for this discussion only, agitation is considered using a submerged helical coil, Oldshue [241] and Kern [70].  2 2=3  1=3  0:14 hc D j L Nr Cr m m ¼ 0:87 (15-553) k m k mw

Condensation is the heat transfer process by which saturated vapor is converted into a liquid by means of removing the latent heat of condensation. Thermodynamically, condensation occurs when the enthalpy of the vapor is reduced to the state of a saturated liquid. In practice, the process is dynamic and heat must be transferred in order to achieve condensation. Therefore, condensation occurs when a vapor contacts a solid surface or a fluid interface whose temperature is below the saturation temperature of the vapor. The four basic mechanisms of condensation are: dropwise, film-wise, direct contact and homogeneous. The first three are categorized as heterogeneous processes, and Figure 15-184 illustrates these condensation mechanisms. In drop-wise condensation, the drops of liquid form from the vapor at particular nucleation sites on a solid surface, and the drops remain separate during growth until they are carried away by gravity or vapor shear. In film-wise condensation, the drops initially formed quickly coalesce to produce a continuous film of liquid on the surface through which heat must be transferred to condense more liquid. In direct contact condensation, the vapor condenses directly on the liquid coolant surface, which is sprayed into the vapor space. In homogeneous condensation, the liquid phase forms directly from supersaturated vapor, away from any macroscopic surface; it is however generally assumed in practice that there are particles of dust or mist particles present in the vapor to serve as nucleation sites.

Using the nomenclature of Equation 15-175, in addition: hc ¼ heat transfer coefficient for outside of coil, Btu/(h) (ft2)(F) Dj ¼ diameter of inside of vessel, ft L ¼ tube length, ft N ¼ agitator speed, rev/h r ¼ density, lb/ft3 m ¼ viscosity, lb/ft-h k ¼ thermal conductivity of liquid, Btu/(h) (ft2) (
F/ft) Cp ¼ specific heat, Btu/(lb) (
F) A related but somewhat more recent work by Oldshue [241] presents heat transfer to and from helical coils in a baffled tank, using standard baffling of T/12 located either inside the coil diameter or outside:  2 0:67  0:37  0:1   dt d Nr Cr m D ¼ 0:17 ho coil k m k T  0:5  m d m t ms (15-554)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

(A)

(B)

(C)

(D) Liquid spray

Vapor

Pool of liquid

FIGURE 15-184A-D Various modes of condensation.

Condensation Outside Tube Bundles Film-type condensation is considered to be the usual condition for most pure vapors, although drop-type condensation gives heat transfer coefficients many times larger when it does occur. It is not considered to be suitable for deliberate employment in process equipment. Generally, special materials must be employed (i.e. of low thermal conductivity, low surface energy, low wetting, or be highly polished) to attain drop-wise condensation. Hence, the process is susceptible to any fouling or oxidation of the surface that may bring the process back into the film-wise mode, with a corresponding reduction in thermal performance. Griffiths [393] provides more information on dropwise condensation. Direct contact condensation is a very efficient process, but it results in mixing the condensate with the coolant. Hence, it is useful only in those cases where the condensate is easily separated, or where the condensate is not reused or where the coolant and condensate are the same substance. Condensate forming as suspended droplets or mist in a subcooled vapor is called homogeneous condensation, of which the most common example in nature is fog. Homogeneous condensation is primarily of concern in fog formation in equipment, and is to be avoided as it is not a design mode. For practical purposes, film-wise condensation is the only type of the above modes to be considered in design. Figure 15-185 indicates the usual condensing process, which is not limited to a vertical tube (or bundle) as shown, but represents the

condensing/cooling mechanism for any tube. The temperature numbers correspond to those of Figure 15-34.

Vertical Tube Bundle [70] See Figures 15-186A and B. Figure 15-186A has been initially represented by McAdams [82] from several investigators. This figure represents the mean coefficient for the entire vertical tube for two values of the Prandtl number ðPrf ¼ cm=kÞ where: c ¼ specific heat of fluid, Btu/(lb) (
F) m ¼ fluid viscosity, lb/(ft) (h) k ¼ thermal conductivity, Btu/(h) (ft2) (
F/ft) Note that the break at Point A on Figure 15-186B at Rec ¼ 2,100 indicates where the film is believed to become turbulent [172]. McAdams [82] discusses the two regions of the figure, streamlined at the top and turbulent on the way down, with a transition region in between: Rec ¼

4G m1

(15-555)

where: G0 ¼ G ¼ w=rt condensate loading for each vertical tube, lb/(h) (ft) w ¼ flow rate, rate of condensation per tube, W/Nt, lb/(h) (tube), from lowest point of tube(s)

Heat Transfer Chapter | 15

FIGURE 15-185 Condensing vapors on cooling metal (or other) wall.

FIGURE 15-186A Condensing fiilm coefficients outside horizontal or vertical tubes.

339

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-186B Correlation of McAdams representing the condensing film coefficients on the outside of vertical tubes.

rt ¼ pdo for vertical tube (perimeter), ft do ¼ tube outside diameter, ft G0 ¼ mass rate of flow of condensate from lowest point on condensing surface divided by the breadth (unit perimeter), lb/(h) (ft). For a vertical tube: G0 ¼ w=pD: 00 G ¼ condensate loading for horizontal tubes, lb/(h) (ft) G0 ¼ condensate loading for vertical tubes, lb/(h) (ft). McAdams [82] and Kern [70] both suggest the same relationship for condensation on the outside of vertical tubes.  2 1=3 1=3 m ð4G0 Þ (15-556) hc ¼  3f 2  ¼ 1:47 ðmf Þ k f rf g g ¼ acceleration of gravity, 4.17  108, ft/(h) (h) Bell [172] suggests the relation:  3 1=4 k1 r1 ðr1  rv Þlg (15-557) hc ¼ 0:943 ½m1 LðTsat  Tw Þ k1 ¼ liquid thermal conductivity, Btu/(h) (ft) (
F) r1 ¼ liquid density, lb/ft3 rv ¼ vapor density, lb/ft3 l ¼ latent heat of vaporization, Btu/lb g ¼ acceleration of gravity, 32.2 ft/(s) (s) L ¼ tube length, ft Tsat ¼ saturation temperature,
F Tw ¼ surface temperature,
F m1 ¼ liquid viscosity, lb/(ft) (h)

(15-560)

For 4 G0o =mf > 2,000 (reference [82]), the following equation is usually applicable to long tubes and high flow rates; the average film coefficient: !1=3
0:4 k3f r2f g 4W (15-561) hcm ¼ 0:0077 m2f mf pDo For steam at atmospheric pressure and Dt from 10e150
F [82]: hcm ¼

4; 000 L1=4 Dt1=3

(15-562)

where: L ¼ tube length, ft Dt ¼ tsv  tw ¼ (temperature of saturation of dew point  temperature of tube wall surface),
F.

kef r2f g mf G0o

(15-558) "

1=3 ¼ 0:945

In the design of a shell-side condenser, the single tube film condensation analysis must be extended to model the process on horizontal tube bundles, which is the most widespread application of film condensation. Thome [394] has raised several important considerations on condensation of horizontal tube bundles: l

l l

4G0o < 2; 000 mt


hcm ¼ 0:945

  W ; lb=h linear foot pNt Do

Horizontal Tube Bundle [70]

where:

For

G0o ¼

k3f r2 tgpNt Do mf W

#1=2

(15-559)

l

In what manner does the condensate flow from one tube to the next? Is subcooling of the film important? Is the influence of vapor shear significant, and if so, how can this be accounted for? At which point does the film go through the transition from laminar to turbulent flow?

During condensation on a tube bundle, the condensate from the tubes above drains onto the tubes below, increasing the amount of condensate flowing on each tube

Heat Transfer Chapter | 15

341

FIGURE 15-187 Condensation flow modes on horizontal tube arrays.

in addition to the new condensate formed on that particular tube. The wave of condensate from tube row to tube row is often referred to as the tube row effect. This effect is not only dependent on how much condensate flows from tube to tube, but also on the physical mode the condensate achieves this in. The flow regimes formed by the condensate as it flows from a tube to that directly below it in an array of horizontal tubes are shown in Figures 15-187 and 15-188. Figure 15-189 shows the three modes (droplet, column and sheet) and their transitions [394].

See also Figures 15-186A, B. For single pure vapors, Kern [70] recommends the following, due to the splashing of condensed liquid (outside) from horizontal tubes as it drips/splashes to and off the lower tubes in the bundle. G00 ¼

W 2=3

LNt

lb=ðhÞ ðlinear ftÞ; see Figure 15-186A

FIGURE 15-188 Condensate spreading over the tube for column type.

(15-563)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

(A)

(B)

(D)

(C)

(E)

FIGURE 15-189 Video images of three flow modes and their transitions.

FIGURE 15-189A Competing tube row methods for condensation on a vertical array of tubes.

FIGURE 15-189B Ilustration of realistic flow liquid on tube bundle.

Heat Transfer Chapter | 15

343

Then the heat transfer for condensation is [70,82] on a horizontal bundle:  2 1=3 1=3 m 1:5ð4G00 Þ (15-564) hcm  3f 2  ¼ ðmf Þ kf rf g The preceding equation automatically allows for the effect of the number of vertical rows of horizontal tubes as proposed by Kern [70] and cited later in this discussion [82]. The flow should be streamlined (laminar) flow, with a Reynolds number of 1,800e2,100 for the condensation [82], see Figures 15-186A and B. Ref ¼ 2G=mf

(15-565)

The critical Reynolds number of 2,100 corresponds to 4G=mf of 4,200 for horizontal tube [82]. G0 ¼ w/L, per horizontal tube, lb/(ft) (h) The thickness of the film [94A] for Reynolds Number < 2,100 ¼ ð3mG0 =r2 gÞ1=3 For steam at atmospheric pressure [82], the average film coefficient, hcm: hcm ¼ 

5; 800

1=4 1=3 Nv D0o ðDtm Þ

(15-566) FIGURE 15-190 Number of condensate streams in a horizontal bundle.

where: Nv ¼ number of rows of tubes in a vertical tier D0 o ¼ tube OD, in. Dtm ¼ (tv  tw)/2,
F tv ¼ temperature of vapor,
F tw ¼ temperature of tube wall,
F hcm ¼ average value of condensing film coefficient, for vertical rows of horizontal tubes, Btu/h (ft2) (
F) kf ¼ thermal conductivity at film temperature, Btu/(h) (ft2) (
F/ft) rf ¼ density at film temperature, tf ,lb/ft3 g ¼ acceleration of gravity, 4.17  108 ft/(h) (h) mf ¼ viscosity at film, lb/(ft) (h) ¼ (centipoise  2.42) W ¼ condensate flow rate, lb/h Do ¼ outside diameter of tubes, ft Nt ¼ total number of tubes in bundle used for condensation L ¼ straight tube length, ft The charts of Chen [26] are also useful for solving the equations for condensing coefficients; however, the correction for the effect of multiple fluid stream is not included. Therefore, the results should be conservative. Devore [34] has presented useful charts for solving a multitube condenser design, as shown in Figures 15-190, 15-191 and 15-192. Figure 15-193 is useful for condensing steam. The charts all follow Nusselt’s basic presentation; however, a correction for turbulence of the film and other deviation is included. Rohsenow and Hartnett [166] present Nusselt’s relation for the heat transfer average for horizontal tubes in

FIGURE 15-191 Turbulence correction factor for horizontal multitube banks.

a bundle condensing vertically from tube to tube, top to bottom tube: h i1=4 gr1 ðr1  rv Þk3 h0fg (15-567) h ¼ 0:728 ½nDo mDT; average for horizontal tubes in vertical bank.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-192 Condensate film coefficients - vertical or horizontal.

where: g ¼ acceleration of gravity, 32.17 ft/s2 Do ¼ tube outside diameter, ft c ¼ specific heat of liquid at constant pressure h ¼ heat transfer coefficient, Btu/(h) (ft2) (
F) h0 fg ¼ hfg þ (3/8) c(Ts e Tw) hfg ¼ l ¼ latent heat, Btu/lb l ¼ latent heat of vaporization, Btu/lb k ¼ thermal conductivity of the liquid at film temperature, Btu/(h) (ft) (
F)

n ¼ number of horizontal tubes in a vertical bank DT ¼ Ts  T0 w ,
F Ts ¼ temperature at saturation pressure,
F Tw ¼ temperature at wall,
F m ¼ viscosity of liquid, lb/(ft) (h) r1 ¼ density of liquid, lb/ft3 rv ¼ density of vapor, lb/ft3 Reference [166] points out that the preceding equation provides results lower than actual experience.

Heat Transfer Chapter | 15

345

where: hc ¼ average condensing coefficient on outside of tube Btu/(h) (ft2) (
F) Tsat ¼ saturation temperature of the vapor,
F Tw ¼ wall temperature of tube,
F L ¼ length of tube for heat transfer, ft W ¼ vapor weight (mass) flow rate, lb/h Do ¼ outside tube diameter, ft Subscripts: 1 ¼ liquid c ¼ condensing v ¼ vapor The preceding equations are reported to predict actual heat transfer coefficients only about 15% lower than experimental values e the difference can be attributed to the rippling of the film and early turbulence and drainage instabilities on the bottom side of the tube [172]. General design practice is to assume that the average coefficient calculated for a single tube is the same as for an entire bundle, based on test data [172]. In horizontal condensers (outside tubes), for N tubes in a vertical row, with the condensate flowing uniformly from one tube to the one below without extensive splashing, the mean condensation heat transfer coefficient, a, for the entire row of N tubes: FIGURE 15-193 Condensing stream film coefficients for vertical surfaces or horizontal tubes.

As reported by References [166] and [168], Chen’s [167] proposed relationship provides better results; Chen assumes subcooling is removed from the condenser: h   3 0 i1=4 ½1 þ 0:2ðc DTÞðn  1Þ gr1 r1  rv k hfg   h ¼ 0:728 ½nDmDT hfg (15-568) where the symbols are the same as for Reference [166]. Agreement with test data is good when ðcDT=hfg Þ < 2. Bell and Mueller [172] present the following equation, which is similar to several of the others for condensing outside single horizontal tubes. hc ¼ 0:728

½k3 r1 ðr1  rv Þlg ½m1 Do ðTsat  Tw Þ

1=4

(15-569)

or: 1=3 k31 r1 ðr1  rv Þ g L hc ¼ 0:951 ½m1 W 

(15-570)

a ¼ N1=4 aðN ¼ 1Þ

(15-571)

where a(N ¼ 1) is the heat transfer coefficient for the top tube row, i.e., the original Nussselt equation for a single tube [394]. This method is applicable if the film flow remains laminar all the way to the bottom of the Nth row. The heat transfer coefficient on the Nth tube row in the bundle a(N) is: aðNÞ 3=4 ¼ N3=4  ðN  1Þ aðN ¼ 1Þ

(15-572)

The mean condensing heat transfer coefficient, hm for the entire row of N tubes (per Knudsen in reference 94A) is related to a film coefficient for the top, h1, single tube by: hmðnewÞ ¼ h1 N1=4 ; ða severe penaltyÞ

(15-573)

h1 is the heat transfer coefficient for the top tube row (calculated from the previous listed equations). Kern [70] concluded from his practice experience in designing condensers that the above tube row expression was too conservative, and that this resulted in condensers that were consistently over-surfaced. To improve his thermal designs, he replaced the exponent of (1/4) in

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-194 Exchanger rating for overhead condenser.

Heat Transfer Chapter | 15

347

FIGURE 15-195 Shell-side pressure loss for 3 shell-side baffle configurations.

Equation 15-573 with a value of (1/6) so that the corresponding equations are: a ¼ N1=6 aðN ¼ 1Þ

(15-574)

and: aðNÞ 5=6 ¼ N5=6  ðN  1Þ aðN ¼ 1Þ hmðrowÞ ¼ h1 ðNÞ

1=6

(15-575) (15-576)

These equations are widely used in the thermal design of condensers. Figure 15-189A presents a comparison of experimental data from different sources compiled by Marto [395] with respect to the Nusselt and Kern tube row methods. The wide bandwidth of the data compared to the two curves may be due to some vapor shear effects in the data, or the influence of inter tube flow mode types encountered during the experiments [394]. It is essential to understand that the tube row expressions are applied in practice by counting the number of vertical inline tube rows. Therefore, for an inline or square tube layout, each tube row from the top to the bottom of the bundle is counted when applying these equations. Alternatively, for staggered tube layouts, the condensate is

normally assumed to flow to the next inline tube row since it cannot flow onto the top of the out-of-line tube in the next lower row. Hence, the total number of tube rows to use is one-half the actual number, which means that staggered layouts are more advantageous for heat transfer. As the condensate in a staggered bundle ends up on the sides of the next out-of-line tubes, this assumption is optimistic, as illustrated in Figure 15-189B adapted from Marto [395]. Therefore the total number of vertical tube rows in a staggered tube bundle is between the number of inline rows and the total number of staggered row, and an average of these two values may be used as a reasonable approximation. Short and Brown [174] in reference [172] found no net penalty against the single tube coefficient in a single row 20 tubes high. Bell [172] concurs that this is borne out in industrial experience, and “current design practice is to assume that the average coefficient for the entire tube bank is the same as for a single tube.”

Step-wise Use of Devore Charts 1. Based upon condensing heat load, log DT and an assumed overall coefficient, U, estimate the required surface area.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

2. Determine the number and size of tubes required to calculate this area. Also set the number of tube passes and tube pitch. 3. Determine the inside film coefficient by methods previously outline for convection. 4. Estimate film temperature of fluid on the outside of tubes and determine DT across condensing film. 0 5. For vertical tubes, determine condensate loading Go 0 (Equation 15-560). For these charts, Go (viscosity in centipoise, at film temperature) is limited to 1090. 6. For horizontal tubes, use Figure 15-190 to determine the equivalent number of condensate streams, ns, based on the total number in a circular bundle, Nt. (a) Then calculate condensate loading (horizontal tubes): G” ¼ W=Lns

(15-577)

Note that this varies from the form used in the Kern relation. (b) Determine the average number of tubes, Na: Na ¼ Nt =ns

(15-578)

(b) Determine turbulence correction factor C4/3 N from Figure 15-191. For compounds other than those shown, select the nearest type for reference and evaluate CN. To obtain more conservative results, reduce the value for C4/3 N but never to less than 1.0. 7. Film coefficients: hcm (a) For vertical tubes, use Figure 15-191 or 15-192 and the corresponding scales for compounds at tf 0 and G (as defined for use with these charts). (b) For horizontal tubes, use Figure 15-191 or 15-192 and corresponding scales for compounds at tf and 00 G (as defined for use with these charts).

FIGURE 15-196 Ratio of heat transfer to pressure loss for 3 shell-side baffle configurations.

Heat Transfer Chapter | 15

349

FIGURE 15-197 Typical flow patterns encountered for condensation inside horizontal tubes.

FIGURE 15-198 Condensing inside horizontal tubes. (Used by permission: Akers, W. W., Deans, H .A., and Crosser, O. K. Chemical Engineering Progress, V. 55, No. 29, ©1959. American Institute of Chemical Engineers. All rights reserved.)

8. Evaluate the overall clean coefficient, Uc. 9. Check the assumed temperature drop across the condensate film, DT. DT ¼ ðUc =hcm Þðth  tc Þ

(15-579)

If these values are not in good agreement, reassume and recalculate. 10. Calculate the overall fouling coefficient, adding the appropriate fouled factors to clean, Uc.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Note: 1.0 Btu/(ft2) (h) (
F) ¼ 1.0 pcu/(h) (ft2) (
C)

11. Determine the required surface area: A ¼ Q=UDT

(15-580)

If this surface area is slightly less than that assumed for the unit, say 10e20%, the unit should be acceptable. If the required area is larger, the new number of same length can be determined by the ratio of required area/assumed area multiplied by the number of tubes in the assumed unit when the effect of any new shell diameter should be reviewed; otherwise the unit should perform satisfactorily.

Subcooling The literature is limited on design data/correlations for subcooling condensed liquids in or on vertical or horizontal condenser units. Certain analytical logic can be used to examine what is taking place, and the corresponding heat transfer functions can be used to establish the relations to break the desired unit into its components (in terms of heat transfer) and combine them to develop a single condensing/ subcooling unit. Also see Reference [70].

Subcooling Condensate Outside Vertical Tubes The area concerned with the subcooling only can be evaluated using a film coefficient calculated from Figure 15-84 for liquids outside tubes. This assumes that the liquid being cooled is held in the area around the tube by a level control or pipe seal, allowing drainage at the rate it builds up and covering a portion of the tubes. Care should be used in determining the temperatures that prevail at tube inlet and outlet, as well as the shell-side in and out for the subcooling portion. This becomes particularly tedious for multipass units.

Subcooling Inside Vertical Tubes Colburn, et al. [173] conducted some fundamental studies using organic liquids; they developed the subcooling coefficient when Rc > 2100: 1=3
2 2 k r Cp ð4GÞ hs ¼ 7:5 (15-581) ðmf Þ ðmf Þ which is used to calculate the area required, and then this area is added to an earlier calculated condensing area. where: hs ¼ subcooling film coefficient, pcu/(h) (ft2) (
F) k ¼ thermal conductivity, Btu/(h) (ft) (
F) r ¼ liquid density, lb/ft3 Cp ¼ heat capacity of condensate, pcu/lb.
C G ¼ condensate rate per unit periphery, lb/(h) (ft) mf ¼ viscosity of condensate at average film temperature, lb/(h) (ft)

Subcooling Condensate Outside Horizontal Tubes Subcooling in horizontal condensers is accomplished by a liquid seal on the liquid outlet or by a baffle, which dams the liquid and allows it to overflow through the outlet. Here also, the subcooling area is calculated separately from the condensing area. The two are then added to obtain the total. Usually the liquid held to be subcooled covers only about 15e30% of the total surface, although some units may run as high as 50%. If the quantity of the liquid is very large, handling it in a separate liquid cooler where higher coefficients can be obtained is possibly a better solution. The cooling of the condensate by free convection is [70]: " ! #0:25 k3f rcf b Dt (15-582) hc ¼ 116 m0f do where: m0f ¼ viscosity in centipoise Dt ¼ temperature difference between tube surface and fluid,
F do ¼ OD tube, in b ¼ coefficient of thermal expansion, %/
F r ¼ density, lb/ft3 kf ¼ thermal conductivity of film, Btu/h (ft2) (
F/ft) cf ¼ specific heat, Btu/lb (
F) at film conditions tf ¼ (tw þ ta)/2,
F, average, film temperature ta ¼ bulk fluid temperature,
F g ¼ acceleration of gravity, ft/h2 G0o ¼ condensate mass flow per unit tube outside circumference, vertical tubes, lb./(h) (ft) The usual range of film coefficient values is 40e50 for organic solvents and light petroleum fractions such as hexanes; 25 for heavier materials such as aniline, straw oil, etc.; and 0.5e3 for low temperature (10e40
F) subcooling of heavier organics and inorganics such as chlorine.

Film Temperature Estimation for Condensing Kern [70] recommends the temperature to use in estimating or determining fluid properties as: tf ¼ 1=2ðtb  tw Þ where: tb ¼ bulk temperature of fluid
F. tw ¼ wall temperature of tube surface,
F

(15-583)

Heat Transfer Chapter | 15

Water flow area, a, ft2 ¼ volumetric flow rate/minimum velocity ¼ cfs/v Select tube size and calculate flow area available:

Dtf ¼ tf  tw McAdams [82] recommends:

Flow area=tube ¼

tf ¼ tsv  3=4DT

(15-584)

Dt ¼ tsv  tw where: tsv ¼ saturation or dew point temperature.
F. In most instances the effect of the difference on physical properties will be small.

Condenser Design Procedure The usual total condenser will follow the following design steps: 1. Establish condensing temperature of vapors, either by the conditions of other parts of the process (distillation column, vacuum jet, etc.) or by the temperature approach to cooling water, remembering that a close approach will require a relatively large surface area. Select the cooling water temperature to ensure performance in the summer months and consider the conditions during the winter (see step 8q). 2. Establish film temperature for condensation from Equation 15-47 or 15-49. 3. Establish physical properties of fluids, shell-side at a different temperature than the tube-side. 4. Calculate the heat load of condensation from latent heat. (This may be a weighted value for a mixture.) 5. Set an allowable temperature rise for the cooling water. 6. Calculate water rate:   W ¼ Q cp Dt; lb h Q ¼ Btu=h

(15-585)


Dt ¼ temperature rise of water, F cp ¼ Btu/lb
F The volumetric flow rate in gpm: gpm ¼

W ð8:33Þð60Þ

(15-586)

(for water, otherwise correct 8.33 lb/gal for sp.gr. of coolant) The volumetric flow rate in ft3/s: ¼

351

gpm ¼ cfs ð7:48Þð60Þ

(15-587)

7. Estimate the number of tubes per pass to maintain minimum water velocity. Set minimum velocity, v in tubes at 3.5e6 ft/s.

tube cross-section; in2 ¼ ft2 =tube 144 (15-588)

Estimated no: tube=pass ¼

a ¼ n0 ft2 tube ðcross-sect:Þ (15-589)

8. Assume a unit: (a) Estimate overall coefficient, U, from Tables 15-28, 15-29 and 15-32 or from your own experience. (b) Roughly calculate a log mean temperature difference DTLMTD. (c) Estimate area ¼ Q/U DTLMTD, ft2 (d) The total tube footage required ¼ A/(ft2 surface/ft tube length), ft ¼ F1. (e) Assuming a tube length, 1: No: passes ¼

(f) (g)

(h) (i)

F1 ¼ Pa ðn0 Þð1Þ

(15-590)

If this value is not reasonable, reassume the tube length, and/or the size of tubes. Try to keep the number of passes fewer than 8 except in special cases, as construction is expensive. From Tables 15-15, pick an exchanger shell diameter that closely contains the required number of tubes at the required number of passes. From the actual tube count selected, establish the actual number of tubes/pass. They may be a few tubes more or less than initially calculated. Calculate the flow area/pass ¼ (number of tubes/pass) (cross-section flow area/tube), ft2/pass. Calculate the velocity in tubes ¼ cfs/(ft2/pass), ft/sec. For the film coefficient, tube-side, read hi from Figure 15-80A or B at the mean water temperature and calculated velocity of (h). Correct to the outside of tube:

hio ¼ ðhi Þ ðtube dia: Film correction; Fw Þ     tube I:D:  ; Btu=h ft2
F (15-591) tube O:D: (j) For the film coefficient, shell-side, calculate G00 o from Equation 15-560 or 15-563, lb/hr (lin. ft) Do not use full tube length as effective, reduce “1” by the estimated tube sheet thickness at each end; usually 11/2 in. per tube sheet for low pressure (to 150 psi) and 3 in. for higher pressure (to about 600 psi) is satisfactory. From Figure 15-186A, read ho, Btu/h (ft2) (
F).

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

(k) Select fouling factors from tube-side and shell-side, from Table 15-25 or 15-26 or your own experience. (l) Calculate the overall coefficient: U ¼

1 ho

 2
1 1 ; Btu=ðhÞ ft ð FÞ þ ro þ rio þ hio

(15-592)

Usually, the tube wall resistance can be neglected, but if you doubt its effect, add it to the resistances. (m) Calculate the log mean temperature difference by using Figure 15-40 or Equation 15-29. (n) Area required: A ¼ Q=U DTLMTD ; ft2 net (o) Area available in assumed unit: A ¼ (ft2 surface/ft tube) (number of tubes total) (net tube length) (p) Compare, and if the available area is equal to or greater than the required area, the selected unit will perform satisfactorily. If the required area is greater than the available area, select a new unit with more tubes, longer tubes, larger tubes or some combination. Repeat from step 8, unless the minimum water velocity can safely be changed, then repeat from step 7. (q) Check the effect of winter operating conditions on the importance of (1) maintaining constant yearly outlet condensate temperature; (2) subcooled condensate as a result of excess surface area due to lower inlet cooling water; and (3) maintaining a minimum water velocity in tubes. Example 15-27. Total Condenser

Ammonia vapors from a stripping operation are to be condensed. Select the condenser pressure, which sets the top of stripper pressure, and design a condenser. Water at 90
F is to be used. Flow: 1,440 lb/h ammonia, at dewpoint. 1. The condenser operating pressure should be so selected as to give a reasonable temperature difference between the condensing temperature and the water temperature. The quantity of water required should not be penalized by requiring a small temperature rise in the water. By referring to a Mollier diagram for ammonia, the condensing temperature at 220 psig is 106.6
F. This is about the lowest operating pressure possible to keep a DT of greater than 10
F between water and ammonia. 2. Heat Load: Q ¼ ð1440Þð470:5 Btu=lb latent heatÞ ¼ 680; 000 Btu=h 3. Minimum water tube velocity: set at 5 ft/s.

4. Water required for 10
F temperature rise: Q ¼ W cp DT W ¼

680; 000 ¼ 68; 000 lb=h ð1Þð10Þ

Volumetric flow rate in gpm : ¼

68; 000 ¼ 136 gpm ð8:33Þð60Þ 3

Note : 1 ft ¼ 7:48 gal

3 Volumetric flow rate in ft s :

 136 ¼ 0:303 ft3 s ð7:48Þð60Þ 5. Water flow area, ft2: Total tube cross-section flow area  ¼ volumetric flow rate water tube velocity   ¼ 0:303 5 ft s ¼ 0:0606 ft2 6. Number of tubes, using 1 in., 12 BWG tube:  2 Tube flow area ¼ 0:479 in:2 144 ¼ 0:00333 ft tube Number of tubes  ¼ Total tube cross-section flow area Tube flow area No: tubes ¼

0:0606 0:00333

 ¼ 18:2 per pass to keep the 5 ft sec water velocity 7. Assumed condenser unit:


Assumed U ¼ 200 Btu h ft2 F

LMTD ¼ 10
F 680; 000 A ¼ ¼ 340 ft2 ð200Þð10Þ Tube length required: Outside area/tube ¼ 0.2618 ft2/ft Total tube footage ¼ 340/0.2618 ¼ 1,300 ft Try 15.25 in. ID shell 4 pass, with 78 tubes total, 16 ft long on 11/4 in. triangular pitch. Trial area ¼ (78) (0.2618) (16 ft long) ¼ 327 ft2 This does not allow for tube area lost inside the two tube sheets of a fixed T.S. unit. 8. Flow area: Total number of tubes/Number of tubes/pass. Number of tube-side passes ¼ 78/18.2 ¼ 4.28, use 4 tube passes Number of tubes/pass ¼ 78/4 ¼ 19.5, use 19 Flow area/pass ¼ (19)(0.00333) ¼ 0.0633 ft2 Velocity in tubes ¼

0:303 cfs 2

0:0633 ft =pass

¼ 4:8 fps=pass

9. For the film coefficient, tube-side, use Figure 15-80A or B: Mean water temperature ¼ 95
F

Heat Transfer Chapter | 15

Velocity ¼ 4.8 ft/s Read hi ¼ 1,150 Btu/h (ft2) (
F) correction for 1 in. tube Fw ¼ 0.96 at 0.782 in. ID. Correction to outside of tube: hio ¼ (1,150) (0.96) (0.782/1.0) ¼ 864 Btu/h (ft2) (
F) 10. Film coefficient, shell-side: W Condensate loading : G00o ¼ LNt2=3 G00o ¼

1440 2=3

ð16 ft  6 in:=12Þð78Þ

¼ 5:1 lb=hðlin ftÞ

(allowing 3-in. thickness/tube sheet, thus reducing effective tube length) Thermal conductivity, ka ¼ 0.29 Btu/(h) (ft2) (
F/ft) Specific gravity ¼ 0.59 Viscosity ¼ 0.085 centipoise From Figure 15-186A or B, read: ho ¼ 2500 Btu/h (ft2) (
F) Although this is satisfactory, because it is so large, use ho ¼ 1500 Btu/h ft2
F In many cases, a “safety” factor of greater than 10e15% is not justified. Select the tube-side fouling of water ¼ 0.002. Select the shell-side fouling of ammonia e 0.001 11. Overall coefficient: 1 1 1 ¼ þ 0:001 þ 0:002 þ U 1; 500 864 1 ¼ 0:00067 þ :003 þ 0:00116 ¼ 0:00483 U

For the tube pressure drop, use Figure 15-98: At water rate ¼

   68; 000 lb=h ¼ 3; 580 lb=h tube pass 19 tubes=pass

Chart reads Dpt ¼ 6.2 psi/100 ft  6:2 Total exchanger Dpt ¼ ð4 passesÞð16 ft tubesÞ 100 ¼ 3:87 psi For usual purposes, the effect of water temperature is not great, and Figure 15-98 can be used. The preceding value checks Stoever [109] with Dpt ¼ 3.85 psi. Total tube-side Dpt ¼ 2.52 þ 3.87 ¼ 6.39 psi. 6.4 psi Allow: 8 psi Total shell-side Dps (refer to the pressure drop section of this chapter) can be neglected for pressure units unless an unusual condition or design exists. To check, follow procedure for unbaffled shell pressure drop. 17. For the specification sheet, see Figure 15-194. 18. Winter operation e In order not to allow the water velocity in the tubes to fall below 3 ft/s in the winter, you may have to compromise with the selected unit as based on 90
F water. If the average four-month winter temperature drops to 70
F, the quantity of water required will be reduced as will the velocity through the tubes. The low velocity is the point of concern. Check to determine the prevailing conditions. DTLMTD :

2

U ¼ 207 Btu=h ðft Þ ð
FÞ ðneglecting tube wall resistanceÞ 12. Log mean temperature difference:

106.6° F

106.6° F

80.0 °F

70.0°F

26.6°F

36.6°F

DTLMTD ¼

DTLMTD ¼

16:6  6:6


 ¼ 10:8 F ðFigure 15-44Þ 16:6 In 6:6

13. Area required: A ¼

Q 680; 000 ¼ 304 ft2 ¼ UDTLMTD ð207Þð10:8Þ

14. Area available in selected unit: 2

A ¼ ð0:2618Þð78Þð15:5Þ ¼ 316 ft net  2   680; 000 U ¼ ¼ 199 Btu=h ft
F ð316Þð10:8Þ 15. Safety factor or percent excess surface: % ¼

ð316  304Þð100Þ ¼ 3:9% 304

16. Pressure drop, tube-side: End return loss (from Figure 15-99) at 4.8 ft/sec ¼ (0.63) (4 passes) ¼ 2.52 psi.

353

ð36:6  26:6Þ ¼ 31:3
F lnð36:6=26:6Þ

This assumes the same quantity of water in order to keep the velocity the same. Revised tube-side film coefficient: At 75
F, hi ¼ 1,025 Corrected:   2 hio ¼ ð1; 025 Þð0:96Þð:782=1:0Þ ¼ 768 Btu h ft ð
FÞ Assume the shell-side film coefficient unchanged, because the previous selection was on conservative side. U ¼

1 1;500

1
¼ 193 Btu=hðft2 Þð FÞ 1 þ 0:001 þ 0:002 þ 660

Revised area required: A ¼

680; 000 2 ¼ 112 ft ð193Þð31:3Þ

This is a significant reduction in area and is primarily due to the increased DT during winter operation. Actually, the unit will subcool the condensate with the excess surface during the winter. Note that this result is based on maintaining the same water quantity through the

354

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

tubes. If a lower velocity is acceptable for the water conditions, then a higher temperature rise can be taken, which reduces the liquid subcooling. Very little water is acceptable for cooling without excessive scaling when the velocity falls below 1 ft/s. 19. Although the previously discussed unit will perform as required, it may be larger than necessary. The water velocity of 4.8 ft/s is not as high as would be preferred. 20. Redesign, using 3/4 in. bimetal tubes. Try for a minimum tube velocity of 6.5 ft/s: Volumetric flow rate in gpm: ¼ (136) (10/5) ¼ 272 gpm Volumetric flow rate ¼ 0.606 ft3/s Water flow area ¼ 0.606/6.5 ¼ 0.0934 ft2 For 3/4 in. tubes with an ID equivalent to about a 12 BWG tube: Tube flow area ¼ 0.223/144 ¼ 0.00155 ft2/tube Number of tubes ¼ 0.0934/0.00155 ¼ 30.1 tubes/pass Assumed unit for trial conditions: A ¼

680; 000 ¼ 226 ft2 ðusing 15
F Dt for estimatingÞ ð200Þð15
FÞ

Outside area/tube ¼ 0.1963 ft2 Number of feet tube ¼ 226/0.1963 ¼ 1,550 ft. Using 16 ft tubes: Number of tubes required ¼ 1,150/16 ¼ 72 For a 4-pass, fixed tube sheet unit, 3/4 in. tubes on 15/16 in. triangular pitch, shell ID ¼ 12 in., number of tubes ¼ 84 No. tubes/pass ¼ 84/4 ¼ 21 Flow area/pass ¼ (21) (0.00155) ¼ 0.0326 ft2 The volumetric flow rate for 6.5 ft/s: ¼ (6.5) (0.0326) ¼ 0.212 ft3/s Volumetric flow rate in gpm: ¼ 0.212 (7.48) (60) ¼ 95.2 gpm

Overall coefficient: U ¼

2

¼ 220 Btu=h ðft Þð
FÞ Water flow of 95.2 gpm gives: Water temperature rise

¼ 14:3
F Log mean temperature difference: Summer: based upon water 90
F / 104.3
F LMTD ¼ 7.2
F as calculated previously Winter: based upon water 70
F / 84.3
F LMTD ¼ 29.0
F as calculated previously Area required: 680; 000 2 Summer : A ¼ ¼ 430 ft ð220Þð7:2Þ Winter : A ¼

correction for 3/4 in. tube ¼ 1.15   2 0:532 ¼ 1; 140 Btu=h ft ð
FÞ hio ¼ ð1; 400Þð1:15Þ 0:75 Film coefficient, shell-side: G00o

¼

1; 440 2=3

15:5ð84Þ

¼ 4:84 lb=h ðlin ftÞ

Because the value of ho read from Figure 15-186A is still about 2,500, use ho ¼1500 Btu/h ft2
F.

680; 000 2 ¼ 106 ft ð220Þð29:0Þ

Area available in selected unit: 2

A ¼ ð0:1963Þð84Þð15:5Þ ¼ 256 ft

To make this unit acceptable for summer operation (the calculated required surface is greater than that available), assume that the water rate can be increased, thereby decreasing water DT and increasing DTLMTD.

106.6° F

106.6° F

95.0 °F

90.0°F

11.6°F

16.6°F

Mass flow rate in lb=h; G ¼ r q

¼ 47; 727 lb=h For the film coefficient, tube-side, use a mean water temperature of 85
F instead of 95
F. This will lean a little more to the winter operation and be safe for summer.  2
hi ¼ 1; 400 Btu h ft F

1 1 1 þ 0:001 þ 0:002 þ 1500 1140

DTLMTD ¼

ð16:6  11:6Þ ¼ 14
F lnð16:6=11:6Þ

Summer area required (not making any correction for change in water film coefficient or condensing coefficient):  7:2 ¼ 147:0 ft2 A ¼ 286 14 Water rate ¼

680; 000 ¼ 136; 000 lb=h ð5
Þð1Þ

Volumetric flow rate in gpm : 136; 000 ¼ 272 gpm ð8:33Þð60Þ 3 Volumetric flow rate in ft s : ¼

¼

272 ft3 ¼ 0:606 s ð7:48Þð60Þ

Velocity in ft=s : ¼

0:606 ft ¼ 18:6 ð0:00155Þð21Þ s

Heat Transfer Chapter | 15

This velocity is too high for satisfactory operation. Therefore, the only way to get more flow area is more tubes and requires the same size shell as the previously designed unit. Recommendation: Use the unit with 1 in. tubes. 21. Nozzles should be sized with or checked against the sizes of the incoming or outgoing lines. Often the exchanger nozzle must be larger than the pipe in order to keep velocities low to prevent erosion or high pressure drop. Water Connections Flow rate ¼ 136 gpm Design for (136) (1.5) ¼ 204 gpm Maximum allowable velocity 6 ft/s Referring to Cameron hydraulic tables: Select 4-in. nozzle, velocity ¼ 5.3 ft/s Select head loss ¼ (0.046 ft) (6 in./12) ¼ 0.023 ft liquid Condensed Ammonia Liquid Out Referring to Cameron Miscellaneous Liquid Table in Fluid Flow Chapter, Vol. I: Volumetric flow rate in gpm : ¼

1; 440 lb=h: ¼ 4:87 gpm ð60Þð8:33Þð0:59Þ

Design rate ¼ (4.87) (1.5) ¼ 7.8 gpm Select a 3 in. nozzle, head loss less than 0.00035 ft. (negligible). Use large nozzle to ensure free drainage of unit and no vapor binding in outlet line. Actually a 1 in. connection would safely carry the liquid flow with a head of about 0.08 ft of liquid. A condenser must be free draining and capable of handling surges. Ammonia Vapor Inlet Design rate ¼ (1400) (1.5) ¼ 2160 lb/h Referring to Figure 15-93, at 220 psia and 17 mol wt, the maximum suggested vapor velocity through a nozzle is: (40) (1.2) ¼ 48 ft/s max. For a 3 in. nozzle, Schedule 40, Cross-section area to flow ¼ 0.0513 ft2 Sp. vol. of NH3 vapor ¼ 1.282 ft3/lb 3 Total flow rate in ft h : 3 ¼ ð2; 160Þ ð1:282Þ ¼ 2; 770 ft h 3 Total flow rate in ft s : ¼

2770 ft3 ¼ 0:8 s 3600

Velocity in 3 in. Sch 40 pipe: 2

Area; ft : 2

p ð3:068=12Þ ¼ 0:0513 ft2 4 Velocity; v : A ¼

¼

0:80 ¼ 15:6 ft=s 0:0513

This is satisfactory, although a 2 in. nozzle would have velocity of 34.3 ft/s. Because this condenser has entering

355

vapors at the dew point, entrainment of some particles is always a real possibility; therefore, a low inlet velocity is preferred. Also, overhead vapor lines should have low pressure drop for vapor at its dew point and a 3 in. line might be indicated when this line is checked.

RODbaffled
(Shell-Side) Exchangers (See Figures 15-22A, B, C and D.) The design techniques of this system of baffling are not adequately covered in the literature, because they are the proprietary information of Phillips Petroleum Co. and are licensed to design firms for specifically designing the units to ensure proper application details. Figures 15-195 and 15-196 illustrate some of the improved features claimed for heat transfer and pressure drop. The specific features of this new type of shell-side construction provide improved resistance to destructive tube vibration compared to the usual plate baffle designs. These units have been applied in practically all of the usual process heat exchanger services including externally finned tubes. These units have been fabricated in large shell diameters. Technical references include Gentry [169], Gentry, Young and Small [170] and Gentry and Small [171].

Condensation Inside Tubes Condensation in horizontal tubes may involve partial or total condensation of the vapor. However, depending on the application, the inlet vapor may be superheated, equal to 1.0 or below 1.0. Thus, the condensation process path may initially begin with a dry wall desuperheating zone, followed by a wet wall desuperheating zone, then a saturated condensing zone and finally a liquid subcooling zone. The condensing heat transfer coefficient is strongly dependent on the local vapor quality, which increases as the vapor quality increases. Additionally, the condensing heat transfer coefficient is dependent on the mass velocity, increasing as the mass velocity increases. Opposed to external condensation, intube condensation is independent of the wall temperature difference (Tsat  Tw) for most operating conditions, except at low mass flow rates. Figure 15-197 illustrates the twophase flow patterns typical of condensation in horizontal tubes. In the top diagram of the figure at high mass flow rates, the flow takes on the annular flow regime, where the liquid film is on the perimeter of the wall, the vapor is in the central core and some liquid is entrained in the vapor from the tips of waves on the interface of the film. As condensation continues along the tube, the vapor velocity decreases, there is a corresponding decrease in vapor shear on the interface and the liquid film becomes thicker at the bottom of the tube than at the top. New condensate formed adds to the thickness of the liquid film. As the quantity of

356

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

liquid increases along the tube, slug flow is encountered, and still further along all the vapor is finally converted to liquid. At low flow rates, as depicted in the lower diagram of Figure 15-197, at the entrance region annular flow is formed but this quickly transforms to intermittent flow with its characteristic large amplitude waves washing the top of the tube, or to stratified-wavy flow with smaller amplitude waves. If the liquid does not span the cross-section of the tube, the vapor may reach the end of the tube without condensing.

Horizontal Tube Bundles [70,82,94] Kern’s [70,94] modification of the Nusselt development is considered useful. 1=3  3 Lk1 r1 ðr1  rv Þg hc ¼ 0:761 ½WT m1   3 1=4 k1 r1 ðr1  rv Þg (15-593) ¼ 0:612 ½m1 Di Dt where: k1 ¼ liquid thermal conductivity, Btu/(h) (ft2) (unit temperature gradient,
F/ft) r1 ¼ liquid density, lb/ft3 rv ¼ vapor density, lb/ft3 m1 ¼ liquid viscosity, lb/(h) (ft), [¼ centipoise  2.42] Di ¼ inside diameter, ft g ¼ acceleration of gravity 4.18  108 ft/h2 Dt ¼ temperature difference ¼ (tw  ts)
F ts ¼ surface temperature,
F tw ¼ saturated vapor temperature,
F hc ¼ condensing film coefficient, mean, Btu/(h) (ft2) (
F) WT ¼ total vapor condensed in one tube, lb/h L ¼ tube length, ft (effective for heat transfer) Because the condensate builds up along the bottom portion of horizontal tubes, the layer builds up thicker and offers more resistance to heat transfer. Kern [70] proposes good agreement with practical experience using the following: G00 ¼ W=ð0:5 LNt Þ; special G00 loading for a single horizontal tube; lb=ðhÞðftÞ (15-594)  2 1=3 m ½ð4G00 Þ1=3 hc ¼  3f 2  ¼ 1:51 ½mf  kf rf g

(15-595)

Other symbols as listed previously. Subscript: f ¼ liquid film These relations are good for single-pass tube-side units; however, for multipass units, the number of available vapor tubes must be determined at the end of the first and each succeeding pass, as the lower liquid carrying tubes must not be considered as available tubes. Thus, G” should be evaluated for each pass, and the individuals evaluated separately, or an average determined as the average of the pass average values of hcm.

Condensation Inside the Tubes (SI Units) Condensation coefficient depends on the position of the condenser. For condensation, the shell-side condensation with horizontal position is the best that gives the maximum value of the coefficient. But if condensation is carried out in the tube-side, then for horizontal position hci is calculated by the following two equations and higher of the two values is considered.
  r ðr  rv Þ g (15-596) i hci ¼ 0:76 kL L L mL s h This equation is Nusselt’s equation and valid for stratified flow. where: hci ¼ condensation coefficient, W/m2.
C kL ¼ thermal conductivity of liquid condensate, W/m
C. rL ¼ density of liquid condensate, kg/m3 rv ¼ density of vapor, kg/m3 g ¼ acceleration due to gravity, 9.81 m2/s. mL ¼ viscosity of liquid condensate (N.s/m2) or kg/m.s. sh ¼ horizontal tube loading or flow of condensate per unit length of tube, kg/(m.s) All liquid condensate properties such as kL, rL, mL must be determined at mean temperature of the condensate film. sh ¼

Wc L  Nt

(15-597)

where: L ¼ tube length, m Wc ¼ total condensate flow, kg/s Nt ¼ total number of tubes   ii

" 0

hci ¼ h i

1þ

pffiffiffiffiffiffiffiffiffiffiffiffi# rL =rv 2

(15-598)

where: Nt ¼ number of effective tubes for condensation L ¼ tube length, ft W ¼ condensate flow rate, lb/h

where: h0 i ¼ 0:021

 kL 0:43 Re0:8 c Prc di

(15-599)

Heat Transfer Chapter | 15

The above equation is referred to as the BoykoKruzhilin equation and is valid for annular flow. h Rec ¼ Reynolds number for the condensate film ¼ 4s m

357

The total unit size is the sum of the area requirements for condensation plus subcooling of the liquid to the desired outlet temperature. For the subcooling portion:

L

Pr ¼ Prandtl number of liquid condensate ¼ CpkLL mL where CpL and mL and kL are properties of liquid condensate that must be determined at the mean temperature of condensate film. For vertical properties:
1=3 rL ðrL  rv Þ g (15-600) hci ¼ 0:926 kL mL s h where, sv ¼

Wc N t p di , Wc v Rec ¼ 4s mL

¼ mass flow rate of liquid conden-

sate, kg/s., This equation is also referred to as Nusselt equation, valid for Rec  2000. For Re > 2000, use Boyko-Kruzhilin equation, given in Equation 15-598.

Condensing Inside Horizontal Tubes The correlation of Akers, et al. [1] has given good results in some industrial designs. The authors report that some vertical and inclined tube data are also correlated on the same basis. The sharp break in the data occurs around a Reynolds number of 5 104, as shown in Figure 15-198. The mass flow rate used to correlate is the arithmetic average of inlet and outlet liquid condensate and vapor flows:   1=2 (15-601) Ge ¼ GL þ Gg r1 rg where: Ge ¼ equivalent mass flow inside tubes, lb/h (ft2 of flow cross-section) GL and Gg ¼ arithmetic averages of condensate and vapor flow respectively, lb/h (ft2 of flow cross-section) The relation applies to systems that potentially are condensable as contrasted to those systems containing noncondensable gases such as air, nitrogen, etc. The entire vapor does not have to be condensed in the unit for the correlation to apply.

Subcooling Condensate in Vertical Tubes Methods for predicting heat transfer and pressure drop for single-phase flow of liquids should be used for the subcooling zone of the condenser. The condensate may still contain some bubbles that have not yet condensed, but their effect on thermal performance will not be significant. The flow may be either laminar or turbulent. For internally enhanced tubes, an appropriate method for the particular enhancement operating in the single-phase mode should be used.

1. McAdams [82] recommends:

cm1=3  4W 1=3 hcm qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ¼ 0:01  k mf pDi k31 r2f g m2f

(15-602)

2. The mean temperature of condensate film before subcooling [82]. tm ¼ tsv  3ðtsv  tw Þ=8

(15-603)

where: tsv ¼ temperature of saturated vapor tw ¼ temperature of surface

Vertical Tube Bundles, Single-Pass Downward Figure 15-199 is the semi-empirical curve of Colburn [30] as recommended by Kern [70]. Upward flow should be avoided as the film coefficient falls considerably below the value for the downward flow; however, see later section for details. The condensation inside vertical tubes is similar to the mechanisms for condensation outside each tube. As the condensate flows down the tube (inside), the liquid film becomes thicker and normally changes from streamlined to turbulent flow at some point between the top and bottom of the tube. Accordingly, the local film coefficient decreases until the fluid film becomes turbulent, and then the film coefficient increases. Colburn [30,70] has indicated that at a point on Figure 15-199 where 4G0 /mf ¼ 2,100 the transition occurs, and the mean coefficient for condensation inside a vertical tube when 4G0 /m > 1,200 satisfies the entire tube. Nusselt’s recommendation is 4G0 /mf ¼ 1,400 [70]. The distance from the top of the tube to the transition region is expressed as [70]: 5=3

xc ¼

2; 668lmf 2=3 r k g1=3 ðTv  tw Þ

(15-604)

where: units are previously listed Tv ¼ temperature of vapor,
F tw ¼ temperature of tube wall,
F xc ¼ distance from top (effective) of tube, ft

Condensing Single-Pass Up-Flow in Vertical Tubes This mechanical configuration is not the usual situation for most vapor condensers; however, it is convenient for special

358

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-199 Condensation down-flow in vertical tubes. Note: hcm ¼ average value of condensing coefficient between two points; G0 ¼ condensate loading, lb/(hr)(ft) ¼ w0 / P, lb/(hr)(lin. ft); w0 ¼ W/Nt, lb/(hr)(tube); W ¼ condensate, lb/hr; p ¼ perimeter, ft per tube. (Used by permission: Colburn, A. P. Transactions of American Institute of Chemical Engineers, V. 30, ©1934. American Institute of Chemical Engineers. All rights reserved.)

arrangements and in particular for mounting directly above a boiling vessel for refluxing vapors. It can also be used in special designs to take very hot vapors and generate steam; however, for all cases, a very real limitation must be recognized. Clements and Colver [29] developed the modified Nusselt equation to correlate hydrocarbon and hydrocarbon mixtures in turbulent film condensation:
3 2 0:75 hx x x grl l ¼ Nux ¼ 1:88  108 (15-605) k1 m1 k1 DT with an average deviation of date of 35.7%, where: x ¼ distance film has fallen g ¼ gravitational constant r1 ¼ liquid density l ¼ latent heat of vaporization m ¼ liquid viscosity k ¼ liquid thermal conductivity DT ¼ temperature difference ¼ (Tbubble Nux ¼ local Nusselt number, hxx/k1 hx ¼ local heat transfer coefficient

point

e Tsurface)

Note: The inner wall temperature data agreed with the bubble point temperature. Figures 15-200 and 15-201 illustrate the test performance data, which are valuable in understanding the mechanism.

Non-shear or Gravity Controlled Condensation Nusselt’s correlations account for condensation on banks of horizontal tubes, and the theory does not follow transitional or turbulent flow in the condensate. Studies have been carried out to extend Nusselt’s theory to non-shear transitional

FIGURE 15-200 Turbulent film condensation of light hydrocarbons and their mixturesdup-flow. (used by permission: Clements, L. D., and Colver, C. P. AIChE Heat Transfer Symposium V. 131, No. 69, ©1973. American Institute of Chemical Engineers. All rights reserved.)

(30 < ReL < 1,600) and turbulent (ReL > 1,600) flow patterns. Chun and Kim [398] have combined several of these relationhips to represent non-shear condensation on the outside of vertical tubes (or a flat surface) as: !1=3 ho m2L 1=3 ¼ 1:33ReL þ 9:56 kL rL ½rL  rg  g  106 Re0:89 Pr0:94 þ 8:22  102 L L (15-606)

Heat Transfer Chapter | 15

359

vg ¼ vapor velocity Tf ¼ condensing film temperature Tsat ¼ saturation temperature Tv ¼ vapor temperature Tw ¼ wall temperature rL ¼ liquid density rv ¼ vapor density l ¼ latent heat of condensation.

FIGURE 15-201 Typical condenser temperature profiles for 43% propane57% n-butane mixture at 176 psi abs.dup-flow. (Used by permission: Clements, L. D., and Colver, C. P. AIChE Heat Transfer Symposium, V. 131, No. 69, ©1973. American Institute of Chemical Engineers. All rights reserved.)

where: ReL ¼

rL vgL L mL ðnonshearÞ

and: PrL ¼

CPL mL kL

Equation 15-606 is valid for 10 < ReL < 31,000 and 1.75 < PrL < 5.0 For condensation on a vertical surface with no significant vapor shear, ho is [399]: 314 2 k3L rL ðrL  rg Þ g l 5 ho ¼ 0:943 4 ðTs  Twall Þ mL L

(15-607)

Various studies have been conducted into the use of extended surfaces to enhance condensation, as condensers play an important role in the refinery and chemical processing industries. Ways to enhance condensation due to cost and size of traditional condenser configurations have been investigated. As space becomes more valuable and emphasis on profit increases, designers continually explore alternative solutions to condensation duties. The fluted plate heat exchanger performs very well in the condensation of vapors. This type of exchanger is designed with enhancements that complement the benefits of typical extended surface condensers. A common method of improving condensation efficiency is to use extended surfaces to allow the vapor to be in continuous contact with the cold metallic surface. Condensation takes place at the top of the convex ridges, as shown in Figure 15-202. Surface tension forces can then pull the condensate into the concave sections of the plate; the condensate drains downward and exits the plate. The condensation coefficient that results is greater than that for a similar system with uniform or increasing film thickness. The fluted metallic block heat exchanger takes advantage of the extended surface condensation as well as some additional enhancements to maximize condensing efficiency. Further, use of a short vapor flow path combined with a small hydraulic diameter allows efficient heat transfer with a low pressure drop. Additionally, as the condensate level is maintained lower, film temperature is reduced and the local heat transfer coefficient in the condensate is increased as turbulent flow develops at lower Reynolds

For condensation on a horizontal tube with no significant vapor shear, ho is [398]: 3  k3L rL ðrL  rg g l 5 ho ¼ 0:725 4 ðTs  Twall Þ mL D 2

1 4

Condensate Vapor

Vapor

Vapor

(15-608)

where: D ¼ tube diameter CPL ¼ liquid heat capacity g ¼ gravitational constant kL ¼ liquid thermal conductivity ho ¼ condensing side film heat transfer coefficient L ¼ tube-side or surface length ReL ¼ liquid Reynolds number PrL ¼ liquid Prandtl number

Cool surface

FIGURE 15-202 Extended surfaces increase vapor contact with the cool metal surface.

360

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

number due to a decreased film thickness. These factors contribute to make the fluted plate exchanger an efficient condenser [400].

Flooding Flooding in an up-flow in a vertical condenser is an important design consideration, because it poses a limit on flows for any selected design. To select the number of tubes required to obtain the area for up-flow without flooding, the diameter of the tube sheet to hold these tubes becomes quite large. The selected number of tubes, to obtain the actual heat transfer required, may dictate that they are very short, e.g. 2 or 3 ft long. This is an unrealistic design. Therefore, tube size may change the balance for the design, or it may be impractical, and a down-flow unit may be more economical. For a given size of vertical condenser in up-flow, the lightest liquid and gas rates occur at the entrance to the tubes; therefore flooding begins at this location. Some advantages exist for particular applications, including: (a) Mounting vertically over refluxing equipment as it can save a separator and instruments, (b) Often lower fouling rates for the tube-side due to the liquid washing effect, and (c) Fractional condensation of multi-component mixture allowing lighter components to flow out vertically. According to English et al. [42], the correlation for the flooding condition is:  0:09 rG m0:14 ðcos qÞ0:32 ðL=GÞ0:07 G ¼ 1550 D0:3 r0:46 1 s 1 (15-609) where: D ¼ tube inside diameter, in. G ¼ superficial vapor mass flow rate, lb/h ft2 (total vapor entering base of vertical condenser tube) L ¼ superficial liquid mass flow rate, lb/h ft2 (liquid leaving the base of the condenser tube, plus entrained liquid) m1 ¼ liquid viscosity, centipoise rG ¼ gas density, lb/ft3 r1 ¼ liquid density, lb/ft3 s ¼ surface tension, dynes/cm q ¼ tube taper angle (measured from horizontal), degrees According to this investigation, the allowable gas rate at flooding can be increased by having the outlet tube ends extend through the bottom tube sheet and be cut off at an angle to the horizontal, rather than just a “square” cut-off.

The angle measured from the horizontal for a vertical tube is as follows: Angle

% Increase* in Maximum Allowable Gas Rate

30


5

60


25

75


54

*Increase compared to square end tubes q ¼ 0


The studies of Diehl and Koppany [35] further examined vertical up-flow limitations. The critical diameter above which the flooding velocity is independent of diameter is given by: dic ¼ where:

s ; in: 80

(15-610)

di ¼ inside tube diameter Subscript c ¼ critical condition s¼ surface tension of liquid, dynes/cm For example, consider Dowtherm at 20 in. Hg vacuum: s ¼ 20:8 dynes=cm dic ¼

20:8 ¼ 0:26 in: 80

Now, at 20 psig, s ¼ 13.05 dynes/cm dic ¼

13:05 ¼ 0:16 in: 80

Therefore for flooding in vertical tubes for a range of these conditions, the tube ID must be greater than 0.26 in.; generally, the recommendation is to use 0.5e1.0 in. ID tubes, approximately, to move far enough away from the critical condition. A criterion given by Hewitt and Hall-Taylor [402] is that flooding should not occur if the following condition is satisfied: i h 1=2 1=4 1=2 1=4 uV rV þ uL rL < 0:6 ½g di ðrL  rV Þ1=4 (15-610A) where uV and uL are the velocities of the vapor and liquid based on each phase flowing in the tube alone and di is the inside diameter of the tube in meters. The critical condition will occur at the bottom of the tube, so the vapor and liquid velocities should be evaluated at this point. Flooding correlation, (no tapered inlet tube considered): !0:5 !0:5 s s ; for F1 F2 > 10 (15-611) Vf ¼ F1 F2 rg rg

Heat Transfer Chapter | 15

For : F1 F2

s rg

2 Vf ¼ 0:714F1 F2

s rg

!0:5

Vf ¼ 4:34 ft=s

< 10 !0:5 31:15 5

(15-612)

where: h . s i0:4 . s  F1 ¼ di ; for di < 1:0 80 80 . s  F1 ¼ 1:0 for di  1:0 80 F2 ¼ ðL=GÞ

0:25

(15-613) (15-614) (15-615)

By assuming no entrainment in each condenser tube, the liquid rate flowing out of the tube must equal the vapor rate entering the tubes (assuming no noncondensables), so L/G ¼ 1, and at steady state, F2 ¼ 1. Using the Dowtherm figures cited previously at 20 in. Hg. vacuum: s ¼ 20:8 dynes=cm rg ¼ 0:0877 lb=ft s rg

3

!0:5 ¼ 15:4

Vf ¼ F1 F2

s rg

361

(15-616)

!0:5

By comparing with solving for the same conditions using a 1 in. tube in the English [42] correlation at 20 in. Hg vacuum, Vf ¼ 14.02 ft/s, compared to 15.4 ft/s from the preceding calculation. English’s [42] flooding correlation incorporates an entrainment load of E/G from 0.01e0.05 lb liquid per lb or vapor. The effect of the tapered inlet tube (as earlier discussed) as now determined by English [42] is only significant at the 60
and 75
tapers, which both produce about the same increase in vapor capacity. Diehl’s correlation is shown in Figure 15-203. where: E ¼ superficial liquid entrainment rate, lb/h/ft2 F1, F2 ¼ correlation factors defined by equations Vf ¼ superficial flooding velocity of the vapor, ft/s Vf7 ¼ superficial flooding velocity of the vapor when inlet tube taper is 70
, ft/s Example 15-28. Desuperheating and Condensing Propylene in Shell

See Figure 15-204. A refrigeration system requires that 52,400 lb/h of propylene refrigerant vapor from the compressors be desuperheated and then condensed. Propylene inlet: 265 psia and 165
F Propylene dew point: 265 psia and 112
F Cooling water in: 90
F

(15-617)

Vf ¼ ð1Þð1Þð15:4Þ ¼ 15:4 ft=s This is the velocity of the vapors in the tube, which will result in flooding at this low pressure. For the condition of 20 psig pressure: s ¼ 13:05 dynes=cm rg ¼ 0:5587 lb=ft s rg

!0:5



13:05 0:5587

¼

3

0:5 ¼ 4:83

F1 ¼ F2 ¼ 1 Because s rg

!0:5

2 Vf ¼ 0:714F1 F2

s rg

< 10

(15-618)

!0:5 31:15 5

(15-619)

FIGURE 15-203 Effect of entrance tube taper on flooding velocity. (Used by permission: Diehl, J. E., and C.R. Kop Company, Chemical Engineering Progress Symposium, Heat Transfer, V. 65, No. 92, ©1968. American Institute of Chemical Engineers. All rights reserved.)

362

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-204 Exchanger ratings and specification for propylene condenser.

Heat Transfer Chapter | 15

Assume that this load can be handled best by two units operating in parallel. In this scenario, if one condenser develops trouble, the entire refrigeration system, and consequently the plant process, is not shut down. Heat Duty Heat content of propylene vapor at 165
F, Btu/lb Heat content of propylene vapor at 112
F, Btu/lb Sensible heat duty ¼ 52,400 (512e485) Btu/h Latent heat of vaporization at 112
F, Btu/lb Latent heat duty, Btu/h ¼ 52,400 (126),

¼ 512 ¼ 485

¼ 126 ¼ 6,600,000

6; 600; 000 ¼ 90 þ 5:76 ¼ 95:8
F ð1; 145; 000Þð1Þ

For log mean temperature differences, see Figure 15-40. DTLMTD desuperheating ¼

ð68  16:2Þ  68  ¼ 36:1
F 2:3 log 16:2

DTLMTD condensing ¼ 19
F Temperature difference correction for desuperheating section only; see Figure 15-41A for one shell pass, two or more tube passes. P ¼

t2  t1 97  95:8 ¼ 0:0173 ¼ T1  t1 165  95:8

R ¼

T1  T2 165  112 ¼ 44:2 ¼ t2  t1 97  95:8

Note that in reading the chart, the values are off the scales, but by approximate interpolation, a value of F ¼ 1.0 is not unreasonable. In any case, the error in using this value will be small. No correction is necessary for the condensing section. Assume overall U values to establish initial order-ofmagnitude of area required: Condensing U ¼ 130 Btu/h ft2
F Desuperheating ¼ 35 Btu/h ft2
F Area estimated ¼ A ¼

6; 600; 000 1; 415; 000 þ 130ð19Þ 35ð36:2Þ

¼ 2; 670 þ 1; 118 ¼ 3; 788ft

2

Try two parallel units of approximately 1,894 ft2 each. Select: 3 /4 in. OD tubes  12 BWG cupro-nickel x 16 ft, 0 in. long Outside surface per lin ft, ¼ 0.1963 ft2 No: tubes ¼

Use two passes in tubes; tubes on 1 in. triangular pitch. From the tube count in Tables 15-15AeF, a 29 in. ID shell will hold 646 tubes, including an allowance for tie rods. The number of tubes per pass ¼ 646/2 ¼ 323. Tube-side coefficient:  8; 015; 000 Btu=h total water flow unit ¼ ¼ 573; 000 lb=h ð2Þð7
FÞ Volumetric flow rate; gpm :

¼ 1,415,000

Water Required Assume a 7
F rise in sea water temperature, the water flow rate: lb water/h ¼ (6,600,000 þ 1,415,000)/(1)(7
) ¼ 1,145,000 Water temperature at the dew point: t ¼ 90 þ

363

1; 894 ¼ 645 ð0:196Þð15 ft long tubesÞ

¼ 1, 147 gpm Volumetric flow rate, ft3/s:  gal ft3 in  1147 $ ð7:48Þ ð60Þ min gal 60s 3 ¼ 2:55 ft s

¼

Flow area for water ¼ (323) (0.233 in.2/tube)/144 ¼ 0.5 ft2 Velocity of water through tubes ¼ 2.55 ft3/s/0.5 ft2 ¼ 5.1 ft/s From Figure 15-80A or B, for water, hi ¼ 1,200 Btu/h (ft2) (
F) Reference to outside surface, tube I.D. ¼ 0.532 in.  0:532 2
¼ 850 Btu=hðft Þð FÞ hio ¼ 1; 200 0:75 Shell-side coefficient: condensing. Assume 2/3 of the tube length is used for condensing y 10 ft. Referring to Figure 15-186, 2/3 Tube loading ¼ Go00 ¼ W/LN2/3 t ¼ (52,400/2)/ (10) (646) Go00 ¼ 26,200/(10) (74) ¼ 35.1 lb/lin. ft Propylene properties at 112
F (liquid): Sp. gr. ¼ 0.473 mf ¼ 0.087 centipoise kf ¼ 0.0725 Btu/h (ft2) (
F/ft) Read, ho ¼ 320, use 300 Btu/h (ft2) (
F) Overall U for condensing: Assume: water side fouling ¼ 0.002, h ft2
F/Btu Propylene side fouling (oil) ¼ 0.0005, h ft2
F/Btu Neglect tube wall resistance. 1 1 1 ¼ þ 0:0005 þ 0:002 þ U 300 850 1 ¼ 0:00333 þ 0:0005 þ 0:002 þ 0:00117 ¼ 0:0070 U 2 
 F U ¼ 143 Btu=hr ðft Condensing area ¼ A ¼

ð6; 600; 000=2Þ 2 ¼ 1; 216 ft unit ð143Þð19Þ

Shell-side coefficient: vapor desuperheating or cooling. Tube length allowed for this ¼ approximately 15 ft  10 ft ¼ 5 ft. Refer to Figure 15-205. Assume a baffle cut of 25% and spacing as shown.

364

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Area required for gas cooling: Agc ¼

ð1; 415; 000=2Þ 2 ¼ 497 ft per unit ð39:4Þð36:1Þ

Total area per unit: A ¼ 1; 220 þ 497 ¼ 1; 717 ft

2

Total area available per unit: A ¼ ð0:196Þð15:5 ftÞð646Þ ¼ 1; 960 ft2 Note that this assumes 3 in. as the thickness for each tube sheet: 16 ft:  6 in=12 ¼ 15:5 ft: FIGURE 15-205 Illustration for Example 15-28.

Note that allowance must be made for the entrance nozzle, which often means that baffles cannot be spaced too close to the tube sheet. Tube bundle cross-flow area: as ¼ (Ds) (c’) (B)/144 (p) c’ ¼ 0.25 in. between tubes as ¼ (29 in.) (0.25) (8 in.)/144 (1 in. pitch) as ¼ 0.403 ft2 Gs ¼ W/as ¼ (52,400/2)/0.403 ¼ 65,000 lb/h (ft2) Vapor properties at 140
F cp ¼ 0.55 Btu/lb (
F) ka ¼ 0.0128 Btu/h (ft2) (
F/ft) m0 ¼ 0.0109 centipoise m ¼ 0.0109 (2.42) ¼ 0.0264 lb/h (ft) Vapor density ¼ 2.2 lb/ft3 ðcp m=ka Þ1=3 ¼ [(0.55) (0.0264)/0.0128]1/3 ¼ 1.042 The Reynolds number for Figure 15-84: Dc ¼ 0:73 in y ð0:73=12Þ ft  ð0:73 in:=12Þð65; 000Þ Re ¼ De Gs m ¼ 0:0264 ¼ 149; 800 Reading Figure 15-84 jH ¼ 240  1=3  0:14 j k cr m m ho ¼ H Dc ka mw m=mw ¼ approximately 0:5 as lowest ratio 240ð0:0128Þð1:042Þð0:9Þ ð0:73=12Þ    ho ¼ 47:3 Btu h ft2 ð
FÞ

ho ¼

For overall U cooling, assume: water side fouling ¼ 0.002 h ft2
F/Btu propylene side fouling ¼ 0.001 h ft2
F/Btu neglect tube wall resistance: 1 1 1 ¼ þ 0:001 þ 0:002 þ U 47:3 850 ¼ 0:0212 þ 0:001 þ 0:002 þ 0:00117 ¼ 0:02537 2

U ¼ 39:4 Btu=h ðft Þ ð
FÞ

00

Overall 00 factor of safety ¼

1; 960  1; 717 ð100Þ ¼ 14:2% 1; 717

This is not excessive. Area available for gas cooling ¼ (5 ft) (0.196) (646) ¼ 633 ft2 Area calculated required for gas cooling ¼ 494 ft 633  494 ð100Þ ¼ 28% 494 Area available for condensing ¼ ð10:5 ftÞ ð0:196Þ

Percent extra area ¼

2

ð646Þ ¼ 1330 ft

Area calculated required for condensing ¼ 1220 ft Percent extra area ¼

2

1; 330  1; 220 ð100Þ ¼ 9% 1; 220

The baffling for the gas cooling area could be adjusted to make more area available for condensing, thereby balancing the unit a little better. In operation, these areas will become balanced, and some condensing will undoubtedly take place in the gas cooling area. In either case, the unit size is within a range that allows reasonable plant operating flexibility without increasing the capital cost of the unit significantly. For the tube-side pressure drop, refer to Figure 15-98: At 5.1 ft/s Read 15 psi/100 ft of tube Tube length ¼ (15/100) (16 þ 16) ¼ 4.8 psi Allow 20% for fouling: Dp ¼ 4.8 (1.2) ¼ 5.76 psi From Figure 15-99, For two-pass exchanger: 1 1 1 Total ¼ 3

entrance return Exit

At 5.1 ft/s tube velocity, Dpr ¼ 0.7 psi/pass Then: 3 (0.7) ¼ 2.1 psi (This is conservative, as some designers use (1) (0.7) ¼ 0.7 psi per pass to cover a unit of this type). Total tube-side Dpr ¼ 5.76 þ 2.1 ¼ 7.86 psi This should be the maximum expected value.

Heat Transfer Chapter | 15

jH ¼ 182, from Figure 15-84.

Shell-side pressure drop due to gas cooling: Reading Figure 15-100 at Re ¼ 149,800, fs ¼ 0.0017 from chart/1.2 ¼ 0.00142 Dps ¼ ¼

fs G2 Ds ðNc þ 1Þ 0:14

2grDe ðm=mw Þ

ð0:00142Þð65; 000Þ2 ð29=12Þð7 þ 1Þ 2ð4:17  108 Þð2:2Þð0:73=12Þð0:9Þ

Dps ¼ 1:16 psi The pressure drop due to condensing is usually negligible in a unit of this type. As a maximum, it may be taken as one-half of the gas flow drop calculated for one baffle. This would be 1.16/8 ¼ 0.145 psi for the condensing portion. Note that this does not recognize tube supports at 50% cut area, but for pressure units, this pressure drop will be nil.

Example 15-29. Steam Heated Feed Preheater-Steam in Shell

Design a preheater for heating the feed to a distillation column. The 54,180 lb/h of feed consists primarily of ethyl benzene and styrene and is to be heated from 50
F to 207
F. Steam is available at 10 psig. The average physical properties of the feed have been calculated over the temperature range, at 128
F: Molecular weight Specific heat, cp, Btu/lb
F Viscosity, cP: Thermal conductivity, Btu/lb. (ft2) (
F/ft) Density, lb/ft3 Heat duty Q ¼ (54,180 ) (0.428) (207 e 50), Btu/h

104 0.428 0.4765 0.0891 53.4 3,640,000

Heat Transfer Surface Required Try an 18 in. diameter shell unit with 82  1 in. OD  12 BWG steel tubes  12 ft long  6 pass tubes. Tube I.D., in. ¼ 0.782 Tubes/pass ¼ (82/6) ¼ 13.67 " # 2 ð0:782Þ ð0:7854Þ cross-section=pass ¼ 13:67 ¼ 0:0455 ft2 ð144Þ tube velocity ¼

ð54; 180Þ ¼ 6:20 ft=s ð53:4Þð3; 600Þð0:0455Þ

D ¼

ð0:782Þ ¼ 0:06512 ft; tube I:D: ð12Þ

G ¼

  ð54; 180Þ ¼ 1; 190; 000 lb=h ft2 ð0:0455Þ

Re ¼

ð0:06512Þð1; 190; 000Þ ¼ 67; 250 ð0:4765Þð2:42Þ

365

  1=3  0:14 k cr m m hi ¼ hi ¼ ð182Þ D ka mw
0:333 ð182Þð0:0891Þ ð0:4281Þð0:4765Þð2:42Þ hi ¼ ð0:06512Þ 0:0891 ¼ ð249Þ ð5:55Þ0:333    hi ¼ 440 Btu h ft2 ð
FÞ 1=hi ¼ 1=440 ¼ 0:002270 1/hio ¼ (0.002270) (1.00/0.782) Assume inside fouling rio ¼ (0.0010) (1.00/0.782) Tube resistance 1/k Assume outside (steam) fouling ro Steam side film, ho, assumed: 1/ho ¼ 1/1,500 Sr

¼ 0.00290 ri ¼ 0.001 ¼ 0.00128 ¼ 0.00024 ¼ 0.00050 ¼ 0.00067 ¼ 0.00559

Note for oil-free steam, it is usually quite safe to assume the steam film heat transfer coefficient ¼ 1,500 Btu/h.ft2
F. Most calculated values will be considerably greater than this. Uo ¼ 1/0.00559 ¼ 179 Btu/h (ft2) (
F) The log mean temperature difference, DTLMTD:

239.3°F

239.3°F

207.0°F

50.0°F

Δt1 = 32.3°F

Δt2 =189.3°F

DTLMTD ¼

ð189:3  32:3Þ 157:0 ¼ ¼ 88:79o F

 ln ð5:8607Þ 189:3 ln 32:3

DTLMTD correction ¼ 1.0, because this is total condensing on one side. area required ¼

ð3640; 000Þ 2 ¼ 229 ft ð179Þð88:79Þð1:0Þ

Area available ¼ ð82Þ ð11:75Þ ð0:2618Þ ¼ 252 ft2 Safety factor based on fouling condition : ¼ y10% Tube-Side Pressure Drop Re ¼ 67,200 From Figure 15-97, f ¼ 0.000165 G ¼ 1,190,000 lb/h ft2 D ¼ 0.06512 ft L ¼ 12.00 ft n ¼ 6.00 passes rL ¼ 53.4 lb/ft3

ð252Þð100Þ ¼ 1:10 ð229Þ

366

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Dpt ¼

ð0:000165Þð1; 190; 000Þ2 ð12:00Þð6:0Þ ð2Þð417; 000; 000Þð53:4Þð0:06512Þ

¼ 5:80 psi; uncorrected for tube passes For pass corrections use fluid flow expansion and contraction as an illustration of one approach to these pressure drop calculations. Assume channel diameter ¼ 17.25 in. (based on approximate layout) Sectional area of channel ¼ ð17:25Þ2 ð0:7854Þ ¼ 233:7 in:2 y17:25 in: diameter 2

Sectional area of tubes ¼ ð82Þ ð0:782Þ ð0:7854Þ ¼ 39:4 in:2 y7:1 in: diameter d 7:1 ¼ ¼ 0:410 D 17:25 Because the number of tubes per pass is equal per pass, assume that the corresponding area of the channel is equal for all passes. Use the data from Table 2-2 and Figure 2-21, Chapter 2, Fluid Flow, Volume 1, 3rd Ed. Reading data from Standards of the Hydraulic Institute: K contraction ¼ ð0:375Þð6 pass þ 1 exit nozzleÞ ¼ 2:63 K expansion ¼ ð0:700Þð6 pass þ 1 inlet nozzleÞ ¼ 4:90 SK ¼ 7:53 Static head, hL ¼ Kv2/2g ¼ 7.53 (6.20)2/2 (32.2) ¼ 4.5 ft liquid Dp Dh ¼ 2:31 ; ft: Sp:Gr or

Dh ðSp:GrÞ ; psi: Dp ¼ 2:31 4:51  1:0 ¼ 1:95 psi: 2:31 Dpt ¼ 5:80 þ 1:95 ¼ 7:75 psi ¼

Use 8.5 psi for design purposes. Shell-Side Pressure Drop: Negligible The unit proposed has been checked as satisfactory for the service. Other designs could be assumed and balanced for reasonable velocities, pressure drops and area.

shell-side baffles are to be steel. The acid vapor is essentially at its dew point. The specification sheet summarizing the design is given in Figure 15-206. Solution: Heat Load 1,496.8 lb/h HCl from 178
F to 90
F 156.6 lb/h H2O vapor from 178
F to 90
F 1,653.4 lb/h to condenser 2. Condense: 149.6 lb/h H2O vapor and 102 lb/h HCl ¼ 251.6 lb/h Condensing heat ¼ 902.1 Btu/lb condensed 1. Cool:

Q cooling ¼ (1,496.8) (0.192) (178  90) ¼ (156.6) (0.450) (178  90) Q condensing ¼ (902.10) (251.6) Total heat duty

¼ 25,300 Btu/h ¼ 6,200 Btu/h ¼ 227,000 Btu/h ¼ 258,500 Btu/h

Water Temperature Rise 60 gpm ¼ ½60

gal ft3 lb in   62:3 3  60 min h 7:48 gal ft

y 30; 000 lb=h DT ¼

Q ð258; 500Þ ¼ ¼ 8:62
F Wcp ð30; 000Þð1Þ

Exit water temperature ¼ 70 þ 8:62 ¼ 78:62
F DT Determination (Water Available at 70
F)
F Vapor side 178 165 145 125 104 90

Q, Btu/hr 0 87,900 172,700 220,400 251,500 258,500


F Water 78.62 75.69 72.86 71.27 70.23 70.00

DT (Vapor-Water) 99.4 89.3 72.1 53.7 33.8 20.0

Integrated DT ¼ 76:48
F; see Figure 15-207 Log mean temperature difference is not used because the distribution of the exchanger area varies through the unit, due to changing heat load. DT correction: use Figure 15-41 178  90 88 ¼ ¼ 0:815 178  70 108 78:62  70 8:62 ¼ ¼ 0:0979 R ¼ 178  90 88

P ¼

Example 15-30. Gas Cooling and Partial Condensing in Tubes

Design a partial condenser to cool a mixture of hydrogen chloride-water vapor from 178
F to 90
F using 60 gal per min of chilled water at 70
F. The unit is to have the acid mixture in the tubes, because this will allow for a cheaper construction than if this material were in the shell. The tubeside material is to be impervious graphite, and the shell and

DT correction ¼ 0.935 DT corrected ¼ (76.48) (0.935) ¼ 71.5
F (integrated value) Tube-Side Coefficient Tubes are 11/4 in. OD  7/8 in.I.D.

Heat Transfer Chapter | 15

FIGURE 15-206 Exchanger rating specifications for hydrogen chloride partial condenser.

367

368

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Allowing for the spread of data and tending to be conservative, use 85% of value read from the chart: Use, f ¼ 85  1=3 ð85Þð0:280Þ 0:615  3:15 1=3 ¼ ð326:5Þð6:92Þ ð0:0729Þ 0:280   2 hi ¼ ð362:5Þ ð1:904Þ ¼ 622 Btu h ft ð
FÞ hi ¼

Referencing to outside of tube: hio ¼

FIGURE 15-207 Heat duty variation with temperature difference as vapor flows through unit.

Sensible Gas Cooling Coefficient mv ¼ 0.0358 lb/h (ft) D ¼ 0.0729 ft cp ¼ 0.217 Btu/lb (
F) (avg.) ka ¼ 0.00979 Btu/h (ft2) (
F/ft) Re ¼

Condensing Coefficient Use method of Akers et al. [1] (method preferably used for pure pressure rather than mixed vapors). Ge ¼ GL þ Gg ðrL =rv Þ

1=2

GL ¼ ð0 þ 251:6Þ=2 ¼ 125:8 lb=h    GL ¼ 125:8 0:1128 ft2 ¼ 1; 115 lb=h ft2 cross-sect:  2  55 ð3:14Þ 0:875 Flow cross-section area=pass ¼ 2 ð4Þ 12 2 ¼ 0:1148 ft pass Gg ¼ average mass velocity of vapor; in to out: 
1; 653:4 þ 1; 401:8 1 1527:6 ¼ ¼ ð2Þ 0:1148 0:1148   2  Gg ¼ 13; 310 lb h ft tube cross-sect 1=2

Gg ðrL =rv Þ

1=2

¼ 13310 ð72:4=0:0831Þ

¼ 392900   2  Ge ¼ 1; 115 þ 392; 900 ¼ 394; 015 lb h ft cross  sect Avg: mol: wt: ¼ 33:14 þ 36:36=2 ¼ 34:75 Note: 114
F is integrated average temperature for the following physical properties. rL at 114
F ¼ 72.4 lb/ft3 cpt at 114
F ¼ 0.615 Btu/lb (
F) kat at 114
F ¼ 0.280 Btu/h (ft2) (
F/ft) mL at 114
F ¼ 1.30 centipoise (35 wt. % avg.) ¼ 3.15 lb/(h) (ft) Note: 1 cP ¼ 2.42 lb/h.ft Re ¼

DGe ð0:0729Þð394015Þ ¼ 9120 ¼ mL 3:15

Reading Figure 15-198, f ¼

 1=3 hcm D cr m ¼ 100 ka ka

ð622Þð0:875Þ ¼ 436 Btu=hðft2 Þð
FÞ ð1:250Þ

Gg D 0:0729 x 13310 ¼ 0:0358 mv

¼ 27; 100 jH ¼ 90:0 ðsee Figure 15-84Þ k cr m1=3 h i ¼ jH D k  1=3 ð90Þð0:00979Þ 0:217  0:0358 hi ¼ ¼ ð12:10Þð0:794Þ1=3 ð0:0729Þ 0:00979  2
hi ¼ ð12:10Þ ð0:9262Þ ¼ 11:20 Btu h ft F  0:875
¼ 7:84 Btu=h ft2 F hio ¼ 11:20 1:25 Shell-Side (Water) Coefficient Use 4 in. baffle spacing and 25% cut baffles in 6 in. OD shell Use flow rate ¼ 30,000 lb/h Shell-side equivalent diameter: h p 2. i 4 ðp=2Þð:86ÞðpÞ  do 4 2 dc ¼ pdo 2 # " 1:625 p ð1:25Þ2 4 ð:86Þ  1:625  4 2 2 ¼ p ð1:25Þ 2 de ¼ 1.06 in y 0.0886 ft De’ ¼ 0.0886 ft Shell-side bundle cross-flow area: as ¼

ðDs Þðc0 ÞðBÞ ð15:25Þð0:375Þð4Þ ¼ ¼ 0:0977 ft2 pð144Þ 1:625ð144Þ

Gs ¼ (30,000) / (0.0977) ¼ 307,000 lb/(h ft2) m (water at 74.3
F) ¼ 0.931 centipoise ¼ 2.25 lb/(h ft) Res ¼

ð0:0886Þð307; 000Þ ¼ 12; 088 ð2:25Þ

Heat Transfer Chapter | 15

jH ¼ 6.10, Figure 15-84 cp ¼ 1.0 ka ¼ 0.348 Btu/h (ft2) (
F/ft)

369

Overall U Calculation

 1=3 k cr m1=3 ð61:0Þð0:348Þ 1:0  2:25 h o ¼ jH ¼ De k ð0:0886Þ 0:348

U ¼

258; 500 Btu ¼ 43:2 ð83:6Þð71:50Þ h ft2
F

Overall U Used (Based on the Over-size Unit)

ho ¼ 446 Btu/h (ft2) (
F) Fouling Factors and Tube Resistance Assume inside fouling factor ¼ 0.00010 Assume water side (shell) fouling factor ¼ 0.0015 Tube resistance for 3/8 in. impervious graphite wall: rt ¼ Lw =k ¼

0:375 1; 020 Btu=hðft2 Þð
F=inÞ

U ¼

Density Avg. Vapor Flow @ Avg. Temperature of 134
F, 0.65 psig Avg. MW vapor @ inlet and exit avg. conditions ¼ 34.65 rv ¼

rt ¼ 0.000368 Condensing Surface Area Uo ¼

1 1 1 þ ri ðdo =di Þ þ rt þ ro þ hio ho

1 1 1 þ 0:001ð1:25=0:875Þ þ 0:000368 þ 0:0015 þ 436 446 1 ¼ 127:7 Btu=hðft2 Þð
FÞ Uo ¼ 0:00783 Area: A ¼ Q=U Dtcorr ¼

ð258; 500Þ Btu ¼ 23:0 ð157Þð71:50Þ h ft2
F

ð34:65Þð15:35Þð520Þ 3 ¼ 0:0835 lb=ft ð379Þð14:70Þð594Þ

Shell-Side DP Re ¼ 12,088, previous calculation, from Figure 15-100 f ¼ 0.00205 Dps ¼

fs G2s D0s ðNc þ 1Þ 2grD0e fs

where: Number of baffles ¼ 22 g Gs De’

¼ ¼ ¼ ¼ ¼ ¼

D0 s rL f

ð227; 000Þ 2 A ¼ ¼ 24:9 ft ð127:6Þð71:50Þ

4.17  108 ft/h2 307,000 lb/h (ft2) 0.0886 ft 15:25 12 ¼ 1:27 ft: 62.27 lb/ft3 essentially 1.0 2

Dps ¼

Sensible Gas Cooling Area Uo ¼

1

1 1 þ 0:001428 þ 0:000368 þ 0:0015 þ 7:84 446 1 Uo ¼ 0:1276 þ 0:001428 þ 0:000368 þ 0:0015 þ 0:002242 1 ¼ 7:51 Uo ¼ 0:133138 ð25; 300 þ 6; 200Þ Area: A ¼ ¼ 58:7 ft2 ð7:51Þð71:50Þ

Total Area A ¼ 24.9 þ 58.7 ¼ 83.6 ft2 “Safety Factor,” or excess area: % S.F. with unit containing 157 ft2 ¼ 157/83.6 ¼ 1.878 ¼ 87.8% This is normally too large a value to be considered an economical design. However, in this case, future flow rates indicate that the 157 ft2 will be close to the needed area. Rather than handling and providing piping and special valves for two units, it is cheaper and easier from an operational viewpoint to install one large unit at this time.

ð0:00205Þð307; 000Þ ð1:27Þð22 þ 1Þ ð834; 000; 000Þð62:27Þð0:0886Þ

Dps ¼ 1.23 psi; use 2.25 psi for system allowances Note that this pressure loss does not account for nozzle entrance or exit losses. These losses may be neglected provided velocities are low and no unusual conditions are imposed upon these connections. For low pressure systems, these losses cannot be ignored. Tube-Side Pressure Drop Re ¼ D Gt/mv m gas @ 114
F: 90.25 mol % HCl in feed, 99.7 wt % exit avg. Wt. % HCl ¼ 95.0 wt. % m0 ¼ ð0:950Þ ð0:0150Þ þ ð1 þ 0:950Þ ð0:0105Þ ¼ 0:01478 centipoise m y 0:0358 lb=ft h Re ¼

ð0:0729Þð13; 560Þ ¼ 27; 650 ð0:0358Þ

f ¼ 0:000204 ðFigure 15-97Þ 2

Dpt ¼

ð0:000204Þð13; 560Þ ð6Þð2Þ ¼ 0:089 psi ð2Þð417; 000; 000Þð0:0831Þð0:0729Þ

rv ¼ at 114
F and 1 atm ¼ 0.0831 lb/ft3

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For bundle entrance and exit losses, refer to copyrighted graph of Donohue [38]. Dpr ¼ (0.051) (2) ¼ 0.102 psi Dptt calculated total ¼ 0.089 þ 0.102 ¼ 0.191 psi Dptt used ¼ (0.191) (1.2) ¼ 0.23 psi

Condensing Vapors in the Presence of Noncondensable Gases Condensation in the presence of a noncondensable gas occurs in numerous heat exchanger applications. The most common example is dehumidification in an air-conditioning system, in which water vapor is partially condensed out as the humid air passes through the evaporator. Another example is shell-side condensation in surface condensers used in power plants. In this instance, a small fraction of air that is dissolved in the feedwater eventually arrives at the condenser together with the steam, where of course it cannot condense. Its concentration therefore builds up near the exit region of the condenser if it is not removed by a steam ejector or some other similar device. In chemical processing plants and refineries, noncondensable gases may be present in the process vapor that leaves a distillation column to go to the overhead condenser, or is produced in a reactor prior to a feed effluent heater. A stream containing a noncondensable gases and vapors to be condensed must be considered so that the continually changing gas vapor physical properties (and some thermal properties), gas film heat transfer coefficient and mass gas flow rate are adequately represented. This operation is usually a constant pressure process. The vapor condenses at its dew point on the tubes, thereby providing a wet surface; and the vapor of the stream diffusing through this film condenses into the liquid of the condensate on the tube (see Figure 15-208). The sensible heat and latent heat of the vapor are transferred through the gas film and the liquid film to the tube surface (except when considerable subcooled condensate film exists, in which case there may be condensation or fogging in the gas film). The rigorous method of design of Colburn [30] and Colburn and Hougen [31] involving trial and error calculations is considered to be the most accurate of the various alternative procedures published to date. Kern [70] presents a very useful analysis of special design problems with examples. The effect of a noncondensable gas in the system alongside a condensable vapor is to significantly reduce the condensing side film coefficient. Henderson and Marcello [62] present data to illustrate the effect. Figures 15-209, 15-210 and 15-210 A present the effect of DT with a steamair system and toluene nitrogen. The following is a reasonable shortcut approach that can be acceptable for many applications, but certainly is not as accurate as the Colburn-Hougen [30,31] method.

FIGURE 15-208 Condensable vapors in presence of a noncondensable gas.

H ¼

1 1 þ Cy

(15-620)

where: H ¼ heat transfer coefficient ration, hm/hNu hM ¼ effective heat transfer film coefficient, Btu/h-ft2
F hNu ¼ condensing film coefficient by Nusselt equation Btu/h-ft2-
F y ¼ mol (volume) percent noncondensable gas in bulk stream C ¼ see following Table [62] % Range Noncondensable

% Standard Deviation

System

C

Steam-air

0.51

0.64e25.1

9.2

Toluene nitrogen

0.149

0.71e59.1

8.7

Benzenenitrogen

0.076

7.1e20.3

14.3

Figures 15-209, 15-210 and 15-210A and Equation 15-620 represent the effective reduction of the pure component (condensable) when inert gases are present, resulting in the reduced effective heat transfer for condensing the mixture. Although it is not stated in the study, from a practical industrial standpoint the effects of air, nitrogen and other

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FIGURE 15-209 Heat transfer ratio for toluene and nitrogen.

FIGURE 15-210A Influence of air content on the heat transfer coefficient of steam containing air.

Condensation of Condensable Mixtures in Horizontal Tubes

FIGURE 15-210 Heat transfer correlations for steam and air system.

common inert gases can be expected to be about the same for other organic systems. A computer program developed by Volta [121] handles the problem of condensing in the presence of a noncondensable gas for down-flow of either a saturated or superheated gas vapor mixture inside vertical tubes. The program is based on a modification of Colburn-Hougen and Bras and is certainly more accurate and easier to use than the lengthy manual calculations. Although the program was written for vertical tubes, it can be used to approximate the result in a horizontal unit, and if the correction factor between vertical and horizontal units and the correction factor between vertical and horizontal tube condensation is applied, the comparison may be improved. The method uses diffusion coefficients. An example using vertical tubes is included. The survey of Marto [181] includes several excellent references to this topic. The proposal of Rose [182] is reported to give good agreement with selected experimental data.

The Silver-Bell-Ghaly method [403] has successfully been applied to predict condensation of miscible mixtures in which all components are condensable but no noncondensable gases are present. When condensing a mixture, the vapor phase must be cooled as the dew point temperature of the mixture falls along the tube, in addition to removing the latent heat. The process is controlled by condensation and by single-phase cooling of the vapor. This approach assumes two things with respect to cooling of the vapor [394]: l

l

Mass transfer has no effect on the single-phase heat transfer process in the vapor. The vapor occupies the entire tube cross-section in determining the vapor phase heat transfer coefficient.

The error in ignoring the first assumption becomes significant for mixtures with large condensing temperature ranges, so their method is reliable for mixtures with small to medium condensing ranges (say smaller than 30 K). The second assumption is conservative, since interfacial waves in annular flows augment the vapor phase transfer coefficient. The effective condensing heat transfer coefficient aeff for condensation of a mixture is determined by: 1 1 ZG ¼ þ aeff aðxÞ aG

(15-621)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

When implementing Equation 15-621, the condensation heat transfer coefficient a(x) is obtained with an in-tube correlation for pure fluids using the local physical properties of the mixture. The single-phase heat transfer coefficient of the vapor aG is determined with the Dittus-Boelter turbulent flow correlation using the vapor fraction of the flow in calculating the vapor Reynolds number. The parameter ZG is the ratio of the sensible cooling of the vapor to the total cooling rate: ZG ¼ xcpG

dTdew dh

(15-622)

where: x ¼ the local vapor quality cpG ¼ the specific heat of the vapor dTdew dh ¼ the slope of the dew point temperature curve with respect to the enthalpy of the mixture as it condenses. (i.e., the slope of the condensation curve) Cavallini et al. [404] have employed this method to hydrocarbon mixtures and to binary and ternary zeotropic refrigerant blends, and Smit, et al. [405] have applied it to binary refrigerant mixtures. Butterworth [406] has provided a detailed description of multi-component condensation.

Condensation of Superheated Vapor Cooling of superheated vapors involves condensation when the wall temperature is below the saturation temperature of the vapor, or one of its components is a mixture. To determine whether condensation occurs, a stepwise computation of the wall temperature is required using the cooling fluid’s heat transfer coefficient and the single-phase heat transfer coefficient of the vapor phase in the thermal resistance analysis. The temperatures of the hot and cold fluids vary along the flow path of the superheated vapor and the local values are used to calculate the wall temperature of the vapor side. If the wall temperature goes below the saturation temperature, then condensation of the superheated vapor will occur in the thermal boundary layer on the tube wall, even though the bulk vapor is superheated. Since condensing heat transfer is much more effective than single-phase heat transfer to a vapor, it is essential to include this effect in the thermal design of the condenser if this zone is significant with respect to the saturated condensing zone. It is common practice to use the same thermal design equation as in the saturated zone to estimate the condensing heat transfer coefficient in this desuperheating zone. The saturated zone method should be determined at a vapor quality of 0.99 and not at 1.0 since some of these methods will “crash” at a vapor quality of 1.0 or go to the single-phase turbulent flow heat transfer coefficient.

BOILING AND VAPORIZATION 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. 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. Nucleate 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 toward 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. Pool 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 15-211 shows a schematic of a boiling curve, showing the regions in the curve. Direct and visual photographic evidence shows that: 1. The nucleate boiling region BC in Figure 15-211 consists of two parts: (a) The isolated bubble region, where bubbles behave independently as illustrated in Figure 15-212A; and (b) The slugs and column region, where the bubbles start to merge and to depart from the heated surface

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373

(A)

E The regions of the curve A to B: natural- convection single-phase liquid – there is no boiling in this region

C

B to C: nucleate boiling

D

F to D to E: film boiling

(B)

Heat flux, (W/m2)

106

(C)

B

105

F

A

1

10

100

1000

ΔTsat (K)

FIGURE 15-211 Boiling curve from a heat- flux controlled surface.

FIGURE 15-212 Visualization results in nucleate and film boiling.

by means of jets which then form large bubbles, or slugs, above the surface (Figure 15-212B). 2. The film boiling region (FDE in Figure 15-211) illustrates where the heated surface is covered with a layer of vapor (Figure 15-212C). 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 15-211) 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 15-213A and B illustrate a typical flux curve for water and hydrocarbons. In the region 1e2, the liquid is being heated by natural convection; in 2e3 nucleate pool boiling occurs, with bubbles forming at active sites on the heat transfer surface, and natural convection currents being set up. Q/A varies as Dtn where n is 3e4, and the peak flux is at point 3, corresponding to the critical Dt for nucleate boiling; at point 3 film boiling begins; and at 4e5e6 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 ¼ 300 Btu/h ft2
F (1,703 W/m2 K) for organics, Umax ¼ 1,000 Btu/h ft2
F (5,768 W/m2 K) for water and (Q/A)crit ¼ 12,000 Btu/h ft2
F (37,855 W/m2 K)

FIGURE 15-213A Heat flux for boiling water at 212
F. (Used by permission: McAdams, W. H. Heat Transmission, 3rd Ed., ©1954. McGraw-Hill Book Co. All rights reserved.)

for organics. 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
F (63,092 W/m2), allowing for a higher DT driving force [408]. 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

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

10

10 (e)

(d)

10

10

10

10

100

1000

FIGURE 15-214 Typical saturated pool boiling curve.

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 15-214 illustrates the classic curve of heat flux vs. temperature difference between surface and liquid saturation temperature for saturated pool boiling. Table 15-83 gives the descriptions of the regimes in Figure 15-214.

Vaporization During Flow

FIGURE 15-213B Heat transfer behavior 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.)

vs. outside the tubes; smooth vs. enhanced tubes surfaces, etc. The maximum heat flux is generally expressed as a function of the reduced pressure, Pr ¼ 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 e.g. a bundle correction factor for boiling outside the tubes, factors for enhanced surfaces are applied.

Vaporization Mechanisms or processes occur during which a liquid at its 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,

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, 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. Mixtures often present problems in the design of reboilers, as shown in Figures 15-215 and 15-216. In this case, where a wide range of mixtures enters a reboiler, the

Heat Transfer Chapter | 15

375

TABLE 15-83 Description of the Typical Saturated Pool Boiling Curve of Figure 15-214 Regime

Description

a. The natural convection

The natural convection regime characterized by a DT less than about 10
F. 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 e 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 vaporliquid 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 the 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 (TwTsat) increases. For water at 1 atm, this occurs at a temperature difference of 100260
F. 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 (TwTsat), (c) the thermophysical properties of the liquid (d) the thermophysical properties of the heat transfer surface and (e) the frequency of contact between the liquid and the tube wall at any given location.

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).

first vapor to be generated is rich in the low boiling components, leaving behind a liquid which is enriched in the high boiling components, especially in the immediate surroundings of the heat transfer surface. The light components must diffuse through this barrier to the surface to

vaporize. A greater driving force is therefore required than is indicated by the mixed mean composition of the remaining liquid. Measuring the heat flux as a function of the boiling surface temperature and comparing this to the saturation temperature for the bulk mixture shows there is

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Boiling surface

Composition entering reboiler

Vapor generation zone

Vapor

Equilibrium conditions, 25%

Actual concentration of heavy component

First vapor generated

T

Bulk liquid

Equilibrium concentration of heavy component

Bubble point Liquid Temperature

0

x, Fraction light component

1.0

FIGURE 15-215 T-x diagram for vaporization of a binary showing equilibrium conditions at start of vaporization and after 25% boilup.

ΔT Assuming well-mixed liquid

FIGURE 15-217 Temperature and concentration profiles after significant boilup for a binary mixture.

and they can be installed either horizontally or vertically as shown in Figure 15-218. They are referred to as: l l l l

Tsurface – Tbubble point of liquid phase remaining

ΔT Actual l

l

h Actual

l

h h Apparent

0

x, Fraction light component

1.0

FIGURE 15-216 Typical diagram of apparent and actual h and DT for boiling a binary, as a function of composition

an apparent result in a decrease in heat transfer coefficient at compositions intermediate to the pure components, as shown in Figure 15-217. The effect here is a distortion of the temperature driving force and that the heat transfer coefficient itself is in fact a monotonically changing function from the pure light component to the pure heavy component. Vaporizers, usually termed reboilers for chemical or petrochemical plant operations, are classified by circulation and reboiler position. These can be either natural circulation with available liquid head, or forced circulation with a pump

Horizontal Vertical Internal Horizontal or vertical as shell and tube units operated by Natural circulation, which includes thermosyphon action Forced circulation or pump-through Horizontal kettle type units

Natural circulation reboilers can be divided into two categories, namely thermosyphon and pool boiling. Thermosyphon reboilers: These can be arranged vertically or horizontally depending on process design and available plot plan. They can be either once-through or recirculation. TEMA types AEL, BEM or NEN single pass fixed tubesheet designs with or without a shell expansion joint are the most commonly used for vertical thermosyphon reboilers. Generally, the boiling liquid is inside of 1 in. OD or larger tube. Medium or low pressure steam is used as the heating medium in the shell-side. The design incorporates a shell-side high point vent and low point drain through the tube sheet; minimizing the return vapor line pressure drop thus makes the piping design simple, a direct-couple nozzle connection between the reboiler top channel and tower is used. Where high fouling boiling is experienced, NEN with a removable channel cover shall be provided. TEMA “J”, “G”, or “H” shells are commonly employed in horizontal thermosyphon reboilers. When the service has a long boiling range, or liquid preheat duty exceeds 20% of the total duty, the “J” shell is an option. “G” or “H” shells are not suitable for boiling ranges over 40
F. The “J” shell design requires a pressure drop 1e2 psi, greater than “G”

Heat Transfer Chapter | 15

377

Internal reboiler

Kettle reboiler

Vertical thermosyphon

Horizontal thermosyphon

Once through natural circulation

Forced circulation FIGURE 15-218 Reboiler types.

and “H” shells, which require only 0.5e1.0 psi. For extremely low Dp and small boiling ranges, an “X” shell with pure cross-flow is preferred. For a high liquid head due to elevation difference between the tower and horizontal reboiler, a flow restriction such as a control valve or orifice is installed in the liquid line to reduce the head. Chen [408] provides a rule of thumb stating that for new equipment, the percentage vaporization should not be designed to exceed 30% for vertical and 40% for horizontal

thermosyphon reboilers. Existing vertical reboilers can allow up to 40% vaporization if the hydraulics perform well. Horizontal reboilers can allow up to 60% vaporization, and if more than 60% vapor is required, a forced circulation reboiler is designed if boiling liquid has to return to the tower. The once-through type thermosyphon reboiler withdraws liquid from the trap out tray and two-phase flow returns to the space below it. The liquid head is kept constant during

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

normal operation, as the circulation rate and the percentage of the vapor returned to the tower thus stay constant if the heat input is kept unchanged. Therefore, the once-through reboiler is considered as one equilibrium stage for a fractionation tower. In contrast to this, the circulation reboiler withdraws the liquid from the bottom of the tower, partially vaporizes the stream and returns it to the space between the bottom tray and the liquid level. This type of reboiler is not counted as an additional equilibrium stage. Forced circulation reboiler: This type of reboiler has the boiling liquid driven by a pump and it generally allows a Dp of 3e5 psi or higher and can be designed with a TEMA “E” shell with segmental baffles. This type of unit is recommended if the boiling fluid is extremely fouling, very viscous or solid bearing (i.e. a slurry). Additionally, it can be specified for vaporization that exceeds 40% and boiling liquid has to return to the tower and where a large circulation rate and heat transfer area are required. Pool boiling reboilers: The characteristics of these types are isothermal boiling and high vaporization fraction up to 100%. All pool boiling reboilers are horizontal. Kettle type reboilers offer a good choice in the refining and petrochemical industries because of their durability, reliability and flexibility of operation. An internal stab-inbundle inserted into the bottom section is not often seen in the refinery. TEMA-type AKT kettle reboilers are employed for high fouling heat media such as heavy oil or slurry process streams. A floating head construction provides access for tube-side cleaning. Type BKU is adopted when steam is used as the heat medium because of it low equipment cost and minimum steal leakage. Type BKM of fixed tube sheet geometry or NKN can be selected for clean boiling services on the shell-side. Table 15-84 provides a helpful breakdown of the major types and characteristics of vaporizers and reboilers used in industry, and Figure 15-219 illustrates a logic flow diagram for selecting a reboiler. See Table 15-84A too. For horizontal thermosyphon/natural units, the boiling fluid is almost always on the shell-side with the heating medium in the tubes. In vertical units, the reboiling of the fluids occurs in the tubes. For kettle units, the boiling occurs in the shell. Collins [185] suggest a “rule of thumb” that if the viscosity of the reboiler is less than 0.5 centipoise (cP), a vertical thermosyphon should be considered, but when the viscosity is more than 0.5 cP, a horizontal reboiler is probably more economical. Because reboilers are used extensively with bottoms boiling of distillation columns, the horizontal units have some advantages [185]. l l

High surface area. Process is on the shell-side, with possibility of less fouling, or easy access for cleaning the outside tubes.

l

l

l

Tubes have easy access for cleaning on tube-side, when fouled. Greater flexibility for operator handling high liquid rates. Lower boiling point elevation than vertical units.

Figures 15-220AeE illustrate horizontal and vertical thermosyphon reboiler flow arrangements. For distillation column bottoms heating, such as is shown in Figures 15-220A and B, the bottoms liquid from the column flows under system pressure and liquid head into and through the shell-side of the horizontal thermosyphon reboiler. The two-phase (liquid þ vapor) mixture flows from the reboiler back into the distillation column either on the bottom tray or just under it, into the column vapor space above the bottoms liquid, with the vapor passing upward into/through the bottom or first tray. The density difference between the liquid in the column and the two-phase mixture in the heat exchanger (reboiler) and the riser (outlet piping from the shell-side of reboiler) causes the thermosyphon circulation through the reboiler [186]. According to Yilmaz [186], the horizontal thermosyphon reboilers are less likely to be fouled by the process than kettle reboilers, due to their better circulation and lower percent vaporization. Vertical thermosyphon reboilers with process through the tubes, Figure 15-220D, are less suitable than horizontal units when heat transfer requirements are large, due to mechanical considerations; that is, the vertical units may often determine the height of the first distillation tray above grade. Also per Yilmaz [186], moderate viscosity fluids boil better in horizontal units than in vertical units. Lowfinned tubing used in horizontal units can improve the boiling characteristics on the shell-side. Due to the high liquid circulation rate for horizontal thermosyphon units, the temperature rise for the boiling process fluid is lower than for kettle reboilers (these are not thermosyphons). Ultimately, this leads to higher heat transfer rates for the horizontal thermosyphon units [186]. Hahne and Grigull [186] present a detailed study of heat transfer in boiling. A number of obvious advantages and disadvantages exist for either horizontal or vertical thermosyphon reboilers. For horizontal units, Yilmaz states that the TEMA types X, G and H (shown in Figure 15-220C) are in more common usage, and types E and J are often used. The choice depends on the heat transfer, fouling and pressure drop on the shell-side. The X Shell is considered to have the lowest comparative pressure drop, greater than H, G and J, with E having the best pressure drop. The circulation through the thermosyphon loop described earlier depends on the pressure balance of the system, including the static pressure of the liquid level, the inlet pressure drop and exit two-phase pressure drops to and from the reboiler, plus the pressure drop through the unit itself.

Heat Transfer Chapter | 15

379

TABLE 15-84 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.

6. 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.

2. Occupy less space.

2. Limited tube length, normally not over 16 ft.

2. Overall heat transfer coefficient, Uo is in the range of 90e160 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 tubesheet design. Horizantal thermosyphon reboiler

1. Moderate heat transfer rate.

1. Extra piping required.

1. Overall heat transfer rate, Uo is in the range of 70e100 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. Continued

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TABLE 15-84 Advantages and Disadvantages of Various Reboiler Typesdcont’d Type

Once-through natural circulation reboiler

Forced circulation reboiler

Advantages

Disadvantages

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 multi-shell 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.

1. As thermosyphon reboiler, has the flexibility to be either vertical or horizontal depending on tower elevation.

1. No control over circulation rate.

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.

4. For very large surface area equipment.

4. High operation cost.

5. Furnace reboiler

5. Leaking of material at stuffing box.

Remarks

1. Vaporization can be up to 40% of total inlet flow.

Forced circulation reboiler will be considered only when kettle-type or horizontal thermosyphon reboiler cannot work.

6. To avoid phase separation. 7. Enable erosion-corrosion balance. 8. Superheating is possible

Yilmaz [186] recommends that the maximum velocity in the exit from the horizontal thermosyphon reboiler be the work of Collins [186].  0:5 (15-617) Vmax ¼ 77:15 rtph where: Vmax ¼ maximum velocity in exit from reboiler, m/sec rtph ¼ homogeneous two-phase density, kg/m3

The arrangement of baffle plates and nozzles, as shown in Figure 15-220C, is important to prevent (a) tube vibration, (b) maldistribution of the process boiling fluid and (c) poor heat transfer coefficients due to uneven and stratified flow resulting in uneven and “dry spot” heat transfer from nonuniform tube wetting, and others [186]. The work of Heat Transfer Research, Inc., has contributed much to the detailed technology; however, this information is proprietary and released only to subscribing

Heat Transfer Chapter | 15

381

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

No

Is isothermal or narrow range boiling?

No

Yes

Is boiling side slurry flow? No

Yes Yes Is fraction of preheating duty to total duty < 10%?

No

Huge heat duty and circulation rate? No Is liquid viscosity > 0.5?

Yes Is vaporization ratio < 40%?

Kettle

Is vaporization ratio < 25%?

Yes No Is reboiler duty very small?

Yes

No

Is reboiler one theoretical stage?

Yes

Yes Stab in reboiler

No

No

Forced circulation reboiler

Horizontal circulation

Horizontal oncethrough Vertical oncethrough

No

Yes

Wide boiling range?

Is reboiler one theoretical stage?

Yes No “H” shell

Yes “J” shell

No Vertical recirculation

FIGURE 15-219 Flow chart for selecting reboilers ref [409].

member organizations. Yilmaz [186] comments that several “unexpected” results have developed from the current horizontal reboiler research studies: l

l

These units provide higher heat fluxes at the same mean temperature difference. These units are superior in thermal performance to vertical tube thermosyphon units.

l

These units are superior in thermal performance to kettle reboilers.

Figure 15-221A compares horizontal and vertical units in the same hydrocarbon boiling service at low pressures, and shows that the horizontal units are more favorable in the same service than vertical units, particularly when the mean temperature difference is low. Figure 15-221B

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

compares horizontal and vertical thermosyphon units with kettle reboilers when boiling the same hydrocarbon mixture; also see Fair [46], Jacobs [273] and Rubin [278]. One way to ensure that a reboiler operates in the nucleate boiling region in order to prevent control problems is to limit the heat flux, by designing the exchanger for either a maximum U or a maximum overall mean temperature difference (MTD) across the exchanger. Alternatively, some design criteria require only that a certain maximum heat flux value ðQ=AÞcrit is not exceeded. Heat flux limit: as a rule of thumb, the maximum heat fluxes recommended for nucleate boiling design are [408]:

FIGURE 15-220A Horizontal thermosyphon reboiler. (A). Recirculating feed system. (B). Once-through feed system. Both are natural circulation. (Used by permission: Yilmaz, S. B. Chemical Engineering Progress, V. 83, No. 11, ©1987. American Institute of Chemical Engineers. All rights reserved.)

Bottom section of distillation column Downcomer

L

W/m2
C 5,1102

Kettle reboiler

9,000

Thermosyphon reboiler

15,000

8,5170

Stripper reboiler

25,000

14,1950

In these cases, the exchanger area is increased to reduce the flux below the specified maximum value. Design methods that arbitrarily over surface a heat exchanger by specifying a maximum flux or heat transfer coefficient to address the film boiling issue are not always successful, as it is more effective to limit the overall MTD such that DTcrit is not exceeded. Thus, the selection of the heating medium and design of the process control scheme are critical to the success of the design [408]. Modern design programs such as that offered by Heat Transfer Research Inc. (HTRI: www.htri.net/), together with physical property databases, such as AIChE’s Design Institute for Physical Properties Research (DIPPR) database, predict the critical boiling heat flux for many fluids and alert the designer to potential film boiling problems. There are instances where constraints may be imposed on the maximum allowable heat flux based on operating experience. For example, the heat flux in crude oil heaters is typically limited to 8,000 Btu/h ft2
F

Tray liquid V

Btu/h ft2
F

Liquid + vapor mixture

V = Vapor L = Liquid

L

LC

Thermosyphon reboiler Liquid

Steam

Condensate Bottoms liquid Bottoms product

FIGURE 15-220B A typical horizontal thermosyphon reboiler.

Heat Transfer Chapter | 15

383

Qc

WD, LE, O

WR

WF, EF

FIGURE 15-220C Shell types selected for horizontal and thermosyphon reboilers, boiling in shell. (Used by permission: Yilmaz, S. B. Chemical Engineering Progress, V. 83, No. 11, ©1987. American Institute of Chemical Engineers. All rights reserved.) X (V) QB

X, EB (I)

WB, EB (I)

FIGURE 15-220E Reboiler heat balance.

FIGURE 15-220D Vertical recirculation thermosyphon reboiler.

(25,237 W/m2) based on the tendency of crude oil to foul at higher heat fluxes. While such experience-based values may appear to be very conservative compared with those derived from empirical formulae, it is essential to obtain as much information as possible about the system before deciding which methods to use to define limits on heat flux and temperature difference. Because the critical heat flux is a function of MTD and DTcrit , it is perhaps more meaningful to know the critical temperature difference. Adding excess surface area is an artificial means of limiting the heat flux, since it does not change U or MTD, which are functions of the physical properties of the system. Table 15-85 shows typical values of maximum flux and DTcrit for pool boiling, and Figure 15-222 shows a heat flux curve for a vertical thermosyphon reboiler that uses steam to boil trichlorosilane (TCS) at 95
C. Qmax¼ 40,000 W/m2 at DTcrit ¼ 14o C. There is a significant dead zone between the transition and

FIGURE 15-220F Nozzle connections for vertical thermosyphon reboilers.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

nucleate boiling region and thus to prevent control problems. The transition region should be avoided, because an increase in the heating medium flow rate and or temperature can result in a lower overall duty. Hagan and Kruglov [401] have provided systematic steps for the design of a reboiler.

Vaporization in Horizontal Shell; Natural Circulation

FIGURE 15-221A Heat transfer data of reboilers boiling a pure hydrocarbon at low pressure in horizontal and vertical reboilers. (Used by permission: Yilmaz, S. B. Chemical Engineering Progress, V. 83, No.11, p. 64, ©1987. American Institute of Chemical Engineers. All rights reserved.)

FIGURE 15-221B Heat transfer data of reboilers boiling a hydrocarbon mixture in horizontal and vertical thermosyphon reboilers compared to a kettle reboiler. (Used by permission: Yilmaz, S. B. Chemical Engineering Progress, V. 83, No. 11, p. 64, ©1987. American Institute of Chemical Engineers. All rights reserved.)

film boiling regions, and from 60
C to 90
C, where an increase is DT has no effect on the heat flux, which results in a difficult system to control [408]. It is good engineering practice (GEP) to design a reboiler to operate in the

Kern [70] deserves a lot of credit for developing design methods for many heat transfer situations, and in particular the natural circulation phenomena as used for thermosyphon reboilers and shown in part in Figures 15-220AeD. The horizontal natural circulation systems do not use a kettle design exchanger, but rather a 1e2 (1 shell-side, 2 tube-side passes) unit, with the vaporized liquid plus any liquid not vaporized circulating back to a distillation column bottoms vapor space or, for example, to a separate drum where the vapor separates and flows back to the process system and where liquid recirculates along with makeup “feed” to the inlet of the horizontal shell and tube reboiler. See Figures 15-220AeC. A large proportion of vaporization operations in industry are handled by horizontal kettle units. The kettle design is used to allow a good vapor disengaging space above the boiling surface on the shell-side, and to keep tubesheet and head end connections as small as possible. Services include vaporizing (reboiling) distillation column bottoms for reintroducing the vapor below the first tray, vaporizing refrigerant in a closed system (chilling or condensing on the process steam side) and boiling a process stream at constant pressure. The tube-side may be cooling or heating a fluid, or condensing a vapor. Physically, the main shell diameter should be about 40% greater than that required for the tube bundle only. This allows the disengaging action. The kettle unit used in the reboiling service usually has an internal weir to maintain a fixed liquid level and tube coverage. The bottoms draw-off is from the weir section. The reboiling handled in horizontal thermosyphon units omits the disengaging space, because the liquid-vapor mixture should enter the distillation tower where disengaging takes place. The chiller often keeps the kettle design but does not use the weir because no liquid bottoms draw off when a refrigerant is vaporized.

Pool and Nucleate Boiling e General Correlation for Heat Flux and Critical Temperature Difference The rate of heat transfer in nucleate boiling depends on the number of surface nucleation sites and the rate of formation

Heat Transfer Chapter | 15

385

TABLE 15-85 Maximum Flux at Critical Temperature Difference for Various Liquids Boiling in Pools Heated by Steam Condensing inside Submerged Tubes Tubes Liquid

Surface on Boiling Side

Liq. Temp. (
F)

Max. Flux Q/A

*Critical Dt, Dto (
F)

Ethyl acetate

Aluminumd

162a

42,000

80

a

62,000

57

a

77,000

70

a

43,000

100

a

50,000

80

a

55,000

80

a

69,000

100

a

72,000

60

a

70,000

100

a

82,000

100

a

47,000

83

a

58,000

79

a

53,000

55

a

54,000

90

a

80,000

66

a

93,000

65

a

120,000

55

a

Ethyl acetate Ethyl acetate Benzene Benzene Benzene Benzene Benzene Benzene Benzene Carbon tetrachloride Carbon tetrachloride Heptane Ethanol Ethanol Ethanol Ethanol Ethanol Propanol i-Propanol i-Propanol Methanol Methanol

d

162

Slightly dirty copper

d

162

Chrome-plated copper d

177

Slightly dirty copper d

177

Aluminum d

177

Copper

d

177

Chrome-plated copper d

177

Copper

d

177

Chrome-plated copper d

177

Steel

d

170

Dirty copper d

170

Copper

d

209

Copper

d

173

Aluminum Copper

173 d

173

Slightly dirty copper d

173

Grooved copper

d

173

126,000

65

d

127

67,000

91

d

151

Chrome-plated copper

Polished nickel-plated copper Polished nickel-plated copper

d

Polished nickel-plated copper d

90,000

84

a

110,000

96

a

78,000

92

a

120,000

110

a

175 149

Slightly dirty copper

d

149

Chrome-plated copper d

Methanol

Steel

149

123,000

105

Methanol

Copperd

149a

124,000

115

n-Butanol

New nickel-plated copperd

173

79,000

83

n-Butanol

New nickel-plated copperd

207

92,000

79

n-Butanol

New nickel-plated copperd

241a

105,000

70

i-Butanol

Polished nickel-plated copperd

222a

115,000

85

Water

Polished nickel-plated copperb

131

115,000

53

Water

Chrome-plated copperc

110

150,000

-

Water

Chrome-plated copperc

130

175,000

65

Water Water Water

b

155

190,000

-

c

150

220,000

64

c

170

243,000

64

New nickel-plated copper Chrome-plated copper Chrome-plated copper

Continued

386

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-85 Maximum Flux at Critical Temperature Difference for Various Liquids Boiling in Pools Heated by Steam Condensing inside Submerged Tubesdcont’d Tubes Liquid

Surface on Boiling Side

Water

Polished nickel-plated copperb

Water Water Water Water Water Water Water

b

New nickel-plated copper c b

Chrome-plated copper

b

New nickel-plated copper

b

Polished nickel-plated copper Chrome-plated copper d

Steel

Max. Flux Q/A

*Critical Dt, Dto (
F)

171

250,000

72

191

260,000

-

190

Chrome-plated copper

c

Liq. Temp. (
F)

300,000

70

212

a

330,000

80

212

a

360,000

68

212

a

370,000

72

212

a

390,000

72

212

a

410,000

150

*The overall temperature difference Dto is defined as the saturation temperature of the steam less the boiling temperature of the liquid. a Boiling at atmospheric pressure. b Steam side was promoted with Benzyl Mercaptan. c Steam side was promoted with Octyc Thiocyante. d Steam probably contained a trace of Oleic acid. Used by permission: McAdams, W. H. Heat Transmission, 3rd Ed., p. 386, ©1954. McGraw-Hill Book Co., Inc. All rights reserved.

FIGURE 15-222 A heat flux curve for a vertical thermosipon reboiler.

of bubbles from those sites. Therefore, it is expected that the heat transfer coefficient in nucleate boiling is greatly influenced by the type of surface and the liquid. Experimental investigations have attempted to relate the heat transfer rate to the number of nucleation sites. The most widely used

empirical correlation in nucleate boiling for surface heat flux is that developed by Rhosenow [409]:
3 1=2
ðrl  rv Þ g cp;l DTe (15-618) q ¼ ml hfg Cs;f hfg Prnl s

Heat Transfer Chapter | 15

where: cp,l ¼ specific heat of liquid at constant pressure hfg ¼ enthalpy of vaporization of the liquid at saturation temperature Prl ¼ Prandtl number of saturated liquid DTe ¼ excess temperature ml ¼ liquid viscosity rl ¼ liquid density rv ¼ vapor density s ¼ surface tension of liquid in its own vapor. The coefficient Cs,f and the exponent n depend on the surface-liquid combination. Table 15-86 shows representative surface-fluid combinations, and the term “cp;l DTe =hfg ” is referred to as the Jacob number. Figure 15-223 shows a typical characteristic curve of boiling from power-controlled method [407]. Kutateladze [410] and Zuber [191] developed an expression for the critical heat flux (the peak heat flux in the boiling curve, Figure 15-224 eTypical boiling curve for sat. water at atmospheric pressure) as:
1=4
1=2 p s g ðrl  rv Þ ðrl þ rv Þ hfg rv qc ¼ 24 r2v rl (15-619) Lienhard et al. [412] replace the constant ðp=24Þ by 0.149.

TABLE 15-86 Values Cs,f for Various Surface-Fluid Combinations Surface-Fluid Combination

Cs, f

n

Scored

0.0068

1.0

Polished

0.0130

1.0

Chemically etched

0.0130

1.0

Mechanically polished

0.0130

1.0

Ground and polished

0.0060

1.0

Water-brass

0.0060

1.0

Water-nickel

0.0060

1.0

Water-platinum

0.0130

1.0

Polished

0.0154

1.7

Benzene-chromium

0.101

1.7

Ethyl alcohol-chromium

0.0027

1.7

Water-Copper

Water-Stainless steel

n-Pentane-copper

387

The situation of film boiling beyond the Leindefrost point (Figure 15-224) is very similar to that of film condensation. In film condensation, a liquid film adheres to the surface and the saturated vapor is condensed to liquid at the interface. However, in film boiling, a vapor film adheres to the surface and a saturated liquid is vaporized at the interface. The rate of heat transfer in film boiling depends on the surface geometry but not on the surface condition, and one can use a similar expression to that developed for the case of film condensation. An equation for film boiling on a cylindrical and spherical surface is: 1=4
hconv D ðrl  rv Þ g h0 fg D3 ¼ C (15-620) NuD ¼ yv kv ðTw  Ts Þ kv where the constant C ¼ 0.62 for a horizontal cylinder and 0.67 for a sphere. A heated platinum plate at 115
C is submerged in water at one atmosphere pressure. Determine the rate of heat transfer per unit area. For nucleate boiling, Table 15-86 gives Cs,f ¼ 0.013 and n ¼ 1.0 . Solution Using Equation 15-618, the saturation temperature of water at one atmosphere pressure ¼ 100
C. The physical properties of water: rl ¼ 960 kg=m3 , rv ¼ 0:60 kg=m3 , hfg ¼ 2.26  106 J/kg, s ¼ 0:055 N=m, Therefore, DTe ¼ ð115  110Þ ¼ 15o C We take: cp,l ¼ 4.216 kJ/kg
C Prl ¼ 1.74 ml ¼ 2.82  104 kg/(m.s) g ¼ 9.81 m/s2 At this value of DTe, boiling is most likely nucleate (Figure 15-224).
 1=2
cp;l DTe 3 ðrl  rv Þ g (15-618) n Cs;f hfg Prl s 1=2
9:81ð960  0:60Þ ¼ ð2:82  104 Þ ð2:26  106 Þ 0:055
3 3  4:216  10  15  ¼ 4:04  105 kW m2 0:013  2:26  106  1:74

q ¼ ml hfg

Levy [77] presented a correlation showing good agreement for pool boiling and nucleate boiling heat transfer flux (Qb/A) below the critical Dt for subcooled and vapor-containing liquids. This covers the pressure range of sub-to-above atmospheric pressure, and is obtained from data from the inside and outside tube boiling. Qb kL cL r2L ðDTÞ ½1  x ¼ A s0 Ts ðrL  rv ÞBL 3

(15-621)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-223 Typical characteristic curve of boiling vis-à-vis the curve.

FIGURE 15-224 Typical boiling curve for saturated water at atmospheric pressure.

x ¼ vapor quality of fluid ¼ 0 for pool boiling and is a low fraction, about 0.1 to 0.3, for most nucleate boiling This is represented in Figures 15-225 and 15-226, where: kL ¼ thermal conductivity of saturated liquid, Btu/h (
F/ft) cL ¼ specific heat of liquid, Btu/lb (
F) rL ¼ liquid, lb/ft3 rv ¼ vapor, lb/ft3 s0 ¼ surface tension of liquid, Btu/ft2, (dynes/cm)  (0.88  107) ¼ Btu/ft2

FIGURE 15-225 Levy correlation for boiling heat transfer equation. (Used by permission: Levy, S. ASME paper no. 58-HT-8, ©1958. American Society of Mechanical Engineers. All rights reserved.)

DT ¼ temperature difference ¼ Tw  Ts,
R Tw ¼ temperature of tube heating surface,
R Ts ¼ saturation temperature of liquid,
R BL ¼ coefficient of Figure 15-226 hfg ¼ latent heat of evaporation, Btu/lb The value of this relationship is that it serves as a maximum limit that may be expected from a designed unit when comparing design Q/A versus Equation 15-621.

Heat Transfer Chapter | 15

FIGURE 15-226 Coefficient BL in Levy boiling heat transfer equation. (Used by permission: Levy, S. ASME paper no. 58-HT-8, ©1958. American Society of Mechanical Engineers. All rights reserved.)

Mikic and Rohsenow [86] present another boiling correlation for pool boiling, which includes the effects of the heating surface characteristics. It is important to design at values of temperature difference below the critical value separating nucleate and film boiling. The work of Cichelli and Bonilla [27] has produced much valuable data, including Figure 15-227, which represents the maximum temperature difference between the fluid saturation temperature and the metal surface for nucleate boiling [27]. This is valuable in the absence of specific data for a system. Equipment should not be designed at greater than these DT values, unless it is recognized that film boiling will be present and the performance will not be as efficient as if nucleate boiling were the mechanism. Figure 15-228 illustrates the effect of pressure on the nucleate boiling of ethyl alcohol [27]. The maximum heat flux, Q/A, as a function of reduced pressure for a system before the transition begins to film type boiling is shown in Figure 15-229A and B. In

FIGURE 15-227 Maximum D T for nucleate boiling correlation. (Used by permission: Cichelli, M. T., and Bonilla, C. F. Transactions, AlChE, V. 41, No. 6, ©1945. American Institute of Chemical Engineers. All rights reserved.)

389

general, a design should not exceed 90% of these peak values. Other correlations are available, some with special limitations and others reasonably general [97]. Table 1585 lists some values of maximum flux and critical DT for pool boiling. The values are very useful when quick data must be estimated or when guides and limits must be established. They are also applicable to natural circulation boiling in tubes. A well recognized and often-used equation for determining a reasonable, even if preliminary, nucleate boiling coefficient is represented by the McNelly equation for boiling outside of tubes: 0:3
0:6
2 0:425
Do Gv cf mf Pa (15-622) hb ¼ fðcL Gv Þ mf kL rL s where Gv ¼



 Q rL V rL ¼ Anf l rv Anf rv

(15-623)

where: hb ¼ boiling side film coefficient, Btu/h-ft2-
F f ¼ surface condition factor: For steel or copper ¼ 0.001 St. steel, nickel ¼ 0.0006 Polished surfaces ¼ 0.0004 Teflon, plastics ¼ 0.0004 cL ¼ liquid specific heat, Btu/lb-
F rL ¼ liquid density, lb/ft3 rv ¼ vapor density, lb/ft3

FIGURE 15-228 Maximum D T values occur at the indicated threshold of film boiling, a typical example using 100% ethyl alcohol from a clean surface. (Used by permission: Cichelli, M. T. and Bonilla, C. F. Transactions. AlChE, V. 41, No. 6, ©1945. American Institute of Chemical Engineers. All rights reserved.)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-229A Maximum heat flux (or burnout). (Used by permission: Cichelli, M. T. and Bonilla, C. E. Transactions. AIChE., V. 41, No. 6, ©1945. American Institute of Chemical Engineers. All rights reserved.)

FIGURE 15-229B Maximum boiling rate in the low pressure region. (Used by permission: Cichelli, M. T. and Bonilla, C. E. Transactions. AlChE, V. 41, No. 6, ©1945. American Institute of Chemical Engineers. All rights reserved.)

mf ¼ liquid viscosity, lb/ft-h Do ¼ tube OD, ft V ¼ vapor rate, lb/h Anf ¼ surface area of tubes, outside, ft2 Q ¼ heat duty, Btu/h, or Qb for boiling kL ¼ liquid thermal conductivity, Btu/h-ft-
F Pa ¼ absolute pressure of boiling fluid, lbf/ft2 s ¼ surface tension of liquid, lb/ft l ¼ latent heat of vaporization, Btu/lb s ¼ surface tension of liquid, Btu/ft2, (dynes/cm)  (0.88  107) ¼ Btu/ft2 l ¼ latent heat of vaporization, Btu/lb Film coefficients calculated by this equation, while useful, are quite strongly influenced by the effects of pressure of the system. In order to somewhat compensate

for this, variable exponents for the pressure term of the equation are used as follows: Pressure, psia

Exponent

Equation

2

Less than 10

2

10e30

1.9

30e300

1.8

> 300

1.7

Experience suggests that the McNelly equation should be used for the higher pressures and the Gilmour [53] equation should be used for low pressures; atmospheric and subatmospheric. In kettle-type horizontal reboilers, often the bundle heat transfer film coefficients obtained may be

Heat Transfer Chapter | 15

higher than those calculated by most of the single tube equations. This suggests the possibility of coefficient improvement by the rising agitation from the boiling liquid below. It is impossible to take this improvement into the design without more confirming data. If the bundle is to be large in diameter, it is possible that the liquid head will suppress the boiling in the lower portion of the horizontal bundle; thereby actually creating a liquid heating in this region, with boiling above this. Under such situations, the boiling in the unit cannot be considered for the full volume; hence, there should be two shell-side coefficients calculated and the resultant areas added for the total.

391

EXAMPLE 15-32 Reboiler Heat Duty After Kern [70]

See Figure 15-230 Assume 25,000 lb/h of a 50-50 mixture of light hydrocarbons (HC) to be separated into a 99.5% (wt) light HC overhead and bottoms of 5% (wt) heavier HC. The reflux ratio determined separately for the column is 3.0 mol reflux/ mol of overhead distillate. Solution Overall material balance: 25; 000 ¼ WD þ WB HC#1 ðmore volatileÞ : 25; 000 ð0:50Þ ¼ 0:995WD þ :05 WB Then simultaneously:

Reboiler Heat Balance Because a reboiler is usually used in conjunction with distillation columns, the terminology and symbols used here will relate to that application. Assume a column with an overhead total condenser and a bottoms reboiler (see Figures 15-220D and E). Assuming an all liquid feed, the heat balance is [70]: QR ¼ ðR þ 1Þ WD EDðVÞ  RWD EDð1Þ þ WB EBð1Þ  Wf Efð1Þ (15-624)

ð25; 000Þ ð0:05Þ ¼ 0:995 ð25; 000  WB Þ þ 0:05ðWB Þ 12; 500 ¼ 24; 875  0:995WB þ 0:05ðWB Þ 1; 237:5 ¼ 0:945 WB WB ¼ 13,095 lb/h total bottoms WD ¼ distillate total ¼ 25,000  13,095 ¼ 11,905 lb/h Assume using enthalpy and latent heat tables/charts. EB(1) ¼ 160 Btu/lb EF(1) ¼ 100 Btu/lb ED(v) ¼ 302 Btu/lb LV ¼ 135 Btu/lb Then, substituting into Equation 15-624, QR ¼ ð3:0 þ 1:0Þ ð11; 905Þ ð302Þ  ð3:0Þ ð11; 905Þ ð95Þ

where: R ¼ reflux ratio, mol condensate returned to column/ mol product withdrawn VRB ¼ vapor formed in reboiler, lb/h W ¼ flow rate, lb/h ED ¼ enthalpy of overhead product removed from column, Btu/lb Qc ¼ heat load or overhead condenser (removed in condenser), Btu/h QR ¼ reboiler duty or heat added, Btu/h L ¼ latent heat of vaporization, Btu/h EB ¼ enthalpy of bottoms, Btu/lb EF ¼ enthalpy of feed, Btu/lb

þð13; 095Þ ð160Þ  25; 000ð100Þ ¼ 14; 381; 240  3; 392; 925 þ 2; 095; 200  2; 500; 000     ¼ 10; 583; 515 Btu h 10:6  106 Btu h Total vapor to be regenerated by reboiler: ¼ 10; 583; 315=135 ¼ 78; 394 lb=h

Subscripts: B ¼ bottoms product c ¼ condensing v ¼ vapor l ¼ liquid R ¼ reboiler D ¼ overhead distillate product F ¼ feed For a heat balance around the entire column [70] with the feed being liquid or vapor: Heat In ¼ Heat Out : WF EFð1 or VÞ þ QR ¼ QC þ WB EBð1Þ þ WD EDð1Þ (15-625) See Vol. 2, 4th edition of this volume series for reboiler and condenser heat balances in a distillation column.

FIGURE 15-230 Kern correlation for natural circulation boiling and sensible film coefficientseoutside and inside tubes. (Used by permission: Kern, D.Q. Process Heat Transfer, 1st Ed., ©1950. McGraw-Hill Book Company. All rights reserved.)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Kettle Horizontal Reboilers Figure 15-231 shows a kettle horizontal reboiler that consists of either a U-bundle or a shell and tube bundle inserted into an enlarged shell. The enlarged shell provides disengaging space for the vapor outside and above the liquid, which is usually held by level control at the top level of the tube bundle or possibly a few inches below the top of the tubes. The heating medium is inside the tubes. Internal reboilers are similar in concept and designed to kettle units, but this style does not have a separate shell, as it is inserted into the circular shell of the sidewall of the distillation column or tank. For an example, see Figure 15239. It is inserted into the body of the liquid to be heated/ boiled. The level of the liquid is also controlled as described earlier. The mechanism of boiling is essentially nucleate pool boiling. In both styles of reboiler, the liquid velocity is relatively low compared to thermosyphon units [90,188]. Jacobs [188] provides an extensive comparison of the advantages and disadvantages of essentially all the reboiler types used in industrial plants. Palen and Taborek [91] have conducted extensive studies of available data and proposed nucleate boiling equations to correlate various data from the available 14 equations down to a selected six for detailed study. The study was limited to various hydrocarbons and hydrocarbon mixtures. Their conclusions after computer correlations of the results from several equations were as follows: Palen [90] recommendation corrects single tube boiling data (outside) to the bundle effect in a horizontal reboiler by: Revised boiling coefficient, hb ¼ hlt BCF This is limited by the maximum heat flux of approximately 12,000e25,000 Btu/(h) (ft2)

The bundle correction factor (BCF) for vapor blanketing: h

BCF ¼ how 0:714 p  Do4:2ð105ÞG i (15-626) 0:24½1:75þln ðl=NÞ  ½1=Nvc vc where: G ¼

ao ðU1 Þ ðDTÞ ¼ mass velocity of vapor (15-627) ðlÞ ðp  Do Þ

U1 is found by Equation 15-642 ¼ overall coefficient for isolated single tube, Btu/(h) (ft2) (
F). G ¼ mass velocity of vapor from a bottom tube based on the (p  Do) spacing, lb/(h) (ft2) ao ¼ tube outside heat transfer surface, ft2/ft p ¼ tube pitch, ft Do ¼ tube OD, ft Nvc ¼ number of tubes in the center vertical row of bundle l ¼ latent heat, Btu/lb DT ¼ mean temperature difference between the bulk of the boiling liquid and the bulk of the heating medium,
F hb ¼ corrected boiling coefficient, Btu/(h) (ft2) (
F) for bundle hlt ¼ nucleate boiling coefficient for an isolated single tube, Btu/(h) (ft2) (
F)

Maximum Bundle Heat Flux [91] Recommended limiting maximum heat flux [91] for the tube density coefficient: Db ðLÞ A 1=2 
P sin a ¼ 0:359 Do N 0:25
gsðr1  rv Þ j ¼ rv l r2v f ¼

qmax ¼ Kfj

(15-628)

(15-629) (15-630)

Gilmour’s bundle correction is hb ¼ h (Nrv)0.185 (vs)0.358, improved to hb ¼ h (Nrv)0.185 (vs/vc)0.385 Nrv ¼ number of holes in vertical center row of bundle vs ¼ superficial vapor velocity vc ¼ maximum flux vc ¼ qmax/lrv , where qmax comes from the Zuber equation (discussed separately)

FIGURE 15-231 Kettle reboiler.

The results for small bundles do not agree as well as the Palen and Taborek [91] equation. Determine qmax from Figure 15-232. Use a safety factor of 0.7 with Equation 15-

Heat Transfer Chapter | 15

630 per the recommendation of Reference 91 for conservative results. where: Db ¼ bundle diameter, ft L ¼ average bundle length, ft A ¼ bundle heat transfer surface, ft2 (outside) a ¼ tube layout angle, degrees N ¼ number of tube holes/tube sheet. Note: U tubes have two holes per tube, so N ¼ 2  number of tubes rv ¼ vapor density, lb/ft3 r1 ¼ liquid density, lb/ft3 g ¼ acceleration of gravity, ft/(h) (h) l ¼ latent heat, Btu/lb s ¼ surface tension, lb (force)/ft K ¼ empirically determined constant used as 176 in the range of f for bundles qmax ¼ maximum heat flux, Btu/(h) (ft2) j¼ maximum flux physical property factor, Btu/(ft3) (h)

393

p ¼ tube pitch, ft Do ¼ tube OD, ft The original Zuber [191] equation for maximum heat flux as modified by Palen [90] is:   0:25 0:5 ½ðrv þ r1 Þ=r1  ; qmax ¼ 25:8ðrv ÞðlÞ sðr1  rv Þg r2v  3 Btu=ðh:Þ= ft (15-631) Symbols are as defined previously. The tube density coefficient, f, is given in Table 15-87A. The tube wall resistance cannot be ignored for reboilers. Based on the outside tube diameter [91]: rw ¼


 Twall ao lnðao =ai Þ ao lnðDo =Di Þ ¼ kw ao  ai 2pkw

(15-632)

where:

FIGURE 15-232 Maximum heat flux: boiling outside horizontal tubes; kettle and internal reboilers. When using the estimate from this curve, a safety factor of 0.7 also should be used. (Used by permission: Palen, J. W., and Small, W. M. Hydrocarbon Processing, V. 43, No. 11, ©1964. Gulf Publishing Company, Houston, Texas. All rights reserved.)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-232A Kettle reboilerdestimate of shell diameter. Example: If the vapor rate is 50,000 lb/hr and the bundle is 25 ft, then V/L is 2,000 lb/(hr)(ft). Entering the curve at this V/L ratio, with an operating pressure of 50 psia and a bundle diameter of 24 in. gives an estimate for shell I.D. of 40 in. (Used by permission: Palen, J. W., and Small, W. M. Hydrocarbon Processing, V. 43, No. 11, ©1964. Gulf Publishing Company, Houston, Texas. All rights reserved.)

rw ¼ tube wall resistance, (h) (ft) (
F)/Btu ai ¼ tube inside heat transfer surface per, ft, ft ao ¼ tube outside heat transfer surface per ft, ft Tw ¼ tube wall thickness, ft k ¼ wall thermal conductivity, Btu/(h) (ft) (
F) Do ¼ tube OD, ft Di ¼ tube ID, ft p ¼ pi ¼ 3.1416

P ¼ reboiler operating pressure, lbf/in.2abs. To account for tube and bundle geometry, Gilmour’s [90,91] equation is modified based on the single tube calculation [90,190]: hb ¼ hst ðNrv Þ

A. A. McNelly Equation [90,91,189] overall deviation þ 50% and 40%: hi ¼ 0:225 Cs ðg cl =lÞ

0:69

ð144Pk1 =sÞ

0:31

½r1 =rv  1 (15-633) 0:33

where: Cs ¼ surface factor, for clean copper and steel tubes ¼ 1.0 and for clean chromium ¼ 0.7 g ¼ acceleration of gravity, ft/hr2 ¼ 4.17  108 l ¼ latent heat, Btu/lb hl ¼ nucleate boiling coefficient for single isolated tube, Btu/(h) (ft2) (
F) c1 ¼ liquid specific heat, Btu/(lb) (
F) s ¼ surface tension, lbf/ft

0:185

ðvs Þ

0:358

(15-634)

vs ¼ superficial vapor velocity, ft/s Nrv ¼ number of tubes in center vertical row of bundle hst ¼ h ¼ theoretical boiling film coefficient for a single tube, Btu/(h) (ft2) (
F) hb ¼ heat transfer coefficient for a reboiler bundle, Btu/(h) (ft2) (
F) B. Gilmour Equation [190] reportedly was used successfully in many reboilers and vaporizers:   0:425 0:6 0:3 ðkL =cl ml Þ ðml =Do GÞ h ¼ 0:001 ðcl GÞ P2 rL s (15-635) where: G ¼ (V/A) (rl /rv ), mass velocity normal to tube surface, lb./(h) (ft2)

Heat Transfer Chapter | 15

TABLE 15-87 Values for Short-Cut Calculation of Circulation Rate (Equation 15-663) Value

Definition

Remarks

x

Two-thirds of outlet fractional vaporization

x ¼ 2xE/3*

RL

Liquid volume fraction based on one-third of outlet fractional vaporization

Figure 15-242 for x ¼ xE/3*

rtp

Two-phase density based on RL

Equation 15-661

Pressure drop ration based on two-thirds the outlet fractional vapor

Figure 15-242 for x ¼ 2xE/3*

f

2

DLCD

Total tube length in which vaporization occurs

DZ

Vertical distance in which two-phase flow occurs

Figure 15-238 and 15-239

E *For sparged reboilers where entering xso; x ¼ x ia þ2x ; and R L is 3 based on x ¼ 2x ia3þx E Used by permission: Fair, J. R. Petroleum Refiner, V. 39, No. 2, p. 105, ©1960. Gulf Publishing Company. All rights reserved.

TABLE 10-87A Tube Density Coefficient for 60
Triangular Pitch f [ [Tube Density Coefficient] [L/A]0.5 Coefficient for a given Do p, in.

3

1 in.

1

0.196

-

/4 in.

1.5

0.294

0.257

1.75

-

0.229

L ¼ Bundle length, ft; bundle heat transfer surface, ft2 Used by permission: Palen, J.W., and W. M. Small, Hydrocarbon Processing, V. 43, No. 11, p. 199,©1964. Gulf Publishing Company, Houston, Texas, All rights reserved.)

For all other factors constant: h ¼ (V/A)0.706 l0:706 a0:416 h ¼ film coefficient of boiling heat transfer, Btu/(h) (ft2) (
F) V ¼ vapor produced, lb./h A ¼ surface area, ft2 a ¼ proportionality constant ¼ 1.0 k ¼ kl ¼ thermal conductivity of liquid, Btu/(h) (ft.) (
F) cl ¼ specific heat of liquid, Btu/lb.-
F P ¼ pressure of boiling liquid, lbf/ft2 D ¼ Do ¼ OD of tube, ft. s ¼ surface tension of liquid, lb/ft ml ¼ viscosity of liquid, lb/(h) (ft) rL ¼ density of liquid, lb/ft3

395

rv ¼ density of vapor, lb/ft3 In tube bundles, if the disengaging space between the bundle and the kettle is small and insufficient to allow the vapor bubbles to “break free” of the liquid and thus tend to blanket the upper tubes with gas, heat transfer will be restricted [190]. For best design, the superficial vapor velocity should be in the range of 0.61.0 ft/s to prevent the bubbles from blanketing the tube through the bundle and thereby preventing liquid contact with the tubes. When the maximum heat flux is approached, this condition can occur, so the 1.0 ft/s vapor velocity is recommended. Palen and Taborek [91] modified the Gilmour equation to better accommodate the effect of surface types and the effect of pressure, with the results agreeing with the entire data 50% and 30%, which is better than other proposed correlations.

.  0:6 0:275 k r m0:3 h ¼ 9:0  104 Cs c0:4 L L L    ½ðq=lÞrL 0:7 P2 s0:425 ð14; 400=PÞm

(15-636)

m ¼ 6.0 e0.0035 Tc Maximum error for data tested is þ50% to 30%, restricted to hydrocarbon with Tc > 600
R. where: Tc ¼ critical temperature,
R q ¼ heat flux, Btu/(h) (ft2) Cs ¼ surface factor, noted with the McNelly equation cited earlier h ¼ theoretical boiling coefficient for a single tube, Btu/(h) (ft2) (
F) P ¼ pressure, lb/ft2 l ¼ latent heat, Btu/lb s ¼ surface tension, lb/ft rL ¼ liquid density lb/ft3 rv ¼ vapor density lb/ft3 mL ¼ liquid viscosity, lb/h-ft cL ¼ liquid specific heat, Btu/lb-
F g ¼ acceleration of gravity, ft/h2 h ¼ theoretical boiling coefficient for a single tube, Btu/ (h) (ft2) (
F) q ¼ heat flux, Btu/(h) (ft2) qmax ¼ maximum heat flux, Btu/(h) (ft2) m ¼ coefficient for equation for h [91] The maximum heat flux recommended by Zuber [191] and confirmed by Palen and Taborek [91] is:   0:25 0:5 ½ðrv þ rL Þ=rL  qmax ¼ 25:8ðrv ÞðlÞ sðrL  rv Þg r2v (15-637) where the symbols are as listed earlier. To avoid confusion with subscripts: L ¼ 1 (liquid) and V ¼ v (vapor). Examination of plant data by the authors [91] revealed that tubes spaced closely together tend to create a vapor blanketing effect and the consequence of lower heat flux than for wider-spaced tube pitches. The authors’

396

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

experience has been to spread out the tube spacing (pitch) from normal heat exchange design to ensure free boiling bubble movement, in order to avoid the very problem expressed in Reference [91]. To account for Gilmour’s effect of the bundle on single tube calculations, see Equation 15-634. Palen and Taborek [91] proposed as the best choice for circular tube bundles (as compared to square) the following film boiling coefficient after analyzing available data (their statistical analysis results). See Table 15-89 4:2105 G

hb ¼ 0:714 hðp  dÞ

0:24ð1:75þInð1=Nrv Þ

ð1=Nrv Þ

(15-638) where: G is the single tube mass velocity through the (p-d) tube space, defined as: G ¼

at ðDtÞU lðp  dÞ

where most symbols are as defined earlier, plus: at ¼ surface area ft2/ft of tube outside surface area p ¼ tube pitch, ft d ¼ tube OD, ft hb ¼ heat transfer coefficient for reboiler bundle, Btu/h-ft2-
F U ¼ overall heat transfer coefficient based on theoretical single tube, h The fit of the data to the proposed equation is on average  30% overdesign, which is good in terms of boiling data and when compared to the Gilmour’s bundle coefficient of þ48% and Kern’s þ61% [91]. h ¼ theoretical boiling coefficient, Btu/(h) (ft2) (
F) hb ¼ heat transfer coefficient for reboiler bundle, Btu/(h) (ft2) (
F) The following is a calculation procedure suggested by Palen and Small [90] for the required boiling coefficient for a horizontal tube bundle: 1. Assume a value of hl. 2. Calculate Ul from Equation 15-642. rw ¼ wall resistance, [Btu/(h) (ft2) (
F)]1 ri ¼ inside fluid fouling resistance, [Btu/(h) (ft2) (
F1)] 3. Calculate hl from the McNelly or Gilmour equation. 4. Compare calculated hl with the assumed value. If the difference is significant, use the calculated value and repeat from Step 2 until convergence is acceptable. 5. Calculate DTb from: DTb ¼ ðU1 =h1 ÞðDTÞ

(15-639)

If DTb is less than 8
F, free convection must be taken into account by a corrected hl ¼ hl0 .

h0l

0:25
3 2 Do rL g bL DTb cL ¼ hl þ 0:53ðkL =Do Þ (15-640) m L kL

where: DTb ¼ mean temperature difference between the bulk of the boiling liquid and the tube wall,
F DT ¼ mean temperature difference between the bulk of the boiling liquid and the bulk of the heating medium,
F hl ¼ nucleate boiling coefficient for an isolated single tube, Btu/(h) (ft2) (
F) hl0 ¼ nucleate boiling coefficient for an isolated single tube corrected for free convection, Btu/(h) (ft2) (
F) b ¼ coefficient of thermal expansion of liquid Other symbols are as cited previously. 6. Calculate the correction to the nucleate boiling film coefficient for the tube bundle number of tubes in vertical row, hb. See previous discussion. 7. Use Equation 15-642 to determine the overall U for bundle. 8. Determine the area required using U of Step 7. 9. Determine the physical properties at temperature: Tb ¼ DTb/2.

Nucleate or Alternate Designs Procedure The following nucleate or alternate designs procedure suggested by Kern [70] is for vaporization (nucleate or pool boiling) only. No sensible heat transfer is added to the boiling fluid. Note: If sensible heat, Qs, is required to bring the fluid up to the boiling point, this must be calculated separately, and the area of heat transfer must be added to that determined for the fluid boiling requirement, Qb. 1. Evaluate the heat load for the unit, Qb. 2. Determined the Log Mean Temperature Difference (LMTD). 3. Assume or estimate a unit size (number and size of tubes, shell, etc.). 4. Determine the tube-side film coefficient for convection or condensation as required, by methods previously described. 5. Determine the shell-side coefficient. a. Evaluate tube wall temperature. b. Evaluate boiling coefficient from Equation 15-621 or Figure 15-230. Note: the use of Figure 15-230 is considered conservative. Many organic chemical and light hydrocarbon units have been successfully designed using it; however, it is not known whether these units are oversized or by how much. 6. Calculate the required area, based on the film coefficient of Steps 4 and 5 together with fouling and tube wall resistances; A ¼ Q/U Dt.

Heat Transfer Chapter | 15

397

TABLE 15-88 Error Comparison of Test Case from Reference 91* Existing Methods Proposed Methods Kern

Gilmour (Eq. 8)

Statistical Model (Eq. 10)

Tube-by-Tube Model (Eq. 12)

Error with no safety factor 1. Ave. % overdesign 2. Ave. % underdesign

61 0

15 40

17 19

15 10

Errors with safety factor included 3. Area safety factor required 4. Ave. % overdesign 5. Max. % overdesign

1.0 61 140

1.80* 48* 110*

1.25 26 75

1.25 30 60

*Excluding case 15, which showed very high error. Used by permission: Palen, J.W., and J. J. Taborek. Chemical Engineering Progress, V. 58, No. 7, p. 43, ©1962. American Institute of Chemical Engineers, Inc. All rights reserved.

7. If the assumed unit does not have sufficient area, select a large sized unit and repeat the preceding procedure until the unit is satisfactory (say 10e20% excess area). 8. Determine the tube-side pressure drop. 9. Determine the shell-side pressure drop; however, it is usually insignificant. It can be evaluated as previously described for unbaffled shells.

Kettle Reboiler e Horizontal Shells See Figure 15-1F. In order to properly handle the boiling-bubbling in a kettle unit, there must be disengaging space, and the velocities must be calculated to be low to prevent liquid droplets being carried out of the unit. Generally, no less than 12 in. of space should exist from the liquid boiling surface to the top centerline of the reboiler shell. When vacuum operations are involved, the height should be greater than 12 in. and vapor outlet nozzle velocities must be selected to be low to essentially eliminate entrainment. The liquid boiling surface should not be greater than 2 in. above the top horizontal tube, and in order to reduce entrainment, it is often advisable to leave one or two horizontal rows of tubes exposed, i.e. above the liquid. This will tend to ensure that the liquid mist/droplets are vaporized and thereby reduce entrainment. As a guide to the relationship between tube bundle diameter and kettle shell diameter, the following can be helpful. Also, often the tube bundle is not completely circular; that is, the upper portions of circular tubes are omitted to leave a flat or horizontal tube row at the top of the bundle, at which level the liquid is often set.

Heat Flux, Boiling, Btu/(ft2) (h)

Ratio of Shell Diameter to Tube Bundle Diameter

20,000

1.9 to 2.5

15,000

1.8 to 2.1

12,000

1.5 to 1.7

8,000

1.3 to 1.6

Less than 8,000

1.2 to 1.5

Figure 15-232A is Palen and Small’s [90] guide to selecting the kettle “larger” diameter for the design of horizontal kettle units. Figure 15-249 shows a kettle-type reboiler of a cracking unit.

Horizontal Kettle Reboiler Disengaging Space [90] Palen [90] suggests that the distance from the centerline of the uppermost tube in a horizontal bundle to the top of the shell should not be less than 40% of the kettle shell diameter. To size the kettle shell [90]: Allowable vapor load: " #0:5 s ; lb=hr-ft3 ðVLÞ ¼ 2; 290rv 5 6:86ð10Þ ðrL  rv Þ (15-641) Vapor space, S ¼ V/(VL), ft3 V ¼ actual reboiler vapors, rate, lb/h

398

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

s ¼ surface tension, lb (force)/ft Dome segment area ¼ (SA) ¼ S/L, ft2 L ¼ average bundle length, ft

Kettle Horizontal Reboilers, Alternative Designs Referring to the procedure of Palen and Small [90] and Palen and Taborek [91], this is an alternative check on the previously suggested procedure. This technique should generally be restricted to single fluids or mixtures with narrow boiling ranges (a wide boiling range gives too optimistic results). The mean temperature difference between the bulk boiling liquid temperature and tube wall should be greater than 8
F; the ratio of pitch to tube diameter should be 1.25 to 2.0; tube bundle diameters should be greater than 1.0 ft and less than 4 ft; and boiling must be less than 400 psia. Vacuum operations may give optimistic results and are not to be used on polar compounds. Due to the development of the data, the method requires the use of a single tube boiling film coefficient. Using this to reach the overall bundle transfer, the overall U value is determined for a theoretical boiling coefficient of an unfouled tube (single) (this is an alternative procedure). See Reference [90] also. Uð1Þ ¼ 1 h1

þ rw

h

Ao Aavg

i

1 þ ri

h i Ao Ai

þ h1i

h i

(15-642)

Ao Ai

where: U(1) ¼ single tube overall heat transfer coefficient, Btu/(h) (ft2) (
F) h1 ¼ nucleate boiling coefficient for single tube, outside Btu/h (ft2) (
F) hi ¼ heating side film heat transfer coefficient, Btu/(h) (ft2) (
F) Note that h1 must be assumed to solve this equation and later verified. Iteration on h1 will possibly result in a balance. For a single tube: hl ¼ 0:225Cs

0:69
0:31

0:33 U1 DTLM CL 144PkL rL 1 l s rv (15-643)

where: DTLM ¼ log mean temperature difference between liquid and hot fluid,
F Cs ¼ surface condition constant ¼ 1.0 for commercial tubes ¼ 0.7 for highly polished tubes

For the entire bundle, the film boiling coefficient (assumes all tubes boiling, no liquid head effect so that some tubes are not boiling): h  i
0:24 1:75þIn N1 cv   4:2105 E 1 hb ¼ hon 0:714 pf  Do Nvc (15-644) where: pf ¼ tube pitch, ft Do ¼ tube OD, ft Ao U0 DTLM  E ¼  l p f  Do Ao ¼ surface area per ft of tube; ft2/ft Nvc ¼ Number of tubes in vertical tier at centerline of bundle DB ¼ 2pf cos q2 DB ¼ bundle diameter, ft q ¼ tube layout angle, degrees ¼ 90
for rotated square ¼ 60
for triangular Now, the hb coefficient can be used with the overall U equation, including shell-side fouling, to calculate a final overall coefficient for boiling. The maximum flux equation of Zuber [128] is suggested as another check for kettle reboilers: 
0:25
Db L gsðrL  rv Þ rv l (15-645) qmax ¼ 176 An r2v where: qmax ¼ tube bundle maximum flux, Btu/h-ft2 Db ¼ tube bundle diameter, ft L ¼ length of tube bundle, straight tube, or average for U-bundle, ft An ¼ net effective total bundle outside tube surface area, ft2 g ¼ gravitational constant, 4.17  108 ft/h2 The usual range of qmax for organic fluids is 15,000e25,000 Btu/h (ft2). For aqueous solutions, the range is 30,000e40,000 Btu/h (ft2)

EXAMPLE 15-33 Kettle-Type Evaporator e Steam in Tubes

Evaporate 25,000 lb/h of carbon tetrachloride (CCl4) at 55 psia and saturation temperature on the shell-side of a

Heat Transfer Chapter | 15

kettle type U-tube evaporator. Use steam as the heating medium. Solution: Preliminary Calculations 1. Determine heat load, Q. B.P. of CCl4 55 psia at 128
C y 262
F Heat of vaporization: 1v of CCl4 at 128
C ¼ 71.5 Btu/lb

2. Determine steam conditions (saturated), and Dt. Use Dt of approximately 60
F (refer to Table 15-85 for guide). Steam temperature ¼ 262 þ 60 ¼ 322
F Steam pressure ¼ 92 psia Latent heat (from steam tables) 1v steam ¼ 893.4 Btu/lb

3. Estimate unit size. Use maximum het flux Q/A ¼ 12,000 Btu/h/ft2. Note that Table 15-85 indicates that this value is quite safe. You could use a higher allowable flux. Many designs are operating based upon this conservative value. A ¼ Q=ðQ=AÞ

399

5. Determine the boiling coefficient. Add a “dirt” factor of 0.001 to hio: 1 1 1 þ :001 ¼ 0:00167 ¼ þ :001 ¼ hio hio 1; 500 hio ¼ 1=:00167 ¼ 600 Calculate tube wall temperature, tw. In this example: tc ¼ 262
F tsteam ¼ 322
F First try: Assume ho ¼ 300 Btu/h ft2
F tw ¼ 262 þ

600 ð322  262Þ 600 þ 300

¼ 262 þ 0:667ð60Þ ¼ 262 þ 40 ¼ 302
F Dtw ¼ 302  262 ¼ 40
F ho for Dtw of 40
F is greater than 300, Figure 15-230. Use 300 maximum (Kern’s recommendation). 6. Determine the required unit size. Add a 0.001 dirt factor to ho. 1 1 1 Lw ¼ þ þ 0:001 þ k U 600 300 ¼ 0:00167 þ 0:00333 þ 0:001 þ 0:00018 ¼ 0:00618  2 1 ¼ 162 Btu=h ft ð
FÞ U ¼ 0:00618 1; 790; 000 2 ¼ 184 ft Area required ¼ 60:05ð162Þ From Figure 15-33B, the equivalent tube length ¼ 31.2 ft. Area available ¼ 30 ð31:2Þ ð0:196Þ ¼ 188 ft2

Select a unit as follows: 3 /4 inch. OD  14 BWG  32 ft, 0 in. steel U tubes, assume effective length is 31 ft, 0 in. for preliminary calculation: Number of tubes ¼

149 31  0:196 ft2 =ft

¼ 24:5

From standard tube sheet layout or Tables 15-15AeF, select a 12 in. ID shell with 30 tubes, 2 passes, for the first trial. 4. Determine condensing tube loading, Figure 15-186A. G00o ¼

2; 000 ¼ 5:6 lb=lin ft ðequivalentÞ 0:05  31  23

Condensate properties at estimated tw of 300
F Sp. G. ¼ 0.916 ka ¼ 0.455 Btu/h. ft
F m ¼ 0.19 centipoise Because of the low tube loading and the physical properties of condensate, the value of the film coefficient is beyond the range of the chart. Therefore, the use of hio ¼ 1,500 is conservative.

The originally assumed unit is satisfactory. It should be noted that only the steam condensing coefficient will change (low tube loading, increasing hio). Because an arbitrary maximum value was used for the coefficients, the overall U will not change nor will the Dt. Therefore, only the available area of the newly sized unit needs to be checked against the previously calculated required area. For a 12 in. shell with 32 tubes available: 2

Area available ¼ 32  31  0:196 ¼ 194 ft A 12 in: shell will be satisfactory: SF ¼

194  184 10 ¼ ¼ 5:44% with 0:002 dirt factor 184 184

Area “safety factor” (which may be interpreted as more allowance for fouling): ¼

188  149 ð100Þ ¼ 26% 149

For a small unit such as this, 26% over surface is not too uneconomical. A smaller unit might be selected;

400

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

however, if the tubes are shortened and the shell diameter is enlarged, the unit will be more expensive. Note that 24 ft (total length) tubes will give 146 ft2 of surface. The only safety factor is the knowledge that the flux selected, Q/A, appears to be quite low. If it were doubled (and this could be done), the smaller unit would be a reasonable selection.

Shah [374] performed simulations on Example 15-33 using HTRI software, and Figure 15-233 shows the results on a heat exchanger specification sheet. His results show that the number of tubes for a 10 inch I.D. shell is 42, compared with 30 tubes from Tables 15-16AeF, and that the HTRI over design is 22%. Further, he stated that there is no need to use a 12 inch shell ID with 32 tubes as per HTRI, 68 tubes can be accommodated in 12 inch shell ID.

Boiling: Nucleate Natural Circulation (Thermosyphon) Inside Vertical Tubes or Outside Horizontal Tubes Natural circulation reboilers are effective and convenient units for process systems operating under pressure. They are usable in vacuum applications but must be applied with care, because the effect of pressure head (liquid leg) on the boiling point of the fluid must be considered. The temperature difference between the heating medium and the boiling point of the fluid may be so small as to be impractical, regardless of the tube length in a vertical unit. The recommended tube length is 8 ft in vertical units, with 12 ft being a maximum. Of course, some designs operate with 4 in. and 6 ft tubes; however, these are usually in vacuum service and they are physically very large in diameter when compared to an 8 ft tube unit (see Figures 15-220D and F). The method presented here requires that the majority of the heat load be latent, with a reasonably small percentage, say 10e20%, being sensible load. Gilmour [51,54] has presented a boiling film relationship, which is the result of the correlation of data covering a good range of organic materials and water from sub-atmospheric to above atmospheric pressure. This range has been the problem in most other attempts at correlation. The correlation was reported, by Earnest E. Ludwig, to have been successfully used on hundreds of vaporizers and reboilers. Palen and Small [90] have examined data using Gilmour’s equations. It has the advantage of avoiding trial and error approaches.

Gilmour Method [52,53] Modified This process is applicable to vertical tube-side vaporization only, and to vertical and horizontal shell-side vaporization.

1. Calculate the heat duty. 2. Estimate a unit based upon suggested values of U from Tables 15-28 and 15-32 and the known DTLMTD. Check to be certain that Dto does not exceed the critical value between shell-side and tube wall or the tube-side temperatures (however expressed). 3. Calculate film coefficient, hs, by    fðcÞ Ggb cm 0:6 rL s 0:425 ðaÞ (15-646) hs ¼  0:3 ka r2 D0 Ggb m

hs ¼ boiling side coefficient, Btu/h (ft2) (
F) f ¼ type metal factor f ¼ 0.001 for copper and steel tubes f ¼ 0.00059 for stainless steel and chromium-nickel f ¼ 0.0004 for polished surfaces a ¼ surface condition factor a ¼ 1.0 for perfectly clean conditions, no pitting or corrosion a ¼ 1.7 for average tube conditions a ¼ 2.5 for worst tube conditions Note: This is not a fouling correction. Read Figure 15-234. a. For shell-side vaporization:  V rL (15-647) Ggb ¼ 0 ðD LÞ rv Note that Gilmour [54] suggests that the correction for the number of vertical tube rows given in Reference [53] be omitted due to the generous fouling factor recommended. Where: Ggb ¼ mass velocity of liquid, lb/h (ft2). For outside horizontal tubes, use projected area (diameter  length) or the tube, not the outside surface area. This assumes that only half of the tube is effective for bubble release. This does not apply to actual heat transfer area. V ¼ vapor rate, lb/h Ts ¼ saturation temperature of liquid,
R rL ¼ density of liquid, lb/ft3 Tw ¼ temperature of heating surface,
R rv ¼ density of vapor, lb/ft3 s ¼ surface tension of liquid, lbf/ft c ¼ specific heat of liquid, Btu/lb (
F) m ¼ viscosity of liquid, lb/(h) (ft) P ¼ pressure at which fluid is boiling, lbf/ft2 abs D0 ¼ tube diameter, ft (side where boiling takes place) Ds0 ¼ shell ID, ft hs ¼ boiling side film coefficient, Btu/h (ft2) (
F) Lo ¼ length of shell, or length of one tube pass, ft

Heat Transfer Chapter | 15

FIGURE 15-233 Heat Exchanger Specification sheet for Example 15-33 (Private communication with Menon Shah [374]).

401

402

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-234 Gilmour correlation for nucleate boiling data. (Used by permission: Gilmour, C. H. Chemical Engineering Progress, V. 54, No. 10, ©1958. American Institute of Chemical Engineers. All rights reserved.)

A ¼ surface area of tube ft2 For outside horizontal tube, use the outside tube surface area. For vertical tubes with inside boiling, use inside surface area of tube, Ai. f ¼ proportionality constant for type of tube material Dtb ¼ boiling temperature difference between boiling fluid and wall surface, on boiling side,
F x ¼ weight percent vapor in fluid stream, for nucleate boiling only b. For tube-side vaporization: r  2 L Ggb ¼ V A rv ; mass velocity of liquid, lb/h (ft ) 4. For boiling in the shell-side of horizontal unit, a check point is:  (15-648A) 6:665 V rv D0s Lo must not exceed 1:0 This is concerned with the maximum vapor rate from a horizontal shell. 5. Check this second factor for condensate flooding in horizontal units with a condensable heating medium, such as steam, in the tubes: W ¼ 9:43D2:56 ft3 condensate=ðsÞðtubeÞ ¼ o Hc ð3; 600Þrn0 (15-648B) n0 ¼ number of tubes per pass W ¼ condensate rate, lb/h

6. 7. 8. 9. 10.

r ¼ density, lb/ft3 Do ¼ tube diameter, outside, ft Hc ¼ height of segment of circle divided by diameter Solve for Hc and then calculate the length of subtended arc. From the total circumference of the tube, the fraction of surface flooded can be calculated. If this fraction exceeds 0.3, recalculate the unit. Calculate the film coefficient for fluid on the side of the tube opposite from the one associated with the boiling or vaporizing operation. Use fouling factors for tube and shell-side if known; otherwise use 0.002 for tubes 8e12 ft long and 0.001e0.002 for shorter tubes. Calculate overall U. Calculate Dt between boiling fluid and wall surface on the boiling side. Calculate surface area: A ¼

Q UDtb

11. Compare the calculated and assumed areas. If acceptable, the design is complete from a thermal standpoint. If not, reassume the area of Step 2 and repeat until a balance is achieved. 12. Pressure drop Boiling on the shell-side: usually negligible unless tubes are very small and close together. For preferred 45
rotated square pitch with 1.25 do, Dps will be low.

Heat Transfer Chapter | 15

Boiling in the tubes: usually low, 3e9 in. fluid. Evaluate using two-phase flow. 13. Inlet and outlet nozzles for boiling side fluid: a. Vertical thermosyphon units [54] pffiffiffiffiffi (15-649) Vapor out; Dn ¼ dit Nt ; in: dit ¼ ID of tube, in. Nt ¼ number of tubes (preferable of 1e2 in. size) Liquid mixture in, Dn ¼ 1/2 (vapor outlet nozzle) size Note that the liquid inlet must be in-line at bottom, and the vapor out must be in-line at top (Figure 15-220F). For a side outlet vapor nozzle, increase the heat transfer area by 30% [53,54]. b. Horizontal or vertical shell-side boiling, size for low velocities and pressure drops. Gilmour’s basic correlation has been presented in graphical form by Chen [26], in Figures 15-235A, 15-235B, 15-236 and 15-237. These charts are based on a metal wall factor f, of 0.001, and if other values are considered, multiply the calculated h value by the ratio of the new factor to 0.001. The use of the charts follows: 1. For a given fluid condition and assumed size of reboiler, evaluate physical property factor f1

2. 3.

403

from Figure 15-235A and physical property factor f2 from Figure 15-235B. Read the boiling coefficient, h, from Figure 15-236 using fx ¼ ðf1 Þ ðf2 Þ. Apply the tube size multiplier from table associated with Figure 15-236 and also the multiplier for pressure correction from Figure 15237. Note that for high pressure systems, the pressure can become quite high, and some designers limit it to an arbitrary value of about 3,000 psia.

Suggested Procedure for Vaporization with Sensible Heat Transfer 1. Follow the general procedure for vaporization only. 2. Determine the sensible heat load separate from vaporization. 3. For organic liquids, evaluate the natural convection film coefficient from Figure 15-230. Equation 15-178 may be used for the inside horizontal tube by multiplying the right side of the equation by 2.25 (1 þ 0.010 Gr1/3 a )/log Re. 4. Calculate the required area for sensible heat transfer. 5. Add area requirements of sensible heat to the area required for vaporization to obtain the total area.

FIGURE 15-235A First physical property factor for boiling coefficient. (Used by permission: Chen, Ning Hsing. Chemical Engineering, V. 66, No. 5, ©1959. McGraw-Hill, Inc. All rights reserved.)

404

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-235B Second physical property factor for boiling coefficient. (Used by permission: Chen, Ning Hsing. Chemical Engineering, V. 66, No. 5, ©1959. McGraw-Hill, Inc. All rights reserved.)

FIGURE 15-236 Uncorrected nucleate boiling coefficient. (Used by permission: Chen, Ning Hsing. Chemical Engineering, V. 66, No. 5, ©1959. McGraw-Hill, Inc. All rights reserved.)

Heat Transfer Chapter | 15

405

2. If sensible heat exchanger exists, follow Steps 2e6 of the “Suggested Procedure for Vaporization with Sensible Heat Transfer,” given previously in this chapter. 3. Pressure drops must be kept low through the piping to the reboiler and through the reboiler to avoid expensive elevation of the distillation equipment. Kern suggests 0.25 psi as preferable to 0.50 psi; however, the final economic balance of the system will determine the allowable pressure drop, because for the same system, either the piping or the exchanger must become larger if the pressure drop is to be reduced.

FIGURE 15-237 Pressure correction factor. (Used by permission: Chen, Ning Hsing. Chemical Engineering, V. 66, No. 5, ©1959. McGraw-Hill, Inc. All rights reserved.)

6. Follow Steps 7 (Gilmour method), etc. of the procedure for vaporization only. If baffles are added for sensible heat (not assumed in free convection), then the pressure drop will be affected accordingly. Gra is the Grashof number using properties at average fluid temperature ¼ D3i rgb0 Dt=m2 :

Procedure for Horizontal Natural Circulation Thermosyphon Reboiler These units normally do not have a disengaging space, but allow the vapor-liquid mixture to enter the distillation unit or other similar item of equipment. Feed is from the bottom with a split flow on the shell-side by means of a shell-side baffle in the center being open at each end. This unit is usually used as the reboiler for the distillation column and, in this service, operates by the thermosyphon action of the difference in static head in the column and in the vapor-liquid phase leaving the reboiler. When tied into the bottom chamber, the liquid is usually recirculated many times, vaporizing only 10e25% of the reboiler feed per pass; however, when used as a draw-off from the bottom tray seal pan, the feed to the reboiler is not recirculated flow. The basic operation is the same, however.

Kern Method [70] 1. Follow the procedure for Steps, 1, 2, 3, 4 and 5 of the earlier section, “Nucleate or Alternate Designs Procedure.”

The length of the tubes should not be selected to be more than 4.5e5.5 times the shell diameter. This performance may be increased by placing two inlets in the bottom and two vapor outlets in the top, and at the same time adding shell-side longitudinal baffling to split the flow into four paths upon entrance. The paths recombine before leaving. The recirculation ratio for a unit is the lb rate of liquid leaving the outlet compared to the lb rate of vapor leaving. The liquid recirculation flow rate entering the unit is set by the differential pressure driving the system.

Vaporization Inside Vertical Tubes; Natural Thermosyphon Action The vertical thermosyphon reboiler is a popular unit for heating distillation column bottoms. However, it is indeed surprising how so many units have been installed with so little data available. This indicates that a lot of guessing, usually on the very conservative side, has created many uneconomical units. No well-defined understanding of the performance of these units exists. Kern’s [70] recommended procedure has been found to be quite conservative for plant-scale units, yet it has undoubtedly been the basis for more designs than any other single approach. For some systems at and below atmospheric pressure operation, Kern’s procedure gives inconsistent results. The problem is in the evaluation of the two-phase gas-liquid pressure drop under these conditions. For units that are vertical one-pass in tubes with liquid in the bottom entrance and a top exit of the liquid-vapor mixture, the separation is accomplished in the equipment to which it is attached, usually a distillation column (Figure 15-220D). For services in which fouling is high or in which downtime cannot be tolerated, two reboilers may be installed on the same distillation column. These reboilers may each be half sized so that downtime will be limited to a half-capacity operation; each may be two-third sized; or each may be a full 100% spare. The latter is, of course, the most expensive from an equipment investment standpoint, but it may pay for itself in uptime. Figure 15-238 shows a typical vertical tube-side thermosyphon reboiler.

406

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

The tubes are usually 11/4 in. OD but never smaller than 1 in. OD, because the flow contains vapor as well as liquid. The recirculation ratio, i.e., liquid-to-vapor ratio in the outlet, is seldom less than 5 and more often is 10e15, sometimes reaching 50.

Fair’s Method [45]

FIGURE 15-238 Typical vertical tube-side thermosyphon reboiler. (Used by permission: Fair, J. R. Petroleum Refiner, Feb. 1960, p. 105.© Gulf Publishing Company. All rights reserved.)

This method for vertical thermosyphon reboilers is based on semi-empirical correlations of experimental data and is stated to predict heat transfer coefficients  30%, which is about the same range of accuracy as most boiling coefficient data. The advantage of this method is that it has had significant design experience in the industry to support it. It is also adaptable to other types of reboilers used in the industry. Fair’s [45] presentation provides the development of the design technique. The method recognizes twophase flow in a vertical reboiler and points out that slug-type flow predominates, and that mist flow should be avoided.

FIGURE 15-239 Typical reboiler arrangements. (Used by permission: Fair, J. R. Petroleum Refiner, Feb. 1960, p. 105. ©Gulf Publishing Company. All rights reserved.)

Heat Transfer Chapter | 15

This procedure develops stepwise calculations along the tube length, using increments of length or vaporization. The increments are chosen to be small enough that average values of RL ; Rg ; f; Xtt and ht may be used in the difference equations. These calculations are well suited to computer application. Select an increment of vaporization, beginning at the end of the sensible heat zone. Use an average value for x for the increment calculations. The circulation rate that must be already developed on the basis of average conditions should be used for the initial calculations. Following Fair’s [45] method outlined in the article, determine, select or assume the following, based on process requirements (reproduced by permission of the author and published, all rights reserved): 1. Boil-up rate. 2. Reboiler outlet temperature, pressure and composition. 3. Physical properties at expected operating temperature. See Figure 15-240 for temperature-pressure effects in vertical thermosyphon reboilers. To facilitate design calculations, Figures 15-242e15-246 have been prepared to give the following information: Figure 15-242 e RL values on the basis of Lockhart and Martinelli. Figure 15-244 e f2 values on the basis of Figure 15-241. Figure 15-245 e htp =hL values on the basis of Equation 32 (Ref. [45]), with modification at 1/Xtt values less than 0.2 as suggested by Dengler and Addoms [12]. Figure 15-243 e 1/Xtt values for use in Figure 15-246 Figure 15-246 e a for correcting the nucleate boiling coefficient.

407

FIGURE 15-241 The factor f for two-phase turbulent-turbulent flow.28 Note: Reference number on chart is in Fair’s article. (Used by permission: Fair, J. R. Petroleum Refiner, Feb. 1960, p. 105. ©Gulf Publishing Company. All rights reserved.)

Flow pattern limits in Figure 15-246 are based on the data of Govier et al. [15], Yoder and Dodge [40], Dengler [11] and Baker [3]. The parameter J in Figures 15-242e15-245 is defined as: !0:1  0:5 rg mL Xtt ¼   0:9 J ¼ rL mg WL Wg

(15-650)

For cases in which a significant percentage change in pressure occurs across the reboiler tubes, J is not constant. In general, however, an average constant value may be assumed. Design calculations may use one of two methods: l

l

Stepwise calculations along the tube length, using increments of length or vaporization. Increments are chosen to be small enough that average values of RL ; Rg ; f; Xtt ; ht ; etc., may be used in the difference equations. Simplified calculations using average values of variables for the overall tube length.

Sufficient information is given in this chapter to enable the more rigorous stepwise calculations to be performed, and these calculations are ideally suited to computers. However, emphasis in this section is given to the simplified method, because it is convenient to use and yet sufficiently reliable for most design cases. Thus, designers without ready access to a computer may quickly rate existing reboilers or design new ones. Process Requirements

FIGURE 15-240 The temperature scale is accentuated to show the temperature-pressure effects in themosyphon reboilers. (Used by permission: Fair, J. R. Petroleum Refiner, Feb. 1960, p. 105. ©Gulf Publishing Company. All rights reserved.)

1. From fractionator calculations list: a. Boil-up rate b. Reboiler outlet temperature, pressure and composition. 2. Obtain physical property data: a. Liquid and gas (vapor) densities, rL and rg .

408

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-242 Design chart for liquid volume fraction using parameter defined in equation 15-168. (Used by permission: Fair, J. R. Petroleum Refiner, Feb. 1960, p. 105. ©Gulf Publishing Company. All rights reserved.)

b. c. d. e. f. g.

Liquid and gas (vapor) viscosities, mL and mg . Liquid specific heat, cL. Liquid thermal conductivity, kL. Latent heat of vaporization, l. Surface tension, s. Slope of vapor pressure curve ðDt=DpÞs .

Preliminary Design 1. Select tubing material and dimensions. 2. Select heating medium. 3. Estimate overall coefficient U using resistance (Tables 15-28, 15-32).

4. Calculate required surface and tube number. Circulation Rate 1. Select flow loop geometry, i.e., type reboiler arrangement. 2. Assume exit fractional vaporization, xE. 3. Evaluate sensible heating zone (Equation 15-651). 4. Obtain average values: a. Two-phase density, rtp at xE/3 b. Pressure drop factor, f, at 2 xE/3. 5. Obtain rtp and f for exit conditions. 6. Calculate circulation rate (Equation 15-663).

Heat Transfer Chapter | 15

409

FIGURE 15-243 Design chart for correlating parameter Xtt. (Used by permission: Fair, J. R. Petroleum Refiner, Feb. 1960, p. 105. ©Gulf Publishing Company. All rights reserved.)

7. Calculate boil-up and check against required value. 8. Repeat calculations, adjusting flow loop geometry if necessary, until assumed xE gives the proper boil-up rate. Heat Transfer e Stepwise Method 1. Choose an increment of vaporization, starting at the end of the sensible heating zone. Use the arithmetic average value of x for increment calculations. The circulation rate already obtained on the basis of average conditions should be used for initial calculations.

2. Calculate or obtain values for: a. Two-phase density rtp . b. Pressure drop factor, f: c. Convective transfer coefficient, htp. d. Boiling coefficient, hb (Table 15-89 or other source, or Equation 15-667). e. Boiling coefficient correction factor, a (Figure 15-246). f. Combined film coefficient, hv (Equation 15-668). g. Length of increment, based on hv.

410

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-244 Design chart for f2 values. (Used by permission: Fair, J. R. Petroleum Refiner, Feb. 1960, p. 105. ©Gulf Publishing Company. All rights reserved.)

h. Static pressure loss (Equation 15-654) i. Frictional loss, Lockhart and Martinelli. j. Acceleration loss: the acceleration loss term of DPacc

1 ¼ gc

Z rtp Vtp dVtp ¼

 Gt  Vtp;out  VL;in gc (15-651)

In the usual case, liquid and gas do not issue from the reboiler with equal velocities. k. Total pressure loss.

3. Continue stepwise calculations to the ends of the tubes. After the pressure loss in the exit piping is taken into account, the residual pressure should equal the fixed pressure below the bottom tray in the tower. 4. If the pressures do not match, the calculations are repeated for a different circulation rate. Alternatively, the circulation rate may be kept constant, and pressure drop contributions (inlet line value, exit line diameter, etc.) can be adjusted. 5. After the proper pressure balance/heat transfer relationships are established, the calculations are summarized in

Heat Transfer Chapter | 15

411

FIGURE 15-245 Design chart for two-phase heat transfer corrections. (Used by permission: Fair, J. R. Petroleum Refiner, Feb. 1960, p. 105. ©Gulf Publishing Company. All rights reserved.)

connection with other heat flow resistances in the reboiler.

From a heat balance: DT=DL ¼

Circulation Rate 1. Select flow loop geometry, i.e., type of reboiler arrangement. 2. Assume exit fractional vaporization, xE. Estimate range 15e40%. 3. Evaluate sensible heating zone by Fractional tube length devoted to sensible heating [145]: ðDt=DpÞs pB  p ¼


 pB  p A Dt=DL Dt þ Dp Dp=DL s

(15-652)

pDt Nt h1 ðtw  t1 Þ 3; 600WT c1

(15-653)

h1 is from the Dittus-Boelter Equation (15-657). This represents the fraction of the total available head between points A and B, which represents the sensible heating zone. This neglects liquid friction in this zone and assumes the liquid level in the distillation column is maintained even with the top of the tube sheet. Equation 15-652 then gives the fractional tube length devoted to sensible heating. Refer to Figure 15-238 and note that: pA ¼ total pressure at point A in flow loop, lbf/in2 (abs) (liquid level in distillation column bottoms)

412

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-246 Design chart for a values. (Used by permission: Fair, J. R. Petroleum Refiner, Feb. 1960, p. 105. ©Gulf Publishing Company. All rights reserved.)

pB ¼ total pressure at point B in flow loop, lbf/in2 (abs); (point at entrance to vertical reboiler) p ¼ total pressure, lbf/in2 (abs) Z ¼ vertical height, ft g ¼ gravitational constant, 32.2 ft/s2 gc ¼ conversion factor, 32.174 (lb)m (ft)/(lbf) (s2) p ¼ 3.1416 Di ¼ I.D. of tube, ft Nt ¼ number of tubes tw ¼ temperature of tube wall,
F tl ¼ temperature of liquid phase,
F WT ¼ mass rate, total flow, lbm/s cl ¼ specific heat, liquid phase, Btu/lb (
F) hl ¼ heat transfer coefficient, liquid phase, Btu/h-ft2-
F xE ¼ weight fraction of vapor or gas (quality), dimensionless at reboiler exit ðDt=DpÞs ¼ slope of vapor pressure curve. This may be calculated from Antoine type vapor pressure equation or obtain from a plot.

rtp ¼ two-phase density lbm/ft3 4. Obtain average values a. two-phase density, rtp at xE =3. b. pressure drop factor, f; 2 xE =3: where: rtp ¼ two-phase density, lbm/ft3 Rg ¼ volume fraction of phase, dimensionless, gas phase RL ¼ 1  Rg; volume fraction of phase, dimensionless, liquid phase rtp ¼ rg Rg þ rL RL Dt ¼ overall temperature difference,
F Dp ¼ pressure loss, lbf/in2 DP ¼ pressure loss, lbf/ft2 p ¼ total pressure, lbf/in2 abs. P ¼ total pressure, lbf/ft2 abs. L ¼ equivalent length of pipe, ft BC ¼ tube length for sensible heating, ft CD ¼ tube length for vaporization, ft G ¼ mass velocity, lb/(s) (ft2)

TABLE 15-89 Nucleate Pool Boiling Data Boiling Coefficient at Designated Dt

Equation Terms* Material

Press. (psia)

m

n

Dt Range

Max. Dt (
F)

5
F

10
F

20
F

30
F

40
F

50
F

Heating Device

Propane

20e35

46

2.5

7e15

.

(515)

1,460

.

.

.

.

HT

Propane

170

87

2.0

15e25

50

.

(870)

1,740

(2610)

.

.

VT

Propane

245

110

2.0

10e30

40

.

1,100

2,200

3,300

.

.

VT

Propane

295

145

2.0

10e25

30

.

1,450

2,900

4,350

.

.

VT

Propane

375

205

2.0

10e25

25

.

2,050

4,100

6,150

.

.

VT

Propane

475

320

2.0

7e15

15

(1600)

3,200

.

.

.

.

VT

n-Butane

20e35

12

n-Pentane

22

2.64

7e15

.

(170)

525

..

.

.

.

HT

-4

4.70

30e60

60

.

.

.

130

385

850

VT

-2

4.5(10 )

n-Pentane

59

2.0(10 )

4.16

20e45

45

.

.

265

850

2,350

.

VT

n-Pentane

115

0.76

3.27

15e35

35

.

.

695

1,700

.

.

VT

n-Pentane

215

23.5

2.91

8e20

25

.

1,900

7,250

.

.

.

VT

-3

n-Heptane

6.6

3.4(10 )

3.85

50e80

80

.

.

.

.

.

240

VT

n-Heptane

14.7

0.60

2.90

30e60

60

.

.

.

380

660

1,010

VT

n-Heptane

50

2.25

2.90

25e40

40

.

.

.

1,450

2,480

.

VT

n-Heptane

115

9.0

2.75

20e35

35

.

.

1,710

3,400

.

.

VT

n-Heptane

215

107

2.20

15e25

25

.

(1,710)

3,900

.

.

.

VT

Kerosine

14.7

1.79

14.7

10e15

>15

(60)

280

.

.

.

.

VT

3.87

45e90

90

.

.

.

.

(195)

370

HT

-3

4.9(10 )

Benzene

50

3.4(10 )

3.87

25e50

50

.

.

.

580

1,350

2,580

VT

Benzene

115

0.77

3.27

15e40

40

.

.

690

1650

3,400

.

VT

Benzene

265

42

2.61

7e25

25

.

1,720

5,200

.

.

.

VT

4

Benzene

465

1.0(10 )

1.96

3e11

11

4.800

9,400

.

.

.

.

VT

Styrene

2.7

11.5

2.05

20e90

.

..

.

270

410

550

700

HP

Styrene

14.7

29.0

2.05

20e50

.

..

.

670

1,030

1,390

1,750

HP

Methanol

14.7

1.61

3.25

10e15

>15

(120)

290

.

.

.

.

HT

413

Continued

Heat Transfer Chapter | 15

Benzene

3.19 -3

414

TABLE 15-89 Nucleate Pool Boiling Datadcont’d

Material

Press. (psia)

m

n

Dt Range

Max. Dt (
F)

5
F

10
F

20
F

30
F

40
F

50
F

Heating Device

Ethanol

14.7

2.4(10-2)

3.73

40e60

60

.

.

.

.

570

1,020

VT

Ethanol

55

1.74

3.08

20e40

40

.

.

870

2,090

3,740

.

VT

Ethanol

114

21.5

2.67

10e30

35

.

1,010

3,160

6,350

.

.

VT

Isopropanol

14.7

6.0

2.40

10e60

60

.

150

400

690

1,050

1,440

VT

n-Butanol

14.7

0.40

3.21

15e30

>30

.

.

230

740

.

.

HT

Carbon Tetrachloride

14.7

0.18

2.90

20e40

.

.

.

55

115

200

.

VT

Carbon Tetrachloride

14.7

0.73

3.14

15e25

>25

.

(100)

440

.

.

.

HT

-2

Acetone

14.7

7.3(10 )

3.85

20e40

40

.

.

370

1,170

2,780

.

HP

Methyl ethyl ketone

14.7

70

1.84

20e50

50

.

.

850

1,200

1,550

1,850

W

Water

14.7

14.3

3.14

5e10

>10

450

2,000

.

.

.

.

HT

Water

14.7

52

2.35

10e35

35

..

1,200

2,780

5,100

.

.

VT

-2

Water

14.7

1.7(10 )

4.90

15e35

35

.

.

2,000

9,600

.

.

W

Water

383

605

2.82

5e30

30

1,130

4,000

14,200

30,000

.

.

W

Oxygen

14.7

4.8

2.47

6e10

>10

.

140

...

.

.

.

VT

Nitrogen

14.7

1.9

2.67

6e12

>12

.

90

.

.

.

VT

Freon-12

60

0.49

3.82

12e20

>20

.

(320)

2,250

.

.

HT

Notation: VT ¼ vertical tube HT ¼ horizontal tube HP ¼ horizontal plate W ¼ wire *Equation: q/A ¼ (mDt)a where Dt ¼ tw e tb,
F Used by permission: Fair, J.R. Petroleum Refiner, V. 39, No. 2, ©1960. Gulf Publishing. All rights reserved.

.

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Boiling Coefficient at Designated Dt

Equation Terms*

Heat Transfer Chapter | 15

415

TABLE 15-90 Design Considerations of Kettle, Vertical and Horizontal Thermosyphon Reboilers Kettle Reboiler

Vertical Thermosyphon

Horizontal Thermosyphon

1.

To avoid impingement, a liquid inlet nozzle can be located on the side of the kettle with deflector.

Place boiling liquid on tube-side. Use 1 in. or larger tubes.

Normally, the boiling fluid is placed on the shell-side. Tube size selection depends on heat medium cleanness on the tube-side

2.

When tube length exceeds 16 ft. and vapor volumetric flowrate is high, two vapor outlet nozzles shall de designed to reduce kettle size

Normally, design tubes to be 8e12 ft. Very seldom is a tube length more than 16 ft.

A “J” shell with segmental baffles or “H” shell is typically selected.

3.

Keep a minimum 1 in. clearance between bottom tubes and shell for U e bundle and fixed tube sheet designs.

Keep top tubesheet elevation the same height as tower normal liquid level for initial design of recirculation e type reboilers (Figure 15-266)

If a “J” is designed, watch out for the boiling fluid phase separation. The horizontal cut shall be used if there is a tendency of phase separation in the shell.

4.

A weir plate to keep the bundle fully submerged shall be designed a minimum of 2 in. above the top of the tube bundle.

Minimize complexity of the two e phase flow return piping by using a direct e couple nozzle connection or 90o elbow if direct e couple nozzle cannot be achieved (Figure 15-266).

IF an “H” shell is selected, length of the long baffle is about 4 ft or one e quarter of the tube length. The long baffle can be either solid or perforated. The perforated long baffle is not used very often in recent designs. No cross baffle shall be designed for the “H” e type reboiler.

5.

A liquid compartment behind the weir plate is usually designed for 3-min hold e up but limited to 6 ft. long due to cost. Maximum liquid level shall be 6 in. below the top of the weir plate, and minimum liquid level shall be 4 in. above the bottom of the shell. Hold up time calculated based on the surge volume between maximum and minimum levels shall be indicated in the equipment data sheet.

When steam is used as a heat medium on the shell-side, a vapor escape space at the tube sheet circumference shall be designed to avoid the dry tube near the tubeeto tube sheet joint. A multiple steam inlet nozzle design is preferred if a large amount of steam is being consumed. Horizontal segmental baffles with 40% cuts at 24 in. spacing are normally designed.

Since horizontal reboiler elevation is much lower than tower liquid level, a manual control valve (globe valve for small pipe size and butterfly valve for large pipe size) is installed to adjust the liquid heat. Sometimes, the reboiler bundle is flooded by boiling liquid and thus loses effective surface area. Reboiler elevation has to be changed to make sure the boiling liquid entering the reboiler is at its bubble point.

6.

Provide a vortex breaker at the liquid withdrawal nozzle.

Design the vertical thermosyphon reboiler by HTRI’s CST program with 5e10% over design factor. Then use HTRI’s RTP program to check the hydraulic balance and percent vaporization at the tube-side outlet. When the design is finalized, run the HTRI e CST program again to check the heat flux and boiling flow regime.

A steam trap is installed at the steam reboiler condensate outlet piping.

7.

HTRI program RKH is used to design kettle reboilers.

Try to design a single vertical reboiler if shell size and length do not exceed the limit.

Two isobaric heat curves with pressures about 5e10 pis apart shall be input to the HTRI e RKH program.

8.

Vapor disengage space height is 12 in. minimum.

For critical services, design the reboiler for 120% or required heat duty and flowrates.

The HTRI e CST program shall be used to check maximum heat flux and tube e side pressure drop.

9.

One or more flash out connection at the bottom of the kettle shall be designed for dirty boiling service

For isobaric heat curves with pressures about 5e10 psia apart shall be input to the HTRI e RTF program.

10.

A condensate pot is installed next to the steam reboiler to recover uncondensed steam through a balance line to the steam supply piping.

11.

Try to avoid two e phase slug flow returning to the tower.

416

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Di ¼ I.D. of tube, ft Gt ¼ mass velocity in tube, lb/(s) (ft2 of cross-section) FB-C ¼ Friction loss from part B to part C in tubes, feet liquid g ¼ gravitational constant, 32.2 ft /(s) (s) k ¼ thermal conductivity, Btu/(h) (ft2) (
F/ft) m ¼ viscosity, lb/(ft) (h) R ¼ volume fraction of phase, dimensionless x ¼ weight fraction of vapor or gas (quality), dimensionless Xtt ¼ correlating parameter, dimensionless, for Figure 15-241 Z ¼ vertical height, ft. DZ ¼ vertical distance in which two-phase flow occurs, ft. f ¼ parameter for two-phase flow, dimensionless (Dt/Dp)s ¼ slope of vapor pressure curve CD ¼ tube length for vaporization D ¼ point D in flow loop f ¼ Force fh ¼ heating medium fouling s ¼ saturated tp ¼ two-phase mixture T ¼ total flow v ¼ vaporization w ¼ tube wall a ¼ cross-sectional area, ft2 A ¼ total (inside) surface for heat transfer, ft2 c ¼ specific heat, Btu/(lb) (
F) d ¼ differential operator f ¼ fanning friction factor, dimensionless F ¼ friction loss, (ft) (lbf)/lbm gc ¼ conversion factor, 32.174 (lbm) (ft)/(lbf) (s2) L ¼ equivalent length of pipe, ft q ¼ heat transfer rate, Btu/h r ¼ resistance to heat transfer, (h) (ft2) (
F)/Btu r0 ¼ composite resistance to heat transfer, (h) (ft2) (
F)/Btu t ¼ temperature,
F T ¼ absolute temperature,
R U ¼ overall heat transfer coefficient, Btu/(h) (ft2) (
F) V ¼ linear velocity, ft/s x ¼ weight fraction of vapor or gas (quality), dimensionless Xtt ¼ correlating parameter, dimensionless Greek letters a ¼ correction factor for nucleate boiling, dimensionless b ¼ correction factor for convective transfer, dimensionless

g ¼ acceleration loss group (Equation 15-663) DP ¼ pressure loss, lbf/ft2 Dt ¼ overall temperature difference,
F l ¼ latent heat of vaporization, Btu/lbm m ¼ viscosity, lbm/(ft) (h) p ¼ constant, 3.141 r ¼ density, lbm/ft3 r ¼ average density, lbm/ft3 s ¼ surface tension, lbf/ft f ¼ average value of f j ¼ parameter for two-phase physical properties dimensionless Subscripts BC ¼ tube length for sensible heating C ¼ point C in flow loop fp ¼ process side fouling F ¼ friction g ¼ gas h ¼ heating medium i ¼ inlet (feed leg) piping system m ¼ mass t ¼ tube l ¼ L ¼ liquid base b ¼ boiling p ¼ process on boiling side tp ¼ two-phase A ¼ point A in flow loop B ¼ point B in flow loop C ¼ point C in flow loop E ¼ reboiler exit system At pressures greater than about 100 psig, the slope of the vapor pressure curve, (Dt/Dp)s is low enough to not influence the sensible heating zone equation, as most of the tube is in vaporization. However, at low pressures and vacuum service, a large portion of the tube is in sensible heat. The pressure at the inlet to the tubesheet at point B [45] pB ¼

ðZA  ZB ÞrL g r ðDFin Þ þ pA  L 144gc 144

(15-654)

Static pressure loss in outlet leg where density, rtp , varies with vaporization. Z (15-655) DPstatic ¼ g=gc rtp dZ where: DF ¼ friction loss at inlet, ft or liquid Z ¼ vertical height, ft pB ¼ boiling pressure, lbf/in2abs g ¼ acceleration of gravity, ft/s2

Heat Transfer Chapter | 15

Subscripts A ¼ point A in flow loop B ¼ point B in flow loop 5. The calculation of the term for Equation 15-652 Dp rg DFBC ¼ 1 cþ  144g DL DL

(15-656)

Fair [45] states that the second term in the preceding equation may be neglected. Fair reports that typical units show the sensible heating zone at 4e60% for DT ¼ 20
F, and 4e49% for DT ¼ 30
F for selected organics and also water. The values vary with pressure, see Table 15-88. 6. The convection heat transfer rate inside the tube is expressed by the Dittus-Boelter equation [45,82]: (15-657)

7. Select mechanical features of the vertical reboiler a. Tubes are preferably 1 in. minimum OD, 11/4 in., 11/2 e2 in. maximum b. Vertical, with tube length preferable 6 ft to a maximum of 12 ft. 8. Determine average values: a. Two-phase density, rtp , at xE/3. b. Pressure drop factor, f, 2xE/3; f is from Figure 15-241. Obtain Xtt to use with Figure 15-241. Due to slippage effects of the gas phase past the liquid phase, the RL is not a simple function of the weight fraction of vapor. Using the parameter [45]: !0:1  0:9  0:5 rg WL mL (15-658) Xtt ¼ Wg rL mg 0:9  0:5  0:1  rg 1x mL ¼ (15-659) rL m x Often, approximately:  0:5 WL rg Xtt y Wg rL

(15-661)

and; Rl ¼ (l  Rg), volumetric fraction of liquid at any point along the vertical tube. Read Rl using Figures 15-242 and 15-243. Rl ¼ volume fraction of liquid phase, dimensionless Rg ¼ volume fraction of vapor phase, dimensionless Obtain f2 from Figure 15-244, for Equation 15-663 for both the average conditions and the exit conditions. 9. ðrg Þ j ¼ ðrl Þ

0:5

ml mg

!0:1 ¼ 

Xtt  0:9 Wl Wg

(15-662)

0:4

kl ½3; 600Di Gt  ½cl ml    di ml;b ½kl b 0:8

hl ¼ 0:023

tp ¼ two-phase rtp ¼ rg Rg þ rl Rl

417

(15-660)

where: Xtt ¼ correlation parameter for turbulentturbulent flow mechanism, dimensionless W ¼ mass flow rate, lb/s c. Determine rtp and f at exit conditions.

j ¼ parameter for two-phase physical properties, for use with Figures 15-242, 15-243, 15-244 and 15-245. Although j is not constant, in general an average constant value may be assumed [45]. 10. Calculate the circulation rate, WT, by (see Table 15-87):

where: rtp ¼ effective average two-phase density, lb/ft3 rtp ¼ average density, lb/ft3, two-phase f2 ¼ effective average (two-phase)/liquid phase pressure drop ratio corresponding to effective average vaporization x ai/at ¼ cross-sectional area ratio, inlet line/total tubes ai/aE ¼ cross-sectional area ratio, inlet line/exit line ai ¼ cross-sectional area, inlet feed pipe, ft2 DZ ¼ height of driving leg for thermal circulation, ft WT ¼ mass rate, lbm/s, total flow, or W Ws ¼ shaft work done by system, ft liquid D ¼ change from one condition to another DLi ¼ change in equivalent length of pipe, ft, inlet piping system Di ¼ inlet diameter, feed pipe ft

418

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

f ¼ fanning friction factor dimensionless f ¼ average value of f L ¼ equivalent length of pipe, ft g ¼ acceleration loss group, dimensionless # " 2  1x rL x2 1 þ ¼ rg Rg RL (Evaluate at outlet values for x, RL and Rg) x¼ average value of weight fraction of vapor gas, dimensionless E ¼ subscript, exit reboiler vapor This equation can be used to shorten the design by carefully selecting the overall average values. If specific data is not available, Fair [45] recommends using the guidelines in Table 15-89. 11. Calculate the boil-up and check against the required process balance value. 12. Calculate boil-up and check against the required balance for process balance. 13. Repeat calculations, adjusting flow as necessary, until the assumed XE (weight fraction of vapor in reboiler exit) produces the proper boil-up rate. Heat Transfer: Simplified Method Fair recommends this method rather than his stepwise method given in the article, because it avoids increments of calculations but is sufficiently reliable for most design cases. This procedure is duplicated by permission [45]. See Table 15-87. 1. The previously established circulation rate is used, but the exchanger dimensions must be checked for heat transfer. Obtain additional overall average values: a. Heat transfer coefficient for liquid, hL (equation following). b. Heat transfer coefficient for two-phase mixture, htp , at x ¼ 0.4xE (Figure 15-245) c. Boiling coefficient correction factors. a0 at x ¼ 0:4xE at x ¼ xE Figure 15-246; a from Equation 15-666. d. Get the nucleate boiling coefficient, hb, from Table 15-89 or other source. (An estimate of the film temperature drop is required.) 2. Calculate the process side heat transfer coefficient, hp, from Equations 15-667 and 15-668. 3. Calculate the total heat transferred to the process fluid and check against the required value. The adjustments

required may result in a new exchanger configuration and a new calculation of circulation rate. Design Comments These comments are directed to the inexperienced designer, and in general, amplify material previously presented. They are somewhat random in nature but are nonetheless important considerations in optimum design. l

l

l

l

l

l

The thermosyphon reboiler has inherent instabilities. A valve or other flow restriction in the inlet line helps to overcome these instabilities. Adjustment possibilities of a valve also compensate for variations in reboiler duty as imposed by changes in operation of the fractionator. For once-through natural circulation reboilers, the liquid backup height is calculated from the pressure balance equation. If this height, plus an allowance for froth, reaches the bottom tray level, flooding of the tower will occur. Economic optimum design usually implies high circulation rates, although not high enough to give “mist” flow. The large fraction of tube length used for sensible heating in vacuum reboilers leaves little density difference for thermal circulation. This fact, plus the frequent need for circulating viscous materials, points toward forced circulation reboilers for vacuum fractionators. For steam distillation columns, it is desirable to sparge the steam uniformly to all reboiler tubes. Because this provides full tube length for two-phase flow, thermal circulation is permitted. In reboiler design, film boiling should be avoided. However, such rules of thumb as 10e12,000 Btu/(h) (ft2) maximum heat flux are frequently quite conservative.

For heating, Fair [45] suggests the Dittus-Boelter equation:  0:8  0:4 kl 3600 Dt Gt cl ml (15-664) hL ¼ 0:023 Di ml kl See symbols previously listed. The two-phase flow heat transfer coefficient is determined from [45]. htp =hl ¼ 3:5 ð1=Xtt Þ

0:5

(15-665)

For the shortcut calculations: a ¼ ðaE þ a0 Þ=2; at average condition

(15-666)

Heat Transfer Chapter | 15

aE ¼ is evaluated at exit conditions a0 ¼ is evaluated at 40% exit vaporization Boiling coefficients: Determine from the McNelly, Gilmour, Kern, or Yilmaz equations previously given, or Fair’s suggestion of the Bliss or Levy equations, which were not given due to constants not being available. Process the side boiling heat transfer coefficient: hp ¼

DLBC hL þ DLCD hv ; Lt

(15-667)

hv ¼ a hb þ htp

(15-668)

Evaluate hb at average inside DT and htp at 40% of the exit vaporization. The 40% value is based upon integration of the htp/hL equation previously given. Subscripts: tp ¼ two-phase v ¼ vaporization b ¼ boiling p ¼ process side (boiling) coefficient t ¼ tube, tube-side a ¼average correction  ¼ bar over symbol ¼ average value Fair emphasizes some helpful points: l

l

l

l

l

l

Installation of a valve in the liquid circulation line as shown on the illustration can aid in overcoming instability and variations in reboiler duty. In the physical arrangement, make certain that the pressure balance level, plus an allowance for froth, establishes a height that is below the bottom tray of the column to avoid flooding it. In addition, the estimated froth height on top of the liquid should still be below the level of the vapor return from the reboiler. “Mist” type flow usually does not occur in an economic design, even though the recirculation rates may be high. In vacuum service, the large fraction of the tube length used for sensible heating leaves little density difference for thermal circulation. This fact, plus the frequent need for circulating viscous materials, points towards forced circulation reboilers for vacuum service. For steam distillation columns, it is desirable to sparge the steam uniformly into all reboiler tubes. This then provides full length for two-phase flow, and thermal circulation is permitted. Film boiling should be avoided; however, nucleate boiling often can be found at heat flux values greater than the rule of thumb values of 10e12,000 Btu/hr-ft2. These are often conservative values. See Figure 15-247 from Fair [46].

419

Examples from Fair [46] (by permission) include the following: EXAMPLE 15-34 C3 Splitter Reboiler

A thermosyphon reboiler is to be designed for a fractionator that separates propane ðC3 H8 Þ as the bottoms product. The conditions below the bottom tray are 401 psia and 164
F. A total of 17,600 lb/h vapor is to be produced. Physical data for propane: ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼

rL mg mL mg ðDt=DpÞs cL kL l s j

24.80 lb/ft3 4.40 lb/(ft) (h) 0.157 lb/(ft) (h) or 0.065 cP 0.036 lb/(ft.) (h) or 0.015 cP 0.24
F/psi 0.85 Btu/(lb) (
F) 0.068 Btu/(h) (ft) (
F) 96.9 Btu/lb 1.24 (104) lbf/ft 0.49

Preliminary Design Boiling is to be inside 3/4 in. 16 BWG steel tubes, 8 ft long. Condensing steam at 25 psig is available for heating. An overall coefficient U ¼ 300 Btu/(h) (ft2) (
F) is expected. For the given duty and a total driving force of 20
F, the inside surface required is 285 ft2. This is equivalent to 96 tubes. Circulation Rate The inlet line consists of 50 equivalent ft of 4 in. standard pipe. The exit line consists of 50 equivalent ft of 6 in. standard pipe. No special flow restriction exists in the inlet line. Preliminary calculations indicate that essentially the entire surface is in the vaporization zone. To facilitate trial and error work, the following constant terms are calculated: DLi ¼ 149:3 Di  2 DLCD ai ¼ 5:79 Dt at  2 DLE ai ¼ 19:31 DE AE g a2i rL DZ ¼ 49:5 hL ¼ 21:1W0:8 T For the first trial, assume 39% vaporization per pass. From Figures 15-242 and 15-244 and for j ¼ 0:49; x 0.13 0.26 0.39

RL 0.31 e 0.19

f2 e 15 25

rtp 11.35 e 8.28

g e e 2.02

420

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-248 Summary of information for Example 15-34. (Used by permission: Fair, J. R. Chemical Engineering, July 8, 1963, Part 1.© McGraw-Hill, Inc. All rights reserved.)

FIGURE 15-247 Dry-wall vapor-binding limitation. (Used by permission: Fair, J. R. Chemical Engineering, July 8, 1963. ©McGraw-Hill, Inc. All rights reserved.)

The circulation rate is calculated as shown in Equation 15-663:   W2T ¼ f49:5ð24:80  11:35Þg 0:008 ð149:4Þ þ 0:012 ð0:55Þ ð5:79Þð15Þ þ 0:008 ð0:37Þ ð19:31Þ ð65Þ þ 0:442 ð2:02Þ ¼ 162ð15  663Þ WT ¼ 12:7 lb=s:

(15-663)

Now, (WT) (xE) ¼ 12.7 (0.39) ¼ 4.95 lb/s vaporized, which is very close to the required vaporization rate of 17,600 lb/h (4.89 lb/s). No further adjustment is required at this point. Heat Transfer Rate e Stepwise Method Based on the calculated circulation rate of 12.7 lb/s, stepwise calculations are carried out for increments of 5% vaporization (Dx ¼ 0.05). A heat balance is taken over each increment based on the combined film coefficient for that increment. The calculations are summarized in Table 15-90 and presented graphically in Figure 15-248.

Several observations may be made: 1. The flow patterns are “bubble” and “slug.” 2. The required vaporization is attained in the 8 ft tube length. 3. The pressure balance is off by about 21 lbf/ft2. In design, this can be corrected by a slight adjustment in liquid level or by adding pressure drop to the inlet line (e.g., a valve). It is assumed here that no further trial calculations are needed. The results of the calculations are 1. Total duty ¼ 17,600 (96.9) ¼ 1,705,000 Btu/h. 2. Average inside coefficient, based on design tw  tb ¼ 5.0
F ¼ 1,200 Btu/(h) (ft2) (
F). 3. Based on a steam film coefficient of 1,500, the clean overall coefficient is 658 Btu/(h) (ft2) (
F) on an inside basis. 4. Including an inside fouling factor of 0.0010 (h) (ft2) (
F)/ Btu and an outside fouling factor of 0.0005 (h) (ft2) (
F)/ Btu, the service overall coefficient is 331 Btu/(h)(ft2) (
F). 5. The overall temperature difference is 10e18
F, depending on fouling. Vacuum operation on the steam side is indicated. Heat Transfer Rate e Simplified Method For WT ¼ 12.7 lb/s circulation, the following values are obtained: hL ¼ 162 Btu/(h) (ft2) (
F) htp/hL ¼ 2.4 (at x ¼ 0.4, xE ¼ 0.16) htp ¼ 386 Btu/(h) (ft2) (
F) a0 ¼ 1.0 Figure 15-246 aE ¼ 0.5 Gt ¼ 27.8 lb/(s) (ft2) hb ¼ 900 Btu/(h) (ft2) (
F) at tw  ts ¼ 5.0
F and data of Fair’s reference 9. cd hv hp ¼ DLBC hl LþDL t hp ¼ hv ¼ 0:75 ð900Þ þ 386    ¼ 1061 Btu ðhÞ ft2 ð
FÞ

Heat Transfer Chapter | 15

421

For the inside surface of 285 ft2, the vaporization is hp Aðtw  ts Þ ð1; 061Þð285Þð5:0Þ ¼ ¼ 4:36 lb=s l ð96:9Þð3; 600Þ

From Equation 15-656: rg Dp DFBC ¼ L c þ  144g DL DL

The value of the process side coefficient, hp ¼ 1,061 Btu/h (ft2) (
F) is lower than the value calculated in a stepwise fashion. A slightly higher value of Dt would correct this.

Dp 45:0ð1:0Þ ¼ ¼ 0:312 psi=ft DL 144

(15-669A)

(neglecting friction sensible zone) hL is from Equation 15-657. Then, by Equation 15-652

EXAMPLE 15-35 Cyclohexane Column Reboiler [45]

A thermosyphon reboiler is to be designed for a fractionator that separates cyclohexane as the bottoms product. The conditions below the bottom tray are 16.5 psia and 182
F. A total of 13,700 lb/h vapor is to be produced. Physical data for cyclohexane: rL rg mL mg (Dt/Dp)s cL kL l s j

¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼

Circulation Rate The inlet line consists of 100 equivalent ft of 6 in. standard pipe. The exit line consists of 50 equivalent ft of 10 in. standard pipe. No special flow restriction is in the inlet line. For the first trial, assume 15% vaporization per pass. This gives a circulation rate of 91,300 lb/h or 25.4 lb/s. For this rate, the following apply: hL ¼ 161 Btu/(h) (ft2) (
F) fL, i ¼ 0.0045 fL, t ¼ 0.0065 fL, E ¼ 0.0045 It will be assumed that the liquid level is maintained even with the top tubesheet. Neglecting inlet line friction, the sensible heating zone length may be estimated from Equation 15-653: (15-669)

Dt 3:14ð0:065Þð218Þð161Þð30Þ ¼ ¼ 5:2
F=ft DL 3600ð25:4Þð0:45Þ


(assuming tw  tL ¼ 20 F)

RL 0.28 e 0.16

f2 e 25 40

rtp 12.74 e 7.37

g e e 9.53

The circulation rate is calculated from Equation 15-663:

Preliminary Design Boiling is to be inside 1 in. 12 BWG steel tubes, 8 ft long. Condensing steam at 50 psig is available for heating. An overall coefficient U ¼ 300 Btu/(h) (ft2) (
F) is expected. For the given duty and a total driving force of 45
F, the inside surface required is 157 ft2. This is equivalent to 96 tubes.

pDt Nt hL ðtw  tL Þ 3600 WT cL

Hence, the length of the sensible zone ¼ 0.41 (8.0) ¼ 3.3 ft. From Figures 15-242 and 15-244 and for j ¼ 0.098, the following values are obtained: x 0.05 1.10 0.15

45.0 lb/ft3 0.200 lb/ft3 0.0208 lb/(ft) (h) or 0.0086 cP 0.97 lb/(ft) (h) or 0.40 cP 3.6
F/psi 0.45 Btu/(lb) (ft) (
F) 0.086 Btu/(h) (ft) (
F) 154 Btu/lb 1.24 (103) lbf/ft 0.098

Dt=DL ¼

pB  p 3:6 ¼ ¼ 0:41 pB  pA 3:6 þ 5:2

This value is in reasonable agreement with the assumed value of 25.4 lb/s. Heat Transfer Rate e Simplified Method For this calculation, the following are obtained: hL ¼ 160 Btu/(h) (ft2) (
F) htp =hL ¼ 3.2 (at x ¼ 0.4 xE ¼ 0.060) htp ¼ 510 Btu/(h) (ft2) (
F) a0 ¼ 0.2 Figure 15-246 aE ¼ 0 Gt ¼ 66.0 lb/s ft2 a ¼ 0.1 hb ¼ 200 Btu/(h) (ft2) (
F) at tw  ts ¼ 30
F From Equation 15-668, hv is: hv ¼ 0.10 (200) þ 510 ¼ 530 Btu/(h) (ft2) (
F) From Equation 15-667, hp is: hp ¼

  ð3:3Þð160Þ þ ð4:7Þð530Þ ¼ 377 Btu=ðhÞ ft2 ð
FÞ; 8:0

For clean conditions, the combined tube wall and steam side resistance is calculated as 0.00090, corrected to inside dimension. Thus, the calculated U is: U ¼

1 377

 2 1 ¼ 282 Btu=ðhÞ ft ð
FÞ þ 0:00090

422

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

This is close to the assumed value of U. It does not, however, consider fouling in service. Additional trial designs may be used, or the temperature difference may be adjusted upward.

Kern’s Method Stepwise [70] In vacuum applications, use this method with caution and compare it with other methods. 1. Determine the heat requirements or duty for any sensible heat as well as the latent heat. 2. Assume a unit size; number and size of tubes; and area. 3. Evaluate sensible heat transfer inside tubes as previously outlined for in-tube transfer. Determine the area required. 4. Evaluate LMTD for isothermal boiling. 5. Trial 1: Estimate area, A, for maximum flux condition, limiting Q/A to 12,000 Btu/h-ft2 surface for organic materials. Experience has shown that a value of 6,000e8,000 is a good starting value for Q/A for organics. Q A ¼ Q=A

(15-670)

Dt ¼ LMTD 8. Assume a recirculation ratio of 4:1. 9. Determine the material balance around unit. Total weight of recirculated liquid ¼ (4) (desired vapor rate, V) Vapor ¼ Desired vapor rate, V Liquid ¼ 4 (desired vapor rate, V) Total ¼ 5 (desired vapor rate, V) ¼ W 10. Pressure balance across reboiler. Static pressure of boiler leg:  Lrðavg:Þ 2:3L vo ¼ log ; psi (15-671) 144 vi 144ðvo  vi Þ where: L ¼ length of reboiler tube, ft vo ¼ specific volume of fluid and outlet of reboiler, ft3/lb vi ¼ specific volume of fluid at inlet to reboiler, ft3/lb log ¼ log base 10 Friction resistance to flow inside tubes, flow rate into tubes (per tube): W Wð144ÞðnÞ ¼ ; lb=h-ft2 cross-section a N t ai

pressure drop ¼ Dpt ¼

fG2 Ln 5:22  1010 Di sft

(15-673)

Let ft ¼ 1:0 11. Total resistance to flow ¼ ðstatic pressure of reboiler legÞ þ ðpressure drop through tubesÞ þ ðfrictional resistance of inlet pipingÞ

6. Re-estimate the unit size assumed in Step 2, making the area the value of Step 5. 7. Evaluate an operating overall coefficient: Q UD ¼ AðDtÞ

n ¼ 1 tube pass where: W ¼ total flow rate, lb/h into tubes Nt ¼ total number of tubes ai ¼ cross-sectional flow area per tube, in2 Di ¼ tube I.D., ft Re ¼ DG/m, per tube G ¼ flow into tubes, lb/h (ft2 cross-section) with m evaluated at the boiling temperature for the liquid. Read friction factor, f, from Figure 15-97. Calculated mean specific gravity in tube is the average of the inlet liquid and outlet vapor-liquid mixture.

(15-672)

þ ðfrictional resistance of outlet pipingÞ þ ðexpansion lossÞ

(15-674)

Note that for preliminary calculations, the frictional resistances in the piping can be neglected but should be included in the final calculations, particularly at high recirculation ratios. 12. Driving force: x2 r L ; psi 144

(15-675)

where: x2 ¼ height of liquid level in column above reboiler bottom tubesheet, ft rL ¼ density of liquid, lb/ft3 13. If the driving force, Step 12, does not equal or slightly exceed the total of resistances in Step 11, the unit should be rebalanced; that is, shorter tubes should be used to give a smaller pressure drop, lower recirculation ratio used to give a smaller pressure drop, or a larger number of total tubes used to give a smaller pressure drop. The liquid can be raised above the level of the tubesheet, but this is not recommended for differential levels greater than 6 in. 14. After a pressure drop balance has been obtained to 0.1e0.2 psi, compute the heat transfer coefficient as follows. Shell-side: Usual procedure for condensing steam or for other heating, medium. Tube-side: Determine heat transfer coefficient from Figure 15-76 (using tube-side curve) at Reynolds

Heat Transfer Chapter | 15

423

number calculated for pressure drop evaluation. If the hi calculated exceeds 300 for organics (Figure 15-230), use a value of 300 and correct to outside coefficient, hio. 15. Calculate the overall heat transfer coefficient from: Uc ¼

ho hio hio þ ho

(15-676)

UD ¼ calculated from assumed unit (corrected for final pressure balance) of Step 7. Resistance of fouling and metal tube wall required for balanced operation of reboiler. r ¼

Uc  UD UC UD

(15-677) FIGURE 15-249 A horizontal kettle-type reboiler of a cracking unit.

If the resistance seems too low for the service, then the unit must be redesigned to obtain the higher dirty coefficient, UD. Design Considerations Table 15-90 provides the engineer with guidelines in the design of various reboiler types [408].

Other Design Methods Several other excellent presentations exist on the subject of reboiler design. Presenting all of the variations here is just not possible; designers should refer to Hughmark [65,66 and 67], Palen and Taborek [91], Palen and Small [90], Frank and Prickett [47], and Hajek [60]. The article of Fair and Klip [93] presents a detailed analysis of the necessary design features and equations for horizontal kettle reboilers, horizontal thermosyphon reboilers and vertical thermosyphon reboilers. Other useful references on reboilers are [185,186,188,190,192,194,195,196,197 and 201]. Figure 15-249 shows a horizontal kettle-type of a cracking unit. EXAMPLE 15-36 Vertical Thermosyphon Reboiler, Kern’s Method [70]

The design of a distillation column requires a reboiler operating at 2.23 psia (vapor space above bottom liquid). The heat duty is 1,528,600 Btu/h. The properties of the acrylonitrile mixture have been calculated to be: Latent heat of vaporization , Btu/lb Average molecular weight Density of vapor, lb/ft3 Density of liquid, lb/ft3 Thermal conductivity of liquid, Btu/h. ft.
F Average cp , Btu/lb-
F Average viscosity m , lb/h.ft

¼ ¼ ¼ ¼ ¼

285 63.4 0.0230 54.5 0.084

¼ 0.425 ¼ 1.3389 cP  (2.42) ¼ 3.24

Design: Select a thermosyphon reboiler as the preferred operation, if design is acceptable. Solution Assume: flux, Q/A ¼ 7,200 Btu/h (ft2) U ¼ 120 Btu/h (ft2) (
F) Max. Dt ¼ 60
F (Steam temp. will be 113
F þ 60 ¼ 173
F. This is vacuum steam, 6.417 psia.) Approximate surface area: A ¼

1; 528; 600 2 ¼ 212 ft 7; 200

Select: Fixed tube sheet vertical unit. 11/4 in. tubes  12 BWG steel for low pressure drop, easier cleaning on 11/2 in. triangular pitch, 4 ft long Assume tube sheets, each 11/2 in. thick, then usable tube length ¼ 3.75 ft No: tubes required ¼

212 2

3:75ð0:3272 ft =ftÞ

¼ 173 tubes

Shell size estimate: 23 in. I.D. shell contains 187 tubes; remove at least three for internal impingement baffle. Available area ¼ (187  3) (3.75) (0.3272) ¼ 226 ft2 Recirculation ratio: assume 20:1 Reboiler vapors required ¼ 1,528,600/285 ¼ 5,364 lb/h Liquid being recirculated ¼ 20 (5,370) ¼ 107,400 lb/h Total liquid flow at reboiler inlet ¼ 107,400 þ 5364 ¼ 112,764 lb/h Specific volume of liquid into reboiler ¼ 1/54.5 ¼ 0.01835 ft3/lb Specific volume of vapor only at outlet ¼ 1/0.023 ¼ 43.5 ft3/lb Total volume of mixture out of the reboiler 107,400 (0.01835) ¼ 1,971 ft3/h

424

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

5364 (43.5) ¼ 233,334 ft3/h Total volume ¼ 235305 ft3/h Specific volume of mixture out of the reboiler ¼ 235,305/112,764 ¼ 2.09 ft3/lb Pressure balance across reboiler: Assume fluid in distillation column at reboiler tubesheet level.

 2:3ð4Þ 2:09 log10 144ð2:09  0:01835Þ 0:01835

¼ 0:0308 log 114 ¼ 0:0308ð2:057Þ ¼ 0:0634 psi Friction resistance to flow inside tubes: Flow rate into tubes ¼

112; 764ð144Þð1Þ   ð187  3Þð0:836 in2 tube

¼ 105; 600 lb=h ðft cross-sectionÞ ð1:03 in:Þð105; 600Þ ¼ 2; 800 ð12Þð3:24Þ

(From Figure 15-97) 2 f ¼ 0:00038 ft in:2  54:5 1 þ 62:3 2:09ð62:3Þ ¼ 0:441 Mean Sp: Gr: for tube ¼ 2

Static pressure of reboiler leg  2:3ð8Þ 0:606 log ¼ 0:331 psi ¼ 144ð0:606  0:01835Þ 0:01835 Friction inside tubes: Flow rate into tubes  2 ð397; 370Þð144Þð1Þ ¼ ¼ 384; 000 lb=hr ft ð178Þð0:836Þ 
ð1:03Þ 384; 000 ¼ 10; 200 Re ¼ ð12Þ ð3:24Þ 54:5 1 þ 62:3 0:606ð62:3Þ ¼ 0:451 Arith: mean gravity ¼ 2 However, for many cases, particularly when the difference in specific volume is large, the log mean average is much better. Log mean average specific volume: vlm ¼


Tube pressure drop ¼ Dpt ¼

0:00038ð112; 764Þ2 ð4Þð1Þ 10

ð5:22Þð10Þ ð1:03=12Þð0:441Þð1Þ

vlm ¼ 0:00978 psi

For the first try, neglect the piping friction into and out of reboiler. This should be designed with a minimum of pressure drop. Total resistance to flow ¼ 0.0634 þ 0.00978 ¼ 0.07318 psi Driving force ¼

¼ 0:606 ft3 =lb

f ¼ 0:00027

2

Re ¼

Specific volume of mixture ¼ 240; 700=397; 370 Pressure balance:

Static pressure of reboiler leg :  2:3L vo log10 ¼ vi 144ðvo  vi Þ ¼

Total volume of mixture out reboiler : ð392; 000Þ ð0:01835Þ ¼ 7; 200ð5; 370Þ ð43:5Þ ¼ 233; 500 3 Total ¼ 240; 700 ft h

xl r L 4ð54:5Þ ¼ ¼ 1:51 psi 144 144

This is not a satisfactory check. Because the resistances are now considerably less than the available driving force, the new estimate for the recirculation ratio must be considerably greater than 20:1. Final Trial: 24 in. OD shell, 6 in. inlet and 10 in. outlet nozzles. After several trials to obtain a balance, try a recirculation ratio of 73:1 and an exchanger with 178, 12 BWG, 8 ft long tubes. Liquid being circulated ¼ 73 (5370) ¼ 392,000 lb/h Liquid flow at reboiler inlet ¼ 392,000 þ 5,370 ¼ 397,370 lb/h

vo  vi Inðvo =vi Þ

1  0:1835 0:606  ¼ 1:606 In 0:1835  ¼ 0:0655 ft3 lb

(15-678) 

1 0:0655 Log mean Sp: Gr: ¼ ¼ 0:245 62:3 2

Dpt ¼

0:00027ð384; 000Þ ð8Þð1Þ 10

5:22ð10Þ ð1:03=12Þð0:245Þð1:0Þ

¼ 0:29 psi

Pressure loss in inlet piping (see Figure 15-220D). Assume piping consists of the following for an inlet pipe: 8 ft, 6 in. pipe two 6 in. wed ells one 6 in. open gate valve Note: If a tee connection to spare reboiler is used, add a tee to the pipe list. For equivalent feet pipe: Two 6 in. wed ells y 2 (11 equiv. ft. See the “Fluid Flow” Chapter 4 in Vol. I, 4th edition of this series.) ¼ 22 ft. One 6 in. open gate valve y 3.5 equiv. ft. 8 in., 6 in. pipe y 8 ft.

Heat Transfer Chapter | 15

Total equiv. ft ¼ 33.5 ft. From the “Fluid Flow” chapter in Vol. I.: Dpt ¼

3:36  106 fLW2 d5 r

A satisfactory average of “f” fitting from the Crane Co. Charts (“Fluid Flow” chapter, Vol. 1, 4th Ed. of this series) is: 0:555 f ¼ 0:0077 þ p ffiffiffiffi 3 DG m ¼ 3:24 lb=ft-h D ¼ 6 in:=12 ¼ 0:5 ft 397; 370 lb=h 0:2006 ft

2

 2 ¼ 1; 928; 000 lb=h ft

Cross-sectional area of 6-in. pipe ¼ 0.2006 ft2

Total resistance to flow: ¼ 0:331 þ 0:289 þ 0:671 þ 0:087 þ 1:45 ¼ 2:83 psi Driving force ¼

 1=3  0:14 jH ðka Þ cm m Di ka mw 1=3
ð45Þð0:084Þ ð0:425Þð2:42Þ hi ¼ ð1Þ 0:084 ð1:03 Þ 12    hi ¼ 101:5 Btu h ft2 ð
FÞ    1:03 ¼ 83:6Btu=h ft2 ð
FÞ hio ¼ 101:5 1:25 hi ¼

3:24

f ¼ 0:0077 þ 0:008313 ¼ 0:01601 d ¼ 6 in: r ¼ 54:5 lb=ft3 W ¼ 397; 370 lb=h 3:36  106 ð0:01601Þð33:5Þð397; 370Þ2 5

ð6Þ ð54:5Þ

¼ 0:671 psi Expansion losses in tubes due to vaporization (Kern [70] recommendation):   Dpt ¼ G2 = 144 g ravg: G ¼ 384; 000 lb=h ðft2 Þ   g ¼ 32:2 ft ðsÞðsÞ ð3; 600Þ2 ¼ 4:17 ð10Þ8 ft h-h 2

Dpt ¼

ð8Þð54:5Þ ¼ 3:03 psi 144

Calculation of Tube-Side Film Coefficient From calculated Reynolds number ¼ 10,200 Read Figure 15-76, jH ¼ 45

0:555 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f ¼ 0:0077 þ p 3 0:5ð1;928;000Þ

Dpt ¼

3:36  106 ð0:0174Þð26Þð397; 370Þ2 ¼ 1:45 psi ð10Þ5 ð1=606Þ

If the driving force is slightly greater than the total resistance to flow, the recirculation ratio will be greater than the trial value of 73. For purposes of design, this is a satisfactory basis on which to proceed.

m

G ¼

Dpt ¼

425

ð384; 000Þ ¼ 0:0874 psi ð144Þð4:17  108 Þð28:1Þ

Loss in outlet piping: 10 in. Assume: one 10 in. e90
elbow y 17 ft pipe 3 ft pipe y 3 ft one 10 in. gate, open y 6 ft Total ¼ 26 ft pipe G ¼ 397,370/0.5457 ft2 ¼ 726,000 lb/h (ft2 crosssection) 0:555 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f ¼ 0:0077 þ p 3 726;000 ð10 12Þð 3:24 Þ

Assume ho ¼ 1,500 Btu/h (ft2) (
F) for steam Fouling: tube-side ¼ 0.001 h (ft2) (
F)/Btu Shell-side ¼ 0.001 h (ft2) (
F)/Btu Neglect tube wall resistance: U ¼

This calculation is not accurate, because it does not account for two-phase flow.

1 1 ¼ 1 0:0146 þ 0:001 þ 1;500 þ 0:001

¼ 68:4 Btu=h ðft2 Þ ð
FÞ Actual area in assumed unit:    A ¼ ð178Þ ð0:3272Þ 8  3 12 ¼ 451 ft2 Factor of safety, or percent area: % ¼

451  392 ð100Þ ¼ 15% 392

This is a satisfactory selection. Overall coefficient information for operational guide: Clean : Uc ¼

  1:500ð83:6Þ ¼ 79:2 Btu=h ft2 ð
FÞ 83:6 þ 1; 500

Dirty based on total available surface: UD ¼

f ¼ 0:0077 þ 0:00972 f ¼ 0:0174

1 83:6

  1; 528; 600 ¼ 56:5 Btu=h ft2 ð
FÞ ð451Þð60Þ

Allowance in selected unit for fouling: r ¼

 2 Uc  UD 79:2  56:5 ¼ ¼ 0:00507 h ft ð
FÞ=Btu Uc UD ð79:2Þð56:5Þ

426

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

This compares to assumed value of 0.001 þ 0.001 ¼ 0.002 h (ft2) (
F)/Btu The Kern method is usually easier to handle for pressure systems than for vacuum systems. The recirculation ratio is higher, and therefore requires more trials to “narrow in” on a reasonable value for the low pressure systems. The omission of two-phase flow in the pressure system, because a ratio on the high side may result, produces a high hi value. In general, however, for systems at atmospheric pressure and above, the method usually gives conservative results when used within Kern’s limitations. Reboiler piping at the liquid inlet and at the vapor outlet can be summarized for convenience in pressure drop calculations into the suggested equivalent feet of Table 15-91. The inlet assumes piping to conveniently pipe the reboiler to a distillation column using welded fittings and a full open gate valve; the vapor outlet assumes short pipe connection, a 90
welded ell and a fully open gate valve. Reference [73] discusses exchanger piping layout. The outlet vapor line should be two nominal pipe sizes larger than the liquid inlet. Table 15-92 is helpful for relating exchanger size and pipe connections, although the same standards cannot apply to every design. To illustrate the effect of the pressure drop on the reboiler selection, Table 15-93 compares several designs for the same heat load and quantity of reboiled vapor.

Simplified Hajek Method e Vertical Thermosyphon Reboiler Although various correlations exist within thermosyphon reboiler data, each seems to have some limitation. The method of Hajek [60] recommended here has shown excellent correlation above and below atmospheric

TABLE 15-91 Equivalent Feet of Inlet and Outlet Piping Vertical Thermosyphon Reboiler Eq ft Pipe Size, In.

Inlet Liquid

Outlet Vapor

1 /2

21

10

2

25

12

3

35

17

4

44

21

6

65

32

8

84

40

10

103

49

12

123

58

14

140

65

16

159

74

1

pressure. Operating data for water, acetic acid, benzene, styrene, ethyl benzene and styrene-ethyl benzene mixtures agree well with predicted data at intermediate operating heat fluxes. Back-calculated fouling factors were about 0.001 for the inside surface. The data of Lee, et al. [75], are also included in the correlation. The data presented are good for vertical natural circulation thermosyphon reboilers with 1 in. 14 BWG Admiralty tubes 4e10 ft. in length, and are based on 10 ft. long tubes. The maximum flux for the shorter tubes is greater. For 4, 6 and 8 ft. tubes, add 17%, 9% and 4%, respectively, but do not adjust the intermediate flux values below the maximum flux. Column liquid level must be at the top tubesheet. Design for no more than 90% of calculated maximum flux when using full shell diameter top outlet elbows. But when using top-tee-type side outlet vapor nozzles, use 76% and 60% of the calculated maximum flux for organics and inorganics respectively. Full shell diameter top outlet vapor nozzles are recommended. Top-tee outlet vapor nozzles usually cause the reboiler to fail before maximum flux is reached. If the latter are used, the vapor nozzle should be a minimum of two-thirds the shell diameter. For 90
elbows off top vapor outlet channels, the area of nozzle for flow must be a minimum of 1.25  the flow area (net) of all tubes. Inlet nozzles should be sized for 2.5 gpm liquid per tube with the inlet line pressure drop not to exceed 1.5 psi per 100 equivalent ft. of inlet piping for total gpm. Nozzles may, in all cases, come into the side of the bottom channel. The design method is illustrated in Example 15-37 and uses Figures 15-250, 15-251, 15-252 and 15-253.

General Guides for Vertical Thermosyphon Reboilers Design Nucleate vaporization rates usually run at 15e40% (but can be as low as 2e10%) per pass through the unit for organic materials, averaging about 25e28% for many typical conditions. Aqueous solutions range from a low of 5% to 25e30%. The temperature difference between the exiting vapor-liquid mixture and the inlet shell-side steam or hot fluid should not exceed 75e82
F, primarily due to fouling problems and possible conversion in the tube to inefficient film boiling in the upper section of the tubes. Frequently used tubes in many vertical thermosyphons are 8 ft. long, with 12 ft. or 14 ft. being the maximum. The most popular size is 11/4 in. OD, sometimes 1 in. is used. Sizes up to 2 in. OD are certainly acceptable, depending on the design criteria. Short tubes of 4 and 6 ft. are used for special applications, including vacuum conditions. The best designs provide for the percentage vaporization per pass to have been completed by the time the fluid mixture reaches the upper end of the tube and the mixture is leaving to enter the bottom chamber of the distillation column. In order to assist in accomplishing this,

TABLE 15-92 Typical Thermosyphon Reboiler Design Standards* SHELL O.D., Inches

NO. TUBES

TUBE SHEET FACES

NOZZLE SIZES APPROX. AREA

VAPOR, Inches

LIQUID Inches

STEAM Inches

DIMENSIONS COND, Inches 1

A Inches

B Inches

C Inches

D Inches

E

16

108

4’-11 3/4

132

,’

20

176

4’-11 3/4

215

,’

8

6

4

2

8 15/16

7 15/16

8

5 3/4

6’e43/400

24

272

4’-11 3/4

333

,’

10

6

6

3

9 15/16

7 15/16

9

7 3/4

6’e53/400

30

431

4’-11 3/4

527

,’

12

6

6

3

11 7/16

7 15/16

9

7 3/4

6’e71/4

36

601

4’-11 3/4

735

,’

16

8

8

4

13 5/16

9 15/16

10 3/4

8

6’e1100

24

272

6’-7 3/4

448

,’

10

6

6

3

915/16

7 15/16

9

6 3/4

8’e13/400

30

431

6’-7 3/4

710

,’

12

6

6

3

11 7/16

7 15/16

9

6 3/4

8’e33/400

36

601

6’-7 3/4

990

,’

16

8

8

4

13 3/16

9 15/16

10 3/4

8

8’e700

42

870

6’-7 3/4

1,440

,’

16

10

8

4

17 11/16

10 15/16

10 1/16

6 13/16

9’e01/2

30

431

9’-11 3/4

1,065

,’

12

6

8

3

11 7/16

7 15/16

9

6 3/4

11’e71/4

36

601

9’-11 3/4

1,520

,’

16

8

8

4

13 3/16

9 15/16

10 3/4

6 3/4

11’e1100

42

870

9’-11 3/4

2,180

,’

16

10

8

4

17 11/16

10 15/16

10 1/16

6 13/16

12’e41/2

6

4

4

1 /2

7 15/16

5 15/16

8

5 3/4

6’e1 3/400

00

00 00

00

*Cross-section area of vapor nozzle off channel must be a minimum of 1.25  total flow area of all tubes (Earnest E. Ludwig). Used by permission: Lee, D.C., Dorsey, J.W., Moore, G.Z., and Mayfield, F.D. Chemical Engineering Progress, V. 52, No. 4, ©1956. American Institute of Chemical Engineers, Inc. All rights reserved.

Heat Transfer Chapter | 15 427

428

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-93 Vertical Thermosyphon Reboiler Comparison: Effect of Pressure Drop and Pipe Size on Selection 3

Tubes

/4 In. 3 4 ft Long

1 In. 3 6 ft Long

1 In. 3 6 ft Long

1 in. 3 6 ft Long

No. tubes

143

50

66

66

Inlet pipe size, in.

6

6

4

6

Outlet pipe size, in.

8

8

6

8

Shell I.D., in.

15.25

12

13.25

13.25

Recirc. ratio

42

40.5

42.1

55.7

DP tubes, psi

0.97

1.55

1.03

1.31

DP inlet pipe, psi

0.084

0.0789

0.41

0.137

DP outlet pipe, psi

0.085

0.0824

0.251

0.111

DP expansion, psi

0.00097

0.00209

0.00118

0.0011

U (calc.)

79.3

92.6

82.4

94.0

U (used)

66.1

92.4

70.0

70.0

105.3

75.2

99.3

99.3

Area, ft

2

FIGURE 15-251 Overall DT at maximum flux; vertical thermosyphon reboilers. (Used by permission: Hajek, J. D. Private communication. Deceased.)

FIGURE 15-252 Vertical thermosyphon reboilers, UDT versus DT for clean and fouled conditions. (Used by permission: Hajek, J. D. Private communication. Deceased.)

FIGURE 15-250 Hajek correlation thermosyphon reboilers overall coefficients at maximum flux. (Used by permission: Hajek, J. D. Private communication. Deceased.)

FIGURE 15-253 Vertical thermosyphon reboilers with a slope of log UDT/log DT for determination of DT at points below maximum flux. Note: n ¼ slope. (Used by permission: Hajek, J. D. Private communication. Deceased.)

Heat Transfer Chapter | 15

the initial reboiler elevation should be set to have the top tubesheet at the same level as the liquid in the column bottom section. A liquid level control adjustment capability to raise or lower this bottoms level must exist to optimize the recirculation. Sometimes the level in the bottom of the column may need to be 25e30% of the reboiler tube length above the elevation of the tubesheet. Therefore, the vapor nozzle return from the reboiler must enter at sufficient elevation to allow for this possibility. Velocities of liquid entering the tubes should be in the range: 1-4.5 ft./s when operating in atmospheric pressure and above. 0.4e1.0 ft./s when operating in a vacuum. A full opening valve or variable orifice should be able to restrict flows of liquid into the bottom of the reboiler so that the instability in the liquid in the column will not be directly introduced into the inlet of the reboiler. Generally, the liquid inlet nozzle size should be about 50% in the inlet tube flow cross-section area. A large line is sometimes used, but a restricting provision should be provided to stabilize operations. EXAMPLE 15-37 Hajek’s Method e Vertical Thermosyphon Reboiler

See Figure 15-254 A fractionator stripping light ends from water is designed to operate at 80% of tray flooding. The heat load is 4,000,000 Btu/h. Design the reboiler for full tower capacity or 5,000,000 Btu/h. A base pressure of 50 psig is required to condense the overhead vapor with cooling water. Steam pressure downstream of the control valve can drop to 200 psig. Use 6 ft-long Admiralty tubes, 1 in. OD by 14 BWG on 11/4 in triangular pitch. Inside and outside fouling resistances are 0.001 and 0.0005, respectively. Physical data required L ¼ 6 ft tube length rL ¼ 57.4 lb/ft3, liquid density lv ¼ 911.8 Btu/lb, heat of vaporization based on vapor to bottom tray P ¼ 64.7 psia, tower base vapor space pressure Pc ¼ 3,206 psia, critical pressure Variables to be determined U ¼ overall heat transfer coefficient, Btu/h (ft2) (
F) DT ¼ overall temperature difference,
F n ¼ slope ¼ log UDT/logDT PR ¼ P/Pc ¼ reduced pressure Determine Overall Coefficient at Maximum Flux ðPR ÞðIv Þ0:6 ¼



64:7 ð911:8Þ0:6 ¼ 1:20 3; 206

(15-679)

429

From Figure 15-250, ðPR Þ ðUÞ ¼ 47   2 ð47Þ 47 ¼ ¼ 2; 326 Btu=h ft ð
FÞ; U ¼ ðPR Þ 0:0202 (15-680) clean based on OD surface Determine Overall DT at Maximum Flux From Figure 15-251,
 
ðLÞðrL Þ ðrL Þ For PR ¼ 0:0202; P þ ¼ 0:0268 144 ðDTÞðPc Þ (15-681)

 ð6Þð57:4Þ ð57:4Þ 64:7 þ ¼ 0:0268 144 ð3; 206ÞðDTÞ DT ¼

ð67:1Þð0:0179Þ ¼ 44:8
F; clean ð0:0268Þ

Maximum flux:  2 UDT ¼ ð2; 326Þ ð44:8Þ ¼ 104; 000 Btu hr-ft Maximum flux is the same for a clean or fouled tube (see Figure 15-252) with DT increasing as U decreases due to fouling. Flux at Operating Levels Below Maximum UDT plotted against DT on log-log paper gives a straight line. See Figure 15-252. Determine UDT at, say, 10
F clean DT to get another point other than at 44.8
F. From Figure 15-253, or PR ¼ 0:0202;

ðnÞðPc Þ1:15 ¼ 244 ðPÞ

(15-682)

ðPc Þ1:15 ¼ ð3; 206Þ1:15 ¼ 10; 760 n ¼

ð244Þð64:7Þ ¼ 1:467 ð10; 760Þ

UDT for 10
F DT ¼ ð104; 000Þ



10 44:8

1:467

¼ 11; 540 Btu=h-ft2 U for 10
F DT ¼

 2 ð11; 540Þ ¼ 1; 154 Btu=h ft ð
FÞ clean ð10Þ

Plot these data as shown in Figure 15-252 to get the flux versus clean surface DT. Fouled DT at Maximum Flux 1 1 ¼ ¼ 0:00043 U max clean 2; 326 ri ¼ 0.0010 inside fouling correct to outside surface   O:D: 1:00 rio ¼ ð0:0010Þ ¼ ð0:0010Þ ¼ 0:0012 I:D: 0:834

430

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-254 Thermosyphon reboiler specifications.

Heat Transfer Chapter | 15

ro ¼ 0.0005 outside steam fouling resistance  1 U max dirty ¼ 0:00043 þ 0:0012 þ 0:0005 ¼ 469 Btu=h ðft2 Þð
FÞ

 ðUDTÞ 104; 000 ¼ ¼ 220
F DT dirty ¼ U dirty 469

Liquid Inlet Nozzle Diameter gpm ¼ (2.5/tube)(96 tubes) ¼ 240 gpm 4 in. is too small; use 6 in. (15-683)

Plot this point as shown on Figure 15-252. Because the correlation is based on 14 BWG Admiralty tubes, no correction was made for tube wall resistance. Fouled DT, to Maintain Plus for 10
F Clean DT   1 1 ¼ ¼ 0:000866 U clean for 10
F DT 1; 154  1 U dirty ¼ 0:000866 þ 0:0012 þ 0:0005 2

¼ 390 Btu=h ðft Þð
FÞ  11; 540 DT dirty ¼ ¼ 29:6
F for UDT ¼ 11; 540 390 Plot this point on Figure 15-252 and connect with the 222
F point to get the fouled flux line. Analysis of Data on Figure 15-252 Boiling point of water in tower ¼ 298
F Assume the reboiler will have a full shell diameter top outlet elbow vapor nozzle. Thus, a flux of (104,000) (0.90) or 93,600 Btu/h (ft2) is possible if the steam temperature is adequate. At the latter flux, the fouled DT ¼ 204
F. This will require a steam temperature of 298 þ 204 or 498
F equivalent to 693 psia steam. Because only 200 psig steam is available downstream of the control valve at the chest, a lower flux must be used. Steam at 215 psia has a temperature ¼ 388
F Available DT ¼ 388  298 ¼ 90
F fouled From Figure 15-252 for the fouled condition at 90
F DT, a flux of only 38,600 Btu/h (ft2) is available. Because this is less than 60% of the maximum flux allowed for water and other inorganics when using a tee type top vapor side outlet, the latter construction will be used to reduce investment slightly. Surface Area Required Q ¼ 5,000,000 Btu/h  5; 000; 000 2 Area ¼ ¼ 130ft 38; 600 Use ð130Þ ð1:10Þ ¼ 143 ft2 Tube length corrected for tubesheets ¼ 5:73 ft: Number of tubes ¼

ð143Þ ¼ 96 tubes ð0:2618Þð5:73Þ

A 16 in. OD shell is required. Vapor Nozzle Diameter (16)(0.667) ¼ 10.7 in. approximately Use a 10 in. vapor nozzle.

431

Design Notes When steam pressures in the chest are near atmospheric, condensate can rise in the shell and drastically reduce the available surface e if the trap is too small to dump steam into the condensate return system, or if the condensate return pressure is greater than the calculated chest pressure required. In these cases, the steam pressure will have to rise in the chest to overcome this error; if steam pressure is available. If not, the reboiler will not deliver the design flux. Proper condensate removal is important. An inverted split cup inside the shell, with the upper capped end above the nozzle and the lower open end 3/4 in. above the bottom tubesheet, should be used to cover the outlet nozzle. This can be made by splitting a pipe that is one size larger than the condensate outlet down the center line. In this case, a 2 in. split is adequate. This cup must be fully seal welded (not tack welded) to force condensate down to the 3/4 in. clearance above the bottom tubesheet. A common error is to allow 6 in. or more above the tubesheet for the centerline of the condensate outlet. In this case, 6 in. of tube is 10% of the surface. If the cup is not used, add 10% more tubes to correct for the dead liquid space near the bottom. This is in addition to the 10% safety factor. In the region of low Dt (less than about 10), the heat flux is about 10 times as great for water under forced convection agitation as for natural circulation [82]. This does not hold at the higher Dt values. The critical Dt is practically unaffected by agitation or increased velocity over the value at natural convection. In general, the heat flux is lower for a given Dt at lower pressures. Likewise, the peak Q/A is lower. When a liquid is vaporized in horizontal tubes, the initial overall coefficient is several times the value for forced convection single phase heat transfer. As the amount of vapor increases up to 100%, the coefficient falls off, down to a gas convection coefficient. The work of McAdams [84,85] represents some of the limited literature for this type of heat transfer.

Reboiler Piping The mechanical design of thermosyphon reboiler piping must carefully examine (a) system pressures and (b) elevation relationship between the liquid level in the distillation column and the vertical or horizontal reboiler. Kern [199] provides an excellent presentation on this topic, including the important hydraulics. Abbot [200] also presents a computer program for this topic.

Film Boiling Normally the designer does not try to establish film boiling conditions for the vaporizers or reboilers. However, for systems set by other controlling processing conditions, these film conditions may be imposed. In such cases, they should be recognized and handled accordingly. The

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principles of design for the equipment are the same as other such equipment, and only the actual value of the coefficient affected needs special attention.

Vertical Tubes, Boiling Outside, Submerged [14] Conditions:

Above critical temperature difference for nucleate boiling 3 /8 in. 1/2 in. OD (data of correlation) 800e5,000 14% (greatest single value in correlation data is 36%)

Tube sizes: Reynolds number: Range or error




4w h0a ¼ 0:002 pDo m

0:6 "

2

#1=3 (15-684)

k3a rv ðrL  rv Þg

where: w ¼ maximum vapor flow per tube, lb/h Do ¼ tube OD, ft m ¼ viscosity of vapor, lb/(ft) (h) ka ¼ thermal conductivity of vapor, Btu/h (ft) (
F) rv ¼ density of vapor, lb/ft3 rL ¼ density of liquid, lb/ft3 g ¼ 4.17  108 ft/h2 ha0 ¼ average heat transfer coefficient over entire tube, Btu/h (ft2)(F) The data for organic fluids and low temperature nitrogen fit. However, methanol data give coefficients many times higher.

Horizontal Tubes: Boiling Outside, Submerged [14] Conditions: Pressure to 500 psi, temperatures of saturated liquid to 700
F Tubes: 0.025e0.75 in. OD (data of correlation) Fluids: Hydrocarbons, alcohols, benzene, chlorinated compounds, low temperature nitrogen and oxygen. 

h0a

1 ¼ a þ 36:5 do 0




k3 rv ðrL  rv Þgl0 Dtb m

 2 cp Dtb l ¼ hfg 1 þ 0:4 0 l 0

where: d ¼ tube OD, in a0 ¼ constant, (in.)/(ft)1/4

1=4 (15-685)

(15-686)

FIGURE 15-255 Horizontal film type cooler or condenser.

ka ¼ thermal conductivity of vapor at arithmetic average mean temperature, Btu/h (ft) (
F) rv ¼ density of vapor at its arithmetic mean temperature, lb/ft3 rL ¼ density of saturated liquid, lb/ft3 l0 ¼ difference in enthalpy between vapor at its arithmetic temperature and saturated liquid, Btu/lb m ¼ viscosity of vapor at mean temperature, lb/h (ft) Dtb ¼ temperature difference between heat transfer surface and boiling liquid,
F ha0 ¼ average film coefficient Btu/h (ft2) (
F) hfg ¼ latent heat of vaporization, Btu/lb cp ¼ specific heat at constant pressure of vapor at arithmetic mean temperature, Btu/lb (
F)

Horizontal Film or Cascade Drip-Coolers e Atmospheric The film cooler, Figure 15-255, fabricated from pipe lengths, is popular and relatively inexpensive for some cooling and condensing applications. The principle of operation is also used in the cast iron sections of Figure 15-5A,B, and 15-256, which are particularly useful for handling sulfuric and other similar acids. The same unit construction is sometimes submerged in cooling tanks or placed in the basins of cooling towers. Graphite impregnated film coolers are used in hydrochloric acid cooling (Figure 15-257). Design Procedure 1. Determine heat duty, Btu/h. 2. Assume exit water temperature about 10e15
F (maximum) greater than inlet water, if possible. 3. Calculate water required with selected temperature rise. This rate should fall between 2e10 gpm per lin ft of plan coil length. Values greater than 10 gpm cause over flooding of tubes and a waste of water. 4. Determine LMTD if flows are counter flow and apply the correction factor of Bowman et al. [8], established for this type of unmixed “shell-side” flow (Figure 15-258) [70].

Heat Transfer Chapter | 15

433

FIGURE 15-256 Typical cast iron cooling section.

FIGURE 15-257 Graphite film coolers. (Used by permission: Bul. 537, Falls Industries, Inc. Research indicates that company went out of business, 1999.)

5. Assume a unit for the service or assume a pipe size and length and determine the number of lengths required. 6. Determine outside film coefficient for spray or drip cooling using the equation of McAdams [81] as presented by Kern [70].  1=3 Gd (15-687) ho ¼ 65 Do where: ho ¼ outside film coefficient,  25%, Btu/(h) (ft2) (
F) Gd ¼ W/2L, lb/h (ft) W ¼ lb cooling water/hr flowing over length of tube L ¼ length of each pipe in bank, ft Do ¼ OD of pipe, ft For most purposes, an estimated value of ho ¼ 500e550 Btu/h ft2
F is conservative.

FIGURE 15-258 MTD correction factors for drip type coolers. (Used by permission: Bowman, R. A., Mueller, A. C., and Nagle, W.M. Transactions of ASME, No. 62, ©1940. American Society of Mechanical Engineers. All rights reserved.)

For a submerged unit, handle as natural convection on outside of pipes; values usually range from 40e130 Btu/h (ft2) (
F) for ho. 7. Determine the inside film coefficient using Equation 15-165 and Figure 15-76 for tube-side heat transfer. If two or more coils are in parallel, be certain that the flow rate per pipe is used in determining hi. Correct hi to outside of tube, giving hio. Note that Figure 15-76 also applies to cast iron cooling sections. 8. Assume fouling factors. Inside tube factors can be selected from Table 15-24 or 15-25 or by referring to Table 15-29. Because the water rate is low over these coolers, they may develop salt crusts, scale, algae, etc.; therefore, the values of fouling will be high, see Table 15-94.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-94 Typical Fouling Factors e Cast Iron Cooling Sections Service

Inside Fouling

Outside Fouling

Concentrated sulfuric acid

0.002

-

Ammonia liquor

0.002

-

Clean water

0.001

0.005

Clean oil

0.002

-

Dirty oil

0.005

-

Tar

0.01

0.01

Sea water, brackish water

0.01e0.05

Used by permission: Cat. HT-23, National U.S. Radiator Corp. Existence of company not confirmed (1998). Value for sea water provided by Ernest E. Ludwig (deceased).

9. Determine overall coefficient U in the usual manner. 1 1 hio

þ ri þ

1 hw

þ ro þ

1 ho

Lw/k ¼ h/hw, wall resistance. For cast iron sections, see Tables 15-95 and 15-96.

TABLE 15-95 Wall Resistance Factors e Cast Iron Cooling Sections Metal Thickness, in.

Wall Transfer, hw, Btu/h (ft2) (
F)

1

1,800

3

1,350

1

900

/4 /8

/2

A ¼

Existence of company not confirmed (1998). Used by permission: Cat, HT-23, National U.S. Radiator Corp.

Q Uðcorrected LMTDÞ

If this area is considerably different from the assumed unit, reassume a new unit and recalculate the preceding steps. If the calculations were started by assuming a pipe size and length, determine the number of lengths from the total area calculation and surface area per length of pipe selected. No: lengths ¼

Dirty water

U ¼

10. Calculate area required:

total surface A (15-688) outside surface area=pipe length

Factor of safety or percent excess area should be at least 10e15%. 11. From a balanced design, determine the pressure drop for the entire length of pipe in bank, including fittings. Use copyrighted chart in Reference [36], fluid flow principles, or Figure 15-259 for cast iron sections. If the pressure drop is too high, reselect and redesign the unit, making parallel units to reduce flow rate (and coefficient hio), or select a larger pipe, reducing the mass rate G, and hence hio. Recalculate the pressure drop. Impregnated graphite coolers (Figure 15-260 and Table 15-97) are used to deal with acids and other corrosive liquids. The selection charts of Figures 15-261, 15-262 and 15-263 can be used to determine the expected transfer coefficients and total external cooling surface for a typical style of unit. Although these charts are specific to the manufacturer’s wall thicknesses and the thermal conductivity of the material, they are nevertheless convenient and generally acceptable. Exact selections should be obtained from the manufacturers by giving them the flow data and performance requirements. Pressure drops can be estimated from Figures 15-264 and 15-265.

TABLE 15-96 Typical Cast Iron Section, Type B, Figure 15-256 Metal Thickness, in.

Cubic Contents, gal

1

2.7

3 1

/4 /8

/2

Wt./Section

Internal Surf. ft2

External Surf. ft2

Eq. Diam. in.

130

11.0

10.0

1.57

2.7

180

11.0

10.8

1.57

2.7

210

11.0

11.5

1.57

Note: Other types of sections are available to accomplish the same type of cooling. Used by permission: Cat, HT-23, National U.S. Radiator Corp. Existence of company not confirmed (1998).

Heat Transfer Chapter | 15

435

FIGURE 15-259 Pressure drop versus rate of flow for water at 70
F in cast iron cooling sections, similar to Figure 15-127.

Heating Media The heating medium can be steam, hot oil or process stream, as are 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 15-266A). The dry wall area can be quickly fouled and will 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 15-266B, could be installed downstream of the reboiler to improve energy efficiency. A review of various steam traps is provided later in the chapter. 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 increased reboiler size and a tendency to foul. To avoid film boiling, the heating medium temperature should not exceed 80
F (27
C) over the 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.

FIGURE 15-260 Typical sectional cooler using assembly of standardized components. (Used by permission: SGL Technic, Inc., Karbate
Division.)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-97 Data for Coolers of Figure 15-260

Cooler Size, in.

Pipe I.D. (Nom.), in.

Pipe O.D. (Nom.), in.

Inside Crosssection, ft2

Effective Inside Area Per Section, ft2

Effective Outside Area Per Section, ft2

Max. No. of Sections per Cooler

Total Effective Outside Area for Max. No. of Sections

11/2

11/2

2

0.01227

10.60

14.14

26

367.6

40

182

3

Weight Each Cooler Section lb

Weight Set of Tie Rod Assemblies, lb

2

2

2 /4

0.0218

14.14

19.44

20

388.8

65

299

3

3

4

0.0491

21.21

28.27

13

367.6

180

381

0.0873

28.27

37.11

10

371.1

285

541

4

4

1

5 /4

Used by permission: Cat. S-6820, ©1953. National Carbon Co. Existence of company not confirmed (1998).

FIGURE 15-261 Cooling water requirements for cooler of Figure 15-260. (Used by permission: SGL Technic, Inc., Karbate
Division.)

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 require equivalent capital investment and operating cost to a steam system. However, it does not require boiler water treatment and blowdown disposal. Boiling flow regimes: Figure 15-214 shows the four boiling flow regimes, namely: natural convection (subcooled), nucleate, transition and film. A good reboiler design should meet the process requirement and provide stable, flexible tower operation. Optimizing reboiler design requires a team effort by various disciplines, namely,

process, fluid system, piping and heat transfer specialists. The heat transfer specialist must ensure that the reboiler is designed 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 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. A reboiler should never be designed in the transition boiling regime. Enhanced heat transfer surface: This is considered when the pinch point is less than 10
F. Low fin tubes are good for clean boiling service applications with a 6e10
F

Heat Transfer Chapter | 15

437

FIGURE 15-262 Overall heat transfer coefficient for Karbate
impervious graphite cascade cooler. (Used by permission: SGL Technic, Inc., Karbate
Division.)

FIGURE 15-263 Required cooling surface. (Used by permission: SGL Technic, Inc., Karbate
Division.)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Heat flux limit: Chen [408] has provided a rule of thumb for the maximum heat flux recommended for nucleate boiling design: Btu/ft2-h

W/m2
C

Kettle reboiler

9,000

51102

Thermosyphon reboiler

15,000

85170

Stripper reboiler

25,000

141950

Steam System Installation and Steam Traps Delivering heat to a process using an external source may be from: l l l

FIGURE 15-264 Tube-side fluid velocity for cascade cooler. (Used by permission: SGL Technic, Inc., Karbate
Division.)

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.

Heating with a fluid that delivers sensible heat Heating with a fluid that delivers latent heat Direct heating with a flame.

Direct heating with open flames in process equipment would require the installation of better quality equipment to resist higher temperatures and safety systems. It is generally preferable to employ some fluid that transports thermal energy when required. This implies that heat is delivered to a circulating fluid via burning a solid, liquid or gas fuel in a central piece of equipment (e.g. a furnace or steam generator) and this fluid transports the energy to the required

FIGURE 15-265 Tube-side liquid pressure drop for cascade cooler. For nonwater liquids, multiply pressure drop by (m0 )0.140(s)0.86 (Used by permission: SGL Technic, Inc., Karbate
Division.)

Heat Transfer Chapter | 15

Riser

(A) Maximum liquid level

439

Reboiler

Steam Downcomer LC

LC

Condensate pot

Steam condensate

Bottom of reboiler should be elevated just above top of condensate pot.

(B)

Distillation column

Controlled Liquid level

LC

LC

Start up bypass

Reboiler

Condensate pot regulates liquid level in exchanger tubes. Physical relationship between liquid level in condensate pot and required liquid level in exchanger tubes is important.

To pump Condensate

FIGURE 15-266A&B Piping arrangement for horizontal thermosyphon reboilers. (Source: R. Kern, How to Design Reboilers Systems, Chemical Engineering, August 1975.)

process units. The circulating fluid used as heating medium may be a fluid that undergoes a change of phase, delivering its latent heat, or it may be a single-phase fluid that performs its function by collecting and delivering sensible heat. Steam is the fluid most commonly used as a heating fluid. Its main advantages are [287]: 1. The raw material to produce it (softened or demineralized water) is relatively inexpensive. 2. The film coefficients for steam condensation are extremely high, implying that the size of the heat transfer equipment will be relatively small. 3. It has a high value of latent heat of condensation and vaporization. There are instances where it is necessary to deliver heat to a process at a very high temperature (> 250
C). If steam was used, its vapor pressure would be high, which invariably increases the cost of process equipment, as the high pressure makes it necessary to use higher plate thicknesses and stricter safety measures. In such situations, it is preferable to use as the heating medium any thermal fluids, such as synthetic or mineral oils that have low vapor

pressures, as they continue being liquids at high temperatures. The process equipment working with them will have low design pressures even for high temperatures. Figure 15-267A shows a schematic diagram of a steam system installation which has the elements described in the following paragraphs. Water Treatment Unit: Dissolved solids may precipitate and produce scaling in the boiler and heat transfer equipment. The required quality of the water in the circuit depends on the boiler’s operating pressure, and the dissolved solids level is maintained by periodic and continuous purges. To reduce purges, the makeup water is treated to eliminate hardness and other dissolved salts. The treatments are by clarifiers, filtration, softening and ion-exchange processes or by reverse-osmosis, depending on the quality of both the raw and treated water. Deaereator and Condensate Tank: Since the steam condensate is free from ions, it is recovered to be recycled to the boiler. Therefore, the treating unit only needs to treat the makeup water that replaces purges and system losses. The deaereator eliminates dissolved air that can cause corrosion in the unit.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

High – pressure header

7

6a

PC

PC

Low– pressure header 5 6b Fuel 8 10

Legends 1. Raw feed water 2. Water treatment

9

3. Deaeraeator and treated water storage 4. Boiler feed pump 5. Steam generator (boiler) 6a High pressure consumptions 6b Low pressure consumptions 1

2

7. Pressure reducing valve

3

8. Process equipment 9. Steam trap 4

10. Control valve

FIGURE 15-267A Components of a steam system.

Boiler and Steam Generator: The steam is generated by the combustion of any fuel. The steam pressure is controlled by regulating the fuel supply. Generally, more than one steam quality is required, e.g. a high pressure steam for turbines operation or high temperature process heating and a low pressure steam for lower thermal level applications. In such cases, low pressure steam is obtained by reducing the pressure in a control valve. Industrial Process: The steam consumption in the different process equipment is illustrated in Figures 15-267B as a stirred jacketed vessel. The steam flow is regulated with an inlet valve and the condensate is removed through a trap that avoids loss of uncondensed steam. If the process fluid mass flow rate is W, the required heat that must be delivered is: Q ¼ Wc Cpc ðt  t1 Þ

(15-689)

The heat delivered by the steam (assuming that the inlet steam is saturated) is: Q ¼ Wh l

(15-690)

Because the steam condenses, thus delivering its heat of condensation. In order to determine that only the condensate exits from the jacket-bottom nozzle, since if this connection were an open pipe or a manual valve at a fixed opening position, it is possible that an important fraction of the

inlet steam would escape through the outlet nozzle without reaching its heat of condensation. Thus, the steam consumption would be much higher than that resulting from Equation 15-690. It would be necessary to install some device that only allows the passage of the condensate that has already delivered its latent heat while retaining the uncondensed steam. This function is performed by devices referred to as steam traps, which are reviewed later in this section. Another problem that is harmful in steam installation is the presence of air.

Effect of Air in Steam Installations/Systems Air can access steam systems during shutdowns or when the installation cools down. Then when steam is later introduced into the system, a steam-air mixture will result. The presence of air in a steam system is harmful for the following reasons [287]. 1. Steam will condense at a temperature that depends on its partial pressure. Since air is present in the mixture, the partial pressure of steam is reduced, and the condensation temperature will be lower, thus decreasing the temperature driving force for heat transfer. 2. When steam condenses over cold surfaces (because air does not condense), the air-steam proportion in the vicinity of the heat transfer surfaces can be considerably

Heat Transfer Chapter | 15

Wc Cold fluid

441

t1 Cpc

Wh Steam

t Wc

Wh Condensate FIGURE 15-267B Steam-heated jacketed vessel.

higher than the bulk of the mixture. This creates diffusional resistances because steam molecules must diffuse through an air-enriched layer to reach the heat transfer surfaces. It has been reported that only 1% of air in a steam system can result in a 50% decrease of the heat transfer coefficients. 3. The presence of air increases corrosion rate in the units.

a fluid (usually an alcohol mixture) that can vaporize or condense depending on the temperature of the trap. The boiling point of the mixture is selected on the basis of the temperature range over which the trap has to operate. These

Generally, the usual practice is to purge the installation during startup. Manual purge valves are installed in cold and dead-end points and are left open for a period, allowing the purging of steam-air mixture so that most of the air is eliminated. This can result in the loss of steam. Air can still enter the system after startup, dissolved in the makeup water, thus purging should be carried out periodically. Steam traps are introduce to perform the air purging, thus discharging air and condensate but retaining the steam.

Steam Traps There are many different types of steam traps, each with its specific advantages and limitations. These are briefly described in the following sections. Thermostatic Bellows Trap (Figure 15-268). The principal elements in a thermostatic bellows are filled with

FIGURE 15-268 Thermostatic steam trap.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

traps operate on the difference in temperature between steam and cooled condensate and air. Steam increases the temperature inside the thermostatic element, which causes the fluid to vaporize and expand, thereby closing the discharge at C. As condensate and noncondensable gases back up in the upstream piping (called the cooling leg), the temperature begins to drop, the thermostatic element contracts, and the valve opens. The amount of the condensate backed up ahead of the trap depends on the load conditions, steam pressure and size of piping. The discharge of the trap is intermittent. Thermostatic traps can be used for venting air from a steam system. When air collects, the temperature drops and the thermostatic air vent automatically discharges the air at slightly below steam temperature over the entire operating pressure. Limitations: These traps are relatively small in size and have high discharge capacity, but they offer little resistance to water hammer and may be affected by corrosion because the bellows is made of a very thin metal sheet. Float-Type Trap (Figure 15-269): This is a mechanical trap that operates on the density principle. A lever C connects the valve float B to the valve and seat D. Once the condensate reaches a certain level in the trap, the float rises, opening the orifice and draining the condensate. A water seal formed by the condensate prevents live steam loss. This type of trap has a continuous condensate discharge because the float adopts an equilibrium position that allows evacuation of all the incoming condensate. These traps can adapt to variable condensate flow and allow a stable operation without the process fluctuation caused by discontinuous discharge traps. Limitations: Since the discharge valve is under water, it is not capable of venting air and noncondensables. Hence, these traps are usually provided with an auxiliary thermostatic vent, as shown in Figure 15-270. When the

accumulation of air and noncondensables cause a significant temperature drop, a thermostatic air vent H in the top of the trap discharges it. Inverted-Bucket Steam Trap (Figure 15-271): The principal element is an inverted bucket (B) that can move vertically inside a casing. The bucket acts through a lever opening and closing the discharge valve. When the bucket is at the lower position, the valve opens and when the bucket rises, the valve closes. The inlet port of the trap is located below the bucket. When the trap is full of condensate, the weight of the bucket makes it sink; thus opening the valve and allowing the condensate to discharge (left side of Figure 15-271). When steam enters the trap, it displaces the condensate and gets trapped below the bucket. This makes the bucket rise and subsequently closes the valve (right side of Figure 15-271). When the trap cools down, the steam condenses and the condensate gets below the bucket, which sinks, reopening the discharge. A small orifice is placed at the top of the bucket to vent the air, otherwise this accumulates below the bucket, and because it does not condense, the trap would remain closed. The air escapes through this orifice and accumulates at the top of the trap. When the trap opens, the air is eliminated by condensate pressure. Limitations: Some steam can still escape through the orifice, so it must be of a small diameter to reduce this. This limits the air purging capacity of this steam trap. Thermodynamic Trap (Figure 15-272): This type has a body (A) with inlet and outlet ports, a cover (B) and a control disk (C) that is free to move vertically. The body has two concentric ring-shaped seats. The inner seat (D) surrounds the inlet orifice (E) and the exterior seat (F) close to the cover. Between these round seats is the discharge

FIGURE 15-269 Float-type steam trap.

FIGURE 15-270 Float-type steam trap with auxiliary vent.

Heat Transfer Chapter | 15

443

FIGURE 15-271 Inverted-bucket steam trap.

FIGURE 15-272 Thermodynamic trap.

orifice (G). Both seats are carefully ground, as is the disk (C), so that the disk closes against the two concentric faces at the same time, separating inlet from outlet. The interior part of the cover has a central stop (H) that limits the lift of the disk, so when the disk is in the upper position, there is still some room between the upper face of the disk and the lower face of the cover. This space is referred to as the control chamber. When the disk closes against the seats, the control chamber remains isolated from the inlet and outlet ports. This type of trap is robust, small and economical. It has only one moving part, the disk, which is made from hardened stainless steel so retains a long service time. Limitations: These traps cannot be used with pressures lower than 1 barg, and their capacity is relatively small. Some steam is always lost when the trap opens thus, reducing the efficiency. Further details on the types, principles, monitoring, uses of steam traps can be obtained from Spirax Sarco Company, and their website is: www.spiraxsarco.com

HEAT TRANSFER IN JACKETED, AGITATED VESSELS/KETTLES Heat Transfer in Agitated Vessels Agitated vessels with an external jacket or an internal coil are increasingly employed in biotechnology and other process applications. The most common type of jackets consists of an outer cylinder that surrounds part of the vessel. The heating or cooling medium circulates in the annular space between the jacket and vessel walls. Alternatively, the condensation of vapor (e.g. steam, or proprietary heat transfer medium) may serve for heating, and the vaporization of liquids (e.g. a refrigerant) may serve for cooling. The heat is transferred through the wall of the vessel. Circulation baffles can be used in the annular space to increase the velocity of the liquid flowing through the jacket, thus enhancing the heat transfer coefficient. An alternative is to introduce the fluid via a series of nozzles spaced down the jacket. In this case, the momentum of the

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

only reduce the inside film resistance, which is one of the number of resistances that determine the overall heat transfer coefficient. Many jacketed vessels are reactors; the types of exothermic or endothermic effects must be taken into account. Stirred tank reactors in which an exothermic reaction is performed may involve the removal of substantial amounts of heat from the reacting mixture. Refluxing of a boiling solvent is a common method; the heat of vaporization of the solvent is removed by the reflux condenser, and the condensed solvent is returned to the reactor. Other methods include cooling the walls of the reactor by means of a jacket with a cooling medium, inserting a cooling coil, or using an external heat exchanger with a pump around the system. In many applications using jacketed vessels, successive batches of material are heated (or cooled) to a given temperature, and therefore the heat transfer involves an unsteady state process. Proper care is essential in terms of charging, agitation and adequate cooling of the reactants to prevent the generated heat from subsequently leading to a runaway reaction. FIGURE 15-273A Typical vessel external jackets for heat transfer.

jets issuing from the nozzles develops a swirling motion in the jacket liquid. The spacing between the jacket and vessel wall depends on the size of the vessel, however, it ranges from 2.0 in. (50 mm) for small vessels to 12 in. (300 mm) for larger vessels. Figure 15-273A illustrates different configurations of jacketed vessels. The pitch of the coils and the area covered can be selected to provide the heat transfer area required. Standard pipe sizes from 2.5 in. to 5.0 in. (60 mm to 120 mm) outside diameter area are often used. Half-pipe construction can produce a jacket capable of withstanding a higher pressure than conventional jacket design. The rate of heat transfer to or from an agitated liquid mass in a vessel depends on the physical properties of the liquid (e.g. density, viscosity and specific heat) and of the heating or cooling medium, the vessel geometry and the degree of agitation. The type and size of the agitator and its location also influence the rate. An agitator is selected on the basis of material properties and the processing required. The heat transfer forms part of a process operation, such as suspended or dissolving solids, dispersing a gas in a liquid, emulsifying immiscible liquids or regulating chemical reactions. When processing is controlled by heat transfer variables, a log mean temperature difference (DTLMTD) and heat transfer surface area will predominate over the agitation variables. Provided it is sufficient to give a homogeneous process fluid temperature, increased agitation can

Design Equation Consider a vessel containing an agitated liquid. Heat transfer occurs mainly through forced convection in the liquid, conduction through the vessel wall, and forced convection in the jacket media. The heat flow may be based on the basic film theory equation and can be expressed by: Rate ¼

Driving force Resistance

or: Q DT ¼ A 1=U

(15-691)

In an idealized situation, the vessel and its jacket each operate continuously under isothermal conditions. Rearranging Equation 15-691 becomes: Q ¼ UADT

(15-692)

In a realistic continuous situation, where the vessel contents are at constant temperature, but with different jacket inlet and outlet temperatures, Equation 15-692 is expressed as: Q ¼ UADTLMTD where DTLMTD is the log mean temperature difference between the bulk temperature of the vessel contents, t, and the temperature in the jacket, T. DTLMTD is expressed as: DTLMTD ¼

½ðt2  T2 Þ  ðt1  T1 Þ ln ½ðt2  T2 Þ=ðt1  T1 Þ

(15-693)

Heat Transfer Chapter | 15

where:

to external cooling, as is so often the required condition for some batch reaction processes. Expected heat transfer overall coefficients for estimating typical organic processes in the vessel with steam, water, or a cooling methanolwater mixture in the jackets are as follows:

t1 ¼ entering fluid temperature in the vessel t2 ¼ leaving fluid temperature in the vessel T1 ¼ entering fluid temperature in the jacket T2 ¼ leaving fluid temperature in the jacket The overall heat transfer coefficient, U, is determined from a series of resistances to the transfer of heat, namely: 1 1 xw 1 ¼ þ FFi þ þ FFj þ k U hi hj

445

Overall Heat Transfer Coefficient, U Steam heating Cooling

(15-694)

where: hi ¼ coefficient on process side of heat transfer area, i.e. inside surface of jacket vessel or outside surface of internal coil, W/m2
C. FFi ¼ fouling factor, inside vessel, m2
C/W. FFj ¼ fouling factor, inside jacket, m2
C/W. k ¼ thermal conductivity, W/m
C. hj ¼ coefficient on inside surface of jacket, W/m2
C. xw ¼ wall thickness of vessel or coil, mm. When the heat transfer is through internal coils or tubular baffles, the difference between the inner and outer heat transfer surfaces may be significant. The heat transfer that is achieved in external jacketed kettles used for reaction and/or mixing and heating/boiling/ cooling varies considerably with the style of jacket. Jackets may be one piece open chambers surrounding the main shell of the vessel, or they may be coil style, usually of the half-pipe design (see Figures 15-273A and B). The halfpipes are continuously welded to the shell and may be grouped in segments or sections of the shell to allow for the rather rapid conversion of a section from external heating

Btu/h. ft2
F




W/m2 C

Btu/h.ft2
F

W/m2
C

Open jacket

25e55

142e312

25e40

142e227

Coils, halfpipe

25e80

142e454

30e55

177e312

Baker and Walter [3] report tests performed on open jacketed agitated vessels and published some of the limited results for this type of equipment. These data indicate the effect of jetting the fluid at various velocities into the jacket. Chapter 6, “Mixing of Liquids,” in Volume 1, 4th Edition, of this series provides more details and discusses various vessel heat transfer mechanisms (outside jackets and/or half-pipes, internal vertical pipes, and internal coils). Jacketed vessels (external) are often used for chemical reaction temperature control and for the heating or cooling mixtures being agitated in vessels. Internal vertical or horizontal coils in a vessel can also be used for temperature control. Gruver and Pike [163] recommend that the use of a single fluid in the jackets/coils is better than requiring complicated controls to switch types of fluids. See Figures 15-273A and B for limited examples of reaction and other process vessels that require heat transfer for proper processing. Markovitz [202] reports improved heat transfer for the inside of jacketed vessels when the surface has been electropolished, which gives a fine, bright surface. Heat transfer in agitated vessels with internal coils containing the heat transfer fluid (process on outside of coil) is expressed by the outside coefficient on coils [183] and as shown in Figure 15-274.   0:14 0:62 hc Dj 60 nDa2 r cp m1=3 m ¼ 0:87 k m k mw (15-695) For heat transfer fluids inside reactor jackets or other process vessels with agitation to fluids in vessels (Figure 15-273A), the heat transfer is expressed [183] as:

FIGURE 15-273B Process vessel with internal coil and agitation to improve heat transfer. (Used by permission: Engineering Manual Dowtherm Heat Transfer Fluids, ©1971. The Dow Chemical Co.)

  0:14 2=3 hj Dj 60 nDa2 r cp m1=3 m ¼ 0:36 k m k mw (15-696)

446

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 15-274 Heat transfer coefficients for jackets and coils with fluid agitation. (Used by permission: Engineering Manual Dowtherm Heat Transfer Fluids, ©1971. The Dow Chemical Co.)

and in Figure 15-274. Also see references [282] and [283]. where: hc ¼ average film coefficient, clean Btu/(h) (ft2) (
F) Di or Dj ¼ I.D. of vessel, ft Da ¼ diameter of agitator, ft

k ¼ thermal conductivity of fluid processed, Btu/(h) (ft2) (
F/ft) n ¼ rev/min of agitator L ¼ length and thickness, ft, of coil or jacket cp ¼ specific heat, Btu/(lb) (
F) m ¼ viscosity ¼ cps  2.42, lb/(h) (ft)

Heat Transfer Chapter | 15

r ¼ density, lb/ft3 r ¼ fouling resistance, or tube resistance, (h) (ft2) (
F)/Btu

heat transfer coefficients of various jacketed agitator vessels.

Fouling Factors and Wall Resistances

Subscripts: w ¼ wall j ¼ jacket side c ¼ clean i ¼ inside

Experience and judgment of fouling severity are required to estimate fouling factors (FFi, FFj) to determine the overall heat transfer coefficient. These will vary with time and will depend on the frequency and efficiency of vessel cleaning. Wall resistances can be significant and should be calculated from accurate thermal conductivity data.

Inside Film (hi) Coefficients When applying the following equations for calculating film coefficients in jacketed vessels, the physical property data should be accurate. This is especially important for the thermal conductivity, k, as its value can have a major impact on the calculated film coefficient and vary widely. The inside film heat transfer coefficient (hi) can be calculated from the following Nusselt number correlation:  c  mb DT W a b ; (15-700) f Nu ¼ CNRe NPr mw H DA where fðDT =H; W=DA Þ represents various geometric correction factors. For a geometrically similar system, Equation (15-700) becomes:  c mb (15-701) Nu ¼ C NaRe NbPr mw For agitated vessels: a   b  c hi D T r N D2A Cp m mb ¼ C kf m mw k

447

(15-702)

where: hi ¼ heat transfer coefficient to vessel wall or coil, W/m2
C DA ¼ agitator diameter, m DT ¼ tank diameter, m N ¼ agitator speed (rev/sec) r ¼ density, kg/m3 kf ¼ thermal conductivity, W/m
C Cp ¼ specific heat capacity, J/kg
C mb ¼ viscosity at bulk fluid temperature, [(N s)/m2] [ kg/(m sec)] mw ¼ viscosity at the wall temperature, [(N s)/m2] [ kg/ (m sec)] The values of the constant C and the exponents a, b and c depend on the type of agitator, whether baffles are used and their type, and whether the transfer is via the vessel wall or to coils. Baffles are normally used in most applications, and the values of a, b and c in the literature are 2/3, 1/3 and 0.14 respectively. Tables 15-98 and 15-99 show correlations for calculating inside film

Outside Coefficient (ho) Jacketed Vessels Annual Jacket with Spiral Baffling In heat transfer applications, this jacket is considered as a helical coil if certain factors are used for calculating outside film coefficients. The equivalent heat transfer diameter, De, for a rectangular cross-section is equal to 4w (w being the width of the annular space). Velocities are calculated from the actual cross-section of the flow area, pw (p being the pitch of the spiral baffle) and the effective mass flow rate W0 through the passage. The effective mass flow rate is approximately 60% of the total mass flow rate of the jacket. (15-703) W0 z 0:6 W At a given Reynolds number, heat transfer coefficients of coils, particularly with turbulent flow are higher than those of long, straight pipes due to friction. This also applies to flow through an annular jacket with spiral baffling. At NRe > 10,000 the Seider-Tate equation for straight pipe, 1 þ 3.5 (De/Dc) can be used to calculate the outside film coefficient.  0:14 ho De mb ¼ 0:027 ðNRe Þ0:8 ðNPr Þ0:33 k mw 

D  e (15-704)  1 þ 3:5 Dc where: De ¼ equivalent diameter for heat transfer, mm (ft) Dc ¼ mean or center line diameter or internal coil helix, mm (ft) hj ¼ heat transfer coefficient on inside surface of jacket m b ¼ viscosity at bulk fluid temperature, [(N s)/m2] [ kg/(m sec)] mw ¼ viscosity at the wall temperature, [(N s)/m2] [ kg/(m sec)] NRe ¼ NPr ¼

r$v$De m Cp $m k

448

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-98 Equations for Calculating Inside Film Coefficients (hi) of Jacketed Agitated Vessels Agitated Type

Baffled

Reynolds Number (NRe)

Nusselt Number (NNu) 0.67

Remarks 0.33

Paddle

Yes/No

20 < NRe < 4,000

0.415(NRe) (mb/mw)0.14

(NPr)

Vessel geometry is discussed by Holland and Chapman [245]

Paddle

Yes/No

> 4,000

0.36(NRe)0.67(NPr)0.33 (mb/mw)0.14

Vessel geometry is discussed by Holland and Chapman [245]

Flat blade turbine

Yes/No

< 400

0.54(NRe)0.67(NPr)0.33 (mb/mw)0.14

DA/DT ¼ 1/3, H/DT ¼ 1.0. Six-bladed turbine. Standard geometry.

Flat blade turbine

Yes

> 400

0.74(NRe)0.67(NPr)0.33 (mb/mw)0.14

DA/DT ¼ 1/3, H/DT ¼ 1.0. Six-bladed turbine. Standard geometry.

Flat blade turbine

Yes

2,000 < NRe < 700,000

1.10(NRe)0.62(NPr)0.33 (mb/mw)0.14

Propeller

Yes

> 5,000

0.64(NRe)0.67(NPr)0.33 (mb/mw)0.14

Three blades

Propeller

Yes

No limitation

0.54(NRe)0.67(NPr)0.25 (mb/mw)0.14

45
pitched, four-bladed impeller, Equation is based on limited data with regard to propeller pitch and vessel baffling. Divide hi obtained with this equation by a factor of about 1.3

Retreating blade turbine

Yes

No limitation

0.33(NRe)0.67(NPr)0.33 (mb/mw)0.14

Glassed-steel impeller. Three retreating blades. The lower constant (0.33) for the glassed-steel impeller is attributed to greater slippage around its curved surfaces than around the sharp corners of the alloy-steel impeller.

Retreating blade turbine

Yes

No limitation

0.37(NRe)0.67(NPr)0.33 (mb/mw)0.14

Alloy-steel impeller. Three retreating blades.

Retreating blade turbine

No

No limitation

0.68(NRe)0.67(NPr)0.33 (mb/mw)0.14

Six retreating blades.

Propeller

Yes

No limitation

0.54(NRe)0.67(NPr)0.25(mb/ mw)0.14

45
pitched four-bladed impeller. Equation is based on limited data with regard to propeller pitch and vessel baffling. Divide hi obtained with this equation by a factor of about 1.3

Anchor

No

30 < NRe < 300

1.0(NRe)0.67(NPr)0.33 (mb/mw)0.18

The overall heat transfer coefficient U, varies inversely with the anchor-to-wall clearance. Anchor to wall clearance less than 1 in.

Anchor

No

300 < NRe < 4,000

0.38(NRe)0.67(NPr)0.33 (mb/mw)0.18

Similar condition as before.

Anchor

No

4,000 < NRe < 37,000

0.55(NRe)0.67(NPr)0.25 (mb/mw)0.14

Anchor to wall clearance of 1 to 5.125 in. Vessel geometry is illustrated by Holland and Chapman [245]

Helical ribbon

No

< 130

0.248(NRe)0.5(NPr)0.33 (mb/mw)0.14  (e/DA)0.22 (i/D)0.28

e ¼ clearance, (DT  DA)/2, ft. DA ¼ impeller diameter, ft. i ¼ agitator ribbon pitch, ft.

Helical ribbon

No

> 130

0.248(NRe)0.67(NPr)0.33 (mb/mw)0.14  (e/DA)0.22 (i/D)0.25

e ¼ clearance, (DT  DA)/2, ft. DA ¼ impeller diameter, ft. i ¼ agitator ribbon pitch, ft.

Heat Transfer Chapter | 15

449

TABLE 15-99 Equations for Calculating Outside Film Coefficients (ho) of Jacketed Agitated Vessels Jacket Type

Reynolds Number (NRe)

Nusselt Number (NNu) 0.8

0.33

Remarks This jacket is considered a special case of a helical coil if certain factors are incorporated into equations for calculating outside-film coefficients. In the equations at left and below, the equivalent heat transfer diameter De, for a rectangular cross-section is equal to four times the width of the annular space, w and De is the mean or centerline diameter of the coil helix. Velocities are calculated from the actual cross-section of the flow area, pw, where p is the pitch of the spiral baffle, and from the effective mass flow rate, W’, through the passage. The leakage around spiral baffles is considerable, amounting to 35e50% of the total mass flowrate. The effective mass flowrate to the jacket: W’ ¼ 0.6W. The NNu for this equation should be expressed in terms of De(NNu ¼ hjDe/k) as should be the Reynolds number (NRe ¼ De v r/m), k being thermal conductivity, v being velocity, m being fluid viscosity and r being fluid density.

Annular jacket with spiral baffling

> 10,000

0.027(NRe) (NPr) (mb/mw)0.14 x (1+ 3.5De/Dc)

Annular jacket with spiral baffling

< 2,100

1.86(NRe)0.33(NPr)0.33 (De/L)0.33 (mb/mw)0.14

Same as the above. L is length of coil or jacket passage, ft.

Annular jacket with spiral baffling

2,100 < NRe < 10,000

1.86(NRe)0.33(NPr)0.33 (De/L)0.33 (mb/mw)0.14

Use the equation, depending on the value of NRe

Annular jacket, no baffles

Laminar flow

1.02(NRe)0.45(NPr)0.33 (De/L)0.4 (mb/mw)0.14  (Djo/Dji)0.8 (NGr)0.05

Dji and Djo are the inside and outside diameters of the jacket respectively. For this equation, De ¼ Djo  Dji. The Grashof number NGr ¼ D3e rg b DtG =m2, where De is equivalent diameter, g is acceleration due to gravity, b is coefficient of volumetric expansion, m is viscosity, r is density and DtG is the difference between the temperature at the wall and that in the bulk fluid. NGr must be calculated from fluid properties at the bulk temperature.

Annular jacket with spiral baffling

< 2,100

1.86(NRe)0.33(NPr)0.33 (De/L)0.33 (mb/mw)0.14

The Nusselt and Reynolds numbers must be calculated with De as the diameter term.

Annular jacket no baffles

Turbulent

0.027(NRe)0.8(NPr)0.33 (mb/mw)0.14  (1+ 3.5De/Dc)

For the equivalent heat transfer diameter for turbulent flow, use De ¼ [(Djo)2  (Dji)2]/Dji, where Dji and Djo are the inside and outside diameters of the jacket respectively. The cross-sectional flow area, Ax ¼ p[(Djo)2  (Dji)2]/4.

Annular jacket with spiral baffling

210 < NRe < 10,000

0.027(NRe)0.8(NPr)0.33 (mb/mw)0.14  (1+ 3.5De/Dc)

Use the equation depending on the value of NRe.

Half-pipe coil jacket

Laminar flow

1.86(NRe)0.33(NPr)0.33 (De/L)0.33 (mb/mw)0.14

When pipe coils are made with a semicircular crosssection, De ¼ pdci/2, where dci is the inner diameter of the pipe, in feet. For calculating the velocity, the crosssectional flow area equals pd2ci =8. When pipe coils are made with a 120
central angle, De ¼ 0.0708 dci, and the cross-sectional area equals 0.154 (dci)2.

Half-pipe coil jacket

Turbulent flow

0.027(NRe)0.8(NPr)0.33 (mb/mw)0.14  (1+ 3.5De/Dc)

Dc is the mean diameter of the coil.

Half-pipe coil jacket

Transition flow

0.027(NRe)0.8(NPr)0.33 (mb/mw)0.14  (1+ 3.5De/Dc)

Use the equation depending on the value of NRe.

Continued

450

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 15-99 Equations for Calculating Outside Film Coefficients (ho) of Jacketed Agitated Vesselsdcont’d Reynolds Number (NRe)

Jacket Type

Nusselt Number (NNu) 0.33

Remarks

0.33

Dimple jacket

Laminar flow

1.86(NRe) (NPr) (De/L)0.33 (mb/mw)0.14

The equivalent diameter De, in a dimpled jacket equals 0.66 in. the cross-sectional flow area equals 1.98 in2 per foot of vessel circumference.

Dimple jacket

Turbulent flow

0.27(NRe)0.8(NPr)0.33 (mb/mw)0.14

The coefficients are not very accurate due to turbulence created by the dimples in the flow steam.

Dimple jacket

Transition flow

0.27(NRe)0.8(NPr)0.33 (mb/mw)0.14

Determine NNu from the equation depending on the value of NRe.

The dimensionless parameters: Prandtl number, NPr ¼

Reynolds number, NRe ¼

rv D m

¼

rNDA2 m

where r ¼ density v ¼ velocity D ¼ diameter DA ¼ impeller diameter N ¼ rotational speed of the agitator m ¼ viscosity

Nusselt number, NNu ¼

Cp m k

hD k

where h ¼ heat transfer coefficient D ¼ diameter k ¼ thermal conductivity

where Cp ¼ specific heat m ¼ viscosity k ¼ thermal conductivity

Viscosity number, mb =mw

Grashof number, NGr ¼

where mb ¼ viscosity at the bulk fluid temperature mw ¼ viscosity at the wall surface temperature ðmb =mw Þ0:14 y 1:0 for water

where De ¼ equivalent diameter r ¼ density g ¼ acceleration due to gravity

De3 r2 g b DtG m2

b ¼ coefficient of volumetric expansion DtG ¼ difference between the temperature at the wall and that in the bulk fluid

At NRe < 2,100:

 0:33  0:14 ho D e mb 0:33 0:33 De ¼ 1:86 ðNRe Þ ðNPr Þ k L mw (15-705)

where L is the length of the coil or jacket passage, in mm (ft).

Annular Jacket with No Baffles In the case of steam condensation, a film heat transfer coefficient hj is used. In the case of liquid circulation, velocities will be very low because of the large cross-sectional area. Outside heat transfer coefficients for unbaffled jackets under laminar flow conditions can be calculated from: hj D e 0:45 0:33 ¼ 1:02 ðNRe Þ ðNPr Þ k

D 0:4 m 0:14 D 0:8 e jo 0:05 b  ðNGr Þ L mw Dji where: Dji ¼ inside diameter of the jacket Djo ¼ outside diameter of the jacket

(15-706)

De ¼ Djo  Dji The Grashof number NGr is expressed by: NGr ¼

D2e r2 g b DtG m2b

where: g ¼ acceleration due to gravity r ¼ fluid density b ¼ coefficient of volumetric expansion DtG ¼ the difference between the temperature at the wall and that in the bulk fluid mb ¼ viscosity at bulk fluid temperature Evidently, from the low value of the exponent in Equation 15-706, the contribution from natural convection and hence its practical significance is small. The following equation can be used to predict heat transfer coefficients from coils to tank walls in agitated tanks. 2=3  1=3  1=4  hDT rND2A Cp m mb ¼ C (15-707) kf m mw k where C is a constant. Table 15-100 gives values of C for various agitator types and surfaces [415]. A computer

Heat Transfer Chapter | 15

TABLE 15-100 The Constant C used in Equation 15-707 for Various Agitator Types and Surfaces [415] Surface

C

Turbine

Jacket

0.62

2

Turbine

Coil

1.50

PADDLE

Paddle

Jacket

0.36

COIL

Paddle

Coil

0.87

3.048

0.170

1.01

200.0

Anchor

Jacket

0.46

720.0

4.130

2.90

1.0

Propeller

Jacket

0.54

1.0

Propeller

Coil

0.83

program called MIXER was developed to determine the heat transfer coefficient for any type of agitator and surface using the value in Table 15-101, fluid physical properties, agitator speed and diameter. Heat Transfer Area Surface area for heating or cooling agitated vessels can be provided by either external jacketing or internal coils (or tubular baffles). Jacketing is usually preferred because of:

l l l

l

TABLE 15-101 Input Data and Computer Results for Example 15-39

Agitator

(Source: N.P. Chopey and T. G. Hicks, Handbook of Chemical Engineering Calculations, McGraw-Hill, 1984.)

l

451

Cheaper construction materials because the jacket is not in contact with process fluid. Less tendency to foul. Easier cleaning and maintenance. Fewer problems in circulating catalysts and viscous fluids. Larger heat transfer surface, unless significant reactor volume is taken up by the coils.

Helical jackets may allow thinner walls to be used for pressure vessels. No restriction is placed on agitator type, whereas if a coil is installed it restricts agitator dimensions. Coils should be considered only if jacketing alone does not provide a sufficient heat transfer area, if the jacket pressure exceeds 150 psig or if high temperature vacuum processing is required. The coil offers the advantage of a higher overall film coefficient because of thinner walls with the latter conditions, but the wall resistance may not be significant compared to that on the process side (e.g., with a viscous liquid). EXAMPLE 15-38

Determine the heat transfer coefficient from a coil immersed in an agitated vessel with a diameter of 10 ft

Input Data

Heat Transfer Coefficient to Fluids in a Vessel Using Mechanical Agitated Coils or Jacket

AGITATOR:

PADDLE

SURFACE:

COIL

VALUE OF A:

0.870

DIAMETER OF VESSEL, m.:

3.048

THERMAL CONDUCTIVITY, W/m.K.:

0.170

DIAMETER OF AGITATOR, m.:

1.010

SPEED OF AGITATOR, rev/ min.:

200.000

DENSITY OF FLUID, kg/m3:

720.000

VISCOSITY OF FLUID, Pa.s:

4.130

SPECIFIC HEAT CAPACITY, kJ/kg.K:

2.900

VISCOSITY AT BULK FLUID TEMPERATURE, Pa.s: 1.000 VISCOSITY AT SURFACE TEMPERATURE, Pa.s:

1.000

REYNOLDS NUMBER:

592794.

PRANDTL NUMBER:

70.453

HEAT TRANSFER COEFFICIENT, W/m2.K.:

1414.238

(3.048 m). The agitator is a paddle measuring 3.5 ft (1.01 m) in diameter and revolving at 200 rev/min. The fluid properties are: r ¼ density ¼ 720 kg=m3 mb ¼ viscosity ¼ 4:13 cP ¼ 4:13  103 ðPa:sÞ Cp ¼ specific heat ¼ 2:9 kJ=kg:K. k ¼ thermal conductivity ¼ 0:17 W=m:K:

452

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Assume ðmb =mw Þ0:14 ¼ 1:0 Solution From Table 15-100, for a paddle type agitator, C ¼ 0.87. The heat transfer coefficient from Equation 15-707 becomes: 2=3    Cp m 1=3 mb 1=4 hDT r N D2A ¼ 0:87 kf m mw k N ¼ number of revolution per sec is 200/60 ¼ 3.3333 rev/sec. The Reynolds number, NRe ¼ r ND2A =m is:

The Prandtl number, NPr ¼ Cp m=k

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 for a wide range of temperatures from 100e700
F 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.

FALLING FILM LIQUID FLOW IN TUBES

The heat transfer coefficient is:  0:17 ð592; 794Þ2=3 ð70:45Þ1=3 hv ¼ 0:87 3:048  hv ¼ 1; 414 W m2 $K Table 15-101 shows the input data and computer results from the MIXER computer program of Example 15-38.

Pressure Drop 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. 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: Dp ¼

fG2 Ln0 5:22ð10Þ ðDi ÞðsÞðm=mw Þ 10

0:14

The Sieder and Tate equation for the pressure drop in shell is: Dp ¼

fG2 Di ðN þ 1Þ 5:22ð10Þ ðDe ÞðsÞðm=mw Þ 10

0:14

Values of f vs. Re number are given in Figure 15-140. Pressure drops from Dowtherm A heat transfer media flowing in pipes may be calculated from Figure 15-52. The effective lengths of fittings, etc., are shown in Chapter 4 of Volume 1 of this series. The vapor flow can be determined from the latent heat data and the condensate flow. In a

The liquid runs in a film-like manner by gravity down the inner walls of the vertical tubes in a falling film exchanger. The tubes do not run full, and therefore the film coefficient is greater than for the same liquid rate in a full tube by [81]:  D2i (15-708) h ðfilm gravityÞ ¼ hðfullÞ 4d0 ðDi  d0 Þ where: Di ¼ ID of tube, ft. d0 ¼ film thickness, ft. For water [81]: 1=3  w ¼ 120ðGÞ1=3 hm ¼ 120 pDi

(15-709)

where: G0 ¼ mass flow rate/unit circumference, lb/(h) (ft.) G0 ¼ w/ (p D) w ¼ mass flow rate, lb/h For other liquids [81] in turbulent flow:

cm1=3 4G 1=3 hm qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi ¼ 0:01 k mf k3t r2 g m21

(15-710)

Properties are evaluated at the length mean average temperature. where: mf ¼ viscosity of liquid at film temperature, tf, lb/(h) (ft.) g ¼ acceleration due to gravity ¼ 4.14  108 ft/(h)(h) r ¼ fluid density, lb/ft3

Heat Transfer Chapter | 15

The heat transfer coefficient hm, is to be used with the length mean Dt. In streamlined flow, 4 G0 /mt < 2,000: !1=3  1=9 5=3 ha cmf 4G0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ¼ 0:67  ka Lr2=3 g1=3 mf k3 r2 g m2 f

f

(i.e., the physical properties of the fluids are identical) Equation 15-712 becomes: 0:65  h2 DT2 N2 D2A2 ¼ (15-713) h1 DT1 N1 D2A1 or

(15-711) where: ha ¼ film heat transfer coefficient based on arithmetic mean Dt Table 15-102 is an experience guide for reasonable service using the types of water indicated inside tubes of the material listed. Sinek and Young [160] present a design procedure for predicting liquid side falling film heat transfer coefficients within 20% and overall coefficients within 10%.

where C is a constant that depends on the agitator design and h is the required inside film heat transfer coefficient. To scale-up a reactor from V1 to V2 with geometrically similar systems having similar bulk average temperatures

1:30  0:65  h2 DT2 N2 DA2 ¼ h1 DT1 N1 DA1  1:30  0:65 N2 h2 DT2 DA1 ¼ N1 h1 DT1 DA2

where DT2 =DT1 ¼ DA2 =DA1 . Equation 15-715 becomes:  1:30  0:65 N2 h2 DA2 DA1 ¼ N1 h1 DA1 DA2 At equal heat transfer coefficients, h1 ¼ h2   0:65 0:30 N2 DA1 ¼ N1 DA2

Scale-Up with Heat Transfer The scale-up criterion of constant heat transfer coefficient is suitable when the predominant problem of the reactor involves the removal of heat. The magnitude of the heat transfer coefficient is governed by the intensity of stirring within the reactor, and is represented by: 0:65   0:33  0:24 hDT r N D2A Cp m mb ¼ C (15-712) kf m mw k

or

  0:46 N2 DA2 ¼ N1 DA1

(15-714)

(15-715)

(15-716)

(15-717)

(15-718)

Assuming that the equation is in the turbulent range, the Power numbers will be equal. The ratio of the power per unit volume (P/V) for large and small scales can be expressed by:  r N32 D5A2 D3A2 ðP=VÞ2 N3 D2  3 ¼ 23 A2 ¼ (15-719) 3 5 ðP=VÞ1 N1 D2A1 r N1 DA1 DA1

TABLE 15-102 Allowable Water Velocities in Tubes Minimum* Velocity, ft/sec

Maximum Velocity, ft/sec

Preferred Velocity, ft/sec

70-3-Cupro nickel; 0.5% Iron

2.5e3

12

6e8

Sea water

90-10-Cupro nickel; 1.25% Iron

2.5e3

10

6e8

Sea water

Aluminum brass

2.5e3

8

5e6

Brackish water

Steel

2.5

5

4

Treated well water

Steel

2.5

8e10

5e6

Cooling tower recirculated water

Steel

2.5

8

6

Fluid

Tube Material

Sea water

*Do not design below these values.

453

454

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Substituting Equation 15-718 into Equation 15-719 gives: 2  1:38  ðP=VÞ2 DA2 DA2 ¼ ðP=VÞ1 DA1 DA1 (15-720) 0:62  DA2 ¼ DA1 The power per unit volume thus increases slightly. For equal heat transfer coefficient at small and large scales, the larger tank will use an impeller at a lower speed. where  3 V2 DT2 ¼ (15-721) V1 DT1  0:15 N2 V2 ¼ (15-722) N1 V1 Having achieved the same heat transfer coefficient on the larger scale, the heat removal facilities must be increased because the heat generation is proportional to V2/ V1, but the surface area of the vessel has increased by ðV2 =V1 Þ2=3 . This can be done by adding coils to the reactor. Larger areas can be added by using an external heat exchanger and a pump around the system. In some cases it may be possible to lower the coolant temperature and thereby increase the rate of heat flow through the existing surface. However, this is usually fixed by stability considerations, which require that the coolant temperature be within a few degrees of the reaction temperature.

a batch may done be 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. The overall heat transfer coefficient U is constant for the process and over the entire surface. 2. Liquid flowrates are at steady state. 3. Specific heats are constant for the process. 4. The heating or cooling medium has a constant inlet temperature. 5. Agitation gives a uniform batch fluid temperature. 6. There is no phase change. 7. 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 q can be derived by the differential heat balance. For an unsteady state operation, as shown in Figure 15-275, the total number of heat transferred is q0 , and per unit time q is:

BATCH HEATING AND COOLING OF FLUIDS The heating and cooling of process fluids in a batchoperated 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 [413] and Dream [414] have compiled a collection of correlations of heat transfer coefficients in agitated vessels. Batch processes are sometimes disadvantageous because: l

l l l

The 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 regeneration is an integral part of the total operating period.

The variables in batch heating or cooling processes are surface requirement, time and temperature. Heating

Accumulation

Transfer

In the batch

rate

where: Dt ¼ T1  t

(15-724)

Equating III and IV gives: Mc

dt ¼ UA Dt dq

(15-725)

Rearranging Equation 15-725 gives: dt UA ¼ $dq Dt Mc

(15-726)

Integrating Equation 15-726 between the limits gives: Zt2 t1

dt UA ¼ T1  t Mc

Zq dq 0

(15-727)

Heat Transfer Chapter | 15

455

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
F (850 W/m2 K). Calculate the time required to heat the tank contents with steam condensing at 320
F (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  t1 UA $q ¼ ln 1 T1  t2 Mc   433  293 ð850Þ ð9:29Þ W m2 kg$K $ ¼ ln q $ 433  398 ð22; 679:5Þ ð2:1Þ ð103 Þ m2 :K kg J q ¼

ð1:386Þð22; 679:5Þ ð2:1Þ ð103 Þ hr ð850Þ ð9:29Þð3600Þ ¼ 2:32 h:

An Excel spreadsheet program (Batch Heating: Internal Coil Isothermal Heating Medium.xls) has been developed for Example 15-39.

Batch Reactor Heating and Cooling Temperature Prediction

FIGURE 15-275 Agitated batch vessel.

Integrating Equation 15-727 from t1 to t2 while the batch processing time passes from 0 to q yields: ln or

 T1  t1 UA ¼ $q T1  t2 Mc

 Mc T1  t1 ln q ¼ T1  t2 UA

(15-728)

where: A ¼ heat transfer surface area. c ¼ specific heat of batch liquid. M ¼ weight of batch liquid. T1 ¼ heating medium temperature. t1 ¼ initial batch temperature. t2 ¼ final batch temperature. U ¼ overall heat transfer coefficient. q ¼ time

EXAMPLE 15-39 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.
F (2.1 kJ/kg.K) is to be heated from 68
F (293 K) to 257
F (398 K). The tank contains a

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:  Mc T  t1 (15-728) ln 1 q ¼ T1  t2 UA Equation 15-728 can also be used to calculate the heatup 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 [415]. Assuming that M, c, U and A are constants, where: K ¼

UA Mc

Equation 15-728 becomes:  1 T  t1 ln 1 q ¼ K T1  t2

(15-729)

(15-730)

Rearranging Equation 15-730 gives the jacket temperature as a function of times as: T1 ¼

t1  t2 eKq 1  eKq

(15-731)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Therefore, by taking a series of readings during a trial heat-up, K can be determined. The heat-up and cooldown times for varying jacket temperatures can be predicted.

where: Dt ¼ T  t1 Then: M c

EXAMPLE 15-40 Batch Reactor Heating and Cooling Temperature Prediction

Assume that in Example 15-39, 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 20
C to reaction temperature of 60
C, and then cooled to 35
C. Using a hot water jacket temperature of 80
C, it took 15 min. to heat the batch from 20
C and 30
C. Calculate the jacket temperatures required to perform the heat-up and cool-down. Solution From Equation 15-729:

The jacket temperature required for a 2 h heat-up can be obtained from Equation 15-731 as: t1  t2 eKq 1  eKq 1

¼

dT ¼ U A Dt dq

(15-734)

Substituting Equation 15-733 into Equation 15-734 and rearranging gives: ZT2 

dT ¼ T  t1

T1

Zq

UA $dq Mc

(15-735)

0

Integrating from T1 to T2, while the time passes from 0 to q gives:  T1  t1 UA ¼ $q ln T2  t1 Mc (15-736)  Mc T1  t1 or q ¼ ln T2  t1 UA where:

K ¼ 0:00017 s1

T1 ¼

(15-733)

20  60 eð0:00017 s 23600 sÞ

1  eð0:00017 ¼ 77
C

123600 s

sÞ

A ¼ heat transfer surface area. c ¼ specific heat of batch liquid. M ¼ weight of batch liquid. T1 ¼ initial batch temperature. T2 ¼ Final batch batch temperature. t1 ¼ cooling medium temperature. U ¼ overall heat transfer coefficient. q ¼ time.

The jacket temperature required for a 3 h cool-down is: T1 ¼

t1  t2 eKq 1  eKq

EXAMPLE 15-41 Batch Cooling: Internal Coil, Isothermal Cooling Medium

1

¼

60  35 eð0:00017 s 33600 sÞ ð0:00017 1s33600 sÞ

1e ¼ 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 q, then: dq0 dT ¼ Mc ¼ U A Dt dq dq

(15-732)

A tank containing 50,000 lb (22,679.5 kg) material with a specific heat of 0.5 Btu/lb
F (2.1 kJ/kg.K) is to be cooled from 230
F (383 K) to 140
F (333 K). 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
F (850 W/m2.K). Calculate the time required to cool the tank contents with a cooling medium at 90
F (305 K). Solution Applying Equation 15-736, the time required to cool the tank contents is:  Mc T1  t1 ln q ¼ (15-736) T2  t1 UA where: M ¼ 50,000 lb c ¼ 0.5 Btu/lb.
F U ¼ 150 Btu/h.ft2.
F A ¼ 100 ft2

Heat Transfer Chapter | 15

T1 ¼ 230
F T2 ¼ 140
F t1 ¼ 90
F

Equation 15-739 becomes:  T1  t UA ¼ ln T2  t Wh Ch

 ð50; 000Þð0:5Þ 230  90 ln q ¼ ð150Þð100Þ 140  90

UA T1  t ¼ eWh Ch T2  t

¼ 1:72 hr: Calculations: SI units

457

(15-740) (15-741)

Rearranging Equation 15-741 gives:

 Mc T1  t1 ln q ¼ T2  t1 UA

T2 ¼ t þ

(15-736)

where: M ¼ 22,679.5 kg c ¼ 2.1kJ/kg.K U ¼ 850 W/m2.K A ¼ 9.29 m2 T1 ¼ 383 K T2 ¼ 333 K t1 ¼ 305 K

T1  t UA Ch

(15-742)

eW h

UA Ch

where K1 ¼ eWh

(15-743)

Equating II and III in Equation 15-737 and substituting Equation 15-742 into Equation 15-737 gives:   dt T1  t ¼ Wh Ch T1  t þ Mc dq K1 (15-744)  K1  1 ¼ Wh Ch ðT1  tÞ K1 Rearranging Equation 15-744 and integrating from t1 to t2 while the processing time passes from 0 to q gives: Zt2 t1

An Excel spreadsheet (Batch Cooling: Internal Coil Isothermal Cooling Medium.xls) has been developed for Example 15-41.

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:

(15-737)

The log mean temperature difference DtLMTD is: DtLMTD ¼

T1  T2

 ln TT12 t t

(15-738)

Equating III and IV in Equation 15-737 and rearranging gives: Wh Ch ðT1  T2 Þ T1  T2 ¼  UA ln TT12 t t

(15-739)

dt ¼ T1  t

Zq

Wh C h Mc

 K1  1 dq K1

(15-745)

0

Integrating Equation 15-745 gives:    T1  t1 Wh Ch K1  1 ¼ q ln T1  t2 Mc K1    K1 Mc T1  t1 ln or q ¼ K1  1 T1  t2 Wh Ch

(15-746) (15-747)

where: A ¼ heat transfer surface area c ¼ specific heat of batch liquid Ch ¼ heating medium specific heat M ¼ weight of batch liquid T1 ¼ heating medium temperature t1 ¼ initial batch temperature t2 ¼ final batch temperature U ¼ overall heat transfer coefficient Wh ¼ heating medium flowrate q ¼ time EXAMPLE 15-42 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/lb
F (2.1 kJ/kg.K) is to be heated from 68
F (293 K) to 257
F (398 K). 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

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

tank contents is 150 Btu/h.ft2.
F (850 W/m2.K). Calculate the time required to heat the tank contents with steam condensing at 320
F (433K) and having a flow rate of 10,000 lb/h (4535.9 kg/h). 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. dq0 dt ¼ Mc ¼ Wh Ch ðT1  T2 Þ ¼ UADtLMTD (15-737) dq dq UA

where K1 ¼ eWh Ch (15-743) 8 9 > > >  > < Btu 150  100 ft2 = ¼ exp $ 2 o lb Btu > > 10; 000  1:043 > :h:ft : F $ o > ; h lb: F ¼ 4:2129 and   K1 Mc T 1  t1 ln (15-747) K1  1 T 1  t2 Wh Ch    4:2129 50; 000  0:5 320  68 ln ¼ 4:2129  1 10; 000  1:043 320  257 

q ¼

¼ 4:36 h: Calculations: SI Units UA

K1 ¼ eWh Ch  850  9:29  3600 1  ¼ exp 4535:9  4:366 1000 9 8 > > > > = < J m2  2 $kg 1000J h > > > > ; :sm :K $ $ h kgK 3600s ¼ 4:20156    K1 Mc T1  t1 ln q ¼ K1  1 T1  t2 Wh Ch    22679:5  2:1 4:2016 433  293 ¼ ln 4535:9  4:366 4:2016  1 433  398 ¼ 4:38 h:

UA

where K2 ¼ eWc Cc and:    T 1  t1 Wc Cc K2  1 ¼ q ln T 2  t1 Mc K2 or:

 q ¼

K2 K2  1



Mc Wc Cc





T  t1 ln 1 T2  t1

(15-749)

where: A ¼ heat transfer surface area c ¼ specific heat of batch liquid Cc ¼ coolant specific heat M ¼ weight of batch liquid T1 ¼ initial batch temperature T2 ¼ final batch temperature t1 ¼ initial coolant temperature U ¼ overall heat transfer coefficient Wc ¼ coolant flow rate q ¼ time EXAMPLE 15-43 Batch Cooling Non-Isothermal Cooling Medium

A tank containing 6613.87 lb (3000 kg) of material with a specific heat of 0.8 Btu/lb
F (3.3489 kJ/kg.K) is to be cooled from 230
F (383 K) to 140
F (333 K). The tank contains a coil with a heat transfer surface area of 43.0 ft2 (3.994 m2) and the overall heat transfer coefficient from coil to the tank contents is 122.9 Btu/h.ft2.
F (697.8 W/m2.K). Calculate the time required to cool the tank contents, if cooling water is available at 89.6
F (305K) and with 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. dq0 dT ¼ Mc ¼ Wc Cc ðt2  t1 Þ ¼ UADtLMTD (15-748) dq dq UA

where K2 ¼ eWc Cc

An Excel spreadsheet (Batch Heating and Cooling with non-isothermal Heating Medium.xls) has been developed for Example 15-42.

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. dq0 dT ¼ Mc ¼ Wc Cc ðt2  t1 Þ ¼ UADtLMTD dq dq (15-748)

  K2 Mc T  t1 ln 1 (15-749) K2  1 T2  t1 Wc Cc    6613:87  0:8 3:3208 230  89:6 ln ¼ 4409:26  1:0 3:3208  1 140  89:6 

q ¼

¼ 1:76 h:

Heat Transfer Chapter | 15

(i.e. no advantage in the magnitude of Dt can be observed by using a multipass design, such as a 2:4 type). The variable temperature from the exchanger t0 will differ from the variable tank temperature t. An energy balance around the tank and the heat exchanger gives:

Calculations: SI units





 Mc T  t1 ln 1 (15-749) T2  t1 Wc Cc    3000  3:3489 3:3228 383  305 ln ¼ 2000  4:184 3:3228  1 333  305 q ¼

K2 K2  1

459

(15-750)

¼ 1:76 h:

Heat accumulation in the batch

An Excel spreadsheet (Batch Heating and Cooling with non-isothermal Cooling Medium.xls) has been developed for Example 15-43.

Heat entering the batch by recirculation

Transfer rate in the external exchanger

The log mean temperature difference DtLMTD is:

Batch Heating: External Heat Exchanger, Isothermal Heating Medium

DtLMTD ¼

Figure 15-276 illustrates an 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

ðT1  tÞ  ðT1  t0 Þ  T1  t ln T1  t0

t0  t ¼  T1  t ln T1  t0

M

t

Wh Ch T1

t

t’

Wh Ch T1

FIGURE 15-276 Batch heating through an external heat exchanger, isothermal heating medium.

(15-751)

460

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Equating III and IV in Equation 15-750 gives: Wh Ch ðt0  tÞ ¼ UADtLMTD

(15-752)

Wh ¼ heating medium flowrate q ¼ time

That is: ðt0  tÞ Wh Ch ðt0  tÞ ¼ UA  t ln TT11t 0

(15-753)

Rearranging Equation (15-753) gives:  T1  t UA ln ¼ T1  t0 W h Ch

(15-754)

Equation 15-754 can be expressed as: UA

T1  t ¼ eWh Ch ðT1  t0 Þ UA where K3 ¼ eWh Ch T1  t ¼ K3 ðT1  t0 Þ

(15-755)

EXAMPLE 15-44 Batch Heating: External Heat Exchanger Isothermal Heating Medium

A tank containing 50,000 lb (22,679.5 kg) of material with a specific heat of 0.5 Btu/lb
F (2.093 kJ/kg.K) is to be heated from 72
F (295 K) to 260
F (400 K). 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 is 150 Btu/h.ft2.
F (852 W/m2K). Calculate the time required to heat the tank contents with steam condensing at 350
F (450K) at a flowrate of 33,000 lb/h (14,969 kg/h) and a specific heat of 0.9 But/lb.
F (3.77 kJ/kg.K). Solution

(15-756)

Therefore: t0 ¼ T1 

 T1  t K3

(15-757)

Equating II and III in Equation 15-750 gives: dt ¼ Wh Ch ðt0  tÞ (15-758) dq Substituting Equation 15-757 into Equation 15-758 and rearranging yields:   Mc dt T1  t t $ ¼ T1  Wh Ch dq K3 (15-759) ðK3  1Þ ðT1  tÞ ¼ K3 Rearranging Equation 15-759 and integrating from t1 to t2 while the time passes from 0 to q gives: Mc

Zt2 t1

dt ¼ T1  t



K3  1 K3



Wh Ch Mc

and   K3 Mc T1  t1 ln (15-761) K3  1 T1  t2 Wh Ch    1:65707 50; 000  0:5 350  72 ln 1:65707  1 33; 000  0:9 350  260 

q ¼

¼ 2:39 h: Calculation: SI units

Zq dq

(15-760)

0

which yields:    T1  t1 K3  1 Wh C h ln ¼ q T1  t2 Mc K3    K3 Mc T1  t1 or q ¼ ln K3  1 T1  t2 Wh Ch where: A ¼ heat transfer surface area c ¼ specific heat of batch liquid Ch ¼ heating medium specific heat M ¼ weight of batch liquid T1 ¼ heating medium temperature t1 ¼ initial batch temperature t2 ¼ final batch temperature U ¼ overall heat transfer coefficient.

and   K3 Mc T1  t1 ln (15-761) K3  1 T1  t2 Wh Ch    1:6568 22; 679:5  2:093 450  295 ¼ ln 1:6568  1 14; 969  3:77 450  400 

q ¼

(15-761)

¼ 2:40 h: An Excel spreadsheet (Batch Heating: External Heat Exchanger Isothermal Heating Medium.xls) has been developed for Example 15-44.

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:

Heat Transfer Chapter | 15

or

   T1  t1 Wc Cc K4  1 ¼ q ln T2  t1 Mc K4    K4 Mc T 1  t1 ln q ¼ K4  1 T 2  t1 Wc C c

(15-762) (15-763)

UA

K4 ¼ eWc Cc A ¼ heat transfer surface area c ¼ specific heat of batch liquid Cc ¼ coolant specific heat M ¼ weight of batch liquid T1 ¼ initial batch temperature T2 ¼ final batch temperature t1 ¼ initial coolant temperature U ¼ overall heat transfer coefficient. Wc ¼ coolant flowrate q ¼ time

EXAMPLE 15-45 Batch Cooling: External Heat Exchanger, Isothermal Cooling Medium

A tank containing 50,000 lb (22,679.5 kg) of material with a specific heat of 0.5 But/lb
F (2.093 kJ/kg.K) is to be cooled from 257
F (398 K) to 104
F (313 K). The tank contains a 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 is 150 Btu/h.ft2.
F (852 W/m2.K). Calculate the time required to cool the tank contents, if cooling water is available at 86
F (303 K), at a flowrate of 10,000 lb/h (4535.9 kg/ h) and the specific heat capacity is 1 Btu/lb.
F (4.186kJ/kg.K). Solution

and   K4 Mc T1  t1 ln (15-763) K4  1 T2  t1 Wc Cc    4:4817 50; 000  0:5 257  86 ¼ ln 4:4817  1 10; 000  1:0 104  86 

¼ 7:24 h Calculation: SI units

and:   K4 Mc T 1  t1 ln K4  1 T 2  t1 Wc Cc    4:4848 22; 679:5  2:093 398  303 ¼ ln 4:4848  1 4535:9  4:186 313  303 

where:

q ¼

461

q ¼

¼ 7:24 h An Excel spreadsheet (Batch Cooling: External heat exchanger, isothermal cooling medium.xls) has been developed for Example 15-45.

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:

K  1 

T  t  Wb Wc C c 1 1 5 q ¼ ln T2  t1 K5 Wc Cc  Wb c M (15-764)    K 5 W c C c  Wb c M T1  t1 or q ¼ ln T2  t1 Wb Wc C c K5  1 (15-765) where: K5 ¼ exp½UAð1=Wb c  1=Wc Cc Þ A ¼ heat transfer surface area c ¼ specific heat of batch liquid Cc ¼ coolant specific heat M ¼ weight of batch liquid T1 ¼ initial batch temperature T2 ¼ final batch temperature t1 ¼ initial coolant temperature U ¼ overall heat transfer coefficient. Wb ¼ batch flowrate Wc ¼ coolant flowrate q ¼ time EXAMPLE 15-46 Batch Cooling: External Heat Exchanger (Counter-Current Flow), Non-Isothermal Cooling Medium

A tank containing 50,000lb (22,679.5 kg) of material with a specific heat of 0.5 Btu/lb.
F (2.093 kJ/kg.K) is to be cooled from 257
F (398 K) to 104
F (313 K). The tank contains an external heat exchanger with a heat transfer area 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.
F (1134 W/m2.K). Calculate the time required to cool the tank contents if cooling water is

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

available at 86
F (303K) and at a flow rate of 10,000 lb/h (4535.9 kg/h). Solution

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:    T1  t1 K6  1 Wb Wh C h ¼ q ln T1  t2 K6 Wh Ch  Wb c M (15-766)    K6 Wh Ch  Wb c M T1  t1 ln or q ¼ T1  t2 Wb Wh Ch K6  1 (15-767)

and

where: K6 ¼ exp½UAð1=Wb c  1=Wh Ch Þ

Calculation: SI units

A ¼ heat transfer surface area c ¼ specific heat of batch liquid Ch ¼ heating medium specific heat M ¼ weight of batch liquid T1 ¼ heating medium temperature t1 ¼ initial batch temperature t2 ¼ final batch temperature U ¼ overall heat transfer coefficient. Wb ¼ batch flowrate Wh ¼ heating medium flowrate q ¼ time EXAMPLE 15-47 Batch Heating: External Heat Exchanger and Non-Isothermal Heating Medium

and

A tank containing 50,000 lb (22,679.5 kg) of material with a specific heat of 0.5 Btu/lb.
F (2.093 kJ/kg.K) is to be heated from 68
F (293 K) to 257
F (398 K). The tank contains an external heat exchanger with a heat transfer of 200 ft2 (18.58 m2). 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.
F (1134 W/ m2.K). Calculate the time required to heat the tank contents with condensing steam at 320
F (433 K) and at a flowrate of 10,000 lb/h (4535.9 kg/h) at a specific heat of 0.9 Btu/lb.
F (3.767 kJ/kg.K). Solution

An Excel spreadsheet (Batch Cooling: External Heat Exchanger (Counter-Current Flow), Non-isothermal Cooling.xls) has been developed for Example 15-46.

Heat Transfer Chapter | 15

and

463

Equating II and III in Equation 15-768 gives: dt ¼ Wb cðt0  tÞ dq Rearranging Equation 15-769 gives: Mc

(15-769)

M dt $ Wb dq The parameter S can be defined by:   t0  t M 1 dt S ¼ ¼ T1  t Wb T1  t dq t0 ¼ t þ

(15-770)

(15-771)

The parameter R can be defined by equations III and IV in Equation 15-768: Calculation: SI units

T1  T2 Wb c ¼ t0  t W h Ch Rearranging Equation 15-771 gives: R ¼

Zt2

dt S$Wb ¼ M T1  t

t1

and   K6 Wh Ch  Wb c M T1  t1 ln T1  t2 Wb Wh Ch K6  1 ) ( kg kJ 1 $kg q $ $ hr kg:K kg $kg$ kJ hr: hr kg:K 
ð0:2884Þð4535:9Þð3:767Þ  ð11; 339:8Þð2:093Þ ¼ ð11; 339:8Þð4535:9Þð3:767Þ   22; 679:5 433  293 ln ¼ 4:29 h 0:2884  1 433  398

 q ¼

An Excel spreadsheet (Batch Heating: External Heat Exchanger and Non-Isothermal Heating Medium.xls) has been developed for Example 15-47.

Batch Heating: External Heat Exchanger (1e2 Multipass Heat Exchangers), NonIsothermal Heating Medium The procedure used for batch heating with external 1e2 multipass heat exchangers with non-isothermal heating media involves using the same heat balance media involves using the same heat balance as defined by the following equation:

(15-768)

(15-772)

Zq dq

(15-773)

0

Integrating from t1 to t2 as the time passes from 0 to q yields:   T1  t1 S$Wb ¼ q (15-774) ln T1  t2 M The time q required for heating is:   M T1  t1 ln q ¼ T1  t2 S Wb

(15-775)

and: n

S ¼ K7

2ðK7  1Þ o n o R þ 1 þ ðR þ 1Þ0:5  R þ 1  ðR2 þ 1Þ0:5 2

(15-776) where:  K7 ¼ exp ¼

0:5 UA  2 R þ1 and Wb c

R ¼

Wb c Wh Ch

A ¼ heat transfer surface area c ¼ specific heat of batch liquid Ch ¼ heating medium specific heat M ¼ weight of batch liquid T1 ¼ initial temperature of heating medium t1 ¼ initial batch temperature t2 ¼ final batch temperature U ¼ overall heat transfer coefficient.

T1  T2 t0  t

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Wb ¼ batch flowrate Wh ¼ heating medium flowrate q ¼ time

Calculation: SI units R ¼

T1  T2 Wb c ¼ t0  t Wh Ch

ð18143:68Þð2:009Þ ¼ 3:199 ð4535:9Þð2:5116Þ 0:5  0:5  2 ¼ 3:1992 þ 1 R þ1 ¼

EXAMPLE 15-48 External Heat Exchanger (1e2 Multipass Heat Exchangers), Non-Isothermal Heating Medium

¼ 3:3522

7500 gal (28387.5 l) of liquid benzene under pressure at 300
F (422 K) is required for a batch extraction process. The storage temperature of the benzene is 100
F (311 K). Available as a heating medium is a 10000 lb/h (4535.9 kg/ h), 28
API oil stream at a temperature of 400
F (478 K). 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 400 ft2 (37.16 m2) of clean double pipe heat exchanger surface, which in counterflow streams yields a Uc of 50 But/h.ft2.
F (238.9 W/m2.K) calculated for the above flowrates. Calculate the time required to heat the contents using a 1e2 exchanger with the same surface and coefficient. Solution Specific gravity of benzene ¼ 0.88 Specific heat of benzene ¼ 0.48 Btu/lb.
F Mass of benzene ¼ 7500  8.33  0.88 ¼ 55,000 lb. R ¼

ð40; 000Þð0:48Þ ¼ 3:2 ð10; 000Þð0:6Þ 0:5  2 0:5  2 ¼ 3:2 þ 1 R þ1 ¼ 3:3526


¼ exp

0:5 UA  2 R þ1 Wb c

ð50Þð400Þ ð3:3526Þ ð40; 000Þð0:48Þ



¼ 32:86 S ¼

¼

2ðK7  1Þ n  2  0:5 o n 0:5 o  R þ 1  R2 þ 1 K7 R þ 1 þ R þ 1

2ð32:86  1Þ 32:86½3:2 þ 1 þ 3:3526  ½3:2 þ 1  3:3526

¼ 0:2576 The time required heating the batch with external 1e2 multipass heat exchangers and non-isothermal heating media is:   M T1  t1 q ¼ ln T1  t2 S Wb  55; 000 400  100 ¼ ln ð0:2576Þð40; 000Þ 400  300 ¼ 5:86 h

2ð19:15  1Þ 19:15½3:199 þ 1 þ 3:3522  ½3:199 þ 1  3:3522

The time required heating the batch with external 1e2 multipass heat exchangers and non-isothermal heating media is:   M T1  t1 q ¼ ln T1  t2 S Wb  24947:56 478  311 ln ¼ ð0:2525Þð18143:68Þ 478  422

¼

K7 ¼ exp

¼

2ðK7  1Þ n 0:5 o n 0:5 o  2  K7 R þ 1 þ R þ 1  R þ 1  R2 þ 1

¼ 0:2525

T1  T2 Wb c ¼ t0  t W h Ch



S ¼

¼ 5:94 h An Excel spreadsheet (Example 15-48. External Heat Exchanger (1-2 Multipass Heat Exchangers), Non-Isothermal Heating Medium.xls) has been developed for Example 15-48.

Batch Cooling: External Heat Exchanger (1e2 Multipass), Non-Isothermal Cooling Medium When cooling a batch with an external 1e2 multipass heat exchanger and a non-isothermal cooling medium, the following equations apply:   T1  t1 W c Cc ¼ S q (15-777) ln T2  t1 Mc The time q required for cooling is:   Mc T1  t1 ln q ¼ T2  t1 SWc Cc

(15-778)

Heat Transfer Chapter | 15

where S is defined by Equation 15-776, and: R ¼

Wc Cc Wb c

(15-779)

The time required cooling the batch with external 1e2 multipass heat exchangers and non-isothermal heating media is: 

where:  K7 ¼ exp

UA Wc C c





R þ1 2

0:5

Mc SWc Cc

q ¼

and

R ¼

465

Wc Cc Wb c



 ln

T1  t1 T2  t1



 ð50; 000Þð0:5Þ 257  86 ln ð0:646  10; 000  1:0Þ 104  86

¼

¼ 8:71 h: Calculation: SI units

A ¼ heat transfer area c ¼ specific heat of batch liquid Cc ¼ Coolant specific heat M ¼ weight of batch liquid T1 ¼ initial batch temperature T2 ¼ final batch temperature t1 ¼ initial coolant temperature U ¼ overall heat transfer coefficient Wb ¼ batch flowrate Wc ¼ coolant flowrate U ¼ overall heat transfer coefficient q ¼ time

R ¼

Wc Cc Wb c

(15-779)

ð4535:9Þð4:186Þ ¼ 0:799 ð11339:8Þð2:093Þ 0:5  0:5  2 ¼ 0:7992 þ 1 ¼ 1:2806 R þ1    UA 0:5 R2 þ 1 K7 ¼ exp W c Cc  ð18:58Þð1134Þ 3600 ¼ exp  1:2806  ð4535:9Þð4:186Þ 1000 ¼

¼ 166:64 and

EXAMPLE 15-49 External Heat Exchanger (1e2 Multipass), Non-Isothermal Cooling Medium

A tank containing 50,000 lb (22,679.5 kg) of material with a specific heat of 0.5 Btu/lb.
F (2.093 kJ/kg.K) is to be cooled from 257
F (398 K) to 104
F (313 K). The tank contains an external heat exchanger with a heat transfer of 200 ft2 (18.58 m2). 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.
F (1134 W/ m2.K). Calculate the time required to cool the tank contents with cooling water available at a temperature of 86
F (303 K), at a flowrate 10,000 lb/h (4535.9 kg/h) at a specific heat of 1.0 Btu/lb.
F (4.186 kJ/kg.K). Solution

S ¼

¼

2ðK7  1Þ n  2  0:5 o n 0:5 o  R þ 1  R2 þ 1 K7 R þ 1 þ R þ 1

2ð166:64  1Þ 166:64:75½0:799 þ 1 þ 1:2806  ½0:799 þ 1  1:2806

¼ 0:6462 The time required to cool the batch with external 1e2 multipass heat exchangers and non-isothermal heating media is:  q ¼ ¼

R ¼

Wc Cc Wb c

(15-779)

ð10; 000Þð1:0Þ ¼ 0:8 ð25; 000Þð0:5Þ 0:5  0:5  2 ¼ 0:82 þ 1 ¼ 1:2806 R þ1   0:5 UA R2 þ 1 K7 ¼ exp Wc Cc  ð200Þð200Þ 1:2806 ¼ exp ð10; 000Þð1:0Þ ¼

¼ 167:75 and S ¼

¼

2ðK7  1Þ n  2  0:5 o n 0:5 o  R þ 1  R2 þ 1 K7 R þ 1 þ R þ 1

2ð167:75  1Þ 167:75½0:8 þ 1 þ 1:2806  ½0:8 þ 1  1:2806

¼ 0:6460

Mc SWc Cc



 T1  t1 ln T2  t1

 ð22; 679:5Þð2:093Þ 398  303 ln ð0:6462  4535:9  4:186Þ 313  303

¼ 8:709 h: An Excel spreadsheet (Example 15-49. External Heat Exchanger (1e2 Multipass Heat Exchangers), NonIsothermal Cooling Medium.xls) has been developed for Example 15-49.

Batch Heating and Cooling: External Heat Exchanger (2e4 Multipass Heat Exchangers Non-Isothermal Heating Medium) When heating a batch with an external 2e4 multipass heat exchanger and a non-isothermal heating medium, the following equations apply:  ln

T1  t1 T1  t2



 ¼

S$Wb M

q

(15-780)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

The time q required for heating is:   M T 1  t1 ln q ¼ T 1  t2 S Wb

(15-781)

 2ðK8  1Þ½1 þ fð1  SÞð1  RSÞg0:5  2 0:5 ðK8  1Þ ðR þ 1Þ þ ðK8 þ 1Þ R þ 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2ð5:73  1Þ 1 þ ð1  SÞð1  3:2SÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð5:73  1Þð3:2 þ 1Þ þ ð5:73 þ 1Þ 3:22 þ 1

(15-782)

Solving for S by trial and error until the RHS equals the LHS, S ¼ 0.273 The time q required for heating is:

S ¼

and 2ðK8  1Þ½1 þ fð1  SÞð1  RSÞg  0:5

S ¼

ðK8  1Þ ðR þ 1Þ þ ðK8 þ 1ÞðR2 þ 1Þ0:5

where

 K8 ¼ exp



 T 1  t1 (15-151) T 1  t2   55; 000 400  100 ln ¼ 0:273  40; 000 400  300

 2 0:5 UA R þ1 2Wb c

q ¼

Batch Heating and Cooling: External Heat Exchanger (2e4 Multipass Heat Exchangers Non-Isothermal Cooling Medium) When cooling a batch with an external 2e4 multipass heat exchanger and a non-isothermal cooling medium, the following equations apply:   T1  t1 Wc Cc ¼ S q (15-783) ln T2  t1 Mc The time q required for cooling is:   Mc T1  t1 ln q ¼ T2  t1 SWc Cc

(15-784)

M S Wb

An Excel spreadsheet (Example 15-50. External Heat Exchanger (2e4 Multipass Heat Exchangers), NonIsothermal Heating Medium.xls) has been developed for Example 15-50.

EXAMPLE 15-51 External Heat Exchanger (2e4 Multipass Heat Exchangers), Non-Isothermal Cooling Medium

Using Example 15-50: for 2e4 multipass heat exchanger, non-isothermal cooling medium and R ¼

Using Example 15-48 for 2e4 multipass heat exchanger, non-isothermal heating medium.   2 0:5 UA R þ1 K8 ¼ exp 2Wb c  ð50Þð400Þ ¼ exp  3:3526 ð2  40; 000  0:48Þ ¼ 5:73



(15-785)

Because S cannot be expressed explicitly, Equation 15-782 can only be solved by trial and error, assuming different value of S until equality is reached. An alternative for solving Equation 15-782 is to employ an Excel spreadsheet and use Solver or Goal Seek.

EXAMPLE 15-50 External Heat Exchanger (2e4 Multipass Exchanger), Non-Isothermal Heating Medium

ln

¼ 5:53 h

where S is defined by Equation 15-782, and: Wc Cc R ¼ Wb c



¼

Wc Cc Wb c

10; 000  1:0 25; 000  0:5

(15-785)

¼ 0:8 0:5  0:5 R þ1 ¼ 0:82 þ 1 ¼ 1:2806   2 0:5 UA R þ1 K8 ¼ exp 2Wb c  ð200Þð200Þ ¼ exp  1:2806 ð2  25; 000  0:5Þ 

2

¼ 7:7601

 2ðK8  1Þ½1 þ fð1  SÞð1  RSÞg0:5 S ¼  0:5 ðK8  1Þ ðR þ 1Þ þ ðK8 þ 1Þ R2 þ 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2ð7:7601  1Þ 1 þ ð1  SÞð1  0:8SÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð7:7601  1Þð0:8 þ 1Þ þ ð7:7601 þ 1Þ 0:82 þ 1 Solving for S by trial and error until the RHS equals the LHS, S ¼ 0.755

Heat Transfer Chapter | 15

The time q required for cooling is:   Mc T1  t1 q ¼ ln (15-784) T2  t1 SWc Cc   55; 000  0:5 257  86 ¼ ln 0:755  10; 000  1:0 104  86

Name

¼ 7:45h: An Excel spreadsheet (Example 15-51. External Heat Exchanger (2e4 Multipass Heat Exchangers), NonIsothermal Cooling Medium.xls) has been developed for Example 15-51.

HEAT EXCHANGER DESIGN WITH COMPUTERS Several descriptions have been presented [43,48, 92,111,125] to illustrate the usefulness of computers in various phases of heat exchanger design. Although any medium-sized digital computer can handle the decision making and storage capacity, a large investment must be made in programming time 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 that attempts to cover all types. Computer methods for the design and analysis of heat exchangers are provided by commercial software companies, including 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 design 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. The HTRI Xchanger suite lacks a mechanical design feature and the HTFS suite handles all types of heat exchangers, 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 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 heat exchangers have five main programs, each for a different type of equipment.

467

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 cross-flow 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 heat exchanger programs offer some or all of the following basic functionalities: l

l

l

l

l

Design: for designing a heat exchanger to meet a heat load duty and pressure drop limits, which are 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).

468

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Nozzles

Plain. Axial. Vapor belts. Impingement plates.

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. Lowfin tubes (database included). Longitudinal fins in double pipe and Unbaffled exchangers. Twisted tape inserts.

Physical Properties All 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 units 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 can be used for preliminary design calculations before detailed designs are explored by the designers.

Hysys 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 stepwise 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.

Troubleshooting of Shell and Tube Heat Exchanger The following provides example causes of problems in heat exchangers, and offers solutions to remedy them. Pressure drops (Dps): Dps are essential for analyzing the 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 Dps are lower than the calculated Dps, this suggests fluid bypassing, as a low Dp on the tube-side indicates that not all the flow is entering the tubes. e 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 malfunctioning gasket or a manufacturing defect. 4. A shell-side Dp 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. e 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. e e e e e e

A high Dp could be caused by [419]: High fouling Debris from startup Improper venting Freezing of the process stream. Slug flow for twoephase streams. Fabrication problem.

Heat Transfer Chapter | 15

Improper or no venting causes a high Dp, and it should be analyzed first where this is established. Fouling: Heat exchanger fouling increases the Dp and thus reduces its efficiency. There are dedicated software programs that can give the available fouling as compared to design fouling (see Figure 15-58, and Elsevier companion website of this text). 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 whether: e There are deviations from the design conditions e Low velocities in the tubes streams flow rates are lower than design (see section on fouling in this text for its control) e 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 e check to ensure that there is a strainer in the piping ahead of the inlet nozzles, otherwise debris may be lodged in the exchanger. 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. e 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. e Another cause of a problem is degradation or lost in thermal stability of a liquid where higher than process design outlet temperatures are concerned. e For cold applications, the outlet temperature of the stream to be cooled must be checked, otherwise the following can occur: l Stream freezing. l Tube plugging. l Brittle tubing. l 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 [419] 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-condensable gases can result 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 tubesheet, there is a space where gases or vapors are trapped. It is important to get the vent connection as close to the tubesheet as possible. One solution is to use more than one vent nozzle [416]. Common problems with two-phase flow patterns are stratified and wave flows (refer to twophase flow patterns in this chapter). 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 ¼ 3:5=ðvsl Þ0:5 For a maximum liquid velocity of 0.5 ft/s, the gas velocity can be as high as 5 ft/s [416]. The solution for stratified and slightly wave flow patterns is to ensure that dry gas is kept away from the tubewall. Use twisted tape inserts if the stream inside the tubes has low fouling characteristics. e 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. e 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. e 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 this chapter).

469

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e Another aspect of condensate flow-holdup 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. e Shell-side baffles can act as dams. Horizontalcut baffles should not be used as vertical-cut baffles are suitable. Ensure that small baffle cuts do not flood too much of the bundle. e 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. e 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. e 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. e 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 Dp 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 Dp and possibly bundle vibration. e This problem occurs when older exchangers are retrofitted into 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 [419] provides an instance where a heat exchanger was piped backward. 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 semiviscous, 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. Operational problems in a reboiler system: These are the following: e The startup should be gradual otherwise thermal stresses may occur. e 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. e 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. e Temperature difference (Tw Tsat) should not be too high. A high temperature driven potential > 90e100
F (> 50e55
C) can cause film boiling with a reduced heat flux and reduced vapor generation. e 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 [420]. Other operational problems are: pressure surging, low heat transfer, leakages and probable causes and cures are given by Lord et al. [367]. Unstable operation with a reboiler: The following is a list of situations where this can occur: e 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. e Wavy and slug flow patterns in the two-phase flow regimes are inherently unstable and must be avoided.

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e 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. e 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.

MAINTENANCE OF HEAT EXCHANGERS Heat exchangers must be regularly maintained and monitored to ensure safe operation and provide the required efficiency with respect to design engineering practice. Neglect in keeping all tubes clean may result in complete stoppage of flow through some tubes, which could cause severe thermal strains, leaking tube joints or structural damage to other components. Sacrificial anodes, when provided should be inspected to ascertain whether they should be cleaned or replaced.

Disassembly for Inspection or Cleaning Before disassembly is carried out, the unit must be first depressurized, vented and drained, neutralized and/or purged of hazardous material. To inspect the inside of the tubes and also to make them accessible for cleaning, the following procedures are taken: 1. Stationary Head End (a) Type A, C, D and N, remove cover only (b) Type B, remove bonnet 2. Rear Head End (a) Type L, N and P, remove cover only. (b) Type M, remove bonnet. (c) Type S and T, remove shell cover and floating head cover. (d) Type W, remove channel cover or bonnet.

Locating Tube Leaks The following procedures may be used to locate perforated or split tubes and leaking joints between tubes and tubesheets. Generally, the entire front face of each tubesheet will be accessible for inspection, as the point where

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water escapes shows a defective tube or tube to tubesheet joint: a. Units with removable channel cover: Remove channel cover and apply hydraulic pressure in the shell. b. Units with bonnet type head: For fixed tubesheet units where tubesheets are an integral part of the shell, remove bonnet and apply hydraulic pressure in the shell. For fixed tubesheet units where tubesheets are not an integral part of the shell and for units with removable bundles, remove bonnet, re-bolt tubesheet to shell or install test flange or gland, whichever is suitable, and apply hydraulic pressure in the shell. c. Units with Type S or T floating head: Remove channel cover or bonnet, shell cover and floating head cover. Install a test ring and bolt in place with gasket and packing. Apply hydraulic pressure in the shell. Where a test ring is unavailable, it is possible to locate leaks in the floating head end by removing the shell cover and applying hydraulic pressure in the tubes. Leaking tube joints may then be located by sighting through the tube lanes. Caution should be exercised when testing partially assembled exchangers to prevent over extension of expansion joints or overloading of tubes and/or tube-to-tubesheet joints. d. Hydrostatic test should be carried out so that the temperature of the metal is over 60
F (16
C) unless the materials of construction (metallurgy) have a lower nil-ductility transition temperature.

Hydrocarbon Leaks Another cause of heat exchanger piping vibration is caused by leaks. For example, a light hydrocarbon liquid leaking into a lower pressure fluid will flash to a vapor. The sudden expansion generates pressure surges, which initiate piping vibration. However, sampling the lower pressure fluid for contamination with light hydrocarbons will indicate the problem [421].

Pass Partition Failure In this instance, the piping associated with one crude preheats exchanger started to vibrate when the flow of crude through the tube-side of the exchanger suddenly stopped after several days of vibration. Upon opening the exchanger’s channel head, the pass partition was found to have collapsed and lodged against the crude outlet nozzle. The mechanical design had an allowable Dp of 50 psi, while the operating Dp is 70 psi. Partially plugged tubes had greatly increased the normal crude Dp. The pass partition had to withstand the high pressure differential. When it finally failed, it was pushed against the channel head outlet nozzle. Lieberman [421] infers that when an

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exchanger piping is seen vibrating, the pressure differential across both the shell and tube-side should be checked and compared to the design strength of the pass partition.

Water Hammer This is caused by the rapid condensation of steam on cold metal, or the mixing of steam with subcooled water, which results in a loud noise. A vertical steam reboiler operated at 20% of its design load can emit bangs; it then runs smoothly and quietly at 50% of the design duty. A kettle reboiler can generate a steam hammer during startup, but once the contents start boiling, the noise level reduces. A severe water hammer problem is sometimes observed in a condensate collection system. When subcooled steam condensate and live steam mix in the same pipe, a strong water hammer occurs. A malfunctioning steam trap that allows steam to blow through into the condensate system is often the problem [421]. Designers must adhere to existing American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code and best engineering practice. Where safety relief valves are connected to these exchangers, tests should be conducted to ascertain that safety relief valves act upon the worst possible conditions such as a block-in line, thermal expansion of the tubes or other extraneous incidents that could result in overpressure of the heat exchangers. Relief valves connected to the heat exchangers should be sized for the worst case scenarios (see chapter 9, vol. 1, 4th ed. of this series). Poor maintenance and non-compliance with standard operating procedures could result in catastrophic failure of the equipment and possible explosion, resulting in fatality and environmental pollution. Two case studies later in the text highlight these points. The following are required by the designer for proper planning of heat exchanger maintenance [286]: 1. Process flowsheet. 2. Plant layout and location of other structures and piping in the vicinity of heat exchangers. 3. Fouling and corrosion tendencies of the process fluid, minimum velocity required to minimize fouling, and type (chemical and mechanical) and frequency of cleaning required. 4. Effects of interfluid mixing and leakages into the atmosphere. 5. Startup and shutdown procedures. 6. Thermal cycling, upset and emergency conditions. 7. Thermal and pressure stresses in the system. 8. Wind and seismic loads. 9. Radiographs, nondestructive examination reports and records of hydrostatic and leak tests. 10. Operating logs and temperature e and pressure e recorder charts.

11. Flow-induced vibrations. 12. Facilities available for repair and maintenance.

GENERAL SYMPTOMS IN SHELL AND TUBE HEAT EXCHANGERS The performance of shell and tube heat exchangers usually reduces due to deposits on the tube surfaces. Also, a multipass exchanger’s capacity to transfer heat may deteriorate because of internal leakage between the passes; as such a leak gradually increases as the gasket surface erodes. A possible reduction in capacity may be due to fouling, and the problem may remain undetected until the channel and cover are removed in preparation for tube cleaning. Pass partition and tubesheet erosion may then be discovered. However, erosion and corrosion often interact and it may not be possible to ascertain which caused the damage. The performance declines when the clearance between the shell and the cross-flow baffles increases, and the cause may be baffle corrosion or damage during reassembly of the equipment. The capacity of the unit declines with increases in the clearance between the baffle or support holes and the tubes due to corrosion. The increased annular clearance subsequently affects the performance of the unit by allowing increased shell-fluid leakage, as it may also contribute to vibration damage to the tubes. Mechanical problems such as baffle wear and tube damage may be due to vibration forcing by the fluid regime, excessive bafflehole-tube clearance or failure to remove sharp upset materials due to drilling from the back side of the baffles or tube supports. Reduced performance may be the result of faulty thermal or mechanical design, poor construction or misuse of the unit. Defects in the thermal design are quite noticeable, but the effects of mechanical misdesign and poor work usually appear after the manufacturer’s guarantee has expired. The kinds of troubles that may be encountered with heat exchangers are: l l l l l

Overdesign. Under design. Maldistribution. Externally caused problems. Mechanical ailments.

Yokell [420] has provided discussion on these and troubleshooting problems in shell and tube heat exchangers.

CASE STUDIES OF HEAT EXCHANGERS EXPLOSION HAZARDS INCIDENTS The complexities of petroleum refining, chemical and petrochemical plants have grown through sophisticated

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process control distributed systems, instrumentation and control and integration of related operations on single sites. These have economic advantages, but because of the largescale of operation, chemicals and fuels such as liquefied petroleum gases are often processed and stored in very large quantities. The consequences of certain types of accident, for example cataclysmic fire, explosion or release of toxic material may affect facilities and personnel not only within the site, but possibly people, buildings and amenities in the neighborhood. Large-scale environmental problems may occasionally arise, as there is a potential problem of a domino effect. Examples of domino or knock-on effects include [422]: l

l

l

l

l

Missiles from disrupted equipment that breach containment. Ship accidents in port areas or coastal waters close to hand, that affect operations of plant on land or on ships in neighboring berths. Accidents on one industrial site that affect nearby sites, building and the surroundings. Small leaks of flammable gas that ignite, and the flame impinges on a large vessel, leading to a large spill of a hazardous substance. Protective systems that are destroyed by flame impingement. The general types of large-scale explosion hazard:

1. Unconfined vapor cloud explosions. 2. Boiling liquid expanding vapor explosions.

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3. Confined vapor cloud explosions. 4. Dust explosions. 5. Explosions involving highly reactive or unstable substances. 6. Explosive release of stored pressure energy. 7. Steam explosions.

Case Studies (Courtesy of US Chemical Safety and Hazard Investigation Board) Two case studies are presented involving heat exchangers hazards with potential catastrophic explosions and damage to the sites and environment. Case Study 1

Figure 15-277 shows an aerial view of the damaged heat exchangers at the Tesoro refinery in Anacortes, Washington, in the US on April 2nd 2010, which resulted in tragic deaths when heat exchangers were brought online (startup). An investigation with final report is still ongoing; however preliminary findings showed that the 40 year old heat exchangers were poorly maintained over the years, as tests revealed microscopic cracks in the metal caused by high temperature hydrogen attack. This resulted in violent rupture of the exchanger tubes, followed by intense fire as large volumes of flammable hydrogen and naphtha ignited and exploded. Figure 15-278 shows photograph of the microscopic cracks in the metal, and Figure 15-279 shows a close-up of ruptured heat exchanger from the refinery accident.

FIGURE 15-277 Aerial view of the damaged heat exchangers at Tesoro Refinery in Washington DC. (Source: wwwcsb.gov)

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FIGURE 15-278 Microscopic cracks in the metal.

FIGURE 15-279 Close-up of ruptured heat exchanger.

Recommendations provided by the US Chemical Safety and Hazard Investigation Board (CSB) include [423]: l Implement comprehensive mechanical integrity programs with an emphasis on thorough inspections of critical equipment. l Monitor process safety performance using appropriate leading and lagging indicators to measure process safety before major accidents occur. l Implement an open safety culture where near-misses and loss of containment incidents are reported and investigated.

Case Study 2. Heat Exchanger Rupture and Ammonia Release at the Goodyear Tire and Rubber Company in Houston Texas, US [423].

Process Description: Ammonia is a commonly used industrial coolant as well as being a feedstock for urea

and ammonia nitrate. Goodyear is an international tire and rubber manufacturing company in Houston, Texas in the US. The company uses pressurized anhydrous ammonia in the heat exchanger to cool the chemicals used to make synthetic rubber. Process chemicals pumped through the tubes inside the heat exchanger are cooled by ammonia flowing around the tubes in a cylindrical steel shell. Goodyear uses three ammonia heat exchangers in its production process lines. The ammonia cooling system supplies the heat exchangers with pressurized liquid ammonia. As the ammonia absorbs heat from the process chemical flowing through tubes in the center of the heat exchanger, the ammonia boils in the heat exchanger shell (Figure 15-280). A pressure control valve in the vapor return line maintains ammonia pressure at 150 psig in the heat exchanger. Ammonia vapor returns to the ammonia cooling system where it is pressurized and cooled, thereby liquefying the ammonia. The process chemicals exiting the heat exchanger flow to the process reactors. Each heat exchanger is

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475

FIGURE 15-280 Ammonia heat exchanger.

equipped with a rupture disk in series with a pressure relief valve (both set at 300 psig) to protect the heat exchanger from excessive pressure. The relief system vented ammonia vapor through the roof to the atmosphere. The Incident: On June 10, 2008, Goodyear operators closed an isolation valve between the heat exchanger shell (ammonia cooling side) and a relief valve to replace a burst

rupture disk under the relief valve that provided over pressure protection. Maintenance workers replaced the rupture disk on that day, but the closed isolation valve was not reopened. On the morning of June 11, an operator closed a block valve, isolating the ammonia pressure control valve from the heat exchanger. The operator then connected a steam line to the process line to clean the

FIGURE 15-281 Damaged heat exchanger at the Goodyear Tire and Rubber Company, Houston, Texas. (Source: www.csb.gov)

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piping. The steam flowed through the heat exchanger tubes, heated the liquid ammonia in the exchanger shell, and subsequently increased the pressure in the shell. The closed isolation and block valves (Figure 15280) prevented the increasing ammonia pressure from safely venting through either the ammonia pressure control valve or the rupture disk and relief valve. The pressure in the heat exchanger shell continued rising

until it violently ruptured at about 7:30 am. [423]. The incident caused a fatality, as the catastrophic rupture threw debris that struck and killed an employee walking through the area. Further, the rupture also released ammonia. Figure 15-281 shows the damaged heat exchanger after the explosion. Maintenance Procedures: Training requirements for operators in the production area included standard operating

FIGURE 15-282 Heat exchanger system. (Source: C. E. Thomas, ref. [424].)

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procedures specifically applicable to the rupture disk maintenance performed on June 10. These involved: l Use of the work order system including obtaining signature verification both before the work starts and after the job was completed. l Use of lockout/tag out procedures for equipment that was undergoing maintenance. The US Chemical Safety and Hazard Investigation Board found evidence of breakdowns in both the work order and lockout/tag out programs that contributed to the incident. The work order procedure required a signature before work commenced and after the work had been completed. However, operators reported that maintenance personnel did not always obtain production operators’ signatures as required. Additionally, work order documentation was not kept at production control stations. Operators used the lockout/tag out procedures to manage the work on the heat exchanger rupture disk, but did not clearly document the progress and status of the maintenance. In this case, information that the isolation valve on the safety relief vent remained in the closed position and locked out was limited to a handwritten note. The company’s work order system for maintenance requires the process operator to sign off when the repairs are completed. However, Goodyear was unable to produce a signed copy of the work order. A heat transfer system can be very complicated with modern process control instrumentation, and since a heat exchanger can explode like a bomb, proper training and care are required during operation as well as startup and shutdown. Figure 15-282 shows the various components found in a typical heat exchanger system. A flow control loop is found on the shell outlet of Ex-203 in Figure 15-282 and fails in the open position. This will prevent the feedstock from overheating and potentially rupturing the heat exchanger. Further, correct line-ups on heat exchangers are essential and operators should carefully review the standard operating procedure [424]. The following are among the important causes that can lead to poor performance of an exchanger [286]: 1. Poor quality of materials of construction. 2. Inadequate thermal design. 3. Poor fabrication, inadequate inspection and testing and not adhering to the code and specification. 4. Mechanical failure due to inadequate analysis of seismic, thermal and cyclic stresses and nozzle loads. 5. Improper installation. 6. Incorrect piping connections. 7. Operating conditions being different than the design conditions. 8. Air or gas binding resulting in less than full utilization of the heat transfer surface. 9. Tube failure due to vibration or erosion. 10. Incorrect steam trapping. 11. Failure to remove preservative materials after storage. 12. Excessive clearances between baffles and shell due to corrosion or faulty fabrication, causing flow maldistribution. 13. Leakages across pass partition plates.

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14. Inadequate support design resulting in uneven settling and tilting, which in turn produce unforeseen stresses and flow maldistribution. 15. Excessive fouling.

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Ganapathy V. Chart gives fast estimate of gas heat-transfer coefficient. Oil Gas J May 5, 1980:243. Ganapathy V. Nomograph finds tube thermal resistance fast. Oil Gas J Dec. 4, 1978:97. Ganapathy V. Nomograph relates clean and dirty heat transfer coefficient, fouling factor. Heating/Piping/Air Conditioning Jan 1979:127. Ganapathy V. Quick estimation of gas heat-transfer coefficient. Chem Eng 1976;83(9):199. Ganapathy V. Shell-side heat transfer coefficients found fast for liquids. Oil Gas J Oct. 30, 1978:114. Ganapathy V. Two charts ease heat-exchanger replacements and reproduction costs. Oil Gas J Feb 19, 1979:104. Gilmour CH. Checking heat exchanger performance. Oil Gas J Jan. 14, 1952. Gilmour CH. Nucleate boiling e a correlation. Chem Eng Prog Oct 1958;54(10):77. Gilmour CH. Thermosystem reboiler design. Oil Gas J Dec. 18, 1961:79. Gottyman CF, O’Neil PS, Milton PE. High efficiency heat exchangers. Chem Eng Prog July 1973;69(7):69. Greene B. A practical guide to shell-and-tube heat exchangers. Hydro Proc 1999;78(1):79. Griffith P. The correlation of nucleate boiling burnout data. University Park, PA, Aug. 11: ASME Heat Transfer Div. meeting; 1957. Paper 57-HT-21. Guerrieri SA, Talty RD. A study of heat transfer to organic liquids in single-tube natural-circulation vertical tube boilers. Louisville, KY: presented at AIChE Het Transfer Sym; Mar. 20, 1955. Guffrey II GE. Sizing up heat transfer fluids and heaters. Chem Eng 1997;104(10):126. Gutterman G. Specity the right heat exchanger. Hydro Proc April, 1980:161. Heat Exchanger Design Book, compilation of articles. Gulf Publishing Company; 1968. Helzner AE. Operating performance of steam-heated reboiler. Chem Eng 1977;84(4):73. Herkenhoff RG. A new way to rate an existing heat exchanger. Chem Eng March 23, 1981:213. Hughmark G. A.,heat transfer in horizontal annular gas-liquid flow, 6th national heat transfer conference. AIChE-ASME 1963. Aug, 11, Preprint No. 49-AIChE. Iloege OC, Plummer DN, Rohsenow WM, Griffith P. An investigation of the collapse and surface rewet in film boiling in forced vertical flow. Trans ASME J Heat Trans May 1975:166. Ishehara K, Palen JW, Taborek J. Critical review of correlations for predicting two-phase flow pressure drop across tube banks. Heat Trans eng Jan.eMarch 1980;1(3). Jacobs JK. Hydro Proc 1961;40(7):189. Jacobs JL, O’Neil PS, Ragi EG. Effective use of high flux tubing in towphase heat transfer, aiche 86th national meeting session 83, Houston. April 1979. Johnson AI. Circulation rates and over-all temperature driving forces in a vertical thermosiphon reboiler. Louisville, KY: presented at AIChE Heat Transfer Sym; Mar. 20, 1955. Johnson DL. Guidelines given for designing vacuum reboilers. Oil Gas J Dec. 3, 1979:63. Joshi HM. Mitigate fouling to improve heat exchanger reliability. Hydro Proc 1999;78(1):93. Karanth NG. Predict heat exchanger outlet temperatures. Hydro Proc Sept 1980:262.

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Kern DQ, Seaton RW. Theoretical analysis of thermal surface fouling. Chem Eng Prog 1959;55(6):71. Kern R. How to design overheat condensing systems. Chem Eng Sept. 15, 1975:129. Kern R. How to design piping for reboiler systems. Chem Eng Aug. 4, 1975:107. Kern R. Thermosyphon reboiler piping simplified. Hydro Proc Dec, 1968;47(12):118. Kistler RS, Kassem AE. Stepwise rating of condensers. Chem Eng Prog 1981;77(7):55. Kraus AD, Kern DQ. The effectiveness of heat exchangers with one shell pass and even numbers of tube passes. ASME AIChE-ASME Heat Trans Conf Aug. 8, 1965. Kreith F. Principles of heat transfer. 3rd ed. Intext Educational Pub; 1973. Lewis MJ. An elementary analysis for predicting the momentus and heat transfer characteristics of a hydraulically rough surface. Trans ASME J Heat Trans May, 1975;97:249. Lineham, J. H., M. Petrick, and M. M. El-Wakil, The Condensation of a Saturated Vapor on a Subcooled Film Drying Stratified Flow, AIChE Sym. on Heat Transfer, v. 66, No. 102. Lord RC, Minton PE, Slusser RP. Design of heat exchangers. Chem Eng Jan. 26, 1970:127. Lord RC, Minton PE, Slusser RP. Design parameters for condensers and reboilers. Chem Eng Mar. 23, 1970:127. Lowry JA. Evaluate reboiler fouling. Chem Eng Feb. 13, 1978:103. Magrini V, Mannei E. On the influence of the thickness and thermal properties of heating walls on the heat transfer coefficients in nucleate pool boiling. Trans ASME J Heat Trans May 1974:173. Malone RJ. Sizing external heat exchangers for batch reactors. Chem Eng Dec. 1, 1980:95. Marriott J. Where and how to use plate heat exchangers. Chem Eng April 5, 1971:127. Mathur J. Performance of steam heat-exchangers. Chem Eng Sept. 3, 1973:101. Maze RW. Air vs. water cooling: how to make the choice. Oil Gas J Nov. 25, 1974:125. Medwell, J. O. and A. A. Nicol, Surface Roughness Effects on Condensate Films, ASME-AIChE Heat Trans. Conference and Exhibit, Los Angeles, California, Aug. 91965), Paper No. 65-HT-43. Milton RM, Gottyman CF. High efficiency hydrocarbon reboilers and condensers. Dallas, TX: AIChE 71st National Meeting; Feb. 21, 1972. Minton RE. Designing sprial-plate heat exchangers. Chem Eng May 4, 1970:103. Morcos SM, Bergles AE. Experimental imidigation of combined forced aid free laminar connection in horizontal tubes. Trans ASME J Heat Trans May 1975;97:212. Mori S, Kataya M, Tanimoto A. Performance of counterflows, parallel plate heat exchangers under laminar flow conditions. Heat Trans Eng JulyeSept, 1980;2:29. Mori Y, Hiyikata K, Utsunomiya K. The effect of noncondensable gas on film condensation along a vertical plate in an enclosed changer. ASME J Heat Trans May 1977;99:p.257. Monroe RC. Fans key to optimum cooling tower design. Oil Gas J May 27, 1974:52. Mukherjee R. Broaden your heat exchanger design skills. Chem Eng Prog 1998;94(3):35. Mukherjee R. Effectively design shell and tube heat exchangers. Chem Eng Prog 1998;94(2):21.

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Murty KN. Assessing fouling in heat exchangers. Chem Eng Aug. 6, 1984:93. Nauss VE, Huber FV. Air-cooled heat exchangers. Pollut Eng July 1974:35. Orrell WH. Physical consideration in designing vertical thermosyphon reboilers. Chem Eng Sept. 17, 1973. Palen JW, Taborek J. Solution of shell side flow pressure drop and heat transfer by stream analysis method. Chem Eng Prog Sym Ser 1969;65(92). Parker JD. Convection defined classified to aid problem solving, heat trans., update e part 3. Penwell Publishing Company; July, 1980. Piret EL, Isbin HS. Two-phase heat transfer in natural circulation evaporator. St. Louis, MO: presented at AIChE Heat Transfer Sym.; Dec. 13, 1953. Polley GT, Gibbard IJ, Pretty B. Debottlenecking using heat transfer enhancement. Chem Eng 1998;105(5):84. Raben IA, Beaubouef RT, Commerford G. A study of nucleate pool boiling of water at low pressure. Boston, Aug: 6th Nat’l. Heat Transfer Conference; 1963. AIChE Preprint No. 28. Raju KS, Chand J. Consider the plate heat exchanger. Chem Eng Aug. 11, 1980:133. Ramalho RS, Tiller FM. Improved design method for multipass exchangers. Chem Eng Mar. 29, 1965:87. Rodriguez F. An engineering view of wind chill. Heat Trans Eng Oct.eDec, 1980;2. Rodriguez F, Smith JC. When non-condensable are present make a nomograph to find the condensate film temperature. Chem Eng Mar. 10, 1958:150. Rohsenow WH. A method of correlating heat transfer data for surface boiling of liquids, heat transfer div. Atlantic City, NJ: ASME; 1951. Meeting No. 25. Paper No. 51-A-110. Rohsenow WM. Nucleation with Boiling Heat Transfer, Heat Trans.. div. Detroit, MI: ASME, Conference; 1970. May. Paper No. 70-HT-18. Rothenberg DH, Nicholson RL. Interacting controls for air coolers. Chem Eng Prog 1981;77(1):80. Rubin FL. How to specify heat exchangers. Chem Eng April 8, 1968:130. Scaccia C, Theoclitus G, Devore A, Bargo GJ, Picozzi GJ. Heat exchangers. Chem Eng Oct. 6, 1980:120. Schwieger RG. Heat exchangers. Power June 1970:33. Shah GC. Troubleshooting reboilers system. Chem Eng Prog July 1979:53. Shah MM. A general predictive technique for heat transfer during saturated film boiling in tubes. Heat Trans Eng Oct.eDec, 1980;2:51. Shoot BE. Better method to find pressure drop, heat exchanger design handbook. Gulf Publishing Company; 1968. 20. Short BE. Flow geometry and heat exchanger performance. Chem Eng Prog 1965;61(7):63. Silvestrini R. Heat exchanger fouling and corrosion. Chem Eng Prog Dec 1979:29. Singh J. Selecting heat-transfer fluids for high-temperature service. Chem Eng June 1, 1981:53. Sloan M. Designing and troubleshooting plate heat exchangers. Chem Eng 1998;105:78. Sloley AW. Properly design thermosiphon reboilers. Chem Eng Prog 1997;93(3):52. Small WM. Not enough fouling? you’re fooling! Chem Eng Prog March 1968;64(3):82.

Small WM, Young RK. The rod-baffled heat exchanger heat. Heat Trans Eng Oct.eDec, 1979;1(2):3. Smittle D. Maximize het recovery from hot flue gases with finned tubing. Power 1980;124(8):76. Spalding, D. B. and S. Kakac, Turbulent Forced Convection in Channels and Bundles, Hemisphere Publishing Copr. Spencer Jr RA. Predicting heat-exchanger performance by successive summation. Chem Eng Dec. 4, 1978:121. Standiford FC. Effect of non-condensables on condenser design and heat transfer. Chem Eng Prog July 1979:59. Starczewski J. Find tube side heat transfer coefficient by nomograph. Hydro Proc Nov 1969:268. Starczewski J. Graphs cut exchanger design time, heat exchanger design handbook. Gulf Publishing Company; 1968. 34. Starczewski J. Short-cut method to exchanger tube-side pressure drop. Hydro Proc May 1971:122. Starczewski J. Short-cut to tubeside heat transfer coefficient. Hydro Proc Feb 1970:129. Starczewski J. Simplify design of partial condensers. Hydro Proc March 1981:131. Steinmeyer DE. Special problems in process heat transfer (fog formation in partial condensers). Dallas: AIChE 71st Nat’l. Meeting; Feb 1972. Stuhlbarg D. How to find optimum exchanger size for forced circulation. Hydro Proc Jan 1970:149. Sultan M, Judd RL. Interaction of the nucleation phenomena at adjacent sites in nucleate boiling. J Heat Trans 1983;105(3):3. Taborek J. Evolution of heat exchanger design techniques. Heat Trans. Eng. Heat Trans Eng JulyeSept. 1979;1(1):15. Taborek, J., G. F. Hewitt, and N. Afgan, Heat Exchanger, Theory and Practice, Hemisphere Publishing Co./McGraw-Hill Book Co. 91983). Tarrec AR, Lim C, Koppel LB. Finding the economically optimum heat exchanger. Chem Eng Oct. 4, 1971:79. Thompson JC. Evaluating heat tracing. Hydro Proc 1997;76(9):75. The Tubular Exchanger Manufacturers Assoc., Inc., Standards. 6th ed. Tarrytown, N.Y: TEMA, Inc; 1978. Turrissini RL, Bruno TV, Dahlberg EP, Setterlund RB. Prevent corrosion failures in place heat exchangers. Chem Eng Progress 1997;93(9):44. Usher JD. Evaluating plate heat-exchangers. Chem Eng Feb. 23, 1970:90. Vachon RI, Nix GH, Tanger GE, Cobb RO. Pool boiling heat transfer from teflon-coated stainless steel. ASME J Heat Trans Aug 1969;91:364. Van Stralen SJD. Heat transfer to boiling binary liquid mixtures. Part 1 Br Chem Eng Jan 1959:8. Wales RE. Mean temperature difference in heat exchangers. Chem Eng Feb. 23, 1981:77. Walker RA, Bott TA. An approach to the prediction of fouling in heat exchanger tubes from existing data. Trans Instn Chem Eng London 1977;51:165e7. Wayne HP. How to keep outdoor lines from freezing. Power March 1955:142. Webb RL. Air-side transfer in finned tube heat exchangers. Heat Trans Eng JaneMarch, 1980;1(3):33. Webb RL. The evolution of enhanced surface geometrics for nucleate boiling. Heat Trans Eng 1981;2(46):3e4. Wett T. High flux heat-exchanger surface allows area to be cut by over 80%. Oil Gas J Dec. 27, 1971:118.

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Chapter 16

Process Integration and Heat Exchanger Networks INTRODUCTION The recent staggering environmental energy-related problems and increased global competition have caused manufacturers in the process industries, petroleum refining and petrochemical industries in particular, to improve the performance of their processes. Additionally, global warming and other environmental issues are forcing governments and industries to review the way we consume fossil fuel, since this results in emissions of carbon dioxide, now recognized as a major cause of greenhouse effect, and of other pollutants such as NOx, H2S and SO2. Further, waste water and other organic substances have caused environmental pollution. The petroleum refining and petrochemical industries have recently dedicated much attention and resources to mitigating their detrimental impact on the environment by conserving resources and reducing the intensity of their energy usage. The past two decades have resulted in significant industrial and academic efforts devoted to the development of holistic process design methodologies that target energy conservation and waste reduction from a systems perspective. 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. The science of developing global tools and techniques for that purpose is called process integration (PI). PI is a holistic approach to process design and operation, which emphasizes the unity of the process [1]. The International Energy Agency (IEA) has 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]. 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 16-1). 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, thereby reducing the overall energy consumption, can be identified, even if the units are not performing at optimum conditions on their own. Such an opportunity would be missed in 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 which 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 (see volumes 1 and 2). Another aspect of PI is pinch analysis (PA). Generally, PI involves four key steps [3]: 1. Task 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

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants. http://dx.doi.org/10.1016/B978-0-7506-8524-5.00016-1 Copyright © 2015 Elsevier Inc. All rights reserved.

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Process ?

Feed Streams

Product Streams

FIGURE 16-1 Process integration starts with the synthesis of a process to convert raw materials into desired products.

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: l

l

l l

l

l

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. Optimizing solutions for the total site, thereby avoiding wasted expenditure on non-optimal local solutions. Identifying the 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 to preserve the reserves of fossil fuels. Water should be consumed in sustainable quantities that do 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. [4]. The first sub-problem to benefit from 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 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: l

l

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 16-2. The reactor design determines the product and

Process Integration and Heat Exchanger Networks Chapter | 16

493

F

Reactor F+P

Separator

Heat and mass balances

Recycle structure

Reactors

The heat and material balance is at this boundary

Separators Exchanger Utilities Process utility interface

Site – wide Utilities

FIGURE 16-2 The onion diagram of hierarchy in process design.

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 (see volume 1), 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 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 [5]. 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 [5] 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 (DTmin.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

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Detailed analysis

Preliminary scoping activities

Conceptual phase

Process design phase

• •

Interact with client Input

Clarify client requirements

Start

• • • •

Turndown Flexibility Site Other

• • •

Technical proposal* Proposal guarantees Project design data Third-party proposals Project execution strategy

Interact with client and project team

Interact with project team

• • • • • •

• • • • •

Process Systems Analytical Control systems Plant layout Operations

Pinch specialist review interaction

Finalize process flow alignment

Basic inputs • • • • •

Network designs Utility loads and levels

Update and finalize Pinch analysis

Preliminary targets Unit interactions Conceptual utility systems

Conceptual Pinch studies to set design basis

Detailed engineering phase

Process design activities

• • • • • •

Flow diagrams Material balances Finalize heat balances Equipment loads Control strategy Utility balances

Detailed engineering activities • • • • • •

Stop

P & ID development Utility flow diagrams Plot plan development Hazard reviews Control system design Operating philosophy

Process Systems Plant layout Operations Cost services

* Includes base heat and material balance

FIGURE 16-3 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.)

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 16-3 illustrates a new work process that achieves these goals. Governments, companies and established institutions in the US, 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 UK has formed a consortium with blue chip companies where collaborative research works are carried out in the field of process integration, with the objectives of reducing energy costs 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 web site [6]. Recent texts and articles have provided much insight into process integration tools [7e10]. Dunn and El-Halwagi [1] list ten discouraging attitudes about process integration and suggested responses as illustrated in Table 16-1, and Table 16-2 shows a summary of industrial applications of process integration tools.

Process integration design tools were originally developed over the past two decades for heat exchanger networks, 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 was focused on increasing heat recovery in chemical process industries. Industrial heat exchanger networks have played excellent roles in recovering process heat. Today, there are hardly any processes 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 or 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 hot process streams can be used to meet heating demand, and the cold process streams can be used to meet 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 20e30%, coupled with capital savings can be realized by PI [11].

Process Integration and Heat Exchanger Networks Chapter | 16

TABLE 16-1 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 progress 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 been 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 but you need to speak to someone else.

Get suggestions from ‘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. 78:1011e1021 (online, 2003).

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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 between 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 therefore the use of systematic techniques becomes necessary. Figure 16-4 shows a 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 exchangers 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 utilities is called the minimum capital cost design. This corresponds to the maximum running cost and maximum utility cost, as shown in Figure 16-5a. 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 extreme duties which cannot be met by mutual exchange of heat from the streams as shown in Figure 16-5b, 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 16-6. 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 of life span, plus interest) capital cost, should be minimized. The importance of optimization can be seen from the fact that, in a process plant, the cost of heat exchangers can be up to two-thirds of the plant cost and an energy cost saving of 20% to 30% is possible by optimizing the heat exchanger network. Table 16-3 shows capital savings achieved in practical case studies [16].

TABLE 16-2 Summary of Industrial Applications of Process Integration Tools Motivation

Approach

Key Results

Specialty chemical process

Debottlenecking of the process and hydrogen management

Soldout product with no additional capacity and significant cost for hydrogen consumption

Systematic elimination of two primary bottlenecks and sitewide integration of hydrogen generation, usage and discharge

12% additional capacity and 25% reduction in hydrogen cost with a payback period of less than one year.

Kraft pulping process

Water management and conservation

High usage of water and buildup of non-process elements upon recycle

Sitewide tracking elements followed by a mass integration study for water minimization

Key results: 55% reduction in water usage with a payback period of less than two years.

Resin production facility

Production debottlenecking

Soldout product with more market demands but a capped production capacity (bottlenecks)

Mass integration techniques to determine subtle causes of process bottlenecks and eliminate them at minimum cost

Increase in capacity by process debottlenecking 4% (> $1 million/year additional revenue).

Organic chemicals production process

Identification of sitewide water stream recycle opportunities to reduce river water discharges

Pressure from local environmentalists and the need to meet more stringent environmental permit requirements

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

Nine process designs selected for implementation, including one separation system resulting in 5% wastewater reduction with a payback period of one year.

Polymer and monomer production processes

Identification of sitewide energy conservation opportunities to reduce energy costs

Reduction in operating costs for manufacturing processes and the need for additional steam generation for production capacity expansion

Sitewide tracking of energy usage followed by a heat integration study to identify energy conservation opportunities

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.

Specialty chemicals production process

Identification of sitewide energy conservation opportunities to reduce energy costs

High operating costs for utilities

Sitewide tracking of energy usage followed by a heat integration study to identify energy conservation opportunities

Five process designs implemented leading to a 25% reduction in energy usage with a payback period of less than one year.

Metal finishing process

Reduce cost of industrial solvent

Major solvent losses leading to a large operating cost and environmental problems

Synthesis of an energy-efficient heatinduced separation network

Recovery of 80% of lost solvent with a payback period of three years.

Papermaking process

Recovery of lost fibers and management of water system

7% losses of purchased fibers during processing and high usage of water

Integrated matching of properties of broke fibers with demands of paper machines (property integration)

Recovery and reuse of 60% of lost fibers and reduction in water usage by 30% with a payback period of less than one year.

Polymer production processes

Identification of sitewide wastewater recycle opportunities

Future expansion (wastewater discharge system expected to exceed its maximum capacity during the production process expansion)

Sitewide tracking of water followed by a mass integration study for water recycle opportunities and reverse osmosis treatment of select wastewater streams

24 process designs implemented resulting in a 30% reduction in site wastewater discharge and with a payback period of less than one year.

Petrochemical facility

Develop power cogeneration strategies and optimize utility systems

Significant usage of steam for process uses and high cost of power usage

Energy integration with emphasis on combined heat and power optimization

25% reduction in steam cost and cogeneration of 20% of power requirement for the process. Payback period is four years.

(Source: Dunn, Russell, and Mahmoud M. El-Halwagi, Review Process integration technology review: background and applications in the chemical process industry, Journ. of ChemTechnol Biotechnol, 78: 1011e1021, 2003).

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Project Objectives

496

Type of Process

Process Integration and Heat Exchanger Networks Chapter | 16

497

Hot utilities

Process streams to be cooled

ΔQH

NETWORK

Process streams to be heated ΔQC

QC − QH =ΔΗ Process streams Cold utilities FIGURE 16-4 Maximum energy recovery.

For a given system, the synthesis of HENs involves answering the following questions [1]: l l

l

l

Which heating/cooling utilities should be employed? What is the optimal heat load to be removed/added by each utility? How should the hot and cold streams be matched (i.e. stream pairings)? What is the optimal system configuration? (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 Heating utility

(A) H

H

Cooling utility

H

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 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 application of

(B)

Heating utility Cooling utility

C

C

C H = Heater C = Cooler

H = Heater C = Cooler

FIGURE 16-5 Two extreme designs of heat exchanger network (a) Maximum capital cost (b) Maximum heat recovery.

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TABLE 16-3 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 to Process Integration for the Efficient Use of Energy, IChemE., 1997.

Capital cost

Heat load Driving force

FIGURE 16-6 Effect of driving force and heat load on capital cost.

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 for process integration, modeling and optimization for energy saving and pollution reduction. A further list of commercial software tools, their vendors and website addresses is provided by Klemes et al. [8]. These software tools provide the

process designer with a practical, mature, 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 considers the overall economics and key feasibility features. Strategic alternatives can be selected for large and complex design problems.

Process Integration and Heat Exchanger Networks Chapter | 16

499

each heating demand is referred to as a cold stream, and conversely, each cooling demand as a hot stream.

FIGURE 16-7 General flow system.

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. Input of stream data, heat capacity flow rate (CP) values or heat contents (DH) and a given DTmin. 2. Calculation of composite curves (CCs), the problem table, energy targets and the hot and cold pinch temperatures. 3. Plots of composite curves and the 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 DTmin values. However, the software has no provision for cost targeting or area targeting and no provision for the HEN grid of a given problem.

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 for extracting the thermal data for a given heat and material balance are as follows: 1. Inspect the general process flowsheet, which may contain heat recovery exchangers. 2. Remove the recovery heat exchangers and replace them with equivalent virtual heaters and coolers. 3. Lump all consecutive heaters and coolers together. 4. 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

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 16-7. The total energy of the system, m_ in and m_ out of the system, the general energy balance is:
 dEsystem _ þ m_ in u þ P þ 1v2 þ gz ¼ Q_  W dt r 2 in
 (16-1) P 1 2  m_ out u þ þ v þ gz r 2 out where r is the fluid density and the specific enthalpy, h (energy/mass) is: P h ¼ uþ (16-2) r The energy balance equation becomes:
 dEsystem _ þ m_ in h þ 1v2 þ gz ¼ Q_  W dt 2 in 
1 2  m_ out h þ v þ gz 2 out

(16-3)

dE _ ¼ 0, m_ in ¼ m_ out ¼ m, For steady state operation, system dt Equation 16-3 after re-arranging becomes: 

  1 2 1 2 _ _  h þ v þ gz Q ¼ m h þ v þ gz 2 2 out in (16-4)

Assuming work done, W, kinetic energy and potential energy of the streams are negligible: _ out  hin  ¼ DH_ Q_ ¼ m½h

(16-5)

_ p dT DH_ ¼ mC

(16-6)

_ p CP ¼ mC

(16-7)

where:

and The heat flow through the system is: Q_ ¼ DH_ ¼ CP$dT

(16-8)

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where:

or CP can also be calculated from:

DH_ ¼ heat content (kW).




CP ¼ heat capacity flowrate,

CP ¼

 kg kJ s $kg:K , (kW/K).

where CP is assumed to be constant for a stream that requires 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.: ZTt dT ¼ CPðTt  Ts Þ ¼ DH

(16-9)

Ts

and the slope of the line representing the stream is: dT 1 ¼ dQ CP

(16-11)

In a heat exchanger, the heat flow, Q is defined by:

dT ¼ Temperature change for stream ¼ ðTout  Tin Þ ¼ ðTtarget  Tsupply Þ, K.

Q ¼ CP

dQ dH DH ¼ ¼ dT dT ðTt  Ts Þ Q ¼ UADTLMTD

where: U ¼ overall heat transfer coefficient, (kW/m2 K). A ¼ heat transfer area, m2. DTLMTD ¼ log mean temperature difference, K. The T-H diagram can be used to represent heat exchange as shown in Figure 16-8. Where a phase transition occurs, the latent heat is used instead of CP to calculate the stream duties: _ Q_ ¼ ml (16-13) where:

(16-10)

(16-12)

m_ ¼ mass rate, kg/s. l ¼ latent heat, kJ/kg.

T

Q =CP(TT - TS) TT

TS

ΔH

FIGURE 16-8 Representation of process streams in the T-H diagram.

H

Process Integration and Heat Exchanger Networks Chapter | 16

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 16-12, 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 (DTmin) is the lower bound on any temperature difference to be encountered in any heat exchanger in the network. The value of DTmin is a design parameter, which is determined by exploring the trade-offs between more heat recovery and larger heat transfer area requirements.

(A)

501

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 their 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 16-9a shows the temperature-enthalpy plot with a minimum temperature difference DTmin ¼ 10 C. The region of overlap between the two streams in Figure 16-9a (i.e. the horizontal distance between the start of the 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 16-9a cannot be heated by recovery and therefore requires steam. This is the minimum hot utility or energy target QHmin ¼ 3 MW. Correspondingly, the part of the hot

(B)

T (oC) 160

T (oC) 160

Steam

150

150

100

100

50

Steam

50 o

∆Tmin = 10 C

30 CW

CW

0 QCmin = 1 MW

∆Tmin = 20oC

30

∆H (MW) QHmin = 3 MW

QRec = 11 MW

0

∆H (MW)

QCmin = 2 MW

QHmin = 4 MW QRec = 10 MW

o

∆Tmin = 10 C 100oC

100 C o

∆Tmin = 20oC

∆Tmin = 10 C Q

H

= 3 MW

H

o

85 C

80 C

40 C Q

30oC

= 4 MW

Q o

o

150oC

∆Tmin = 20oC

o

= 11 MW

30oC

C Q

= 1MW

50oC

150oC Q

= 10 MW

30oC

C Q

=2 MW

30oC

FIGURE 16-9 Thermodynamic limits on heat recovery with one hot stream and one cold stream.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

(A)

(B) Condenser 60oC

Condenser

Stream 1

60oC ΔH = 2100 kW

85oC

190oC

ΔH = 2000 kW

85oC

190oC

Cool CP = 20

R2 C1

C1

R2

120oC

120oC Stream 3

Reboiler

Reboiler

ΔH = 1100 kW H

ΔH = 3200 kW Heat

R1

R1

CP = 80

140oC

o

100 C

o

140 C

100oC

120oC

C

Cool

CP = 40

40oC

50oC

Stream 4

Stream 2

ΔH = 2880 kW

ΔH = 720 kW

120oC

Process flowsheet

ΔH = 3600 kW

ΔH = 2880 kW

Heat CP = 36

40oC

50oC Data Extraction flowsheet

FIGURE 16-10 Process and data extraction flowsheets for Example 16-1.

stream which extends beyond the start of the cold stream in Figure 16-9a, cannot be cooled by heat recovery and requires cooling water. This is the minimum cold utility or energy target QCmin ¼ 1 MW. 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 of the reference enthalpy for the cold stream. Figure 16-9b shows the two streams moved to a relative position such that DTmin ¼ 20 C. 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 2 MW. 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

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 16-10a. 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 16-10b 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 16-4 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 16-7. That is, _ p CP ¼ mC

Example 16-1 Setting Energy Targets and Heat Exchanger Network

Consider the process flowsheet shown in Figure 16-10a 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

(16-7)

The CP of a stream is measured as enthalpy change per unit temperature. A minimum temperature difference DTmin ¼ 10 C is assumed. The hot utility is steam available at 200 C and the cold utility is cooling water available between 25 C to 30 C.

Process Integration and Heat Exchanger Networks Chapter | 16

TABLE 16-4 Heat Exchange Stream Data for the Flowsheet in Figure 16-12

Target Temp.  C

Heat Capacity Flow Rate, CP kW/ C

Stream

Type

Supply Temp.  C

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

DH kW

Starting from the thermal data for a process as shown in Table 16-4, pinch analysis provides a target for the minimum energy consumption. The energy targets are obtained by means of the composite curves. Figure 16-11 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 1611a, and their composite representation is shown in Figure 16-11b. Stream 1 has a CP of 20 kW/ C and is cooled from 190 C to 85 C, releasing 2100 kW of heat. Stream 2 is cooled from 140 C to 50 C and with a CP of 40 kW/ C and losses of 3600 kW. The construction of the hot composite curve (as shown in Figure 16-11b) simply involves the addition of the enthalpy changes of the streams in the respective temperature intervals. In the temperature interval 190 C to 140 C 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 140 C to 85 C, both streams 1 and 2 are present.

(A)

Therefore, the CP of the hot composite equals the sum of the CP’s of the two streams, i.e. 20 þ 40 ¼ 60. In the temperature interval 85 C to 50 C, 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 16-12 shows the composite curve of the cold streams. 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 16-13, separating them by the minimum temperature difference DTmin of 10 C. 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 monotonically while the cold composite curve increases monotonically. This allows maximum overlap between the curves and hence maximum heat recovery. Figure 16-13 shows the composite curve at DTmin ¼ 10 C 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 16-13, 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 ¼ 460 kW at DTmin ¼ 10 C, which is less than the existing process energy consumption of 1100 kW. The potential energy saving is therefore 1100  460 ¼ 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 ¼ 80 kW at DTmin ¼ 10 C.

(B)

T (oC)

T (oC)

200

200 1

150

150 2

100

100

50

50

1000

2000

3000

4000

5000

The hot streams plotted separately

503

6000 H (kW)

1000

2000

3000

4000

The composite hot stream

FIGURE 16-11 The hot streams can be combined to obtain a composite hot stream.

5000

6000 H (kW)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

(A)

(B)

T (oC)

T (oC)

200

200

150

150

100

2

1

100 50

50

1000

2000

3000

4000

5000

6000 H (kW)

The cold streams plotted separately

1000

2000

3000

4000

The composite cold stream

5000

6000 H (kW)

FIGURE 16-12 The cold streams can be combined to obtain a composite cold stream.

Specifying the hot utility or cold utility or DTmin 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 DTmin ¼ 20 C, and Figure 16-14 shows that hot and cold utility targets are now increased to 860 kW and 480 kW respectively. Tables 16-5, 6 and 7 respectively show typical DTmin values used in various types of processes, process utility matches and in retrofit targeting of various refinery

processes respectively. However, experience-based DTmin 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 DTmin values with caution, and ensure that the choice is supported by quantitative information such as the DTmin versus energy plot. Although the DTmin e 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 16-15 shows what happens to the cost of the system as the relative position of the composite curves is

FIGURE 16-13 Composite curves for hot and cold streams at DTmin [ 10oC for Example 16-1.

Process Integration and Heat Exchanger Networks Chapter | 16

505

FIGURE 16-14 Composite curves for hot and cold streams at DTmin [ 20oC for Example 16-1.

changed over a range of values of DTmin. 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 DTmin between the curves increases, the energy target increases and consequently the capital cost decreases. This TABLE 16-5 Typical DTmin Values for Various Types of Processes

No. 1

2

Industrial Sector Oil refining

Petrochemical

Experience DTmin Values 20e40 C

10e20 C

Comments Relatively low heat transfer coefficients, parallel composite curves in many applications, fouling of heat exchangers. Reboiling and condensing duties provide better heat transfer coefficients, low fouling.

3

Chemical

10e20 C

As for Petrochemicals.

4

Low temperature processes

3e5 C

Power requirement for refrigeration system is very expensive DTmin decreases with low refrigeration temperatures.

Source: Introduction to Pinch Technology, Linnhoff March, © 1998, Linnhoff March [48].

results from increased temperature differences throughout the process, decreasing the heat transfer area. Correspondingly, the energy cost increases as DTmin 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.

TABLE 16-6 Typical DTmin Values Used for Matching Utility Levels Against Process Streams Match

DTmin Values 

Comments

Steam against process stream

10e20 C

Good heat transfer coefficient for steam condensing or evaporation

Refrigeration against process stream

3e5 C

Refrigeration is expensive

Flue gas against process stream

40 C

Low heat transfer coefficient for flue gas

Flue gas against steam generation

25e40 C

Good heat transfer coefficient for steam

Flue gas against air (e.g. air preheat)

50 C

Air on both sides. Depends on acid dew point temperature

Cooling water (CW) against process stream

15e20 C

Depends on whether or not CW is competing against refrigeration. Summer/ winter operations should be considered

Source: Introduction to Pinch Technology, Linnhoff March , © 1998, Linnhoff March.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 16-7 Typical DTmin Values Used in Retrofit Targeting of Various Refinery Processes Process CDU

DTmin

Comments 

Parallel (tight) composites.



30e40 C

VDU

20e30 C

Relatively wider composites (compared to CDU) but lower heat transfer coefficients.

Naphtha reformer/ hydrotreater unit

30e40 C

Heat exchanger network dominated by feed-effluent exchanger with DP limitations and parallel temperature driving forces. Can get closer DTmin with Packinox exchangers (up to 10e20 C).

FCC

30e40 C

Similar to CDU and VDU.

Gas oil hydrotreater/ hydrotreater

30e40  C

Feed-effluent exchanger dominant. Expensive high pressure exchangers required. Need to target separately for high pressure section (40 C) and low pressure section (30 C).

Residue hydrotreating

40 C

As above for GAS oil hydrotreater/hydrotreater.

hydrogen production unit

20e30 C

Reformer furnace requires high DTmin (30e50 C). Rest of the process: 10e20 C.

Source: Introduction to Pinch Technology, Linnhoff March, © 1998, Linnhoff March.

THE HEAT RECOVERY PINCH AND ITS SIGNIFICANCE Figure 16-16a 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 DTmin between the curves. If the correct economic DTmin is known, this fixes the relative position of the composite curves and hence the energy target. The DTmin 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 DTmin is normally observed at only one point between the hot and cold composite curves, which is referred to as the heat recovery pinch.

The trade-off between energy and capital in the composite curves suggests that individual exchangers should have a temperature difference no smaller than DTmin. An initial assumption in the design of heat exchanger network is that no individual heat exchanger has a temperature difference smaller than the DTmin between the composite curves. Figure 16-16a 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 a 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 16-16b. 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 16-17). It follows that any network design that transfers heat a across the pinch must by an overall enthalpy balance, require a more than the minimum from hot and cold utilities as shown in Figure 16-16c. As a corollary, any utility cooling a above the pinch must incur extra hot utility a, 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 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. No 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.

Process Integration and Heat Exchanger Networks Chapter | 16

507

T

T

2 1

H

H

Total Cost

Capital

1

∆Tmin

2 ∆Tmin, opt

FIGURE 16-15 The correct setting for DTmin is fixed by economic trade-offs.

(A)

(C)

(B)

T

Q

T

T

+ α

Heat sink

Heat sink

}

ΔT

{ α

Heat flow

Heat source Heat source

Q

+ α

H

H

FIGURE 16-16 The pinch and its significance.

H

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-17 Shifted composite curves for hot and cold streams at DTmin [ 10oC for Example 16-1.

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 DTmin. 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 16-14 and 16-15) include a pedagogic aspect of understanding by providing the engineer with an overview of the problem, they illustrate important economic trade-offs, and finally they represent information in a very concentrated form. The results can be extracted from Figures 16-10a and b respectively and shown in Table 16-8. Table 16-8 shows that the difference between the hot and cold pinch temperatures equals DTmin, as also observed on the composite curves. A general strategy for process modification can be established from Figure 16-18. In pinch analysis, this strategy is referred to as the plus/minus principle as proposed by Linnhoff and Vredeveld [23]. Considering Figure 16-18, any process change which: l l

increases the total hot stream heat duty above the pinch, decreases the total cold stream heat duty above the pinch,

l l

decreases the total hot stream heat duty below the pinch, increases the total cold stream heat duty below the pinch,

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

TABLE 16-8 Results of Pinch Analysis for Example 16-1 DTmin [ 10 C

DTmin [ 20 C

Minimum external heating, kW

460

860

Minimum external cooling, kW

80

480

Pinch temperature,  C

65

70

Hot stream pinch temperature,  C

70

80

Cold stream pinch temperature,  C

60

60

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509

(B)

(A)

Hot utility target

T

T

Shift hot streams Temperature

Temperature

+

-

QHmin

+

Shift cold streams Excess energy flow

QCmin Cold utility target

Enthalpy

H

The plus-minus principle.

Enthalpy

H

Shifting streams through the pinch in the right direction enacts the plus-minus principle.

FIGURE 16-18 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).

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 16-18. Therefore, the capital energy trade-off (and hence DTmin) should be readjusted after process changes, using any commercial software for 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 detailed reviews, see references [2,18,24,25].

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 Flower [26] have developed a method of calculating energy targets algebraically, which is referred to as the ‘Problem Table’. The procedure is as follows:

FIGURE 16-19 Grid diagram of interval temperature vs. heat capacity flow rate of hot and cold streams.

1. Select a global DTmin 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

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

temperatures, and by adding half to the cold stream temperatures: Hot streams: Tshift ¼ Tact 

DTmin 2

(16-14)

Tshift ¼ Tact þ

DTmin 2

(16-15)

Cold streams:

The use of the shifted temperature rather than the actual temperatures allows the minimum temperature difference to be taken into account, i.e. DTmin. 3. Note any duplicate 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 duplicate 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  Tiþ1) to give the net heat released (positive) or required (negative) in the interval. For the ith interval: X  X CPh  CPc ðTi  Tiþ1 Þ (16-16) DHi ¼ where: DHi ¼ net heat released (required) in the ith interval. P CPh ¼ sum of the heat capacities of all hot streams in the interval. P CPc ¼ sum of the heat capacities of all cold streams in the interval. ðTi  Tiþ1 Þ ¼ interval temperature difference.

8. Starting 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. the 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 16-9 in Example 16-1 and DTmin ¼ 10 C 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. A heat balance is carried out within each shifted temperature interval according to Equation 16-16. The results show that some of the shifted intervals are seen to have a surplus of heat and some have 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 þ 1. Figure 16-20 shows the cascade for Example 16-1. First,

TABLE 16-9 Heat Exchange Stream Data for the Flowsheet in Figure 16-12 Stream

Type

Supply Temp.  C

Target Temp.  C

Shifted Supply Temp.  C

Shifted Target Temp.  C

Heat Capacity Flow Rate, CP kW/ C

DH 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 Networks Chapter | 16

Interval

( T i − Ti+1 )

ΔΗ i

ΔΗ i

Infeasible

ΔΗ i

Temp.,

Heat

o

Cascade

Cascade

Hot

Hot

Utility

Utility

C

185 1

20

1000

2

1000 10

60

600

1600 20

24

480

480

105 4

-56

-1400

480

-1400

80

2540 -1400

680 15

-76

-1140

-1140

65 6

2060

2080 25

5

1460 600

600

125 3

460 1000

1000

135

1140 -1140

-460 20

4

80

0 80

80

45()

Feasible

Surplus/Deficit Heat

0 50

511

-380

80

Cold

Cold

Utility

Utility

FIGURE 16-20 The Problem Table.

assume that no heat is supplied to the first interval from a hot utility. The first interval has a surplus of 1000 kW, 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 1400 kW, which reduces the heat cascaded from this interval to 680 kW. The fifth interval has a deficit of 1140 kW, which leaves 460 kW to be cascaded to the next interval. In the sixth interval, there is a surplus of 80 kW, resulting in a 380 kW deficit. Looking at the heat flows in Figure 16-20, 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 16-20, i.e. 460 kW. 460 kW is added to the first interval from a hot utility (see column 9, Figure 16-20). This does not change the heat balance within each interval but increases all the heat flows between intervals by 460 kW, giving one heat flow of zero at an interval temperature of 65 C. 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 ¼ 460 kW and QCmin ¼ 80 kW respectively. Therefore, the actual hot and cold streams pinch temperatures are 70 C and 60 C respectively. These results agree with the results from the composite curves in Figure 16-13. Further, the cold utility target minus the hot utility target (80  460 kW) should equal the bottom line (380 kW) of the infeasible heat cascade in the Problem Table of Figure 16-20. These calculations provide useful cross-checks

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

that the stream data and heat cascades have been determined correctly. The composite curves are useful for providing a conceptual understanding of the process, but the Problem Table algorithm is a more convenient tool. There are commercial software packages that generate these and others, such as the grand composite curve and the heat exchanger network grid. From the Problem Table (Figure 16-20), the following results are obtained: Pinch temperature

¼ 65 C

Hot stream pinch temperature

¼ 70 C

Cold stream pinch temperature

¼ 60 C

Minimum hot utility requirement

¼ 460 kW

Minimum cold utility requirement

¼ 80 kW

Maximum energy recovery

¼ 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. the outermost layer of the onion model shown in Figure 16-2, and also shown in the composite curves in Figure 16-13. However, these curves do not provide information about the 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 16-10 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

e

Sole water

273

e

Mechanical cooling I

253

e

Mechanical cooling II

233

e

Liquid nitrogen

193

e

Table 16-10 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 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) [27e29]. This diagram allows a better view of the amount of heat available at various temperatures. 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 DTmin. A typical grand composite curve is shown in Figure 1621. It shows the heat flow through the process against temperature after the addition minimum hot and cold utility requirements. The modified temperatures (i.e. shifted temperatures) are simply the average of the hot and cold temperatures (þ/ DTmin/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 16-21 is the pinch. The open ‘jaws’ at the 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 16-21. 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 DTmin to satisfy a local deficit. Figure 16-22a shows the same grand composite curve with two levels of saturated steam used as a hot utility. The steam system in Figure 16-22a shows the low pressure steam being desuperheated by injection of boiler feedwater after pressure reduction to maintain saturated conditions. Figure 16-22b shows the same grand composite curve but with hot oil used as a hot utility.

PLACING UTILITIES USING THE GRAND COMPOSITE CURVE Figure 16-22 shows several different examples of multiple utility 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

Process Integration and Heat Exchanger Networks Chapter | 16

513

QHmin

Tshifted

HEAT SINK

Pockets of Heat Recovery

HEAT SOURCE

ΔH

QCmin FIGURE 16-21 The grand composite curve shows the utility requirements in both enthalpy and temperature terms.

(A)

(B) o

HP

TShifted, C

(C)

HP

T Shifted, oC

o

TShifted, C

Theoretical flame temperature Flue gas MP Utility pinches LP

LP

Process pinch

Utility pinches

Process pinch CW

CW R R

R

Enthalpy, kW

Enthalpy, kW

FIGURE 16-22 The grand composite curve for multiple utilities targeting.

Enthalpy, kW

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

minimum overall energy use. Also, when placing utilities in the GCC, interval and not actual utility is represented. In Figure 16-22a, 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 16-22b, 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 an 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 utility pinches since they are caused by utility levels. A violation of a utility pinch (cross utility pinch heat flow) results in shifting 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 16-22c 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 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 higher 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. Identify 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 16-23 shows the Grand Composite Curve at DTmin ¼ 10 C for Example 16-1.

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 DTmin , the location of the closest approach temperature. Consider the schematic of a counter current heat exchanger, shown in Figure 16-24. The hot stream, with a heat capacity flow of CPh, enters at Thi and exits 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 DT1 . Correspondingly, on the hot end where the temperatures are the highest, the approach temperature difference is DT2 . The energy balance for the hot and cold streams is: Q ¼ CPh ðThi  Tho Þ

or

Thi  Tho ¼

Q CPh

(16-17)

Process Integration and Heat Exchanger Networks Chapter | 16

515

Grand Composite

200 180 160

Shifted Temperature (ºC)

140 120 100 80 60 40 20 0

0

1000

500

1500

2000

3000

2500

Net Heat Flow (kW) FIGURE 16-23 The grand composite curve at DTmin [ 10 C for Example 16-1.

FIGURE 16-24 Schematic of a counter current heat exchanger.

Q ¼ CPc ðTco  Tci Þ or

Tco  Tci ¼

Q CPc

(16-18)

Subtracting Equation 16-18 from Equation 16-17 gives: ðThi  Tho Þ  ðTco  Tci Þ ¼ or

Q Q  CPh CPc


ðThi  Tco Þ  ðTho  Tci Þ ¼ Q

1 1  CPh CPc

(16-19)  (16-20)

DT2  DT1 ¼

QðCPc  CPh Þ CPh $CPc

(16-21)

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, DT1 ¼ DTmin and Equation 16-21 becomes DT2 ¼ DTmin þ

QðCPc  CPh Þ CPh $CPc

(16-22)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Ensuring that DT2  DTmin , 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 DT2 < DTmin . Correspondingly, when a heat exchanger is positioned on the cold side of the pinch DT2 ¼ DTmin and Equation 16-21 becomes: DT1 ¼ DTmin 

QðCPc  CPh Þ CPh $CPc

l

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 theoretical minimum 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 retrofit applications, the design procedure corrects the exchangers that are passing the heat across the pinch.

(16-23)

In this case, ensuring that there are no approach temperature violations (i.e. DT1  DTmin ), 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. Select a DTmin. 2. Calculate the minimum hot and cold utilities used based on this value of DTmin. 3. Using the grand composite curve, pick which utilities to use and their amounts. 4. 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 cold utilities. 5. Estimate the number of exchangers for each partition as N1, 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: l

l

No heat transfer between the process streams across the pinch temperature.

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 Hindmarsh [30], which focused on a 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 the 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 DTmin). The matching rules ensure sufficient driving forces, and they attempt to minimize the 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 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.

Process Integration and Heat Exchanger Networks Chapter | 16

This means that above the pinch, all hot streams must be brought to pinch temperature by interchange 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. No exchanger may have a temperature difference smaller than DTmin. 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 is matched), although the tick-off heuristic can occasionally penalize the design. At the pinch, the enthalpy balance restrictions mean that certain matches must be made if the design is to achieve minimum utility usage without violating the DTmin 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 by utility cooling. Therefore, all hot streams above the pinch must be matched (i.e. ticked-off) with cold streams. That is, all hot streams

517

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 no hot streams left above the pinch, hot utility is used. Conversely, below the pinch, all cold 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 matches 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 16-24. On the left 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. 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 DTmin 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. Divide the problem at the pinch into separate problems. 2. Commence the design for each of the separate problems at the pinch where driving forces are limited and then 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.

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4. Determine the loads on individual units using the tickoff 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 ¼ NS þ NU  1

(16-24)

where: NS ¼ number of streams. NU ¼ 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

NHot  NCold

NHot  NCold

where: CPHot ¼ Capacity flow rate of hot stream. CPCold ¼ Capacity flow rate of cold stream. NHot ¼ Number of hot streams at the pinch (including full as well as split streams). NCold ¼ 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 16-25a illustrates a possible HEN for Example 16-1. The overall network resulting from the above and below pinch designs as shown in Figure 16-25a 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

¼ 65 C

Hot stream pinch temperature

¼ 70 C

Cold stream pinch temperature

¼ 60 C

Minimum hot utility requirement

¼ 460 kW

Minimum cold utility requirement

¼ 80 kW

Maximum energy recovery

¼ 5620 kW

Network Design Above the Pinch Applying: CPHot  CPCold

(16-25)

or CPleaving pinch  CPentering

pinch

(16-26)

1. Stream 1 is matched with stream 3, and transferring the full amount of heat required to bring stream 1 to the target temperature gives: DHex ¼ CPDT or ¼ CPðTs  Tt Þ ¼ 20ð190  85Þ ¼ 2100 kW The heat load in stream 3 from the pinch temperature to its target temperature of 120 C is: DHex ¼ CPDT ¼ 36ð120  60Þ ¼ 2160 kW: This requires an excess of 60 kW, which requires heating to bring the stream to its target temperature. Therefore, a heater is included to provide the remaining heat load: DHhot ¼ 2160  2100 ¼ 60 kW

Process Integration and Heat Exchanger Networks Chapter | 16

FIGURE 16-25A A grid representation of the heat exchanger network for Example 16-1.

2. Stream 2 is matched with stream 4, while satisfying CP restriction, transferring the full amount of heat to bring stream 2 to the pinch temperature:

The intermediate temperatures in the streams are: Stream 4: the heat load is: DHex ¼ CPDT

DHex ¼ CPDT

DT ¼

¼ 40ð140  70Þ

ðT  60Þ ¼

¼ 2800 kW:

The heater load ¼ 400 kW

DHex ¼ CPDT

DT ¼

¼ 80ð100  60Þ

This calculation checks with the value given by the problem table in Figure 16-20. The proposed network design above the pinch is shown in Figure 16-25b.

DH CP

ðT  95Þ ¼

¼ 3200 kW:

DHhot ¼ 3200  2800 ¼ 400 kW

2800 ¼ 35 80

T ¼ 95 C

3. The heat required to bring stream 4 to its target temperature from the pinch temperature is:

Another heater is included in stream 4 to provide the remaining heat load:

DH CP

400 ¼ 5 80

T ¼ 100 C In stream 3: DHex ¼ CPDT 2100 ¼ 36ðT  60Þ 58:3 ¼ T  60 T ¼ 118:3 C

519

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-25B The CP table for the possible designs above and below the pitch for Example 16-1.

The heater load is 60 kW:

The amount of heat in stream 2 from the pinch temperature to its target temperature is:

DHhot ¼ CPDT

DHex ¼ CPDT ¼ 40ð70  50Þ

60 ¼ ðT  118:3Þ 36

¼ 800 kW:

1:7 ¼ T  118:3 T ¼ 120 C

A cooler is required in stream 2 as the remaining heat load is: DHCold ¼ 800  720 ¼ 80 kW

Network Design Below the Pinch CPHot  CPCold

(16-27)

CPleaving pinch  CPentering pinch

(16-28)

Applying or

1. There is one hot stream 2 and one cold stream 3 below the pinch, as stream 1 has its target temperature at 85 C > 70 C (the hot pinch temperature) and stream 3 starts at the cold pinch temperature (40 C). So stream 2 is matched with stream 3, transferring the full amount to bring stream 3 to its pinch temperature: DHex ¼ CPDT ¼ 36ð60  40Þ ¼ 720 kW:

This value also checks with the value by the problem table in Figure 16-20. The intermediate temperatures in the streams are: In stream 2: DHex ¼ CPDT 720 ¼ ð70  TÞ 40 18 ¼ ð70  TÞ T ¼ 52 C The cooler load is 80 kW and the target temperature is: DHex ¼ CPDT 80 ¼ ð52  TÞ 40 T ¼ 50 C Verification of the temperature difference between the heat exchanger units in the network  than the minimum temperature approach DTmin ¼ 10 C.

Process Integration and Heat Exchanger Networks Chapter | 16

Above the Pinch

521

Here, the temperature difference at either end of unit 3 is  DTmin (10 C), indicating that unit 3 has not violated the minimum temperature approach. There is a temperature cross in this unit, which is tolerable.

The heat exchange between streams 2 and 4, unit 1 assuming counter current flow through unit 2 at constant CP is:

140oC

70oC

ΔT1 =140 – 95 = 45o C

ΔT2 = 70 − 60 = 10o C

1 95oC

60oC

Here, the temperature difference at either end of the unit is  DTmin (10 C), 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. The heat exchange between streams 1 and 3, unit 2, assuming counter current flow at constant CP is:

Example 16-2

Consider the network of heat exchangers in Figure 16-26 with DTmin ¼ 10 F. Is the heat flowing across the pinch temperatures? If so redesign the network for minimum utility requirements (i.e. QHmin and QCmin).

190°C

85°C

2

ΔT1 = 190 − 118.3 = 71.7 o C

ΔT2 = 85 − 60 = 25o C

60°C

118.3°C

Solution The utilities in the network are: Cooling water; DHCW ¼ CP$DT ¼ 4ð100  250Þ

The temperature difference at either end of unit 2 is greater than DTmin ¼ 10 C, indicating that unit 2 has not violated the minimum temperature approach, but there is temperature cross in the unit as the exit temperature of the cold stream is greater than the exit temperature of the hot stream.

¼ 600 Btu=hr ðDHCW Þ ¼ 600 Btu=hr:

Steam; DHSteam ¼ CP$DT ¼ 2ð400  250Þ ¼ 300 Btu=hr:

Below the Pinch

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 DTmin [ 10 F (Figure 16.27)

The heat exchange between streams 2 and 3, unit 3 assuming counter current flow at constant CP is:

70oC ΔT1 = 70 − 60 = 10o C

60oC

52oC

3

ΔT2 = 52 − 40 = 12o C

40oC

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

400oF

Steam

250oF 300oF

100oF

250oF

CPh = 4 Btu/hr. oF

CW 150oF CPc = 2 Btu/hr. oF

FIGURE 16-26 Heat exchanger network for Example 16-2.

The results from the Problem Table (Figure 16-28) show that:

Stream Population

Interval Temperature o

405 C

Pinch temperature Hot stream pinch temperature Cold stream pinch temperature Minimum hot utility requirement Minimum cold utility requirement

1

295oC

155oC

2

4

2

FIGURE 16-27 The grid diagram of interval temperature vs. heat capacity flow rate of hot and cold streams for Example 16-2.

Interval

( T i − Ti+1 )

ΔΗ i

Temp., C

o

ΔΗ i Heat Cascade

Feasible ΔΗ i Heat Surplus/Deficit Cascade Infeasible

Hot Utility 405 1

-2

-220

-220

295 2

220 -220

-220 140

2

280

280

155 3

Hot Utility 0

110

0 280

60 60

295 F 300 F 290 F 220 Btu/hr 520 Btu/hr

A possible HEN is shown in Figure 16-29, and one with the minimum utility requirements is shown in Figure 16-30. To avoid heat flow across the pinch, use a larger heat exchanger.

95oC CP

¼ ¼ ¼ ¼ ¼

4

240

240

95

280 240

300 Cold Utility FIGURE 16-28 The Problem Table.

520 Cold Utility

Process Integration and Heat Exchanger Networks Chapter | 16

523

FIGURE 16-29 A grid representation of the heat exchanger network for Example 16-2.

cost of the heating and cooling utilities ($/106 kJ) are 3 and 5 respectively. Stream data are given in Table 16-12. A value of DTmin ¼ 10 K is used. Using pinch analysis, determine the minimum heating and cooling utilities for the process.

Example 16-3 (Process Integration by Mahmoud El-Halwagi, pages 239e255, Elsevier, 2006 [3])

Consider the pharmaceutical processing facility illustrated in Figure 16-31. The feed mixture (C1) is first heated to 550 K and then fed to an adiabatic reactor where an endothermic reaction takes place. The off-gases leaving the reactor (H1) at 520 K are cooled to 330 K prior to being forwarded to the recovery unit. The mixture leaving the bottom of the reactor is separated into a vapor fraction and a slurry fraction. The vapor fraction (H2) exits the separation unit at 380 K and is to be cooled to 300 K prior to storage. The slurry fraction is washed with a hot immiscible liquid at 380 K. The wash liquid is purified and recycled to the washing unit. During purification, the temperature drops to 320 K. Therefore, the recycled liquid (C2) is heated to 380 K. Two utilities are available for service, HU1 and CU1. The

Solution Using the stream data in Table 16-12, the Excel spreadsheet software in A User Guide on Process Integration for the Efficient Use of Energy, [21] is used to construct the Problem Table, determine the pinch problem, pinch temperature, hot and cold streams pinch temperatures, hot and cold utility requirements, plots of the composite curves, grand composite curve, the maximum energy recovery at DTmin ¼ 10 C, plots of hot and cold pinch temperatures at varying DTmin (i.e. minimum to maximum values) and minimum utility requirements for hot and cold streams at varying DTmin (i.e. minimum to maximum values).

400oF

220 Btu/h

Steam CW 290oF

300oF CPh = 4 Btu/h oF

230oF 280 Btu/h

100oF 520 Btu/h

150oF CPc = 2 Btu/h oF

FIGURE 16-30 Heat exchanger network for Example 16-2.

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330K

To Recovery

H1

300K

520K

To storage

H2 Adiabatic Reactor

C1 300K

380K

550K C2 320K

Separation

380K

Washing

Purification

To Finishing

Impurities

FIGURE 16-31 Simplified flowsheet for the pharmaceutical process. (Used by permission: Mahmoud M. El-Halwagi, Process Integration Process Systems Engineering Volume 7, AP Academic Press, 2006.)

TABLE 16-11 Stream Data for Example 16-2 Stream

Actual Ts,  F

Temperature Tt,  F

Shifted Ts,  F

Temperature Tt,  F

CP Btu/hr. F

Hot

300

100

295

95

4

Cold

150

400

155

405

2

TABLE 16-12 Stream Data for Pharmaceutical Process for Example 16-3 Stream

Flow Rate 3 Specific Heat (kW/K)

Supply Temperature (K)

Target Temperature (K)

Enthalpy Change (kW)

H1

10

520

330

1900

H2

5

380

300

400

HU1

?

560

520

?

C1

19

300

550

4750

C2

2

320

380

120

CU1

?

290

300

?

Process Integration and Heat Exchanger Networks Chapter | 16

525

TABLE 16-13 Completed Stream Data for Pharmaceutical Process for Example 16-3 Stream

Flow Rate 3 Specific Heat (kW/K)

Supply Temperature (K)

Target Temperature (K)

Enthalpy Change (kW)

H1

10

520

330

1900

H2

5

380

300

400

HU1

65.5

560

520

2620

C1

19

300

550

4750

C2

2

320

380

120

CU1

5.0

290

300

50

The results show the following at DTmin ¼ 10 C: Type of Pinch Problem Pinch temperature Hot stream pinch temperature Cold stream pinch temperature Minimum hot utility requirement Minimum cold utility requirement Maximum energy recovery

¼ ¼ ¼ ¼ ¼ ¼ ¼

Single Pinch problem 305 C 310 C 300 C 2620 kW 50 kW 2250 kW

The completed stream data with utility loads are shown in Table 16-13, Figures 16-32 to 16-41 provide snapshots for Example 16-3 and a possible HEN is shown in Figure 16-42.

FIGURE 16-32 Screenshot of the input data for Example 16-3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

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FIGURE 16-33 Screenshot of the grid diagram showing the shifted temperature vs. heat capacity flow rate and the pinch location for Example 16-3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

DESIGN FOR THRESHOLD PROBLEMS Generally, processes require both hot and cold utilities in the design of a 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, DTmin, is increased up to or beyond a threshold value DTthreshold. The value of DTmin at which one utility target falls to zero is referred to as DTthreshold, 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 DTmin  DTthreshold,, 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 DTmin 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 heating demands [32,33]. There are two subtypes of threshold problems (see Figure 16-43). 1. Low-threshold DTmin, where problems of this type can be treated exactly as pinch-type problems. 2. High-threshold DTmin, 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 16-44a 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 the non-utility end using the pinch design rules, and Figure 16-44b shows a typical sketch of the grand composite curve with zero heat flow.

Process Integration and Heat Exchanger Networks Chapter | 16

527

FIGURE 16-34 Screenshot of the grid diagram showing the actual temperature vs. heat capacity flow rate for Example 16-3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

The relationship for threshold problems can be summarized as [13]: 0 DTmin < DTthreshold

Either hot or cold utility usage (but not both) is required and the problem is not pinched.

DTmin ¼ DTthreshold

The same hot or cold utility requirement as for lower values of DTmin is required but the problem is now pinched.

DTmin > DTthreshold

Both hot and cold utilities are required. The problem is pinched.

It is possible to apply the pinch design method to threshold problems providing that DTmin is adjusted to the threshold value, although in this instance the designer would not be too concerned about a DTmin 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 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 with 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) using 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. Above 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

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FIGURE 16-35 Screenshot of the grid diagram showing the shifted streams, shifted temperature vs. heat capacity flow rate for Example 16-3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

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 16-45 shows a complete algorithm for stream splitting streams above and below the pinch respectively.

Advantages and Disadvantages of Stream Splitting Advantage: Stream splitting removes one extra heat exchanger in the network.

Disadvantages: 1. In 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 16-4 (Source: Seider et al. Product and Process Design Principles e Synthesis, Analysis, and Evaluation 3rd ed. Wiley 2009 [26])

Consider the process flowsheet in Figure 16-46, where the duties required for each heat exchanger are given in MW, and the source and target stream temperatures are shown in Table 16-14. a. The 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 DTmin ¼ 10 C. Verify or refute this claim.

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529

FIGURE 16-36 Screenshot of the Problem Table, heat cascade, pinch identification, problem type, minimum hot and cold utility requirements for Example 16-3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

The results show the following at DTmin ¼ 10 C: b. If verified, design a HEN to meet MER targets for DTmin ¼ 10 C. Solution Using the data in Table 16-14 and Figure 16-46, the stream data and the CP values are shown in Table 16-15. 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. Construct 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 DTmin ¼ 10 C. e. Plots of the hot and cold pinch temperatures at varying DTmin (i.e. minimum to maximum values) and of the minimum utility requirements for hot and cold streams at varying DTmin (i.e. minimum to maximum values).

Type of pinch problem Pinch temperature Hot stream pinch temperature Cold stream pinch temperature Minimum hot utility requirement Minimum cold utility requirement Maximum energy recovery

¼ ¼ ¼ ¼ ¼ ¼ ¼

Threshold problem 255 C 260  C 250 C 0 MW 240 MW 1400 MW

Therefore, the proposed design does not meet the targets. The following Figures 16-47 to 16-56 show snap-shots of the results for Example 16-4, and a possible HEN is shown in Figure 16-57. Figure 16-57 shows a three-way split of stream H1 to fully meettheheatingrequirementsofstreamsC1andC2andpartially meet the requirements of stream C4. Note that the stream-split fractions are also adjusted to ensure no violations of DTmin. 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.

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FIGURE 16-37 Screenshot of hot and cold stream composite curves for Example 16-3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Example 16-5 Source e 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 16-58. 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 150 C, cooling water at 20 C and refrigerant at 5 C. The temperature rise of both the cooling water and refrigerant can be neglected. Extract the steam data from the flowsheet and present them as hot and cold streams with supply and target temperatures and heat capacity flow rates. Sketch the composite curves for the process at DTmin ¼ 10 C. 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.

Stream data extraction The process flowsheet is shown in Figure 16-58 and data extraction from the flowsheet is shown in Table 16-16. 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. Construct 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 DTmin ¼ 10 C. e. Plots of the hot and cold pinch temperatures at varying DTmin (i.e. minimum to maximum values) and of the minimum utility requirements for hot and cold streams at varying DTmin (i.e. minimum to maximum values).

Process Integration and Heat Exchanger Networks Chapter | 16

531

FIGURE 16-38 Screenshot of hot and cold stream shifted composite curves for Example 16-3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

The results show the following at DTmin ¼ 10 C: Type of pinch problem Pinch temperature Hot stream pinch temperature Cold stream pinch temperature Minimum hot utility requirement Minimum cold utility requirement Maximum energy recovery

¼ ¼ ¼ ¼ ¼ ¼ ¼

Two pinches 75 C 80 C 70 C 9000 kW 9155 kW 15790 kW

Hot process streams  Cold utility ¼ 6500 þ 13300 þ 145  5000  9155 ¼ 15790 kW Cold process streams  Hot utility ¼ 6500 þ 11890 þ 6400  9000 ¼ 15790 kW This is evident from the overlap of the composite curves in Figures 16-64 and 16-65 (Note: Example 16-5 is a problem with two pinches, in addition to the process pinch at 75 C, there is a utility pinch at 25 C corresponding to cooling water).

Figures 16-59 to 16-68 show snap-shots of the results for Example 16-5, and a possible HEN is shown in Figure 16-69. There is however a DTmin violation of heat

exchanger unit 4 (i.e. 15 C  8 C ¼ 7 C, which is < DTmin )

HEAT EXCHANGER AREA TARGETS The area of a single counter current heat exchanger is defined by: A ¼

Q UDTLMTD

(16-29)

where: A ¼ surface area for heat exchanger, m2 Q ¼ heat transferred, kW U ¼ overall heat transfer coefficient, W/m2. C DTLMTD ¼ log mean temperature difference,  C 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.

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FIGURE 16-39 Screenshot of the grand composite curve for Example 16-3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

DTLMTD ¼ ¼

DTH  DTC lnðDTH =DTC Þ ðTh1  Tc2 Þ  ðTh2  Tc1 Þ  Th1  Tc2 ln Th2  Tc1 (16-30)

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 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: ATotal ¼

1 U

Intervals Xk

DHk DTLMTD;k k ¼ 1;::::K

(16-31)

where: ATotal ¼ heat exchange area for vertical heat transfer for the whole network. K ¼ total number of enthalpy intervals. The problem with Equation 16-31 is that the overall heat transfer coefficient is not constant throughout the process. To overcome this, Equation 16-31 can be extended to allow for individual film heat transfer coefficients, h, on each stream [33,35]. ATotal ¼

Intervals Xk

1

k ¼ 1;::::K

DTLMTD;k

"

Hot X streams I i ¼ 1;::::I

streams J qj;k qi;k ColdX þ hi;k hj;k j ¼ 1;:::J

#

(16-32)

Process Integration and Heat Exchanger Networks Chapter | 16

533

FIGURE 16-40 Screenshot of actual interval temperature of hot and cold duties for Example 16-3. Maximum energy recovery at DTmin [ 10 C [ 2300 L 50 [ 2250 kW. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

where: qi ¼ heat duty on hot stream i in enthalpy interval k. j ¼ heat duty on cold stream j in enthalpy interval k. hi, hj ¼ film heat transfer coefficients for hot stream i and cold stream j (including wall and fouling resistances). I ¼ total number of hot streams in enthalpy interval k. J ¼ total number of cold streams in enthalpy interval k. K ¼ total number of enthalpy intervals. Equation 16-32 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 16-32 cannot predict the true minimum network area, and deliberate nonvertical matching may be required to achieve the minimum area. Consider Figure 16-70a, 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 in area overall. Conversely, in Figure 16-70b, 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 Equation 16-32 does not predict the minimum network area. If higher temperature differences (DTs) are used for matches with low film heat transfer coefficients and vice versa, the area target from crisscrossing can actually be lower than that from vertical matching, and Equation 16-32 does not predict the true minimum network area. The true minimum area must be predicted using linear programming [36,37]. In practice, Equation 16-32 gives an area accurate to within 10%,

FIGURE 16-41 Screenshot of plots of pinch temperatures of hot and cold streams and minimum utility requirements at varying DTmin (i.e. minimum to maximum values) for Example 16-3. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

FIGURE 16-42 A grid representation of the heat exchanger network for Example 16-3.

Process Integration and Heat Exchanger Networks Chapter | 16

ST T

(A) Utilities [MW] CW ST

ΔΤmin

CW ΔΤmin

10oC

ΔH

[MW]

ΔH

[MW]

Low Threshold ΔΤmin ST T

(B) Utilities [MW]

ST CW

10oC

ΔΤmin = 10o C

ΔΤmin

High Threshold ΔΤmin FIGURE 16-43 Threshold problems.

(B)

Grand composite curve

Shifted temperature (oC)

Hot and cold composite curves

Actual temperature (oC)

(A)

Heat flow, kW

Net heat flow, kW

FIGURE 16-44 (A) Hot and cold composite curve; and (B) grand composite curve for threshold problems.

535

536

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

(A)

(B)

Stream data at pinch

Below the pinch

Above the pinch

N

≤N

Yes

CP

?

No

Split a cold stream

≤ CP

Yes

≥N

N

For every pinch match ?

No

Yes

CP

?

Split a hot stream

≥ CP

For every pinch match ?

No

Yes

Place matches Split a stream (usually hot)

CP

= Capacity flow rate of cold stream

CP

= Capacity flow rate of hot stream

N N

Stream data at pinch

No

Place matches

Split a stream (usually cold)

= Number of cold streams = Number of hot streams

FIGURE 16-45 Algorithm for stream splitting at the pinch.

unless film heat transfer coefficients differ by more than one 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. Tabulated 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 16-6 (Source: R. Smith, Chemical Process Design, McGraw-Hill, 1995 [20])

Table 16-17 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 16-17 at DTmin ¼ 10 C, the BCCs are determined as shown in Figure 16-71. These curves incorporate the steam within the construction of the hot composite curve, and the cooling water for the cold

composite curve. Figure 16-71 shows the curves divided into enthalpy intervals, where there is either a change of slope on the hot composite curve, or a change of slope on the cold composite curve. Figure 16-72 shows the stream population for each enthalpy interval together with the hot and cold stream temperatures. P P ðqi =hi Þk, ðqj =hj Þk and ðDTLMTD Þk Calculations for terms on the hot and cold streams at intervals of k are given in Table 16-17: Enthalpy Interval 1

ΔTH = ( Th1 − Tc2 )

250oC

Hot stream

= 250 − 230 = 20o C 230oC

240oC ΔTC = ( Th 2 − Tc1 ) o

= 240 − 225 = 15o C

225 C Cold stream

The log mean temperature difference is: DTLMTD ¼

 ðDTH  DTC Þ ¼ 20  15 lnð20=15Þ lnðDTH =DTC Þ

¼ 17:38 C  P  Hot stream : qi hi k ; ðkW kW m2 : C ¼ m2 : C

Process Integration and Heat Exchanger Networks Chapter | 16

537

Effluent Feed

1

25oC

200oC 350MW

st 200oC 260oC 450MW 180 MW

Reactor

st 200oC

2 300MW

Recycle 2 cw

Recycle 1

cw Product o

40 C

790MW

200MW 50oC

o

o

40 C

40 C

Flash Separator Flash Liquid

Distillation column

40oC

100oC 3 120MW

120oC

FIGURE 16-46 Process flowsheet for Example 16-4. (Used by permission: Seider et al. Product and Process Design Principles Synthesis, Analysis and Evaluation. 3rd ed. Wiley, 2009.)

TABLE 16-14 Stream Data for Example 16-4 Process Stream

Ts ( C)

Tt ( C)

Feed

25

200

Effluent

260

40

Recycle 1

40

200

Flash liquid

40

100

Recycle 2

50

200

Product

120

40

538

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

TABLE 16-15 Completed Stream Data from Figure 16-46 for Example 16-4 Stream

ID

Ts ( C)

Tt ( C)

Heat Capacity Flow, CP (MW/ C)*

DH (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

120

Recycle- 2

C4

50

200

3.0

450

*CP ¼ DH/DT

(16-11)

FIGURE 16-47 Screenshot of the input data for Example 16-4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Process Integration and Heat Exchanger Networks Chapter | 16

539

FIGURE 16-48 Screenshot of the grid diagram showing the shifted temperature vs. heat capacity flow rate and the pinch location for Example 16-4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

X P  0:15ð250  240Þ ðCP DTi =hi Þ1 ¼ qi hi k ¼ 0:001 ¼ 1500 ðm2 : CÞ Cold stream :

P

ðqj =hj Þk

X  X

 0:3ð230  225Þ qj hj k ¼ CP DTj hj 1 ¼ 0:0008

 ¼ 1875 m2 : C

DTLMTD ¼

 ðDTC  DTH Þ ¼ 39:5  15 =lnð39:5=15Þ lnðDTC =DTH Þ

¼ 25:30 C  P 

Hot stream : qi hi k ; kW kW m2 : C ¼ m2 : C X X  ðCP DTi =hi Þ1 qi hi k ¼

Enthalpy Interval 2

240oC

The log mean temperature difference is:

Hot stream

ΔTH = ( Th1 − Tc2 )

239oC ΔTC = ( Th 2 − Tc1 ) = 239 − 199.5 = 39.5o C

= 240 − 225 = 15o C 225oC

Cold stream

199.5oC

¼

7:5ð240  239Þ 0:15ð240  239Þ þ 0:003 0:001

¼ 2650ðm2 : CÞ X  Cold stream : qj hj k

540

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-49 Screenshot of the grid diagram showing the actual temperature vs. heat capacity flow rate for Example 16-4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

X

ðqj =hj Þk ¼

X

 CP DTj hj 1

0:3ð225  199:5Þ 0:0008 

¼ 9562:5 m2 : C

¼

X X  0:15ð239  200Þ ðCP DTi =hi Þ1 ¼ qi hi k ¼ 0:001 ¼ 5850ðm2 : CÞ P Cold stream : ðqj =hj Þk X

X  CP DTj hj 1 ðqj =hj Þk ¼

Enthalpy Interval 3 Hot stream

0:3ð199:5  180Þ 0:0008 

¼ 7312:5 m2 : C

200oC Δ TC = ( Th 2 − Tc1)

239oC Δ TH = (Th1− Tc2 )

¼

= 200 − 180.0= 20o C

= 239.0 − 199.5 = 39.5o C 199.5oC

o

180.0 C Cold stream

Enthalpy Interval 4 Hot stream

The log mean temperature difference is: DTLMTD ¼

 ðDTH  DTC Þ ¼ 39:5  20 lnð39:5=20Þ lnðDTH =DTC Þ

¼ 28:65 C  P 

Hot stream : qi hi k ; kW kW m2 : C ¼ m2 : C

150oC Δ TC = (Th 2 − Tc1)

200oC Δ TH = ( Th1− Tc2 )

= 150 − 140.0= 10o C

= 200.0 − 180.0 = 20o C 180.0oC

o

140.0 C Cold stream

Process Integration and Heat Exchanger Networks Chapter | 16

541

FIGURE 16-50 Screenshot of the grid diagram showing the shifted streams, shifted temperature vs. heat capacity flow rate for Example 16-4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

The log mean temperature difference is: DTLMTD ¼

 ðDTH  DTC Þ ¼ 20  10 lnð20=10Þ lnðDTH =DTC Þ

¼ 14:43 C  P 

qi hi k ; kW kW m2 : C ¼ m2 : C Hot stream : X X  ðCP DTi =hi Þ1 qi hi k ¼ ¼

0:15ð200  150Þ 0:25ð200  150Þ þ 0:001 0:0008 2 

¼ 23; 125ðm : CÞ P Cold stream : ðqj =hj Þk X

X  CP DTj hj 1 ðqj =hj Þk ¼ 0:2ð180  140Þ 0:3ð180  140Þ þ 0:0006 0:0008

2  ¼ 28; 333:3 m : C

¼

Enthalpy Interval 5 Hot stream 95.0oC Δ TC = (Th 2 − Tc1 )

150oC Δ TH = (Th1− Tc2 )

= 95 − 30.0 = 65o C

= 150.0 − 140.0 = 10o C 140.0oC

o

30.0 C Cold stream

The log mean temperature difference is: DTLMTD ¼

 ðDTC  DTH Þ ¼ 65  10 lnð65=10Þ ¼ 29:38 C lnðDTC =DTH Þ

Hot stream :

 P 

qi hi k ; kW kW m2 : C ¼ m2 : C

X X  0:15ð150  95Þ ðCP DTi =hi Þ1 ¼ qi hi k ¼ 0:001

2  0:25ð150  95Þ ¼ 25; 437:5 m : C þ 0:0008 P Cold stream : ðqj =hj Þk

542

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-51 Screenshot of the Problem Table, heat cascade, pinch identification, problem type, minimum hot and cold utility requirements for Example 16-4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

X

X

 0:2ð140  30Þ CP DTj hj 1 ¼ 0:0006 

¼ 36; 666:7 m2 : C

ðqj =hj Þk ¼

Enthalpy Interval 6 Hot stream 80oC Δ TC = ( Th 2 − Tc1 )

95oC Δ TH = ( Th1− Tc2 )

X X  ðCPDTi =hi Þ1 qi hi k ¼ ¼

¼ 6937:5ðm2 : CÞ P Cold stream : ðqj =hj Þk X

X  CP DTj hj 1 ðqj =hj Þk ¼ 0:2ð30  25Þ 1:0ð30  25Þ þ 0:0006 0:001

2  ¼ 6666:7 m : C

¼

= 80 − 30.0 = 55o C

= 95 − 30 = 65o C

30.0oC

o

25.0 C Cold stream

0:15ð95  80Þ 0:25ð95  80Þ þ 0:001 0:0008

Enthalpy Interval 7 Hot stream

DTLMTD ¼

 ðDTH  DTC Þ ¼ 65  55 lnð65=55Þ ¼ 59:86 C lnðDTH =DTC Þ

Hot stream :

 P 

qi hi k ; kW kW m2 : C ¼ m2 : C

40oC Δ TC = (Th 2 − Tc1 )

80oC

The log mean temperature difference is: Δ TH = (Th1 − Tc2 )

= 40 − 20.0 = 20o C

= 80 − 25 = 55o C o

25.0 C

o

20.0 C Cold stream

Process Integration and Heat Exchanger Networks Chapter | 16

543

FIGURE 16-52 Screenshot of hot and cold streams composite curves for Example 16-4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

The log mean temperature difference is:

 ðDTH  DTC Þ ¼ 55  20 lnð55=20Þ ¼ 34:6 C lnðDTH =DTC Þ  P 

Hot stream : qi hi k ; kW kW m2 : C ¼ m2 : C

DTLMTD ¼

X  X 0:15ð80  40Þ qi hi k ¼ ðCP DTi =hi Þ1 ¼ 0:001 ¼ 6000:0ðm2 : CÞ P Cold stream : ðqj =hj Þk X X

 CP DTj hj 1 ðqj hj Þk ¼ 0:2ð25  20Þ 1:0ð25  20Þ þ 0:0006 0:001

2  ¼ 6666:7 m : C

¼

Table 16-18 shows the network area target at  DTmin ¼ 10 C is 7410 m2. Shenoy [18] provides detailed calculations of the area target for the network of 1e2 shell and tube heat exchangers as well as countercurrent exchangers. For Example 16-6, the

targets obtained using the procedure and software given by Shenoy are summarized as: Above Pinch þ Below Pinch ¼ Total 2706.94 þ 4703.03 ¼ 7409.97 (countercurrent area target) 3094.06 þ 5795.68 ¼ 8889.74 (1e2 shell and tube area target) 7 þ 12 ¼ 19 (number of shells target) For a network of 1e2 exchangers, Equation 16-32 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]:

Anetwork;12 ¼

Interval XK

" x

k

1 DTLMTD FT;k

Hot X stream; I i



qi hi þ

Cold X stream; J j



#

qj hj (16-33)

544

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-53 Screenshot of hot and cold streams shifted composite curves for Example 16-4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

A line of constant Xp is compared with a line of constant FT as shown in Figure 16-73, 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 illustrated in Figure 16-74 must be considered.

Table 16-19 shows the input data and the results with three shells required. The heat transfer area is: A ¼

Q Q ¼ U DTLMTD FT U CMTD

¼

3:5  106 ¼ 619 m2 ð100  56:55Þ

HEN SIMPLIFICATION Example 16-7

A hot stream is to be cooled from 300 C to 100 C by exchange with a cold stream heated from 60 C to 200 C in a single unit. 1e2 shell and tube exchangers are to be used subjected to Xp ¼ 0.9. The duty of the exchanger is 3.5 MW and the overall heat transfer coefficient is estimated to be 100 W/m2  C. Calculate the number of shells required and the heat transfer area. Solution A computer program PROG15A has been developed to determine the FT factor, and subsequently the log mean temperature difference, the corrected log mean temperature difference and the required number of shells required.

Cases often arise where the general results in HENs are rather complex and have 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

Process Integration and Heat Exchanger Networks Chapter | 16

545

FIGURE 16-54 Screenshot of the grand composite curve for Example 16-4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

another without affecting stream duties. Hohmann [31] was the first to observe and introduce the term heat load loop, and this 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 DTmin, 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 16-24 (i.e. uHX, min ¼ 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 16-20, referred to as Test Case 3 (TC3).

Example 16-8 Test Case 3, TC3 Linnhoff and Hindmarsh [30].

Using the data from Linnhoff and Hindmarsh [30], TC3, determine the minimum utility requirements at DTmin ¼ 20 C 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 for the following steps: a. Construct 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 DTmin ¼ 20 C. e. Plots of the hot and cold pinch temperatures at varying DTmin (i.e. minimum to maximum values) and of the minimum utility requirements for hot and cold streams at varying DTmin (i.e. minimum to maximum values). The results show the following at DTmin ¼ 20 C in the Excel spreadsheet (Example 16-8a.xlsx), on the companion website: Type of Pinch problem Pinch temperature Hot stream pinch temperature Cold stream pinch temperature Minimum hot utility requirement Minimum cold utility requirement Maximum energy recovery

¼ ¼ ¼ ¼ ¼ ¼ ¼

Single pinch problem 80 C 90 C 70 C 107.5 kW 40 kW 380 kW

546

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-55 Screenshot of actual interval temperature of hot and cold duties for Example 16-4. Maximum energy recovery at DTmin [ 10 C [ 1640 L 240 [ 1400 MW. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Figures 16-75 and 16-76 show the composite curves, the grand composite curve respectively, and Figure 16-77 from the Excel spreadsheet (Example 16-8b.xls) shows a screenshot of plots of the temperatures of hot and cold streams and utility requirements at varying DTmin. Figures 16-78a, b and c show possible HENs of TC3, although Figure 16-78c contains more units than Figures 16-78a or b. In trying to match the hot and cold streams respectively, the following inequalities should be noted: CPHot  CPCold

above the pinch:

(16-25)

For a cold end pinch match: CP difference ¼ CPHot  CPCold Immediately above the pinch: Overall CP difference ¼

N Cold X

CPHot  CPCold

below the pinch:

(16-26)

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 ¼ CPCold  CPHot

(16-34)

CPCold 

NHot X

1

CPHot

(16-36)

CPCold

(16-37)

1

Immediately below the pinch: Overall CP difference ¼

NHot X 1

and

(16-35)

CPHot 

N Cold X 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 16-21 shows the CP table for the hot end of TC3. By inspection, the number of hot stream is less than the number of cold streams, and the CP inequality is satisfied for each of the possible matches. The overall CP difference

Process Integration and Heat Exchanger Networks Chapter | 16

547

FIGURE 16-56 Screenshot of plots of pinch temperature of hot and cold streams and minimum utility requirements at varying DTmin > DTthreshold (24 C) (i.e., minimum to maximum values) for Example 16-4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

is from the total (5.5  2.0) ¼ 3.5. The individual CP difference for the two possible matches is: Stream 1 and stream 4 : CP difference ¼ 3  2 ¼ 1 Stream 1 and stream 3 : CP difference ¼ 2:5  2 ¼ 0:5: Since both of these values are less than the overall CP difference, both satisfy all of the feasibility criteria. Table 16-22 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 hot 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 16-78a and b show two possible splittings of hot stream 2. Figures 16-78a and b show seven units HENs, whereas the minimum number is five. Hence, there are two loops shown in these figures. 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 16-78a. The 20 kW exchanger is eliminated by shifting it to the 120 kW exchanger, thus increasing its duty to 140 kW. The resulting HEN is shown in Figure 16-79. The heat balance calculation of the new load of 140 kW shows that temperature on the cold end is 18 C (< DTmin ¼ 20 C), which is a violation of DTmin (see Figure 16-80 for calculations), although there is no change in the utility consumption. Therefore, using a heat load loop to transfer the 20 kW across the pinch results in a violation of DTmin, 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 105 kW load on the cold side, this becomes 122.5 kW. The temperature difference between stream 2 (from the stream splitting of CP ¼ 8.0) and stream 3 is 11 C (see Figure 16-80 for calculations), which is again a violation of DTmin ¼ 20 C. 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 DTmin. The driving forces are often restored using heat load paths.

548

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-57 A possible grid representation of the heat exchanger network of Example 16-4.

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 DTmin violation incurred during network simplification. Consider the 140 kW exchanger in Figure 16-81, where there is an 18 C driving force on the cold end. However, to restore this value to 20 C, the exit temperature on stream 1 can be increased from 80 C to 82 C. Since the CP of stream 1 is 2 kW/ C, the exchanger duty must be reduced by 4 kW to 136 kW. The exchanger forms a part 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 4 kW to the heater duty on stream 3, and 4 kW to the cooler duty on stream 1 (see Figure 16-81). The HEN modification is that a 20 kW exchanger has been eliminated from the network without violating the DTmin on the remaining exchanger. The hot and cold utilities have subsequently increased by 4 kW.

In summary, the procedure for reducing units at minimum energy sacrifice is: l l l

l l

Identify a loop (across the pinch), if one exists. Break it by subtracting and adding loads. Recalculate network temperatures and identify the DTmin violations. Find a relaxation path and formulate T ¼ f(X). Restore DTmin .

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.

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

Process Integration and Heat Exchanger Networks Chapter | 16

80 C

Dryer Dryer

549

100 C Air CP = 80

Steam

20 C

Water CP = 140 60 C

5C

10 C

CP = 5,000

Fan CW

CW

Refrigeration 30 C

59 C

30 C CW Solvent CP = 5

30 C Refrigeration

Absorption column

Distillation column

CW

90 C

101 C

Air/Solvent CP = 100 15 C

8C

100 C

100 C Steam

CP = 6,500

CP = kW/K Steam Water /Solvent CP = 145

FIGURE 16-58 Flowsheet for the manufacture of cellulose acetate fiber. (Used by permission: Smith, R., Chemical Process Design and Integration. John Wiley, 2007.)

shells for each match in interval k will 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 (see Chapter 15, computer programs PROG151 and PROG151A). The minimum shell count for the interval is: NSHELLS;k ðSk  1Þ

(16-38)

where R ¼

CPc Th1  Th2 tc2  tc1 ¼ and P ¼ CPh tc2  tc1 Th1  tc1

(16-39)

FT depends on the inlet and outlet temperatures of the streams in a 1e2 exchanger. Figure 16-82 illustrates three situations that can be encountered, when using 1e2 exchangers [34]. 1. Figure 16-82a 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 1e2 shell exchanger.

2. Figure 16-82b 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 cross increases in Figure 16-82c, 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 1e2 or counter flow exchangers that comprise a single shell. If heat exchangers are countercurrent devices, then the number of units equals the number of shells, providing individual shells do not exceed certain upper size limit. If equipment used is not completely

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-59 Screenshot of the input data for Example 16-5. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

K ¼ Total number of enthalpy intervals on the composite curves.

countercurrent, as with 1e2 shell and tube heat exchanger, then: NShells  Nunits

(16-40)

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]: NShells ¼

Intervals XK

NSHELLS;k ðSk  1Þ

(16-41)

k

where NShells ¼ total number of shells over k enthalpy intervals NSHELLS;k ¼ real (or fractional) number of shells resulting from temperatures of enthalpy interval k. Sk ¼ number of streams in enthalpy interval k.

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]. l

l

l

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 they are easier to repair than a shell if corrosion does occur.

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551

FIGURE 16-60 Screenshot of the grid diagram showing the shifted temperature vs. heat capacity flow rate and the pinch location for Example 16-5. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

l

l

l

Streams whose pressure drop must be minimized should go on the shell side (DP 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.

CAPITAL COST TARGETS 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]: Operating Cost ðOCÞ ¼ ðChu $QHmin Þ þ ðCcu $QCmin Þ (16-42) where Chu ¼ cost of unit load of hot utility

Ccu ¼ cost of unit load of cold utility. QHmin ¼ minimum hot utility requirement. QCmin ¼ 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 ðCCÞ ¼ a þ bAc (16-43) 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 16-43 some area distribution must be assumed, the simplest being that all exchangers have the same area [18].

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-61 Screenshot of the grid diagram showing the actual temperature vs. heat capacity flow rate for Example 16-5. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Network Capital Cost (CC)

where Af is the annualized factor defined by: c

CC ¼ N½a þ bðANetwork =NÞ 

(16-44)

Af ¼

for a network of counter current exchangers: c

CC ¼ aN þ bSmin ðA12 =Smin Þ

(16-45)

for a network of 1e2 shell and tube exchangers. where N ¼ minimum number of units in a MER network. ANetwork and A12 ¼ appropriate area targets. Smin ¼ minimum number of shells target.

Total Annual Cost Since the energy cost is a recurring expense and the capital cost is one-off investment, the expected life of the plant has to be considered while calculating the annual cost. The total annual cost (TAC) is: TAC ¼ OC þ CC$Af

(16-46)

i ð1 þ iÞn n ð1 þ iÞ  1

(16-47)

where i ¼ fractional interest rate per year. n ¼ number of years. Shenoy [18] provides cost data for various heat exchanger specifications, as shown in Table 16-23. 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 the 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,

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553

FIGURE 16-62 Screenshot of the grid diagram showing the shifted streams, shifted temperature vs. heat capacity flow rate for Example 16-4. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

cooling water, refrigerants, etc.). Other constraints such as safety, controllability, plant layout, flexibility, operability, etc. 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.

SUPERTARGETING OR DTMIN OPTIMIZATION The energy targeting is dependent on the minimum approach temperature DTmin in order to provide a minimum driving force for heat transfer, and Tables 16-5, 16-6 and 16-7 show values of DTmin 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/shell. However, there are tradeoffs 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 16-46), both of which are dependent on DTmin. The higher the value of DTmin, the higher are the energy requirements (i.e. QHmin and QCmin), resulting in increased operating costs. Similarly, increased DTmin gives lower area requirements and consequently lower capital costs. As DTmin 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 DTmin for which the total annual cost is a minimum. Therefore, for any HEN problem, there is an optimal value of DTmin 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 DTmin 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

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FIGURE 16-63 Screenshot of the Problem Table, heat cascade, pinch identification, problem type, minimum hot and cold utility requirements, multiple utility targeting, cooling water shifted temperature at 25 C gives cascade value [ 5895 kW, refrigeration target [ 3260 kW for Example 16-5. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

design at an arbitrary value of DTmin, that may not guarantee cost optimality. Therefore, supertargeting ensures that an initial design at an optimal DTmin requires minimal computation and saves considerable effort in post-design optimization. Example 16-9 HEN for Maximum Energy Recovery (Warren D. Seider et al. [26])

Design a heat exchanger network for maximum energy recovery with no more than 15 heat exchangers (including utility heaters) and DTmin ¼ 10 C for the streams in Table 16-24. 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. Construct 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 DTmin ¼ 10 C. e. Plots of the hot and cold pinch temperatures at varying DTmin (i.e. minimum to maximum values) and of the minimum utility requirements for hot and cold streams at varying DTmin (i.e. minimum to maximum values) (see Excel spreadsheet, Examples 16-9a.xlsx and Example 16-9b.xlsm for calculations). The results show the following at DTmin ¼ 10 C: Type of Pinch problem Pinch temperature Hot stream pinch temperature Cold stream pinch temperature Minimum hot utility requirement Minimum cold utility requirement Maximum energy recovery

¼ ¼ ¼ ¼ ¼ ¼ ¼

Single pinch problem 135 C 140 C 130 C 760 kW 960 kW 5540 kW

A possible HEN is shown in Figure 16-83. The total number of heat exchangers including the utilities ¼ 13.

Process Integration and Heat Exchanger Networks Chapter | 16

555

FIGURE 16-64 Screenshot of hot and cold streams composite curves for Example 16-5. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

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. l Divide the problem at the pinch. l Start at the pinch and move away. l Start with biggest stream ‘IN’. l Observe CPOUT > CPIN, splitting streams where necessary. l Place all pinch matches first. l Maximize loads on all pinch matches to minimize number of units (the tick-off rules). l Fill in the rest. l Merge above and below the pinch designs. b. Evolve the MER network for network simplicity and capital energy trade-off l Exploit heat load loops and heat load paths. l Optimize network performance using advanced tools in SuperTarget Process.

Retrofit design can be carried out using one of the following three methods. 1. Pinch design method with maximum reuse of existing exchangers. 2. Correction of cross pinch exchangers. 3. Analysis of exchanger paths. Figure 16-84 shows a flow chart indicating which retrofit method is most suitable for a project.

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

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-65 Screenshot of hot and cold streams shifted composite curves for Example 16-5. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

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. the reaction area and separation area of the process. These areas are kept separate for reasons such as start-up, shutdown, operational flexibility, safety etc. 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 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 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

Process Integration and Heat Exchanger Networks Chapter | 16

557

FIGURE 16-66 Screenshot of the Grand Composite Curve showing multiple utility targeting for Example 16-5. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

procedure first places the matches which exhibit the energy penalty and then remaining matches on either side of the pinch.

TARGETING BY LINEAR PROGRAMMING The targeting procedures presented earlier cannot be applied where there are forbidden stream matches. Forbidden matches may occur from considerations due to plant layout, process operability or safety. These additional constraints may result in higher utility requirements for the heat exchanger network design. Therefore, an alternative targeting procedure that can handle these constraints is used, involving linear programming. See references [18,29,45,46,47,48]. A linear program is an optimization technique in which a linear function is maximized or minimized subject to a set of linear inequality or equality constraints. Let Qj be the heat flow leaving the subnetworks (SNs), jth SN and let Qo be the amount of hot utility

supplied to SN1. Then the energy balance for SN j can be written as: nX o X ðCPÞhot;i  ðCPÞcold;i DTj Qj ¼ Qj1 þ (16-48) where the summations extend over the streams that exist in SN j. The energy deficit in each SN is the difference between the energy required to heat the cold streams and the energy available from cooling the hot streams, and is expressed by: # " X X ðCPÞcold;i  ðCPÞhot;i DT (16-49) deficit ¼ i

where DT is the magnitude of the temperature difference across the SN and the summations are over only those streams that exist in the SN. Using Equations 16-48 and 16-49, Qj ¼ Qj1  ðdeficitÞj

(16-50)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-67 Screenshot of actual interval temperature of hot and cold duties for Example 16-5 Maximum energy recovery at DTmin [ 10 C [ 24945LL 9155 [ 15790 kW (15.8 MW). (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

or Qj  Qj1 þ ðdeficitÞj ¼ 0

(16-51)

For a problem with one hot and one cold utility and N SNs, QN is the heat flow to the cold utility, i.e. the cold utility requirement. Therefore, to find the minimum utility requirements for the problem, Qo and QN must be minimized, while satisfying the energy balance equation for each SN. In addition, all the heat flows must be non-negative. These conditions can be stated mathematically as: min f ¼ Qo þ QN

(16-52)

Subject to : Qj  Qj1 þ ðdeficitÞj ¼ 0 ðj ¼ 1; 2; ...; NÞ Qj  0 ðj ¼ 0; 1; 2; ..::NÞ

(16-53) (16-54)

Notice that the objective function, f, and the constraints are linear in the variables, Qj, and as such the problem is a

linear program, which can be solved using any of the widely available LP software packages, such as Excel Solver.

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 electrical 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.

Process Integration and Heat Exchanger Networks Chapter | 16

559

FIGURE 16-68 Screenshot of plots of pinch temperature of hot and cold streams and minimum utility requirements at varying DTmin (i.e. minimum to maximum values) for Example 16-5. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

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. The 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, burn 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 500 C. 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 a 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

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

CPHot ≤ CPCold

Design away From the pinch

NHot ≤ NCold

CPHot ≥ CPCold

Design away From the pinch

CP (kW/oC)

NHot ≥ NCold

T = 80 C

15 oC CP = 86

100 oC

33.6 C C

∆H (kW)

100

9000

5 oC 140

13300

4010 kW CP = 54 T = 80 C

59oC 60oC

C

30 oC

C 145 kW

59oC

5

145

5000

5000

6500

6500

145

11890

80

6400

5000 kW 6500 kW

110 °C

H

100 °C

90 °C

H

89.3 C

CP = 40 T = 70 C

100 kW

2800 kW

8 oC

2490 kW CP = 105 6500 kW

2400 kW

100°C

20oC

H 4000 kW

T = 70 C

H Hot utility

Heat exchange between streams

C Cold utility CP = Heat capacity flow rate N = Number of streams

FIGURE 16-69 A grid representation of the heat exchanger network for Example 16-5.

(A)

(B)

T oC

A

CP= 10 h =0.01 A

B

350o

CP=50 h =0.1 B 290

AREA = 1616 m2 300o

o

D 250o D

200

C

o

C CP=50 h =0.1

260o

A B

CP=10 h =0.01 CP=kWK-1 h = kWm-2 K-1

H (kW) C D

AREA = 1250 m2

FIGURE 16-70 If film heat transfer coefficients differ significantly, then nonvertical 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. Engg. 7, 729.)

Process Integration and Heat Exchanger Networks Chapter | 16

TABLE 16-16 Stream data from Figure 16-58 for Example 16-5 Stream

Ts ( C)

Tt ( C)

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

*Q is the calculated heat load (mCp dT)

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 heatpumped 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.

Figure 16-85 is a schematic heat engine and heat pump. A heat engine is a device that 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 ¼ Q1  Q2 W  hc Q1

first law:

second law

(16-55) (16-56)

and hc ¼ 1 

T2 T1

Carnot efficiency

(16-57)

However, since real heat engines are irreversible, the equation introducing machine efficiency he for the heat engine may be written as: W ¼ he hc Q1

0  he < 1

(16-58)

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 into the source at T1, and consumes work W. From thermodynamics: W ¼ Q1  Q2 W  hc Q1

first law:

(16-59)

second law

(16-60)

T2 T1

(16-57)

and hc ¼ 1 

For real irreversible heat pumps: W ¼ hc Q1 =he ¼

Principle of Operation

561

Q1 COP

0  he < 1

(16-61)

where:

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.

COP ¼ coefficient of performance. An important characteristic of heat pumps is their coefficient of performance, defined as the ratio between the

TABLE 16-17 Complete Stream and Utility Data for the Example 16-6 [20]

DH (MW)

Heat Capacity Flow Rate, CP(MW/ C)

Heat Transfer Film Coefficient h (MW/m2. C)

180

32.0

0.2

0.0006

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

Stream

Supply Temp. TS ( C)

Target Temp. TT ( C)

1. Reactor 1 feed

20

2. Reactor 1 product

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-71 The enthalpy intervals for the balanced composite curves of Example 16-6.

COP value can be derived from the calculated DTpump and can then be used to determine the necessary duties. COP can be expressed by [8]:

heat delivered to the heat sink and the consumed shaft work (mechanical power). Qsin k ¼ Qsource þ W COP ¼

(16-62)

Qsin k Q þW ¼ source W W

0:874 COP ¼ 100:18 DTpump

(16-63)

For ideal (reversible) heat engines and pumps, the equalities in Equations 16-56 and 16-60 apply, therefore:

The COP is a nonlinear function of the temperature difference between the heat sink and the heat source, and this difference is also referred to as temperature lift. The

2

1

Hot Stream Temperature

250oC

Steam

he ¼ 1

4

3

240oC

239oC

200oC

5

7

6

150oC

95oC

80oC

40oC

CP=0.15 h = 0.001 4

CP=0.25 h = 0.0008 CP=0.2 h = 0.0006

CP=0.3 h = 0.0008

Enthalpy

(16-65)

CP=7.5 h = 0.003

2

Cold Stream Temperature

(16-64)

230oC 69 MW

225oC 67.5 MW

199.5oC 59.85 MW

1

3

180oC 54 MW

140oC 34 MW

CP=1.0 h = 0.001

CW

30oC

25oC

20oC

12 MW

6 MW

0 MW

FIGURE 16-72 The enthalpy interval population for Example 16-6. (Used by permission: Smith R. Chemical Process Design, McGraw-Hill, 1995.)

Process Integration and Heat Exchanger Networks Chapter | 16

563

TABLE 16-18 Network Area Target for Example 16-6 P ðqi =hi Þk

P ðqj =hj Þk

DTLMTD

Hot Streams

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

23,125 0

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 P ATotal ¼ 7409.6 m2

Cold Streams

Thus the three basic functions of heat pumps are: 1. Receipt of heat from the waste heat source. 2. Increase of the waste heat temperature. 3. Delivery of the useful heat at the elevated temperature. Under the right circumstances a heat pump can reduce energy costs and provide an attractive cost reduction project when [48]: 1. The heat output is at a temperature where it can replace purchased energy such as boiler steam or gas firing. 2. The cost of energy to operate the heat pump is less than the value of the energy saved. 3. The net operating cost savings (reduction in purchased energy minus operating cost) is sufficient to pay back the capital investment in an acceptable time period. For industrial applications, simple payback of two to three years is typical.

1 Ak [ DTLMTD ½

P

Enthalpy Interval

ðqi =hi Þk D

P

ðqj =hj Þk 

Heat Pump Evaluation Heat pump evaluation consists of four steps [48]: 1. Determining whether a heat pump is a potential fit with the heat recovery application. 2. Making an initial selection of heat pump type. 3. Conducting preliminary cost/benefits analysis. 4. Performing a detailed feasibility study to ascertain benefits and cost with sufficient confidence to move forward with the implementation.

Application of a Heat Pump Plant personnel can review ways to determine whether a heat pump might be applicable in their facility by asking the following questions: l l

Where is heat available from the process? Where is heat required in the process?

FIGURE 16-73 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. Engg., 7: 751, 1990; Used by permission: R, Smith, Chemical Process Design, McGraw-Hill, 1995.)

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FIGURE 16-74 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, 19988. Used by permission: R, Smith, Chemical Process Design, McGraw-Hill, 1995.)

TABLE 16-19 Input Data and Computer Results for the Number of Shells Required of Example 16-7 DATA15.DAT 300.0

100.0

60.0

200.0

1

THE CORRECTED LMTD IN A SHELL AND TUBE HEAT EXCHANGER

l l

What is the value of saved energy? Will the facility gain non-energy benefits such as environmental improvements or product quality?

Reviews on positive and negative indicators for heat pump applicability and qualitative guidance on heat pump feasibility are provided elsewhere [48].

Appropriate Integration of Heat Engines A heat engine has two main objectives: supplying for process heat demand and generating power. Appropriate integration of a heat engine with the process provides the most energy efficient combination of these objectives. Figure 16-86 shows three possibilities for integrating a heat engine with a process. The process is represented by two

HOT FLUID INLET TEMPERATURE, oC:

300.000

HOT FLUID OUTLETTEMPERATURE, oC:

100.000

COLD FLUID INLET TEMPERATURE, oC:

60.000

COLD FLUID OUTLET TEMPERATURE, oC:

200.000

NUMBER OF SERIES EXCHANGER SHELLS:

1.

THE PARAMETER P VALUE IS:

0.5833

THE PARAMETER R VALUE IS:

1.4286

THE NUMBER OF SHELLS REQUIRED:

3.

Stream

Ts ( C)

Tt ( C)

mCp (kW/K)

Heat Load (kW)*

THE F- FACTOR:

0.8636

H1

150

60

2.0

180

THE LOG MEAN TEMPERATURE DIFFERENCE, oC:

65.4814

H2

90

60

8.0

240

C3

20

125

2.5

262.5

THE CORRECTED LMTD, oC:

56.5524

C4

25

100

3.0

225.0

TABLE 16-20 Stream Data for Example 16-8

Process Integration and Heat Exchanger Networks Chapter | 16

565

FIGURE 16-75 Screenshot of the hot and cold composite curves for Example 16-8. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

regions: one above and the other below the pinch. If a heat engine is integrated across the pinch, as shown in Figure 16-86a, it does not provide any benefit due to integration, and is therefore counterproductive. The process still requires QHmin (i.e. minimum hot utility requirement), and the heat engine performs no better than if operated as stand-alone. There is no saving by integrating a heat engine across the pinch [20]. Alternatively, if the heat engine is placed so that it rejects heat into the process above the pinch temperature as in Figure 16-86b, it transfers the heat to process heat sink, thereby reducing the hot utility demand. Due to the heat engine, the overall hot utility requirement is only increased by W (i.e. the shaft work). This implies a 100% efficient heat engine, thus the heat engine is appropriately placed. If the heat engine is placed so that it takes in energy from the process below the pinch temperature as shown in Figure 16-86c, it takes that energy from an overall process heat source. Here, the engine runs on process heat free of fuel cost and reduces the overall cold utility requirement by W.

The heat engine is again appropriately placed [20]. Therefore, appropriate placement of heat engines is either above the pinch or below the pinch, but not across the pinch. The principle of heat engine provides the basic rules for integration. The rules assume that the process is able to absorb all the heat rejected by the heat engine. The designers must therefore apply the grand composite curve in setting the integration of the heat engine with the process.

Opportunities for Placing Heat Engines Figure 16-87 shows the placement of steam and gas turbines against the grand composite curve. These placements are appropriate as they are on one side of the pinch; Figure 16-87a shows the integration of a steam turbine system with a process. Starting from the targets of steam demands (A and B), the key parameters for the steam turbine system are set. For a given boiler steam pressure, the overall fuel demand and shaft work (W) can be determined. The overall fuel demand ¼ A þ B þ W þ QLoss,

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-76 Screenshot of the grand composite curve for Example 16-8. (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.)

where QLoss is the heat loss from the boiler. Therefore, targets are set for the overall fuel demand and shaft work potential for the process starting from the grand composite curve. Figure 16-87b illustrates an example of the appropriate integration of a gas turbine with the process. The exhaust heat of the gas turbine is utilized for satisfying process heating demand. This is represented by placement of thermal profile of the exhaust heat against the grand composite curve. The gas turbine exhaust heat therefore saves the equivalent hot utility demand of the process. The heat from the gas turbine fuel demand is obtained by the sum of process heating demand (A), shaft work (W) and the heat loss below the pinch temperature (QLoss).

Appropriate Integration of Heat Pumps Heat pumps provide a way of using waste heat for useful process heating, and the pinch analysis principle for integration of heat pumps is useful in setting key design

parameters for the heat pumps. Figure 16-88 shows the three arrangements that a heat pump may take relative to the pinch. First, heat can be taken from above the pinch and rejected at a higher temperature also above the pinch as shown in Figure 16-88a. This saves hot utility by the amount W but only at the expense of an equal input of power W. However, because power is much more expensive than heat, this is not an efficient solution. Second, Figure 16-88b illustrates how the heat pump takes in heat from below the pinch and rejects it at a higher temperature also below the pinch. This is even more inefficient because W units of heat from power are rejected to a part of the process that already had an excess of heat. Third, as shown in Figure 16-88c, heat is taken in from below the pinch and rejected at a temperature above the pinch. This provides savings in both hot and cold utilities because it is pumping heat from a source, i.e. below the pinch to a sink, which is above the pinch. The appropriate way to integrate a heat pump is therefore across the pinch.

Process Integration and Heat Exchanger Networks Chapter | 16

567

FIGURE 16-77 Screenshot of plots of pinch temperature of hot and cold streams and minimum utility requirements at varying for Example 16-8. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration, e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

The overall economics of the heat pump depend on the heat savings due to heat pump compared with the cost of power input and the capital cost of the heat pump and associated heat exchangers.

Opportunities for Placing Heat Pumps The economics for placing the heat pump depend on the balance between process heat savings against power requirement for heat pumping. A large process heat duty with small temperature differential across the heat pump is required to ensure an economical heat pump. Figure 1689a shows the grand composite curve with a region of small temperature change and large enthalpy change above and below the pinch. This pointed ‘nose’ at the pinch indicates that a heat pump can be installed across the small temperature change for a relatively large saving in heating and cooling demands. The energy saving will therefore be high for a relatively small expense in power (high coefficient of performance, COP). Figure 16-89b

shows that the heat pump option may be uneconomical since the temperature difference across the heat pump is quite large, which can result in high power requirement for the heat pump. Refrigeration systems are another class of heat pumping applicable to sub-ambient temperature regions. The principles of appropriate placement as discussed earlier also apply to refrigeration systems. Additionally, techniques have been developed which provide a more detailed approach for the placement of refrigeration levels against the grand composite curve.

Appropriate Placement of Compression and Expansion in Heat Recovery Systems In considering the placement of various equipment items in heat recovery systems, it is advisable to assign terms such as heat sources and heat sinks. A process consists of a heat sink above and a heat source below the pinch. On this basis, compression should be placed above the pinch since

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-78A A grid representation of the heat exchanger network for Example 16-8.

FIGURE 16-78B A grid representation of the heat exchanger network for Example 16-8.

it adds heat to the system. Similarly, expansion should be placed below the pinch since it adds cooling to the system. This is contrary to the common practice for minimizing/ maximizing power requirements/production for compression/expansion and only applies when heat recovery

problems are involved. Compression and expansion can be used to improve heat recovery in instances where the target state has the same pressure as the supply state, and process streams can be subject to both expansion and compression.

Process Integration and Heat Exchanger Networks Chapter | 16

569

FIGURE 16-78C A grid representation of the heat exchanger network for Example 16-8.

TABLE 16-21 The CP Table for the Hot End of TC3 for Example 16-8 CPHot £ CPCold Stream Number

Hot

Cold

NHot £ NCold Stream Number

1

2

3

4

2.5

3

Total

2

5.5

TABLE 16-22 The CP Table for the Cold End of TC3 for Example 16-8 CPHot ‡ CPCold Stream Number

Hot

Cold

NHot ‡ NCold Stream Number

2

8

3.0

4

1

2

2.5

3

Total

10

5.5

PRESSURE DROP AND HEAT TRANSFER IN PROCESS INTEGRATION Many factors such as composition, temperature, flow rate and phase can affect the heat capacity, Cp. However, another factor that should be considered is the pressure. Polley et al. [49] considered the pressure drop in the heat exchanger network. They used the following relationship between the pressure drop, DP, the heat transfer

coefficient, h, and the heat transfer area A as represented by: DP ¼ K A hm

(16-66)

where: K ¼ pressure drop relationship constant. m ¼ the heat exchanger’s tube and shell side specific coefficients.

570

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-79 Breaking the loop of the heat exchanger network for Example 16-8.

CP kW/oC

CP kW/oC

o

Tph = 90 C 80oC

150oC

125oC

H

2

2.5

140 kW

In cold stream 1, before breaking 120 = 2.5 (T – 70) the loop : 48 = T - 70

3.5

69oC

20oC

2.5

122.5 kW

∆H = CP ∆T

In hot stream 1, 140 = 2 (150 -T) 70 = 150 -T T = 80oC

60oC

Tpc = 70oC

62oC

118oC

90oC

Assuming counter current flow through the heat exchanger 150oC

∆T1 = 32oC 118oC

T = 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 flow through the heat exchanger Removing the 17.5 kW heating utility in the 90oC cold stream above the ∆T1 = 11oC pinch, and adding to 105kW below the pinch 69oC gives 122.5 kW

∆H = CP ∆T 122.5 = 2.5 (T – 20) 49 = T - 20 T = 69oC

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 = 62 oC

FIGURE 16-80 Calculations of the temperature differences resulting from the breaking of the loop for Example 16-8.

60oC ∆T2 = 40oC 20oC

Process Integration and Heat Exchanger Networks Chapter | 16

571

FIGURE 16-81 Identifying a path to restore the DTmin constraint for Example 16-8.

The allowable pressure drop (rather than the heat transfer coefficients) is specified for each stream. Then the heat transfer coefficients are calculated iteratively to minimize the total area. Thus, when approaching area targets, the design is modified on the basis of the fixed pressure drops rather than fixed film coefficients. For detail reviews of pressure and pressure drop in heat integration and HEN retrofits, see references [50e53].

TOTAL SITE ANALYSIS Pinch analysis can be applied to an entire production complex consisting of factories that incorporate several processes by determining the site utilities as an integral part of the production processes. Here, the site utility system is used to achieve heat recovery between the processes. This differs from conventional application of pinch analysis, which normally deals with heat recovery within individual processes. An important benefit now reported of total site analysis compared with the conventional approach is a much better relationship between the energy saving and the reduction of CO2 emissions, often from about 40% to nearly 100%. This occurs because the utility system is now involved as part of the heat recovery scheme, so that the balance of fuel and power is established in the site context. Dhole and Linnhoff [54] have applied pinch analysis to total sites by introducing procedures which enable the designer to set site-wide targets for fuel, cogeneration, emissions such as CO2, SO2, NOx, etc. and cooling prior to design. The targets allow the designer to analyze various site-related options, such as site expansion, process and

utilities modifications, in both grassroots and retrofit situations. The work of Dhole and Linnhoff and Raissi [55] has been further developed by Klemes et al. [56], in which thermodynamic targets for heat and power cogeneration can be set on the basis of the steam composition curves. However, this has been further refined and improved by Mavromatis and Kokossis [57], later by Varbanov et al. [58] and most recently byVarbanov and Klemes [59]. The results of a total site analysis of one major complex revealed possible overall energy and CO2 reductions of about 15e20% [48,54]. Using the total site analysis, the most promising options for utilities and/or process can be screened at the targeting stage. Use of steam acts an intermediate mechanism for heat transfer; therefore its cost is no longer a factor. All designs are directly determined in terms of fuel and power at the site boundary. Figure 16-90 shows a schematic of a typical total site and Figure 16-91 shows a flow diagram of total site road map consisting of a series of mutually compatible projects, where each project package is explored for its technical and economic feasibility. Several energy integration aspects are considered by plotting composite enthalpy changes versus the temperature in order to produce the grand composite curve as shown in Figure 16-92. These are: 1. Heat recovery among the streams inside the process. 2. The profile above the process pinch represents a net heat sink, whereas the profile below the process pinch represents a net heat source.

572

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

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

R = 1.0

0.6

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 16-82 Designs with a temperature approach or small temperature cross can be accommodated in a single 1e2 shell, whereas designs with a large temperature cross become infeasible. (Ahmad, Linnhoff and Smith, Trans. ASME, J Heat Transfer, 110: 304, 1988, Used by permission: R. Smith, Chemical Process Design, Mc. Graw-Hill, 1995.)

Process Integration and Heat Exchanger Networks Chapter | 16

573

TABLE 16-23 Cost Data for Various Exchanger Specifications [18] Exchanger Specification

Capital Cost ($)

Spiral (SS-SS)

30000 þ 19700A0.59

Plate & frame (SS - SS)

30000 þ 1900A0.78

Shell & tube (CS - CS)

30000 þ 750A0.81

Shell & tube (SS - SS)

30000 þ 1650A0.81

Shell & tube (CS e SS)

30000 þ 1350A0.81

Note: A is exchanger area, m2, SS is stainless steel and CS is carbon steel.

TABLE 16-24 Stream Data for Example 16-9 Stream

Supply Temp. ( C)

Target Temp. ( C)

Cp, kW/ C

DH, 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

DH ¼ CP dT

3. Minimum temperature for external heating and cooling, GCC provides the opportunity to produce targets for multiple utility levels. Figure 16-93 identifies the residual heat sources and heat sinks from the GCC by moving from a single-process level to that of the total site. The site heat source profile is then constructed by combining the heat source information from all available processes into a single profile. This is analogous to the hot composite curve for a single process. Similarly, the site heat sink profile is obtained by combining the heat sink information from all available processes, which is again analogous to the cold composite curve. Combining these profiles, the total site profiles provide a simultaneous view of heat surplus and heat deficit for all the processes on the site, as shown in Figure 16-94.

The amount of heat recovery that can take place on the total site through the steam mains can be obtained from the total site composite curves, as shown in Figure 16-95. An overlap that occurs by shifting the sink composite curve parallel to the enthalpy axis through the source composite curve represents the amount of heat recovery that can be obtained through the mains. The limit to the heat recovery is reached when the two-site composite curves touch and cannot be shifted further. Total site pinch divides the problem into a net heat sink (above the pinch) and a net heat source (below the pinch). The remaining site sink profile heat demand is met by the supply of steam from a central boiler. Below the site pinch, the excess heat is removed by cooling (e.g. water) or produces very low pressure steam. The area enclosed by the site composite curves is proportional to the cogeneration potential of the site’s utility system [54].

Design away From the pinch

CPHot ≤ CPCold

T = 140 C ∆H =900 kW

CP = 2.2

H1

320 oC

H2

CPHot ≥ CPCold

CP (kW/oC)

800 kW 60 C

CP = 5.8

50 oC 64.4 C

120 C ∆H =1080 kW

∆H =1620 kW

C

∆H (kW)

20 oC

10 9

900 2700

20 oC

8

2800

10

800

8

2400

400 kW

CP = 1 ∆H =1840 kW o

370 C

H3

400 kW

∆H =960 kW

90 C

560 kW C

T = 140 C o

50 C

∆H =800 kW

∆H =2400 kW o

H

430 C

C1

C2

560 kW

1840 kW

∆H =1020 kW o

100 oC

∆H =180 kW

300 C

C3

6

1200

180 kW

1020 kW

T = 130 C

∆H =500 kW o

230 C

30oC

∆H =500 kW

H 396 kW

80 kW

24 kW

30oC

∆H =400 kW 400 kW ∆H =300 kW o

430 C

C4

5

1000

4

400

1

400

500 kW

o

30 C

∆H =100 kW

H 180 kW

120 kW

C5

C6

100 kW

T = 130 C

H Hot utility

QCmin =960 kW

QHmin =760 kW

Heat exchange between streams

C Cold utility Design away From the pinch

CPHot ≤ CPCold

H2

T = 140 C ∆H =900 kW

CP = 2.777

H1

320 oC

CPHot ≥ CPCold

CP (kW/oC) 100 kW C 40 C C

60 C

CP = 5.667 ∆H =1080 kW

∆H =1620 kW

50 oC

∆H (kW)

20 oC

10 9

900 2700

20 oC

8

2800

10

800

8

2400

6

1200

180 kW

CP =0.555 ∆H =1840 kW o H3

370 C

∆H =960 kW C 680 kW

T = 140 C

o

∆H =800 kW

50 C

C1

800 kW ∆H =2400 kW o

H

430 C

C2

560 kW

1840 kW

∆H =1020 kW o

o

100 C

∆H =180 kW

300 C

1020 kW

C3

180 kW

T = 130 C

∆H =500 kW o

30oC

∆H =500 kW

230 C 500 kW

30oC

∆H =400 kW 400 kW ∆H =300 kW o

430 C

QHmin =760 kW

1000

C5

4

400

C6

1

400

o

30 C

∆H =100 kW

H 200 kW

5

C4

500 kW

100 kW

100 kW

T = 130 C

QCmin =960 kW

H Hot utility C Cold utility

FIGURE 16-83 A grid representation of the heat exchanger network for Example 16-9.

Heat exchange between streams

Process Integration and Heat Exchanger Networks Chapter | 16

Retrofit project with large scope for savings

Is the current heat integration significant?

Yes

No

Pinch Design Method

Are composite curves parallel with little use of intermediate utilities?

Re-use existing exchangers

Yes

No

Cross-Pinch Analysis

Path Analysis

FIGURE 16-84 Hierarchy of retrofit design.

Temperature (T1) Reservoir

Heat

Heat

Q1

Heat engine

Work

W

Q1

Heat pump

Temperature (T2) Heat

Q2

Heat Q 2

Reservoir

FIGURE 16-85 Thermodynamic basis of heat engines and heat pumps.

575

576

(A)

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

(B)

Integrate across the pinch A

Integrate below the pinch

(C)

Integrate above the pinch A – (Q – W)

A

Q

T*

T*

Q

T* Heat Engine

W

Q-W Heat Engine

W Q Heat Engine

W

QHE -W B

B+(Q-W) Inappropriate placement

B-Q Appropriate placement

Appropriate placement

FIGURE 16-86 Appropriate placement principle for heat engines.

Steam turbine

(A)

Gas turbine

(B)

Q Loss

Fuel B

Fuel Tshifted

W

Tshifted

Fuel W A

T1 Exhaust heat

B

Pinch

Tcorr

H

To

H Q Loss

Fuel = A + B + W + Q Loss

A Fuel = A + W + Q Loss

FIGURE 16-87 Placement of steam and gas turbines against the grand composite curve.

Process Integration and Heat Exchanger Networks Chapter | 16

(A)

(B)

Integrate above the Pinch A-W

T

T Heat pump

Integrate across the Pinch A – (Q + W)

A

Q+ W

T

(C)

Integrate below the Pinch

577

W

Q+ W

Q Heat pump

Q+ W

W

Q Heat pump

W

Q B

B-Q

B+W

Inappropriate placement

Inappropriate placement

Appropriate placement

FIGURE 16-88 Placement of heat pumps.

(A)

(B) Tshifted Tshifted

W

Heat pump

H

H

FIGURE 16-89 A pointed ‘nose’ at the process or utility pinch indicates a good heat pump opportunity.

Figure 16-96 summarizes the key steps in total site improvement based on pinch analysis. The key steps are listed below [48]: a. Single-Process Pinch Analysis: Starting from the process heat and material balances of individual processes, pinch analysis establishes key options for process modifications, energy recovery (savings in non-central utilities) and targets for multiple utilities. The grand composite curves are ready for total site analysis. Initial trade-off is set between process fuel and steam levels.

b. Total-Site Pinch Analysis: Total site profiles are constructed from the individual process grand composite curves and the site infrastructure (e.g. steam system) is simulated. These tools are used together to set targets for infrastructure improvements and process- wise improvements. Re-visit step a. and reset infrastructure assumptions such as steam mains pressures if they are changed in step b. c. Identification of Specific Projects: The targets obtained during individual process analysis are translated into specific network design changes. Simultaneously, the

578

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Emissions

Emissions

Power

Fuel

Condenser Fuel High pressure Medium pressure Low pressure

Emissions

Fuel

Process C

Process B

Process A

Cooling water

FIGURE 16-90 Layout of a typical total site.

Major steam savings

Implement major projects

Utility investment strategy

LP steam level to maximize power gen

BFW heating Define future demands

Specify CHP plant and utility system

Further heat recovery projects (other plants)

Install package boilers

Further heat recovery projects (other plants)

CHP

Identify potential steam savings

VCM plant

Boiler replacement

No CHP

Solvents plant

LP steam level for inter-plant heat recovery

FIGURE 16-91 Total site road map.

Process Integration and Heat Exchanger Networks Chapter | 16

T*

HP MP

ΔTmin

LP

CW ΔH FIGURE 16-92 Grand composite curve.

T*

T*

T*

ΔH

ΔH Mirror the heat sources

Remove the pocket

FIGURE 16-93 Identification of net heat sources and sinks from a GCC.

300 250 200

Sources

Sinks

T [oC]

200 150 100 50 0 6

4

2

0 2 Enthalpy, MW

FIGURE 16-94 Total site profiles.

4

6

ΔH

579

VHP

QREC

T

HP

HP

MP

MP MP

LP

LP

LP

Pinch CW CW

FIGURE 16-95 Total site composites.

Process Heat and Material Balances

Analysis

Analysis

Single Process Pinch Analysis

Steam System Simulation (Evaluation)

Total Site Profiles (Ideas) Total Site Pinch Analysis

Design

Within Process Boundary

In Site-Wide Infrastructure

Identification of Specific Projects

Selection of Alternatives

Road-map for Total Site Improvement Final Selection of Project Alternatives

Project Detailing FIGURE 16-96 Key steps in total site improvement.

Process Integration and Heat Exchanger Networks Chapter | 16

H2 Make Up

581

HP Purge

Recycle

LP Purge

Actual Sources

Actual Sink Reactor

Feed HP Separator

LP Separator

Product

FIGURE 16-97 A hydrogen consumer process flow diagram.

H2 Purity

H2 Purity

Hydrogen Supply Composite Curve

Flow rate H2 Purity

Hydrogen Demand Composite Curve

Flow rate H2 Purity

Hydrogen Surplus Cascade

Minimize pinch

Flow rate

FIGURE 16-98 The hydrogen composite curves.

Flow rate

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

COD

Process stream

Pinch

COD

Dissolved O2 stream

1/COD

Substrate Supply line Process stream

Dissolved O2 stream

D

Slope =μm/S Intercept = 1/S 1/D

1/D Slope – growth rate, O2 solubility

μm - Specific growth

Residence time, oxidation energy load

S - Saturation D - Dilution

FIGURE 16-99 Oxygen pinch method (Zhelev, T, The conceptual design approach e A process integration approach on the move. Resources, Conservation and Recyling, 50, 143e147, 2007.)

TABLE 16-25 Data from Wang and Smith [77] Operation Number

Contaminant Mass Flow kg/h

Cin ppm

Cout ppm

Flowrate t/h

1

2

0

100

20

2

5

50

100

100

3

30

50

800

40

4

4

400

800

10

800 C (ppm) Minimum Water Supply Flow rate 90 t/h 400 Minimize Flow rate

100

0

1

9

21

41

m (kg/h)

FIGURE 16-100 Limiting composite curve and the water pinch.

Process Integration and Heat Exchanger Networks Chapter | 16

20 t/h 40 t/h

20 t/h

Operation 1

Operation 3

Feedwater

Wastewater

90 t/h

90 t/h 50 t/h

5.7 t/h

Operation 2

Operation 4

44.3 t/h

FIGURE 16-101 Water treatment system design using water-pinch methodology.

T

T

ΔT1

ΔT2

H

H Total

Energy

Cost

Capital

ΔT1

ΔT2

ΔTmin

FIGURE 16-102 Capital and energy cost targets allow the capital-energy trade-off to be established ahead of design.

583

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

(A)

(B) T

T

Process grand composite Process grand composite

Flue gas matched against the process is limited by the process above the pinch

H The modified process allows a steeper flue gas line which gives a reduction in fuel and emissions even though the process duty has not changed.

H

FIGURE 16-103 The grand composite curve allows the minimum flue gas to be established.

infrastructure improvement options are developed in more details at an equipment level. d. Final Selection of Project Alternatives (from Total-Site Road Map): The specific projects identified in step c. are put together in a coherent plan for a total site

involving alternative routes of compatible projects. This is followed by final selection of process-wise and infrastructure options for implementation. This stage is followed by project detailing.

APPLICATIONS OF PROCESS INTEGRATION Hydrogen Pinch Studies Increasing demand for hydrogen in the refinery and chemical plants has resulted in better hydrogen network

TABLE 16-26 Environment Impact Resulting from Reduced Power Station Emissions at Ludwigshafen Site [92]

FIGURE 16-104 Pinch technology achieved considerable energy savings on hte BASF site at Ludwigshafen against th background of increased levels of production [83].

Carbon dioxide, CO2

220 te/h

Sulfur dioxide, SO2

2.0 te/h

Nitrogen oxides, NOx

0.7 te/h

ASH

21 kg/h

Carbon monoxide, CO

7 kg/h

Waste water from water treatment

70 te/h

Thermal stressing air/water

550 MW

Process Integration and Heat Exchanger Networks Chapter | 16

TABLE 16-27 Steps in Constructing HEN Design [8] 1.

Become familiar with the analyzed process. The most efficient way is to closely liaise with the process designer and/or plant manager, especially if the plant is already operating.

2.

Develop a mass and heat balance. This should be based on the designed process flowsheet data and calculations and/or on measurements taken from the operating plant (if the study is for a retrofit).

3.

Select the streams. This is a critical step and not as straightforward as it may seem.

4.

Remove all the existing units related to the PI analysis. For heat integration, remove all heat-transferring units, for mass water integration; remove all water interconnections (the pipes). This step is also critical e without it, the optimized design would not differ from the initial design.

5.

Extract the stream data for the PI analysis. Different data are relevant for each PI analysis type. For HI heat loads and temperatures are extracted.

6.

Make a qualified initial guess for the DTmin value; this value can be adjusted later at various stages of the design optimization.

7.

Perform the pinch analysis: obtain the Pinch temperatures and the utility targets.

8.

Design the initial (heat exchangers) network using the criterion of maximizing energy recovery.

9.

Check for a cross pinch transfer and for inappropriate placement of utilities.

10.

Check for proper placement of reactors, separation columns, heat engines, and heat pumps.

11.

Investigate the potential for further modifying the process in order to minimize energy consumption and reduce capital costs. Investigate the potential benefits of applying the plus-minus principle.

12.

Investigate the potential for integration with other processes e that is Total Site Analysis.

13.

Consider the implications of pressure drop (trade-offs between heat savings and extra energy for pumping) and the physical layout (capital cost of heat exchangers and / or piping).

14.

Make the preselection of heat exchange equipment and perform the preliminary costing. Provision should be made for variations in the future price of energy.

15.

Make the first optimization run of the predesign plant or site and make adjustments to DTmin .

16.

Based on the optimization, extract adjusted data and return to step 7. Perform an additional loop (or loops) while screening and scoping for potential simplifications.

17.

Consider real plant constraints; these include safety, technology limitations, controllability, operability, flexibility, availability, and maintainability.

18.

Pay attention to start-up and shutdown of the process; some early designs for highly integrated plants had problems in this area.

19.

Run a second optimization for the final tuning accounting for the information added during steps 16 to 18. If necessary, return to any appropriate previous step for adjustment.

20.

The design is now ready for detailing. However, optimization is a never-ending procedure, and designs may need to be modified in response to changes in operating conditions (e.g. plant capacity) or the economic environment (e.g. tax policy; prices for energy, materials and production).

585

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TABLE 16-28 Representative Results from Pinch Studies in the Chemical and Petroleum Industries Type of Facility

Study Highlights

Petroleum refinery

$840,000/year savings at 1.5 year payback, plus capital savings of $390,000 for planned retrofit.

Petroleum refinery

Scope for 32% reduction in net fuel consumption.

Petroleum refinery

Revised heat exchanger network in crude distillation unit to reduce costs by $1million/year at less than 1.5 year payback.

Petroleum refinery

Revised heat exchanger network in hydrocracker to save $2.7 million/year in steam/fuel costs at 1.6 year payback.

Petroleum refinery

Steam cost savings of $5million/year with 1e4 year payback.

Pharmaceutical company

Increased heat recovery to reduce fuel costs by 13% at less than 1 year payback.

Pharmaceutical company

Identified measures to reduce thermal energy requirements by 30%; annual savings of $70,000/year at 1.3e2.5 year payback.

Specialty chemical plant: kelp harvesting and extraction

Steam savings of $2.8million/year at 1e2 year payback.

Wax extraction plant

Cost savings of $930,000/year at 2.3 year payback.

TABLE 16-29 Stream Data for Case Study 1 Stream

Ts ( C)

Tt ( C)

mCp (kW/ C)

Heat Load, Q (kW)*

Column 1 Overheads

150

100

43.0

2150

Column 1 distillate

100

40

5.0

300

Column 2 Overheads

175

150

360.0

9000

Column 2 distillate

150

40

20.0

2200

Column 2 bottoms

230

40

25.0

4750

Column 1 feed

15

180

50.0

8250

Column 1 reboiler

215

220

680.0

3400

Boiler feed water (Column 2 reboiler)

230

235

1600.0

8000

*Q ¼ mCp dT.

synthesis. Hydrogen pinch is analogous to heat integration pinch, and is intended to offer structured analysis techniques and methodologies to optimize and to improve a hydrogen network. Typically, a refinery or chemical plant can be divided into hydrogen producing units (e.g. catalytic reformer hydrogen plant, ethylene plant) and hydrogen consuming units (hydrotreaters, hydrocrackers and isomerization). Some hydrogen consumers, however, also produce hydrogen because their purge streams usually contain a significant amount of hydrogen

with an appropriate value. A hydrogen pinch study involves the following: 1. 2. 3. 4.

Data collection/data extraction. Targeting. Results: conclusions/recommendations. Further evaluations/engineering of results.

Figure 16-97 shows a typical hydrogen consumer, where the actual hydrogen stream to the reactor is shown,

Process Integration and Heat Exchanger Networks Chapter | 16

156.2oC

150oC

LP Steam raising

100oC

150oC

175oC

CW

CW

Column 1

587

To Store

Column 2

To Store o

40 C

40oC

Feed 15oC

150oC

180oC

235oC HP Steam

HP Steam 215oC

230oC

230oC 170oC

CW To Store 40oC

FIGURE 16-105 Flowsheet of case study 1. (Used by permission: Gary Smith and Ajit Patel. Step by step through the pinch. The Chemical Engineer, p. 26, Nov 1987.)

and as such the actual hydrogen sink is a mixture of both the hydrogen make-up stream and the recycle stream. Similarly, the actual hydrogen purges, the hydrogen sources are the actual streams from the (high pressure and low pressure) separators. By adding up all hydrogen supplies a hydrogen supply composite curve (similar to the hot composite curve) can be constructed. These are all hydrogen producers, as well as the purges; i.e. the actual sources from the consumers. Correspondingly, a hydrogen demand composite curve (similar to the cold composite curve) can be constructed from the actual hydrogen sinks (make-up plus recycle) of the respective hydrogen consumers. By plotting these two curves together, the hydrogen composite curves of a refinery are

obtained, as shown in Figure 16-98. These curves form the basis for a hydrogen surplus cascade. This is constructed by calculating the respective area, which is equivalent to the amount of hydrogen surplus at that level. These are then plotted in a diagram as lines, as the purpose is to minimize the hydrogen pinch, which implies minimal hydrogen consumption by the overall refinery, and minimal hydrogen waste into the fuel gas system. A given hydrogen network may include hydrogen purification such as a pressure swing absorption unit, a membrane unit or cryogenic separation. Such a purifier may be appropriately placed above the pinch, because a higher purity will push the pinch point to the right. This presents an

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-106 Screenshot of the input data for case study 1. (Used by permission: Ian Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

opportunity for further reduction in the make-up, but may also cause the pinch point to shift. A purifier can also be appropriately placed across the pinch, because this will open up the pinch. It is not appropriate to place it below the pinch, because this will only result in a higher purity fuel gas. The first study in this field by Towler et al. [60] focused on cost and added value referred to as value composites, based on interactions with the refinery linear programming (LP) model for operational planning. The value composite curve is developed to provide insight into economic trade-offs that affect the hydrogen management problem in the network. However, this approach did not account for the physical constraints that influence the design of the hydrogen network. Alves and Towler [61] proposed the concept of hydrogen surplus to locate the minimum utility target in a new hydrogen distribution network. Alves [62] developed a procedure for assessing the available hydrogen resources on a site by applying the

hydrogen pinch analysis. It involves constructing hydrogen composite curves accounting for the demands and sources of hydrogen on a site in terms of stream purity versus flowrate. This is used to construct hydrogen surplus diagram similar to the GCC in heat integration. These instruments allow engineers to find the system hydrogen pinch and set targets for hydrogen recovery, production and import by a refinery. This methodology has been improved by Hallele and Liu [63], accounting for pressure as a factor, and thus making the best use of the existing compressors in the refinery. Their improved method accounts for important costs and trade-offs including production, compressors, fuel and piping costs. Agrawal and Shenoy [64] presented a unified conceptual approach employing the nearest neighbors algorithm to design hydrogen networks, which evolve to account for the pressure constraints imposed by compressors or improved by regeneration through purification processes such as pressure swing adsorption. Recently, Wei et al. [65]

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589

FIGURE 16-107 Screenshot of the Problem Table, heat cascade, pinch identification, problem type, minimum hot and cold utility requirements for case study 1. (Used by permission: Ian Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

proposed a modified hydrogen network model, which allows for marginal changes in hydrogen purity and hydrogen partial pressure in hydroprocessor reactors, and Jla [66] has provided a more detailed description of the mathematical modeling approach. Roozbeh et al. [67] provided a design hierarchy, heuristics and guidelines for the design of oil refineries hydrogen network, based upon pinch technology and extending the heat integration concepts to mass integration. They were able to maximize the amount of hydrogen recovered across the site during the design, and thus provided opportunity for refineries to make more efficient use of hydrogen with considerable savings on total cost. Nelson and Liu [68] presented an automated Excel spreadsheet that enables the user to quickly and accurately identify the hydrogen purity at the pinch point and the minimum flowrates of hydrogen utilities without an iterative graphical construction. The method

employed in the spreadsheet minimizes fresh hydrogen consumption while maximizing hydrogen recovery and reuse in petroleum refinery and petrochemical industries.

Oxygen Pinch This results from the design of more cost effective waste treatment systems. Zhelev and Ntlhakana [69] introduced the idea to analyze the problem so that targets are derived prior to designing a system for minimizing the oxygen consumption of the microorganisms used for waste degradation. Flow sheet and design changes were suggested based on the target. Agitation and other forms of aeration require energy, so an analysis based on the oxygen pinch principles leads again to their original application associated with energy conservation. The method also provides other indicators/quantitative targets for oxygen solubility,

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-108 Screenshot of hot and cold streams composite curves for case study 1. (Used by permission: Ian Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

residence time and oxidation energy load. In a further development, a combined water and oxygen pinch analysis has been proposed [70]. By combining the two criterion, up to 30% cost savings for waste water treatment could be achieved. Figure 16-99 shows plots of oxygen pinch.

Carbon Dioxide (CO2) Management The global issue of carbon dioxide emissions and reduction in greenhouse gases has been known for some time, and world leaders have committed to realistic reductions. Correspondingly, refiners must now ensure the CO2 issue from: l l l

A global perspective A country perspective An industry perspective

Generally, a large multinational oil company will operate across various industries and possibly spread

across many countries worldwide. Countries are more likely to target specific industries to meet their Kyoto obligations, and to ensure this, oil companies should adopt a CO2 management policy across their various enterprises. The CO2 management strategy should investigate the impact of changes to a product train in terms of CO2 production and should answer various pertinent issues regarding whether changes can reduce CO2 when challenged via one of the different perspectives indicated above. Clarke [71] employed a linear programming model to optimize the various CO2 options available and to select the optimal route to be used. The model can be run with fixed emissions targets (a process constraint) or with an economic incentive (an economic constraint) on capturing CO2 or avoiding its emission. These targets are varied and the model run to develop staged investment profiles, and ensure that the refinery margin is maintained while reviewing various CO2 options and constraints.

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591

FIGURE 16-109 Screenshot of hot and cold streams shifted composite curves for case study 1. (Used by permission: Ian Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Employing pinch analysis with total site concept for emission targeting has been reviewed earlier by Dhole and Linnhoff [54], Klemes et al. [72] and Perry et al. [73]. Tan and Foo [74] presented an application of pinch analysis to energy sector planning, employing the carbon emission constraints referred to as Carbon Emission Pinch Analysis (CEPA). Their objectives were identifying the minimum quantity of zero emission energy resources required to meet the specified energy requirements and emission limits of different sectors or regions in a system and designing an energy allocation plan that targets the specified emission limits and at the same time minimizing use of the energy resources.

Mass and Water Pinch The success of heat integration has led researchers to investigate other viable areas of pinch analysis. One such area is the mass exchanger by employing mathematical programming [75,76]; and Shenoy [18], who has introduced a simple

pinch analysis concept that maps a single key component mass exchanger network problem to an equivalent heat exchanger network problem. Wang and Smith [77] provided a methodology for calculating the minimum flow rate of water (including reuse) required to remove contaminants from water, using operations. Their main objectives were to simultaneously minimize the consumption of fresh water and the disposal of wastewater by maximizing the internal water reuse. They showed that significant water savings can be achieved compared with the case when only freshwater is used. Wastewater generation can be further reduced by applying water regeneration, allowing further reuse of recycling. The pinch analysis to water minimization can be translated to cases of single contaminant problems by constructing the composite curve of water and then using a plot of the contaminant concentration versus contaminant load. However, extending the water pinch analysis to multiple contaminant problems is more complex and difficult to do. The major issue is selecting the contaminant

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-110 Screenshot of the grand Composite Curve of case study 1. (Used by permission: Ian Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

that can be used for plotting the composite curves. Several options are available, and one useful option is mathematical programming, where water pinch acts as a preliminary scoping and visualization tool. Table 16-25 gives the problem data of Wang and Smith, Figure 16-100 shows the limiting composite curve of the four operations using water and Figure 16-101 shows the final system design for the water operations. The figure shows that of the original targeted freshwater amount of 90 t/h, 20 t/h is fed to operation 1 and 50 t/h is fed to operation 2. The remaining 20 t/h is fed to operation 3 along with 20 t/h from operation 1. Of the original 50 t/h fed to operation 2, 5.7 t/h is fed to operation 4 and the remaining 44.3 t/h goes directly to wastewater. Prakash and Shenoy [78] show how the water network in Figure 16-101 can be synthesized by the nearest neighbor algorithm. A graphical and solver software tool can be used to set up the inventory ‘water balance’ of the process water streams with respect to flow and contaminants level.

However, sophisticated software such as WaterTrackerTM or WaterPinchTM can be employed to produce a list of influent and effluent process streams. An effluent could be considered to be a source (a supplier) while an influent could be considered to be a sink (a consumer). These software tools can be used to optimize the water use/reuse of the process by looking for the most cost-effective combination of sources and sinks. Chemical Processing provided an excellent webcast on boosting water efficiency and improving wastewater treating [79], and Foo [80] presented an outline on domestic and industrial water usage employing water pinch analysis.

Site Wide Integration The site may consist of multiple units where individual processes are located; for example a refinery may consist of a crude distillation unit (CDU), a vacuum distillation unit (VDU), a naphtha hydrotreater, a diesel hydrotreater,

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593

The Grand Composite Curve 300

Shifted Temperature (oC)

250

200

150

LP Steam raising 100

Modified GCC after steam raising 50

1.29 MW Cold utility 0 2000

4000

6000

8000

10000

12000

Net Heat Flow, kW FIGURE 16-111 Use of the grand composite curve in targeting for the maximum production of low pressure steam. (Used by permission: Gary Smith and Ajit Patel, Step by step through the pinch. The Chemical Engineer, Nov 1987.)

a fluidized catalytic cracking (FCC), a visbreaker unit, a coker unit, an aromatics and utility unit, a sulfur recovery unit, an ultra low sulfur diesel unit (ULSD), etc. Similarly, a petrochemical complex may consist of a methanol unit, an ethylene unit, a polyethylene unit, an ethylene glycol unit, a styrene unit, etc. All these units will have one utility system that provides hot and cold utilities as well as power to the whole site. Each unit demands steam at different temperatures, while at the same time each unit may produce steam at different levels (e.g. HP, MP, LP). It is possible to integrate different units directly, but this may result in control, safety, operational or piping rerouting problems. Thus, different units are generally integrated indirectly through the utility system. Site-wide integration addresses the correct level of steam for a site and the trade-off between heat and power, where power can either be imported or cogenerated. The benefit of a site-wide analysis is that correct pricing for different levels of steam is no longer needed. The impact of any modification in terms of fuel or power can be readily determined. There is no need for a ‘cost of steam’, as energy pricing is only carried out with respect to either

FIGURE 16-112 Composite curves including provision for maximum low pressure steam raising. (Used by permission: Gary Smith and Ajit Patel, Step by step through the pinch, The Chemical Engineer, Nov 1987.)

fuel or power at the battery limit. Further, site-wide analysis has increased our understanding of the global emissions associated with any processing industry. Minimizing the emissions of a process involves a sharper separation, since distillation forms the essential unit of the refining/chemical process industry, and to obtain a sharp separation, the reboiler and condenser duties will increase or processes may be added that further require additional heating and cooling. External energy can be obtained by burning fuel, which results in the generation of emissions. If extra power is applied, the emissions of the utility company will increase. Hence, to reduce the emissions in the process might in reality result in greater emissions associated with burning the fuel, which compounds the global emissions.

Flue Gas Emissions It has been shown that the relationship between energy efficiency and flue gas emissions persists, and the more inefficient we are in our use of energy, the more fuel we

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-113 Screenshot of actual interval temperature of hot and cold duties for case study 1. Maximum energy recovery (MER) at DTmin [ 20 C [ 18400 L 10150 [ 8.25 MW. (Used by permission: Ian Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChem.E, BH 2007.)

burn and thus the greater are the flue gas emissions. Pinch Analysis (PA) can be employed to enhance energy efficiency through better heat integration and hence reduce flue gas emissions. Various investigations have shown that PA can be carried out at the correct economic level of energy recovery, as basic modifications to the process can be directed to reduce flue gas emissions. Smith and Delaby [81] have established techniques to target CO2 emissions associated with energy, and combining these techniques with site-wide analysis will assist in trading off different emissions [82]. With a given relevant algorithm, we can determine the trade-off between capital cost and energy recovery as indicated in Figure 16-102. For various values of DTmin (obtained by changing the relative location of the composite curves), we can determine the energy target (and thus the hot and cold utility requirements), the overall area required and the number of units. As discussed earlier, the larger the DTmin, the larger is the energy target and the

lower the overall heat transfer area. The capital cost of a heat recovery system depends mainly on three factors: 1. The number of separate heat exchange matches (or units). 2. The total heat exchange area. 3. The cost of the utility system necessary to provide the outstanding hot and cold utilities (e.g. boiler plant, cooling water system, refrigeration plant, etc). The minimum number of heat exchange matches (or units) depends on the number of streams involved and on the pinch location, and can be determined prior to design. The minimum total heat exchange area can also be determined prior to any network design. This information is combined and used to predict ahead of design the overall cost for each DTmin, where the lowest possible overall cost is established in Figure 16-102. Figure 16-103a shows the grand composite of a process. Because the process requires high temperatures, a furnace is required. Figure 16-103a illustrates the steepest

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595

FIGURE 16-114 Screenshot of plots of pinch temperatures of hot and cold streams and minimum utility requirements at varying DTmin (i.e. minimum to maximum values) for case study 1. (Used by permission: Ian Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

flue gas that can be drawn against the existing process. This corresponds with the smallest flue gas flow rate, the smallest fuel consumption and hence the smallest flue gas emissions [83]. Figure 16-103b shows the grand composite curve of the same process, which has been modified to open up temperature difference forces in the high temperature part of the process. The overall process duty is unchanged, but the systematic modifications of the process, as shown in Figure 16-103b, allow the steeper flue gas line to be drawn, which results in reductions in flue gas emissions. PA has been successfully employed to carry out an energy efficiency campaign in BASF Company at their Ludwigshafen factory, and process integration technology was used to increase the energy efficiency of the individual chemical processes on the site. Each individual project was justified based on its energy saving potential, which required a payback in one year or less. The total energy saved was 790 MW [84]. Table 16-26 shows the

environmental relief resulted from reduced power station emissions on the site, and Figure 16-104 shows this change graphically and how it was achieved against a background of increased production levels [83]. PA has been simultaneously employed for these reduced emissions with corresponding improved profitability. PA can be used to establish the appropriate economic level of energy recovery given the trade-off between energy and capital. Presently, there is no cost that is associated with environmental relief, such as emission of greenhouse gases (e.g. CO2) or gaseous acidic emission (SO2). However, if the regulatory bodies responsible for environmental emissions are to improve restrictions on SO2, then this requires converting to an alternative fuel or the installation of a flue gas desulfurization plant. In this instance, PA can be employed to evaluate the trade-offs between reduced energy consumption, investment in heat recovery systems for improved energy efficiency and investment in flue gas clean-up. Similarly, trade-offs for CO2

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-115 A possible grid representation of heat exchanger network design for case study 1.

FIGURE 16-116 Modified flowsheet to show improved energy recovery for case study 1. (Used by permission: Gary Smith and Ajit Patel, Step by step through the pinch, The chemical Engineer, November 1987.)

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597

FIGURE 16-117 Flowsheet of crude oil fractionation preheat train.

TABLE 16-30 Stream Data for Crude Oil Preheat Train for Case Study 2 Stream No.

Name of Stream

Temperature in,  C

Temperature Out,  C

CP, kW/ C

1

Fuel oil

349

90

192.27

2

Gas oil

341

65

95.65

3

Kerosene

268

38

60.43

4

Reflux

251

77

97.70

5

Heavy Naphtha

235

38

7.11

6

Light Naphtha (Main)

168

71

444.33

7

Light Naphtha (Pre-flash)

136

71

193.85

8

Desalted feed

15.6

121

378.56

9

Pre-flash feed

120

194

509.46

10

Crude tower feed

189

368

585.47

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

_ p Stream Data of Crude Oil Preheat Train for case study 2 TABLE 16-31 mC Heat Capacity Flow Rate CP [ (DH/DT) (MW/K)

Heat Capacity Flow Rate CP [ (DH/DT), (kW/K)*

49.8 27.0 21.1 12.9 0.0

0.215 0.197 0.178 0.168

192.27

341 210 172 111 65

26.4 12.6 8.8 3.5 0.0

0.105 0.100 0.087 0.076

95.65

3

268 135 38

13.9 5.2 0.0

0.065 0.054

60.43

4

251 169 77

17.0 8.4 0.0

0.105 0.091

97.70

5

235 127 38

1.4 0.6 0.0

0.008 0.007

7.11

6

168 136 118 108 71

43.1 23.9 15.3 11.2 0.0

0.600 0.478 0.410 0.303

444.33

7

136 118 108 71

12.6 8.0 5.9 0.0

0.256 0.210 0.159

193.85

8

15.6 121

0.0 39.9

0.379

378.56

9

120 122 163 186 194

0.0 0.8 18.1 31.9 37.7

0.400 0.422 0.600 0.725

509.46

10

189 237 265 368

0.0 22.9 36.8 104.8

0.477 0.496 0.660

585.47

Temperature ( C)

Enthalpy H (MW)

1

349 243 213 167 90

2

Stream

*CP is calculated.

Process Integration and Heat Exchanger Networks Chapter | 16

599

TABLE 16-32 Stream Data of Aromatics Plant for Case Study 3 [39] Stream

Ts ( C)

Tt ( C)

mCp (kW/ C)

Heat Load (kW)*

h (kW/m2  C)

H1

327

40

100

28700

0.5

H2

220

160

160

9600

0.5

H3

220

60

60

9600

0.5

H4

160

45

400

46000

0.5

C1

100

300

100

20000

0.5

C2

35

164

70

9030

0.5

C3

85

138

350

18550

0.5

C4

60

170

60

6600

0.5

C5

140

300

200

32000

0.5

OIL

330

230

1.0

CW

10

30

2.5

*Q ¼ mCp dT

FIGURE 16-118 Screenshot of the input data flow crude oil fractionation preheat train for case study 2. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd Ed., IChemE., BH 2007.)

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

FIGURE 16-119 Screenshot of the Problem Table, heat cascade, pinch identification, problem type, minimum hot and cold utility requirements for crude oil fractionation preheat train for case study 2. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd Ed., IChemE., BH 2007.)

emissions cannot be carried out unless a ‘carbon tax’ is introduced to prevent the greenhouse effect, and regulatory bodies responsible for environmental emissions could employ PA to target emissions rather than target energy consumption. For a given set of process heating and cooling demands, an energy target for a given setting of the capital/energy trade-offs is obtained (see Figure 16-102). This energy target, together with a given fuel and type of combustion equipment, results in a minimum flue gas emission. Therefore, once the combustion equipment and the fuel type have been set, the minimum flue gas emission is correspondingly set by the process heating and cooling demands and by the capital/energy trade-offs for heat recovery. PA could therefore be used to set practical and economically based targets for flue gas emissions. These targets could be used to screen alternative process options, compare centralized power generation with local cogeneration, or to impose a carbon tax on those companies that do not meet their targets [83].

PITFALLS IN PROCESS INTEGRATION Process integration (PI) has now been established as a powerful optimization tool for designing processes that are sustainable, environmentally friendly and above all energy efficient. Pinch analysis, a tool in PI, has developed from the early work on targeting and heat exchanger network design to cover a wide range of aspects of process design, particularly energy usage. Many new techniques and optimization tools have been developed and reviews of these are given by Lam et al. [22] and by Klemes et al. [8]. However, potential pitfalls when using PI involve the improper formulation of the problem and incorrect data extraction. Here, the following suggestions are considered for avoiding traps in extracting data for PI [84]: l

Be careful to segment multicomponent streams that undergo phase transitions in order to capture the shape of the boiling or condensing curve correctly.

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601

FIGURE 16-120 Screenshot of composite curves of hot and cold streams for crude oil fractionation preheat train for case study 2. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd Ed., IChemE., BH 2007.)

l

l

l

l

Beware of non-isothermal mixing e do the streams need to be at different temperatures when mixed? Do not extract too many features of the existing or previous design e for pinch purposes, a stream is defined by its source and target temperatures, not by an existing heat duty. Recognize soft constraints that can be exploited in the design, for example, temperatures of rundown streams to storage. Question any use of direct heat transfer e is it necessary for safety or other process reasons or could indirect heat transfer be used instead?

The most basic issues involve how the engineer/ designer starts a PI-based project and how it is run. The following steps allow systematic development of heat integration, which can be applied with minor adjustments to mass, water and other integration. These steps are shown in Table 16-27 [8].

CONCLUSIONS Process integration, and in particular pinch analysis, have proved to be powerful tools that have resulted in significant improvements in the energy and capital efficiency of industrial facilities worldwide. It has been successfully applied in many chemical process industries (CPIs) from refining, petrochemicals, chemicals to food, paper and water treatment. Both continuous and batch processes have been analyzed on an individual and site wide basis. Practitioners have shown that pinch analysis is equally applicable to new designs and to retrofits of existing facilities. Some have reported savings averaging 30e40% on energy costs, coupled with significant capital cost savings on new plant designs. Payout times have been reported as low as 6 to 12 months [85]. Pinch analysis has successfully been employed in debottlenecking of the atmospheric vacuum unit (AVU) in the petroleum refinery resulting in a 40% increase in AVU capacity over existing operations. Further, a MER network

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FIGURE 16-121 Screenshot of the shifted composite curves of hot and cold streams for crude oil fractionation preheat train for case study 2. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd Ed., IChemE., BH 2007.)

achieved the target energy savings of 34.3 MMkcal/h with a crude preheat temperature of 302 C [86]. Pinch analysis provides the process designer with an extensive tool for process and utility system analysis. It is essential to integrate such a tool into the conceptual process design phase, as the decisions in this phase could affect the life cycle of the process facility. The complete engineering of a project represents approximately 10% of the life cycle of the process facility, and the process design represents only 10% of the engineering effort. But the process design effort sets approximately 90% of the total capital investment, thus allowing the process designer to develop a more cost effective conceptual design for the process and utility systems. Pinch analysis improves the life cycle value of the facility; however, pinch analysis tools and understanding do not guarantee results as these must be applied at the right point in the process design phase. In the conventional approach to process design, the process flow alignment is set and optimized against a set of project-specific requirements such as maximum product yields, selectivity and conversion. The process

is often classified into sections or units, which are designed and optimized by different design teams. Downstream engineering groups are responsible for detailed system hydraulics, instrumentation, control system design, detailed utility system design, equipment selection and plant layout. The process design engineer primarily focuses on the process units and often has minimal input into the design and optimization of the overall integration with the utility systems. Thus, opportunities for properly matching the utilities to the process are often missed. The full benefit of pinch analysis can be realized if it is carried out early in the design process before major design parameters have been fixed. Implementation problems could arise if the work process incorporates pinch analysis as a separate and independent evaluation. This is because the performance targets set as part of independent study are not always full achieved in the final design as they succumb to unforeseen constraints identified during detailed engineering. This can occur because pinch analysis is often founded upon one or more key integrations in and around

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603

FIGURE 16-122 Screenshot of the grand composite curve for crude oil fractionation preheat train for case study 2. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd Ed., IChemE., BH 2007.)

the pinch regions. An engineering difficulty with one of these key integrations sometimes nullifies the proposed structure and therefore requires rework of the entire design. In conclusion, to be truly successful, pinch analysis should be used to promote once-through engineering. The in-depth knowledge-base that resides in the downstream engineering disciplines must be incorporated during the conceptual phase of the project when pinch analysis is being conducted. It would be impracticable and infeasible to conduct pinch analysis after completion of the process design phase, where critical parameters have been fixed; it would be impracticable and infeasible to conduct pinch analysis without direct interaction with the process specialists and downstream engineering disciplines. It is the role of pinch analysis to identify what might be, although input from other engineering disciplines could determine what can be and this interaction occurs as a result of the work process, without which the use of pinch analysis will never realize its full potential. PI can be applied to environmental impact assessment (EIA) for determining, assessing and mitigating a proposed

project’s biological, physical, chemical, economic and social impacts on the environment. In considering the EIA procedure from the point of view of process engineering activities, various design alternatives can be proposed, which do not produce an optimum or near-optimum design except in the simplest cases. The process engineering team performs a techno-economic analysis and safety assessment such as hazard and operability studies (HAZOPs) or hazard identification analysis (HAZID) of the alternatives. The team must identify, predict and evaluate the environmental impacts for each alternative and develop mitigating techniques for any unacceptable impacts. If the impacts are acceptable, the environmental impact statement (EIS) is prepared and discussed with decision makers and the public, resulting in the project being accepted, altered or rejected. A large number of alternatives may be generated and analyzed, however, environmental regulations are typically considered as constraints when generating alternatives. PI can be employed to overcome these limitations, where it serves as an effective framework for facilitating process engineering activities associated with the EIA, reducing engineering

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FIGURE 16-123 Screenshot of actual intervals table of hot duty and cold duty for crude oil fractionation preheat train for case study 2. Maximum energy recovery at (DTmin) of 20 C [ 164196.96 L 44055.066 [ 120141.894 kW [ 120.1 MW. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd Ed., IChemE., BH 2007.)

efforts and thus providing valuable insights and at the same time systematizing the design effort, thus reconciling the various process and environmental objectives [87]. Petroleum refining and CPIs offer opportunities for energy savings from PA. The Electric Power Research Institute (EPRI) and its utility members in the US and overseas have sponsored a variety of energy related projects in the CPIs. The calculated payback periods for most projects have been below two years and energy cost savings have typically been over $1million. Table 16-28 summarizes a few of the studies investigated. Finally, enterprising and challenging works earlier foreseen by Smith in his review [88] are now being realized. Such works by Shenoy [89], involve targeting and design of

energy allocation networks for carbon emission reduction where the composite table algorithm based on the limiting composite curve is employed to target the minimum clean energy resources (zero carbon and low carbon) required to energy sector planning problems with carbon emission constraints aimed at reducing climate change effects; mathematical formulation of targeting during energy allocation with carbon capture and storage [90], and an algorithm to establish minimum resource targets for diverse PI problems involving heat/mass exchange, water, hydrogen, carbon emission and material reuse networks. Declercq [91] recently presented a PA technique with crisscross optimization prior to design with a view to minimizing required heat exchanger surface area. This process eliminates the weakness of

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605

FIGURE 16-124 Screenshot of the results of hot, cold pinch temperatures and utilities requirements for varying DTmin values and plots of these parameters for crude oil fractionation preheat train for case study 2. (Used by permission: Ian C. Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd Ed., IChemE., BH 2007.)

existing tools and improves the reliability of the results and the quality of the data from which to start the design. Others shall continually evolve with time.

INDUSTRIAL APPLICATIONS, CASE STUDIES AND EXAMPLES Case Study 1 (From Gary Smith and Ajit Patel, the Chemical Engineer p26, November 1987).

The flowsheet for the process is shown in Figure 16-105, and consists of two distillation columns in series. The current heat integration scheme uses the overheads of column 2 first to preheat the feed to column 1 and then to raise the low pressure (LP) steam; the bottoms of column 2 further heat the feed to column 1. All the remaining heating and cooling loads are supplied using high pressure (HP) steam and cooling water utilities. A minimum approach temperature (DTmin) of 20 C between all streams exchanging heat is assumed (i.e. the temperature of the hot and cold streams in an exchanger must be over 20 C

apart). Provide the stream data from Figure 16-101 and design a scheme which makes the “best” use of energy available (i.e. the maximum heat recovery) giving the minimum energy requirements. Further provide the HEN for this scheme. Table 16-29 shows the stream data of Figure 16-105. Solution The Excel spreadsheet software in A User Guide on Process Integration for the Efficient Use of Energy, [21] is used to carry out the following steps: a. Construct 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 DTmin ¼ 20 C. e. Create plots of the hot and cold pinch temperatures at varying DTmin (i.e. minimum to maximum values) and of the minimum utility requirements for hot and cold streams at varying DTmin (i.e. minimum to maximum values) (see Excel spreadsheets, Case Study-1a.xlsx and 1b.xlsm for calculations).

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CPHot ≤ CPCold Tph = 168oC

1

3 4 5

∆H (MW)

∆H =34.8MW

349 oC

2

CP (MW/oC)

E1

341 oC

268oC

0.19227

E3

∆H =16.72MW E2

0.09565

E4

∆H =6.04MW E5

251oC

235oC

49.79

26.572

0.06043

13.898

0.0977

16.999

∆H =8.109MW E6

∆H =0.476MW

0.00711

1.40

8.109MW

194 oC

0.50946

37.7

0.58647

104.98

6.04MW 4.72MW

Tpc = 148oC

4.5616MW

368 oC

12.0MW

H 62.74 MW 30.238MW

FIGURE 16-125A Network design above the pinch for case study 2.

The results show the following at DTmin ¼ 20 C: Type of pinch problem

¼ Pinch region problem Pinch temperature ¼ 220 C/225 C Hot stream pinch temperature ¼ 235 C Cold stream pinch temperature ¼ 215 C Minimum hot utility requirement ¼ 11.4 MW Minimum cold utility ¼ 10.15 MW requirement Maximum energy recovery ¼ 8.25 MW

Figures 16-106 to 16-110, 16-113 and 16-114 show screenshots of the input data, Problem Table, composite curves, shifted composite curves, the grand composite curve, MER, and plots of hot, cold pinch temperatures and utilities requirements for varying DTmin. Figure 16-115 shows the HEN with a total of 13 heat exchangers including the utilities. The minimum temperature approach (MTA) between these exchangers is  20 C, indicating that DTmin is not violated. The calculated hot and cold utility requirements at DTmin ¼ 20 C are 11.4 MW and 10.15 MW respectively. The hot pinch temperature is 150 C, and the corresponding cold pinch

Process Integration and Heat Exchanger Networks Chapter | 16

607

CPHot ≥ CPCold CP (MW/oC)

o

Tph = 168 C ∆H =14.99MW

1

E7

∆H (MW)

0.69 E8

90 oC

C

0.19227

49.79

0.69 MW ∆H =9.85 MW

2

E9

65 oC

C

0.09565

26.572

7.55 MW

∆H =7.855MW

3

E10

38 oC

0.06043

77 oC

0.0977

38oC

0.00711

1.40

71oC

0.44433

43.10

71oC

0.19385

12.60

C

13.898

6.44 MW ∆H =8.89MW

4

C

16.999

8.89 MW ∆H =1.40MW

5

C 1.40 MW

6

∆H =8.89MW

C

E11

13.10 MW 136 oC

7

∆H =43.1MW

E12

C 6.45 MW 15.6oC

121 oC

9.9 MW 30MW

4.4 MW

120oC

8

9

0.37856

39.9

0.50946

37.7

30 MW 1.412 MW

Tpc = 148oC 6.15 MW

FIGURE 16-125B Network design below the pinch for case study 2.

temperature is 130 C. Figure 16-111 shows the GCC, which is a graphical representation of the heat cascade, obtained by plotting the net heat flow at each of the adjusted temperature interval boundaries. The LP steam temperature is converted from an actual to an interval temperature. As the steam is being raised, it is a cold stream (i.e. accepting heat) and thus the interval temperature is (130 þ 20/2) ¼ 140 C. Figure 16-111 on the GCC shows that the heat available at 140 C for steam raising is 8.5 MW. Allowing for the heat required to provide the sensible heat to raise the condensate temperature from 108 C to 130 C (see Figure 16-115), the total energy required for steam raising is 8.86 MW.

This LP steam raising is shown on the GCC (Figure 16-111). Inspection of this modified GCC shows that the heat rejected to cooling water has been by 8.86 MW to 1.29 MW (10.15  8.86). This heat is used to raise LP steam. A comparison with the base case design shows that the amount of LP steam generated has been increased from 2.16 MW to 8.5 MW. Figure 16-112 shows composite curves that include the maximum amount of steam raising. At the point of closest approach, ignoring the two column reboiler streams, which require external utility, the curves are separated by a vertical distance DTmin ¼ 20 C. This point of closest approach is referred to as the recovery pinch, and at this point the

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FIGURE 16-125C Combined Network design for case study 2.

C1 R1 H1 F1 D1

B

A

Treated naphtha feed

D2 F

C2

D E

X P1 F2

C

G H2

H3 R2

R3 C3

Crude aromatics product

FIGURE 16-126 Schematic flowsheet of naphtha reformer (aromatics plant) case study 3.

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temperature driving forces are at a minimum. Thus, the pinch represents the most constrained part of the heat exchanger network. The pinch in Figure 16-112 splits the problem into two parts, namely the heat sink (above the pinch) and the heat source (below the pinch). 1. In the heat sink area, there is a net deficit of heat that requires external heating only. 2. In the heat source area, there is a net surplus of heat that requires external cooling only. Figure 16-116 shows a modified flowsheet with an improved energy recovery.

Case Study 2 Crude Preheat Train Introduction The fractionation of crude oil into its major components such as naphtha, gasoline, kerosene and fuel oil is a common process in refinery plants. In the fractionation process as shown in Figure 16-117, a facility needed uprating by 25% to handle increased demand. Design studies carried out by a contractor suggested that it was not possible to increase the throughput of the plant without installing a new fired heater, and that this seemed to be the cheapest capital option. However, space in the plant was very restricted and the only location which could be found for the new heater (a hot oil circuit) was away from the main plant and on the opposite side of a busy site road, over which the hot oil would have had to be carried on a pipe bridge. This rerouting was unacceptable for operability and safety reasons, and conventional techniques to redesign the plant with reduced energy consumption failed to meet its expectation. Design a suitable HEN for atmospheric crude fractionation based on the stream data in Table 16-30 [78]. Process Description The process flowsheet is shown in Figure 16-117 where the crude oil feed stream is preheated in three sections by interchange with the hot fractions returning from the distillation columns. This first section runs from storage to a desalter unit, the second from the desalter to a preflash column which separates out some light naphtha, and the third from the bottom of the preflash to the crude tower. Process heating is provided by a fired heater, which preheats the crude into the crude tower and provides reboiling for the stripper. The proposed additional fired heating was to have taken the form of a hot oil circuit placed immediately upstream of the existing heater. Layout constraints meant that the heater for the proposed oil circuit would have been placed away from the main plant. Table 16-30 shows the stream data for case study 2, and Table 16-31 shows the mCp data using stream

609

segmentation (piecewise linear approximation to accurately account for the variation of Cp with temperature). The approximate analysis below is based on average mCp values for each stream as given in Table 16-30. The exact and detailed analysis based on stream segments is provided by Kemp [21]. Solution The Excel spreadsheet software in A User Guide on Process Integration for the Efficient Use of Energy, [21] is used to carry out the following steps: a. Construct 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 DTmin ¼ 20 C. e. Plots of the hot and cold pinch temperatures at varying DTmin (i.e. minimum to maximum values) and of the minimum utility requirements for hot and cold streams at varying DTmin (i.e. minimum to maximum values. See Excel spreadsheets, Case Study-2a.xlsx and 2b.xlsm for calculations). The results show the following at DTmin ¼ 20 C: Type of pinch problem Pinch temperature Hot stream pinch temperature Cold stream pinch temperature Minimum hot utility requirement Minimum cold utility requirement Maximum energy recovery

¼ Single pinch problem ¼ 158 C ¼ 168 C ¼ 148 C ¼ 62.25 MW ¼ 44.04 MW ¼ 8.25 MW

Figures 16-118 to 16-124 show screenshots of the input data, Problem Table, composite curves, shifted composite curves, the grand composite curve, MER and plots of hot, cold pinch temperatures and utilities requirements for varying DTmin. The problem table in Figure 16-119 shows the infeasible cascade column 7 with the highest negative value of 62.26 MW. This is the minimum amount of heat that must be supplied from the hot utilities. This same amount of heat is added in column 8, and the resulting numbers give the feasible cascade of heat in kW. The point in the last column where the adjusted cascaded heat is zero represents the pinch point where there is no heat flow. The topmost value in the last column, 62.26 MW, is the minimum amount of heat that must be supplied from the

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FIGURE 16-127 Screenshot of the input data of aromatic plant for case study 3. (Polley, G. T. and M. H. Panjeh Shahi, Trans. IChemE. Vol 69, Part A., November 1991. Used by permission: Ian Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

hot utilities, and the bottommost value of 44.06 MW is the minimum amount of heat that must be removed by cold utilities. Also, the difference between the minimum cold utility requirement and the minimum hot utility requirement (44055  62258 kW giving 18.2 MW) is the bottom value of the infeasible cascade table in Figure 16-119. The GCC is shown in Figure 16-122. The pinch point occurs at 158 C at zero heat flow. The pinch point at 168 C is the hot stream temperature and the pinch point at 148 C is the cold stream temperature. The GCC in Figure 16-122 is divided into two regions: above the pinch (i.e. heat sink) and below the pinch (i.e. heat source). For the maximum heat or energy recovery, cold utilities cannot be used above the pinch and hot utilities cannot be

used below the pinch. Also, heat cannot be transferred across the pinch. Above the Pinch For the maximum energy recovery, cold utility cannot be used above the pinch. But hot utility can be used. There are five hot streams and two cold streams above the pinch. Stream No. 5 has 0.476 MW of heat available, and is very low as compared to the heat loads (heat available or required) of other streams existing above the pinch. Hence Stream No. 5 is not considered in the heat exchange above the pinch heat load, but the same load is transferred or included in the design of HEN below the pinch. The cold Stream No. 9 is split into four streams to exchange the heat with four hot streams. The second cold Stream No. 10 is

Process Integration and Heat Exchanger Networks Chapter | 16

611

FIGURE 16-128 Screenshot of the Problem Table, heat cascade, pinch identification, problem type, minimum hot and cold utility requirements of aromatic plant for case study 3. (Polley, G. T. and M. H. Panjeh Shahi, Trans. IChemE. Vol 69, Part A., November 1991, Used by permission: Ian Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

split into two streams to exchange heat with Streams Nos. 1 and 2 of the hot streams. One heater is required above the pinch. Below the Pinch For maximum energy recovery, hot utility cannot be used below the pinch, but cold utility can be used. If stream

splitting is required, then it should be split near the pinch. The heat exchangers should be designed such that they utilize the utilities far away from the pinch. Below the pinch, Stream No. 9 (cold stream) is again split into four streams to exchange its heat with the same four streams from Stream Nos. 1 to 4. Another cold Stream No. 8 is split into two streams to exchange the heat with Stream Nos. 1

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FIGURE 16-129 Screenshot of composite curves of hot and cold streams of aromatic plant for case study 3. (Polley, G. T. and M. H. Panjeh Shahi, Trans. IChemE. Vol 69, Part A., November 1991, Used by permission: Ian Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

and 6. A total of seven coolers are required below the pinch. Figure 16-124 shows plots of the pinch temperature against DTmin, and at varying minimum hot and cold utilities vs. DTmin. The latter plot shows that the minimum hot and cold utilities increase as DTmin increases. An optimal value of DTmin can be estimated with knowledge of capital and operating costs of the heat exchangers in the network. Figures 16-125a, b and c, respectively, show the HEN design above the pinch, below the pinch and combined, respectively.

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 The plant concerned in this study was part of one of the largest aromatics complexes in Europe. It was commissioned in 1969 and used state-of-the-art conventional technology. The original study was performed by ICI and reported in the first edition of the User Guide on Process

Process Integration and Heat Exchanger Networks Chapter | 16

Integration for the Efficient Use of Energy by Bodo Linnhoff et al. [16]. Since then, it has also been subject to a large amount of analysis by researchers; e.g. Polley, G.T. et al. The data extracted in this analysis are taken from Polley et al. [39]. Process Description A schematic diagram of the process flowsheet is shown in Figure 16-126. The feedstock is a central fraction of naphtha chiefly containing paraffins and cycloparaffins which are formed into product containing paraffins and aromatic compounds. The process can be described as follows, indicating the streams which will be extracted. Stream 1 (cold): The feed is vaporized (H1) and passed through a desulfurization reactor (R1).

613

Stream 2 (hot): Heat is recovered from the reactor effluent in two interchangers (A, B) prior to condensation (C1) and gas separation (F1). Stream 3 (cold): The liquid from the separation stage is re-heated by reactor effluent (B) and fed to a stripping column (D1) in which the light ends and sulfurcontaining compounds are removed. Stream 4 (cold): The two-phase mixture is preheated in a series of process interchangers (D, C). The mixture is finally raised to the reaction temperature of 500 C by a radiant furnace (H2) fired by a mixture of gas and fuel oil. Reactions: The reactions take place in a pair of reformers (R2, R3). Stream 11 (cold): Between the reformers, the mixture is re-heated to reaction temperature by a fired heater (H3).

FIGURE 16-130 Screenshot of the grand composite curve of aromatic plant for case study 3. (Polley, G. T. and M. H. Panjeh Shahi, Trans. IChemE. Vol 69, Part A., November 1991, Used by permission: Ian Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

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FIGURE 16-131 Screenshot of actual interval temperature of hot and cold duties of aromatic plant for case study 3. Maximum energy recovery (MER) at DTmin [ 20 C [ 93900 L 29400 kW [ 64.5 MW. (Polley, G. T. and M. H. Panjeh Shahi, Trans. IChemE. Vol 69, Part A., November 1991, Used by permission: Ian Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Stream 5 (hot): The reformer effluent, at 490 C, is cooled in interchanger C and then passed to exchanger X, which heats other cold streams (actually the reboilers of columns D1 and D2). Stream 6 (hot): The mixture emerging from X is cooled further in three exchangers which preheat the feed (D, E) and provide the heat source for other process requirements (F, heating cold stream 10). Final cooling and gas separation takes place in C2 and F2. Stream 7 (cold): The gas recycle is compressed (P1) and preheated (E) prior to mixing with the liquid reformer feed.

Stream 8 (cold): The liquid from the flash drum is passed to a column for stabilization (D2) and a conventional feed/tails interchanger (G) is installed to reduce the reboil requirement by adding feed preheat. Stream 9 (hot): The reformate stream passes through exchanger G and is finally cooled in C3 prior to storage. Stream Data Extraction The process flowsheet is shown in Figure 16-126, and the basic data employed in the design problem are taken from Polley, G.T. et al. [39] and are shown in Table 16-32.

Process Integration and Heat Exchanger Networks Chapter | 16

615

FIGURE 16-132 Screenshot of plots of pinch temperatures of hot and cold streams and minimum utility requirements at varying DTmin (i.e. minimum to maximum values of crude oil fractionation preheat train for case study 3. (Polley, G. T. and M. H. Panjeh Shahi, Trans. IChemE. Vol 69, Part A., November 1991, Used by permission: Ian Kemp, Pinch Analysis and Process Integration e A User Guide on Process Integration for the Efficient Use of Energy, 2nd ed. IChemE., BH 2007.)

Determine the minimum utility requirements at a minimum approach temperature of DTmin ¼ 10:6o C and design a suitable HEN. Solution The Excel spreadsheet software in A User Guide on Process Integration for the Efficient Use of Energy, [21] is used to carry out the following steps: a. Construct 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 DTmin ¼ 20 C. e. Plots of the hot and cold pinch temperatures at varying DTmin (i.e. minimum to maximum values) and of the minimum utility requirements for hot and cold streams

at varying DTmin (i.e. minimum to maximum values) (see Excel spreadsheets, Case Study-3a.xlsx and 3b.xlsm for calculations). The results show the following at DTmin ¼ 20 C: Type of pinch problem Pinch temperature Hot stream pinch temperature Cold stream pinch temperature Minimum hot utility requirement Minimum cold utility requirement Maximum energy recovery

¼ ¼ ¼ ¼ ¼ ¼ ¼

Single pinch problem 110 C 120 C 100 C 21.68 MW 29.4 MW 64.5 MW

Figures 16-127 to 16-132 show screenshots of the input data, Problem Table, composite curves, shifted composite curves, the grand composite curve, MER, and plots of hot,

120 C

320 C

74.5 C 3450 kW

190 C

80 C 1200 kW

158.5 C

153.25 C

106.87 C 24750 kW

155.7 C

100 C

130 C

4550 kW

18550 kW

194.5 C

C

143 C

QCmin = 29.4 MW

QHmin = 21.68 MW

FIGURE 16-133 Initial design of HEN of aromatic plant for case study-3. (Used by permission: Polley, G. T. and M. H. Panjeh Shahi, Trans. IChemE. Vol 69, Part A, November 1991.)

CP (kW/ 127 C

74.9 C 3486 kW

196.2 C

86.2 C 1573 kW

155.3 C

149.3 C

102.9 C 23177 kW

20000 kW

143.6 C 1427 kW

109.5 C 5214 kW

18550 kW

6600 kW

197.4 C

149.4 C

20515 kW

QHmin = 20.5 MW

QCmin = 28.3 MW

FIGURE 16-134 Final design of HEN of aromatic plant for case study-3. (Used by permission: Polley, G. T. and M. H. Panjeh Shahi, Trans. IChemE, Vol. 69, Part A, November 1991.)

Process Integration and Heat Exchanger Networks Chapter | 16

cold pinch temperatures and utilities requirements for varying DTmin. Figures 16-133 and 16-134 show the initial and final designs of HEN of aromatic plant for case study 3.

GLOSSARY OF TERMS Area targets Counter current e the minimum amount of heat transfer area required when all exchangers are counter current. 1-2 Shell and Tube e The minimum amount of heat transfer area required when all exchangers are shell and tube. Appropriate placement Positioning of utilities, heat engines, heat pumps or an extracted process (e.g. separation system) above or below the pinch and grand composite curve for best overall energy performance. Background process The stream data for the remainder of the process after the extracted streams have been removed. Balanced composite curves Composite curves including the hot and cold utility streams. This plot is similar to the composite curve, except that both process and utility streams’ enthalpy values are combined. Balance grand composite curves Grand composite curves including the hot and cold utility streams. Balanced grid Network grid diagram including the hot and cold utility streams. Capital cost index Minimum capital cost, based on area targets. Cascade Set of heat flows through a heat recovery problem, in strict descending temperature order (as calculated in Problem Table analyses). Cascade analysis This method of batch process analysis is based on breaking the process into time intervals and developing timedependent heat cascades. Cold stream Process stream requiring heating. Composite curve Combined temperature-enthalpy plot of all hot and cold streams in a problem. The plot displays the graphical combination (or composites) of all hot or cold process streams in a heat exchange network. Cooling Minimum cold utility load required for the heat exchanger network. Cost index targets Capital e The minimum capital cost of the heat exchangers, based on area targets. Operating e The minimum operating cost of the utilities, based on energy targets. Total Annual e The minimum annualized cost of the heat exchanger network, based on capital and operating targets. CP table Tabulated values of stream heat capacity flow rates, immediately above or below the pinch. Cycle time The total duration of a batch. Cyclic matching Repeated matching of pairs of process streams. Data extraction Definition of data for energy integration studies, from a given flowsheet. Debottlenecking Increasing the production capacity of a plant by identifying and removing rate-limiting steps, such as slow processing stages or heavily occupied equipment items. Degrees of freedom The value of the degrees of freedom indicates whether the HEN design can be controlled or not: NDoF < 0 indicates that there are not enough manipulated variables in the HEN design and it is not possible to control all target temperatures.

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NDoF ¼ 0 indicates that there are enough manipulated variables in the HEN design to control the target streams’ temperatures. NDoF > 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 ¼ 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 e 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 e 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. Infeasible 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.

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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 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 DTmin , 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, DTmin 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 e The minimum total number of units required for the HEN system. Minimum for MER e 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. Shells e 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. 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. Pumpround 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. 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 DTmin =2 and the cold composite curve is shifted up by DTmin =2. Shifted temperature Stream temperatures altered to include the effect of the required DTmin , usually by reducing hot stream temperatures by DTmin =2 and increasing cold stream by DTmin =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.

Process Integration and Heat Exchanger Networks Chapter | 16

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 DH 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 DTmin values from zero up to a threshold (or throughout). The value of DTmin at which one utility target falls to zero is termed “DTthreshold ”, 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. 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

619

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 ð ¼ Q=DTLMTD Þ 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. DHi (kW) The enthalpy balance is determined by ðTi  Tiþ1 Þ P P ð CPHOT  CPCOLD Þi where i ¼ interval, T ¼ shifted temperature, CPHOT ¼ heat capacity flow rate of the hot stream (kW/ K), CPCOLD ¼ heat capacity flow rate of the cold stream (kW/K). DTmin Minimum temperature difference allowed in the process between hot and cold streams. For a given value DTmin , the utility quantities predicted are the minima required to solve the heat recovery problem. In general, DTmin 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 DT values down to DTmin . A value of 10 C or 20 C is best, but in some industries, a very much lower or higher value is appropriate. DTmin contribution ðDTcont Þ Temperature difference value assigned to individual process streams. Match-dependent DTmin values are given by the sum of the contributions in a match.

SUMMARY AND HEURISTICS A very simple procedure exists which 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. Only 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.

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5. When we break loops that cross the pinch in order to eliminate heat exchangers from a network, we often violate the DTmin 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. 9. If possible, always install distillation columns either above or below the pinch. Three design heuristics have been proposed by Linnhoff and Hindmarsh [30]: l

l l

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 ¼ Installed capital cost law coefficient A ¼ Heat exchanger area Ai ¼ Contribution to overall area target from enthalpy interval i of the composite curves Amin ¼ Minimum overall area target for a heat exchanger network ATotal .M ¼ Minimum overall area for heat exchanger network after accepting match M b ¼ Installed capital cost law coefficient CC ¼ Annual operating capital cost of unit duty of cold utility CH ¼ Annual operating capital cost of unit duty of hot utility CP ¼ Heat capacity flowrate NC ¼ Number of cold streams in an enthalpy interval NH ¼ Number of hot streams in an enthalpy interval NS ¼ Number of streams NU ¼ Total number of distinct hot and cold utilities DHi ¼ Total enthalpy change of enthalpy interval i on the composite curve Q ¼ Heat exchanger duty QCmin ¼ Minimum cold utility target QHim ¼ Minimum hot utility target QRec ¼ Maximum heat recovery Tcold ¼ Temperature of cold composite curve Thot ¼ Temperature of hot composite curve TS ¼ Supply temperature TT ¼ Target temperature DT ¼ Temperature difference DTLMTD ¼ Log mean temperature difference DTmin ¼ Minimum temperature difference on composite curves U ¼ Overall heat transfer coefficient for a heat exchanger uHX, min ¼ Minimum number of heat exchanger in a HEN

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[26] Seider WD, Seader JD, Lewin DR. 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. Rugby, U.K: Inst Chem Engrs; 1982. [28] Hall SG. 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, Hindmarsh E. The pinch design method for heat exchanger networks. Chem Eng Sci 1983;38(5):745e63. [31] Hohmann EC. Optimum networks for heat exchanger. PhD Thesis. University of S. California; 1971. [32] Varbanov P, Klemes J. Analysis and integration of fuel cells combined cycles for development of low carbon energy technologies. Energy 2008;33(10):1508e17. [33] Linnhoff B, Ahmad S. Cost optimum heat exchanger networks e 1. minimum energy and capital using simple models for capital cost. Comput Chem Eng 1990;14(7):729e50. [34] Smith R. Chemical process design and integration. John Wiley; 2007. [35] Townsend DW, Linnhoff B. Surface area targets for heat exchanger networks. IChemE Annual Res Meeting, Bath, April 1984. [36] Professor D. R. Lewin, Private communications. [37] Ahmad S, Hui DCW. Heat recovery between areas of integrity. Comput Chem Eng 1991;15(12):809e32. [38] Ludwig, Ernest E. In: Applied Process Design for Chemical and Petrochemical Plants. 3rd ed., vol. 3. Gulf Professional Publishing; 2001. [39] Polley GT, Panjeh Shahi MM, Jegede FO. Pressure drop considerations in retrofit of heat exchanger networks. Trans IChemE Part A 1990;68:211. [40] Polley GT, Panjeh Shahi MM. Synthesis and detailed heat exchanger design. Trans I ChemE Part A 1991;69:445. [41] Ahmad S, Smith R. Targets and design multipass heat exchangers, an alternative approach. Trans ASME J Heat Trans 1988;110:304. [42] Kern DQ. Process heat transfer. New York: McGraw-Hill; 1950. [43] Ahmad S, Smith R. Targets and design for minimum number of shells and heat exchanger networks. IChemE ChERD 1989;67:481. [44] Ahmad S, Linnhoff B, Smith R. Cost optimum heat exchanger networks e 2. Targets and design for detailed capital cost models. Comput Chem Eng 1990;14(7):751e67. [45] Cerda J, Westerberg AW, Mason D, Linnhoff B. Minimum utility usage in heat exchanger network synthesis e a transportation problem. Chem Eng Sci 1983;38:373e87. [46] Floudas CA, Ciric AR, Grossmann IE. Automatic synthesis of optimum heat exchanger network configurations. AIChE J 1986;32:276e98. [47] Ciric AR, Floudas CA. Heat exchanger network synthesis with decomposition. Comput Chem Eng 1991;15:385e96. [48] Linnhoff March. Introduction to Pinch Technology. 1998. www.ou. edu/class/che-design/a-design/Introduction%20to%20Pinch% 20Technology-LinnhoffMarch.pdf. [49] Polley G, Panjeh Shahi MH, Jegede FO. Pressure drop considerations in the retrofit of heat exchanger networks. Chem Eng Res Des 1990;68(3):211e20. [50] Nie XR, Zhu XX. Heat exchanger network retrofit considering pressure drop and heat transfer enhancement. AIChE J 1999;45(6):1239e54.

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[51] Asante NDK, Zhu XX. An automated and interactive approach for heat exchanger network retrofit. ChERD 1997;75(Part A):349e60. [52] Vaclavek V, Novotna A, Dedkova J. Pressure as a further parameter of composite curves in energy process integration. Appl Thermal Eng 2003;23(14):1785e95. [53] Panjeh Shahi MH, Tahoumi N. Pressure drop optimization and debottlenecking of heat exchanger networks. Energy 2008;33(6):942e51. [54] Dhole VR, Linnhoff B. Total site targets for fuel, co-generation, emissions and cooling. Comput Chem Eng 1993b;17(Suppl.):101e9. [55] Raissi K. Total site integration. PhD Thesis. Manchester, U.K.: UMISIT; 1994. [56] Klemes J, Dhole VR, Raissi K, Perry SJ, Puigjaner L. Targeting and design methodology for reduction of fuel, power and CO2 on total sites. Appl Thermal Eng 1997;17(8/10):993e1003. [57] Mavromatis SP, Kokossis AC. Conceptual optimization of utility networks for operation variationse 1. Targets and level optimisation. Chem Eng Sci 1998;53(8):1585e608. [58] Varbanov PS, Doyle S, Smith R. Modelling and optimisation of utility systems. Trans IChemE Chem Eng Res Dev 2004;82(45):561e78. [59] Varbanov PS, Klemes J. Total sites integrating renewable with extended heat transfer and recovery. Heat Transfer Eng 2010;31(9):733e41. [60] Towler GP, Mann R, Serriere AJ, Gabande CMD. Refinery hydrogen management: cost analysis of chemically integrated facilities. Ind Eng Chem Res May 1996;35(7):2378e88. [61] Alves JJ, Towler GP. Analysis of refinery hydrogen distribution systems. Ind Eng Chem Res 2002;41:5759e69. [62] Alves JJ. Analysis and design of refinery hydrogen distribution systems. PhD Thesis. Dept. of Process Integration, University of Manchester; 1999. [63] Hallale N, Liu F. Refinery hydrogen management for clean fuels production. Adv Environ Res 2001;6:81e98. [64] Agrawal V, Shenoy UV. Unified conceptual approach to targeting and design of water and hydrogen networks. AIChE J March 2006;52(3):1071e82. [65] Wei ZJ, Yuhang L, Zhang Nan, Guy K. Optimising and revamping a refinery hydrogen network. Revamps Petroleum Technol Quarterly 2011:37e46. [66] Jla N. Refinery hydrogen network optimization with improved hydroprocessor modeling. PhD Thesis. Centre for Process Integration, University of Manchester; 2010. [67] Roozbeh S, et al. Design of oil refineries hydrogen network using process integration principles. Iran J Chem Chem Eng 2008;27(4). [68] Nelson AM, Liu YA. Hydrogen pinch analysis made easy. Chem Eng June 2008:56e61. [69] Zhelev T, Ntlhakana L. Energy environment closed loop through oxygen pinch. Comput Chem Eng 1999;23(Suppl.):79e83. [70] Zhelev T, Bhaw N. Combined water-oxygen pinch analysis for better waste water treatment. Manag Waste Manag 2000;20(8):665e70. [71] Clarke SC. CO2 Management e A Refiners Perspective, Foster Wheeler Energy Ltd., Shinfield Park, Reading, Berkshire, U.K. [72] Klemes J, Bulatov I, Cockeril T. Techno-economic modeling and cost functions of CO2 capture processes. Comput Chem Eng 2007;31(5e6):445e55. [73] Perry S, Klemes J, Bulatov I. Integrating waste and renewable energy to reduce the carbon footprint of locally integrated energy sectors. Energy 2008;33(10):1487e97.

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[74] Tan R, Foo DCY. Pinch analysis approach to carbon-constrained energy sector planning. Energy 2007;32(8):1422e9. [75] El-Halwagi MM, Manousiouthakis V. Synthesis of mass-exchange networks. AIChE J 1989;35:1233e44. [76] El-Halwagi MM, Manousiouthakis V. Simultaneous synthesis of massexchange and regeneration networks. AIChE J 1990;36:1209e19. [77] Wang YP, Smith R. Wastewater minimization. Chem Eng Sci 1994;49:981e1006. [78] Towler G. Private communications, 2013 [79] Chemical processing webcast: boost water efficiency and improve wastewater treatment. Chem Process 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, Delaby O. Targeting flue gas emissions. Trans I ChemE Eng Res Des 1991;69(A6):492e505. [82] Linnhoff B, Dhole VR. Targeting for CO2 emissions for total site. Chem Ind Tech 1993;16:256. [83] Smith R, Petela EA, Spriggs HD. Minimization of environmental emissions through improved process integration. Heat Recovery Syst CHP 1990;10(4):329e39. [84] Smith R. State of the art in process integration. Appl Therm Eng 2000;20:1337e45. [85] Natural Resources Canada. Pinch analysis for the efficient use of energy, water and hydrogen. 2003. ISBN: 0-662-34944-4 © Her Majesty the Queen in Right of Canada. [86] Mehta R. Crude unit integrated energy analysis. Petroleum Technol Quarterly Summer 2002:93e9. [87] Kreith F, Goswami DY. Handbook of energy efficiency and renewable energy e process energy efficiency: pinch technology e 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 UV. Targeting and design of energy allocation networks for carbon emission reduction. Chem Eng Sci 2010;65:6155e68. [89] Shenoy AU, Shenoy UV. Targeting and design of energy allocation networks with carbon capture and storage. Chem Eng Sci 2012;68:313e27. [90] Shenoy UV. Unified targeting algorithm for diverse process integration problems of resource conservation networks. Chem Eng Res Des 2011;89:2686e705. [91] Declercq D. Private Communication, Pinch Technology Second Generation-Analysis with Crisscross optimization prior to design. Design with loop optimization For minimum area and minimum cost. http://www.pincho.com, 2014. [92] Korner H. Optimaler energieeinsatz in der chemischen industrie. Chem Ing Tech 1988;60:551e8.

BIBLIOGRAPHY March Linnhoff. Introduction to pinch technology, ©. 1998. Linnhoff March. Varbanov P, Klemes J, Shah RK, Shihn H. Power cycle integration and efficiency increase of molten carbonate fuel cell system. J Fuel Cell Sci Technol 2006;3(4):375e83. Gundersen Truls. A process integration primer, international energy agency. SINTEF Energy Res May 10, 2000. Industrial Heat Pumps for Steam and Fuel Savings e A Best Practices Steam Technical Brief. US department of energy e energy efficiency and renewable energy. Nov. 2005. www.eere.energy.gov. Ahmad S, Polley GT, Petela EA. Retrofit of heat exchanger networks subject to pressure drop constraints, Paper No. 34a, AIChE Spring Meeting, Houston, April 1989.

Chapter 17

Refrigeration Systems Refrigeration may be defined as the process by which heat energy is abstracted from a region of lower temperature and discarded/delivered to a region of relatively high temperature by expanding mechanical work. The term refrigeration implies the maintenance and production of temperature below that of the surroundings in a given space or substance. This is made possible by the absorption of heat at a low temperature level and release of the same at a high temperature level. The process is usually accomplished by evaporation of a liquid having low saturation temperature at the pressure of evaporation and returning the vapor to its original liquid state for re-evaporation to continue the process. The complete cycle comprises of four operational steps, namely: compression of the refrigerant, condensation of the vapor into liquid, expansion of the liquid, and finally, the evaporation of the liquid refrigerant. Process refrigeration is used at many different temperature levels to condense or cool gases, vapors, or liquids. Refrigeration is necessary when the process requires cooling to a temperature not reliably available from the usual water service or other coolant source, and includes JouleThompson, or polytropic expansion of natural gas or process system vapors. In general, auxiliary refrigeration is used for temperature requirements from 80e85
F (27e29
C) to as near absolute zero as the process demands. The usual petrochemical and chemical range does not go much below 200
F (129
C). Refrigeration systems are common in the natural gas processing industry, processes of petroleum refining, petrochemicals and chemical process industries in the manufacturing of synthetic rubber, textiles, plastics, etc. It also finds significant industrial applications in natural gas liquid (NGL) recovery, liquefied petroleum gas (LPG) recovery, hydrocarbon dew point control, reflux condensation for light hydrocarbon fractionators and liquefied natural gas (LNG) plants. The large-scale commercial application of refrigeration principles includes the liquefaction process for the production of pure gases such as oxygen (O2) and nitrogen (N2) from air. This section does not include low temperature air separation for oxygen, nitrogen, argon, etc. or the separation of process gases at liquid air temperatures. A valuable technical presentation about refrigeration is given in the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) handbook [1].

It is well known that the nature of heat flow is such that whenever a temperature difference exists between two regions, heat flows in the direction of decreasing temperature, i.e. from a higher temperature region to a lower temperature one, and that heat transfer occurs in nature without requiring any device. However, the reverse process cannot occur by itself. The transfer of heat from a low temperature medium (source) to a high temperature one (sink) requires some special devices called refrigerators. The mechanism of refrigeration employs a substance used as working fluid for carrying heat from the source to the sink. The fluid is referred to as a refrigerant. The efficiency of a refrigerator, as well as the economy of cold production in the small-scale or largescale application area, greatly depends on the thermophysical properties and the nature of the working fluid. Figure 17-1 shows a schematic of a refrigerator with its basic working principle as well as the direction of heat

Hot atmosphere

QH

Refrigerator

Wnet

QL

Refrigerated space

FIGURE 17-1 Schematic of a refrigerator.

Ludwig’s Applied Process Design for Chemical and Petrochemical Plants. http://dx.doi.org/10.1016/B978-0-7506-8524-5.00017-3 Copyright © 2015 Elsevier Inc. All rights reserved.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

transfer. Here, QL is the amount of heat released to the hot atmosphere at high temperature TH, and Wnet indicates the network input to the refrigerator. The heat pump (described in Chapter 16) is another device by which heat flows from a low temperature region to a high temperature one. Refrigerators and heat pumps are basically the same device but differ in their objectives, in that the high temperature output heat is desired for heating, and the low temperature input heat is desired for cooling. The objective of a refrigerator is to maintain the refrigerated space or region at low temperature by removing heat from it while discarding this heat to a high temperature region. The objective of a heat pump is to maintain the heated space (i.e. the region to be heated) at high temperature by delivering heat. From Figure 17-1, if QL is the amount of heat removed at the low temperature TL and QH is the amount of heat released at high temperature TH, then by the first law of thermodynamics the external work required for transferring the heat is: Wnet ¼ QH QL

(17-1)

The efficiency or performance capability of a refrigeration system is judged by the ratio between the refrigerating effects, or the amount of heat removed and the work required. This is expressed in terms of a suitable index known as the coefficient of performance, COPR. It is expressed as: COPR ¼

Heat removed Refrigerant effect or Work required Work input QL Q ¼ L ¼ QH QL Wnet

(17-2)

It is necessary to note that in most of the cases, the coefficient of performance (COP) of a refrigerator can be greater than 1.0, i.e. the amount of heat removed from the refrigerated space can be greater than the amount of work input and normally varies between 2 and 7.

CAPACITY OF REFRIGERATOR In order to express the cooling capacity of a refrigerating machine, i.e. the rate of heat removal from the refrigerated space, the common and standard unit used is a ton of refrigeration. The ton of refrigeration (Btu/unit time), also referred to as the refrigeration duty (or refrigeration capacity), is the total amount of heat absorbed in the chiller by the process. One ton of refrigeration is defined as a capacity to freeze one ton of water from 0
C (32
F) in 24 h. It is the withdrawal of heat at a rate of 200 Btu/min. The latent heat of ice is 144 Btu/lb. Ton of refrigeration ¼

2000 lb  144 Btu=lb ð24  60Þ

¼ 200 Btu=min:

In MKS units, it is defined to be equal to cooling at the rate of 72,000 kcal per 24 h. or 300 kcal per h., or 50 kcal per min. 1 ton of refrigeration ¼

72; 000 kcal ¼ 50 kcal=min: ð24  60Þ

¼ 200 Btu=min: ¼ 200  1:055 kJ=min ðsince 1 Btu ¼ 1:055 kJÞ 200  1:055 ¼ 3:517 kJ=s: 60 ¼ 3:517 kW:

¼

Selection of a refrigerant is dependent upon availability, economics, expenditure and temperature requirements. In some instances, in a natural gas processing plant, ethane (C2H6) and propane (C3H8) may be available, whereas in an olefins plant, ethylene (C2H4) and propylene (C3H6) are readily available. Propane and propylene may be unsuitable in an ammonia plant because of the risk of contamination, while ammonia may be suited for the purpose.

THE CARNOT REFRIGERATION CYCLE The Carnot cycle is a reversible cycle, implying that all processes that constitute the Carnot cycle as well as the direction of all heat and work interactions are reversible. Thus, a cycle that operates in the counterclockwise or reverse order on a T-S diagram is known as a reversed Carnot cycle. Figure 17-2 shows a schematic of a Carnot refrigerator. A reversed Carnot engine or Carnot refrigerator is a thermodynamically ideal isothermal-source refrigerator. The performance of all refrigeration systems is judged with respect to the Carnot refrigeration cycle working between the same limits of temperature. The ideal refrigerator consists of two reversible isothermal (constant temperature) processes, in which QL, the amount of heat is absorbed at the lower temperature TL, and heat QH is released at the higher temperature TH, and two reversible adiabatic/isentropic (constant entropy) processes. The steps in the operation of a Carnot refrigerator can be discussed with the help of T-S and P-V diagrams, illustrated in Figures 17-3A and B respectively. The processes involved in the Carnot refrigerator are as follows:

Process 1-2 e Reversible Isothermal Compression The working medium is compressed, while energy is released to the sink (high temperature region at TH) to maintain the refrigerant temperature at a constant level.

Refrigeration Systems Chapter | 17

QH

Warm environment at TH

1

2

Cooler

Compressor

Turbine

4

3

Evaporator

QL

Refrigerated space at TL

FIGURE 17-2 Schematic of Carnot refrigeration cycle.

(A)

(B) QL

T = Constant

2

1 S= Constant

S= Constant Wnet TL

Isothermal

1

2

3

Pressure (P)

Temperature (T)

TH

Adiabatic

4 T = Constant

QH

3

Isothermal

4

Heat removed Entropy (S)

Volume (V) P -V diagram of Carnot refrigeration cycle.

Legends 1-2: Isothermal compression with heat rejection 2-3: Adiabatic expansion 3-4: Isothermal expansion with heat absorption 4-1: Adiabatic compression T-S diagram of Carnot refrigeration cycle. FIGURE 17-3 T-S and P-V diagrams of Carnot refrigeration cycle.

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Process 2-3 e Reversible Adiabatic Expansion The working medium is expanded reversibly and adiabatically from the sink temperature TH to the source temperature TL.

Process 3-4 e Reversible Isothermal Expansion with Heat Absorption from the Low Temperature Source

l

l

Energy is transferred from the low temperature source (the region to be cooled) at TL to the refrigeration medium, while work is done by the medium to maintain the refrigerant at a constant temperature.

Process 4-1 e Reversible Adiabatic Compression

PERFORMANCE OF A CARNOT REFRIGERATOR For a Carnot refrigerator: Heat absorbed ¼ QH ¼ TH ðS2 S1 Þ

(17-3)

Hear removed ¼ QL ¼ TL ðS2 S1 Þ

(17-4)

Work done ¼ Wnet ¼ QH QL ¼ TH ðS2 S1 ÞTL ðS2 S1 Þ (17-5) refrigerator

QL QL ¼ Wnet QH QL TL ðS2 S1 Þ ¼ TH ðS2 S1 ÞTL ðS2 S1 Þ ¼

(17-6)

or QL TL ¼ Wnet TH TL The work done, Wnet is: Wnet ¼ QL




TH TL TL

(17-7)  (17-8)

Equation 17-8 is the minimum work required for conveying the heat QL from a low temperature TL to a high temperature TH. The characteristics of a Carnot refrigeration cycle can be summarized as follows: l

l

l

l

The refrigerant is then compressed reversibly and adiabatically (isentropically) from the source temperature to the sink temperature.

COP Carnot

l

No refrigeration cycle can have a higher COP than a reversible cycle operating between the same temperatures. The COP of a Carnot refrigeration cycle is a function only of the upper and lower temperatures of the cycle, and it is true that the reversed Carnot cycle is the

most efficient refrigeration cycle operating between these two specified temperature levels. Equation 17-6 indicates that the coefficient of performance of a reversed Carnot cycle increases as the difference between the upper and lower temperature decreases. The value of TL is more effective than that of TH on the COP of a cycle. The efficiency of a Carnot refrigeration cycle does not depend on the working fluid. It is impossible to construct refrigeration equipment, which can convey heat from a low temperature to a high temperature region, with a lower expenditure of work than that given by Equation 17-8. In practice, the COP of an actual refrigeration cycle is always less than that of an ideal one.

We can conclude that the Carnot cycle cannot be executed in actual devices as it is not a realistic model for the refrigeration cycle. However, it can be treated as a standard against which the actual refrigeration cycles are compared. Among the four reversible processes in a reversible Carnot cycle, the two isothermal heat transfer processes are easily achievable in practice. The processes, i.e. isothermal expansion with heat absorption and isothermal compression with heat rejection take place in the evaporator and the condenser respectively. These processes require infinite time, i.e. they have to be executed very slowly, for which significant heat transfer area is required. In spite of this, two isothermal processes are not difficult to achieve, but the processes of adiabatic compression and adiabatic expansion cannot be executed in a practical refrigeration cycle. These have some limitations as explained below [2].

Problems in Compression Firstly, the compression process in the reversible Carnot cycle involves the wet compression of the liquid-vapor mixture. In practice, when a reciprocating compressor is used, wet compression is not found suitable. After evaporation of refrigerant, it enters the compressor. Due to the appreciable speed of the compressor, the piston reciprocates so quickly that the vapor-bound liquid may remain in the cylinder, which may cause mechanical damage to the compressor valves and even to the cylinder. Secondly, the vapor-bound liquid droplets of refrigerant may wash away the lubricating oil in the compressor, which contributes to wear of the cylinder.

Problems in Expansion Process 2-3 represents the adiabatic expansion of liquid refrigerant with a high moisture content in a turbine. This process would be executed with infinite speed. However, such speed fluctuations in actual devices are not acceptable. It is impractical when expanding a liquid or very wet vapor against a

Refrigeration Systems Chapter | 17

For the freezer box: The coefficient of performance of the Carnot refrigerator obtained for the second case ¼ 3.54 The power consumption is:

fast-moving piston in a cylinder. This problem can be avoided if the turbine in a Carnot cycle is replaced by a throttle valve or a very long narrow-bore capillary tube, which maintains the necessary pressure drop from the condenser pressure to the evaporator pressure and maintains the required mass flow rate.

Hence, the increase in percentage of work input
 QL 0:209 QL ¼ 0:282 0:209Q  100 ¼ 34:9 per cent:

a. A 1 ton Carnot refrigerating machine is used to keep a refrigerated space at a temperature of 10
C, while the environment is at 45
C. Determine the power consumption of the machine. b. If the machine is used to maintain a freezer box at a temperature of 25
C while the temperature of environment is 45
C, then how much cooling effect could it produce? Assume that the power consumption in both cases is the same. Note: 1 ton of refrigeration ¼ 3.517 kW.

Wnet ¼

QL 1 ton 3:517 kW ¼ ¼ COP Carnot refrigerator 4:78 4:78

¼ 0:735 kW: b. Hence, TL ¼ 25
C ¼ 248 K and TH ¼ 45
C ¼ 318 K. The coefficient of performance of a Carnot refrigerating machine is given by: The coefficient of performance: TL 248 ¼ ¼ 3:54 COPCarnot refrigerator ¼ TH  TL ð318  248Þ Cooling effect produced, QL is:   QL ¼ ðWnet Þ COPCarnot refrigerator ¼ 0:735 kW x 3:54 ¼ 2:6 kW

Example 17-2

Assume that the Carnot refrigerating machine in Example 17-1 is of unknown capacity. Considering both paths (a) and (b), what is the increase in the percentage of work input required for the freezer box over the refrigerated space for the same extent of refrigerating effect? Solution For the refrigerated space: The coefficient of performance of the Carnot refrigerator for the first case is 4.78. The power consumption is: Wnet;1 ¼

QL QL ¼ 0:209 QL ¼ COPCarnot refrigerator 4:78

QL QL ¼ 0:282 QL ¼ COPCarnot refrigerator 3:54

Wnet; 2 ¼

Example 17-1

Solution a. The temperature at which heat is absorbed, TL ¼ 10
C ¼ 263 K The temperature at which heat is removed, TH ¼ 45
C ¼ 318 K The coefficient of performance, COPCarnot refrigerator ¼ ¼ THTL TL ¼ ð318263 263Þ ¼ 4:78 The power consumption of the refrigerating machine is:

627

L

The difficulties associated with the Carnot refrigeration cycle can be successfully eliminated by introducing the vapor-compression refrigeration cycle through the incorporation of two modifications: the complete evaporation of the working fluid before it enters the compressor and replacement of the turbine by a throttling device such as an expansion valve or capillary tube.

MECHANICAL REFRIGERATION The refrigeration effect is achieved by one of the following cycles: l l l

Vapor e compression e expansion. Absorption. Steam jet (water vapor compression).

These cycles can be further broken down into four distinct steps by means of the Pressure-Enthalpy (P-H) diagram as shown in Figure 17-4: l l l l

Expansion. Evaporation. Compression. Condensation.

Expansion Step This operation involves the proper functioning of an expansion valve or throttle valve. After condensation, the liquid refrigerant is stored in the liquid phase until needed. From liquid storage, liquid refrigerant enters the expansion valve where the pressure is required to be such to allow the liquid to vaporize at a temperature of about 10
C (263 K). The expansion valve serves the purpose of controlling the refrigerant flow and of dropping the refrigerant from condenser to evaporator conditions, both in temperature and pressure. The starting point in a refrigeration cycle is the availability of the liquid refrigerant. In Figure 17-4, point A represents the bubble point at its saturation pressure, PA and enthalpy hLA. In the expansion step, the pressure and temperature are reduced by flashing the liquid through a control valve to pressure PB. The lower pressure, PB is determined by the desired refrigerant temperature TB (point B). At point B,

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Compressor Bubble-point curve Condenser

SC Pressure P, psia

D

C

Dew-point curve Critical point

Evaporator

A

PA, PD

TA

D

D TA

TB

TD SD

TB =TC

PB, PC

C

B

TB A

B

Δh

hLA

hLB

Expansion valve

Qcd hVB

hVB

hVD

Enthalpy h, Btu/lb Process flow diagram

Pressure-enthalpy diagram

FIGURE 17-4 Process flow diagram and pressure-enthalpy diagram.

the enthalpy of the saturated liquid is hLB, while the corresponding saturated vapor enthalpy is hVB. Since the expansion step (AeB) occurs across the expansion valve and no energy has been exchanged, the process is considered to be isenthalpic (i.e. constant enthalpy). Therefore, the total stream enthalpy at the outlet of the valve is the same as the inlet, hLA. In Figure 17-4, point B is inside the envelope, where liquid and vapor coexist. Hence, to determine the amount of vapor formed in the expansion process [3], we proceed as follows. Let X be the fraction of liquid at pressure PB with an enthalpy hLB. Therefore, the fraction of the vapor formed during the expansion process with an enthalpy hVB is (1X). The heat balance equation, and the fraction of liquid formed are: ðXÞhLB þ ð1  XÞhVB ¼ hLA

(17-9)

X ¼

ðhVB  hLA Þ ðhVB  hLB Þ

(17-10)

ð1  XÞ ¼

ðhLA  hLB Þ ðhVB -hLB Þ

(17-11)

Evaporation Step The vapor formed in the expansion process (AeB) does not provide any refrigeration to the process. Heat is absorbed from the process by the evaporation of the liquid portion of the refrigerant. As shown in Figure 17-4, this is a constant temperature, constant pressure step (BeC). The enthalpy of the vapor at point C is hVB. The evaporation takes place in a heat exchanger known as an evaporator or a chiller.

The process refrigeration is provided by the cold liquid X, and its refrigerant effect is defined as follows: XðhVB  hLB Þ and substituting from Equation 17-11, the effect is: Effect ¼ hVB  hLA

(17-12)

The refrigerant flow rate is: m ¼

Qref ðhVB  hLA Þ

(17-13)

Compression Step This operational step employs a compressor. The function of the compressor is two-fold. The first is that of withdrawing the fluid from the evaporator at a rate that is sufficient to maintain the necessary reduced pressure and temperature in the evaporator. The other is that of compressing and delivering the fluid at a temperature which is adequately above that of the atmosphere or of the region or substance to which the fluid must next discard its load of energy. The refrigerant vapors leave the chiller at the saturation pressure Pc. The corresponding temperature equals TC at an enthalpy of hVB. The entropy at this point is SC. These vapors are compressed isentropically (i.e. constant entropy) to pressure PA along line C  D0 in Figure 17-4. The isentropic (ideal) work, Wi for compressing the refrigerant from PB to PA is: Wi ¼ mðh0 VD  hVB Þ 0

(17-14)

The quantity h VD is determined from refrigerant properties at PA and entropy of SC. Since the refrigerant is not an ideal fluid, and since the compressors for such services

Refrigeration Systems Chapter | 17

629

W ¼

Wi mðh0 VD  hVB Þ ¼ ¼ mðhVD  hVB Þ hi hi

(17-15)

The enthalpy at discharge is given by: hVD

ðh0 VD hVB Þ ¼ þ hVB hi

(17-16)

Pressure P, kPa

do not operate ideally, the isentropic efficiency hi is defined to compensate for the inefficiencies of the compression process. The actual work of compression, W can be determined from: P=C

3

1

4

P=C T=C

(17-17)

where 254.4 Btu/h ¼ 1 hp

2 S=C

H=C QL

The work of compression can also be expressed as: W GHP ¼ 254:4

QH

h3=h4 h1 Enthalpy h, kJ/kg

h2

FIGURE 17-5 P-H diagram of vapor-compression refrigeration cycle.

Condensation Step The high pressure refrigerant vapor enters the condenser, and heat is removed from it to change the superheated vapor to saturated or sub-cooled liquid. The superheated refrigerant leaving the compressor at PA and TD (point D in Figure 17-4) is cooled at a nearly constant pressure to the dew point temperature, TA, and refrigerant vapors begin to condense at a constant temperature. During the desuperheating and condensation process, all heat and work added to the refrigerant during the evaporation and compression processes must be removed so that the cycle can be completed by reaching Point A (the starting point) on the P-H diagram as shown in Figure 17-4. By adding the refrigeration duty to the heat of compression, the condensing duty, Qcd is: Qcd ¼ m½ðhVB  hLA Þ þ ðhVD  hVB Þ ¼ mðhVD  hLA Þ

(17-18)

Ws ¼ pdV

(17-20)

H ¼ U þ pV

(17-21)

and enthalpy:

Differentiating Equation 17-21 gives: dH ¼ dU þ pdV þ Vdp

Performance of Vapor-Compression Cycle Using Figure 17-5, the performance of the several phases of the cycle, both for the actual operation and for the ideal cycle per unit mass of the refrigerant vapor circulated in the system can be determined as follows: From the first law of thermodynamics: (17-19)

(17-22)

Rearranging Equation 17-22, gives: dU ¼ dH  pdV  vdp

(17-23)

Substituting Equations 17-20 and 17-23 into Equation 17-19 gives: dH  pdV  Vdp ¼ dq  pdV

The condensing pressure of the refrigerant is dependent on the cooling medium available such as air, cooling water or other refrigerant. The cooling medium is the heat sink for the refrigeration cycle. The compressor discharge vapor is superheated, thus the refrigerant condensing curve is not a straight line; it is a combination of desuperheating and constant temperature condensing. This should be taken into consideration for proper design of the condenser.

dU ¼ dq  Ws

where:

(17-24)

At constant pressure: dq ¼ dH

(17-25)

For the compressor: W ¼ ðh2  h1 Þ; kJ=kg for isentropic compression (17-26) For the condenser: QH ¼ ðh2  h3 Þ; kJ=kg

(17-27)

For the expansion valve: h3 ¼ h 4

(17-28)

QL ¼ ðh1  h4 Þ; kJ=kg

(17-29)

For the evaporator:

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

Refrigerating effect ¼ ðh1  h4 Þ; kJ=kg

(17-30)

COP vapor  compression cycle ¼

Refrigerating effect Q ¼ L Wnet Work input ¼

(17-31)

h 1  h4 h 2  h1

(17-31A)

If the total refrigerating effect capacity, i.e. the rate of heat removal from the low-temperature source is QoL , then the mass flow rate of the refrigerant mo required for circulation is determined by the following relationship: mo ¼

QoL Refrigerating capacity ¼ h1  h4 Refrigerating effect

(17-32)

For a 1 ton refrigerator, the rate of circulation in kg/h is: mo ¼

Solution i. The mass flow rate of the refrigerant is determined as:

(17-33)

QoL 10 ton ¼ ðh1  h4 Þ ð183:2  69:5Þ 10  3:516 113:7 ¼ 0:309 kg=s

¼

Example 17-3

A refrigerant using refrigerant R-12 as the working fluid operates on a vapor-compression cycle between 273 K and 313 K. Determine the following: i. The COP of the vapor-compression cycle. ii. The refrigerating effect. iii. The COP of an ideal Carnot refrigerator. iv. The work of compression. Given that: TL ¼ 273 K and TH ¼ 313 K Enthalpy of saturated vapor at 273 K, h1 ¼ 187 kJ/kg Enthalpy of saturated liquid at 313 K, h3 ¼ h4 ¼ 74 kJ/kg Enthalpy of superheated vapor at 273 K, h2 ¼ 204 kJ/kg. of

the

Refrigerating effect QL ¼ Wnet Work input h1  h4 ¼ h2  h1 187  74 ¼ ¼ 6:65 204  187

Wnet ¼

mo W hisentropic

For isentropic compression; W ¼ h2  h1 ; kJ=kg ¼ 208:3  183:2 ¼ 25:1 kJ=kg: hisentropic ¼ Isentropic efficiency of compression ¼ 0.8 Therefore, Wnet ¼ (0.309 x 25.1) / 0.8 ¼ 9.7 kW iii. The amount of heat rejected in the condenser is: QH ¼ QoL þ Wnet ¼ 10 ton þ 9:7 kW ¼ ð10 x 3:516Þ þ 9:7 ¼ 44:86 kW iv. The coefficient of performance compression cycle is:

(17-31)

of

the

vapor-

QL h1  h4 183:2  69:5 ¼ ¼ W h2  h1 208:3  183:2 ¼ 4:53

COPvaporcompression cycle ¼ (17-31A)

The coefficient of performance of the Carnot cycle is:

ii. The refrigerating effect can be obtained by: h1  h4 ¼ 187  74 ¼ 113 kJ/kg

COPCarnot

cycle

¼

TL 258 ¼ ¼ 4:69 TH  TL 313  258

Thus, the relative coefficient of performance is defined by:

iii. The COP of an ideal Carnot refrigerator is: The coefficient of performance, COPCarnot ¼ TH TL TL ¼ ð313273 273Þ ¼ 6:825

ii. The power consumption of the compressor is:

vapor-

COP vapor  compression cycle ¼

Avapor-compression refrigeration system using CFC 12 (Freon) rated at 10 tons is employed in a chemical manufacturing plant to maintain the temperature of the evaporator and condenser at 15
C and 40
C respectively. The isentropic efficiency of compressor is 80%. Determine the following: i. Mass flow rate of the refrigerant. ii. Power consumption of the compressor. iii. Amount of heat rejected in the condenser. iv. Difference in COP between vapor-compression and Carnot cycle. Enthalpy of saturated vapor at 258 K, h1 ¼ 183.2 kJ/kg Enthalpy of saturated liquid at 313 K, h3 ¼ h4 ¼ 69.5 kJ/kg Enthalpy of superheated vapor, h2 ¼ 208.3 kJ/kg.

mo ¼

12600 h1  h 4

Solution i. The coefficient of performance compression cycle is given by:

Example 17-4

refrigerator

iv. The work of compression is: h2  h1 ¼ 204  187 ¼ 17 kJ/kg

Actual coefficient of performance Theoretical coefficient of performance 4:53 ¼ 0:97 ¼ 4:69

COPrelative ¼

Refrigeration Systems Chapter | 17

TYPES OF REFRIGERATION SYSTEMS The three most used systems are as follows: Approx. Temperature Coolant Range,
F (
C)

System y







Refrigerant

Steam jet

35 to 70 F (1.7
to 21
C)

Water

Absorption Water-Lithium Bromide Ammonia

40
to 70
F (4.4
to 21
C) 40
to þ 30
F (40
to 1.1
C)

Lithium Bromide Solution (water*) Ammonia*water

Mechanical compression (Reciprocatingcentrifugal or rotary screw)

200
to þ40
F (129
to 4.4
C)

Ammonia, halogenated hydrocarbons, propane ethylene, and others

Plus: Cyrogenics

150
to 200
F (101
to 93
C)

Liquefaction of gases, and power/temperature recovery from natural gas

*refrigerant y Vacuum system, discussed in detail, Chapter 6, Vol. 1, 4th Ed., this text series.

The most common light hydrocarbon refrigerant cooling temperature ranges are (evaporation temperature): Methane 200
to 300
F (129
to 184
C) Ethylene and ethane 75
to 175
F (59
to 115
C) Propylene and propane þ40
to 50
F (4.4
to 46
C) Mehra [4e7] has developed a valuable series of working charts for the common industrial refrigerants along with application examples for ethylene, propylene, ethane and propane.

TERMINOLOGY Ton of refrigeration: The heat equivalent to melting 2,000 lb (one ton) of ice in 24 hours. One ton equals 12,000 Btu/h or 200 Btu/min. To be comparative, refrigeration equipment must have the refrigerant level (or evaporation temperature) specified.

SELECTION OF A REFRIGERATION SYSTEM FOR A GIVEN TEMPERATURE LEVEL AND HEAT LOAD In general, the simplest system is selected for any specific refrigeration requirement, because it should be the least expensive from first cost and operating cost viewpoints. Factors that are weighed in arriving at the process-directed refrigeration system, in addition to the purchase and operating costs:

631

1. Temperature Level of Evaporating Refrigerant Refrigerant temperatures greater than 32
F (0
C) suggest the steam jet or lithium bromide absorption system. Between 30
F and 40
F (1.1
C and 40
C), the ammonia-water absorption or a mechanical compression system is indicated. At less than 40
F (40
C), mechanical compression is used, except in special desiccant situations. The economics of temperature level selection will depend on utility (steam, power) costs at the point of installation and the type of payout required, because in some tonnage ranges, the various systems are competitive based on first costs. In most process systems, the evaporation of the refrigerant is carried out in shell and tube heat exchange equipment, and allowances must be made for a reasonable temperature approach between the process fluid which always leaves the evaporator at a higher temperature (by 3
e15
F) [16
to 9
C] than the refrigerant.

2. Suction of Absorbing Pressure of Refrigerant When the process circulating coolant and required refrigerant evaporator temperature level are established, the suction pressure to the compressor of a mechanical machine or the absorbing pressure of an absorption system is set. Keeping the low pressure point of the system at atmospheric pressure or above avoids air in-leakage that would later have to be purged. This is impossible for some systems; however, the issue is important and must be recognized, as explosive mixtures can be formed with some refrigerants. Moisture also enters the systems with air in-leakage.

3. Discharge or Condensing Pressure In mechanical systems, the temperature of the available water (or coolant) to condense the refrigerant from the compressor determines the pressure level of this part of the system. Generally speaking, it is less expensive to operate at as low a pressure level on the discharge as is consistent with the suction pressure and with the physical characteristics of the refrigerant. Sometimes the cost of the refrigerant and the cost of its replacement on loss dictate that the optimum situation is not determined by the system and refrigerant’s physical properties.

4. Refrigerant Characteristics Available refrigerants for various levels or conditions of operation may be toxic, flammable, irritating on exposure, hydroscopic and expensive. These characteristics cannot be ignored, as large systems contain large quantities of refrigerant, and a leak or other failure can cause a potentially serious condition in a building or process area.

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Ludwig’s Applied Process Design for Chemical and Petrochemical Plants

The thermodynamic properties of the refrigerant determine its suitability for a given condition of operation, particularly when compared with the same requirements or other refrigerants. The quantity of refrigerant needed for a particular level of evaporation is a function of its latent heat, except when using steam jet refrigeration, because the use of its chilled water involves only sensible heat transfer to process fluids.

5. System Maintenance The maintenance requirements for operation of the different types of refrigeration systems vary somewhat and should be evaluated along with the particular performance.

6. Evaporator and Condenser Pressures The operating pressure in the condenser should not be high. If it is, the materials used in the construction of evaporators and condensers should be good enough to withstand pressure, which in turn will result in high initial cost of the system. The evaporator pressure should preferably be positive, i.e. above atmosphere pressure, to prevent the leakage of air and moisture into the refrigeration system. Table 17-1 shows evaporator pressure at 15
C (258 K) and condenser pressure at 29
C (302 K) for several refrigerants [2]. Table 17-1 shows that carbon dioxide operates at extremely high pressure, thus requiring strong metal for compressors and piping vessels, while refrigerant 11 and refrigerant 113 operate below atmospheric pressures where some equipment is required to purge air from the system.

7. Freezing Point The freezing point of the refrigerant should be appreciably below the operating temperature of the system to avoid clogging the pipes. The freezing temperatures of important refrigerants are given in Table 17-2 [2].

TABLE 17-1 Evaporator and Condenser Pressures

Refrigerant

Evaporator Pressure at L15
C (kgf/cm2)

Condenser Pressure at 290
C (kgf/cm2)

Ammonia

2.34

11.5

Carbon dioxide

23.7

71.2

Refrigerant 11

0.2055

1.2855

Refrigerant 12

1.8

7.32

Refrigerant 22

3.03

12.26

Refrigerant 113

0.0704

0.5527

TABLE 17-2 Freezing Temperature of Refrigerants Refrigerant

Freezing Temperature in
C

Ammonia

77.8 (195.2 K)

Carbon dioxide

56.7 (216.3 K)

Refrigerant 11

111 (162.0 K)

Refrigerant 12

157.8 (115.2 K)

Refrigerant 22

160 (113.0 K)

Refrigerant 113

35 (238.0 K)

Water

0 (273.0 K)

8. Boiling Point The boiling point of a refrigerant should be appreciably lower than the temperature levels at which the refrigerator works, otherwise there is a chance of moisture and air leakage into the system.

9. Critical Temperature and Pressure A refrigerant should have a critical temperature and pressure well above the operating temperature and pressure of the system. If the system operates above the critical temperature, then the condensation of the gas becomes impossible after compression at high pressure.

10. Latent Heat Evaporation of the liquid is an important step in the refrigeration cycle, which produces cooling. Thus, the latent heat of refrigerant should be as large as possible. Also, the weight of the refrigerant to be circulated in the system will be less if its latent heat is high, thereby reducing the initial cost of the refrigerant. The size of the system will also be small, further reducing the initial cost.

11. Specific Volume The specific volume of the refrigerant vapor that a compressor is required to pump roughly determines the size of the compressor. For a reciprocating compressor, a low suction value of the volume pumped is normally desirable, allowing a small displacement. In case of centrifugal compressors, a high suction value of the volume is desired, where the efficiency of the compressor can be increased.

12. Coefficient of Performance The coefficient of performance is a factor of paramount importance in selecting a refrigerant. Table 17-3 shows the approximate COP of some refrigerants.

Refrigeration Systems Chapter | 17

TABLE 17-3 Coefficient of Performance of Refrigerants Refrigerant

Coefficient of Performance

Refrigerant 11

5.09

Refrigerant 133

4.92

Ammonia

4.76

Refrigerant 12

4.70

Refrigerant 22

4.66

Carbon dioxide

2.56

13. Flammability and Explosiveness A good refrigerant must be nonflammable and nonexplosive. In the refrigeration system, to avoid the danger of explosion or fire hazard during high compression, the refrigerants should not be flammable or explosive even when mixed with air/oil. Hydrocarbons such as propane, ethane and butane are highly flammable and explosive. Ammonia is explosive when mixed with air in concentrations of 16 to 25 per cent (ammonia) by volume. The halogenated hydrocarbons are considered to be nonflammable.

14. Corrosiveness This factor is very important while selecting a refrigerant. Certain metals are attacked by refrigerants. For example, ammonia reacts with copper, brass or other cuprous alloys in the presence of water. Therefore, in the ammonia system, iron and steel are commonly used. Halogenated hydrocarbons may react with zinc but not with copper, aluminum, iron and steel. The Freon group does not react with steel, copper, brass, zinc, tin or aluminum, but these chemicals are corrosive to magnesium and some other metals.

17. Ozone Depletion Potential (ODP) The ODP is an index by which the capability of a manmade synthetic chemical used as a refrigerant to deplete the ozone layer is measured. The halogenated refrigerants have ozone depletion potential, whereas the natural refrigerants (hydrocarbon, air, CO2, NH3 and water) do not. A good refrigerant should have no ozone depletion potential. Table 17-4 shows the ODP of some refrigerants.

18. Global Warning Potential (GWP) This is an index that indicates the ability of a gas to absorb infrared rays. The greenhouse gases such as CO2, SO2, CH4, perfluorocarbons, chlorofluorocarbons, hydrofluorocarbons and hydro chlorofluorocarbons are responsible for global warning. Therefore, the refrigerant should have low or negligible GWP, and Table 17-5 shows the GWP of some refrigerants.

TABLE 17-4 Ozone Depletion Potential of Some Common Refrigerants Refrigerants

Ozone Depletion Potential

Carbon dioxide (CO2)

0.0

Ammonia (NH3)

0.0

Propane (C3H8)

0.0

Chlorofluorocarbons, 12

0.82

Hydro-chlorofluorocarbons 22

0.055

Hydrofluorocarbons-134a

0.0

15. Leakage Tendency and Detectability The leakage and detectability of a refrigerant are an important factor to be considered, as leakage should be easily detectable to avoid the loss of refrigerant from the system. Ammonia leakage can be easily detected by its odor. Halogenated hydrocarbon refrigerants are odorless, so the leakage of such refrigerants cannot be easily detected. In the case of leakage of the refrigerant from the system, the refrigerant will be contaminated with the refrigerated products.

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TABLE 17-5 Ozone Depletion Potential of Some Common Refrigerants Refrigerants

Ozone Depletion Potential

Carbon dioxide (CO2)

1

Ammonia (NH3)