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Library of Congress Cataloging-in-Publication Data

Seader, J. D. Separation process principles : chemical and biochemical operations / J. D. Seader, Ernest J. Henley, D. Keith Roper.—3rd ed. p. cm. Includes bibliographical references and index. ISBN 978-0-470-48183-7 (hardback)

1. Separation (Technology)–Textbooks. I. Henley, Ernest J. II. Roper, D. Keith. III. Title. TP156.S45S364 2010 6600 .2842—dc22 2010028565

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

About the Authors

J. D. Seader is Professor Emeritus of Chemical Engi- neering at the University of Utah. He received B.S. and M.S. degrees from the University of California at Berke- ley and a Ph.D. from the University of Wisconsin- Madison. From 1952 to 1959, he worked for Chevron Research, where he designed petroleum and petro- chemical processes, and supervised engineering research, including the development of one of the first process simulation programs and the first widely used vapor- liquid equilibrium correlation. From 1959 to 1965, he supervised rocket engine research for the Rocketdyne Division of North American Aviation on all of the engines that took man to the moon. He served as a Pro- fessor of Chemical Engineering at the University of Utah for 37 years. He has authored or coauthored 112 technical articles, 9 books, and 4 patents, and also coau- thored the section on distillation in the 6th and 7th edi- tions of Perry’s Chemical Engineers’ Handbook. He was a founding member and trustee of CACHE for 33 years, serving as Executive Officer from 1980 to 1984. From 1975 to 1978, he served as Chairman of the Chemical Engineering Department at the University of Utah. For 12 years he served as an Associate Editor of the journal, Industrial and Engineering Chemistry Research. He served as a Director of AIChE from 1983 to 1985. In 1983, he presented the 35th Annual Institute Lecture of AIChE; in 1988 he received the Computing in Chemical Engineering Award of the CAST Division of AIChE; in 2004 he received the CACHE Award for Excellence in Chemical Engineering Education from the ASEE; and in 2004 he was a co-recipient, with Professor Warren D. Seider, of the Warren K. Lewis Award for Chemical Engineering Education of the AIChE. In 2008, as part of the AIChE Centennial Celebration, he was named one of 30 authors of groundbreaking chemical engineering books.

Ernest J. Henley is Professor of Chemical Engineering at the University of Houston. He received his B.S. degree from the University of Delaware and his Dr. Eng. Sci. from Columbia University, where he served as a professor from 1953 to 1959. He also has held professorships at the Stevens Institute of Technology, the University of Brazil, Stanford University, Cambridge University, and the City University of New York. He has authored or coauthored 72 technical articles and 12 books, the most recent one being Probabi- listic Risk Management for Scientists and Engineers. For

17 years, he was a trustee of CACHE, serving as President from 1975 to 1976 and directing the efforts that produced the seven-volume Computer Programs for Chemical Engineer- ing Education and the five-volume AIChE Modular Instruc- tion. An active consultant, he holds nine patents, and served on the Board of Directors of Maxxim Medical, Inc., Proce- dyne, Inc., Lasermedics, Inc., and Nanodyne, Inc. In 1998 he received the McGraw-Hill Company Award for ‘‘Outstand- ing Personal Achievement in Chemical Engineering,’’ and in 2002, he received the CACHE Award of the ASEE for ‘‘rec- ognition of his contribution to the use of computers in chemi- cal engineering education.’’ He is President of the Henley Foundation.

D. Keith Roper is the Charles W. Oxford Professor of Emerging Technologies in the Ralph E. Martin Depart- ment of Chemical Engineering and the Assistant Director of the Microelectronics-Photonics Graduate Program at the University of Arkansas. He received a B.S. degree (magna cum laude) from Brigham Young University in 1989 and a Ph.D. from the University of Wisconsin- Madison in 1994. From 1994 to 2001, he conducted research and development on recombinant proteins, microbial and viral vaccines, and DNA plasmid and viral gene vectors at Merck & Co. He developed processes for cell culture, fermentation, biorecovery, and analysis of polysaccharide, protein, DNA, and adenoviral-vectored antigens at Merck & Co. (West Point, PA); extraction of photodynamic cancer therapeutics at Frontier Scientific, Inc. (Logan, UT); and virus-binding methods for Milli- pore Corp (Billerica, MA). He holds adjunct appoint- ments in Chemical Engineering and Materials Science and Engineering at the University of Utah. He has auth- ored or coauthored more than 30 technical articles, one U.S. patent, and six U.S. patent applications. He was instrumental in developing one viral and three bacterial vaccine products, six process documents, and multiple bioprocess equipment designs. He holds memberships in Tau Beta Pi, ACS, ASEE, AIChE, and AVS. His current area of interest is interactions between electromagnetism and matter that produce surface waves for sensing, spectroscopy, microscopy, and imaging of chemical, bio- logical, and physical systems at nano scales. These surface waves generate important resonant phenomena in biosensing, diagnostics and therapeutics, as well as in designs for alternative energy, optoelectronics, and micro-electromechanical systems.

iii

Preface to the Third Edition

Separation Process Principles was first published in 1998 to provide a comprehensive treatment of the major separation operations in the chemical industry. Both equilibrium-stage and mass-transfer models were covered. Included also were chapters on thermodynamic and mass-transfer theory for sep- aration operations. In the second edition, published in 2006, the separation operations of ultrafiltration, microfiltration, leaching, crystallization, desublimation, evaporation, drying of solids, and simulated moving beds for adsorption were added. This third edition recognizes the growing interest of chemical engineers in the biochemical industry, and is renamed Separation Process Principles—Chemical and Bio- chemical Operations. In 2009, the National Research Council (NRC), at the re- quest of the National Institutes of Health (NIH), National Science Foundation (NSF), and the Department of Energy (DOE), released a report calling on the United States to launch a new multiagency, multiyear, multidisciplinary ini- tiative to capitalize on the extraordinary advances being made in the biological fields that could significantly help solve world problems in the energy, environmental, and health areas. To help provide instruction in the important bio- separations area, we have added a third author, D. Keith Roper, who has extensive industrial and academic experience in this area.

NEW TO THIS EDITION

Bioseparations are corollaries to many chemical engineering separations. Accordingly, the material on bioseparations has been added as new sections or chapters as follows:

 (^) Chapter 1: An introduction to bioseparations, including a description of a typical bioseparation process to illustrate its unique features.  (^) Chapter 2: Thermodynamic activity of biological species in aqueous solutions, including discussions of pH, ioniza- tion, ionic strength, buffers, biocolloids, hydrophobic interactions, and biomolecular reactions.  (^) Chapter 3: Molecular mass transfer in terms of driving forces in addition to concentration that are important in bioseparations, particularly for charged biological com- ponents. These driving forces are based on the Maxwell- Stefan equations.  (^) Chapter 8: Extraction of bioproducts, including solvent selection for organic-aqueous extraction, aqueous two- phase extraction, and bioextractions, particularly in Karr columns and Podbielniak centrifuges.

 (^) Chapter 14: Microfiltration is now included in Section 3 on transport, while ultrafiltration is covered in a new sec- tion on membranes in bioprocessing.  (^) Chapter 15: A revision of previous Sections 15.3 and 15. into three sections, with emphasis in new Sections 15. and 15.6 on bioseparations involving adsorption and chromatography. A new section on electrophoresis for separating charged particles such as nucleic acids and proteins is added.  (^) Chapter 17: Bioproduct crystallization.  (^) Chapter 18: Drying of bioproducts.  (^) Chapter 19: Mechanical Phase Separations. Because of the importance of phase separations in chemical and biochemical processes, we have also added this new chapter on mechanical phase separations cover- ing settling, filtration, and centrifugation, including mechanical separations in biotechnology and cell lysis. Other features new to this edition are:

 (^) Study questions at the end of each chapter to help the reader determine if important points of the chapter are understood.  (^) Boxes around important fundamental equations.  (^) Shading of examples so they can be easily found.  (^) Answers to selected exercises at the back of the book.  (^) Increased clarity of exposition: This third edition has been completely rewritten to enhance clarity. Sixty pages were eliminated from the second edition to make room for biomaterial and updates.  (^) More examples, exercises, and references: The second edition contained 214 examples, 649 homework exer- cises, and 839 references. This third edition contains 272 examples, 719 homework exercises, and more than 1, references.

SOFTWARE

Throughout the book, reference is made to a number of software products. The solution to many of the examples is facilitated by the use of spreadsheets with a Solver tool, Mathematica, MathCad, or Polymath. It is particu- larly important that students be able to use such pro- grams for solving nonlinear equations. They are all described at websites on the Internet. Frequent reference is also made to the use of process simulators, such as

v

ASPEN PLUS, ASPEN HYSYS.Plant, BATCHPLUS, CHEMCAD, PRO/II, SUPERPRO DESIGNER, and UNI- SIM. Not only are these simulators useful for designing separation equipment, but they also provide extensive physical property databases, with methods for computing thermodynamic properties of mixtures. Hopefully, those studying separations have access to such programs. Tuto- rials on the use of ASPEN PLUS and ASPEN HYSYS. Plant for making separation and thermodynamic-property calculations are provided in the Wiley multimedia guide, ‘‘Using Process Simulators in Chemical Engineering, 3rd Edition’’ by D. R. Lewin (see www.wiley.com/college/ lewin).

TOPICAL ORGANIZATION

This edition is divided into five parts. Part 1 consists of five chapters that present fundamental concepts applica- ble to all subsequent chapters. Chapter 1 introduces oper- ations used to separate chemical and biochemical mixtures in industrial applications. Chapter 2 reviews or- ganic and aqueous solution thermodynamics as applied to separation problems. Chapter 3 covers basic principles of diffusion and mass transfer for rate-based models. Use of phase equilibrium and mass-balance equations for single equilibrium-stage models is presented in Chapter 4, while Chapter 5 treats cascades of equilibrium stages and hyb- rid separation systems. The next three parts of the book are organized according to separation method. Part 2, consisting of Chapters 6 to 13, describes separations achieved by phase addition or creation. Chapters 6 through 8 cover absorption and stripping of dilute solutions, binary distillation, and ternary liquid–liquid extraction, with emphasis on graphical methods. Chapters 9 to 11 present computer-based methods widely used in pro- cess simulation programs for multicomponent, equilibrium- based models of vapor–liquid and liquid–liquid separations. Chapter 12 treats multicomponent, rate-based models, while Chapter 13 focuses on binary and multicomponent batch distillation. Part 3, consisting of Chapters 14 and 15, treats separa- tions using barriers and solid agents. These have found increasing applications in industrial and laboratory opera- tions, and are particularly important in bioseparations. Chapter 14 covers rate-based models for membrane sepa- rations, while Chapter 15 describes equilibrium-based and rate-based models of adsorption, ion exchange, and chro- matography, which use solid or solid-like sorbents, and electrophoresis. Separations involving a solid phase that undergoes a change in chemical composition are covered in Part 4, which consists of Chapters 16 to 18. Chapter 16 treats selective leaching of material from a solid into a liquid solvent. Crystallization from a liquid and desublimation from a vapor are discussed in Chapter 17, which also includes evaporation. Chapter 18 is concerned with the drying of solids and includes a section on psychrometry.

Part 5 consists of Chapter 19, which covers the mec- hanical separation of phases for chemical and biochemical processes by settling, filtration, centrifugation, and cell lysis. Chapters 6, 7, 8, 14, 15, 16, 17, 18, and 19 begin with a detailed description of an industrial application to famil- iarize the student with industrial equipment and practices. Where appropriate, theory is accompanied by appropriate historical content. These descriptions need not be pre- sented in class, but may be read by students for orienta- tion. In some cases, they are best understood after the chapter is completed.

HELPFUL WEBSITES

Throughout the book, websites that present useful, sup- plemental material are cited. Students and instructors are encouraged to use search engines, such as Google or Bing, to locate additional information on old or new dev- elopments. Consider two examples: (1) McCabe–Thiele diagrams, which were presented 80 years ago and are cov- ered in Chapter 7; (2) bioseparations. A Bing search on the former lists more than 1,000 websites, and a Bing search on the latter lists 40,000 English websites. Some of the terms used in the bioseparation sections of the book may not be familiar. When this is the case, a Google search may find a definition of the term. Alternatively, the ‘‘Glossary of Science Terms’’ on this book’s website or the ‘‘Glossary of Biological Terms’’ at the website: www .phschool.com/science/biology_place/glossary/a.html may be consulted. Other websites that have proven useful to our students include:

(1) www.chemspy.com—Finds terms, definitions, syno- nyms, acronyms, and abbreviations; and provides links to tutorials and the latest news in biotechnology, the chemical industry, chemistry, and the oil and gas industry. It also assists in finding safety information, scientific publications, and worldwide patents. (2) webbook.nist.gov/chemistry—Contains thermo- chemical data for more than 7,000 compounds and thermophysical data for 75 fluids. (3) www. ddbst.com—Provides information on the com- prehensive Dortmund Data Bank (DDB) of thermo- dynamic properties. (4) www.chemistry.about.com/od/chemicalengineerin1/ index.htm—Includes articles and links to many web- sites concerning topics in chemical engineering. (5) www.matche.com—Provides capital cost data for many types of chemical processing (6) www.howstuffworks.com—Provides sources of easy- to-understand explanations of how thousands of things work.

vi Preface to the Third Edition

Although Chapter 4 is included in some of the outlines, much of the material may be omitted if single equilibrium- stage calculations are adequately covered in sophomore courses on mass and energy balances, using books like ‘‘Ele- mentary Principles of Chemical Processes’’ by R.M. Felder and R.W. Rousseau or ‘‘Basic Principles and Calculations in Chemical Engineering’’ by D.M. Himmelblau and J.B. Riggs. Considerable material is presented in Chapters 6, 7, and 8 on well-established graphical methods for equilibrium-stage calculations. Instructors who are well familiar with process simulators may wish to pass quickly through these chapters and emphasize the algorithmic methods used in process simu- lators, as discussed in Chapters 9 to 13. However, as reported by P.M. Mathias in the December 2009 issue of Chemical Engineering Progress, the visual approach of graphical meth- ods continues to provide the best teaching tool for developing insight and understanding of equilibrium-stage operations. As a further guide, particularly for those instructors teach- ing an undergraduate course on separations for the first time or using this book for the first time, we have designated in the Table of Contents, with the following symbols, whether a section (§) in a chapter is:  (^) Important for a basic understanding of separations and

therefore recommended for presentation in class, unless alr- eady covered in a previous course. O (^) Optional because the material is descriptive, is covered

in a previous course, or can be read outside of class with little or no discussion in class.  (^) Advanced material, which may not be suitable for an

undergraduate course unless students are familiar with a pro- cess simulator and have access to it. B (^) A topic in bioseparations.

A number of chapters in this book are also suitable for a graduate course in separations. The following is a suggested course outline for a graduate course:

GRADUATE COURSE ON SEPARATIONS

2–3 Credit Hours: Chapters 10, 11, 12, 13, 14, 15, 17

ACKNOWLEDGMENTS

The following instructors provided valuable comments and suggestions in the preparation of the first two editions of this book:

Richard G. Akins, Kansas State University Paul Bienkowski, University of Tennessee C. P. Chen, University of Alabama in Huntsville

William A. Heenan, Texas A&M University– Kingsville Richard L. Long, New Mexico State University Jerry Meldon, Tufts University

William L. Conger, Virginia Polytechnic Institute and State University Kenneth Cox, Rice University R. Bruce Eldridge, University of Texas at Austin Rafiqul Gani, Institut for Kemiteknik Ram B. Gupta, Auburn University Shamsuddin Ilias, North Carolina A&T State University Kenneth R. Jolls, Iowa State University of Science and Technology Alan M. Lane, University of Alabama

John Oscarson, Brigham Young University Timothy D. Placek, Tufts University Randel M. Price, Christian Brothers University Michael E. Prudich, Ohio University Daniel E. Rosner, Yale University Ralph Schefflan, Stevens Institute of Technology Ross Taylor, Clarkson University Vincent Van Brunt, University of South Carolina

The preparation of this third edition was greatly aided by the following group of reviewers, who provided many excel- lent suggestions for improving added material, particularly that on bioseparations. We are very grateful to the following Professors:

Robert Beitle, University of Arkansas

Joerg Lahann, University of Michigan Rafael Chavez-Contreras, University of Wisconsin- Madison Theresa Good, University of Maryland, Baltimore County Ram B. Gupta, Auburn University Brian G. Lefebvre, Rowan University

Sankar Nair, Georgia Institute of Technology Amyn S. Teja, Georgia Institute of Technology W. Vincent Wilding, Brigham Young University

Paul Barringer of Barringer Associates provided valuable guidance for Chapter 19. Lauren Read of the University of Utah provided valuable perspectives on some of the new mat- erial from a student’s perspective.

J. D. Seader Ernest J. Henley D. Keith Roper

viii Preface to the Third Edition

Brief Contents

PART 1—FUNDAMENTAL CONCEPTS

Chapter 1 Separation Processes 2

Chapter 2 Thermodynamics of Separation Processes 35

Chapter 3 Mass Transfer and Diffusion 85

Chapter 4 Single Equilibrium Stages and Flash Calculations 139

Chapter 5 Cascades and Hybrid Systems 180

PART 2—SEPARATIONS BY PHASE ADDITION OR CREATION

Chapter 6 Absorption and Stripping of Dilute Mixtures 206

Chapter 7 Distillation of Binary Mixtures 258

Chapter 8 Liquid–Liquid Extraction with Ternary Systems 299

Chapter 9 Approximate Methods for Multicomponent, Multistage Separations 359

Chapter 10 Equilibrium-Based Methods for Multicomponent Absorption, Stripping, Distillation, and Extraction 378

Chapter 11 Enhanced Distillation and Supercritical Extraction 413

Chapter 12 Rate-Based Models for Vapor–Liquid Separation Operations 457

Chapter 13 Batch Distillation 473

PART 3—SEPARATIONS BY BARRIERS AND SOLID AGENTS

Chapter 14 Membrane Separations 500

Chapter 15 Adsorption, Ion Exchange, Chromatography, and Electrophoresis 568

PART 4—SEPARATIONS THAT INVOLVE A SOLID PHASE

Chapter 16 Leaching and Washing 650

Chapter 17 Crystallization, Desublimation, and Evaporation 670

Chapter 18 Drying of Solids 726

PART 5—MECHANICAL SEPARATION OF PHASES

Chapter 19 Mechanical Phase Separations 778

ix

Contents

About the Authors iii

Preface v

Nomenclature xv

Dimensions and Units xxiii

PART 1

FUNDAMENTAL CONCEPTS

1. Separation Processes 2 1.0
   ^ Instructional Objectives 2 1.1
   ^ Industrial Chemical Processes 2 1.2
   ^ Basic Separation Techniques 5 1.3 O^ Separations by Phase Addition or Creation 7 1.4 O^ Separations by Barriers 11 1.5 O^ Separations by Solid Agents 13 1.6 O^ Separations by External Field or Gradient 14 1.7
   ^ Component Recoveries and Product Purities 14 1.8
   ^ Separation Factor 18 1.9 B^ Introduction to Bioseparations 19 1.10
   ^ Selection of Feasible Separations 27 Summary, References, Study Questions, Exercises
2. Thermodynamics of Separation Operations 35 2.0
   ^ Instructional Objectives 35 2.1
   ^ Energy, Entropy, and Availability Balances 35 2.2
   ^ Phase Equilibria 38 2.3 O^ Ideal-Gas, Ideal-Liquid-Solution Model 41 2.4 O^ Graphical Correlations of Thermodynamic Properties 44 2.5 O^ Nonideal Thermodynamic Property Models 45 2.6 O^ Liquid Activity-Coefficient Models 52 2.7 O^ Difficult Mixtures 62 2.8
   ^ Selecting an Appropriate Model 63 2.9 B^ Thermodynamic Activity of Biological Species 64 Summary, References, Study Questions, Exercises
3. Mass Transfer and Diffusion 85 3.0
   ^ Instructional Objectives 85

3.1
^ Steady-State, Ordinary Molecular Diffusion 86 3.2
^ Diffusion Coefficients (Diffusivities) 90 3.3
^ Steady- and Unsteady-State Mass Transfer Through Stationary Media 101 3.4
^ Mass Transfer in Laminar Flow 106 3.5
^ Mass Transfer in Turbulent Flow 113 3.6
^ Models for Mass Transfer in Fluids with a Fluid–Fluid Interface 119 3.7
^ Two-Film Theory and Overall Mass-Transfer Coefficients 123 3.8B^ Molecular Mass Transfer in Terms of Other Driving Forces 127 Summary, References, Study Questions, Exercises

4. Single Equilibrium Stages and Flash Calculations 139 4.0
   ^ Instructional Objectives 139 4.1
   ^ Gibbs Phase Rule and Degrees of Freedom 139 4.2
   ^ Binary Vapor–Liquid Systems 141 4.3
   ^ Binary Azeotropic Systems 144 4.4
   ^ Multicomponent Flash, Bubble-Point, and Dew-Point Calculations 146 4.5
   ^ Ternary Liquid–Liquid Systems 151 4.6O^ Multicomponent Liquid–Liquid Systems 157 4.7
   ^ Solid–Liquid Systems 158 4.8
   ^ Gas–Liquid Systems 163 4.9
   ^ Gas–Solid Systems 165 4.10^ Multiphase Systems 166 Summary, References, Study Questions, Exercises
5. Cascades and Hybrid Systems 180 5.0
   ^ Instructional Objectives 180 5.1
   ^ Cascade Configurations 180 5.2O^ Solid–Liquid Cascades 181 5.3
   ^ Single-Section Extraction Cascades 183 5.4
   ^ Multicomponent Vapor–Liquid Cascades 185 5.5O^ Membrane Cascades 189 5.6O^ Hybrid Systems 190

xi

5.7
^ Degrees of Freedom and Specifications for Cascades 191 Summary, References, Study Questions, Exercises

PART 2

SEPARATIONS BY PHASE ADDITION OR

CREATION

6. Absorption and Stripping of Dilute Mixtures 206 6.0
   ^ Instructional Objectives 206 6.1O^ Equipment for Vapor–Liquid Separations 207 6.2O^ General Design Considerations 213 6.3
   ^ Graphical Method for Trayed Towers 213 6.4
   ^ Algebraic Method for Determining N 217 6.5O^ Stage Efficiency and Column Height for Trayed Columns 218 6.6O^ Flooding, Column Diameter, Pressure Drop, and Mass Transfer for Trayed Columns 225 6.7
   ^ Rate-Based Method for Packed Columns 232 6.8O^ Packed-Column Liquid Holdup, Diameter, Flooding, Pressure Drop, and Mass-Transfer Efficiency 236 6.9^ Concentrated Solutions in Packed Columns 248 Summary, References, Study Questions, Exercises
7. Distillation of Binary Mixtures 258 7.0
   ^ Instructional Objectives 258 7.1O^ Equipment and Design Considerations 259 7.2
   ^ McCabe–Thiele Graphical Method for Trayed Towers 261 7.3O^ Extensions of the McCabe–Thiele Method 270 7.4O^ Estimation of Stage Efficiency for Distillation 279 7.5O^ Column and Reflux-Drum Diameters 283 7.6
   ^ Rate-Based Method for Packed Distillation Columns 284 7.7O^ Introduction to the Ponchon–Savarit Graphical Equilibrium-Stage Method for Trayed Towers 286 Summary, References, Study Questions, Exercises
8. Liquid–Liquid Extraction with Ternary Systems 299 8.0
   ^ Instructional Objectives 299 8.1O^ Equipment for Solvent Extraction 302

8.2 O^ General Design Considerations 308 8.3
^ Hunter–Nash Graphical Equilibrium-Stage Method 312 8.4 O^ Maloney–Schubert Graphical Equilibrium-Stage Method 325 8.5 O^ Theory and Scale-up of Extractor Performance 328 8.6 B^ Extraction of Bioproducts 340 Summary, References, Study Questions, Exercises

9. Approximate Methods for Multicomponent, Multistage Separations 359 9.0
   ^ Instructional Objectives 359 9.1
   ^ Fenske–Underwood–Gilliland (FUG) Method 359 9.2
   ^ Kremser Group Method 371 Summary, References, Study Questions, Exercises
10. Equilibrium-Based Methods for Multicomponent Absorption, Stripping, Distillation, and Extraction 378 10.0^ Instructional Objectives 378 10.1^ Theoretical Model for an Equilibrium Stage 378 10.2^ Strategy of Mathematical Solution 380 10.3^ Equation-Tearing Procedures 381 10.4^ Newton–Raphson (NR) Method 393 10.5^ Inside-Out Method 400 Summary, References, Study Questions, Exercises
11. Enhanced Distillation and Supercritical Extraction 413 11.0
    ^ Instructional Objectives 413 11.1
    ^ Use of Triangular Graphs 414 11.2
    ^ Extractive Distillation 424 11.3^ Salt Distillation 428 11.4^ Pressure-Swing Distillation 429 11.5^ Homogeneous Azeotropic Distillation 432 11.6
    ^ Heterogeneous Azeotropic Distillation 435 11.7^ Reactive Distillation 442 11.8^ Supercritical-Fluid Extraction 447 Summary, References, Study Questions, Exercises
12. Rate-Based Models for Vapor–Liquid Separation Operations 457 12.0^ Instructional Objectives 457 12.1^ Rate-Based Model 459 12.2^ Thermodynamic Properties and Transport-Rate Expressions 461

xii Contents

19.3
^ Design of Particle Separators 789 19.4
^ Design of Solid–Liquid Cake-Filtration Devices Based on Pressure Gradients 795 19.5
^ Centrifuge Devices for Solid–Liquid Separations 800 19.6
^ Wash Cycles 802

19.7 B^ Mechanical Separations in Biotechnology 804 Summary, References, Study Questions, Exercises

Answers to Selected Exercises 814 Index 817

(^) Suitable for an UG course o (^) Optional  (^) Advanced B (^) Bioseparations

xiv Contents

Nomenclature

All symbols are defined in the text when they are first used. Symbols that appear infrequently are not listed here.

Latin Capital and Lowercase Letters

A area; absorption factor ¼ L/KV; Hamaker constant

A (^) M membrane surface area

a activity; interfacial area per unit volume; molecular radius

ay surface area per unit volume

B bottoms flow rate

B^0 rate of nucleation per unit volume of solution

b molar availability function ¼ h – T 0 s; component flow rate in bottoms

C general composition variable such as concen- tration, mass fraction, mole fraction, or vol- ume fraction; number of components; rate of production of crystals

C (^) D drag coefficient

C (^) F entrainment flooding factor

C (^) P specific heat at constant pressure

C oP (^) V ideal-gas heat capacity at constant pressure

c molar concentration; speed of light

c liquid concentration in equilibrium with gas at its bulk partial pressure

c^0 concentration in liquid adjacent to a membrane surface

c (^) b volume averaged stationary phase solute concentration in (15-149)

c (^) d diluent volume per solvent volume in (17-89)

c (^) f bulk fluid phase solute concentration in (15-48)

c (^) m metastable limiting solubility of crystals

c (^) o speed of light in a vacuum

c (^) p solute concentration on solid pore surfaces of stationary phase in (15-48) c (^) s humid heat; normal solubility of crystals; solute concentration on solid pore surfaces of stationary phase in (15-48); solute saturation concentration on the solubility curve in (17-82)

c s^ concentration of crystallization-promoting additive in (17-101)

c (^) t total molar concentration

Dclimit limiting supersaturation

D, D diffusivity; distillate flow rate; diameter

D ij^0 multicomponent mass diffusivity DB bubble diameter DE eddy-diffusion coefficient Deff effective diffusivity Di impeller diameter Dij mutual diffusion coefficient of i in j DK Knudsen diffusivity DL longitudinal eddy diffusivity D^ N arithmetic-mean diameter DP particle diameter D^ p average of apertures of two successive screen sizes DS surface diffusivity Ds shear-induced hydrodynamic diffusivity in (14-124) D^ S surface (Sauter) mean diameter DT tower or vessel diameter D^ V volume-mean diameter D^ W mass-mean diameter d component flow rate in distillate d (^) e equivalent drop diameter; pore diameter d (^) H hydraulic diameter ¼ 4 r (^) H d (^) i driving force for molecular mass transfer d (^) m molecule diameter d (^) p droplet or particle diameter; pore diameter dys Sauter mean diameter E activation energy; extraction factor; amount or flow rate of extract; turbulent-diffusion coefficient; voltage; evaporation rate; convec- tive axial-dispersion coefficient E^0 standard electrical potential E (^) b radiant energy emitted by a blackbody E (^) MD fractional Murphree dispersed-phase efficiency E (^) MV fractional Murphree vapor efficiency E (^) OV fractional Murphree vapor-point efficiency E (^) o fractional overall stage (tray) efficiency DEvap^ molar internal energy of vaporization e entrainment rate; charge on an electron F, = Faraday’s contant ¼ 96,490 coulomb/ g-equivalent; feed flow rate; force F (^) d drag force f pure-component fugacity; Fanning friction factor; function; component flow rate in feed

xv

LES length of equilibrium (spent) section of adsorption bed

LUB length of unused bed in adsorption

l (^) M membrane thickness

l (^) T packed height

M molecular weight

M (^) i moles of i in batch still

M (^) T mass of crystals per unit volume of magma

M (^) t total mass

m slope of equilibrium curve; mass flow rate; mass; molality

m (^) c mass of crystals per unit volume of mother liquor; mass in filter cake

m  (^) i molality of i in solution

m (^) s mass of solid on a dry basis; solids flow rate

my mass evaporated; rate of evaporation

MTZ length of mass-transfer zone in adsorption bed

N number of phases; number of moles; molar flux ¼ n=A; number of equilibrium (theoreti- cal, perfect) stages; rate of rotation; number of transfer units; number of crystals/unit volume in (17-82)

N (^) A Avogadro’s number ¼ 6.022  10 23 molecules/mol

N (^) a number of actual trays

NBi Biot number for heat transfer

NBiM Biot number for mass transfer

N (^) D number of degrees of freedom

NEo Eotvos number

NFo Fourier number for heat transfer ¼ at=a^2 ¼ dimensionless time

NFoM Fourier number for mass transfer ¼ Dt=a^2 ¼ dimensionless time

NFr Froude number ¼ inertial force/gravitational force

N (^) G number of gas-phase transfer units

N (^) L number of liquid-phase transfer units

NLe Lewis number ¼ NSc=NPr

NLu Luikov number ¼ 1 =NLe

Nmin mininum number of stages for specified split NNu Nusselt number ¼ dh=k ¼ temperature gradi- ent at wall or interface/temperature gradient across fluid (d ¼ characteristic length)

N (^) OG number of overall gas-phase transfer units

N (^) OL number of overall liquid-phase transfer units

NPe Peclet number for heat transfer ¼ NReNPr ¼ convective transport to molecular transfer

NPe (^) M Peclet number for mass transfer ¼ N (^) ReN (^) Sc ¼ convective transport to molecular transfer

NPo Power number

NPr Prandtl number ¼ C (^) Pm=k ¼ momentum diffusivity/thermal diffusivity

NRe Reynolds number ¼ dur=m ¼ inertial force/ viscous force (d ¼ characteristic length) NSc Schmidt number ¼ m=r D ¼ momentum diffusivity/mass diffusivity NSh Sherwood number ¼ dkc=D ¼ concentration gradient at wall or interface/concentration gra- dient across fluid (d ¼ characteristic length) NSt Stanton number for heat transfer ¼ h=GC (^) P NStM Stanton number for mass transfer ¼ kcr=G NTU number of transfer units N (^) t number of equilibrium (theoretical) stages NWe Weber number ¼ inertial force/surface force N number of moles n molar flow rate; moles; crystal population density distribution function in (17-90) P pressure; power; electrical power P (^) c critical pressure P (^) i molecular volume of component i/molecular volume of solvent P (^) M permeability P^  (^) M permeance P (^) r reduced pressure, P=P (^) c P s^ vapor pressure p partial pressure p partial pressure in equilibrium with liquid at its bulk concentration pH ¼  log (aHþ) pI isoelectric point (pH at which net charge is zero) pK (^) a ¼  log (Ka) Q rate of heat transfer; volume of liquid; volumetric flow rate Q (^) C rate of heat transfer from condenser Q (^) L volumetric liquid flow rate Q (^) ML volumetric flow rate of mother liquor Q (^) R rate of heat transfer to reboiler q heat flux; loading or concentration of adsorb- ate on adsorbent; feed condition in distillation defined as the ratio of increase in liquid molar flow rate across feed stage to molar feed rate; charge R universal gas constant; raffinate flow rate; resolution; characteristic membrane resist- ance; membrane rejection coefficient, retention coefficient, or solute reflection coefficient; chromatographic resolution R (^) i membrane rejection factor for solute i Rmin minimum reflux ratio for specified split R (^) p particle radius r radius; ratio of permeate to feed pressure for a membrane; distance in direction of diffusion; reaction rate; molar rate of mass transfer per

Nomenclature xvii

unit volume of packed bed; separation distance between atoms, colloids, etc. r (^) c radius at reaction interface

r (^) H hydraulic radius ¼ flow cross section/wetted perimeter

S entropy; solubility; cross-sectional area for flow; solvent flow rate; mass of adsorbent; stripping factor ¼ KV=L; surface area; Svedberg unit, a unit of centrifugation; solute sieving coefficient in (14-109); Siemen (a unit of measured conductivity equal to a reciprocal ohm)

S (^) o partial solubility

S (^) T total solubility

s molar entropy; relative supersaturation; sedimentation coefficient; square root of chromatographic variance in (15-56)

s (^) p particle external surface area

T temperature

T (^) c critical temperature

T 0 datum temperature for enthalpy; reference tem- perature; infinite source or sink temperature T (^) r reduced temperature ¼ T=Tc

Ts source or sink temperature

Ty moisture-evaporation temperature

t time; residence time t average residence time

tres residence time

U overall heat-transfer coefficient; liquid side- stream molar flow rate; internal energy; fluid mass flowrate in steady counterflow in (15-71)

u velocity; interstitial velocity

u bulk-average velocity; flow-average velocity

u (^) L superficial liquid velocity

u (^) mf minimum fluidization velocity

u (^) s superficial velocity after (15-149)

u (^) t average axial feed velocity in (14-122)

V vapor; volume; vapor flow rate

V^0 vapor molar flow rate in an intermediate sec- tion of a column; solute-free molar vapor rate

V (^) B boilup ratio

V (^) V volume of a vessel V^  vapor molar flow rate in stripping section

V^  (^) i partial molar volume of species i

V^ ^ (^) i partial specific volume of species i

V (^) max maximum cumulative volumetric capacity of a dead-end filter

y molar volume; velocity; component flow rate in vapor

y  average molecule velocity

yi species velocity relative to stationary coordinates

yi (^) D species diffusion velocity relative to the molar-average velocity of the mixture yc critical molar volume yH humid volume yM molar-average velocity of a mixture yr reduced molar volume, v=v (^) c y 0 superficial velocity W rate of work; moles of liquid in a batch still; moisture content on a wet basis; vapor sidestream molar flow rate; mass of dry filter cake/filter area W (^) D potential energy of interaction due to London dispersion forces Wmin minimum work of separation WES weight of equilibrium (spent) section of adsorption bed WUB weight of unused adsorption bed W (^) s rate of shaft work w mass fraction X mole or mass ratio; mass ratio of soluble mate- rial to solvent in underflow; moisture content on a dry basis X* equilibrium-moisture content on a dry basis X (^) B bound-moisture content on a dry basis X (^) c critical free-moisture content on a dry basis X (^) T total-moisture content on a dry basis X (^) i mass of solute per volume of solid x mole fraction in liquid phase; mass fraction in raffinate; mass fraction in underflow; mass fraction of particles; ion concentration x^0 normalized mole fraction ¼ xi=

XN

j¼ 1

xj

Y mole or mass ratio; mass ratio of soluble mate- rial to solvent in overflow y mole fraction in vapor phase; mass fraction in extract; mass fraction in overflow Z compressibility factor ¼ Py=RT; height z mole fraction in any phase; overall mole frac- tion in combined phases; distance; overall mole fraction in feed; charge; ionic charge

Greek Letters a thermal diffusivity, k=rCP; relative volatility; average specific filter cake resistance; solute partition factor between bulk fluid and stationary phases in (15-51) a* ideal separation factor for a membrane aij relative volatility of component i with respect to component j for vapor–liquid equilibria; parameter in NRTL equation aT thermal diffusion factor bij relative selectivity of component i with respect to component j for liquid–liquid

xviii Nomenclature