Separation Process Principles: Chemical and Biochemical Operations - 3rd Edition

Separation Process Principles Chemical and Biochemical Operations Seader Henley Roper 3rd Edition This page intentionally left blank FFIRS 09162010 84825 Page 1 SEPARATION PROCESS PRINCIPLES Chemical and Biochemical Operations THIRD EDITION J D Seader Department of Chemical Engineering University of Utah Ernest J Henley Department of Chemical Engineering University of Houston D Keith Roper Ralph E Martin Department of Chemical Engineering University of Arkansas John Wiley Sons Inc FFIRS 09162010 84825 Page 2 Vice President and Executive Publisher Don Fowley Acquisitions Editor Jennifer Welter Developmental Editor Debra Matteson Editorial Assistant Alexandra Spicehandler Marketing Manager Christopher Ruel Senior Production Manager Janis Soo Assistant Production Editor Annabelle AngBok Designer RDC Publishing Group Sdn Bhd This book was set in 1012 Times Roman by Thomson Digital and printed and bound by Courier Westford The cover was printed by Courier Westford This book is printed on 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contact your local representative Library of Congress CataloginginPublication Data Seader J D Separation process principles chemical and biochemical operations J D Seader Ernest J Henley D Keith Roper3rd ed p cm Includes bibliographical references and index ISBN 9780470481837 hardback 1 Separation TechnologyTextbooks I Henley Ernest J II Roper D Keith III Title TP156S45S364 2010 660 0 2842dc22 2010028565 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 FBETW 09302010 Page 3 About the Authors J D Seader is Professor Emeritus of Chemical Engi neering at the University of Utah He received BS and MS degrees from the University of California at Berke ley and a PhD 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 Perrys 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 corecipient 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 BS 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 sevenvolume Computer Programs for Chemical Engineer ing Education and the fivevolume 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 McGrawHill 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 MicroelectronicsPhotonics Graduate Program at the University of Arkansas He received a BS degree magna cum laude from Brigham Young University in 1989 and a PhD 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 adenoviralvectored antigens at Merck Co West Point PA extraction of photodynamic cancer therapeutics at Frontier Scientific Inc Logan UT and virusbinding 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 US patent and six US 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 microelectromechanical systems iii This page intentionally left blank Separation Process Principles was first published in 1998 to provide a comprehensive treatment of the major separation operations in the chemical industry Both equilibriumstage and masstransfer models were covered Included also were chapters on thermodynamic and masstransfer theory for separation 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 PrinciplesChemical and Biochemical Operations FPREF 09292010 Page 6 ASPEN PLUS ASPEN HYSYSPlant BATCHPLUS CHEMCAD PROII 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 thermodynamicproperty calculations are provided in the Wiley multimedia guide Using Process Simulators in Chemical Engineering 3rd Edition by D R Lewin see wwwwileycomcollege 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 ratebased models Use of phase equilibrium and massbalance equations for single equilibriumstage 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 liquidliquid extraction with emphasis on graphical methods Chapters 9 to 11 present computerbased methods widely used in pro cess simulation programs for multicomponent equilibrium based models of vaporliquid and liquidliquid separations Chapter 12 treats multicomponent ratebased 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 ratebased models for membrane sepa rations while Chapter 15 describes equilibriumbased and ratebased models of adsorption ion exchange and chro matography which use solid or solidlike 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 McCabeThiele 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 1000 websites and a Bing search on the latter lists 40000 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 books website or the Glossary of Biological Terms at the website www phschoolcomsciencebiologyplaceglossaryahtml may be consulted Other websites that have proven useful to our students include 1 wwwchemspycomFinds 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 webbooknistgovchemistryContains thermo chemical data for more than 7000 compounds and thermophysical data for 75 fluids 3 www ddbstcomProvides information on the com prehensive Dortmund Data Bank DDB of thermo dynamic properties 4 wwwchemistryaboutcomodchemicalengineerin1 indexhtmIncludes articles and links to many web sites concerning topics in chemical engineering 5 wwwmatchecomProvides capital cost data for many types of chemical processing 6 wwwhowstuffworkscomProvides sources of easy tounderstand explanations of how thousands of things work vi Preface to the Third Edition FPREF 09292010 Page 7 RESOURCES FOR INSTRUCTORS Resources for instructors may be found at the website www wileycomcollegeseader Included are 1 Solutions Manual prepared by the authors giving detailed solutions to all homework exercises in a tuto rial format 2 Errata to all printings of the book 3 A copy of a Preliminary Examination used by one of the authors to test the preparedness of students for a course in separations equilibriumstage operations and mass transfer This closedbook 50minute exami nation which has been given on the second day of the course consists of 10 problems on topics studied by students in prerequisite courses on fundamental princi ples of chemical engineering Students must retake the examination until all 10 problems are solved correctly 4 Image gallery of figures and tables in jpeg format appropriate for inclusion in lecture slides These resources are passwordprotected and are available only to instructors who adopt the text Visit the instructor sec tion of the book website at wwwwileycomcollegeseader to register for a password RESOURCES FOR STUDENTS Resources for students are also available at the website wwwwileycomcollegeseader Included are 1 A discussion of problemsolving techniques 2 Suggestions for completing homework exercises 3 Glossary of Science Terms 4 Errata to various printings of the book SUGGESTED COURSE OUTLINES We feel that our depth of coverage is one of the most impor tant assets of this book It permits instructors to design a course that matches their interests and convictions as to what is timely and important At the same time the student is provided with a resource on separation operations not cov ered in the course but which may be of value to the student later Undergraduate instruction on separation processes is generally incorporated in the chemical engineering curricu lum following courses on fundamental principles of thermo dynamics fluid mechanics and heat transfer These courses are prerequisites for this book Courses that cover separation processes may be titled Separations or Unit Operations EquilibriumStage Operations Mass Transfer and Rate Based Operations or Bioseparations This book contains sufficient material to be used in courses described by any of the above four titles The Chap ters to be covered depend on the number of semester credit hours It should be noted that Chapters 1 2 3 8 14 15 17 18 and 19 contain substantial material relevant to bioseparations mainly in later sections of each chapter Ins tructors who choose not to cover bioseparations may omit those sections However they are encouraged to at least ass ign their students Section 19 which provides a basic aware ness of biochemical separation processes and how they differ from chemical separation processes Suggested chapters for several treatments of separation processes at the under graduate level are SEPARATIONS OR UNIT OPERATIONS 3 Credit Hours Chapters 1 3 4 5 6 7 8 14 15 or 17 4 Credit Hours Chapters 1 3 4 5 6 7 8 9 14 15 17 5 Credit Hours Chapters 1 3 4 5 6 7 8 9 10 13 14 15 16 17 18 19 EQUILIBRIUMSTAGE OPERATIONS 3 Credit Hours Chapters 1 4 5 6 7 8 9 10 4 Credit Hours Chapters 1 4 5 6 7 8 9 10 11 13 MASS TRANSFER AND RATEBASED OPERATIONS 3 Credit Hours Chapters 1 3 6 7 8 12 14 15 4 Credit Hours Chapters 1 3 6 7 8 12 14 15 16 17 18 BIOSEPARATIONS 3 Credit Hours Chapter 1 Sections 19 29 Chapters 3 4 Chapter 8 including Section 86 Chapters 14 15 17 18 19 Note that Chapter 2 is not included in any of the above course outlines because solution thermodynamics is a pre requisite for all separation courses In particular students who have studied thermodynamics from Chemical Bio chemical and Engineering Thermodynamics by SI Sandler Physical and Chemical Equilibrium for Chemi cal Engineers by N de Nevers or Engineering and Chemical Thermodynamics by MD Koretsky will be well prepared for a course in separations An exception is Section 29 for a course in Bioseparations Chapter 2 does serve as a review of the important aspects of solution thermodynamics and has proved to be a valuable and popular reference in previous editions of this book Students who have completed a course of study in mass transfer using Transport Phenomena by RB Bird WE Stewart and EN Lightfoot will not need Chapter 3 Students who have studied from Fundamentals of Momentum Heat and Mass Transfer by JR Welty CE Wicks RE Wilson and GL Rorrer will not need Chapter 3 except for Section 38 if driving forces for mass transfer other than concentra tion need to be studied Like Chapter 2 Chapter 3 can serve as a valuable reference Preface to the Third Edition vii 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 ionization 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 components These driving forces are based on the MaxwellStefan equations FTOC 09162010 92731 Page 9 Brief Contents PART 1FUNDAMENTAL 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 2SEPARATIONS BY PHASE ADDITION OR CREATION Chapter 6 Absorption and Stripping of Dilute Mixtures 206 Chapter 7 Distillation of Binary Mixtures 258 Chapter 8 LiquidLiquid Extraction with Ternary Systems 299 Chapter 9 Approximate Methods for Multicomponent Multistage Separations 359 Chapter 10 EquilibriumBased Methods for Multicomponent Absorption Stripping Distillation and Extraction 378 Chapter 11 Enhanced Distillation and Supercritical Extraction 413 Chapter 12 RateBased Models for VaporLiquid Separation Operations 457 Chapter 13 Batch Distillation 473 PART 3SEPARATIONS BY BARRIERS AND SOLID AGENTS Chapter 14 Membrane Separations 500 Chapter 15 Adsorption Ion Exchange Chromatography and Electrophoresis 568 PART 4SEPARATIONS 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 5MECHANICAL SEPARATION OF PHASES Chapter 19 Mechanical Phase Separations 778 ix Richard G Akins Kansas State University Paul Bienkowski University of Tennessee C P Chen University of Alabama in Huntsville William A Heenan Texas AM UniversityKingsville 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 Sanmukh S Ilias North Carolina AT State University Kenneth R Jolls Iowa State University of Science and Technology Alan M Lane University of Alabama About the Authors iii Preface v Nomenclature xv 193 Design of Particle Separators 789 194 Design of SolidLiquid CakeFiltration Devices Based on Pressure Gradients 795 195 Centrifuge Devices for SolidLiquid Separations 800 196 Wash Cycles 802 197B Mechanical Separations in Biotechnology 804 Summary References Study Questions Exercises Answers to Selected Exercises 814 Index 817 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 LKV Hamaker constant A M membrane surface area a activity interfacial area per unit volume molecular radius a u surface area per unit volume B bottoms flow rate b molar availability function h T0S component flow rate in bottoms C general composition variable such as concentration mass fraction mole fraction or volume 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 P v idealgas heat capacity at constant pressure c molar concentration speed of light c liquid concentration in equilibrium with gas at its bulk partial pressure c concentration in liquid adjacent to a membrane surface c b volume averaged stationary phase solute concentration in 15149 c d diluent volume per solvent volume in 1789 c f bulk fluid phase solute concentration in 1548 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 1548 solute saturation concentration on the solubility curve in 1782 c s humid heat normal solubility of crystals solute concentration on solid pore surfaces of stationary phase in 1548 solute saturation concentration on the solubility curve in 1782 c t total molar concentration c limit limiting supersaturation D D diffusivity distillate flow rate diameter G Gibbs free energy mass velocity rate of growth of crystal size g universal constant 32174 lbm ftlbf s² H Henrys law constant height or length enthalpy height of theoretical chromatographic plate H ads heat of adsorption H cond heat of condensation H crys heat of crystallization H dil heat of dilution H sol integral heat of solution at saturation H sol heat of solution at infinite dilution H vap molar enthalpy of vaporization H G height of a transfer unit for the gas phase I G N G H L height of a transfer unit for the liquid phase I L N L H OG height of an overall transfer unit based on the gas phase I G N O G H OL height of an overall transfer unit based on the liquid phase I L N O L h humidity h m molal humidity h p percentage humidity h r relative humidity h s saturation humidity h W saturation humidity at temperature T W HETP height equivalent to a theoretical plate same as HETP HTU height of a transfer unit I electrical current ionic strength i current density J i molar flux of i by ordinary molecular diffusion relative to the molaraverave velocity of the mixture j D ChiltonColburn jfactor for mass transfer N StuN v S²3 j H ChiltonColburn jfactor for heat transfer N SN v P²3 j M ChiltonColburn jfactor for momentum transfer E f2 j i mass flux of i by ordinary molecular diffusion relative to the massaverage velocity of the mixture K equilibrium ratio for vaporliquid equilibria overall masstransfer coefficient K a acid ionization constant K D equilibrium ratio for liquidliquid equilibria distribution or partition ratio equilibrium LES length of equilibrium spent section of adsorption bed LUB length of unused bed in adsorption lM membrane thickness lT packed height M molecular weight Mi moles of i in batch still MT mass of crystals per unit volume of magma Ml total mass m slope of equilibrium curve mass flow rate mass molarity mc mass of crystals per unit volume of mother liquor mass in filter cake mi molality of i in solution ms mass of solid on a dry basis solids flow rate mu mass evaporated rate of evaporation MTZ length of masstransfer zone in adsorption bed N number of phases number of moles molar flux nA number of equilibrium theoretical perfect stages rate of rotation number of transfer units number of crystalsunit volume in 1782 NA Avogadros number 6022 1023 moleculesmol Nd number of actual trays NBi Biot number for heat transfer NBiM Biot number for mass transfer ND number of degrees of freedom NEo Eotvos number NFo Fourier number for heat transfer α1a2 dimensionless time NFoM Fourier number for mass transfer D1a2 dimensionless time NFr Froude number inertial forcegravitational force NG number of gasphase transfer units NL number of liquidphase transfer units NLe Lewis number NscNFr NLu Luikov number 1NLe Nmin minimum number of stages for specified split Nnu Nusselt number dhk temperature gradient at wall or interfacetemperature gradient across fluid d characteristic length NOG number of overall gasphase transfer units NOL number of overall liquidphase transfer units NPe Peclet number for heat transfer NReNFr convective transport to molecular transfer NPeM Peclet number for mass transfer NReNSc convective transport to molecular transfer NPo Power number NFr Prandtl number CμLk momentum diffusivitythermal diffusivity viD species diffusion velocity relative to the molaraverage velocity of the mixture vE critical molar volume vH humid volume vM molaraverage velocity of a mixture vr reduced molar volume vve v0 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 cakefilter area WD 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 Ws rate of shaft work w mass fraction X mole or mass ratio mass ratio of soluble material to solvent in underflow y mole or mass ratio mass fraction in overflow Z compressibility factor PuRT height mole fraction in any phase overall mole fraction in combined phases distance overall mole fraction in feed charge ionic charge O overall atm atmosphere o 0 reference condition initial condition avg average out leaving B bioprodut OV overhead vapor BET BrunauerEmmettTeller P permeate BOH undissociated weak base R reboiler rectification section retentate BP bubblepoint method r reduced reference component radiation BSA bovine serum albumin res residence time BWR BenedictWebbRubin equation of state S solid stripping section sidestream solvent stage salt bar 09869 atmosphere or 100 kPa SC steady counterflow s source or sink surface condition solute saturation bbl barrel T total Btu British thermal unit t turbulent contribution C coulomb V vapor C₁ paraffin with i carbon atoms w wet solidgas interface CBER Center for Biologics Evaluation and Research w wb wet bulb CF concentration factor ws wet solid CFR Code of Federal Regulations X exhausting stripping section eGMP current good manufacturing practices x y z directions CHO Chinese hamster ovary cells surroundings initial CMC critical micelle concentration a αamino base c αcarboxylic acid E excess extract phase F feed floc flocculation H high boiler HA undissociated neutral species of a weak acid HCP hostcell proteins HEPA highefficiency particulate air HHK heavier than heavy key component HIV Human Immunodeficiency Virus HK heavykey component HPTFF highperformance TFF hp horsepower h hour I intermediate boiler IMAC immobilized metal affinity chromatography IND investigational new drug J Joule K degrees Kelvin kg kilogram kmol kilogrammole L liter low boiler LES length of an ideal equilibrium adsorption section LHS lefthand side of an equation LK lightkey component LLE liquidliquid equilibrium LKP LeeKesslerPlöcker equation of state LM log mean LMH liters per square meter per hour LRV log reduction value in microbial concentration LUB length of unused sorptive bed LW lost work lb pound LBr poundforce RDC rotatingdisk contactor RHS righthand side of an equation RK RedlichKwong equation of state RKS RedlichKwongSoave equation of state RNA ribonucleic acid RO reverse osmosis R degrees Rankine rp revolutions per hour rpm revolutions per minute rps revolutions per second SC simultaneouscorrection method SDS sodium dodecylsulfate SEC size exclusion chromatography SF supercritical fluid SFE supercriticalfluid extraction SG silica gel SG specific gravity SOP standard operating procedure SPM stroke speed per minute scanning probe microscopy SPR surface plasmon resonance SR stiffness ratio sumrates method STP standard conditions of temperature and pressure usually 1 atm and either 0C or 60F s second scf standard cubic feet scfd standard cubic feet per day scfh standard cubic feet per hour scfm standard cubic feet per minute stm steam TBP tributyl phosphate TFF tangentialflow filtration TIRF total internal reflectance fluorescence TLL tieline length TMP transmembrane pressure drop TOMAC trioctylmethylammonium chloride Chemical engineers must be proficient in the use of three systems of units 1 the International System of Units SI System Système International dUnités which was established in 1960 by the 11th General Conference on Weights and Measures and has been widely adopted 2 the AE American Engineering System which is based largely upon an English system of units adopted when the Magna Carta was signed in 1215 and is a preferred system in the United States and 3 the CGS centimetergramsecond System which was devised in 1790 by the National Assembly of France and served as the basis for the development of the SI System A useful index to units and systems of units is given on the website http wwwsizescomunitsindexhtm Engineers must deal with dimensions and units to express the dimensions in terms of numerical values Thus for 10 gallons of gasoline the dimension is volume the unit is gallons and the value is 10 As detailed in NIST National Institute of Standards and Technology Special Publication 811 2009 edition which is available at the website httpwwwnistgovphyslabpubssp811indexcfm units are base or derived Derived Dimension SI Unit AE Unit CGS Unit Area Length² m² ft² cm² Volume Length³ m³ ft³ cm³ Mass flow rate Mass Time kgs lbmh gs Molar flow rate Molar amountTime mols lbmolh mols Velocity LengthTime ms fth cms Acceleration Velocity Time ms² fth² cms² Force Mass Acceleration newton N 1 kg ms² lbf dyne 1 g cms² Pressure ForceArea pascal Pa 1 Nm² 1 kgm s² lbin² atm Energy Force Length joule J 1 N m 1 kg m²s² ft lbf Btu erg 1 dyne cm 1 g cm²s² cal Power EnergyTime watt W 1 Js 1 N ms 1 kg m²s³ Density MassVolume kgm³ lbmft³ gcm³ deci 10¹ d CONVERSION FACTORS PART01 06052010 33135 Page 1 Part One Fundamental Concepts Chapters 15 present concepts that describe methods for the separation of chemical mixtures by industrial processes including bioprocesses Five basic separa tion techniques are enumerated The equipment used and the ways of making mass balances and specifying component recovery and product purity are also illustrated Separations are limited by thermodynamic equili brium while equipment design depends on the rate of mass transfer Chapter 2 reviews thermodynamic princi ples and Chapter 3 discusses component mass transfer under stagnant laminarflow and turbulentflow condi tions Analogies to conductive and convective heat transfer are presented Singlestage contacts for equilibriumlimited multi phase separations are treated in Chapters 4 and 5 as are the enhancements afforded by cascades and multistage arrangements Chapter 5 also shows how degreesof freedom analysis is used to set design parameters for equipment This type of analysis is used in process sim ulators such as ASPEN PLUS CHEMCAD HYSYS and SuperPro Designer 1 Chapter 1 C01 09292010 Page 3 solids and separation of solids by size Most of the equip ment in biochemical or chemical plants is there to purify raw material intermediates and products by the separation tech niques discussed in this book Blockflow diagrams are used to represent processes They indicate by square or rectangular blocks chemical reaction and separation steps and by connecting lines the process streams More detail is shown in processflow dia grams which also include auxiliary operations and utilize symbols that depict the type of equipment employed A blockflow diagram for manufacturing hydrogen chloride gas from chlorine and hydrogen 2 is shown in Figure 12 Central to the process is a reactor where the gasphase combustion reaction H2 þ Cl2 2HCl occurs The auxil iary equipment required consists of pumps compressors and a heat exchanger to cool the product No separation operations are necessary because of the complete conver sion of chlorine A slight excess of hydrogen is used and the product 99 HCl and small amounts of H2 N2 H2O CO and CO2 requires no purification Such simple pro cesses that do not require separation operations are very rare and most chemical and biochemical processes are dominated by separations equipment Many industrial chemical processes involve at least one chemical reactor accompanied by one or more separation trains 3 An example is the continuous hydration of ethylene to ethyl alcohol 4 Central to the process is a rea ctor packed with catalyst particles operating at 572 K and 672 MPa in which the reaction C2H4 þ H2O C2H5OH occurs Due to equilibrium limitations conversion of ethyl ene is only 5 per pass through the reactor However by recovering unreacted ethylene and recycling it to the reactor nearcomplete conversion of ethylene feed is achieved Recycling is a common element of chemical and bio chemical processes If pure ethylene were available as a feed stock and no side reactions occurred the simple process in Figure 13 could be realized This process uses a reactor a partial condenser for ethylene recovery and distillation to produce aqueous ethyl alcohol of nearazeotropic composi tion 93 wt Unfortunately impurities in the ethylene feedand side reactions involving ethylene and feed imp urities such as propylene to produce diethyl ether isopropyl alcohol acetaldehyde and other chemicalscombine to inc rease the complexity of the process as shown in Figure 14 After the hydration reaction a partial condenser and high pressure water absorber recover ethylene for recycling The pressure of the liquid from the bottom of the absorber is red uced causing partial vaporization Vapor is then separated from the remaining liquid in the lowpressure flash drum whose vapor is scrubbed with water to remove alcohol from the vent gas Crude ethanol containing diethyl ether and acet aldehyde is distilled in the crudedistillation column and cat alytically hydrogenated to convert the acetaldehyde to ethanol Diethyl ether is removed in the lightends tower and scrubbed with water The final product is prepared by distilla tion in the final purification tower where 93 wt aqueous ethanol product is withdrawn several trays below the top tray light ends are concentrated in the socalled pasteuriza tiontray section above the productwithdrawal tray and recycled to the catalytichydrogenation reactor and waste water is removed with the bottoms Besides the equipment shown additional equipment may be necessary to concen trate the ethylene feed and remove impurities that poison the catalyst In the development of a new process experience shows that more separation steps than originally anticipated are usually needed Ethanol is also produced in biochemical fermentation processes that start with plant matter such as barley corn sugar cane wheat and wood Sometimes a separation operation such as absorption of SO2 by limestone slurry is accompanied by a chemical rea ction that facilitates the separation Reactive distillation is discussed in Chapter 11 More than 95 of industrial chemical separation opera tions involve feed mixtures of organic chemicals from coal natural gas and petroleum or effluents from chemical reactors processing these raw materials However concern has been expressed in recent years because these fossil feedstocks are not renewable do not allow sustainable development and res ult in emission of atmospheric pollutants such as particulate matter and volatile organic compounds VOCs Many of the same organic chemicals can be extracted from renewable biomass which is synthesized biochemically by cells in agri cultural or fermentation reactions and recovered by biosepara tions Biomass components include carbohydrates oils Figure 11 Refinery for converting crude oil into a variety of marketable products Figure 12 Process for anhydrous HCl production 11 Industrial Chemical Processes 3 Separation Processes Figure 15 General separation process Feed mixture to be separated Separation process Product 1 Product 2 Product N1 Figure 16 Basic separation techniques a separation by phase creation b separation by phase addition c separation by barrier d separation by solid agent e separation by force field or gradient 13 SEPARATIONS BY PHASE ADDITION OR CREATION If the feed is a singlephase solution a second separable phase must be developed before separation of the species can be achieved The second phase is created by an energyseparating agent ESA andor added as a massseparating agent MSA An ESA involves heat transfer or transfer of shaft work to or from the mixture An example of shaft work is the creation of vapor from a liquid phase by reducing the pressure An MSA may be partially immiscible with one or more mixture components and frequently is the constituent of highest concentration in the added phase Separation Operation Symbola Initial or Feed Phase Created or Added Phase Separating Agents Industrial Exampleb Separation Operation Symbola Initial or Feed Phase Created or Added Phase Separating Agents Industrial Exampleb Separation Operation Separation Symbolz Initial or Feed Phase Created or Added Phase Separating Agents Industrial Exampleb C01 09292010 Page 11 product from a stripper is thermally stable it may be reboiled without using an MSA In that case the column is a reboiled stripper 9 Additional separation operations may be re quired to recover MSAs for recycling Formation of minimumboiling azeotropes makes azeo tropic distillation 10 possible In the example cited in Table 11 the MSA nbutyl acetate which forms a twoliquid heter ogeneous minimumboiling azeotrope with water is used as an entrainer in the separation of acetic acid from water The azeotrope is taken overhead condensed and separated into acetate and water layers The MSA is recirculated and the dis tillate water layer and bottoms acetic acid are the products Liquidliquid extraction 11 and 12 with one or two solvents can be used when distillation is impractical espe cially when the mixture to be separated is temperature sensitive A solvent selectively dissolves only one or a fraction of the components in the feed In a twosolvent extraction each has its specific selectivity for the feed compo nents Several countercurrently arranged stages may be neces sary As with extractive distillation additional operations are required to recover solvent from the streams leaving the extraction operation Extraction is widely used for recovery of bioproducts from fermentation broths If the extraction tem perature and pressure are only slightly above the critical point of the solvent the operation is termed supercriticalfluid extraction In this region solute solubility in the supercritical fluid can change drastically with small changes in temperature and pressure Following extraction the pressure of the sol ventrich product is reduced to release the solvent which is recycled For the processing of foodstuffs the supercritical fluid is an inert substance with CO2 preferred because it does not contaminate the product Since many chemicals are processed wet but sold as dry solids a common manufacturing step is drying Operation 13 Although the only requirement is that the vapor pres sure of the liquid to be evaporated from the solid be higher than its partial pressure in the gas stream dryer design and operation represents a complex problem In addition to the effects of such external conditions as temperature humidity air flow and degree of solid subdivision on drying rate the effects of internal diffusion conditions capillary flow equili brium moisture content and heat sensitivity must be consid ered Because solid liquid and vapor phases coexist in drying equipmentdesign procedures are difficult to devise and equipment size may be controlled by heat transfer A typ ical dryer design procedure is for the process engineer to send a representative feed sample to one or two reliable dryer manufacturers for pilotplant tests and to purchase equipment that produces a dried product at the lowest cost Commercial dryers are discussed in 5 and Chapter 18 Evaporation Operation 14 is defined as the transfer of volatile components of a liquid into a gas by heat transfer Applications include humidification air conditioning and concentration of aqueous solutions Crystallization 15 is carried out in some organic and in almost all inorganic chemical plants where the desired product is a finely divided solid Crystallization is a purifica tion step so the conditions must be such that impurities do not precipitate with the product In solution crystallization the mixture which includes a solvent is cooled andor the solvent is evaporated In melt crystallization two or more soluble species are separated by partial freezing A versatile meltcrystallization technique is zone melting or refining which relies on selective distribution of impurities between a liquid and a solid phase It involves moving a molten zone slowly through an ingot by moving the heater or drawing the ingot past the heater Single crystals of very highpurity sili con are produced by this method Sublimation is the transfer of a species from the solid to the gaseous state without formation of an intermediate liquid phase Examples are separation of sulfur from impurities purification of benzoic acid and freezedrying of foods The reverse process desublimation 16 is practiced in the re covery of phthalic anhydride from gaseous reactor effluent A common application of sublimation is the use of dry ice as a refrigerant for storing ice cream vegetables and other per ishables The sublimed gas unlike water does not puddle Liquidsolid extraction leaching 17 is used in the met allurgical natural product and food industries To promote rapid solute diffusion out of the solid and into the liquid sol vent particle size of the solid is usually reduced The major difference between solidliquid and liquid liquid systems is the difficulty of transporting the solid often as slurry or a wet cake from stage to stage In the pharmaceu tical food and natural product industries countercurrent solid transport is provided by complicated mechanical devices In adsorptivebubble separation methods surfaceactive material collects at solution interfaces If the very thin sur face layer is collected partial solute removal from the solu tion is achieved In ore flotation processes solid particles migrate through a liquid and attach to rising gas bubbles thus floating out of solution In foam fractionation 18 a natural or chelateinduced surface activity causes a solute to migrate to rising bubbles and is thus removed as foam The equipment symbols shown in Table 11 correspond to the simplest configuration for each operation More complex versions are frequently desirable For example a more complex version of the reboiled absorber Operation 5 in Table 11 is shown in Figure 17 It has two feeds an inter cooler a side stream and both an interreboiler and a bottoms reboiler Design procedures must handle such complex equipment Also it is possible to conduct chemical reactions simultaneously with separation operations Siirola 6 des cribes the evolution of a commercial process for producing methyl acetate by esterification The process is conducted in a single column in an integrated process that involves three reaction zones and three separation zones 14 SEPARATIONS BY BARRIERS Use of microporous and nonporous membranes as semi permeable barriers for selective separations is gaining adher ents Membranes are fabricated mainly from natural fibers and synthetic polymers but also from ceramics and metals Mem branes are fabricated into flat sheets tubes hollow fibers or spiralwound sheets and incorporated into commercial 14 Separations by Barriers 11 Figure 17 Complex reboiled absorber Table 12 Separation Operations Based on a Barrier Table 13 Separation Operations Based on a Solid Agent Figure 18 Hydrocarbon recovery process Table 16 Computed Split Fractions SF and Split Ratios SR for Hydrocarbon Recovery Process C01 09292010 Page 17 1 Remove unstable corrosive or chemically reactive components early in the sequence 2 Remove final products one by one as overhead distillates 3 Remove early in the sequence those components of greatest molar percentage in the feed 4 Make the most difficult separations in the absence of the other components 5 Leave for later in the sequence those separations that produce final products of the highest purities 6 Select the sequence that favors nearequimolar amounts of overhead and bottoms in each column Unfortunately these heuristics sometimes conflict with each other and thus a clear choice is not always possi ble Heuristic 1 should always be applied if applicable The most common industrial sequence is that of Heuristic 2 When energy costs are high Heuristic 6 is favored When one of the separations such as the separation of isomers is particularly difficult Heuristic 4 is usually applied Seider et al 7 present more rigorous methods which do require column design and costing to determine the optimal sequence They also consider complex sequences that include separators of different types and complexities EXAMPLE 12 Selection of a separation sequence using heuristics A distillation sequence produces the same four final products from the same five components in Figure 19 The molar percentages in the feed are C3 50 iC4 15 nC4 25 iC5 20 and nC5 35 The most difficult separation by far is that between the isomers iC4 and nC4 Use the heuristics to determine the best sequences All products are to be of high purity Solution Heuristic 1 does not apply Heuristic 2 favors taking C3 iC4 and nC4 as overheads in Columns 1 2 and 3 respectively with the iC5 nC5 multicomponent product taken as the bottoms in Col umn 3 as in Sequence 1 in Figure 19 Heuristic 3 favors the removal of the iC5 nC5 multicomponent product 55 of the feed in Column 1 as in Sequences 3 and 4 Heuristic 4 favors the separation of iC4 from nC4 in Column 3 as in Sequences 2 and 4 Heuristics 3 and 4 can be combined with C3 taken as overhead in Column 2 as in Sequence 4 Heuristic 5 does not ap ply Heuristic 6 favors taking the multicomponent product as bot toms in Column 1 4555 mole split nC4 as bottoms in Column 2 2025 mole split and C3 as overhead with iC4 as bottoms in Column 3 as in Sequence 3 Thus the heuristics lead to four pos sible sequences as being most favorable Figure 19 Distillation sequences to produce four products Table 18 Number of Alternative Distillation Sequences Number of Final Products Number of Columns Number of Alternative Sequences 2 1 1 3 2 2 4 3 5 5 4 14 6 5 42 17 Component Recoveries and Product Purities 17 Table 17 Comparison of Calculated Product Purities with Specifications Table 19 Key Component Separation Factors for Hydrocarbon Recovery Process Using the fractional purity of O2 in the permeate the total permeate is np 10505 21kmolh By a total permeate material balance npN2 21 105 105 kmolh By an overall N2 material balance npN2 085N829 705 kmolh Case 3 Two materialbalance equations one for each component can be written For nitrogen with a fractional purity of 100 050 050 in the permeate nNN2 085N829 79 kmolh 1 For oxygen with a fractional purity of 100 085 015 in the retentate nOO2 050N21 015N21 21 kmolh 2 Solving 1 and 2 simultaneously for the total products gives np 171 kmolh nR 829 kmolh Therefore the component flow rates are nRO2 085829 705 kmolh nRN2 829 705 124 kmolh nOO2 050171 86 kmolh npN2 171 86 85 kmolh Case 4 First compute the O2 flow rates using the split ratio and an overall O2 material balance nRO2 nRO2 npO2 11 21 npO2 nRO2 Solving these two equations simultaneously gives nRO2 10 kmolh npO2 21 10 11 kmolh Since the retentate contains 85 mol N2 and therefore 15 mol O2 the flow rates for N2 are nRN2 85 15 10 567 kmolh npN2 79 567 223 kmolh 19 INTRODUCTION TO BIOSEPARATIONS Bioproducts are products extracted from plants animals and microorganisms to sustain life and promote health support agriculture and chemical enterprises and diagnose and remedy disease From the bread beer and wine produced by ancient civilizations using fermented yeast the separation and purification of biological products bioproducts have grown in commercial significance to include processscale recovery of antibiotics from mold which began in the 1940s and isolation of recombinant DNA and proteins from transformed bacteria in biotechnology protocols initiated in the 1970s Bioproducts used in pharmaceutical agricultural and biotechnology market sectorsincluding commodity foods beverages and biofuelsaccounted for an estimated 282 billion in sales in 2005 with an average annual growth rate of 12 that projects to 50 billion in sales by 2010 191 Bioproducts To identify features that allow selection and specification of processes to separate bioproducts from other biological species1 of a host cell it is useful to classify biological species by their complexity and size as small molecules biopolymers and cellular particulates as shown in Table 110 and to further categorize each type of species by name in Column 2 according to its biochemistry and function within a biological host in Column 3 Small molecules include primary metabolites which are synthesized during the primary phase of cell growth by sets of enzymecatalyzed biochemical reactions referred to as metabolic pathways Energy from organic nutrients fuels these pathways to support cell growth and relatively rapid reproduction Primary metabolites include organic commodity chemicals amino acids mono and disaccharides and vitamins Secondary metabolites are small molecules produced in a subsequent stationary phase in which growth and reproduction slows or stops Secondary metabolites include more complex molecules such as antibiotics steroids phytochemicals and cytotoxins Small molecules range in complexity and size from H2 2 daltons Da produced by cyanobacteria to avastin B12 1355 Da or vancomycin antibiotic 1449 Da whose synthesis originally occurred in bacteria Amino acid and monosaccharide metabolites are building blocks for highermolecularweight biopolymers from which cells are constituted Biopolymers provide mechanical strength chemical inertness and permeability and store energy and information They include proteins polysaccharides nucleic acids and lipids Cellular particulates include cells and cell derivatives such as extracts and hydrolysates as well as subcellular components Proteins the most abundant biopolymers in cells are long linear sequences of 20 naturally occurring amino acids covalently linked endtoend by peptide bonds with molecular weights ranging from 10000 Da to 100000 Da Their structure is often helical with an overall shape ranging from globular to sheetlike with loops and folds as determined largely by attraction between oppositely charged groups on the amino acid chain and by hydrogen bonding Proteins participate in storage transport defense regulation inhibition and catalysis The first products of biotechnology were bioactive proteins that initiated or inhibited specific biological processes 8 These included hormones thrombolytic agents clotting factors and immune agents Recently bioproduction of monoclonal antibodies for pharmaceutical applications has grown in significance Monoclonal antibodies are proteins that bind with high specificity and affinity to particles recognized as foreign to a host organism Monoclonal antibodies have been introduced to treat breast cancer Herceptin Bcell lymphoma Rituxan and rheumatoid arthritis Remicade and Enbrel Carbohydrates are mono or polysaccharides with the general formula CH2On n 3 photosynthesized from CO2 They primarily store energy as cellulose and starch in plants and as glycogen in animals Monosaccharides 3 n 9 are aldehydes or ketones Condensing two monosaccharides forms a disaccharide like sucrose αDglucose plus βDfructose lactose βDglucose plus βDgalactose from milk or whey or maltose which is hydrolyzed from germinating cereals like C01 09292010 Page 22 Figure 110 Typical eukaryotic cells Figure 111 Typical prokaryotic bacterial cell 22 Chapter 1 Separation Processes Figure 112 results in excess water which is removed early in the bioprocess train to reduce equipment size and improve process economics Purity The mass of hostcell products HCP product variants DNA viruses endotoxins resin and membrane leachables and small molecules is limited in biotechnology products for therapeutic and prophylactic application The Center for Biologics Evaluation and Research CBER of the Food and Drug Administration FDA approves HCP limits established by the manufacturer after review of process capability and safety testing in toxicology and clinical trials The World Health Organization WHO sets DNA levels at 10 pg per dose Less than one virus particle per 106 doses is allowed in rDNAderived protein products Sterility of final products is ensured by sterile filtration of the final product as well as by controlling microbial contaminant levels throughout the process C01 09292010 Page 24 Approval and Manufacturing The FDA ensures safety and efficacy of bioproducts used in human diagnostic prophylactic and therapeutic applications They review clinical trial data as well as manufacturing process information eventually approv ing approximately 1 in 10 candidates for introduction into the market as an investigational new drug IND Manufacture of drugs under current good manufacturing practices cGMP considers facility design and layout equipment and procedures including operation cleaning and sterilization documented by standard operating procedures SOPs analysis in labs that sat isfy good laboratory practices GLP personnel training con trol of raw materials and cultures and handling of product Drug manufacturing processes must be validated to assure that product reproducibly meets predetermined specifications and quality characteristics that ensure biological activity purity quality and safety Bioseparation synthesis Bioprocesses are required to eco nomically and reliably recover purified bioproducts from chemical and biological species in complex cell matrices in quantities sufficient to meet market demands Beginning with a raw cellular source 1 cellular particulates are recov ered or retained by sedimentation or filtration 2 biopoly mers are usually purified by filtration adsorption extraction or precipitation and 3 small biomolecules are often recov ered by extraction Economics documentation consideration of genetic engineering and ordering of process steps are key features of bioseparation synthesis Bioprocess economics Largescale recovery operations must be efficient since the cost of recovering biomole cules and treating aqueous organic and solid wastes can dominate total product manufacturing costs Ineffi cient processes consume inordinate volumes of expen sive solvent which must be recovered and recycled or disposed of Costs resulting from solvent tankage and consumption during downstream recovery represent a significant fraction of biologicalrecovery costs Devel opment of a typical pharmaceutical bioproduct cost 400 million in 1996 and required 14 years65 years from initial discovery through preclinical testing and another 75 years for clinical trials in human volunteers Bioprocess documentation The reliability of process equipment must be welldocumented to merit approval from governmental regulatory agencies Such approval is important to meet cGMP quality standards and purity requirements for recovered biological agents particularly those in prophylactic and therapeutic applications which require approval by subdivisions of the FDA including the CBER Genetic engineering Conventional bioproductrecovery processes can be enhanced via genetic engineering by fus ing proteins to active species or intracellular insertion of active DNA to stimulate in vivo production of desired pro teins Fusion proteins consist of a target protein attached to an affinity peptide tag such as histidine hexamer which binds transition metals eg nickel zinc and copper immobilized on sorptive or filtration surfaces Incorporat ing purification considerations into early upstream cell culture manufacturing decisions can help streamline purification 193 Bioseparation Steps A series of bioseparation steps are commonly required upstream of the bioreactor eg filtration of incoming gases and culture media after the bioreactor ie downstream or recovery processes and during eg centrifugal removal of spent media fermentation and cell culture operations A gen eral sequence of biorecovery steps is designed to remove solvent insolubles eg particle removal unrelated soluble species and similar species A nondenaturing protein recovery process for example consists of consecutive steps of extraction clarification concentration fractionation and purification The performance of each purification step is characterized in terms of product purity activity and recovery which are evaluated by purity ¼ bioproduct mass bioproduct mass þ impurities mass activity ¼ units of biological activity bioproduct mass yield ¼ bioproduct mass recovered bioproduct mass in feed Recovery yields of the final product can range from about 20 to 6070 of the initial molecule present in the feed stream Some clarification of raw fermentation or cellculture feed streams prior is usually required to analyze their bioproduct content which makes accurate assessment of recovery yields difficult It is particularly important to preserve biological activity during the bio separation steps by maintaining the structure or assembly of the bioproduct Table 111 classifies common bioseparation operations according to their type purpose and illustrative species removed Subsequent chapters in this book discuss these bio separation operations in detail Following this subsection the production of penicillin KV is summarized to illustrate integration of several biosepa ration operations into a sequence of steps Modeling of the penicillin process as well as processes to produce citric acid pyruvic acid cysing riboflavin cyclodextrin recombinant human serum albumin recombinant human insulin mono clonal antibodies antitrypsin and plasmid DNA are dis cussed by Heinzle et al 18 Extraction of cells from fermentation or cell culture broths by removing excess water occurs in a harvest step Extraction of soluble biological species from these cellular extracts which contain unexcreted product occurs by homogenization which renders the product soluble and ac cessible to solidfluid and solutesolute separations Lysis breaking up of whole cells by enzymatic degradation ultra sonication Gaulinpress homogenization or milling releases and solubilizes intracellular enzymes 24 Chapter 1 Separation Processes C01 09292010 Page 25 Clarification of solid cell debris nucleic acids and insoluble proteins by centrifugal precipitation or membrane filtration decreases fouling in later process steps Selective precipitation is effected by adding salt organic solvent detergent or polymers such as polyethyleneimine and poly ethylene glycol to the buffered cell lysate Sizeselective membrane microfiltration may also be used to remove cell debris colloidal or suspended solids or virus particles from the clarified lysate Ultrafiltration tangentialflow filtration hollow fibers and asymmetrical membrane filtration are commonly used membranebased configurations for clarifi cation Incompletely clarified lysate has been shown to foul deadend stackedmembrane adsorbers in concentrations as low as 5 Concentration reduces the volume of total material that must be processed thereby improving process economics Extraction of cells from media during harvest involves con centration or solvent removal Diafiltration of clarified extract into an appropriate buffer prepares the solution for concentration via filtration Alternatively the targeted prod uct may be concentrated by batch adsorption onto a solid resin The bioproduct of interest and contaminants with simi lar physical properties are removed by an eluting solvent Microfiltration to clarify lysate and concentrate by adsorption has been performed simultaneously using a spiralwound membrane adsorber Fractionation of the targeted product usually requires one or more complementary separation processes to dis tinguish between the product and the contaminants based on differences in their physicochemical features As examples filtration batch adsorption isoelectric focusing and isotachophoresis are methods used to separate biolog ical macromolecules based on differences in size mass isoelectric point charge density and hydrophobicity respectively Additional complementary separation steps are often necessary to fractionate the product from any number of similar contaminants Due to its high specific ity adsorption using affinity ion exchange hydrophobic interaction and reversedphase chemistries is widely used to fractionate product mixtures Purification of the concentrated fractionated product from closely related variants occurs by a highresolution technique prior to final formulation and packaging of phar maceutical bioproducts Purification often requires differen tial absorption in an adsorptive column that contains a large number of theoretical stages or plates to attain the required purity Batch electrophoresis achieves high protein resolution at laboratory scale while productionscale continuous appa ratus for electrophoresis must be cooled to minimize ohmic heating of bioproducts Crystallization is preferred where possible as a final purification step prior to formulation and packaging Counterflow resolution of closely related species has also been used Formulation The dosage form of a pharmaceutical bio product results from formulating the bioactive material by adding excipients such as stabilizers eg reducing com pounds polymers tablet solid diluents eg gums PEG oils liquid diluent eg water for injection WFI or Table 111 Synthesis of Bioseparation Sequences Separation Operation Purpose Species Removed Homogenization Extract target from cells Cell disruption FluidSolid Separations Reduce volume Solvent Flocculation Clarify target species Culture media PrecipitationCentrifugation Fermentation broth Crystallization Insolubles Extraction Hostcell debris Filtration Aggregates EvaporationDrying SoluteSolute Separations Fractionate target species Unrelated Solutes Chromatography Small metabolites Extraction Proteins Crystallization Lipids Tangentialflow filtration Nucleic acids Carbohydrates Purify target species Related Solutes Truncatedmisfolded Oligomers FluidSolid Separations Formulation Polishing PrecipitationCentrifugation Preserve target species Buffers Crystallization Prepare for injection Solutions Filtration EvaporationDrying 19 Introduction to Bioseparations 25 194 Bioprocess Example Penicillin In the chemical industry a unit operation such as distillation or liquidliquid extraction adds pennies to the sale price of an average product For a 40 centslb commodity chemical the component separation costs do not generally account for more than 1015 of the manufacturing cost An entirely different economic scenario exists in the bioproduct industry For example in the manufacture of tissue plasmicin activator tPA a blood clot dissolver Datar et al as discussed by Shuler and Kargi 9 enumerate 16 processing steps for this process are 22000g and it takes a 709 million investment to build a plant to produce 1 kgyr of product Purified product yields are only 28 Drug prices must also include recovery of an average 400 million cost of development within the products lifetime Furthermore product lifetimes are usually shorter than the nominal 20year patent life of a new drug since investigational new drug IND approval typically occurs years after patient approval Although some therapeutic proteins sell for 100000000kg this is an extreme case more efficient tPA processes using CHO cell cultures have separation costs averaging 10000g Following solvent extraction potassium acetate and acetic acid are added to promote the crystallization of the potassium salt of penicillin V penicillin KV A basket centrifuge with water washing then produces a crystal cake containing only 5 wt moisture Approximately 4 of the penicillin is lost in the crystallization and centrifugal filtration steps The crystals are dried to a moisture content of 005 wt in a fluidizedbed dryer Not shown in Figure 112 are subsequent finishing steps to produce if desired 250 and 500 mg tablets which may contain small amounts of lactose magnesium stearate povidone starch stearic acid and other inactive ingredients The filtrate from the centrifugal filtration step contains 71 wt solvent nbutyl acetate which must be recovered for recycle to the solvent extraction step This is accomplished in the separation and purification step which may involve distillation adsorption threeliquidphase extraction andor solvent sublation an adsorptionbubble technique The penicillin process produces a number of waste streamseg wastewater containing nbutyl acetatethat require further processing which is not shown in Figure 112 C01 09292010 Page 28 the candidate separation operations and economicsThe most important feed conditions are composition and flow rate because the other conditions temperature pressure and phase can be altered to fit a particular operation However feed vaporization condensation of a vapor feed or compres sion of a vapor feed can add significant energy costs to chem ical processes Some separations such as those based on the use of barriers or solid agents perform best on dilute feeds The most important product conditions are purities because the other conditions listed can be altered by energy transfer after the separation is achieved Sherwood Pigford and Wilke 11 Dwyer 12 and Keller 13 have shown that the cost of recovering and purify ing a chemical depends strongly on its concentration in the feed Kellers correlation Figure 114 shows that the more dilute the feed the higher the product price The five highest priced and most dilute in Figure 114 are all proteins When a very pure product is required large differences in volatility or solubility or significant numbers of stages are needed for chemicals in commerce For biochemicals espe cially proteins very expensive separation methods may be required Accurate molecular and bulk thermodynamic and transport properties are also required Data and estimation methods for the properties of chemicals in commerce are given by Poling Prausnitz and OConnell 14 Daubert and Danner 15 and others A survey by Keller 13 Figure 115 shows that the degree to which a separation operation is technologically mature correlates with its commercial use Operations based on barriers are more expensive than operations based on the use of a solid agent or the creation or addition of a phase All separation equipment is limited to a maximum size For capacities requiring a larger size parallel units must be pro vided Except for size constraints or fabrication problems capacity of a single unit can be doubled for an additional investment cost of about 60 If two parallel units are installed the additional investment is 100 Table 113 lists operations ranked according to ease of scaleup Those ranked near the top are frequently designed without the need for pilotplant or laboratory data provided that neither the process nor the final product is new and equipment is guaran teed by vendors For new processes it is never certain that product specifications will be met If there is a potential im purity possibility of corrosion or other uncertainties such as Table 112 Factors That Influence the Selection of Feasible Separation Operations A Feed conditions 1 Composition particularly of species to be recovered or separated 2 Flow rate 3 Temperature 4 Pressure 5 Phase state solid liquid or gas B Product conditions 1 Required purities 2 Temperatures 3 Pressures 4 Phases C Property differences that may be exploited 1 Molecular 2 Thermodynamic 3 Transport D Characteristics of separation operation 1 Ease of scaleup 2 Ease of staging 3 Temperature pressure and phasestate requirements 4 Physical size limitations 5 Energy requirements E Economics 1 Capital costs 2 Operating costs Urokinase Factor VIII Luciferase Insulin Rennin Ag Co Hg Ni Cu Zn Citric Acid Penicillin 1000000000 100000000 10000000 Price lb Weight fraction in substrate 1000000 100000 10000 1000 100 10 1 01 001 0001 1 010 104 105 106 107 108 109 Figure 114 Effect of concentration of product in feed material on price 13 Technological maturity Use maturity Distillation Gas absorption Extazeo dist Solvent ext Crystallization Ion exchange Adsorption gas feed Membranes gas feed Membranes liquid feed Chromatography liquid feed Adsorption liquid feed Supercritical gas absext Liquid membranes Fieldinduced separations Affinity separations Invention Technology asymptote Use asymptote First application Figure 115 Technological and use maturities of separation processes 13 28 Chapter 1 Separation Processes C01 09292010 Page 29 product degradation or undesirable agglomeration a pilot plant is necessary Operations near the middle usually require laboratory data while those near the bottom require pilot plant tests Included in Table 113 is an indication of the ease of pro viding multiple stages and whether parallel units may be required Maximum equipment size is determined by height limitations and shipping constraints unless field fabrication is possible and economical The selection of separation techniques for both homogeneous and heterogeneous phases with many examples is given by Woods 16 Ultimately the process having the lowest operating maintenance and capital costs is selected provided it is controllable safe nonpolluting and capable of producing products that meet specifications EXAMPLE 15 Feasible separation alternatives Propylene and propane are among the light hydrocarbons produced by cracking heavy petroleum fractions Propane is valuable as a fuel and in liquefied natural gas LPG and as a feedstock for producing propylene and ethylene Propylene is used to make acrylonitrile for synthetic rubber isopropyl alcohol cumene propylene oxide and polypropylene Although propylene and propane have close boiling points they are traditionally separated by distillation From Figure 116 it is seen that a large number of stages is needed and that the reflux and boilup flows are large Accordingly attention has been given to replacement of distillation with a more economical and less energyintensive process Based on the factors in Table 112 the characteristics in Table 113 and the list of species properties given at the end of 12 propose alternatives to Figure 116 Table 113 Ease of Scaleup of the Most Common Separation Operations Operation in Decreasing Ease of Scaleup Ease of Staging Need for Parallel Units Distillation Easy No need Absorption Easy No need Extractive and azeotropic distillation Easy No need Liquidliquid extraction Easy Sometimes Membranes Repressurization required between stages Almost always Adsorption Easy Only for regeneration cycle Crystallization Not easy Sometimes Drying Not convenient Sometimes Figure 116 Distillation of a propylenepropane mixture 110 Selection of Feasible Separations 29 114 Material balance for a distillation sequence The feed to Column C3 in Figure 18 is given in Table 15 The separation is to be altered to produce a distillate of 95 mol pure isobutane with a recovery SF in the distillation of 96 Because of the sharp separation in Column C3 between icA and icC assume all propane goes to the distillate and all icCs go to the bottoms a Compute the flow rates in lbmolh of each component in each of the two products leaving Column C3 b What is the percent purity of the nbutane bottoms product c If the isobutane purity in the distillate is fixed at 95 what recovery of isobutane in the distillate will maximize the purity of normal butane in the bottoms product C01 09292010 Page 31 11 Sherwood TK RL Pigford and CR Wilke Mass Transfer McGrawHill New York 1975 12 Dwyer JL Biotechnology 1 957 Nov 1984 13 Keller GE II AIChE Monogr Ser 8317 1987 14 Poling BE JM Prausnitz and JP OConnell The Properties of Gases and Liquids 5th ed McGrawHill New York 2001 15 Daubert TE and RP Danner Physical and Thermodynamic Propert ies of Pure ChemicalsData Compilation DIPPR AIChE Hemisphere New York 1989 16 Woods DR Process Design and Engineering Practice Prentice Hall Englewood Cliffs NJ 1995 17 Cussler EL and GD Moggridge Chemical Product Design Cam bridge University Press Cambridge UK 2001 18 Heinzle E AP Biwer and CL Cooney Development of Sustainable Bioprocesses John Wiley Sons Ltd England 2006 19 Clark JH and FEI Deswarte Introduction to Chemicals from Bio mass John Wiley Sons Ltd West Sussex 2008 20 Kamm B PR Gruber and M Kamm Eds BiorefineriesIndustrial Processes and Products Volumes 1 and 2 WileyVCH Weinheim 2006 STUDY QUESTIONS 11 What are the two key process operations in chemical engineering 12 What are the main auxiliary process operations in chemical engineering 13 What are the five basic separation techniques and what do they all have in common 14 Why is mass transfer a major factor in separation processes 15 What limits the extent to which the separation of a mixture can be achieved 16 What is the most common method used to separate two fluid phases 17 What is the difference between an ESA and an MSA Give three disadvantages of using an MSA 18 What is the most widely used industrial separation operation 19 What is the difference between adsorption and absorption 110 The degree of separation in a separation operation is often specified in terms of component recoveries andor product purities How do these two differ 111 What is a key component 112 What is a multicomponent product 113 What are the three types of bioproducts and how do they differ 114 Identify the major objectives of the steps in a biopurification process 115 Give examples of separation operations used for the steps in a bioprocess EXERCISES Section 11 11 Fluorocarbons process Shreves Chemical Process Industries 5th edition by George T Austin McGrawHill New York 1984 contains process descrip tions flow diagrams and technical data for commercial processes For each of the fluorocarbons processes on pages 353355 draw a blockflow diagram of the reaction and separation steps and describe the process in terms of just those steps giving attention to the chem icals formed in the reactor and separator Section 12 12 Mixing vs separation Explain using thermodynamic principles why mixing pure chemicals to form a homogeneous mixture is a spontaneous process while separation of that mixture into its pure species is not 13 Separation of a mixture requires energy Explain using the laws of thermodynamics why the separation of a mixture into pure species or other mixtures of differing compo sitions requires energy to be transferred to the mixture or a degrada tion of its energy Section 13 14 Use of an ESA or an MSA Compare the advantages and disadvantages of making separa tions using an ESA versus using an MSA 15 Producing ethers from olefins and alcohols Hydrocarbon Processing published a petroleumrefining hand book in November 1990 with processflow diagrams and data for commercial processes For the ethers process on page 128 list the separation operations of the type given in Table 11 and indicate what chemicals is are being separated 16 Conversion of propylene to butene2s Hydrocarbon Processing published a petrochemical handbook in March 1991 with processflow diagrams and data for commercial processes For the butene2 process on page 144 list the separation operations of the type given in Table 11 and indicate what chemicals is are being separated Section 14 17 Use of osmosis Explain why osmosis is not an industrial separation operation 18 Osmotic pressure for recovering water from sea water The osmotic pressure p of sea water is given by p ¼ RTcM where c is the concentration of the dissolved salts solutes in g cm3 and M is the average molecular weight of the solutes as ions If pure water is to be recovered from sea water at 298 K and con taining 0035 g of saltscm3 of sea water and M ¼ 315 what is the minimum required pressure difference across the membrane in kPa 19 Use of a liquid membrane A liquid membrane of aqueous ferrous ethylenediaminetetraace tic acid maintained between two sets of microporous hydrophobic hollow fibers packed in a permeator cell can selectively and contin uously remove sulfur dioxide and nitrogen oxides from the flue gas of power plants Prepare a drawing of a device to carry out such a separation Show locations of inlet and outlet streams the arrange ment of the hollow fibers and a method for handling the membrane Exercises 31 112 Electrical charge for small particles In electrophoresis explain why most small suspended particles are negatively charged 113 Flow field in fieldflow fractionation In fieldflow fractionation could a turbulentflow field be used Why or why not 114 Material balance for a distillation sequence The prism gas permeation process developed by the Monsanto Company is selective for hydrogen when using hollowfiber membranes made of siliconecoated poly sulphone A gas at 167 MPa and 40C and containing in molh 424 H2 70 CH4 and 05 N2 is separated into a nonpermeate gas at 162 MPa and a permeate gas at 456 MPa a If the membrane is nonpermeable to nitrogen the Prism membrane separation factor SP on a mol basis for hydrogen relative to methane is 3413 and the split fraction SF for hydrogen to the permeate gas is 06038 calculate the flow of each component and the total flow of nonpermeate and permeate gas b Compute the mol purity of hydrogen in the permeate gas c Using a heatcapacity ratio γ of 14 estimate the outlet temperatures of the exiting streams assuming the ideal gas law reversible expansions and no heat transfer between gas streams d Draw a processflow diagram and include pressure temperature and component flow rates C01 09292010 Page 33 119 Distillation sequences The feed stream in the table below is to be separated into four nearly pure products None of the components is corrosive and based on the boiling points none of the three separations is difficult As seen in Figure 19 five distillation sequences are possible a Determine a suitable sequence of three columns using the heuristics of 17 b If a fifth component were added to give five products Table 18 indicates that 14 alternative distillation sequences are possible Draw in a man ner similar to Figure 19 all 14 of these sequences Component Feed rate kmolh Normal boiling point K Methane 19 112 Benzene 263 353 Toluene 85 384 Ethylbenzene 23 409 Section 19 120 Bioproduct separations Current and future pharmaceutical products of biotechnology include proteins nucleic acids and viral gene vectors Example 14 identified five physical and biochemical features of these biological species by which they could be distinguished in a bioseparation iden tified a bioseparation operation that could be used to selectively remove or retain each species from a mixture of the other two and summarized important considerations in maintaining the activity of each species that would constrain the operating parameters of each bioseparation Extend that example by listing the purity requirements for FDA approval of each of these three purified species as a parenteral product which is one that is introduced into a human organism by intravenous subcutaneous intramuscular or intramedullary injection 121 Separation processes for bioproducts from E coli Recombinant protein production from E coli resulted in the first products from biotechnology a List the primary structures and components of E coli that must be removed from a fermentation broth to purify a heterologous protein product one that differs from any protein normally found in the organism in question expressed for pharmaceutical use b Identify a sequence of steps to purify a conjugate heterologous protein a compound comprised of a protein molecule and an attached nonprotein prosthetic group such as a car bohydrate that remained soluble in cell paste c Identify a separa tion operation for each step in the process and list one alternative for each step d Summarize important considerations in establishing operating procedures to preserve the activity of the protein e Sup pose net yield in each step in your process was 80 Determine the overall yield of the process and the scale of operation required to produce 100 kg per year of the protein at a titer of 1 gL 122 Purification process for adenoassociated viral vector An AAV viral gene vector must be purified from an anchorage dependent cell line Repeat Exercise 121 to develop a purification process for this vector Section 110 123 Separation of a mixture of ethylbenzene and xylenes Mixtures of ethylbenzene EB and the three isomers ortho meta and para of xylene are available in petroleum refineries a Based on differences in boiling points verify that the separation between metaxylene MX and paraxylene PX by distillation is more difficult than the separations between EB and PX and MX and orthoxylene OX b Prepare a list of properties for MX and PX similar to Table 114 Which property differences might be the best ones to exploit in order to separate a mixture of these two xylenes c Explain why melt crystallization and adsorption are used com mercially to separate MX and PX 124 Separation of ethyl alcohol and water When an ethanolwater mixture is distilled at ambient pressure the products are a distillate of nearazeotropic composition 894 mol ethanol and a bottoms of nearly pure water Based on differences in certain properties of ethanol and water explain how the following operations might be able to recover pure ethanol from the distillate a Extractive distillation b Azeotropic distillation c Liquidliq uid extraction d Crystallization e Pervaporation f Adsorption 125 Removal of ammonia from water A stream of 7000 kmolh of water and 3000 parts per million ppm by weight of ammonia at 350 K and 1 bar is to be processed to remove 90 of the ammonia What type of separation would you use If it involves an MSA propose one 126 Separation by a distillation sequence A lighthydrocarbon feed stream contains 454 kmolh of pro pane 1361 kmolh of isobutane 2268 kmolh of nbutane 1814 kmolh of isopentane and 3174 kmolh of npentane This stream is to be separated by a sequence of three distillation columns into four products 1 propanerich 2 isobutanerich 3 nbutanerich and 4 combined pentanesrich The firstcolumn distillate is the pro panerich product the distillate from Column 2 is the isobutanerich product the distillate from Column 3 is the nbutanerich product and the combined pentanes are the Column 3 bottoms The recovery of the main component in each product is 98 For example 98 of the propane in the process feed stream appears in the propane rich product a Draw a processflow diagram similar to Figure 18 b Complete a material balance for each column and summarize the results in a table similar to Table 15 To complete the balance you must make assumptions about the flow rates of 1 isobutane in the distillates for Columns 1 and 3 and 2 n butane in the distillates for Columns 1 and 2 consistent with the specified recoveries Assume that there is no propane in the distillate from Column 3 and no pentanes in the distil late from Column 2 c Calculate the mol purities of the products and summarize your results as in Table 17 but without the specifications 127 Removing organic pollutants from wastewater The need to remove organic pollutants from wastewater is common to many industrial processes Separation methods to be considered are 1 adsorption 2 distillation 3 liquid liquid extraction 4 membrane separation 5 stripping with air and 6 stripping with steam Discuss the advantages and disadvantages of each method Consider the fate of the organic material 128 Removal of VOCs from a waste gas stream Many waste gas streams contain volatile organic compounds VOCs which must be removed Recovery of the VOCs may be accomplished by 1 absorption 2 adsorption 3 condensation 4 freezing 5 membrane separation or 6 catalytic oxidation Discuss the pros and cons of each method paying particular atten tion to the fate of the VOC For the case of a stream containing 3 mol acetone in air draw a flow diagram for a process based on Exercises 33 133 Separation of an aqueous solution of bioproducts Clostridium beijerinckii is a grampositive rodshaped motile bacterium Its Ba 101 strain can ferment starch from corn to a mixture of acetone A nbutanol B and ethanol E at 37C under anaerobic conditions with a yield of more than 99 Typically the molar ratio of bioproducts is 3A6B1E When a semidefined fermentation medium containing glucose or maltodextrin supplemented with sodium acetate is used production at a titers of up to 33 g of bioproducts per liter of water in the broth is possible After removal of solid biomass from the broth by centrifugation the remaining liquid is distilled in a sequence of distillation columns to recover 1 acetone with a maximum of 10 water 2 ethanol with a maximum of 10 purity with a maximum of 05 water and 4 water W which can be recycled to the fermentation reactor If the four products distill according to their normal boiling points in C of 565 A 117 B 784 E and 100 W devise a suitable distillation sequence using the heuristics of 173 Chapter 2 Thermodynamics of Separation Operations 20 INSTRUCTIONAL OBJECTIVES After completing this chapter you should be able to Make energy entropy and availability balances around a separation process Explain phase equilibria in terms of Gibbs free energy chemical potential fugacity fugacity coefficient activity and activity coefficient Understand the usefulness of equilibrium ratios Kvalues and partition coefficients for liquid and vapor phases Derive Kvalue expressions in terms of fugacity coefficients and activity coefficients Explain how computer programs use equations of state eg SoaveRedlichKwong or PengRobinson to compute thermodynamic properties of vapor and liquid mixtures including Kvalues Explain how computer programs use liquidphase activitycoefficient correlations eg Wilson NRTL UNIQUAC or UNIFAC to compute thermodynamic properties including Kvalues For a given weak acid or base including amino acids calculate pH pKa degree of ionization pI and net charge Identify a buffer suited to maintain activity of a biological species at a target pH and evaluate effects of temperature ionic strength solvent and static charge on pH and effects of pH on solubility Determine effects of electrolyte composition on electrostatic doublelayer dimensions energies of attraction critical flocculation concentration and structural stability of biocolloids Characterize forces that govern ligandreceptorbinding interactions and evaluate dissociation constants from free energy changes for from batch solution or continuous sorption data Thermodynamic properties play a major role in separation operations with respect to energy requirements phase equilibria biological activity and equipment sizing This chapter develops equations for energy balances for entropy and availability balances and for determining densities and compositions for phases at equilibrium The equations contain thermodynamic properties including specific volume enthalpy entropy availability fugacities and activities all as functions of temperature pressure and composition Both ideal and nonideal mixtures are discussed Equations to determine ionization state solubility and interaction forces of biomolecular species are introduced However this chapter is not a substitute for any of the excellent textbooks on thermodynamics Experimental thermodynamic property data should be used when available to design and analyze the operation of separation equipment When not available properties can often be estimated with reasonable accuracy Many of these estimation methods are discussed in this chapter The most comprehensive source of thermodynamic properties for pure compounds and nonelectrolyte and electrolyte mixtures including excess volume excess enthalpy activity coefficients at infinite dilution azeotropes and vaporliquid liquidliquid and solidliquid equilibriais the computerized Dortmund Data Bank DDB wwwddbstcom initiated by Gmehling and Onken in 1973 It is updated annually and is widely used by industry and academic institutions In 2009 the DDB contained more than 39 million data points for 32000 components from more than 64000 references Besides openly available data from journals DDB contains a large percentage of data from nonEnglish sources chemical industry and MS and PhD theses 21 ENERGY ENTROPY AND AVAILABILITY BALANCES Industrial separation operations utilize large quantities of energy in the form of heat andor shaft work Distillation separations account for about 3 of the total US energy consumption Mix et al 1 The distillation of crude oil into its fractions is very energyintensive requiring about 40 of the total energy used in crudeoil refining Thus it is important to know the energy consumption in a separation process and to what degree energy requirements can be reduced Consider the continuous steadystate flow system for the separation process in Figure 21 One or more feed streams flowing into the system are separated into two or more product streams For each stream molar flow rates are denoted by n the component mole fractions by z the temperature by T the pressure by P the molar enthalpies and entropies by h and s respectively and the molar availabilities by b If chemical reactions occur in the process enthalpies and entropies are referred to the elements as discussed by Felder and Rousseau 2 otherwise they can be referred to the compounds Flows of heat in or out are denoted by Q and shaft work crossing the boundary of the system by Ws At steady state if kinetic potential and surface energy changes are neglected the first law of thermodynamics states that the sum of energy flows into the system equals the sum of the energy flows leaving the system In terms of symbols the energy balance is given by Eq 1 in Table 21 where all flowrate heattransfer and shaftwork terms are positive Molar enthalpies may be positive or negative depending on the reference state The first law of thermodynamics provides no information on energy efficiency but the second law of thermodynamics given by Eq 2 in Table 21 does In the entropy balance the heat sources and sinks in Figure 21 are at absolute temperatures Ts For example if condensing steam at 150C supplies heat Q to the reboiler of a distillation column Ts 150 273 423 K Unlike the energy balance which states that energy is conserved the entropy balance predicts the production of entropy ΔSirr which is the irreversible increase in the entropy of the universe This term which must be positive is a measure of the thermodynamic inefficiency In the limit as a reversible process is approached ΔSirr tends to zero Unfortunately ΔSirr is difficult to apply because it does not have the units of energy unit time power A more useful measure of process inefficiency is lost work LW It is derived by combining Eqs 1 and 2 to obtain a combined statement of the first and second laws which is given as Eq 3 in Table 21 To perform this derivation it is first necessary to define an infinite source or sink available for heat transfer at the absolute temperature Ts T0 of the surroundings This temperature typically 300 K represents the largest source of coolant heat sink available This might LW nHbF 1 ToTk nBpb nHcB 1 ToTC 27221338 30341683 297890001 3031378 159212243 30313068 11314 687 30323886 298110001 303303 5529000 kJh same result Wmin nHpb nHg nHbF 159212243 30318068 11314687 30323886 272213338 30341683 382100 kJh η Wmin Wmin 382100 5529000 382100 00646 or 646 Regardless of which thermodynamic formulation is used for estimating Kvalues their accuracy depends on the correlations used for the thermodynamic properties vapor pressure activity coefficient and fugacity coefficients For practical applications the choice of Kvalue formulation is a compromise among accuracy complexity convenience and past experience For liquidliquid equilibria 29 becomes 229 Kvalues for water and methane are estimated from 3 and 6 respectively in Table 23 using P 2 atm with the following results T C K H2O K CH4 αMW 20 001154 18800 1629000 80 02337 34100 146000 Note that the pressure effect and the mixing effect are significant Liquid molar volume and density From 238 for ethylbenzene ρEB 28980268350656179² 8169 kgm³ Liquid molar enthalpy datum ideal gas at 29815 K Use 5 in Table 24 for the mixture For the enthalpy of vaporization of ethylbenzene ΔHvapEB 831435065 744061 0 35065 987052 35065 6413065 1018350655 39589800 Jkmol Similarly ΔHvap S 40886700 Jkmol Then applying 5 Table 24 using hEB and hS from above hL 048487351900 39589800 051526957700 40886700 33109000 Jkmol 24 GRAPHICAL CORRELATIONS OF THERMODYNAMIC PROPERTIES Plots of thermodynamic properties are useful not only for the data they contain but also for the pictorial representation which permits the user to make general observations establish correlations and make extrapolations All process simulators that contain modules that calculate thermodynamic properties also contain programs that allow the user to make plots of the computed variables Handbooks and all thermodynamic textbooks contain generalized plots of thermodynamic properties as a function of temperature and pressure A typical plot is Figure 23 which shows vapor pressures of common chemicals for temperatures from below the normal boiling point to the critical temperature where the vapor pressure curves terminate Kvalues Because 7 Table 24 will be used to compute the Kvalues first estimate the vapor pressures using 239 For ethylbenzene ln PEB 865008 744061 0 35065 00062312135065 413065 1018350656 963481 PEB exp963481 15288 Pa 15288 kPa Similarly Ps 11492 kPa Relative volatility From 221 αEBS KEB KS 1147 0862 1331 The RK equation given as 3 in Table 25 is an improvement over the van der Waals equation Shah and Thodos 19 showed that the RK equation when applied to nonpolar compounds has accuracy comparable with that of equations containing many more constants Furthermore the RK equation can approximate the liquidphase region If the RK equation is expanded to obtain a common denominator a cubic equation in v results Alternatively 2 where A aPR2T2 247 B bPRT 248 Equation 246 a cubic in Z can be solved analytically for three roots eg see Perrys Handbook 8th ed p 310 At supercritical temperatures where only one phase exists one real root and a complex conjugate pair of roots are obtained Below the critical temperature where vapor andor liquid phases can exist three roots are obtained with the largest value of Z applying to the vapor and the smallest for the liquid ZV and ZL The intermediate value of Z is discarded To apply the RK equation to mixtures mixing rules are used to average the constants a and b for each component The recommended rules for vapor mixtures of C components are a C i1 yiaaj05 249 b C i1 ybibi 250 EXAMPLE 25 Specific Volume of a Mixture from the RK Equation Use the RK equation to estimate the specific volume of a vapor mixture containing 2692 wt propane at 400F 4776 K and a saturation pressure of 4103 psia 2829 kPa Compare the results with the experimental data of Glanville et al 20 Predictions of liquid properties based on Gibbs freeenergy models for predicting liquidphase activity coefficients and other excess functions such as volume and enthalpy of mixing are developed in this section Regularsolution theory which describes mixtures of nonpolar compounds using only constants for the pure components is presented first followed by models useful for mixtures containing polar compounds which require experimentally determined binary interaction parameters If these are not available groupcontribution methods can be used to make estimates All models can predict vaporliquid equilibria and some can estimate liquidliquid and even solidliquid and polymerliquid equilibria When the RK equation is substituted into the equations of Table 26 the results for the vapor phase are hᵥ ᵢ1 yᵢhᵢ RT Zᵥ 1 3A2B ln 1 BZᵥ 253 sᵥ ᵢ1 yᵢsᵢ R ln Ppᵥ R ᵢ1 yᵢ ln yᵢ R ln Zᵥ B 254 φᵥ exp Zᵥ 1 Zᵥ B AB ZᵥZ ln 1 BZᵥ 255 Note that the material balances are always precisely satisfied Users of simulation programs should never take this as an indication that the results are correct but instead should always verify results in all possible ways 262 RegularSolution Model 263 Nonideal Liquid Solutions Table 27 Classification of Molecules Based on Potential for Forming Hydrogen Bonds Figure 211 Typical variations of activity coefficients with composition in binary liquid systems a ethanolIInheptaneV b acetone IIIformamideII c chloroformIVmethanolII d acetoneIIIchloroformIV e waterInbutanolII Table 29 Empirical and Semitheoretical Equations for Correlating LiquidPhase Activity Coefficients of Binary Pairs Figure 212 Activity coefficients for ethanolnhexane for nhexane Nevertheless ethanol is more volatile than nhexane up to an ethanol mole fraction of xE 0322 the minimumboiling azeotrope This occurs because of the close boiling points of the two species and the high activity coefficients for ethanol at low concentrations At the azeotropic composition γ1 x1γP1 y2P2 282 for both species γ1P1 γ2P2 283 γ2 1 284 and γ1 γ2 P2 P1 285 for x1 less than the azeotropic composition These criteria are most readily applied at x1 0 For example for the nhexane 2ethanol 1 system at 1 atm when the liquidphase mole fraction of ethanol approaches zero the temperature approaches 6875C 15575F the boiling point of pure nhexane At this temperature P1 10 psia 689 kPa and P2 147 psia 1013 kPa Also from Figure 212 γ1 2172 when γ2 10 Thus γ1γ2 2172 but P2P1 147 Therefore a minimumboiling azeotrope will occur Maximumboiling azeotropes are less common They occur for closeboiling mixtures when negative deviations from Raoults law arise giving γ1 10 Criteria are derived in a manner similar to that for minimumboiling azeotropes At x1 1 where species 2 is more volatile γ1 10 286 γ2 10 287 and γ2 γ1 P1 P2 288 For azeotropic binary systems interaction parameters Λ12 and Λ21 can be determined by solving 4 of Table 29 at the azeotropic composition as shown in the following example EXAMPLE 28 Wilson Constants from Azeotropic Data From measurements by Sinor and Weber of the azeotropic condition for the ethanol Enhexane H system at 1 atm 1013 kPa 14696 psia calculate Λ12 and Λ21 Solution The azeotrope occurs at xE 0332 xH 0668 and T 58C 33115 K At 1 atm 269 can be used to approximate Kvalues Thus at azeotropic conditions γi PiPi Therefore 14696 14696 2348 Substituting these values together with the above corresponding values of x1 into the binary form of the Wilson equation in Table 29 gives 2348 ln0332 0668AHE AHE AHE 0668 0332 0668AHE 0332AHE 0668 1430 ln1068 0332AHE 0332 0332 0668AHE 0332AHE 0668 Solving these two nonlinear equations simultaneously AHE 0041 and AHE 0281 From these constants the activitycoefficient curves can be predicted if the temperature variations of AHE and AHE are ignored The results are plotted in Figure 215 The fit of experimental data is good except perhaps for nearidealdilution conditions where γE 4982 and γH 928 The former is considerably greater than the value of 2172 obtained by Oyre and Prausnitz from a fit of all data points A comparison of Figures 212 and 215 shows that wildly differing γE values have little effect on γ in the region xE 015 to 100 where the Wilson curves are almost identical For accuracy over the entire composition range data for at least three liquid compositions per binary are preferred The Wilson equation can be extended to liquidliquid or vaporliquidliquid systems by multiplying the righthand side of 278 by a third binarypair constant evaluated from experimental data However for multicomponent systems of three or more species the third binarypair constants must be the same for all binary pairs Furthermore as shown by Hiranuma representation of ternary systems 1 atm Experimental data Wilson equation constants from azeotropic condition Liquidphase activity coefficients for ethanolnhexane system C02 09292010 Page 77 6 For nonideal liquid solutions of nonpolar andor polar components freeenergy 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1950 50 Reynolds O Trans Roy Soc London 174A 935982 1883 51 Boussinesq J Mem Pre Par Div Sav XXIII Paris 1877 52 Prandtl L Z Angew Math Mech 5 136 1925 reprinted in NACA Tech Memo 1231 1949 53 Reynolds O Proc Manchester Lit Phil Soc 14 7 1874 54 Colburn AP Trans AIChE 29 174210 1933 55 Chilton TH and AP Colburn Ind Eng Chem 26 11831187 1934 56 Prandtl L Physik Z 11 1072 1910 57 Friend WL and AB Metzner AIChE J 4 393402 1958 58 Nernst W Z Phys Chem 47 52 1904 59 Higbie R Trans AIChE 31 365389 1935 60 Danckwerts PV Ind Eng Chem 43 14601467 1951 61 Levenspiel O Chemical Reaction Engineering 3rd ed John Wiley Sons New York 1999 62 Toor HL and JM Marchello AIChE J 4 97101 1958 63 Whitman WG Chem Met Eng 29 146148 1923 64 van Driest ER J Aero Sci 10071011 1036 1956 65 Reichardt H Fundamentals of Turbulent Heat Transfer NACA Report TM1408 1957 66 Drew TB EC Koo and WH McAdams Trans Am Inst Chem Engrs 28 56 1933 67 Nikuradse J VDIForschungsheft p 361 1933 68 Launder BE and DB Spalding Lectures in Mathematical Models of Turbulence Academic Press New York 1972 69 Heng L C Chan and SW Churchill Chem Eng J 71 163 1998 70 Churchill SW and SC Zajic AIChE J 48 927940 2002 71 Churchill SW Turbulent Flow and Convection The Prediction of Turbulent Flow and Convection in a Round Tube in JP Hartnett and TF Irvine Jr Ser Eds Advances in Heat Transfer Academic Press New York Vol 34 pp 255361 2001 72 Yu B H Ozoe and SW Churchill Chem Eng Sci 56 1781 2001 73 Churchill SW and C Chan Ind Eng Chem Res 34 1332 1995 74 Churchill SW AIChE J 43 1125 1997 75 Lightfoot EN Transport Phenomena and Living Systems John Wiley Sons New York 1974 134 Chapter 3 Mass Transfer and Diffusion C04 10042010 Page 157 46 MULTICOMPONENT LIQUIDLIQUID SYSTEMS Quarternary and higher multicomponent mixtures are encountered in extraction processes particularly when two solvents are used Multicomponent liquidliquid equilibria are complex and there is no compact graphical way of rep resenting phaseequilibria data Accordingly the computa tion of equilibriumphase compositions is best made by process simulators using activitycoefficient equations that account for the effect of composition eg NRTL UNI QUAC or UNIFAC One such method is a modification of the RachfordRice algorithm for vaporliquid equilibrium from Tables 43 and 44 For extraction symbol transforma tions are made and moles are used instead of mass VaporLiquid Equilibria LiquidLiquid Equilibria Feed F Feed F þ solvent S Equilibrium vapor V Extract E L1 Equilibrium liquid L Raffinate R L2 Feed mole fractions zi Mole fractions of combined F and S Vapor mole fractions yi Extract mole fractions xð1Þ i Liquid mole fractions xi Raffinate mole fractions xð2Þ i Kvalue Ki Distribution coefficient KDi C VF C ¼ EF Industrial extraction processes are commonly adiabatic so if the feeds are at identical temperatures the only energy effect is the heat of mixing which is usually sufficiently small that isothermal assumptions are justified The modified RachfordRice algorithm is shown in Figure 418 This algorithm is applicable for an isothermal vapor liquid or liquidliquid stage calculation when Kvalues depend strongly on phase compositions The algorithm requires that feed and solvent flow rates and compositions be fixed and that pressure and temperature be specified An initial estimate is made of the phase compositions xð1Þ i and xð2Þ i and corresponding estimates of the distribution coefficients are made from liquidphase activity coefficients using 230 with for example the NRTL or UNIQUAC equations dis cussed in Chapter 2 Equation 3 of Table 44 is then solved iteratively for C ¼ EF þ S from which values of xð2Þ i and xð1Þ i are computed from Eqs 5 and 6 respectively of Table 44 Resulting values of xð1Þ i and xð2Þ i will not usually sum to 1 for each phase and are therefore normalized using equations of the form x 0 i ¼ xiSxj where x 0 i are the normal ized values that force P x 0 j to equal 1 Normalized values replace the values computed from Eqs 5 and 6 The itera tive procedure is repeated until the compositions xð1Þ i and xð2Þ i no longer change by more than three or four significant digits from one iteration to the next Multicomponent liquidliquid equilibrium calculations are best carried out with a process simulator Initial estimate of x y Calculate K fx y T P Iteratively calculate Calculate x and y New estimate of x and y if not direct iteration Estimate Kvalues Converged Start F z fixed P T of equilibrium phases fixed Not converged a Composition loop Compare estimated and calculated values of x and y ψ Initial estimate of x y Calculate K fx y T P Calculate k 1 Calculate x and y Estimate Kvalues Converged exit Start F z fixed P T of equilibrium phases fixed Not converged b Normalize x and y Compare estimated and normalized values Compare k 1 and k ψ ψ ψ Figure 418 Algorithm for isothermalflash calculation when Kvalues are compositiondependent a separate nested iterations on C and x y b simultaneous iteration on C and x y 46 Multicomponent LiquidLiquid Systems 157 C05 09172010 Page 181 one below If S2 is boiling vapor produced by steam or partial vaporization of P2 by a boiler and S1 is liquid reflux pro duced by partial condensation of P1 this is a simple distilla tion column If two solvents are used where S1 selectively dissolves certain components of the feed while S2 is more selective for the other components the process is fractional liquidliquid extraction Figure 52e is an interlinked system of two distillation col umns containing six countercurrent cascade sections Reflux and boilup for the first column are provided by the second column This system can take a threecomponent feed F and produce three almost pure products P1 P2 and P3 In this chapter a countercurrent singlesection cascade for a leaching or washing process is considered first Then cocurrent crosscurrent and countercurrent singlesection cascades are compared for a liquidliquid extraction process After that a singlesection countercurrent cascade is devel oped for a vaporliquid absorption operation Finally mem brane cascades are described In the first three cases a set of linear algebraic equations is reduced to a single relation for estimating the extent of separation as a function of the num ber of stages the separation factor and the ratio of mass or energyseparating agent to the feed In later chapters it will be seen that for cascade systems easily solved equations can not be obtained from rigorous models making calculations with a process simulator a necessity 52 SOLIDLIQUID CASCADES The Nstage countercurrent leachingwashing process in Figure 53 is an extension of the singlestage systems in 47 The solid feed entering stage 1 consists of two components A and B of mass flow rates FA and FB Pure solvent C which enters stage N at flow rate S dissolves solute B but not insoluble carrier A The concentrations of B are expressed in terms of mass ratios of solutetosolvent Y Thus the liquid overflow from each stage j contains Yj mass of soluble mate rial per mass of solutefree solvent The underflow is a slurry consisting of a mass flow FA of insoluble solids a constant ratio of mass of solventtomass of insoluble solids R and Xj mass of soluble materialtomass of solutefree solvent For a given feed a relationship between the exiting underflow con centration of the soluble component XN the solvent feed rate S and the number of stages N is derived next All soluble material B in the feed is leached in stage 1 and all other stages are then washing stages for reducing the amount of soluble material lost in the underflow leaving the last stage N thereby increasing the amount of soluble mate rial leaving in the overflow from stage 1 By solvent material balances for constant R the flow rate of solvent leaving in the Stage 1 Feed Product 1 Product 2 Massseparating agent Stage 2 Stage 3 Stage 4 Figure 51 Cascade of contacting stages 1 2 3 S a b d e c S F S1 S2 F F P1 P1 F 4 5 6 2 1 3 P2 P2 P2 P2 P2 P1 P1 P1 P3 P3 P3 P4 P4 1 S F 5 7 8 9 6 3 2 4 Figure 52 Cascade configurations a countercurrent b crosscurrent c twodimensional diamond d twosection countercurrent e interlinked system of countercurrent cascades Y1 Y2 X1 Solid feed 1 2 Insoluble A Soluble B FA FB Y3 X2 Yn 1 Yn Xn1 XN2 Xn YN 1 YN XN1 XN S Solvent C n N1 N Figure 53 Countercurrent leaching or washing system 52 SolidLiquid Cascades 181 C05 09172010 Page 187 Effective Ae or Se factor Effective Ae or Se factor 01 090 080 070 060 050 040 030 020 010 005 002 001 0005 0002 0001 00005 00001 000005 000001 0000005 0000001 00000005 00000001 000000001 000000005 090 080 070 060 050 040 030 020 010 005 002 001 0005 0002 0001 00005 00001 000005 000001 0000005 0000001 00000005 00000001 000000001 000000005 015 02 025 03 035 04 045 05 06 01 015 02 025 03 035 04 045 05 06 07 08 09 10 15 Number of theoretical plates 2 25 3 35 4 45 5 6 7 8 9 10 07 08 09 10 15 2 25 3 35 4 45 5 6 7 8 9 10 φA or φS φA φS fraction not stripped fraction not absorbed Functions of absorption and stripping factors φA or φS Ae 1 Ae N 1 1 Se 1 Se N 1 1 1 1 2 2 3 3 4 4 6 10 20 30 5 6 7 8 9 10 12 14 20 30 Figure 59 Plot of Kremser equation for a singlesection countercurrent cascade From WC Edmister AIChE J 3 165171 1957 54 Multicomponent VaporLiquid Cascades 187 C05 09172010 Page 189 cascade called a stripping section is similar to that of the stripper shown in Figure 58b However instead of using a stripping vapor the liquid leaving the bottom stage enters a partial reboiler that produces the stripping vapor and a bot toms product rich in noctane Vapor leaving the top of the bottom section is combined with the vapor feed to the top section resulting in a distilla tion column shown in Figure 512c Twosection cascades of this type are the industrial workhorses of the chemical indus try because they produce nearly pure liquid and vapor prod ucts The twosection cascade in Figure 512c is applied to the distillation of binary mixtures in Chapter 7 and multi component mixtures in Chapters 9 and 10 55 MEMBRANE CASCADES Membraneseparation systems often consist of multiple membrane modules because a single module may not be large enough to handle the required feed rate Figure 513a shows a number of modules of identical size in parallel with retentates and permeates from each module combined For example a membraneseparation system for separating hydrogen from methane might require a membrane area of 9800 ft2 If the largest membrane module available has 3300 ft2 of membrane surface three modules in parallel are required The parallel units function as a single stage If in addition a large fraction of the feed is to become permeate it may be necessary to carry out the membrane separation in two or more stages as shown in Figure 513b for four stages with the number of modules reduced for each successive stage as the flow rate on the feedretentate side of the mem brane decreases The combined retentate from each stage becomes the feed for the next stage The combined permeates for each stage which differ in composition from stage to stage are combined to give the final permeate as shown in Figure 513b where required interstage compressors andor pumps are not shown Singlemembrane stages are often limited in the degree of separation and recovery achievable In some cases a high purity can be obtained but only at the expense of a low recovery In other cases neither a high purity nor a high recovery can be obtained The following table gives two examples of the separation obtained for a single stage of gas permeation using a commercial membrane Feed Molar Composition More Permeable Component Product Molar Composition Percent Recovery 85 H2 H2 99 H2 60 of H2 15 CH4 1 CH4 in the permeate in the feed 80 CH4 N2 97 CH4 57 of CH4 20 N2 3 N2 in the retentate in the feed Stage 3 187F 1635F D 361 Stage 2 205F Stage 1 215F Feed Feed a b c Boilup V1 L2 Reflux LD 281 xHD 0872 Feed F 100 TF 1923F xHF 050 Q 904 MBH L1 639 xH1 0290 Boiler Stage 1 Stage 2 Stage 3 Stage 2 Partial reboiler Partial reboiler Bottoms Stage 3 Stage 4 Stage 5 Stage 6 Stripping section Rectifying section Stage 7 Total condenser Distillate Reflux LR VN Total condenser Q 874 MBH Figure 512 Development of a twosection cascade a rectifying section b stripping section c multistage distillation Retentate Feed Permeate Stage 1 a One stage Retentate Feed Permeate Stage 1 Stage 2 Stage 3 Stage 4 b Multiple stage Figure 513 Parallel units of membrane separators 55 Membrane Cascades 189 C05 09172010 Page 190 In the first example the permeate purity is quite high but the recovery is not In the second example the purity of the retentate is reasonably high but the recovery is not To improve purity and recovery membrane stages are cascaded with recycle Shown in Figure 514 are three membrane separation systems studied by Prasad et al 5 for the pro duction of pure nitrogen retentate from air using a membrane material that is more permeable to oxygen The first system is just a single stage The second system is a cas cade of two stages with recycle of permeate from the second to the first stage The third system is a cascade of three stages with permeate recycles from stage 3 to stage 2 and stage 2 to stage 1 The two cascades are similar to the singlesection countercurrent stripping cascade shown in Figure 58b Prasad et al 5 give the following results for the three con figurations in Figure 514 Membrane System Mol N2 in Retentate Recovery of N2 Single Stage 98 45 Two Stage 995 48 Three Stage 999 50 Thus high purities are obtained with a singlesection mem brane cascade but little improvement in the recovery is pro vided by additional stages To obtain both high purity and high recovery a twosection membrane cascade is necessary as discussed in 143 56 HYBRID SYSTEMS Hybrid systems encompassing two or more different separa tion operations in series have the potential for reducing energy and rawmaterial costs and accomplishing difficult separations Table 51 lists hybrid systems used commer cially that have received considerable attention Examples of applications are included Not listed in Table 51 are hybrid systems consisting of distillation combined with extractive distillation azeotropic distillation andor liquidliquid extr action which are considered in Chapter 11 The first example in Table 51 is a hybrid system that com bines pressureswing adsorption PSA to preferentially remove methane with a gaspermeation membrane operation to remove nitrogen The permeate is recycled to the adsorp tion step Figure 515 compares this hybrid system to a sin glestage gaspermeation membrane and a singlestage pressureswing adsorption Only the hybrid system is capable of making a sharp separation between methane and nitrogen Products obtainable from these three processes are compared in Table 52 for 100000 scfh of feed containing 80 meth ane and 20 nitrogen For all processes the methanerich Feed 1 Permeate Retentate Feed 1 2 Permeate Recycle Retentate Feed 1 2 3 Permeate Recycle Recycle Retentate Figure 514 Membrane cascades Table 51 Hybrid Systems Hybrid System Separation Example Adsorptiongas permeation NitrogenMethane Simulated moving bed Metaxyleneparaxylene with adsorptiondistillation ethylbenzene eluent Chromatographycrystallization Crystallizationdistillation Crystallizationpervaporation Crystallizationliquidliquid extraction Sodium carbonatewater Distillationadsorption Ethanolwater Distillationcrystallization Distillationgas permeation Propylenepropane Distillationpervaporation Ethanolwater Gas permeationabsorption Dehydration of natural gas Reverse osmosisdistillation Carboxylic acidswater Reverse osmosisevaporation Concentration of wastewater Strippergas permeation Recovery of ammonia and hydrogen sulfide from sour water Feed Membrane Membrane a Membrane alone Retentate Permeate N2rich Feed PSA b Adsorption alone Exhaust Adsorbate CH4rich Feed PSA c Adsorptionmembrane hybrid Recycle N2rich CH4rich Figure 515 Separation of methane from nitrogen 190 Chapter 5 Cascades and Hybrid Systems C05 09172010 Page 191 product contains 97 mol methane Only the hybrid system gives a nitrogenrich product of greater than 90 mol and a high recovery of methane 98 The methane recovery for a membrane alone is only 57 while the adsorber gives 86 No application is shown in Table 51 for crystallization and distillation However there is much interest in these processes because Berry and Ng 6 show that such systems can over come limitations of eutectics in crystallization and azeotropes in distillation Furthermore although solids are more difficult to process than fluids crystallization requires just a single stage to obtain high purity Figure 516 includes one of the distillation and crystallization hybrid configurations of Berry and Ng 6 The feed of A and B as shown in the phase dia gram forms an azeotrope in the vaporliquid region and a eutectic in the liquidsolid region at a lower temperature The feed composition in Figure 516d lies between the eutectic and azeotropic compositions If distillation alone is used the dis tillate composition approaches that of the minimumboiling azeotrope Az and the bottoms approaches pure A If melt crystallization is used the products are crystals of pure B and a mother liquor approaching the eutectic Eu The hybrid sys tem in Figure 516 combines distillation with melt crystalliza tion to produce pure B and nearly pure A The feed is distilled and the distillate of nearazeotropic composition is sent to the melt crystallizer Here the mother liquor of neareutectic composition is recovered and recycled to the distillation col umn The net result is nearpure A obtained as bottoms from distillation and pure B obtained from the crystallizer The combination of distillation and membrane pervapora tion for separating azeotropic mixtures particularly ethanol water is also receiving considerable attention Distillation produces a bottoms of nearly pure water and an azeotrope distillate that is sent to the pervaporation step which pro duces a nearly pure ethanol retentate and a waterrich perme ate that is recycled to the distillation step 57 DEGREES OF FREEDOM AND SPECIFICATIONS FOR CASCADES The solution to a multicomponent multiphase multistage separation problem involves materialbalance energybalance and phaseequilibria equations This implies that a sufficient number of design variables should be specified so that the number of remaining unknown variables equals the number of independent equations relating the variables The degrees offreedom analysis discussed in 41 for a single equili brium stage is now extended to one and multiplesection cascades Although the extension is for continuous steady state processes similar extensions can be made for batch and semicontinuous processes Table 52 Typical Products for Processes in Figure 515 Flow Rate Mol Mol Mscfh CH4 N2 Feed gas 100 80 20 Membrane only Retentate 471 97 3 Permeate 529 65 35 PSA only Adsorbate 706 97 3 Exhaust 294 39 61 Hybrid system CH4rich 810 97 3 N2rich 190 8 92 a Distillation alone Feed A B Distillation Nearly pure A Minimumboiling azeotrope Az b Melt crystallization alone Feed A B Melt crystallization Pure B Eutectic mother liquor Eu c Distillationcrystallization hybrid d Phase diagram for distillationcrystallization hybrid system Feed A B Distillation Melt crystallization Pure B Nearly pure A Eu Az A B 0 100 B in A Eutectic Solid Vapor Liquid Feed Azeotrope Temperature Figure 516 Separation of an azeotropic and eutecticforming mixture 57 Degrees of Freedom and Specifications for Cascades 191 C05 09172010 Page 194 Table 53 Degrees of Freedom for Separation Operation Elements and Units Schematic Element or Unit Name NV Total Number of Variables NE Independent Relationships ND Degrees of Freedom a Q V L Total boiler reboiler 2C þ 7 C þ 3 C þ 4 b Q L V Total condenser 2C þ 7 C þ 3 C þ 4 c Q Vout Lout Lin Partial equilibrium boiler reboiler 3C þ 10 2C þ 6 C þ 4 d Q Vout Lout Vin Partial equilibrium condenser 3C þ 10 2C þ 6 C þ 4 e Vout Lin Vin Lout Adiabatic equilibrium stage 4C þ 12 2C þ 7 2C þ 5 f Vout Q Lin Vin Lout Equilibrium stage with heat transfer 4C þ 13 2C þ 7 2C þ 6 g Vout Lin Vin Lout Q F Equilibrium feed stage with heat transfer and feed 5C þ 16 2C þ 8 3C þ 8 h Vout Lin Vin Lout Q as Equilibrium stage with heat transfer and sidestream 5C þ 16 3C þ 9 2C þ 7 i Stage N Stage 1 Vout Lin Vin Lout QN QN 1 Q2 Q1 Nconnected equilibrium stages with heat transfer 7N þ 2NC þ 2C þ 7 5N þ 2NC þ 2 2N þ 2C þ 5 j L3 Q L1 L2 Stream mixer 3C þ 10 C þ 4 2C þ 6 k L3 Q bL1 L2 Stream divider 3C þ 10 2C þ 5 C þ 5 aSidestream can be vapor or liquid bAlternatively all streams can be vapor 194 Chapter 5 Cascades and Hybrid Systems C05 09172010 Page 195 Table 54 Typical Variable Specifications for Design Cases Variable Specificationa Unit Operation ND Case I Component Recoveries Specified Case II Number of Equilibrium Stages Specified a Absorption two inlet streams N 1 MSAC F 2N þ 2C þ 5 1 Recovery of one key component 1 Number of stages b Distillation one inlet stream total condenser partial reboiler N F 2 Total condenser Divider Partial reboiler 2N þ C þ 9 1 Condensate at sat uration temperature 2 Recovery of light key component 3 Recovery of heavykey component 4 Reflux ratio minimum 5 Optimal feed stageb 1 Condensate at satu ration temperature 2 Number of stages above feed stage 3 Number of stages below feed stage 4 Reflux ratio 5 Distillate flow rate c Distillation one inlet stream partial condenser partial reboiler vapor distillate only N F 2 Partial condenser Partial reboiler 2N þ C þ 6 1 Recovery of light key component 2 Recovery of heavy key component 3 Reflux ratio minimum 4 Optimal feed stageb 1 Number of stages above feed stage 2 Number of stages below feed stage 3 Reflux ratio 4 Distillate flow rate d Liquidliquid extraction with two solvents three inlet streams N F 1 MSA1 C CMSA2 2N þ 3C þ 8 1 Recovery of key component 1 2 Recovery of key component 2 1 Number of stages above feed 2 Number of stages below feed e Reboiled absorption two inlet streams N F 2 Partial reboiler MSAC 2N þ 2C þ 6 1 Recovery of light key component 2 Recovery of heavykey component 3 Optimal feed stageb 1 Number of stages above feed 2 Number of stages below feed 3 Bottoms flow rate f Reboiled stripping one inlet stream N 2 F Partial reboiler 2N þ C þ 3 1 Recovery of one key component 2 Reboiler heat dutyd 1 Number of stages 2 Bottoms flow rate Continued 57 Degrees of Freedom and Specifications for Cascades 195 C05 09172010 Page 196 Table 54 Continued Variable Specificationa Unit Operation ND Case I Component Recoveries Specified Case II Number of Equilibrium Stages Specified g Distillation one inlet stream partial condenser partial reboiler both liquid and vapor distillates N F 2 Partial reboiler Partial condenser Liquid Divider Vapor 2N þ C þ 9 1 Ratio of vapor dis tillate to liquid distillate 2 Recovery of light key component 3 Recovery of heavykey component 4 Reflux ratio minimum 5 Optimal feed stageb 1 Ratio of vapor distil late to liquid distillate 2 Number of stages above feed stage 3 Number of stages below feed stage 4 Reflux ratio 5 Liquid distillate flow rate h Extractive distillation two inlet streams total condenser partial reboiler single phase condensate N MSAC 2 F Partial reboiler Total condenser Liquid Divider 2N þ 2C þ 12 1 Condensate at saturation temperature 2 Recovery of light key component 3 Recovery of heavykey component 4 Reflux ratio minimum 5 Optimal feed stageb 6 Optimal MSA stageb 1 Condensate at satu ration temperature 2 Number of stages above MSA stage 3 Number of stages between MSA and feed stages 4 Number of stages below feed stage 5 Reflux ratio 6 Distillate flow rate i Liquidliquid extraction two inlet streams N 1 MSAC F 2N þ 2C þ 5 1 Recovery of one key component 1 Number of stages j Stripping two inlet streams N 1 MSAC F 2N þ 2C þ 5 1 Recovery of one key component 1 Number of stages aDoes not include the following variables which are also assumed specified all inlet stream variables C þ 2 for each stream all element and unit pressures all element and unit heattransfer rates except for condensers and reboilers bOptimal stage for introduction of inlet stream corresponds to minimization of total stages cFor case I variable specifications MSA flow rates must be greater than minimum values for specified recoveries dFor case I variable specifications reboiler heat duty must be greater than minimum value for specified recovery 196 Chapter 5 Cascades and Hybrid Systems C05 09172010 Page 198 Heat duties QC and QR are not good design variables because they are difficult to specify A specified condenser duty QC might result in a temperature that is not realizable Similarly it is much easier to calculate QR knowing the total flow rate and enthalpy of the bottom streams than vice versa QR and QC are so closely related that both should not be spec ified Preferably QC is fixed by distillate rate and reflux ratio and QR is calculated from the overall energy balance Other proxies are possible but the problem of indepen dence of variables requires careful consideration Distillate product rate QC and LRD for example are not independent It should also be noted that if recoveries of more than two key species are specified the result can be nonconvergence of the computations because the specified composition may not exist at equilibrium As an alternative to the solution to Example 54 the degrees of freedom for the unit of Figure 519 can be det ermined quickly by modifying a similar unit in Table 54 The closest unit is b which differs from that in Figure 519 by only a sidestream From Table 53 an equilibrium stage with heat transfer but without a sidestream f has ND ¼ 2C þ 6 while an equilibrium stage with heat transfer and a sidestream h has ND ¼ 2C þ 7 or one additional degree of freedom When this sidestream stage is in a cascade an additional degree of freedom is added for its location Thus two degrees of freedom are added to ND ¼ 2N þ C þ 9 for unit operation b in Table 54 The result is ND ¼ 2N þ C þ 11 which is identical to that determined in Example 54 In a similar manner the above example can be readily modified to include a second feed stage By comparing val ues for elements f and g in Table 53 we see that a feed adds C þ 2 degrees of freedom In addition one more degree of freedom must be added for the location of this feed stage in a cascade Thus a total of C þ 3 degrees of freedom are added giving ND ¼ 2N þ 2C þ 14 SUMMARY 1 A cascade is a collection of stages arranged to a accomplish a separation not achievable in a sin gle stage andor b reduce the amount of mass or energyseparating agent 2 Cascades are single or multiplesectioned and con figured in cocurrent crosscurrent or countercurrent arrays Cascades are readily computed if equations are linear in component split ratios 3 Equation 510 gives stage requirements for counter current solidliquid leaching andor washing involving constant underflow and mass transfer of one component 4 Stages required for singlesection liquidliquid extraction with constant distribution coefficients and immiscible solvent and carrier are given by 519 522 and 529 for respectively cocurrent crosscurrent and the most efficient countercurrent flow 5 Singlesection stage requirements for a countercurrent cascade for absorption and stripping can be estimated with the Kremser equations 548 550 554 and 555 Such cascades are limited in their ability to achieve high degrees of separation 6 A twosection countercurrent cascade can achieve a sharp split between two key components The top recti fying section purifies the light components and inc reases recovery of heavy components The bottom stripping section provides the opposite functions 7 Equilibrium cascade equations involve parameters referred to as washing W extraction E absorption A and stripping S factors and distribution coefficients such as K KD and R and phase flow ratios such as SF and LV 8 Singlesection membrane cascades increase purity of one product and recovery of the main component in that product 9 Hybrid systems may reduce energy expenditures and make possible separations that are otherwise difficult andor improve the degree of separation 10 The number of degrees of freedom number of specifica tions for a mathematical model of a cascade is the dif ference between the number of variables and the number of independent equations relating those equations For a singlesection countercurrent cascade the recovery of one component can be specified For a twosection countercurrent cascade two recoveries can be specified REFERENCES 1 Berdt RJ and CC Lynch J Am Chem Soc 66 282284 1944 2 Kremser A Natl Petroleum News 2221 4349 May 21 1930 3 Edmister WC AIChE J 3 165171 1957 4 Smith BD and WK Brinkley AIChE J 6 446450 1960 5 Prasad R F Notaro and DR Thompson J Membrane Science 94 Issue 1 225248 1994 6 Berry DA and KM Ng AIChE J 43 17511762 1997 7 Kwauk M AIChE J 2 240248 1956 8 Gilliland ER and CE Reed Ind Eng Chem 34 551557 1942 STUDY QUESTIONS 51 What is a separation cascade What is a hybrid system 52 What is the difference between a countercurrent and a cross current cascade 53 What is the limitation of a singlesection cascade Does a twosection cascade overcome this limitation 54 What is an interlinked system of stages 198 Chapter 5 Cascades and Hybrid Systems C05 09172010 Page 199 55 Which is more efficient a crosscurrent cascade or a counter current cascade 56 Under what conditions can a countercurrent cascade achieve complete extraction 57 Why is a twosection cascade used for distillation 58 What is a group method of calculation 59 What is the Kremser method To what type of separation operations is it applicable What are the major assumptions of the method 510 What is an absorption factor What is a stripping factor 511 In distillation what is meant by reflux boilup rectification section and stripping section 512 Under what conditions is a membrane cascade of multiple stages in series necessary 513 Why are hybrid systems often considered 514 Give an example of a hybrid system that involves recycle 515 Explain how a distillationcrystallization hybrid system works for a binary mixture that exhibits both an azeotrope and a eutectic 516 When solving a separation problem are the number and kind of specifications obvious If not how can the required number of specifications be determined 517 Can the degrees of freedom be determined for a hybrid system If so what is the easiest way to do it EXERCISES Section 51 51 Interlinked cascade arrangement Devise an interlinked cascade like Figure 52e but with three columns for separating a fourcomponent feed into four products 52 Batchwise extraction process A liquidliquid extraction process is conducted batchwise as shown in Figure 520 The process begins in Vessel 1 Original where 100 mg each of solutes A and B are dissolved in 100 mL of water After adding 100 mL of an organic solvent that is more selec tive for A than B the distribution of A and B becomes that shown for Equilibration 1 with Vessel 1 The organicrich phase is transferred to Vessel 2 Transfer leaving the waterrich phase in Vessel 1 Transfer The water and the organic are immiscible Next 100 mL of water is added to Vessel 2 resulting in the phase distribu tion shown for Vessel 2 Equilibration 2 Also 100 mL of organic is added to Vessel 1 to give the phase distribution shown for Vessel 1 Equilibration 2 The batch process is continued by adding Vessel 3 and then 4 to obtain the results shown a Study Figure 520 and then draw a corresponding cascade diagram labeled in a manner similar to Figure 52b b Is the process cocurrent countercurrent or crosscurrent c Compare the separation with that for a batch equilibrium step d How could the cascade be modified to make it countercurrent See O Post and LC Craig Anal Chem 35 641 1963 53 Twostage membrane cascade Nitrogen is removed from a gas mixture with methane by gas permeation see Table 12 using a glassy polymer membrane that is selective for nitrogen However the desired degree of separation cannot be achieved in one stage Draw sketches of two different twostage membrane cascades that might be used Section 52 54 Multistage leaching of oil In Example 49 8325 of the oil is leached by benzene using a single stage Calculate the percent extraction of oil if a two coun tercurrent equilibrium stages are used to process 5000 kgh of soy bean meal with 5000 kgh of benzene b three countercurrent stages are used with the flows in part a c Also determine the number of countercurrent stages required to extract 98 of the oil with a solvent rate twice the minimum 55 Multistage leaching of Na2CO3 For Example 51 involving the separation of sodium carbonate from an insoluble oxide compute the minimum solvent feed rate What is the ratio of actual solvent rate to the minimum solvent rate Determine and plot the percent recovery of soluble solids with a cas cade of five countercurrent equilibrium stages for solvent flow rates from 15 to 75 times the minimum value 56 Production of aluminum sulfate Aluminum sulfate alum is produced as an aqueous solution from bauxite ore by reaction with aqueous sulfuric acid fol lowed by threestage countercurrent washing to separate soluble aluminum sulfate from the insoluble content of the bauxite which is then followed by evaporation In a typical process 40000 kgday of solid bauxite containing 50 wt Al2O3 and 50 inert is crushed and fed with the stoichiometric amount of 50 wt aqueous sulfuric acid to a reactor where the Al2O3 is Organic Aqueous 74 A 148 B 37 A 296 B Organic Aqueous 111 A 444 B Organic Aqueous 25 A 99 B 12 A 197 B Organic Aqueous Equilibration 3 Transfer Equilibration 4 Transfer 37 A 296 B 296 A 148 B 148 A 296 B 296 A 37 B 148 A 74 B 222 A 222 B 222 A 222 B 148 A 148 B 74 A 296 B 74 A 148 B 148 A 296 B 444 A 111 B 296 A 74 B 148 A 148 B 296 A 148 B 148 A 74 B 197 A 12 B 99A 25 B 296 A 37 B Vessel 4 Vessel 3 Organic Aqueous 667 A 333 B 333 A 667 B Organic Aqueous 100 A 100 B Organic Aqueous 222 A 222 B 111 A 444 B Organic Aqueous Equilibration 1 Original Equilibration 2 Transfer 333 A 667 B 444 A 111 B 222 A 222 B 667 A 333 B Vessel 2 Vessel 1 Figure 520 Liquidliquid extraction process for Exercise 52 Exercises 199 C05 09172010 Page 202 532 Degrees of freedom for a reboiled stripper A reboiled stripper shown in Figure 523 is to be designed Determine a the number of variables b the number of equations relating the variables and c the number of degrees of freedom Also indicate d which additional variables if any need to be specified 533 Degrees of freedom of a thermally coupled distillation system The thermally coupled distillation system in Figure 524 sepa rates a mixture of three components Determine a the number of variables b the number of equations relating the variables and c the number of degrees of freedom Also propose d a reasonable set of design variables 534 Adding a pasteurization section to distillation column When feed to a distillation column contains impurities that are much more volatile than the desired distillate it is possible to separate the volatile impurities from the distillate by removing the distillate as a liquid sidestream from a stage several stages below the top As shown in Figure 525 this additional section of stages is referred to as a pasteurizing section a Determine the number of degrees of free dom for the unit b Determine a reasonable set of design variables 535 Degrees of freedom for a twocolumn system A system for separating a feed into three products is shown in Figure 526 Determine a the number of variables b the number of equations relating the variables and c the number of degrees of freedom Also propose d a reasonable set of design variables 536 Design variables for an extractive distillation A system for separating a binary mixture by extractive distilla tion followed by ordinary distillation for recovery and recycle of the solvent is shown in Figure 527 Are the design variables shown sufficient to specify the problem completely If not what additional design variabless should be selected 537 Design variables for a threeproduct distillation column A single distillation column for separating a threecomponent mixture into three products is shown in Figure 528 Are the design variables shown sufficient to specify the problem completely If not what additional design variables would you select Condenser Pump Steam Feed F D1 D2 D3 P L QC Figure 522 Conditions for Exercise 531 Overhead Feed 40F 300 psia kmolh 10 544 676 1411 1547 560 333 Comp N2 C1 C2 C3 C4 C5 C6 Bottoms 9 2 Figure 523 Conditions for Exercise 532 Liquid Liquid Liquid Total condenser M N 1 2 Partial reboiler Feed Product 1 Product 2 Product 3 Vapor Vapor Figure 524 Conditions for Exercise 533 Volatile impurities Distillate Bottoms Feed 2 Pasteurizing section M N Figure 525 Conditions for Exercise 534 Product 2 Product 3 Cooler Product 1 Feed 2 F N S 2 M Total condenser Valve Partial reboiler Partial reboiler Figure 526 Conditions for Exercise 535 202 Chapter 5 Cascades and Hybrid Systems C05 09172010 Page 203 500 kmolhr 2 30 35 Phenol recycle Cyclohexane product Benzene product 501 kmolh 300 kmolh 1atm bubblepoint liquid kmolh Cyclohexane Benzene 55 45 Makeup phenol 30C 1 atm Essentially 1 atm pressure throughout system 200 kmolh 10 15 2 Steam Steam cw cw cw Figure 527 Conditions for Exercise 536 872 kg molh 1 of benzene in the feed 9995 mol benzene 140 kPa cw 204 kPa 2 10 20 Valve kmolh 2615 846 51 Benzene Toluene Biphenyl 200C 1140 kPa 40 Figure 528 Conditions for Exercise 537 Exercises 203 PART02 09292010 9303 Page 205 Part Two SeparationsbyPhase AdditionorCreation In Part Two of this book common industrial chemical separation methods of absorption stripping distillation and liquidliquid extraction which involve mass trans fer of components from a liquid to a gas from a gas to a liquid or from a liquid to another immiscible liquid are described Separations based on solidgas or solid liquid phases are covered in Parts Three and Four Second phases are created by thermal energy energy separating agent or addition of mass massseparating agent Design and analysis calculations for counter current vaporliquid and liquidliquid operations are pre sented in Chapters 6 to 13 where two types of mathematical models are considered 1 stages that attain thermodynamic phase equilibrium and 2 stages that do not whose design is governed by rates of mass transfer Equilibriumstage models corrected with stage efficien cies are in common use but wide availability of digital computations is encouraging increased use of more accu rate and realistic masstransfer models Absorption and stripping which are covered in Chapter 6 rely on the addition of a massseparating agent but may also use heat transfer to produce a sec ond phase These operations are conducted in single section cascades and therefore do not make sharp separations but can achieve high recoveries of one key component The equipment consists of columns con taining trays or packing for good turbulentflow contact of the two phases Graphical and algebraic methods for computing stages and estimating tray efficiency col umn height and diameter are described Distillation of binary mixtures in multiplestage trayed or packed columns is covered in Chapter 7 with emphasis on the McCabeThiele graphical equili briumstage model To separate nonazeotropic binary mixtures into pure products twosection rectifying and stripping cascades are required Energyuse analyses and equipmentsizing methods for absorption and stripping in Chapter 6 generally apply to distillation dis cussed in Chapter 7 Liquidliquid extraction which is widely used in bio separations and when distillation is too expensive or the chemicals are heat labile is presented in Chapter 8 Col umns with mechanically assisted agitation are useful when multiple stages are needed Centrifugal extractors are advantageous in bioseparations because they provide short residence times avoid emulsions and can separate liquid phases with small density differences That chapter emphasizes graphical equilibriumstage methods Models and calculations for multicomponent mix tures are more complex than those for binary mixtures Approximate algebraic methods are presented in Chap ter 9 while rigorous mathematical methods used in pro cess simulators are developed in Chapter 10 Chapter 11 considers design methods for enhanced distillation of mixtures that are difficult to separate by conventional distillation or liquidliquid extraction An important aspect of enhanced distillation is the use of residuecurve maps to determine feasible products Extractive azeotropic and salt distillation use massaddition as well as thermal energy input Also included in Chapter 11 is pressureswing distillation which involves two columns at different pressures reactive distillation which couples a chemical reaction with product separation and supercriticalfluid extrac tion which makes use of favorable properties in the vicinity of the critical point to achieve a separation Masstransfer models for multicomponent separation operations are available in process simulators These models described in Chapter 12 are particularly useful when stage efficiency is low or uncertain Batch distillation is important in the specialty prod uct chemical industry Calculation methods are pre sented in Chapter 13 along with an introduction to methods for determining an optimal set of operation steps 205 C06 09302010 Page 208 611 Trayed Columns Absorbers and strippers are mainly trayed towers plate col umns and packed columns and less often spray towers bub ble columns and centrifugal contactors all shown in Figure 62 A trayed tower is a vertical cylindrical pressure vessel in which vapor and liquid flowing countercurrently are con tacted on trays or plates that provide intimate contact of liq uid with vapor to promote rapid mass transfer An example of a tray is shown in Figure 63 Liquid flows across each tray over an outlet weir and into a downcomer which takes the liquid by gravity to the tray below Gas flows upward through openings in each tray bubbling through the liquid on the tray When the openings are holes any of the five twophaseflow regimes shown in Figure 64 and analyzed by Lockett 2 may occur The most common and favored regime is the froth regime in which the liquid phase is continuous and the gas passes through in the form of jets or a series of bubbles The spray regime in which the gas phase is continuous occurs for low weir heights low liquid depths at high gas rates For low gas rates the bubble regime can occur in which the liquid is fairly quiescent and bubbles rise in swarms At high liquid rates small gas bubbles may be undesirably emul sified If bubble coalescence is hindered an undesirable foam forms Ideally the liquid carries no vapor bubbles occlusion to the tray below the vapor carries no liquid droplets entrain ment to the tray above and there is no weeping of liquid through the holes in the tray With good contacting equili brium between the exiting vapor and liquid phases is approached on each tray unless the liquid is very viscous Shown in Figure 65 are tray openings for vapor passage a perforations b valves and c bubble caps The simplest is perforations usually 1 8 to 1 2 inch in diameter used in sieve perforated trays A valve tray has openings commonly from 1 to 2 inches in diameter Each hole is fitted with a valve consisting of a cap that overlaps the hole with legs or a cage to limit vertical rise while maintaining the valve cap in a hor izontal orientation Without vapor flow each valve covers a hole As vapor rate increases the valve rises providing a larger opening for vapor to flow and to create a froth A bubblecap tray consists of a cap 3 to 6 inches in diame ter mounted over and above a concentric riser 2 to 3 inches in diameter The cap has rectangular or triangular slots cut around its side The vapor flows up through the tray opening into the riser turns around and passes out through the slots and into the liquid forming a froth An 11ftdiameter tray might have 50000 3 16 inchdiameter perforations or 1000 2inchdiameter valve caps or 500 4inchdiameter bubble caps In Table 62 tray types are compared on the basis of cost pressure drop masstransfer efficiency vapor capacity and flexibility in terms of turndown ratio ratio of maximum to minimum vapor flow capacity At the limiting flooding vapor velocity liquiddroplet entrainment becomes excessive causing the liquid flow to exceed the downcomer capacity thus pushing liquid up the column At too low a vapor rate liquid weeping through the tray openings or vapor pulsation becomes excessive Because of their low cost sieve trays are preferred unless flexibility in throughput is required in which case valve trays are best Bubblecap trays predominant in pre1950 installations are now rarely specified but may be Table 61 Representative Commercial Applications of Absorption Solute Absorbent Type of Absorption Acetone Water Physical Acrylonitrile Water Physical Ammonia Water Physical Ethanol Water Physical Formaldehyde Water Physical Hydrochloric acid Water Physical Hydrofluoric acid Water Physical Sulfur dioxide Water Physical Sulfur trioxide Water Physical Benzene and toluene Hydrocarbon oil Physical Butadiene Hydrocarbon oil Physical Butanes and propane Hydrocarbon oil Physical Naphthalene Hydrocarbon oil Physical Carbon dioxide Aq NaOH Irreversible chemical Hydrochloric acid Aq NaOH Irreversible chemical Hydrocyanic acid Aq NaOH Irreversible chemical Hydrofluoric acid Aq NaOH Irreversible chemical Hydrogen sulfide Aq NaOH Irreversible chemical Chlorine Water Reversible chemical Carbon monoxide Aq cuprous ammonium salts Reversible chemical CO2 and H2S Aq monoethanolamine MEA or diethanolamine DEA Reversible chemical CO2 and H2S Diethyleneglycol DEG or triethyleneglycol TEG Reversible chemical Nitrogen oxides Water Reversible chemical 208 Chapter 6 Absorption and Stripping of Dilute Mixtures C06 09302010 Page 209 preferred when liquid holdup must be controlled to provide residence time for a chemical reaction or when weeping must be prevented 612 Packed Columns A packed column shown in Figure 66 is a vessel containing one or more sections of packing over whose surface the liq uid flows downward as a film or as droplets between packing elements Vapor flows upward through the wetted packing contacting the liquid The packed sections are contained between a gasinjection support plate which holds the pack ing and an upper holddown plate which prevents packing movement A liquid distributor placed above the holddown plate ensures uniform distribution of liquid over the cross sectional area of the column as it enters the packed section If the height of packing is more than about 20 ft liquid channeling may occur causing the liquid to flow down near the wall and gas to flow up the center of the column thus greatly reducing the extent of vaporliquid contact In that case liquid redistributors need to be installed Commercial packing materials include random dumped packings some of which are shown in Figure 67a and struc tured arranged ordered or stacked packings some shown Clear liquid Froth foam Froth Weir Downcomer apron Gas flow Gas flow Tray below Tray above ht hl Tray diameter DT Length of liquid flow path ZL Figure 63 Tray details in a trayed tower Adapted from BF Smith Design of Equilibrium Stage Processes McGraw Hill New York 1963 a b c e d Figure 64 Possible vaporliquid flow regimes for a contacting tray a spray b froth c emulsion d bubble e cellular foam Reproduced by permission from MJ Lockett Distillation Tray Fundamen tals Cambridge University Press London 1986 Liquid in Liquid in Liquid in Liquid in Gas out Gas out Gasliquid dispersion Liquid out Liquid out Vapor out Vapor in Liquid out Liquid out Gas out Liquid out a b c d e Gas out Gas in Gas in Gas in Liquid in Gas in Figure 62 Industrial equipment for absorption and stripping a trayed tower b packed column c spray tower d bubble column e centrifugal contactor Table 62 Comparison of Types of Trays Sieve Trays Valve Trays BubbleCap Trays Relative cost 10 12 20 Pressure drop Lowest Intermediate Highest Efficiency Lowest Highest Highest Vapor capacity Highest Highest Lowest Typical turndown ratio 2 4 5 61 Equipment For VaporLiquid Separations 209 C06 09302010 Page 212 A novel device is the centrifugal contactor which consists of a stationary ringed housing intermeshed with a ringed rotat ing section The liquid phase is fed near the center of the pack ing from which it is thrown outward The vapor flows inward Reportedly high masstransfer rates can be achieved It is pos sible to obtain the equivalent of several equilibrium stages in a very compact unit These shortcontacttime type of devices are practical only when there are space limitations in which case they are useful for distillation 614 Choice of Device The choice of device is most often between a trayed and a packed column The latter using dumped packings is always favored when column diameter is less than 2 ft and the packed height is less than 20 ft Packed columns also get the nod for corrosive services where ceramic or plastic materials are preferred over metals particularly welded column inter nals and also in services where foaming is too severe for the use of trays and pressure drop must be low as in vacuum operations or where low liquid holdup is desirable Other wise trayed towers which can be designed more reliably are preferred Although structured packings are expensive they are the best choice for installations when pressure drop is a factor or for replacing existing trays retrofitting when a higher capacity or degree of separation is required Trayed towers are preferred when liquid velocities are low whereas columns with random packings are best for highliquid Mellapak Flexipac Montz Flexiceramic Flexeramic b Figure 67 Continued b structured packing materials Table 63 Comparison of Types of Packing Random Raschig Rings and Saddles Through Flow Structured Relative cost Low Moderate High Pressure drop Moderate Low Very low Efficiency Moderate High Very high Vapor capacity Fairly high High High Typical turndown ratio 2 2 2 212 Chapter 6 Absorption and Stripping of Dilute Mixtures C06 09302010 Page 213 velocities Use of structured packing should be avoided at pressures above 200 psia and liquid flow rates above 10 gpmft2 Kister 33 Turbulent liquid flow is desirable if mass transfer is limiting in the liquid phase while a continu ous turbulent gas flow is desirable if mass transfer is limiting in the gas phase Usually the continuous gas phase is mass transferlimiting in packed columns and the continuous liq uid phase is masstransferlimiting in tray columns 62 GENERAL DESIGN CONSIDERATIONS Absorber and stripper design or analysis requires considera tion of the following factors 1 Entering gas liquid flow rate composition T and P 2 Desired degree of recovery of one or more solutes 3 Choice of absorbent stripping agent 4 Operating P and T and allowable gas pressure drop 5 Minimum absorbent stripping agent flow rate and actual absorbent stripping agent flow rate 6 Heat effects and need for cooling heating 7 Number of equilibrium stages and stage efficiency 8 Type of absorber stripper equipment trays or packing 9 Need for redistributors if packing is used 10 Height of absorber stripper 11 Diameter of absorber stripper The ideal absorbent should have a a high solubility for the solutes b a low volatility to reduce loss c stability and inertness d low corrosiveness e low viscosity and high diffusivity f low foaming proclivities g low toxicity and flammability h availability if possible within the pro cess and i a low cost The most widely used absorbents are water hydrocarbon oils and aqueous solutions of acids and bases The most common stripping agents are steam air inert gases and hydrocarbon gases Absorber operating pressure should be high and temperature low to minimize stage requirements andor absorbent flow rate and to lower the equipment volume required to accommodate the gas flow Unfortunately both compression and refrigeration of a gas are expensive Therefore most absorbers are operated at feedgas pressure which may be greater than ambient pres sure and at ambient temperature which can be achieved by cooling the feed gas and absorbent with cooling water unless one or both streams already exist at a subambient temperature Operating pressure should be low and temperature high for a stripper to minimize stage requirements and stripping agent flow rate However because maintenance of a vacuum is expensive and steam jet exhausts are polluting strippers are commonly operated at a pressure just above ambient A high temperature can be used but it should not be so high as to cause vaporization or undesirable chemical reactions The possibility of phase changes occurring can be checked by bubblepoint and dewpoint calculations For given feedgas liquid flow rate extent of solute absorption stripping operating P and T and absorbent stripping agent composition a minimum absorbent strip ping agent flow rate exists that corresponds to an infinite number of countercurrent equilibrium contacts between the gas and liquid phases In every design problem a tradeoff exists between the number of equilibrium stages and the absorbent stripping agent flow rate a rate that must be greater than the minimum Graphical and analytical methods for computing the minimum flow rate and this tradeoff are developed in the following sections for mixtures that are dilute in solutes For this essentially isothermal case the energy balance can be ignored As discussed in Chapters 10 and 11 process simulators are best used for concentrated mixtures where multicomponent phase equilibrium and masstransfer effects are complex and an energy balance is necessary 63 GRAPHICAL METHOD FOR TRAYED TOWERS For the countercurrentflow trayed tower for absorption or stripping shown in Figure 68 stages are numbered from top where the absorbent enters to bottom for the absorber and from bottom where the stripping agent enters to top for the stripper Phase equilibrium is assumed between the vapor and liquid leaving each tray Assume for an absorber that only solute is transferred from one phase to the other Let L0 ¼ molar flow rate of solutefree absorbent V0 ¼ molar flow rate of solutefree gas carrier gas X ¼ mole ratio of solute to solutefree absorbent in the liquid Y ¼ mole ratio of solute to solutefree gas in the vapor Operating line bottom top YN1 V XN L XN1 L YN V X0 L Y1 V Y0 V X1 L E q ui li br iu m c u r v e E q ui li bri u m cu rv e 1 1 n n N N Y X a b Operating line bottom top Y X Figure 68 Continuous steadystate operation in a countercurrent cascade with equilibrium stages a absorber b stripper 63 Graphical Method for Trayed Towers 213 C06 09302010 Page 224 usually containing 0035 to 0043inch holes with a hole area of approximately 10 A detailed study by Fair Null and Bolles 23 showed that overall plate stage efficiencies of Oldershaw columns operated over a pressure range of 3 to 165 psia are in conservative agreement with distillation data obtained from sievetray pilotplant and industrialsize col umns ranging in size from 15 to 4 ft in diameter when oper ated in the range of 40 to 90 of flooding described in 66 It may be assumed that similar agreement might be realized for absorption and stripping The smalldiameter Oldershaw column achieves essen tially complete mixing of liquid on each tray permitting the measurement of a point efficiency from 630 Somewhat larger efficiencies may be observed in muchlargerdiameter columns due to incomplete liquid mixing resulting in a higher Murphree tray efficiency EMV and therefore higher overall plate efficiency Eo Fair et al 23 recommend the following scaleup proce dure using data from the Oldershaw column 1 Determine the flooding point as described in 66 2 Establish opera tion at about 60 of flooding 3 Run the system to find a combination of plates and flow rates that gives the desired degree of separation 4 Assume that the commercial col umn will require the same number of plates for the same ratio of L to V If reliable vaporliquid equilibrium data are available they can be used with the Oldershaw data to determine over all column efficiency Eo Then 637 and 634 can be used to estimate the average point efficiency For commercialsize columns the Murphree vapor efficiency can be determined from the Oldershaw column point efficiency using 634 NPe NPe NPe05 NPe20 NPe10 NPe50 NPe30 NPe20 10 20 30 0 NPe15 NPe10 NPe05 NPe10 NPe20 NPe30 NPe50 NPe10 NPe30 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 900 800 700 600 500 400 300 200 100 90 80 70 60 50 40 30 20 10 30 28 26 24 22 20 18 16 14 12 10 EMVEOV λ Eov 1 2 3 4 5 6 7 8 9 10 EMVEOV Eov λ Figure 618 a Effect of longitudinal mixing on Murphree vaportray efficiency b Expanded range for effect of longitudinal mixing on Murphree vaportray efficiency Weir Downcomer Column wall Perforated plate Figure 619 Oldershaw column 224 Chapter 6 Absorption and Stripping of Dilute Mixtures C06 09302010 Page 238 Table 66 Characteristics of Packings Characteristics from Billet Packing Material Size FP ft2ft3 a m2m3 e m3m3 Ch Cp CL CV cs CFI Random Packings Berl saddles Ceramic 25 mm 110 2600 0680 0620 1246 0387 Berl saddles Ceramic 13 mm 240 5450 0650 0833 1364 0232 Bialecki rings Metal 50 mm 1210 0966 0798 0719 1721 0302 2916 1896 Bialecki rings Metal 35 mm 1550 0967 0787 1011 1412 0390 2753 1885 Bialecki rings Metal 25 mm 2100 0956 0692 0891 1461 0331 2521 1856 Dinpak1 rings Plastic 70 mm 1107 0938 0991 0378 1527 0326 2970 1912 Dinpak rings Plastic 47 mm 1312 0923 1173 0514 1690 0354 2929 1991 EnviPac1 rings Plastic 80 mm no 3 600 0955 0641 0358 1603 0257 2846 1522 EnviPac rings Plastic 60 mm no 2 984 0961 0794 0338 1522 0296 2987 1864 EnviPac rings Plastic 32 mm no 1 1389 0936 1039 0549 1517 0459 2944 2012 Cascade MiniRings Metal 30 PMK 1805 0975 0930 0851 1920 0450 2694 1900 Cascade MiniRings Metal 30 P 1640 0959 0851 1056 1577 0398 2564 1760 Cascade MiniRings Metal 15 1749 0974 0935 0632 2697 1841 Cascade MiniRings Metal 15 T 1880 0972 0870 0627 2790 1870 Cascade MiniRings Metal 10 2325 0971 1040 0641 2703 1996 Cascade MiniRings Metal 05 3560 0955 1338 0882 2038 0495 2644 2178 Hackettes Plastic 45 mm 1395 0928 0643 0399 2832 1966 Hiflow rings Ceramic 75 mm 15 541 0868 0435 Hiflow rings Ceramic 50 mm 29 897 0809 0538 1377 0379 2819 1694 Hiflow rings Ceramic 38 mm 37 1118 0788 0621 1659 0464 2840 1930 Hiflow rings Ceramic 20 mm 6 stg 2658 0776 0958 Hiflow rings Ceramic 20 mm 4 stg 2612 0779 1167 0628 1744 0465 Hiflow rings Metal 50 mm 16 923 0977 0876 0421 1168 0408 2702 1626 Hiflow rings Metal 25 mm 42 2029 0962 0799 0689 1641 0402 2918 2177 Hiflow rings Plastic 90 mm 9 697 0968 0276 Hiflow rings Plastic 50 mm hydr 1184 0925 0311 1553 0369 2894 1871 Hiflow rings Plastic 50 mm 20 1171 0924 1038 0327 1487 0345 Hiflow rings Plastic 25 mm 1945 0918 0741 1577 0390 2841 1989 Hiflow rings super Plastic 50 mm S 820 0942 0414 1219 0342 2866 1702 Hiflow saddles Plastic 50 mm 864 0938 0454 Intalox saddles Ceramic 50 mm 40 1146 0761 0747 Intalox saddles Plastic 50 mm 28 1221 0908 0758 NorPak1 rings Plastic 50 mm 14 868 0947 0651 0350 1080 0322 2959 1786 NorPak rings Plastic 35 mm 21 1418 0944 0587 0371 0756 0425 3179 2242 NorPak rings Plastic 25 mm type B 2020 0953 0601 0397 0883 0366 3277 2472 NorPak rings Plastic 25 mm 10 stg 1979 0920 0383 0976 0410 2865 2083 238 C06 09302010 Page 239 NorPak rings Plastic 25 mm 31 1800 0927 0601 NorPak rings Plastic 22 mm 2490 0913 0397 NorPak rings Plastic 15 mm 3114 0918 0343 0365 Pall rings Ceramic 50 mm 43 1552 0754 1066 0233 1278 0333 3793 3024 Pall rings Metal 50 mm 27 1126 0951 0784 0763 1192 0410 2725 1580 Pall rings Metal 35 mm 40 1394 0965 0644 0967 1012 0341 2629 1679 Pall rings Metal 25 mm 56 2235 0954 0719 0957 1440 0336 2627 2083 Pall rings Metal 15 mm 70 3684 0933 0590 0990 Pall rings Plastic 50 mm 26 1111 0919 0593 0698 1239 0368 2816 1757 Pall rings Plastic 35 mm 40 1511 0906 0718 0927 0856 0380 2654 1742 Pall rings Plastic 25 mm 55 2250 0887 0528 0865 0905 0446 2696 2064 Raflux1 rings Plastic 15 mm 3079 0894 0491 0595 1913 0370 2825 2400 Ralu flow Plastic 1 165 0940 0640 0485 1486 0360 3612 2401 Ralu flow Plastic 2 100 0945 0640 0350 1270 0320 3412 2174 Ralu1 rings Plastic 50 mm hydr 943 0939 0439 1481 0341 Ralu rings Plastic 50 mm 952 0983 0640 0468 1520 0303 2843 1812 Ralu rings Plastic 38 mm 150 0930 0640 0672 1320 0333 2843 1812 Ralu rings Plastic 25 mm 190 0940 0719 0800 1320 0333 2841 1989 Ralu rings Metal 50 mm 105 0975 0784 0763 1192 0345 2725 1580 Ralu rings Metal 38 mm 135 0965 0644 1003 1277 0341 2629 1679 Ralu rings Metal 25 mm 215 0960 0714 0957 1440 0336 2627 2083 Raschig rings Carbon 25 mm 2022 0720 0623 1379 0471 Raschig rings Ceramic 25 mm 179 1900 0680 0577 1329 1361 0412 Raschig rings Ceramic 15 mm 380 3120 0690 0648 1276 0401 Raschig rings Ceramic 10 mm 1000 4400 0650 0791 1303 0272 Raschig rings Ceramic 6 mm 1600 7719 0620 1094 1130 Raschig rings Metal 15 mm 170 3784 0917 0455 Raschig rings Ceramic 25 1900 0680 0577 1329 1361 0412 2454 1899 Raschig Superrings Metal 03 315 0960 0750 0760 1500 0450 3560 2340 Raschig Superrings Metal 05 250 0975 0620 0780 1450 0430 3350 2200 Raschig Superrings Metal 1 160 0980 0750 0500 1290 0440 3491 2200 Raschig Superrings Metal 2 976 0985 0720 0464 1323 0400 3326 2096 Raschig Superrings Metal 3 80 0982 0620 0430 0850 0300 3260 2100 Raschig Superrings Plastic 2 100 0960 0720 0377 1250 0337 3326 2096 Tellerettes Plastic 25 mm 40 1900 0930 0588 0538 0899 2913 2132 TopPak rings Aluminum 50 mm 1055 0956 0881 0604 1326 0389 2528 1579 VSP rings Metal 50 mm no 2 1046 0980 1135 0773 1222 0420 2806 1689 VSP rings Metal 25 mm no 1 1996 0975 1369 0782 1376 0405 2755 1970 Continued 239 C06 09302010 Page 246 masstransfer coefficients are significantly affected by the technique used to pack the column and the number of liquid feeddistribution points across the column which must be more than 25 pointssq ft Billet and Schultes 67 measured and correlated volumet ric masstransfer coefficients and HTUs for 31 different chemical systems with 67 different types and sizes of pack ings in columns of diameter 24 inches to 46 ft with addi tional data 69 for Hiflow rings and Raschig Superrings G Gas mass velocity lbhft2 HTU versus L kLa versus L Curve Packing Height G T C Solute A 200 400 1000 01 02 04 10 20 40 10 20 40 100 200 400 4000 Water mass velocity lbhft2 A A B C C B 10000 20000 kLa lbmolhft3lbmolft3 HTUL ft 40000 05 in saddles 153 in 100 2326 02 B 10 in saddles 170 in 230 2326 02 C 15 in saddles 220 in 230 2324 02 Figure 638 Effect of liquid rate on liquid phase mass transfer of O2 From TK Sherwood and FAL Holloway Trans AIChE 36 3970 1940 with permission 50 mm F 055 m12s1kg12 Hiflow ring ceramic CO2airwater 1 bar 293 K 1 15 2 3 4 Liquid load uL 103 m3m2 s Volumetric liquidphase masstransfer coefficient kLa s1 3 4 6 10 15 20 30 6 10 15 20mm F 085 m12s1kg12 Figure 639 Effect of liquid load on liquidphase mass transfer of CO2 From R Billet Packed Column Analysis and Design RuhrUniversity Bochum 1989 with permission uL 15 m3 m2h Gas capacity factor F m12s1kg12 Volumetric liquidphase masstransfer coefficient kLa s1 CO2airwater 1 bar 50mm Hiflow ring plastic 294 K 50mm Pall ring plastic 299 K 04 10 15 20 06 08 1 15 2 3 Figure 640 Effect of gas rate on liquidphase mass transfer of CO2 From R Billet Packed Column Analysis and Design RuhrUniversity Bochum 1989 with permission 50mm Hiflow ring 04 2 3 4 5 7 06 1 2 3 Volumetric gasphase masstransfer coefficient kG a s1 Gas capacity factor F m12s1kg12 uL 417 x 103m3m2 s 50mm Pall ring Figure 641 Effect of gas rate on gasphase mass transfer of NH3 From R Billet Packed Column Analysis and Design RuhrUniversity Bochum 1989 with permission F 116 m12s1kg12 Liquid load uL 103 m3m2 s Volumetric gasphase mass transfer coefficient kG a s1 1 2 3 4 6 15 2 4 6 10 12 50mm Hiflow ring 50mm Pall ring Figure 642 Effect of liquid rate on gasphase mass transfer of NH3 From R Billet Packed Column Analysis and Design RuhrUniversity Bochum 1989 with permission 246 Chapter 6 Absorption and Stripping of Dilute Mixtures C06 09302010 Page 251 6 The equilibrium stages and flow rates for an absorber or stripper can be determined from the equilibrium line 61 and an operating line 63 or 65 using graphi cal algebraic or numerical methods Graphical methods such as Figure 611 offer visual insight into stageby stage changes in compositions of the gas and liquid streams and the effects of changes in the variables 7 Estimates of overall stage efficiency defined by 621 can be made with the correlations of Drickamer and Bradford 622 OConnell 623 and Figure 614 More accurate procedures involve the use of a laboratory Oldershaw column or semitheoretical equations eg of Chan and Fair based on masstransfer considerations to determine a Murphree vaporpoint efficiency 630 The Murphree vaportray efficiency is obtained from 631 to 634 and the overall efficiency from 637 8 Tray diameter is determined from 644 based on entrainment flooding considerations shown in Figure 623 Vapor pressure drop weeping entrainment and downcomer backup can be estimated from 649 668 669 and 670 respectively 9 Packedcolumn height is determined using HETP 673 or HTUNTU 689 concepts with the latter having a more theoretical basis in the twofilm theory of mass transfer For straight equilibrium and operating lines HETP is related to the HTU by 694 and the number of stages to the NTU by 695 10 In the preloading region liquid holdup in a packed col umn is independent of vapor velocity The loading point is typically 70 of the flooding point and most packed columns are designed to operate in the preloading region from 50 to 70 of flooding The flooding point from Figure 635 the GPDC chart is used to determine col umn diameter 6102 and loading point 6105 11 An advantage of a packed column is its low pressure drop as compared to that in a trayed tower Packed column pressure drop is estimated from Figure 635 6106 or 6115 12 Numerous rules of thumb for estimating the HETP of packed columns exist The preferred approach is to esti mate HOG from semitheoretical masstransfer correla tions such as those of 6132 and 6133 based on the work of Billet and Schultes 13 Obtaining theoretical stages for concentrated solutions involves numerical integration because of curved equili brium andor operating lines REFERENCES 1 Washburn EW EdinChief International Critical Tables McGraw Hill New York Vol III p 255 1928 2 Lockett M Distillation Tray Fundamentals Cambridge University Press Cambridge UK p 13 1986 3 Okoniewski BA Chem Eng Prog 882 8993 1992 4 Sax NI Dangerous Properties of Industrial Materials 4th ed Van Nostrand Reinhold New York pp 440441 1975 5 Lewis WK Ind Eng Chem 14 492497 1922 6 Drickamer HG and JR Bradford Trans AIChE 39 319360 1943 7 Jackson RM and TK Sherwood Trans AIChE 37 959978 1941 8 OConnell HE Trans AIChE 42 741755 1946 9 Walter JF and TK Sherwood Ind Eng Chem 33 493501 1941 10 Edmister WC The Petroleum Engineer C45C54 Jan 1949 11 Lockhart FJ and CW Leggett in KA Kobe and JJ McKetta Jr Eds Advances in Petroleum Chemistry and Refining Vol 1 Interscience New York Vol 1 pp 323326 1958 12 Holland CD Multicomponent Distillation PrenticeHall Englewood Cliffs NJ 1963 13 Murphree EV Ind Eng Chem 17 747 1925 14 Hausen H Chem Ing Tech 25 595 1953 15 Standart G Chem Eng Sci 20 611 1965 16 Lewis WK Ind Eng Chem 28 399 1936 17 Gerster JA AB Hill NH Hochgraf and DG Robinson Tray Efficiencies in Distillation Columns Final Report from the University of Delaware American Institute of Chemical Engineers New York 1958 18 BubbleTray Design Manual AIChE New York 1958 19 Gilbert TJ Chem Eng Sci 10 243 1959 20 Barker PE and MF Self Chem Eng Sci 17 541 1962 21 Bennett DL and HJ Grimm AIChE J 37 589 1991 22 Oldershaw CF Ind Eng Chem Anal Ed 13 265 1941 23 Fair JR HR Null and WL Bolles Ind Eng Chem Process Des Dev 22 5358 1983 24 Souders M and GG Brown Ind Eng Chem 26 98103 1934 25 Fair JR PetroChem Eng 33 211218 Sept 1961 26 Sherwood TK GH Shipley and FAL Holloway Ind Eng Chem 30 765769 1938 27 Glitsch Ballast Tray Bulletin No 159 Fritz W Glitsch and Sons Dal las TX from FRI report of Sept 3 1958 28 Glitsch V1 Ballast Tray Bulletin No 160 Fritz W Glitsch and Sons Dallas TX from FRI report of Sept 25 1959 29 Oliver ED Diffusional Separation Processes Theory Design and Evaluation John Wiley Sons New York pp 320321 1966 30 Bennett DL R Agrawal and PJ Cook AIChE J 29 434442 1983 31 Smith BD Design of Equilibrium Stage Processes McGrawHill New York 1963 32 Klein GF Chem Eng 899 8185 1982 33 Kister HZ Distillation Design McGrawHill New York 1992 34 Lockett MJ Distillation Tray Fundamentals Cambridge University Press Cambridge UK p 146 1986 35 American Institute of Chemical Engineers AIChE BubbleTray De sign Manual AIChE New York 1958 36 Chan H and JR Fair Ind Eng Chem Process Des Dev 23 814 819 1984 References 251 C06 09302010 Page 252 37 Chan H and JR Fair Ind Eng Chem Process Des Dev 23 820 827 1984 38 Scheffe RD and RH Weiland Ind Eng Chem Res 26 228236 1987 39 Foss AS and JA Gerster Chem Eng Prog 52 28J to 34J Jan 1956 40 Gerster JA AB Hill NN Hochgraf and DG RobinsonTray Effi ciencies in Distillation Columns Final Report from University of Delaware American Institute of Chemical Engineers AIChE New York 1958 41 Fair JR PetroChem Eng 3310 45 1961 42 Colburn AP Ind Eng Chem 28 526 1936 43 Chilton TH and AP Colburn Ind Eng Chem 27 255260 904 1935 44 Colburn AP Trans AIChE 35 211236 587591 1939 45 Billet R Packed Column Analysis and Design RuhrUniversity Bochum 1989 46 Stichlmair J JL Bravo and JR Fair Gas Separation and Purifica tion 3 1928 1989 47 Billet R and M Schultes Packed Towers in Processing and Environ mental Technology translated by JW Fullarton VCH Publishers New York 1995 48 Leva M Chem Eng Prog Symp Ser 5010 51 1954 49 Leva M Chem Eng Prog 881 6572 1992 50 Kister HZ and DR Gill Chem Eng Prog 872 3242 1991 51 Billet R and M Schultes Chem Eng Technol 14 8995 1991 52 Ergun S Chem Eng Prog 482 8994 1952 53 Kunesh JG Can J Chem Eng 65 907913 1987 54 Whitman WG Chem and Met Eng 29 146148 1923 55 Sherwood TK and FAL Holloway Trans AIChE 36 3970 1940 56 Cornell D WG Knapp and JR Fair Chem Eng Prog 567 68 74 1960 57 Cornell D WG Knapp and JR Fair Chem Eng Prog 568 48 53 1960 58 Bolles WL and JR Fair Inst Chem Eng Symp Ser 56 335 1979 59 Bolles WL and JR Fair Chem Eng 8914 109116 1982 60 Bravo JL and JR Fair Ind Eng Chem Process Des Devel 21 162170 1982 61 Bravo JL JA Rocha and JR Fair Hydrocarbon Processing 641 5660 1985 62 Fair JR and JL Bravo I Chem E Symp Ser 104 A183A201 1987 63 Fair JR and JL Bravo Chem Eng Prob 861 1929 1990 64 Shulman HL CF Ullrich AZ Proulx and JO Zimmerman AIChE J 1 253258 1955 65 Onda K H Takeuchi and YJ Okumoto J Chem Eng Jpn 1 5662 1968 66 Billet R Chem Eng Prog 639 5365 1967 67 Billet R and M Schultes Beitrage zur VerfahrensUnd Umwelttech nik RuhrUniversitat Bochum pp 88106 1991 68 Higbie R Trans AIChE 31 365389 1935 69 Billet R and M Schultes Chem Eng Res Des Trans IChemE 77A 498504 1999 70 M Schultes Private Communication 2004 71 Sloley AW Chem Eng Prog 951 2335 1999 72 Stupin WJ and HZ Kister Trans IChemE 81A 136146 2003 STUDY QUESTIONS 61 What is the difference between physical absorption and chemical reactive absorption 62 What is the difference between an equilibriumbased and a ratebased calculation method 63 What is a trayed tower What is a packed column 64 What are the three most common types of openings in trays for the passage of vapor Which of the three is rarely specified for new installations 65 In a trayed tower what is meant by flooding and weeping What are the two types of flooding and which is more common 66 What is the difference between random and structured packings 67 For what conditions is a packed column favored over a trayed tower 68 In general why should the operating pressure be high and the operating temperature be low for an absorber and the opposite for a stripper 69 For a given recovery of a key component in an absorber or stripper does a minimum absorbent or stripping agent flow rate exist for a tower or column with an infinite number of equi librium stages 610 What is the difference between an operating line and an equilibrium curve 611 What is a reasonable value for the optimal absorption factor when designing an absorber Does that same value apply to the opti mal stripping factor when designing a stripper 612 When stepping off stages on an YX plot for an absorber or a stripper does the process start and stop with the operating line or the equilibrium curve 613 Why do longer liquid flow paths across a tray give higher stage efficiencies 614 What is the difference between the Murphree tray and point efficiencies 615 What is meant by turndown ratio What type of tray has the best turndown ratio Which tray the worst 616 What are the three contributing factors to the vapor pressure drop across a tray 617 What is the HETP Does it have a theoretical basis If not why is it so widely used 618 Why are there so many different kinds of masstransfer coefficients How can they be distinguished 619 What is the difference between the loading point and the flooding point in a packed column 620 When the solute concentration is moderate to high instead of dilute why are calculations for packed columns much more difficult 252 Chapter 6 Absorption and Stripping of Dilute Mixtures C07 10042010 Page 289 STUDY QUESTIONS 71 What equipment is included in a typical distillation operation 72 What determines the operating pressure of a distillation column 73 Under what conditions does a distillation column have to operate under vacuum 74 Why are distillation columns arranged for countercurrent flow of liquid and vapor 75 Why is the McCabeThiele graphical method useful in this era of more rigorous computeraided algebraic methods used in process simulators 76 Under what conditions does the McCabeThiele assumption of constant molar overflow hold 77 In the McCabeThiele method between which two lines is the staircase constructed 78 What is meant by the reflux ratio What is meant by the boilup ratio 79 What is the qline and how is it related to the feed condition 710 What are the five possible feed conditions 711 In the McCabeThiele method are the stages stepped off from the top down or the bottom up In either case when is it best during the stepping to switch from one operating line to the other Why 712 Can a column be operated at total reflux How 713 How many stages are necessary for operation at minimum reflux ratio 714 What is meant by a pinch point Is it always located at the feed stage 715 What is meant by subcooled reflux How does it affect the amount of reflux inside the column 716 Is it worthwhile to preheat the feed to a distillation column 717 Why is the stage efficiency in distillation higher than that in absorption 718 What kind of a small laboratory column is useful for obtain ing plate efficiency data EXERCISES Note Unless otherwise stated the usual simplifying assumptions of saturatedliquid reflux optimal feedstage location no heat losses steady state and constant molar liquid and vapor flows apply to each exercise Section 71 71 Differences between absorption distillation and stripping List as many differences between 1 absorption and distillation and 2 stripping and distillation as you can 72 Popularity of packed columns Prior to the 1980s packed columns were rarely used for distilla tion unless column diameter was less than 25 ft Explain why in recent years some trayed towers are being retrofitted with packing and some new largediameter columns are being designed for pack ing rather than trays 73 Use of cooling water in a condenser A mixture of methane and ethane is subject to distillation Why cant water be used as a condenser coolant What would you use 74 Operating pressure for distillation A mixture of ethylene and ethane is to be separated by distilla tion What operating pressure would you suggest Why 75 Laboratory data for distillation design Under what circumstances would it be advisable to conduct lab oratory or pilotplant tests of a proposed distillation 76 Economic tradeoff in distillation design Explain the economic tradeoff between trays and reflux Section 72 77 McCabeThiele Method In the 50 years following the development by Sorel in 1894 of a mathematical model for continuous steadystate equilibriumstage distillation many noncomputerized methods were proposed for solving the equations graphically or algebraically Today the only method from that era that remains in widespread use is the McCabeThiele graphical method What attributes of this method are responsible for its continuing popularity 78 Compositions of countercurrent cascade stages For the cascade in Figure 739a calculate a compositions of streams V4 and L1 by assuming 1 atm pressure saturatedliquid and vapor feeds and the vaporliquid equilibrium data below where compositions are in mole b Given the feed compositions in cas cade a how many stages are required to produce a V4 containing 85 mol alcohol c For the cascade configuration in Figure 739b with D ¼ 50 mols what are the compositions of D and L1 d For the configuration of cascade b how many stages are required to produce a D of 50 mol alcohol EQUILIBRIUM DATA MOLEFRACTION ALCOHOL x 01 03 05 07 09 y 02 05 068 082 094 V4 V4 LR L1 L1 100 mol 70 alcohol 30 H2O 100 mol 30 alcohol 70 H2O 100 mol 30 alcohol 70 H2O 4 3 1 a b 2 4 D 50 mol Total condenser 3 2 1 Figure 739 Data for Exercise 78 Exercises 289 C07 10042010 Page 290 79 Stripping of air Liquid air is fed to the top of a perforatedtray reboiled stripper operated at 1 atm Sixty of the oxygen in the feed is to be drawn off in the bottoms vapor product which is to contain 02 mol nitrogen Based on the assumptions and equilibrium data below cal culate a the mole N2 in the vapor from the top plate b the vapor generated in the still per 100 moles of feed and c the num ber of stages required Assume constant molar overflow equal to the moles of feed Liq uid air contains 209 mol O2 and 791 mol N2 The equilibrium data Chem Met Eng 35 622 1928 at 1 atm are Temperature K MolePercent N2 in Liquid MolePercent N2 in Vapor 7735 10000 10000 7798 9000 9717 7873 7900 9362 7944 7000 9031 8033 6000 8591 8135 5000 8046 8254 4000 7350 8394 3000 6405 8562 2000 5081 8767 1000 3100 9017 000 000 710 Using operating data to determine reflux and distillate composition A mixture of A more volatile and B is separated in a plate dis tillation column In two separate tests run with a saturatedliquid feed of 40 mol A the following compositions in mol A were obtained for samples of liquid and vapor streams from three consec utive stages between the feed and total condenser at the top Mol A Test 1 Test 2 Stage Vapor Liquid Vapor Liquid M þ 2 795 680 750 680 M þ 1 740 600 680 605 M 679 510 605 530 Determine the reflux ratio and overhead composition in each case assuming that the column has more than three stages 711 Determining the best distillation procedure A saturatedliquid mixture of 70 mol benzene and 30 mol toluene whose relative volatility is 25 is to be distilled at 1 atm to produce a distillate of 80 mol benzene Five procedures described below are under consideration For each procedure calculate and tabulate a moles of distillate per 100 moles of feed b moles of total vapor generated per mole of distillate and c mol benzene in the residue d For each part construct a yx diagram On this indi cate the compositions of the overhead product the reflux and the composition of the residue e If the objective is to maximize total benzene recovery which if any of these procedures is preferred The procedures are as follows 1 Continuous distillation followed by partial condensation The feed is sent to the directheated still pot from which the residue is continuously withdrawn The vapors enter the top of a heli cally coiled partial condenser that discharges into a trap The liq uid is returned refluxed to the still while the residual vapor is condensed as a product containing 80 mol benzene The molar ratio of reflux to product is 05 2 Continuous distillation in a column containing one equilibrium plate The feed is sent to the directheated still from which resi due is withdrawn continuously The vapors from the plate enter the top of a helically coiled partial condenser that discharges into a trap The liquid from the trap is returned to the plate while the uncondensed vapor is condensed to form a distillate contain ing 80 mol benzene The molar ratio of reflux to product is 05 3 Continuous distillation in a column containing the equivalent of two equilibrium plates The feed is sent to the directheated still from which residue is withdrawn continuously The vapors from the top plate enter the top of a helically coiled partial condenser that discharges into a trap The liquid from the trap is returned to the top plate refluxed while the uncondensed vapor is con densed to a distillate containing 80 mol benzene The molar ratio of reflux to product is 05 4 The operation is the same as for Procedure 3 except that liquid from the trap is returned to the bottom plate 5 Continuous distillation in a column with the equivalent of one equilibrium plate The feed at its boiling point is introduced on the plate The residue is withdrawn from the directheated still pot The vapors from the plate enter the top of a partial condenser that discharges into a trap The liquid from the trap is returned to the plate while the uncondensed vapor is condensed to a dis tillate of 80 mol benzene The molar ratio of reflux to product is 05 712 Evaluating distillation procedures A saturatedliquid mixture of 50 mol benzene and toluene is distilled at 101 kPa in an apparatus consisting of a still pot one the oretical plate and a total condenser The still pot is equivalent to an equilibrium stage The apparatus is to produce a distillate of 75 mol benzene For each procedure below calculate if possible the moles of distillate per 100 moles of feed Assume an a of 25 Procedures a No reflux with feed to the still pot b Feed to the still pot with reflux ratio ¼ 3 c Feed to the plate with a reflux ratio of 3 d Feed to the plate with a reflux ratio of 3 from a partial condenser e Part b using minimum reflux f Part b using total reflux 713 Separation of benzene and toluene A column at 101 kPa is to separate 30 kgh of a bubblepoint solution of benzene and toluene containing 06 massfraction tolu ene into an overhead product of 097 massfraction benzene and a bottoms product of 098 massfraction toluene at a reflux ratio of 35 The feed is sent to the optimal tray and the reflux is at satura tion temperature Determine the a top and bottom products and b number of stages using the following vaporliquid equilibrium data EQUILIBRIUM DATA IN MOLE FRACTION BENZENE 101 kPA y 021 037 051 064 072 079 086 091 096 098 x 01 02 03 04 05 06 07 08 09 095 290 Chapter 7 Distillation of Binary Mixtures C07 10042010 Page 291 714 Calculation of products A mixture of 545 mol benzene in chlorobenzene at its bubble point is fed continuously to the bottom plate of a column containing two equilibrium plates with a partial reboiler and a total condenser Sufficient heat is supplied to the reboiler to give VF ¼ 0855 and the reflux ratio LV in the top of the column is constant at 050 Under these conditions using the equilibrium data below what are the compositions of the expected products EQUILIBRIUM DATA AT COLUMN PRESSURE MOLE FRACTION BENZENE x 0100 0200 0300 0400 0500 0600 0700 0800 y 0314 0508 0640 0734 0806 0862 0905 0943 715 Loss of trays in a distillation column A continuous distillation with a reflux ratio LD of 35 yields a distillate containing 97 wt B benzene and a bottoms of 98 wt T toluene Due to weld failures the 10 stripping plates in the bottom section of the column are ruined but the 14 upper rectifying plates are intact It is suggested that the column still be used with the feed F as saturated vapor at the dew point with F ¼ 13600 kgh con taining 40 wt B and 60 wt T Assuming that the plate efficiency remains unchanged at 50 a Can this column still yield a distil late containing 97 wt B b How much distillate is there c What is the residue composition in mole For vaporliquid equilibrium data see Exercise 713 716 Changes to a distillation operation A distillation column having eight theoretical stages seven stages þ partial reboiler þ total condenser separates 100 kmolh of saturatedliquid feed containing 50 mol A into a product of 90 mol A The liquidtovapor molar ratio at the top plate is 075 The saturatedliquid feed enters plate 5 from the top Determine a the bottoms composition b the LV ratio in the stripping sec tion and c the moles of bottoms per hour Unknown to the operators the bolts holding plates 5 6 and 7 rust through and the plates fall into the still pot What is the new bottoms composition It is suggested that instead of returning reflux to the top plate an equivalent amount of liquid product from another column be used as reflux If that product contains 80 mol A what is now the compo sition of a the distillate and b the bottoms EQUILIBRIUM DATA MOLE FRACTION OF A y 019 037 05 062 071 078 084 09 096 x 01 02 03 04 05 06 07 08 09 717 Effect of different feed conditions A distillation unit consists of a partial reboiler a column with seven equilibrium plates and a total condenser The feed is a 50 mol mixture of benzene in toluene It is desired to produce a distillate containing 96 mol benzene when operating at 101 kPa a With saturatedliquid feed fed to the fifth plate from the top cal culate 1 minimum reflux ratio LRDmin 2 the bottoms composition using a reflux ratio LRD of twice the minimum and 3 moles of product per 100 moles of feed b Repeat part a for a saturated vapor fed to the fifth plate from the top c With saturatedvapor feed fed to the reboiler and a reflux ratio LV of 09 calculate 1 bottoms composition and 2 moles of product per 100 moles of feed Equilibrium data are in Exercise 713 718 Conversion of distillation to stripping A valvetray column containing eight theoretical plates a partial reboiler and a total condenser separates a benzenetoluene mixture containing 36 mol benzene at 101 kPa The reboiler generates 100 kmolh of vapor A request has been made for very pure toluene and it is proposed to run this column as a stripper with the satu ratedliquid feed to the top plate employing the same boilup at the still and returning no reflux to the column Equilibrium data are given in Exercise 713 a What is the minimum feed rate under the proposed conditions and what is the corresponding composition of the liquid in the reboiler at the minimum feed b At a feed rate 25 above the minimum what is the rate of production of toluene and what are the compositions in mol of the product and distillate 719 Poor performance of distillation Fifty mol methanol in water at 101 kPa is continuously dis tilled in a sevenplate perforatedtray column with a total con denser and a partial reboiler heated by steam Normally 100 kmolh of feed is introduced on the third plate from the bottom The over head product contains 90 mol methanol and the bottoms 5 mol One mole of reflux is returned for each mole of overhead product Recently it has been impossible to maintain the product purity in spite of an increase in the reflux ratio The following test data were obtained Stream kmolh mol alcohol Feed 100 51 Waste 62 12 Product 53 80 Reflux 94 What is the most probable cause of this poor performance What further tests would you make to establish the reason for the trouble Could some 90 product be obtained by further increasing the re flux ratio while keeping the vapor rate constant Vaporliquid equilibrium data at 1 atm Chem Eng Prog 48 192 1952 in molefraction methanol are x 00321 00523 0075 0154 0225 0349 0813 0918 y 01900 02940 0352 0516 0593 0703 0918 0963 720 Effect of feed rate reduction operation A fractionating column equipped with a steamheated partial reboiler and total condenser Figure 740 separates a mixture of 50 mol A and 50 mol B into an overhead product containing 90 mol A and a bottoms of 20 mol A The column has three theoretical plates and the reboiler is equivalent to one theoretical plate When the system is operated at LV ¼ 075 with the feed as a saturated liquid to the bottom plate the desired products are obtained The steam to the reboiler is controlled and remains con stant The reflux to the column also remains constant The feed to the column is normally 100 kmolh but it was inadvertently cut back to 25 kmolh What will be the composition of the reflux and the vapor leaving the reboiler under these new conditions Assume Exercises 291 C07 10042010 Page 296 742 Oldershaw column efficiency For the conditions of Exercise 741 a laboratory Oldershaw col umn measures an average Murphree vaporpoint efficiency of 65 Estimate EMV and Eo Section 75 743 Column diameter Figure 746 shows conditions for the top tray of a distillation col umn Determine the column diameter at 85 of flooding for a valve tray Make whatever assumptions necessary 744 Column sizing Figure 747 depicts a propylenepropane distillation Two sieve tray columns in series are used because a 270tray column poses structural problems Determine column diameters tray efficiency using the OConnell correlation number of actual trays and column heights 745 Sizing a vertical flash drum Determine the height and diameter of a vertical flash drum for the conditions shown in Figure 748 746 Sizing a horizontal flash drum Determine the length and diameter of a horizontal reflux drum for the conditions shown in Figure 749 747 Possible swaged column Results of design calculations for a methanolwater distillation operation are given in Figure 750 a Calculate the column diame ter at the top and at the bottom assuming sieve trays Should the column be swaged b Calculate the length and diameter of the hor izontal reflux drum 748 Tray calculations of flooding pressure drop entrain ment and froth height For the conditions given in Exercise 741 estimate for the top tray and the bottom tray a of flooding b tray pressure drop in psi c whether weeping will occur d entrainment rate and e froth height in the downcomer 749 Possible retrofit to packing If the feed rate to the tower of Exercise 741 is increased by 30 with conditionsexcept for tower pressure dropremaining the same estimate for the top and bottom trays a of flooding b tray pressure drop in psi c entrainment rate and d froth height in the downcomer Will the new operation be acceptable If not should you consider a retrofit with packing If so should both sections of the column be packed or could just one section be packed to achieve an acceptable operation 3356 lbmolh benzene 09 lbmolh monochlorobenzene 2740 lbmolh benzene 07 lbmolh monochlorobenzene Top tray 23 psia 204F Figure 746 Data for Exercise 743 Bubblepoint liquid feed lbmolh 360 240 1358F 300 psia 116F 280 psia LD 159 35 lbmolh of C3 90 180 91 55 1 C3 1251 lbmolhr C3 C3 Figure 747 Data for Exercise 744 lbmolh 1876 1764 825 nC4 nC5 nC6 lbmolh 1124 2236 2175 nC4 nC5 nC6 2243F 1029 psia Figure 748 Data for Exercise 745 Saturated liquid 1 atm y 099 001 nC6 nC7 D 120 lbmolh LD 3 Figure 749 Data for Exercise 746 Saturated liquid 2625F 40 psia 189F 33 psia 188975 lbh 101 mol methanol 462385 lbh 9905 mole methanol 442900000 Btuh Feed 32 9 1 Figure 750 Data for Exercise 747 296 Chapter 7 Distillation of Binary Mixtures C08 09202010 Page 301 and interfacial tension between the two phases is more than 30 dynecm The column has an inside diameter of 55 ft and a total height of 28 ft and is divided into 40 compartments each 75 inches high containing a 40inchdiameter rotor disk located between a pair of stator donut rings of 46inch inside diameter Settling zones exist above the top stator ring and below the bottom stator ring Because the light liquid phase is dispersed the liquidliquid interface is maintained near the top of the column The rotors are mounted on a cen trally located shaft driven at 60 rpm by a 5hp motor equipped with a speed control the optimal disk speed being determined during plant operation The HETP is 50 inches equivalent to 667 compartments per equilibrium stage The HETP would be only 33 inches if no axial longitudinal mix ing discussed in 85 occurred Because of the corrosive nature of aqueous acetic acid solutions the extractor is con structed of stainless steel Since the 1930s thousands of simi lar extraction columns with diameters ranging up to at least 25 ft have been built As discussed in 81 a number of other extraction devices are suitable for the process in Figure 81 Liquidliquid extraction is a reasonably mature operation although not as mature or as widely applied as distillation absorption and stripping Procedures for determining the stages to achieve a desired solute recovery are well establi shed However in the thermodynamics of liquidliquid extraction no simple limiting theory such as that of ideal solutions for vaporliquid equilibrium exists Frequently experimental data are preferred over predictions based on activitycoefficient correlations Such data can be correlated and extended by activitycoefficient equations such as NRTL or UNIQUAC discussed in 26 Also considerable labora tory effort may be required to find an optimal solvent A vari ety of industrial equipment is available making it necessary to consider alternatives before making a final selection Unfortunately no generalized capacity and efficiency corre lations are available for all equipment types Often equip ment vendors and pilotplant tests must be relied upon to determine appropriate equipment size The petroleum industry represents the largestvolume application for liquidliquid extraction By the late 1960s more than 100000 m3day of liquid feedstocks were being processed 2 Extraction processes are well suited to the petroleum industry because of the need to separate heatsensitive liquid feeds according to chemical type eg aliphatic aromatic naphthenic rather than by molecular weight or vapor pressure Table 81 lists some representative industrial extraction processes Other applications exist in the biochemical industry including the separation of antibi otics and recovery of proteins from natural substrates in the recovery of metals such as copper from ammoniacal leach liquors in separations involving rare metals and radioactive isotopes from spentfuel elements and in the inorganic chemical industry where highboiling constituents such as phosphoric acid boric acid and sodium hydroxide need to be recovered from aqueous solutions In general extraction is preferred over distillation for 1 Dissolved or complexed inorganic substances in organic or aqueous solutions 2 Removal of a contaminant present in small concentra tions such as a color former in tallow or hormones in animal oil 3 A highboiling component present in relatively small quantities in an aqueous waste stream as in the recov ery of acetic acid from cellulose acetate 4 Recovery of heatsensitive materials where extraction may be less expensive than vacuum distillation 5 Separation of mixtures according to chemical type rather than relative volatility 6 Separation of closemelting or closeboiling liquids where solubility differences can be exploited 7 Separation of mixtures that form azeotropes The key to an effective extraction process is a suitable sol vent In addition to being stable nontoxic inexpensive and easily recoverable a solvent should be relatively immiscible Table 81 Representative Industrial LiquidLiquid Extraction Processes Solute Carrier Solvent Acetic acid Water Ethyl acetate Acetic acid Water Isopropyl acetate Aconitic acid Molasses Methyl ethyl ketone Ammonia Butenes Water Aromatics Paraffins Diethylene glycol Aromatics Paraffins Furfural Aromatics Kerosene Sulfur dioxide Aromatics Paraffins Sulfur dioxide Asphaltenes Hydrocarbon oil Furfural Benzoic acid Water Benzene Butadiene 1Butene aq Cuprammonium acetate Ethylene cyanohydrin Methyl ethyl ketone Brine liquor Fatty acids Oil Propane Formaldehyde Water Isopropyl ether Formic acid Water Tetrahydrofuran Glycerol Water High alcohols Hydrogen peroxide Anthrahydroquinone Water Methyl ethyl ketone Water Trichloroethane Methyl borate Methanol Hydrocarbons Naphthenes Distillate oil Nitrobenzene Naphthenes aromatics Distillate oil Phenol Phenol Water Benzene Phenol Water Chlorobenzene Penicillin Broth Butyl acetate Sodium chloride aq Sodium hydroxide Ammonia Vanilla Oxidized liquors Toluene Vitamin A Fishliver oil Propane Vitamin E Vegetable oil Propane Water Methyl ethyl ketone aq Calcium chloride LiquidLiquid Extraction with Ternary Systems 301 C08 09202010 Page 302 with feed componentss other than the solute and have a dif ferent density from the feed to facilitate phase separation by gravity It must have a high affinity for the solute from which it should be easily separated by distillation crystallization or other means Ideally the distribution partition coefficient 220 for the solute between the liquid phases should be greater than one or a large solventtofeed ratio will be required When the degree of solute extraction is not particu larly high andor when a large extraction factor 424 can be achieved an extractor will not require many stages This is fortunate because masstransfer resistance in liquidliquid systems is high and stage efficiency is low in contacting devices even if mechanical agitation is provided In this chapter equipment for liquidliquid extraction is discussed with special attention directed to devices for bio separations Equilibrium and ratebased calculation proce dures are presented mainly for extraction in ternary systems Use of graphical methods is emphasized Except for systems dilute in solutes calculations for multicomponent systems are best conducted using process simulators as discussed in Chapter 10 81 EQUIPMENT FOR SOLVENT EXTRACTION Equipment similar to that used for absorption stripping and distillation is sometimes used for extraction but such devices are inefficient unless liquid viscosities are low and differences in phase density are high Generally centrifugal and mechani cally agitated devices are preferred Regardless of the type of equipment the number of equilibrium stages required is com puted first Then the size of the device is obtained from experimental HETP or masstransferperformancedata char acteristic of that device In extraction some authors use the acronym HETS height equivalent to a theoretical stage rather than HETP Also the dispersed phase in the form of droplets is referred to as the discontinuous phase the other phase being the continuous phase 811 MixerSettlers In mixersettlers the two liquid phases are first mixed in a vessel Figure 82 by one of several types of impellers Figure 83 and then separated by gravityinduced settling Figure 84 Any number of mixersettler units may be con nected together to form a multistage countercurrent cascade During mixing one of the liquids is dispersed in the form of small droplets into the other liquid The dispersed phase may be either the heavier or the lighter phase The mixing is com monly conducted in an agitated vessel with sufficient resi dence time so that a reasonable approach to equilibrium eg 80 to 90 is achieved The vessel may be compart mented as in Figure 82 If dispersion is easily achieved and equilibrium rapidly approached as with liquids of low inter facial tension and viscosity the mixing step can be achieved by impingement in a jet mixer by turbulence in a nozzle mixer orifice mixer or other inline mixing device by shear ing action if both phases are fed simultaneously into a Variablespeed drive unit Compartment spacer Rotating plate Feed in Emulsion out Turbine Figure 82 Compartmented mixing vessel with turbine agitators Adapted from RE Treybal Mass Transfer 3rd ed McGrawHill New York 1980 c e d b a Figure 83 Some common types of mixing impellers a marine type propeller b centrifugal turbine c pitchedblade turbine d flatblade paddle e flatblade turbine From RE Treybal Mass Transfer 3rd ed McGrawHill New York 1980 with permission Slotted impingement baffle Heavy liquid out Light liquid out Tap for scum Emulsion in Figure 84 Horizontal gravitysettling vessel Adapted from RE Treybal Liquid Extraction 2nd ed McGrawHill New York 1963 with permission 302 Chapter 8 LiquidLiquid Extraction with Ternary Systems C08 09202010 Page 303 centrifugal pump or by injectors wherein the flow of one liquid is induced by another The settling step is by gravity in a settler decanter In Figure 84 a horizontal vessel with an impingement baffle to prevent the jet of the entering twophase dispersion emul sion from disturbing the gravitysettling process is used Vertical and inclined vessels are also common A major prob lem in settlers is emulsification in the mixing vessel which may occur if the agitation is so intense that the dispersed droplet size falls below 1 to 15 mm micrometers When this happens coalescers separator membranes meshes elec trostatic forces ultrasound chemical treatment or other ploys are required to speed settling If the phasedensity dif ference is small the rate of settling can be increased by substituting centrifugal for gravitational force as discussed in Chapter 19 Many single and multistage mixersettler units are availa ble and described by Bailes Hanson and Hughes 3 and Lo Baird and Hanson 4 Worthy of mention is the Lurgi extraction tower 4 for extracting aromatics from hydro carbon mixtures where the phases are mixed by centrifugal mixers stacked outside the column and driven from a single shaft Settling is in the column with phases flowing inter stagewise guided by a complex baffle design 812 Spray Columns The simplest and one of the oldest extraction devices is the spray column Either the heavy phase or the light phase can be dispersed as seen in Figure 85 The droplets of the dis persed phase are generated at the inlet usually by spray noz zles Because of lack of column internals throughputs are large depending upon phasedensity difference and phase viscosities As in gas absorption axial dispersion backmix ing in the continuous phase limits these devices to applica tions where only one or two stages are required Axial dispersion discussed in 85 is so serious for columns with a large diametertolength ratio that the continuous phase is completely mixed and spray columns are thus rarely used despite their low cost 813 Packed Columns Axial dispersion in a spray column can be reduced but not eliminated by packing the column This also improves mass transfer by breaking up large drops to increase interfacial area and promoting mixing in drops by distorting droplet shape With the exception of Raschig rings 5 the packings used in distillation and absorption are suitable for liquidliquid extraction but choice of packing material is more critical A material preferentially wetted by the continuous phase is preferred Figure 86 shows performance data in terms of HTU for Intalox saddles in an extraction service as a func tion of continuous UC and discontinuous UD phase superfi cial velocities Because of backmixing the HETP is generally larger than for staged devices hence packed col umns are suitable only when few stages are needed 814 Plate Columns Sieve plates reduce axial mixing and promote a stagewise type of contact The dispersed phase may be the light or the heavy phase For the former the dispersed phase analogous to vapor bubbles in distillation flows up the column with redispersion at each tray The heavy phase is continuous flowing at each stage through a downcomer and then across the tray like a liquid in a distillation tower If the heavy phase is dispersed upcomers are used for the light phase Columns have been built with diameters larger than 45 m Holes from 064 to 032 cm in diameter and 125 to 191 cm apart are used and tray spacings are closer than in distillation10 to 15 cm for lowinterfacialtension liquids Plates are usually built without outlet weirs on the downspouts In the Koch Kascade Tower perforated plates are set in vertical arrays of complex designs If operated properly extraction rates in sieveplate col umns are high because the dispersedphase droplets coalesce and reform on each sieve tray This destroys concentration gradients which develop if a droplet passes through the Heavy liquid Light liquid Light liquid Heavy liquid Light liquid Heavy liquid b a Heavy liquid Light liquid Figure 85 Spray columns a light liquid dispersed heavy liquid continuous b heavy liquid dispersed light liquid continuous 152 305 456 608 760 912 50 0 100 150 2 4 6 8 0 061 122 183 243 200 Uc continuous phase velocity fth UD dispersed phase velocity Uc mh 250 300 HTU m HTU ft UD 565 fth UD 246 fth Figure 86 Efficiency of 1inch Intalox saddles in a column 60 inches high with MEKwaterkerosene From RR Neumatis JS Eckert EH Foote and LR Rollinson Chem Eng Progr 671 60 1971 with permission 81 Equipment for Solvent Extraction 303 C08 09202010 Page 304 entire column undisturbed Sieveplate extractors are subject to the same limitations as distillation columns flooding entrainment and to a lesser extent weeping An additional problem is scum formation at phase interfaces due to small amounts of impurities 815 Columns with Mechanically Assisted Agitation If interfacial tension is high the density difference between liquid phases is low andor liquid viscosities are high gravi tational forces are inadequate for proper phase dispersal and turbulence creation In that case mechanical agitation is nec essary to increase interfacial area per unit volume thus decreasing masstransfer resistance For packed and plate columns agitation is provided by an oscillating pulse to the liquid either by mechanical or pneumatic means Pulsed perforatedplate columns found considerable application in the nuclear industry in the 1950s but their popularity declined because of mechanical problems and the unreliability of pulse propagation 6 Now the most preva lent agitated columns are those that employ rotating agita tors such as those in Figure 83 driven by a shaft extending axially through the column The agitators create shear mixing zones which alternate with settling zones Nine of the more popular arrangements are shown in Figure 87ai Agitation can also be induced in a column by moving plates back and forth in a reciprocating motion Figure 87j or in a novel hor izontal contactor Figure 87k These devices answer the 1947 plea of Fenske Carlson and Quiggle 7 for equipment that can efficiently provide large numbers of stages in a device without large numbers of pumps motors and piping They stated Despite advantages of liquidliquid sepa rational processes the problems of accumulating twenty or more theoretical stages in a small compact and relatively simple countercurrent operation have not yet been fully solved In 1946 it was considered impractical to design for more than seven stages which represented the number of mixersettler units in the only largescale commercial solventextraction process in use Light liquid out Light liquid out a c d b Tie rod Turbine impeller Inner horizontal baffle Wiremesh packing Feed if operated for fractional extraction Rotating shaft Heavy liquid out Light liquid in Light liquid out Heavy liquid in Wiremesh packing Turbine agitator Outer horizontal baffle Heavy liquid in Baffle Compartment baffle Heavy liquid out Light liquid in Impeller Perforated distributor Tie rod Light liquid in Heavy liquid out Heavy liquid in Flat impeller Perforated packing Rotating shaft Lower inlet port Flow control plates Upper inlet port Motor Feed if operated for fractional extraction Figure 87 Commercial extractors with mechanically assisted agitation a Scheibel columnfirst design b Scheibel columnsecond design c Scheibel columnthird design d OldshueRushton Mixco column continued 304 Chapter 8 LiquidLiquid Extraction with Ternary Systems C08 09202010 Page 305 Perhaps the first mechanically agitated column of impor tance was the Scheibel column 8 in Figure 87a in which liquid phases are contacted at fixed intervals by unbaffled flatbladed turbinetype agitators Figure 83 mounted on a vertical shaft In the unbaffled separation zones located between the mixing zones knitted wiremesh packing pre vents backmixing between mixing zones and induces coales cence and settling of drops The mesh material must be wetted by the dispersed phase For largerdiameter installa tions 1 m Scheibel 9 added outer and inner horizontal annular baffles Figure 87b to divert the vertical flow in the mixing zone and promote mixing For systems with high interfacial tension and viscosities the wire mesh is removed The first two Scheibel designs did not permit removal of the agitator shaft for inspection and maintenance Instead the entire internal assembly had to be removed To permit removal of just the agitator assembly shaft especially for largediameter columns eg 15 m and allow an access way through the column for inspection cleaning and repair Scheibel 10 offered a third design shown in Figure 87c Here the agitator assembly shaft can be removed because it has a smaller diameter than the opening in the inner baffle The OldshueRushton extractor 11 Figure 87d con sists of a column with a series of compartments separated by annular outer statorring baffles each with four vertical baf fles attached to the wall The centrally mounted vertical shaft drives a flatbladed turbine impeller in each compartment A third type of column with rotating agitators that appeared about the same time as the Scheibel and OldshueRushton columns is the rotatingdisk contactor RDC 12 13 Figure 87e an example of which is described at the beginning of this chapter and shown in Figure 81 On a worldwide basis it is an extensively used device with hundreds of units in use by 1983 4 Horizontal disks mounted on a centrally located Settling zone Light liquid outlet e f g Variablespeed drive Heavy liquid outlet Light liquid inlet Heavy liquid inlet Interface Rotor disk Stator ring Contact zone Agitator Settling zone Shell Stator Transport zone i h N Heavy phase out Light phase in Heavy phase in Light phase out Variablespeed drive Figure 87 Continued e rotatingdiskcontactor RDC f asymmetric rotatingdisk contactor ARD g section of ARD contactor h Kuhni column i flow pattern in Kuhni column 81 Equipment for Solvent Extraction 305 C08 09202010 Page 306 rotating shaft are the agitation elements The ratio of disk diameter to column diameter is 06 The distance H in m between disks depends on column diameter DC in m accord ing to H ¼ 013 DC ð Þ067 Mounted at the column wall are annular stator rings with an opening larger than the agitator disk diameter typically 07 of DC Thus the agitator assembly shaft is easily removed from the column Because the rota tional speed of the rotor controls the drop size the rotor speed can be continuously varied over a wide range A modification of the RDC concept is the asymmetric rotatingdisk contactor ARD 14 which has been in indus trial use since 1965 As shown in Figure 87f the contactor consists of a column a baffled stator and an offset multistage agitator fitted with disks The asymmetric arrangement shown in more detail in Figure 87g provides contact and transport zones that are separated by a vertical baffle to which is attached a series of horizontal baffles This design retains the efficient shearing action of the RDC but reduces backmixing because of the separate mixing and settling compartments Another extractor based on the Scheibel concept is the Kuhni extraction column 15 in Figure 87h where the col umn is compartmented by a series of stator disks made of perforated plates The distance H in m between stator disks depends on column diameter DC in m according to 02 H 03 DC ð Þ06 A centrally positioned shaft has dou bleentry radialflow shroudedturbine mixers which pro mote in each compartment the circulation action shown in Figure 87i The ratio of turbine diameter to column diameter ranges from 033 to 06 For columns of diameter greater than 3 m three turbinemixer shafts on parallel axes are normally provided to preserve scaleup Rather than provide agitation by impellers on a vertical shaft or by pulsing Karr 16 17 devised a reciprocating per foratedplate extractor column in which plates move up and down approximately 27 times per second with a 6525 mm stroke using less energy than for pulsing the entire volume of liquid Also the close spacing of the plates 2550 mm pro motes high turbulence and minimizes axial mixing thus giv ing high masstransfer rates and low HETS The annular baffle plates in Figure 87j are provided periodically in the plate stack to minimize axial mixing The perforated plates use large holes typically 916inch diameter and a high hole area typically 58 The central shaft which supports both sets of plates is reciprocated by a drive at the top of the col umn Karr columns are particularly useful for bioseparations because residence time is reduced and they can handle sys tems that tend to emulsify and feeds that contain particulates A modification of the Karr column is the vibratingplate extractor VPE of Prochazka et al 18 which uses perfo rated plates of smaller hole size and smaller hole area The small holes provide passage for the dispersed phase while one or more large holes on each plate provide passage for the continuous phase Some VPE columns have uniform motion of all plates others have two shafts for countermotion of alternate plates Another novel device for providing agitation is the Graesser rainingbucket contactor RTL developed in the late 1950s 4 primarily for processes involving liquids of small density difference low interfacial tension and a tend ency to form emulsions Figure 87k shows a series of disks mounted inside a shell on a horizontal rotating shaft with horizontal Cshaped buckets fitted between and around the periphery of the disks An annular gap between the disks and the inside shell periphery allows countercurrent longitudinal flow of the phases Dispersing action is very gentle with each phase cascading through the other in opposite directions toward the twophase interface which is close to the center Highspeed centrifugal extractors have been available since 1944 when the Podbielniak POD extractor shown in Figure 87l with residence times as short as 10 s was Light phase outlet Spider plate Center shaft and spacers Tie rods and spacers Teflon baffle plate Heavy phase outlet j Perforated plate Light phase feed sparger Heavy phase feed sparger Eccentric shaft Connecting rod Variable speed drive Counterweight Metal baffle plate Stub shaft Seal k Figure 87 Continued j Karr reciprocatingplate column RPC k Graesser rainingbucket RTL extractor 306 Chapter 8 LiquidLiquid Extraction with Ternary Systems C08 09202010 Page 307 successfully used in penicillin extraction 19 Since then the POD has found wide application in bioseparations because it provides very low holdup prevents emulsification and can separate liquid phases of density differences as small as 001 gcm3 Most fermentationproduced antibiotics are processed in PODs In the POD several concentric sieve trays encircle a horizontal axis through which the two liquid phases flow countercurrently The feed and the solvent enter at opposite ends of the POD As a result of the centrifugal force and den sity difference of the liquids the heavy liquid is forced out to the rim As it propagates through the perforations it displaces an equal volume of light liquid flowing toward the shaft Thus the two liquids flowing countercurrently are forced to pass each other through the perforations on each band leading to intense contact Processing time is about one minute an order of magnitude shorter than that of other devices which is very important for many of the unstable fermentation products The light liquid exits at the end where the heavy liquid enters and vice versa The countercurrent series of dispersion and coales cence steps results in multiple stages from 2 to 7 of extrac tion Inlet pressures to 7 atm are required to overcome pressure drop and centrifugal force The POD is available in the following five sizes where the smaller total volumetric flows refer to emulsifiable broths Additional material on cen trifugal separators appears in Chapters 14 and 19 Total Volumetric Flow m3h Max Speed rpm 005010 10000 69 3200 1534 2100 3068 2100 60136 1600 Figure 87 Continued l Cross section of a Podbielniak centrifugal extractor POD 81 Equipment for Solvent Extraction 307 C08 09202010 Page 308 816 Comparison of Industrial Extraction Columns Maximum loadings and sizes for industrial extraction col umns as given by Reissinger and Schroeter 5 20 and Lo et al 4 are listed in Table 82 As seen the Lurgi tower RDC and Graesser extractors have been built in very large sizes Throughputs per unit crosssectional area are highest for the Karr extractor and lowest for the Graesser extractor Table 83 lists the advantages and disadvantages of the various types of extractors and Figure 88 shows a selection scheme for commercial extractors For example if only a small number of stages is required a mixersettler unit might be selected If more than five theoretical stages a high throughput and a large load range m3m2h are needed and floor space is limited an RDC or ARD contactor should be considered 82 GENERAL DESIGN CONSIDERATIONS Liquidliquid extractors involve more variables than vapor liquid operations because liquids have more complex struc tures than gases To determine stages one of the three cascade arrangements in Figure 89 or an even more com plex arrangement must be selected The singlesection cas cade of Figure 89a which is similar to that used for absorption and stripping will transfer solute in the feed to the solvent The twosection cascade of Figure 89b is similar to that used for distillation Solvent enters at one end and reflux derived from the extract enters at the other end The feed enters in between With two sections depending on sol ubilities it is sometimes possible to achieve a separation between feed components if not a dualsolvent arrangement with two sections as in Figure 89c with or without reflux at the ends may be advantageous For this configuration which involves a minimum of four components two in the feed and two solvents calculations by a process simulator are preferred as discussed in Chapter 10 The configurations in Figure 89 are shown with packed sections but any extraction equipment may be chosen Operative factors are 1 Entering feed flow rate composition temperature and pressure 2 Type of stage configuration one or twosection Table 82 Maximum Size and Loading for Commercial Liquid Liquid Extraction Columns Column Type Approximate Maximum Liquid Throughout m3m2h Maximum Column Diameter m Lurgi tower 30 80 Pulsed packed 40 30 Pulsed sieve tray 60 30 Scheibel 40 30 RDC 40 80 ARD 25 50 Kuhni 50 30 Karr 100 15 Graesser 10 70 Above data apply to systems of 1 High interfacial surface tension 30 to 40 dynecm 2 Viscosity of approximately 1 cP 3 Volumetric phase ratio of 11 4 Phasedensity difference of approximately 06 gcm3 Table 83 Advantages and Disadvantages of Different Extraction Equipment Class of Equipment Advantages Disadvantages Mixersettlers Good contacting Handles wide flow ratio Low headroom High efficiency Many stages available Reliable scaleup Large holdup High power costs High investment Large floor space Interstage pumping may be required Continuous counterflow contactors no mechanical drive Low initial cost Low operating cost Simplest construction Limited throughput with small density difference Cannot handle high flow ratio High headroom Sometimes low efficiency Difficult scaleup Continuous counterflow contactors mechanical agitation Good dispersion Reasonable cost Many stages possible Relatively easy scaleup Limited throughput with small density difference Cannot handle emulsifying systems Cannot handle high flow ratio Centrifugal extractors Handles lowdensity difference between phases Low holdup volume Short holdup time Low space requirements Small inventory of solvent High initial costs High operating cost High maintenance cost Limited number of stages 27 in single unit 308 Chapter 8 LiquidLiquid Extraction with Ternary Systems C08 09202010 Page 309 3 Desired degree of recovery of one or more solutes for onesection cascades 4 Degree of feed separation for twosection cascades 5 Choice of solvents 6 Operating temperature 7 Operating pressure greater than the bubble point 8 Minimumsolvent flow rate and actualsolvent flow rate as a multiple of the minimum rate for onesection cascades or reflux rate and minimum reflux ratio for twosection cascades 9 Number of equilibrium stages 10 Emulsification and scumformation tendency 11 Interfacial tension 12 Phasedensity difference 13 Maximum residence time to avoid degradation 14 Type of extractor 15 Extractor cost and horsepower requirement The ideal solvent has 1 High selectivity for the solute relative to the carrier to minimize the need to recover carrier from the solvent 2 High capacity for dissolving the solute to minimize solventtofeed ratio 3 Minimal solubility in the carrier 4 A volatility sufficiently different from the solute that recovery of the solvent can be achieved by distillation but not so high that a high extractor pressure is needed or so low that a high temperature is needed if the solvent is recovered by distillation 5 Stability to maximize the solvent life and minimize the solvent makeup requirement 6 Inertness to permit use of common materials of construction 7 Low viscosity to promote phase separation minimize pressure drop and provide a highsolute masstransfer rate No Large number of theoretical stages required 5 Small number of theoretical stages required 5 Emulsion formation poor separation Small volume Separators centrifugal extractors Centrifugal extractors Graesser RDC ARD Separators Low height Low height Small floor area Small floor area High throughput 50m3h Small load range Pulsating sieve tray column Kuhni Lurgi tower extractor RDC ARD Large load range Small load range Large load range Low throughput 50m3h Process Yes Yes Mixersettler battery centrifugal extractors Yes Mixersettler battery Graesser Yes Yes All column types centrifugal extractors Yes Yes Yes Yes With reserva tions Yes Yes Pulsating packed column Karr column Yes Yes Scheibel Oldshue Rushton Yes No No No No No No No Figure 88 Scheme for selecting extractors From KH Reissinger and J Schroeter I Chem E Symp Ser No 54 3348 1978 82 General Design Considerations 309 C08 09202010 Page 313 En ¼ mass flow rate of extract leaving stage n Rn ¼ mass flow rate of raffinate leaving stage n yin ¼ mass fraction of species i in extract leaving stage n and xin ¼ mass fraction of species i in raffinate leaving stage n Although Figure 813 implies that the extract is the light phase either phase can be the light phase Phase equilibrium is represented as in 45 on an equilateraltriangle diagram as proposed by Hunter and Nash 26 or on a righttriangle diagram as proposed by Kinney 27 Assume the ternary sys tem is A solute C carrier and S solvent at a temperature T such that liquidliquid equilibrium data are as shown in Figure 814 where the bold line is the equilibrium curve also called the binodal curve because the plait point separates the curve into an extract to the left and a raffinate to the right and the dashed lines are tie lines connecting compositions of equilibrium phases Because the tie lines slope upward from the C side toward the S side at equilibrium A has a concentra tion higher in S than in C Thus in this example S is an effec tive solvent for extracting A Alternatively because the tie lines slope downward from the S side toward the C side C is not an effective solvent for extracting A from S Some systems such as isopropanolwaterbenzene exhibit a phenomenon called solutropy wherein moving from the plait point into the twophase region of the diagram the tie lines first slope in one direction but then the slope diminishes until an intermediate tie line becomes horizontal Below that tie line the remaining tie lines slope in the other direction Sometimes the solutropy phenomenon disappears if molefraction coordinates rather than massfraction coor dinates are used 831 Number of Equilibrium Stages From the degreesoffreedom discussions in 41 and 58 the following sets of specifications for the ternary component cascade of Figure 813 can be made where in addition all sets include the specification of F xiF yiS and T Set 1 S and xi ð ÞRN Set 4 N and xi ð ÞRN Set 2 S and yi ð ÞE1 Set 5 N and yi ð ÞE1 Set 3 xi ð ÞRN and yi ð ÞE1 Set 6 S and N where xi ð ÞRN and yi ð ÞE1 and all exiting phases lie on the equi librium curve Calculations for sets 1 to 3 involve determination of N and are made using triangular diagrams Sets 4 to 6 involve a spec ified N and require an iterative procedure First consider set 1 with the procedures for sets 2 and 3 being minor modifica tions The technique sometimes called the HunterNash method 26 involves three kinds of constructions on the triangular diagram and is more difficult than the McCabe Thiele staircase method for distillation Although the proce dure is illustrated here only for a Type I system parallel principles apply to a Type II system The constructions are shown in Figure 814 where A is the solute C the carrier and S the solvent On the equilibrium curve extract compositions Mmax RN S C Carrier Solute Solvent 90 A 80 70 60 50 40 30 20 10 10 90 20 80 30 70 40 60 50 50 60 40 70 30 80 20 90 10 F E1 M Plait point Tie line Operating line Equilibrium curve Figure 814 Construction 1 Location of product points Extract E1 E2 R1 Feed 1 2 E3 R2 En 1 En Rn1 RN2 Rn EN 1 EN RN 1 Raffinate RN Solvent S n N1 N F Figure 813 Countercurrentflow Nequilibriumstage liquidliquid extraction cascade 83 HunterNash Graphical EquilibriumStage Method 313 C08 09202010 Page 319 into phases A0 and A00 The location of M and the amounts of extract and raffinate are given by the same mixing rule and inverseleverarm rule used for equilateraltriangle diagrams The mixture separates spontaneously into 11600 kgh of raf finate ðxS ¼ 008 xA ¼ 032 Þ and 24500 kgh of extract ðxS ¼ 0375 xA ¼ 048 Þ Figure 823 represents the portion of an nstage counter currentflow cascade where x and y are weight fractions of solute in the raffinate and extract respectively and L and V are total amounts of raffinate and extract The feed to stage N is LNþ1 ¼ 180 kg of 35 wt A in a saturated mixture with C and S xNþ1 ¼ 035 ð Þ and the solvent to stage 1 is VW ¼ 100 kg of pure S yW ¼ 00 Thus the solventtofeed ratio is 100180 ¼ 0556 These points are shown in Figure 824 The mixing point for LN1 and VW is M1 as determined by the inverseleverarm rule Suppose the final raffinate LW leaving stage 1 is to con tain xW ¼ 005 glycol By an overall balance M1 ¼ VW þ LNþ1 ¼ VN þ LW ð811Þ Because VW LN1 and M1 lie on a straight line the mixing rule requires that VN LW and M1 also lie on a straight line Furthermore because VN leaves stage N at equilibrium and LW leaves stage 1 at equilibrium these streams lie on the extract and raffinate sides respectively of the equilibrium xA xC A A P P E E R R C D F D D F S xA yA P E G R C S b 10 00 10 45 Line a c Operating point 45 Line ys1 ys1 y1 y xs xs xF x xF F I C J S ys ys x y y1 A K 1 Operating curve Equilibrium curve Figure 821 Development of other coordinate systems from the equilateraltriangle diagram a to righttrian gle diagram b to auxiliary distribution curve c Location of operating point on auxiliary McCabe Thiele diagram From RE Treybal Liquid Extraction 2nd ed McGraw Hill New York 1963 with permission xC 08 xC 07 xC 06 xC 05 xC 04 xC 03 xC 02 xC 0 A M F Tie line Phase envelope Raffinate Extract 1 0 Wt fraction C xC 09 xC 01 10 09 08 07 06 05 04 03 02 01 00 01 S C A 02 03 04 05 0 1 Wt fraction A Wt fraction S 0 1 06 07 08 09 10 A Plait point Figure 822 Righttriangle diagram for system of Figure 814 VW 100 yW 0 LW xW 005 VW 100 yW 0 LW xW 005 VN2 yN2 LN 1 55 xN 1 035 VN3 yN3 LN 1 600 xN 1 035 VW 100 VN yN VN 1 yN 1 VN 2 yN 2 N2 N 1 N a b c LN xN LN 1 xN 1 LN 1 180 xN 1 035 Feed VW yW 0 Solvent LW xW 005 Figure 823 Multistage countercurrent contactors 83 HunterNash Graphical EquilibriumStage Method 319 C08 09202010 Page 321 30 In Figure 819 for the equilateraltriangle diagram or in Figure 824 for the righttriangle diagram the intersections of the equilibrium curve with a line drawn through a difference operating point represent the compositions of passing streams Thus for each such operating line on the triangular diagram one point on the operating line for the yx plot is determined The operating lines passing through the differ ence point need not correspond to actual passing streams Usually five or six such fictitious operatingline intersections covering the range of compositions in the cascade are suffi cient to establish the curved operating line For example in Figure 821c the arbitrary operating line that intersects the equilibrium curve at I and J in the righttriangle diagram be comes point K in the yx diagram operating line The yx plot of Figure 825 includes an operating line established in this manner based on the data of Figure 824 but with a sol venttofeed ratio of 0208that is VW ¼ 100 LN1 ¼ 480 25 greater than the minimum ratio of 0167 The stages are stepped off in the McCabeThiele manner starting from the feed end The result is three equilibrium stages 835 Extract and Raffinate Reflux A singlesection extraction cascade can be refluxed as in Figure 826a to resemble distillation In Figure 826a L is used for raffinate flows V for extract flows and stages are numbered from the solvent end of the process Extract reflux LR is provided by sending the extract VN to a solventrecovery step which removes most of the solvent and gives a solute rich solution LR þ D divided into extract reflux LR which is returned to stage N and product D At the other end of the cascade a portion B of the raffinate L1 is withdrawn in a stream divider and added as raffinate reflux VB to fresh sol vent S The remaining raffinate B is sent to a solvent removal step not shown to produce a carrierrich raffinate product When using extract reflux minimum and total reflux conditions corresponding to infinite and minimum stages bracket the optimal extract reflux ratio Raffinate reflux is not processed through the solventremoval unit because fresh solvent is added at this end of the cascade It is necessary however to remove solvent from extract reflux The analogy between a twosection liquidliquid extrac tor with feed entering a middle stage and distillation is con sidered in some detail by Randall and Longtin 32 Different aspects of the analogy are listed in Table 85 Most important is that the solvent MSA in extraction takes the place of heat ESA in distillation The use of raffinate reflux has been judged to be of little if any benefit by Skelland 31 who shows that the amount of raffinate reflux does not affect the number of stages required Accordingly only a twosection cascade that includes extract reflux as shown in Figure 826b is considered here Extract reflux LR Raffinate reflux Extract D Feed F VN VF VN1 VN2 LF1 LN LN1 V2 VF1 VF2 L3 V1 L2 VB L1 LF LF1 Stream divider Solvent removal N 1 2 1 Mixer a Solvent SB Solvent SB Solvent SD Solvent SD Raffinate B Raffinate B N F 1 F Extract reflux LR Extract D Feed F VN VF VN1 VN2 LF1 LN LN1 V2 VF1 VF2 L3 V1 L2 LF LF1 Stream divider Solvent removal N 1 Enriching section Stripping section Enriching section Stripping section 2 1 b N F 1 F Figure 826 Liquidliquid extraction with reflux a with extract and raffinate reflux b with extract reflux only 83 HunterNash Graphical EquilibriumStage Method 321 C08 09202010 Page 322 Analysis of a refluxed extractor involves direct extensions of procedures already developed As will be shown however results for a Type I system depend critically on feed composi tion and the phase diagram and it is difficult to draw any general conclusions with respect to the effect or even feasi bility of extract reflux For the twosection cascade with extract reflux shown in Figure 826b a degreesoffreedom analysis can be per formed The resultusing as elements two countercurrent cascades a feed stage a splitter and a divideris ND ¼ 2N þ 3C þ 13 All but four of the specifications usu ally are Variable Specification Number of Variables Pressure at each stage N Temperature for each stage N Feed stream flow rate composition temperature and pressure C þ 2 Solvent composition temperature and pressure C þ 1 Split of each component in the splitter solventremoval step C Temperature and pressure of the two streams leaving the splitter 4 Pressure and temperature of the divider 2 2N þ 3C þ 9 The four additional specifications can be one of the fol lowing sets Set 1 Set 2 Set 3 Solvent rate Reflux ratio Solvent rate Solute concentration in extract solventfree Solute concentration in extract solventfree Reflux ratio Solute concentration in raffinate solventfree Solute concentration in raffinate solventfree Number of stages Optimal feedstage location Optimal feedstage location Feedstage location Sets 1 and 2 of 831 are of interest in the design of a new extractor because two specifications deal with products of des ignated purities Set 2 is analogous to the design of a binary distillation using the McCabeThiele method where purities of the distillate and bottoms reflux ratio and optimal feed stage location are specified For a singlesection cascade it is not feasible to specify the split of the feed with respect to two components Instead as in absorption and stripping recovery of just one component in the feed is specified For binary distillations product purity may be limited by formation of azeotropes A similar limitation can occur for a Type I system when using a twosection cascade with extract reflux because of the plait point which separates the two liquid region from the homogeneous singlephase region This Table 85 Analogy between Distillation and Extraction Distillation Extraction Addition of heat Addition of solvent Reboiler Solvent mixer Removal of heat Removal of solvent Condenser Solvent separator Vapor at the boiling point Solventrich solution saturated with solvent Superheated vapor Solventrich solution containing more solvent than that required to saturate it Liquid below the boiling point Solventlean solution containing less solvent than that required to saturate it Liquid at the boiling point Solventlean solution saturated with solvent Mixture of liquid and vapor Twophase liquid mixture Relative volatility Relative selectivity Change of pressure Change of temperature D distillate D extract product solute on a solventfree basis B bottoms B raffinate solventfree basis L saturated liquid L saturated raffinate solventfree V saturated vapor V saturated extract solventfree A more volatile component A solute to be recovered C less volatile component C carrier from which A is extracted F feed F feed x mole fraction A in liquid X mole or weight ratio of A solventfree AA C y mole fraction A in vapor Y SA C 322 Chapter 8 LiquidLiquid Extraction with Ternary Systems C08 09202010 Page 350 supercritical fluid SF by an SFpermeable membrane bar rier to efficiently segregate exiting raffinate and extract while maintaining a large interfacial area independent of fluid velocity A subsequent expansion chamber flashes gaseous CO2 from the extractant An ionic surfactant and cosurfactant eg octane or cosolvent eg isooctane may be added to supercritical ethane ethylene or methane to form a dispersed phase for reversedmicelle extraction and back extraction of amino acids and proteins A fluorocarbon surfactant ammo nium carboxylate perfluoropolymer has been added to CO2 to lower the critical point of the fluid and extract proteins with reverse micelles 113 SUMMARY 1 A solvent can be used to selectively extract one or more components from a liquid mixture 2 Although liquidliquid extraction is a reasonably mature separation operation considerable experimental effort is often needed to find a solvent and residencetime requirements or values of HETS NTU or masstransfer coefficients 3 Masstransfer rates in extraction are lower than in vapor liquid systems Column efficiencies are frequently low 4 Commercial extractors range from simple columns with no mechanical agitation to centrifugal devices that spin at several thousand revolutions per minute The selection scheme in Table 83 is useful for choosing suitable extractors for a given separation 5 Solvent selection is facilitated by consideration of a number of chemical and physical factors given in Tables 84 and 82 6 For extraction with ternary mixtures phase equilibrium is conveniently represented on equilateral or righttrian gle diagrams for both Type I solute and solvent com pletely miscible and Type II solute and solvent not completely miscible systems 7 For determining equilibriumstage requirements of sin glesection countercurrent cascades for ternary systems the graphical methods of Hunter and Nash equilateral triangle diagram Kinney righttriangle diagram or Varteressian and Fenske distribution diagram of McCabeThiele type can be applied These methods can also determine minimum and maximum solvent requirements 8 A twosection countercurrent cascade with extract reflux can be employed with a Type II ternary system to enable a sharp separation of a binaryfeed mixture Obtaining stage requirements of a twosection cascade is conveniently carried out by the graphical method of Maloney and Schubert using a Janecke equilibrium diagram Addition of raffinate reflux is of little value 9 When few equilibrium stages are required mixersettler cascades are attractive because each mixer can be designed to approach an equilibrium stage With many ternary systems the residencetime requirement may be only a few minutes for a 90 approach to equilibrium using an agitator input of approximately 4 hp1000 gal Adequate phasedisengaging area for the settlers may be estimated from the rule of 5 gal of combined extract and raffinate per minute per square foot of dis engaging area 10 For mixers utilizing a sixflatbladed turbine in a closed vessel with side vertical baffles extractor design correla tions are available for estimating for a given extraction mixingvessel dimensions minimum impeller rotation rate for uniform dispersion impeller horsepower mean droplet size range of droplet sizes interfacial area per unit volume dispersed and continuousphase mass transfer coefficients and stage efficiency 11 For column extractors with and without mechanical agi tation correlations for determining flooding and column diameter and height are suitable only for preliminary sizing For final extractor selection and design recom mendations of equipment vendors and scaleup proce dures based on data from pilotsize equipment are desirable 12 Sizing of most column extractors must consider axial dispersion which can reduce masstransfer driving forces and increase column height Axial dispersion is most significant in the continuous phase 13 Small biomolecules eg antibiotics may be extracted from fermentation broths with common organic solvents Caffeine oils or volatiles may be extracted from solid seeds or beans using supercritical fluids Labile biopoly mers eg proteins are extracted using aqueous two phase systems like PEGdextranwater or PEGpotas sium phosphatewater 14 Partitioning eg KD values of bioproducts during organicsolvent or aqueous twophase extraction is influ enced by pH temperature salts and solute valence Hy drogen bonding ion pairing and Lewis acidbase complexation also influence partitioning in organic solvent extraction Size of solute and polymer and affin ity ligand affect partitioning in aqueous twophase extraction Values of KD may be predicted from theory using a minimum of experimental data REFERENCES 1 Derry TK and TI Williams A Short History of Technology Oxford University Press New York 1961 2 Bailes PJ and A Winward Trans Inst Chem Eng 50 240258 1972 350 Chapter 8 LiquidLiquid Extraction with Ternary Systems C08 09202010 Page 351 3 Bailes PJ C Hanson and MA Hughes Chem Eng 832 86100 1976 4 Lo TC MHI Baird and C Hanson Eds Handbook of Solvent Extraction WileyInterscience New York 1983 5 Reissinger KH and J Schroeter Alternatives to Distillation I Chem E Symp Ser No 54 3348 1978 6 Humphrey JL JA Rocha and JR Fair Chem Eng 9119 7695 1984 7 Fenske MR CS Carlson and D Quiggle Ind Eng Chem 39 1932 1947 8 Scheibel EG Chem Eng Prog 44 681 1948 9 Scheibel EG AIChE J 2 74 1956 10 Scheibel EG US Patent 3389970 June 25 1968 11 Oldshue J and J Rushton Chem Eng Prog 486 297 1952 12 Reman GH Proceedings of the 3rd World Petroleum Congress The Hague Netherlands Sec III 121 1951 13 Reman GH Chem Eng Prog 629 56 1966 14 Misek T and J Marek Br Chem Eng 15 202 1970 15 Fischer A Verfahrenstechnik 5 360 1971 16 Karr AE AIChE J 5 446 1959 17 Karr AE and TC Lo Chem Eng Prog 7211 68 1976 18 Prochazka J J Landau F Souhrada and A Heyberger Br Chem Eng 16 42 1971 19 Barson N and GH Beyer Chem Eng Prog 495 243252 1953 20 Reissinger KH and J Schroeter LiquidLiquid Extraction Equip ment Choice in JJ McKetta and WA Cunningham Eds Encyclopedia of Chemical Processing and Design Vol 21 Marcel Dekker New York 1984 21 Cusack RW P Fremeaux and D Glatz Chem Eng 982 6676 1991 22 Robbins LA Chem Eng Prog 7610 5861 1980 23 Naser SF and RL Fournier Comput Chem Eng 15 397414 1991 24 Darwent B and CA Winkler J Phys Chem 47 442454 1943 25 Treybal RE Liquid Extraction 2nd ed McGrawHill New York 1963 26 Hunter TG and AW Nash J Soc Chem Ind 53 95T102T 1934 27 Kinney GF Ind Eng Chem 34 11021104 1942 28 Venkataranam A and RJ Rao Chem Eng Sci 7 102110 1957 29 Sawistowski H and W Smith Mass Transfer Process Calculations Interscience New York 1963 30 Varteressian KA and MR Fenske Ind Eng Chem 28 13531360 1936 31 Skelland AHP Ind Eng Chem 53 799800 1961 32 Randall M and B Longtin Ind Eng Chem 30 1063 1188 1311 1938 31 908 1295 1939 32 125 1940 33 Maloney JO and AE Schubert Trans AIChE 36 741 1940 34 Flynn AW and RE Treybal AIChE J 1 324328 1955 35 Ryon AD FL Daley and RS Lowrie Chem Eng Prog 5510 7075 1959 36 Happel J and DG Jordan Chemical Process Economics 2nd ed Marcel Dekker New York 1975 37 Rushton JH and JY Oldshue Chem Eng Prog 49 161168 1953 38 Laity DS and RE Treybal AIChE J 3 176180 1957 39 Skelland AHP and GG Ramsey Ind Eng Chem Res 26 7781 1987 40 Skelland AHP and JM Lee Ind Eng Chem Process Des Dev 17 473478 1978 41 MacMullin RB and M Weber Trans AIChE 31 409458 1935 42 Lewis JB I Jones and HRC Pratt Trans Inst Chem Eng 29 126 1951 43 Coulson JM and JF Richardson Chemical Engineering Vol 2 4th ed Pergamon Oxford 1991 44 Vermuelen T GM Williams and GE Langlois Chem Eng Prog 51 85F 1955 45 Gnanasundaram S TE Degaleesan and GS Laddha Can J Chem Eng 57 141144 1979 46 Chen HT and S Middleman AIChE J 13 989995 1967 47 Sprow FB AIChE J 13 995998 1967 48 Davies JT Turbulence Phenomena Academic Press New York p 311 1978 49 Cornish ARH Trans Inst Chem Eng 43 T332T333 1965 50 Skelland AHP and LT Moeti Ind Eng Chem Res 29 2258 2267 1990 51 Batchelor GK Proc Cambridge Phil Soc 47 359374 1951 52 Stichlmair J ChemieIngenieurTechnik 52 253 1980 53 Logsdail DH JD Thornton and HRC Pratt Trans Inst Chem Eng 35 301315 1957 54 Landau J and R Houlihan Can J Chem Eng 52 338344 1974 55 Gayler R NW Roberts and HRC Pratt Trans Inst Chem Eng 31 5768 1953 56 Thornton JD Chem Eng Sci 5 201208 1956 57 Reman GH and RB Olney Chem Eng Prog 523 141146 1955 58 Strand CP RB Olney and GH Ackerman AIChE J 8 252261 1962 59 Reman GH Chem Eng Prog 629 5661 1966 60 Karr AE and TC LoPerformance of a 36inch Diameter Recipro catingPlate Extraction Column paper presented at the 82nd National Meeting of AIChE Atlantic City NJ Aug 29Sept 1 1976 61 Thornton JD Science and Practice of LiquidLiquid Extraction Vol 1 Clarendon Press Oxford 1992 62 Strigle RF Jr Random Packings and Packed Towers Gulf Publish ing Company Houston TX 1987 63 Sleicher CA Jr AIChE J 5 145149 1959 64 Miyauchi T and T Vermeulen Ind Eng Chem Fund 2 113126 1963 65 Sleicher CA Jr AIChE J 6 529531 1960 66 Miyauchi T and T Vermeulen Ind Eng Chem Fund 2 304310 1963 67 Garcia AA MR Bonen J RamirezVick M Sadaka and A Vuppa Bioseparation Process Science Blackwell Science Malden MA 1999 68 Ghosh R Principles of Bioseparations Engineering World Scientific Singapore 2006 69 Harrison RG P Todd SR Rudge and DP Petrides Bioseparations Science and Engineering Oxford University Press New York 2003 70 Shuler ML and F Kargi Bioprocess Engineering 2nd ed Prentice Hall PTR Upper Saddle River NJ 2002 71 Ward OP Bioprocessing Van Nostrand Reinhold New York 1991 References 351 C08 09202010 Page 352 72 Gu T LiquidLiquid Partitioning Methods for Bioseparations in S Ahuja Ed Handbook of Bioseparations Academic Press San Diego CA 2000 73 Belter PA EL Cussler and WS Hu Bioseparations Downstream Processing for Biotechnology John Wiley Sons New York 1988 74 Rydberg J Introduction to Solvent Extraction in J Rydberg C Musikas and GR Choppin Eds Principles and Practices of Solvent Extraction pp 117 Dekker New York 1992 75 Vandamme EJ Biotechnology of Industrial Antibiotics Dekker New York 1984 76 Essien DE and DL Pyle Fermentation Ethanol Recovery by Sol vent Extraction in MS Verrall and MJ Hudson Eds Separations for Biotechnology pp 320332 Ellis Horwood Chichester 1987 77 Hildebrand JH JM Prausnitz and RL Scott Regular and Related Solutions Van Nostrand New York 1970 and Handbook of Chemistry and Physics CRC Press Boca Raton FL 1986 78 Likidis Z and K Schugeri Biotechnol Lett 94 229232 1987 79 Schugerl K Solvent Extraction in Biotechnology Recovery of Pri mary and Secondary Metabolites SpringerVerlag Berlin 1994 80 Krishna R CY Low DMT Newsham CG OliveraFuentes and GL Standart Chem Eng Sci 406 893903 1985 81 Wesselingh JA and R Krishna Mass Transfer Ellis Horwood Chi chester England 1990 82 Walter H DE Brooks and D Fisher Eds Partitioning in Aqueous TwoPhase Systems Theory Methods Uses and Applications to Bio technology Academic Press New York 1985 83 Sutherland IA and D Fisher Partitioning A Comprehensive Bibli ography in H Walter DE Brooks and D Fisher Eds Partitioning in Aqueous TwoPhase Systems Theory Methods Uses and Applications to Biotechnology pp 627676 Academic Press Orlando FL 1985 84 Albertsson PA Partition of Cell Particles and Macromolecules 3rd ed John Wiley Sons New York 1986 85 Zaslavsky BY Aqueous TwoPhase Partitioning Physical Chemis try and Bioanalytical Applications Dekker New York 1995 86 Walter H and G Johansson Eds Methods in Enzymology Vol 228 Academic Press San Diego CA 1994 87 Sasakawa S and H Walter Biochemistry 11 2760 1972 88 Albertsson PA and F Tjerneld Phase Diagram in H Walter and G Johansson Eds Methods in Enzymology Vol 228 pp 313 Academic Press San Diego CA 1994 89 Flory PJ J Chem Phys 10 5161 1942 90 Diamond AD and JR Hsu Aqueous TwoPhase Systems for Bio molecule Separation in CL Cooney and AE Humphrey Eds Advances in Biochemical EngineeringBiotechnology Vol 47 pp 89135 Springer Verlag Berlin 1992 91 King RS HW Blanch and JM Prausnitz AIChE J 34 1585 1988 92 Haynes CA HW Blanch and JM Prausnitz Fluid Phase Equili brium 53 463 1989 93 Huddleston JG R Wang and JA Flanagan J Chromatogr A 668 3 1994 94 Hartounian H EW Kaler and SI Sandler Ind Eng Chem Res 33 2294 1994 95 Walter H S Sasakawa and PA Albertsson Biochemistry 11 3880 1972 96 Diamond AD and JT Hsu Biotechnology and Bioengineering 34 10001014 1989 97 Harris JM and M Yalpani Polymer Ligands Used in Affinity Par titioning and Their Synthesis in H Walter DE Brooks and D Fisher Eds Partitioning in Aqueous TwoPhase Systems Theory Methods Uses and Applications to Biotechnology pp 589626 Academic Press New York 1985 98 Kopperschlager G Affinity Extraction with Dye Ligands in H Walter and G Johansson Eds Methods in Enzymology Vol 228 p 313 Academic Press San Diego CA 1994 99 Vermeulen T JS Moon A Hennico and T Miyauchi Chem Eng Prog 629 95101 1966 100 Danckwerts PV Chem Eng Sci 2 113 1953 101 Wehner JF and RH Wilhelm Chem Eng Sci 6 8993 1956 102 Geankoplis CJ and AN Hixson Ind Eng Chem 42 11411151 1950 103 Gier TE and JO Hougen Ind Eng Chem 45 13621370 1953 104 Watson JS and HD Cochran Jr Ind Eng Chem Process Des Dev 10 8385 1971 105 Kumar A and S Hartland Ind Eng Chem Res 38 10401056 1999 106 Green DW and RH Perry Eds Perrys Chemical Engineers Handbook 8th ed McGrawHill New York 2008 107 Karr AE W Gebert and M Wang Canadian Journal of Chemical Engineering 58 249252 1980 108 Balasubramaniam D C Wilkinson K Van Cott and C Zhang J Chromatography A 989 119129 2003 109 Hammer S A Pfennig and M Stumpf J Chem Eng Data 39 409413 1994 110 Diamond AD AIChE J 36 10171024 1990 111 Croll T PD Munro DJ Winzor M Trau and LK Nielsen J Polym Sci Part B Polym Phys 41 437443 2003 112 Prausnitz JM RN Lichtenthaler and EG de Azevedo Molecular Thermodynamics of FluidPhase Equilibria 3rd ed Prentice Hall PTR Up per Saddle River NJ 1999 113 Cooper AI and JM DeSimone Current Opinion in Solid State and Materials Science 16 761768 1996 STUDY QUESTIONS 81 When liquidliquid extraction is used are other separation operations needed Why 82 Under what conditions is extraction preferred to distillation 83 What are the important characteristics of a good solvent 84 Can a mixersettler unit be designed to closely approach phase equilibrium 85 Under what conditions is mechanically assisted agitation necessary in an extraction column 86 What are the advantages and disadvantages of mixersettler extractors 87 What are the advantages and disadvantages of continuous counterflow mechanically assisted extractors 88 What is the difference between a Type I and a Type II ter nary system Can a system transition from one type to the other by changing the temperature Why 89 What is meant by the mixing point For a multistage extrac tor is the mixing point on a triangular diagram the same for the feeds and the products 810 What happens if more than the maximum solvent rate is used What happens if less than the minimum solvent rate is used 352 Chapter 8 LiquidLiquid Extraction with Ternary Systems C09 09182010 Page 360 including a deisobutanizer and a debutanizer In Case 1 of Table 91 the deisobutanizer is selected as the first column in the sequence Since the allowable quantities of nbutane in the isobutane recycle and isobutane in the nbutane product are specified isobutane is the LK and nbutane is the HK These two keys are adjacent in volatility Because a fairly sharp separation between these two keys is indicated and the nonkey components are not close in volatility to the butanes as a preliminary estimate it is assumed that the nonkey com ponent separation is perfect Alternatively in Case 2 if the debutanizer is placed first in the sequence specifications in Figure 92 require that n butane be the LK However the HK selection is uncertain because no recovery or purity is specified for any component less volatile than nbutane Possible HK components for the debutanizer are iC5 nC5 or C6 It is simplest to select iC5 so that the two keys are again adjacent For example suppose that 13 lbmolh of iC5 in the feed is allowed to appear in the distillate Because the split of iC5 is then not sharp and nC5 is close in volatility to iC5 it is proba ble that the nC5 in the distillate will not be negligible An estimate of the distributions of nonkey components for Case 2 is given in Table 91 iC4 may also distribute but a prelimi nary estimate of zero is made In Case 3 C6 is selected as the heavy key for the debutan izer at a rate of 001 lbmolh in the distillate as shown in Table 91 Now iC5 and nC5 will distribute between the Start Specified feed Specify splits of two key components Estimate splits of nonkey components Flash the feed at column pressure Repeat only if estimated and calculated splits of nonkey components differ considerably Bubblepointdewpoint calculations Adiabatic flash procedure Fenske equation Fenske equation Underwood equations Gilliland correlation Kirkbride equation Energybalance equations Determine column pressure and type of condenser Calculate minimum theoretical stages Calculate minimum reflux ratio Calculate condenser and reboiler duties Exit Calculate splits of nonkey components Calculate feed stage location Calculate actual theoretical stages for specified reflux ratio minimum value Figure 91 Algorithm for multicomponent distillation by FUG method Distillation process Alkylation reactor effluent Isobutane recycle Component nC4 lbmolh 25 Alkylate product Component nC4 lbmolh 6 nButane product Component iC4 lbmolh 12 0 Componenta aC6 C7 C8 C9 are taken as normal paraffins iC4 nC4 iC5 nC5 C3 lbmolh 307 380 473 36 15 23 391 2722 310 13000 C6 C6 C8 C7 C9 Figure 92 Separation specifications for alkylationreactor effluent 360 Chapter 9 Approximate Methods for Multicomponent Multistage Separations C09 09182010 Page 374 Pounds per Hour Component fE fU Raffinate l10 Extract y1 FA 09870 197 03 DMA 00 00 200 DMF 0000374 0422 13 4007 W 09922 00 35572 378 MC 09909 908 98822 36690 103310 The calculated flow rates L10 and V1 are almost exactly equal to the assumed rates Therefore an additional iteration is not necessary The degree of DMF extraction is very high More cases with less solvent andor fewer stages should be calculated SUMMARY 1 The FenskeUnderwoodGilliland FUG method for simple distillation of ideal and nearly ideal multi component mixtures is useful for preliminary estimates of stage and reflux requirements 2 Based on a specified split of two key components in the feed mixture the Fenske equation is used to determine Nmin at total reflux The Underwood equations are used to determine Rmin for an infinite number of stages The empirical Gilliland correlation relates Nmin and Rmin to the actual R and actual N 3 Distribution of nonkey components and feedstage loca tion can be estimated with the Fenske and Kirkbride equa tions respectively 4 The Underwood equations are more restrictive than the Fenske equation and must be used with care and caution 5 The Kremser group method can be applied to strippers and liquidliquid extractors for dilute solute conditions to make estimates of component recoveries for specified val ues of entering flow rates and equilibrium stages REFERENCES 1 Kremser A Natl Petroleum News 2221 4349 1930 2 Edmister WC AIChE J 3 165171 1957 3 Kobe KA and JJ McKetta Jr Eds Advances in Petroleum Chemis try and Refining Interscience New York Vol 2 pp 315355 1959 4 Bachelor JB Petroleum Refiner 366 161170 1957 5 Fenske MR Ind Eng Chem 24 482485 1932 6 Shiras RN DN Hanson and CH Gibson Ind Eng Chem 42 871876 1950 7 Underwood AJV Trans Inst Chem Eng 10 112158 1932 8 Gilliland ER Ind Eng Chem 32 11011106 1940 9 Underwood AJV J Inst Petrol 32 614626 1946 10 Barnes FJ DN Hanson and CJ King Ind Eng Chem Process Des Dev 11 136140 1972 11 Tavana M and DN Hanson Ind Eng Chem Process Des Dev 18 154156 1979 12 Fair JR and WL Bolles Chem Eng 759 156178 1968 13 Gilliland ER Ind Eng Chem 32 12201223 1940 14 Robinson CS and ER Gilliland Elements of Fractional Distilla tion 4th ed McGrawHill New York pp 347350 1950 15 Brown GG and HZ Martin Trans AIChE 35 679708 1939 16 Van Winkle M and WG Todd Chem Eng 7821 136148 1971 17 Molokanov YK TP Korablina NI Mazurina and GA Nikiforov Int Chem Eng 122 209212 1972 18 Guerreri G Hydrocarbon Processing 488 137142 1969 19 Donnell JW and CM Cooper Chem Eng 57 121124 1950 20 Oliver ED Diffusional Separation Processes Theory Design and Evaluation John Wiley Sons New York pp 104105 1966 21 Strangio VA and RE Treybal Ind Eng Chem Process Des Dev 13 279285 1974 22 Kirkbride CG Petroleum Refiner 239 87102 1944 23 Stupin WJ and FJ LockhartThe Distribution of NonKey Compo nents in Multicomponent Distillation presented at the 61st Annual Meeting of the AIChE Los Angeles CA December 15 1968 24 Souders M and GG Brown Ind Eng Chem 24 519522 1932 25 Horton G and WB Franklin Ind Eng Chem 32 13841388 1940 26 Edmister WC Ind Eng Chem 35 837839 1943 27 Smith BD and WK Brinkley AIChE J 6 446450 1960 STUDY QUESTIONS 91 Rigorous computerbased methods for multicomponent dis tillation are readily available in process simulators Why then is the FUG method still useful and widely applied for distillation 92 When calculating multicomponent distillation why is it best to list the components in order of decreasing volatility In such a list do the two key components have to be adjacent 93 What does the Fenske equation compute What assumptions are made in its derivation 94 For what conditions should the Fenske equation be used with caution 95 Is use of the Fenske equation restricted to the two key com ponents If not what else can the Fenske equation be used for 374 Chapter 9 Approximate Methods for Multicomponent Multistage Separations C09 09182010 Page 375 besides the estimation of the minimum number of equilibrium stages corresponding to total reflux 96 What is a pinch point or region For multicomponent distil lation under what conditions is the pinch point located at the feed location What conditions cause the pinch point to migrate away from the feed location 97 What is the difference between a Class 1 and a Class 2 sepa ration Why is the Class 1 Underwood equation useful even if the separation is Class 2 98 What is internal reflux How does it differ from external reflux Does the Underwood equation compute internal or external reflux How can one be determined from the other 99 What is the optimal range of values for RRmin 910 What key parameter is missing from the Gilliland correlation 911 When can a serious problem arise with the Gilliland correlation 912 What is the best method for estimating the distribution of nonkey components at the actual operating reflux 913 Is the Kremser method a group method What is meant by a group method 914 Under what conditions can the Kremser method be applied to liquidliquid extraction EXERCISES Section 91 91 Type of condenser and operating pressure A mixture of propionic and nbutyric acids which can be as sumed to form ideal solutions is to be separated by distillation into a distillate containing 95 mol propionic acid and a bottoms of 98 mol nbutyric acid Determine the type of condenser and esti mate the distillation operating pressure 92 Type of condenser and operating pressure Two distillation columns are used to produce the products indi cated in Figure 919 Establish the type of condenser and an operat ing pressure for each column for the a direct sequence C2C3 separation first and b indirect sequence C3nC4 separation first Use Kvalues from Figures 24 and 25 93 Type of condenser and operating pressure For each of the distillations D1 and D2 indicated in Figure 920 establish the type of condenser and an operating pressure 94 Stages for a deethanizer For the deethanizer in Figure 921 estimate the number of stages assuming it is equal to 25 times Nmin 95 Fenske equation for a column with a vapor sidestream For the complex distillation in Figure 922 use the Fenske equa tion to determine Nmin between the a distillate and feed b feed and sidestream and c sidestream and bottoms Use Raoults law for Kvalues 96 Comparison of Fenske equation with McCabeThiele method A 25 mol mixture of acetone A in water W is to be sepa rated by distillation at 130 kPa into a distillate containing 95 mol acetone and a bottoms of 2 mol acetone The infinitedilution activity coefficients are g1 A ¼ 812 and g1 W ¼ 413 Calculate Nmin by the Fenske equation Compare the result to that calculated using the McCabeThiele method Is the Fenske equation reliable for this separation 97 Distribution of nonkeys and minimum stages For the distillation in Figure 923 calculate Nmin and the distri bution of the nonkey components by the Fenske equation using Fig ures 24 and 25 for Kvalues 98 Type of condenser operating pressure nonkey distribu tion and N min For the distillation in Figure 924 establish the condenser type and operating pressure calculate Nmin and estimate the distribution of the nonkey components Obtain Kvalues from Figures 24 and 25 Sequence of two distillation columns kmolh 160 365 5 kmolh 5 24 5 kmolh 5 230 1 C2 C3 nC4 nC5 C1 C2 C3 C1 C2 C3 nC4 C3 nC4 nC5 kmolh 160 370 240 25 5 Figure 919 Data for Exercise 92 C2 Benzene Toluene C1 kmolh D 1 D 2 20 5 500 100 C2 Benzene C1 kmolh 20 4995 5 Toluene Benzene kmolh 10 995 Benzene Toluene C2 kmolh 0005 485 05 Figure 920 Data for Exercise 93 average relative volatility 90F Comp C2 C3 nC4 C1 kmolh 160 370 240 25 5 nC5 2 kmolh of C2 Comp α C1 C2 nC4 C3 nC5 2 kmolh of C3 822 242 100 0378 0150 Figure 921 Data for Exercise 94 Exercises 375 C10 09292010 Page 387 the rectifyingsection rate across the feed zone is approximately 33 higher than the average converged vapor rate A better initial vapor rate estimate in the stripping section can be made by comput ing the reboiler duty from the condenser duty based on the specified reflux rate and then determining the vapor rate from the reboiler The separation is between C2 LK and C3 HK thus C1 is a lighter thanlight key LLK and nC4 and nC5 are heavier than the heavy key HHK Each of these four exhibits a different compositionprofile curve as shown in Figures 1012 and 1013 Except at the feed zone and at each end of the column both liquid and vapor LK mole fractions decrease smoothly and continuously from the top of the col umn to the bottom The inverse occurs for C3 HK Mole fractions of methane LLK are almost constant over the rectifying section except near the top Below the feed zone methane rapidly disappears from both vapor and liquid streams The inverse is true for the two HHK components In Figure 1013 feed composition is somewhat different from the composition of vapor entering the feed stage from below or vapor leaving the feed stage 1 2 3 4 5 6 7 8 9 10 11 12 13 C1 C1 C2 C2 C3 C3 C5 C4 C4 Mole fraction in liquid leaving stage 01 02 03 04 05 06 Feed composition 07 08 09 0 Distillate Theoretical stage number Reboiler vapor Figure 1013 Converged vapor composition profiles for Example 102 1 2 3 4 5 6 7 8 9 10 11 12 13 C1 C3 C2 C5 C4 Mole fraction in liquid leaving stage 01 02 03 04 05 06 07 08 09 0 External reflux Theoretical stage number Bottoms Figure 1012 Converged liquid composition profiles for Example 102 1 2 3 4 5 6 7 8 9 10 11 12 13 Converged liquid Converged vapor Initial assumed vapor 1500 1000 Flow rate leaving stage lbmolh 500 0 Feed Theoretical stage number Reboiler Condenser Figure 1011 Converged interstage flow rates for Example 102 103 EquationTearing Procedures 387 C10 09292010 Page 388 For problems where distillate flow rate and N are speci fied it is difficult to specify the optimal feedstage location However after a rigorous calculation is made a McCabe Thiele plot based on the key components 13 can be con structed to determine if the feed stage is optimally located For this plot mole fractions of the LK are on a nonkeyfree basis The resulting diagram for Example 102 is shown in Figure 1014 where the trend toward a pinchedin region is more noticeable in the rectifying section just above stage 7 than in the stripping section just below stage 7 This suggests that a better separation might be made by shifting the feed entry to stage 6 Figure 1015 shows the effect of feedstage location on the percent loss of ethane to the bottoms product As predicted from Figure 1014 the optimal feed stage is 6 1033 SumRates SR Method for Absorption and Stripping The species in most absorbers and strippers cover a wide range of volatility Hence the BP method of solving the MESH equations fails because bubblepoint temperature cal culations are too sensitive to liquidphase composition and the stage energy balance 105 is much more sensitive to stage temperatures than to interstage flow rates as discussed in 1032 In this case Friday and Smith 7 showed that an alternative procedure devised by Sujata 14 could be used This sumrates SR method was further developed in con junction with the tridiagonalmatrix formulation for the modified M equations by Burningham and Otto 15 Figure 1016 shows the BurninghamOtto SR algorithm A FORTRAN computer program for the method is available 16 Problem specifications consist of conditions and stage locations for feeds stage pressure sidestream flow rates stage heattransfer rates and number of stages Tear variables Tj and Vj are assumed to initiate the calcula tions It is sufficient to assume a set of Vj values based on the assumption of constantmolar flows working up from the absorber bottom using specified vapor feeds and vapor side stream flows if any An initial set of Tj values can be obtained from assumed topstage and bottomstage values and a linear variation with stages in between Values of xij are established by solving 1012 by the Thomas algorithm These values are not normalized but uti lized directly to produce new values of Lj by applying 104 in a form referred to as the sumrates equation L kþ1 ð Þ j ¼ L k ð Þ j X C i¼1 xij ð1033Þ 10 08 06 04 02 10 08 06 xC2 xC2 xC3 04 02 0 1 2 3 4 5 6 Feed 7 entry 8 9 10 11 12 13 yC2 yC2 yC3 Figure 1014 Modified McCabeThiele diagram for Example 102 18 16 14 12 10 8 6 Feedstage location Percent of C2 to bottoms 7 5 4 Figure 1015 Effect of feedstage location on separation for Example 102 Initialize tear variables Tj Vj Compute x from 1012 by Thomas method Compute new Lj from sumrates relation 1033 and new Vj from 1034 Normalize xij for each stage by 1019 Calculate corresponding yij from 102 Normalize yij Start Compute new Tj from 105 Specify all Fj zij feed conditions TFj PFj or hFj Pj Uj Wj Qj N Adjust tear variables Tridiagonal matrix equation evaluations one component at a time Sequential evaluations one equation at a time Simultaneous solution of equations by NewtonRaphson procedure Set k 1 to begin first iteration Yes Converged Exit Set k k 1 to begin next iteration No Not converged Is from 1032 001N τ Figure 1016 Algorithm for BurninghamOtto SR method 388 Chapter 10 EquilibriumBased Methods for Multicomponent Absorption Stripping Distillation and Extraction C10 09292010 Page 393 Stage yij xij j Vj H B DMF Water H B DMF Water 1 1100 00 00909 06818 02273 07895 02105 00 00 2 1080 00 00741 06944 02315 08333 01667 00 00 3 1060 00 00566 07076 02359 08824 01176 00 00 4 1040 00 00385 07211 02404 09375 00625 00 00 5 1020 00 00196 07353 02451 10000 00 00 00 The converged solution is obtained by the ISR method with the fol lowing stage flow rates and compositions Stage yij xij j Vj H B DMF Water H B DMF Water 1 11131 00263 00866 06626 02245 07586 01628 00777 00009 2 11047 00238 00545 06952 02265 08326 01035 00633 00006 3 10656 00213 00309 07131 02347 08858 00606 00532 00004 4 10421 00198 00157 07246 02399 09211 00315 00471 00003 5 10282 00190 00062 07316 02432 09438 00125 00434 00003 Computed products for the two cases are Extract lbmolh Raffinate lbmolh Case A Case B Case A Case B H 293 56 2707 2944 B 964 430 36 570 DMF 7375 4858 125 142 Water 2499 4997 01 50 11131 10341 2869 3659 On a percentage extraction basis the results are Case A Case B Percent of benzene feed extracted 964 430 Percent of nheptane feed extracted 98 187 Percent of solvent transferred to raffinate 126 145 Thus the solvent with 75 DMF extracts a much larger percent age of the benzene but the solvent with 50 DMF is more selec tive between benzene and nheptane For Case A the variations with stage of Kvalues and the relative selectivity are shown in Figure 1023 where the relative selectivity is bBH ¼ KBKH The distribution coefficient for nheptane varies by a factor of almost 175 from stage 5 to stage 1 while the coefficient for benzene is almost constant The relative selectivity varies by a factor of almost 2 104 NEWTONRAPHSON NR METHOD BP and SR methods for vaporliquid systems converge with difficulty or not at all for very nonideal liquid mixtures or for cases where the separator is like an absorber or stripper in one section and a fractionator in another section eg the reboiled absorber in Figure 17 Furthermore BP and SR methods are generally restricted to limited specifications Universal procedures for solving separation problems are based on the solution of the MESH equations or combina tions thereof by simultaneouscorrection SC techniques which employ the NewtonRaphson NR method To develop an SC procedure it is necessary to select and order the unknown variables and corresponding functions MESH equations As discussed by Goldstein and Stanfield 21 grouping of functions by type is computationally most efficient for problems involving many components but few stages For problems involving many stages but relatively few components it is most efficient to group the functions according to stage location The latter grouping presented here is described by Naphtali 22 and was implemented by Naphtali and Sandholm 23 Their procedure utilizes the mathematical techniques presented in 103 A computer program for their method is given by Fredenslund et al 24 However that program does not have the flexibility of speci fications found in process simulators The stage model of Figures 101 and 103 is again employed However rather than solving the N2C þ 3 MESH equations simultaneously 103 and 104 are com bined with the other MESH equations to eliminate 2N varia bles and thus reduce the problem to the simultaneous solution of N2C þ 1 equations This is done by first multiplying 103 and 104 by Vj and Lj respectively to give Vj ¼ X C i¼1 yij ð1054Þ Lj ¼ X C i¼1 lij ð1055Þ Kwater KDMF Kbenzene Knheptane Knheptane Kbenzene β K β 1000 100 10 10 010 001 1 2 3 Stage number 4 5 Figure 1023 Variation of distribution coefficient and relative selectivity for Example 105 Case A 104 NewtonRaphson NR Method 393 C11 10042010 Page 415 1111 Distillation Regions and Boundaries From Chapters 4 and 8 the composition of a ternary mixture can be represented on a triangular diagram either equilateral or right where the three apexes represent pure components Although Stichlmair 3 shows that vaporliquid phase equi libria at a fixed pressure can be plotted by letting the triangu lar grid represent the liquid phase with superimposing lines of constant equilibriumvapor composition for two of the three components this representation is seldom used It is more useful when developing a feasibleseparation process for a ternary mixture to plot only equilibriumliquidphase compositions on the triangular diagram Figure 113 where compositions are in mole fractions shows plots of this type for three different ternary systems Each curve is the locus of possible equilibriumliquidphase compositions during distil lation of a mixture starting from any point on the curve The boiling points of the three components and their binary and or ternary azeotropes at 1 atm are included on the diagrams The zeotropic alcohol system of Figure 113a does not form any azeotropes If a mixture of these three alcohols is dis tilled there is only one distillation region similar to the bi nary system of Figure 111a Accordingly the distillate can be nearly pure methanol A or the bottoms can be nearly pure 1propanol C However nearly pure ethanol B the intermediateboiling component cannot be produced as a distillate or bottoms To separate this ternary mixture into the three components a sequence of two columns is used as shown in Figure 114 where the feed distillate and bottoms product compositions must lie on a straight totalmaterial balance line within the triangular diagram In the socalled direct sequence of Figure 114a the feed F is first separated into distillate A and a bottoms of B and C then B is separated 557C 785C Ethanol 647C Methanol B C A Acetone 562C b 1362C Ethylbenzene 1271C 1351C 2Ethoxy ethanol B C A Octane 1258C c 972C 1Propanol 785C Ethanol B C A Methanol 647C a 1161C Region 2 Region 1 Azeotrope Figure 113 Distillation curves for liquidphase compositions of ternary systems at 1 atm a Mixture not forming an azeo trope b Mixture forming one minimumboiling azeotrope c Mixture forming two mini mumboiling azeotropes C A A A A B A B C A B C B C C C B B B F B C C A B F A B a b 1 2 1 2 Figure 114 Distillation sequences for ternary zeotropic mixtures a Direct sequence b Indirect sequence 111 Use of Triangular Graphs 415 C11 10042010 Page 420 In the description the term species refers to both pure com ponents and azeotropes Step 0 Label the ternary diagram with the purecompo nent normalboilingpoint temperatures It is pref erable to designate the top vertex of the triangle as the low boiler L the bottomright vertex as the high boiler H and the bottomleft vertex as the intermediate boiler I Plot composition points for the binary and ternary azeotropes and add labels for their normal boiling points This determines the value of B See Figure 117 Step 0 where two minimumboiling and one maximumboiling binary azeotropes and one ternary azeotrope are designated by filled square markers Thus B ¼ 3 Step 1 Draw arrows on the edges of the triangle in the direction of increasing temperature for each pair of adjacent species See Figure 117 Step 1 where six species are on the edges of the triangle and six arrows have been added Step 2 Determine the type of singular point for each pure component vertex by using Figure 116 with the arrows drawn in Step 1 of Figure 117 This deter mines the values for N1 and S1 If a ternary azeo trope exists go to Step 3 if not go to Step 5 In Figure 117 Step 2 L is a saddle because one arrow points toward L and one points away from L H is a stable node because both arrows point toward H and I is a saddle Therefore N1 ¼ 1 and S1 ¼ 2 Step 3 for a ternary azeotrope Determine the type of singular point for the ternary azeotrope if one exists The point is a node if a N1 þ B 4 and or b excluding the purecomponent saddles the ternary azeotrope has the highest secondhighest Input compositions and temperatures Initialize A Fill in the edges step 1 Determine pure component singular point types step 2 GlobalLocal indeterminacy Rule out infeasible connections with pure components Calculate N2 and S2 step 5 Test data consistency step 6 Connect it with the binary saddles when possible Rule out infeasible connections for the remaining binary saddles Local indeterminacy VLE model Compute actual residue curve map Calculate Bib number of intermediate boiling binary azeotropes Connect the temary saddle to all binary azeotropes and pure component nodes step 4 Make connections for the binary saddles step 8 Ternary saddle step 3 N1 B 6 Bib S2 step 7 Ternary node Yes Yes No No Yes Yes No No End End End Figure 118 Flowchart of algorithm for sketching an approximate residuecurve map From ER Foucher MF Doherty and MF Malone IEC Res 30 763 1991 with permission 420 Chapter 11 Enhanced Distillation and Supercritical Extraction C11 10042010 Page 423 1115 Feasible ProductComposition Regions at Total Reflux BowTie Regions The feasibledistillation regions for azeotropeforming ter nary mixtures are not obvious Fortunately residuecurve maps and distillationcurve maps can be used to make pre liminary estimates of regions of feasibleproduct composi tions for nonideal ternary systems These regions are determined by superimposing a column materialbalance line on either type of curvemap diagram Consider first the sim pler zeotropic ternary system in Figure 1111a which shows an isobaric residuecurve map with three residue curves Assume this map is identical to a corresponding distillation curve map for totalreflux conditions and to a map for a finite but very high reflux ratio Suppose ternary feed F in Figure 1111a is continuously distilled isobarically at a high R to produce distillate D and bottoms B A straight line that connects distillate and bottoms compositions must pass through the feed composition at some intermediate point to satisfy materialbalance equations Three materialbalance lines are included in the figure For a given line D and B composition points designated by open squares lie on the same distillation curve This causes the materialbalance line to intersect the distillation curve at these two points and be a chord to the distillation curve The limiting distillatecomposition point for this zeotropic system is pure lowboiling component L From the material balance line passing through F as shown in Figure 1111b the corresponding bottoms composition with the least amount of component L is point B At the other extreme the limiting bottomscomposition point is highboiling compo nent H A materialbalance line from this point through feed point F ends at D These two lines and the distillation curve define the feasible productcomposition regions shown shaded Note that because for a given feed both the distillate and bottoms compositions must lie on the same distillation curve shaded feasible regions lie on the convex side of the distillation curve that passes through the feed point Because of its appearance the feasibleproductcomposition region is called a bowtie region For azeotropes where distillation boundaries are present a feasibleproductcomposition region exists for each distilla tion region Two examples are shown in Figure 1112 Fig ure 1112a has two distillation regions caused by two minimumboiling binary azeotropes A curved distillation boundary connects the minimumboiling azeotropes In the lower righthand distillation region 1 the lowestboiling species is the noctane2ethoxyethanol minimumboiling azeotrope while the highestboiling species is 2ethoxy ethanol Accordingly for feed F1 straight lines are drawn F H a I L F B for pure L distillate D for pure H bottoms H b I L Figure 1111 Productcomposition regions for a zeotropic system a Materialbalance lines and distillation curves b Productcomposition regions shown shaded From S Widagdo and WD Seider AIChE J 42 96 130 1996 with permission F2 F1 B1 B2 D2 1161C nOctane 1258C Acetone 562C 557C a b 1362C Ethylbenzene 1351C 2Ethoxy ethanol 1271C 647C Methanol 612C Chloroform 644C 534C D1 D3 D1 D2 B3 B4 B2 B1 F3 F4 4 2 3 1 F2 F1 575C D4 2 1 Figure 1112 Product composition regions for given feed compositions a Ternary mixture with two minimumboiling binary azeotropes at 1 atm b Ternary mixture with three binary and one ternary azeotrope at 1 atm 111 Use of Triangular Graphs 423 C11 10042010 Page 428 acetone and chloroform A curved distillation boundary extending from that azeotrope to the purebenzene apex divides the diagram into two distillation regions The first column which produces nearly pure acetone operates in Region 1 the second column oper ates in Region 2 This ternary system was studied in detail by Fidkowski Doherty and Malone 17 A design based on their studies that uses the CHEMCAD process simulator is summarized in Table 113 The first column contains 65 theoretical stages with the combined feed entering stage 30 from the top For R ¼ 10 the acetone distillate purity is achieved with an acetone recovery of better than 9995 In Column 2 which contains 50 theoretical stages with feed enter ing at stage 30 an R ¼ 11783 gives the required chloroform purity in the distillate but with a recovery of only 8223 This is not seri ous because the chloroform leaving in the bottoms is recycled with benzene to Column 1 resulting in a 989 overall recovery of chlo roform The benzene makeup rate is 01141 mols Feed distillate and bottoms compositions are designated in Figure 1120 113 SALT DISTILLATION Water as a solvent in the extractive distillation of acetone and methanol in Example 113 has the disadvantages that a large amount is required to adequately alter a and even though the solvent is introduced into the column several trays below the top enough water is stripped into the distillate to reduce the acetone purity to 956 mol The water vapor pressure can be lowered and thus the purity of acetone distillate increased by using an aqueous inorganicsalt solution as the solvent A 1927 patent by Othmer 23 describes use of a concentrated calcium chloride brine Not only does calcium chloride which is highly soluble in water reduce the volatility of water but it also has a strong affinity for methanol Thus a of acetone with respect to methanol is enhanced The separation of brine solu tion from methanol is easily accommodated in the subsequent distillation with the brine solution recycled to the extractive distillation column The vapor pressure of the dissolved salt is so small that it never enters the vapor provided entrainment is avoided An even earlier patent by Van Raymbeke 24 describes the extractive distillation of ethanol from water using solutions of calcium chloride zinc chloride or potassium car bonate in glycerol Salt can be added as a solid or melt into the column by dissolving it in the reflux before it enters the column This was demonstrated by Cook and Furter 25 in a 4inchdiameter 12tray rectifying column with bubble caps separating ethanol from water using potassium acetate At salt concentrations below saturation and between 5 and 10 mol an almost pure ethanol distillate was achieved The salt which must be soluble in the reflux is recovered from the aqueous bottoms by evaporation and crystallization Salt distillation is accompanied by several problems First and foremost is corrosion particularly with aqueous chloridesalt solutions which may require stainless steel or a more expensive corrosionresistant material Feeding and dissolving a salt into the reflux poses problems described by Cook and Furter 25 The solubility of salt will be low in the reflux because it is rich in the morevolatile component the salt being most soluble in the lessvolatile component Salt must be metered at a constant rate and the saltfeeding mech anism must avoid bridging and prevent the entry of vapor which could cause clogging when condensed The salt must be rapidly dissolved and the reflux must be maintained near the boiling point to avoid precipitation of alreadydissolved salt In the column presence of dissolved salt may increase foaming requiring addition of antifoaming agents andor col umndiameter increase Concern has been voiced for the pos sibility of salt crystallization within the column However the concentration of the lessvolatile component eg water increases down the column so the solubility of salt increases down the column while its concentration remains relatively constant Thus the possibility of clogging and plugging due to solids formation is unlikely In aqueous alcohol solutions both salting out and salting in have been observed by Johnson and Furter 26 as shown in the vaporliquid equilibrium data in Figure 1121 In a sodium nitrate salts out methanol but in b mercuric chlo ride salts in methanol Even low concentrations of potassium acetate can eliminate the ethanolwater azeotrope as shown in Figure 1121c Mixed potassium and sodiumacetate salts were used in Germany and Brazil from 1930 to 1965 for the separation of ethanol and water Table 113 Material and Energy Balances for Homogeneous Azeotropic Distillation of Example 114 Material Balances with Flows in mols Species F F1 D1 B1 ¼ F2 D2 B2 Acetone Chloroform Benzene 120000 98858 00000 120000 120000 760000 119948 01046 00207 00052 118954 759793 00052 97812 00934 00000 21142 758859 Energy Balances Heat duty kcalh Column 1 Column 2 Condenser Reboiler 950000 958400 891600 1102000 428 Chapter 11 Enhanced Distillation and Supercritical Extraction C11 10042010 Page 429 Surveys of the use of inorganic salts for extractive distilla tion including effects on vaporliquid equilibria are given by Johnson and Furter 27 Furter and Cook 28 and Furter 29 30 A survey of methods for predicting the effect of inorganic salts on vaporliquid equilibria is given by Kumar 31 Columnsimulation results using the NewtonRaphson method are presented by LlanoRestrepo and AguilarArias 99 for the ethanolwatercalcium chloride system and by Fu 100 for the ethanolwaterethanediolpotassium ace tate system who shows simulation results that compare favorably with those from an industrial column Salt distillation can be applied to organic compounds that have little capacity for dissolving inorganic salts by using organic salts called hydrotropes Typical are alkali and alkalineearth salts of the sulfonates of toluene xylene or cymene and the alkali benzoates thiocyanates and salicy lates Mahapatra Gaikar and Sharma 32 found that the addition of aqueous solutions of 30 and 66 wt ptoluene sulfonic acid to 26xylenol and pcresol at 1 atm increased the a from approximately 1 to about 3 as shown in Figure 1121d Hydrotropes can also enhance liquidliquid extrac tion as shown by Agarwal and Gaikar 33 114 PRESSURESWING DISTILLATION If a binary azeotrope disappears at some pressure or changes composition by 5 mol or more over a moderate range of pressure consideration should be given to using two ordinary distillation columns operating in series at different pressures This process is referred to as pressureswing distillation Knapp and Doherty 34 list 36 pressuresensitive binary azeotropes mainly from the compilation of Horsley 11 The effect of pressure on temperature and composition of two minimumboiling azeotropes is shown in Figure 1122 The mole fraction of ethanol in the ethanolwater azeotrope increases from 08943 at 760 torr to more than 09835 at 90 torr Not shown in Figure 1122b is that the azeotrope dis appears at below 70 torr A more dramatic change in compo sition with pressure is seen in Figure 1122b for the ethanol benzene system which forms a minimumboiling azeotrope at 448 mol ethanol and 1 atm Applications of pressure swing distillation first noted by Lewis 35 in a 1928 patent include separations of the minimumboiling azeotrope of tetrahydrofuranwater and maximumboiling azeotropes of hydrochloric acidwater and formic acidwater 10 09 08 07 06 05 04 03 02 01 00 Mole fraction of methanol in vapor 02 04 Mole fraction of methanol in liquid saltfree basis 06 No salt No salt 08 10 10 09 08 07 06 05 04 03 02 01 00 Mole fraction of methanol in vapor 02 04 Mole fraction of methanol in liquid saltfree basis b a 06 08 10 30 wt pTSA 66 wt pTSA mole potassium acetate 59 70 125 saturated curve 2 3 4 5 5 wt solutes wt pTSA 1 0 0 02 04 06 08 02 04 wt 2 6 xylenol in liquid solventfree d Mole fraction of ethanol in liquid saltfree basis c wt of 2 6 xylenol in vapor Mole fraction of ethanol in vapor 10 08 06 04 02 10 09 08 07 06 05 04 03 02 01 06 08 10 10 4 3 2 1 No salt Figure 1121 Effect of dissolved salts on vaporliquid equilibria at 1 atm a Saltingout of methanol by saturated aqueous sodium nitrate b Saltingin of methanol by saturated aqueous mercuric chloride c Effect of salt concentration on ethanolwater equilibria d Effect of ptoluene sulfonic acid pTSA on phase equilibria of 26xylenolpcresol From AI Johnson and WF Furter Can J Chem Eng 43 356358 1965 with permission 114 PressureSwing Distillation 429 C11 10042010 Page 433 and the binary AE azeotrope An example of an indirect sequence is included in Figure 1126b Here the AE azeo trope is recycled to Column 1 from the bottoms of Column 2 Alternatively as in Figure 1126c for Group 3 A and E may be switched to make A the low boiler and E the interme diate boiler which again forms a maximumboiling azeo trope with A All sequences for Group 3 are confined to the same subtriangle as for Group 2 Groups 4 and 5 in Figures 1126d and e are similar to Groups 2 and 3 However A and B now form a maximum boiling azeotrope In Group 4 the entrainer is the intermediate boiler which forms a minimumboiling azeotrope with B The entrainer may also form a maximumboiling azeotrope with A andor a maximumboiling stable node ternary azeotrope A feasible sequence is restricted to the subtriangle formed by vertices A B and the BE azeotrope In the sequence the dis tillate from Column 2 which is the minimumboiling BE azeotrope is mixed with fresh feed to Column 1 which pro duces a distillate of pure A The bottoms from Column 1 has a composition such that when fed to Column 2 a bottoms of L E Residuecurve map arrangement Applicable residuecurve maps Typical sequence Lowest boiler Intermediate boiler Highest boiler Binary feed A Lower boiler B Higher boiler Entrainer E H B I A L H I 410 b L H I 412 m L H I 420 m L H I 421 m L H I 411 L I H F A AE azeotrope B 1 2 L A Residuecurve map arrangement Applicable residuecurve maps Typical sequence Lowest boiler Intermediate boiler Highest boiler Binary feed A Lower boiler B Higher boiler Entrainer E H B I E L H I 401 c L H I 402 m L H I 411 L H I 421m L H I 412m L I H F A AE azeotrope B 1 2 Figure 1126 Continued b Group 2 A and B form a minimumboiling azeotrope L ¼ E E forms a maximumboiling azeotrope with A c Group 3 A and B form a minimumboiling azeotrope I ¼ E E forms a maximumboiling azeotrope with A 115 Homogeneous Azeotropic Distillation 433 C11 10042010 Page 434 pure B can be produced Although a direct sequence is shown the indirect sequence can also be used Alternatively as shown in Figure 1126e for Group 5 B and E may be switched to make E the high boiler In the sequence shown as in that of Figure 1126d the bottoms from Column 1 is such that when fed to Column 2 a bottoms of pure B can be pro duced The other conditions and sequences are the same as for Group 4 The distillation boundaries for the hypothetical ternary systems in Figure 1126 are shown as straight lines When a distillation boundary is curved it may be crossed provided that both the distillate and bottoms products lie on the same side of the boundary It is often difficult to find an entrainer for a sequence involving homogeneous azeotropic distillation and ordinary distillation However azeotropic distillation can also be incor porated into a hybrid sequence involving separation operations other than distillation In that case some of the restrictions for the entrainer and resulting residuecurve map may not apply For example the separation of the close boiling and minimumazeotropeforming system of benzene and cyclohexane using acetone as the entrainer violates the restrictions for a distillationonly sequence because the ternary system involves only two minimumboiling binary azeotropes However the separation can be made by the sequence shown in Figure 1127 which involves 1 homogeneous azeotropic distillation with acetone entrainer to produce a bottoms prod uct of nearly pure benzene and a distillate close in composi tion to the minimumboiling binary azeotrope of acetone and cyclohexane 2 solvent extraction of distillate with water to give a raffinate of cyclohexane and an extract of acetone and water and 3 ordinary distillation of extract to recover ace tone for recycle In Example 116 the azeotropic distillation is subject to productcompositionregion restrictions L A Residuecurve map arrangement Applicable residuecurve maps Sequence Binary feed A Lower boiler B Higher boiler Entrainer E H B I E d L H I 314 L H I 413 L H I 414 m Lowest boiler Intermediate boiler Highest boiler L I H F A BE azeotrope B 1 2 H I 410 L A Residuecurve map arrangement Applicable residuecurve maps Sequence H E I B e L H I 314 L L H I 413 F A BE azeotrope B 1 2 Binary feed A Lower boiler B Higher boiler Entrainer E Figure 1126 Continued d Group 4 A and B form a maximumboiling azeotrope I ¼ E E forms a minimumboiling azeotrope with B e Group 5 A and B form a maximumboiling azeotrope H ¼ E E forms a minimumboiling azeotrope with B 434 Chapter 11 Enhanced Distillation and Supercritical Extraction C11 10042010 Page 437 Figure 1129 clearly shows how a distillation boundary is crossed by the tie line through AZ4 to form two liquid phases in the decanter This phase split is utilized in a typical opera tion where the tower is treated as a column with no con denser a main feed that enters a few trays below the top of the column and the reflux of benzenerich liquid as a second feed The composition of the combined two feeds lies in Re gion 1 Thus from the residuecurve directions products of the tower can be a bottoms of nearly pure ethanol and an overhead vapor approaching the AZ4 composition When that vapor is condensed phase splitting occurs to give a waterrich phase that lies in Region 3 and an entrainerrich phase in Region 2 If the waterrich phase is sent to a reboiled stripper the residue curves indicate that a nearly purewater bottoms can be produced with the overhead vapor rich in ethanol recycled to the decanter When the entrainerrich phase in Region 2 is added to the main feed in Region 1 the overall composition lies in Region 1 To avoid formation of two liquid phases on the top trays of the azeotropic tower the composition of the vapor leaving the top tray must have an equilibrium liquid that lies outside of the twophaseliquid region in Figure 1129 Shown in Fig ure 1130 from Prokopakis and Seider 44 are 18 vapor compositions that form two liquid phases when condensed but are in equilibrium with only one liquid phase on the top tray as restricted to the very small expanded window That window is achieved by adding to the entrainerrich reflux a portion of the waterrich liquid or some condensed vapor prior to separation in the decanter Figure 1131 taken from Ryan and Doherty 45 shows three proposed heterogeneous azeotropic distillation schemes that utilize only distillation for the other columns Most common is the threecolumn sequence in Figure 1131a in which an aqueous feed dilute in ethanol is preconcentrated in Column 1 to obtain a nearly purewater bottoms product and distillate close in composition to the binary azeotrope The latter is fed to the azeotropic tower Column 2 where nearly pure ethanol is recovered as bottoms and the tower is refluxed by most or all of the entrainerrich liquid from the decanter The waterrich phase which contains ethanol and a small amount of entrainer is sent to the entrainerrecovery column which is a distillation column or a stripper Distillate from the recovery column is recycled to the azeotropic col umn Alternatively the distillate from Column 3 could be recycled to the decanter As shown in all three sequences of Figure 1131 portions of either liquid phase from the decanter can be returned to the azeotropic tower or to the next column in the sequence to control phase splitting on the top trays of the azeotropic tower A fourcolumn sequence is shown in Figure 1131b The first column is identical to the first column of the threecolumn sequence of Figure 1131a The second col umn is the azeotropic column which is fed by the near azeotrope distillate of ethanol and water from Column 1 and by a recycle distillate of about the same composition from Column 4 The purpose of Column 3 is to remove as distillate entrainer from the waterrich liquid leaving the decanter and recycle it to the decanter Ideally the composition of this distillate is identical to that of the vapor distillate from Column 2 The bottoms from Column 3 is separated in Column 4 into a bottoms of nearly pure water and a distillate that approaches the ethanolwater aze otrope and is therefore recycled to the feed to Column 2 Pham and Doherty 46 found no advantage of the four column over the threecolumn sequence A novel twocolumn sequence described by Ryan and Doherty 45 is shown in Figure 1131c The feed is sent to Column 2 a combined preconcentrator and entrainer recovery column The distillate from this column is feed for the azeotropic column The bottoms from Column 1 is nearly pure ethanol while Column 2 produces a bottoms of nearly pure water For feeds dilute in ethanol Ryan and Doherty found that the twocolumn sequence has a lower investment cost but a higher operating cost than a threecolumn sequence For ethanol rich feeds the two sequences are eco nomically comparable 01 Water Ethanol Ethanol mole fraction 02 03 09 08 04 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 05 06 07 08 09 Benzene See expanded region Binodal curve Ternary azeotrope Corresponding single liquidphase compositions see inside triangular diagram Vaporphase compositions by number see expanded region 07 06 05 04 03 02 01 01 17 7 031 030 029 028 027 026 025 024 023 054 055 056 057 3 14 12 2 6 5 9 16 18 13 8 4 15 11 1 10 Benzene mole fraction 02 03 04 05 06 07 08 09 Figure 1130 Overhead vapor compositions not in equilibrium with two liquid phases From J Prokopakis and WD Seider AIChE J 29 4960 1983 with permission 116 Heterogeneous Azeotropic Distillation 437 C11 10042010 Page 439 The ethanolbenzenewater residuecurve map of Figure 1129 is one of a number of residuecurve maps that can lead to feasible distillation sequences that include heterogeneous azeotropic distillation Pham and Doherty 46 note that a feasible entrainer is one that causes phase splitting over a portion of the threecomponent region but does not cause the two feed components to be placed in different distillation regions Figure 1132 shows seven such maps where the dashdot lines are liquidliquid solubility binodal curves Convergence of computer simulations for heterogeneous azeotropic distillation columns by the methods described in Chapter 10 is difficult especially when convergence of the entire sequence is attempted It is preferable to uncouple the columns by using a residuecurve map to establish by materialbalance calculations flow rates and compositions of feeds and products for each column This procedure is illus trated for a threecolumn sequence in Figure 1133 where the dashdot lines separate the three distillation regions the shortdash line is the liquidliquid solubility curve and the remaining lines are materialbalance lines Each column in the sequence is computed separately Even then the calcula tions can fail because of nonidealities in the liquid phase and possible phase splitting making it necessary to use more robust methods such as the boundaryvalue traybytray method of Ryan and Doherty 45 the homotopycontinua tion method of Kovach and Seider 47 and the collocation method of Swartz and Stewart 48 1161 Multiplicity of Solutions Solutions to nonlinear mathematical models are not always unique The existence of multiple steadystate solutions for continuous stirredtank reactors has been known since at least 1922 and is described in a number of textbooks on chemical reaction engineering where typically one or more of the multiple solutions are unstable and therefore unoper able The existence of multiplicity in steadystate separation problems is a relatively new discovery Gani and Jørgensen 49 define three types of multiplicity all of which can occur in distillation simulations 1 Output multiplicity where all input variables are spec ified and more than one solution for the output varia bles typically sets of product compositions and temperature profiles are found 2 Input multiplicity where one or more output variables are specified and multiple solutions are found for the unknown input variables 3 Internalstate multiplicity where multiple sets of internal conditions or profiles are found for the same values of the input and output variables Entrainer B B B B A A A A Entrainer Entrainer Entrainer Entrainer B B B A A A Entrainer Entrainer d c b a g f e Figure 1132 Residuecurve maps for heterogeneous azeotropic distillations that lead to feasible distillation sequences HN Pham and MF Doherty Chem Eng Sci 45 18451854 1990 with permission Bottom composition from entrainer recovery column Entrainer recovery column material balance line Binary feed to azeocolumn Ethanol Azeocolumn material balance line Bottom composition from azeocolumn 00 01 02 03 04 05 06 07 08 09 10 Water Benzene Overall vapor composition from azeocolumn Liquid in equillbrium with overhead vapor composition from azeocolumn Distillate composition from entrainer recovery column Overall feed composition to azeocolumn Azeotrope 10 09 08 07 06 05 04 03 02 01 00 Figure 1133 Materialbalance lines for the threecolumn sequence of Figure 1131a From PJ Ryan and MF Doherty AIChE J 35 15921601 1989 with permission 116 Heterogeneous Azeotropic Distillation 439 C11 10042010 Page 440 Output multiplicity for azeotropic distillation was first dis covered by Shewchuk 50 in 1974 With different starting guesses two steadystate solutions for the dehydration of ethanol by heterogeneous azeotropic distillation with benzene were found In a more detailed study Magnussen Michelsen and Fredenslund 51 found with difficulty for a narrow range of ethanol flow rate in the top feed to the column three steadystate solutions one of which was unstable One of the two stable solutions predicts a far purer ethanol bottoms prod uct than the other stable solution Thus from a practical stand point it is important to obtain all stable solutions when more than one exists Subsequent studies some contradictory show that multiple solutions persist only over a narrow range of D or B but may exist over a wide range of R provided there are sufficient stages Composition profiles of five solutions found by Kovach and Seider 47 for a 40tray ethanolwater benzene heterogeneous azeotropic distillation are given in Figure 1134 The variation in the profiles is extremely large showing again that it is important to locate all multiple solu tions when they exist Unfortunately process simulators do not seek multiple solutions and finding these solutions is diffi cult because 1 azeotropic columns are difficult to converge to even one solution 2 multiple solutions may exist only in a restricted range of input variables 3 multiple solutions can be found only by changing initialcomposition guesses and 4 choice of an activitycoefficient correlation and interaction parameters can be crucial The best results are obtained when advanced mathematical techniques such as continuation and bifurcation analysis are employed as described by Kovach and Seider 47 Widagdo and Seider 19 Bekiaris Meski Radu and Morari 52 and Bekiaris Meski and Morari 43 The last two articles provide explanations why multiple solu tions occur in azeotropic distillations EXAMPLE 117 Heterogeneous Azeotropic Distillation Studies by Black and Ditsler 53 and Black Golding and Ditsler 54 show that npentane is a superior entrainer for dehydrating ethanol Like benzene npentane forms a minimumboiling heterogeneous ternary azeotrope with ethanol and water Design a system for dehydrating 1682 kmolh of 8094 mol ethanol and 1906 mol water as a liquid at 3443 K and 333 kPa using npen tane as an entrainer to produce 995 mol ethanol and water with less than 100 ppm by weight of combined ethanol and npentane Solution This ternary system has been studied by Black 55 who proposed the twocolumn flow diagram in Figure 1135 Included are an 18 equilibriumstage heterogeneous azeotropic distillation column C1 equipped with a total condenser and a partial reboiler a decanter D1 a 4equilibriumstage reboiled stripper C2 and a condenser E1 to condense the overhead vapor from C2 Each reboiler adds another equilibrium stage Column C1 operates at a bottoms pressure of 3446 kPa with a column pressure drop of 131 kPa Column C2 operates at a top pressure of 3089 kPa with a col umn pressure drop of 30 kPa These pressures permit the use of cool ing water in the condensers Purity specifications are placed on the bottoms products Feed enters C1 at Stage 3 from the top The etha nol product is withdrawn from the bottom of C1 A small npentane makeup stream not shown in Figure 1135 enters Stage 2 from the top The overhead vapor from C1 is condensed and sent to D1 where a pentanerich liquid phase and a waterrich liquid phase are formed The pentanerich phase is returned to C1 as reflux while the waterrich phase is sent to C2 where the water is stripped of residual pentane and ethanol to produce a bottoms of the specified water purity Twenty of the condensed vapor from C2 is returned to D1 To ensure that two liquid phases form in the decanter but not on the trays of C1 the remaining 80 of the condensed vapor from C2 is combined with the pentanerich phase from D1 for use as additional reflux to C1 The specifications are included on Figure 1135 A very important step in the design of a heterogeneous azeotropic distillation column is the selection of a suitable method for predict ing liquidphase activity coefficients and determination of binary interaction parameters The latter usually involves regression of both vaporliquid VLE and liquidliquid LLE data for all binary pairs If available ternary data can also be included in the regression Unfortunately for most activitycoefficient prediction methods it is difficult to simultaneously fit VLE and LLE data For this reason different binary interaction parameters are often used for the azeo tropic column where VLE is important and for the decanter where LLE is important This has been found especially desirable for the ethanolwaterbenzene system For this example however a single set of binary interaction parameters with a modification by Black 56 of the Van Laar equation 265 was adequate The binary interaction parameters are listed by Black et al 54 The calculations were made with Simulation Sciences Inc soft ware using their rigorous distillation routine to model the columns and a threephaseflash routine 4103 to model the decanter Because the entrainer was internal to the system except for a very small makeup rate it was necessary to provide initial guesses for the component flow rates in the combined decanter feed Guessed values in kmolh were 250 for npentane 30 for ethanol and 75 for water The converged material balance is given in Table 115 Product specifications are met and 226 kmolh of npentane circu lates through the top trays of the azeotropic distillation column The computed condenser and reboiler duties for Column C1 are 11165 and 11350 MJh respectively The reboiler duty for Column C2 is 486 MJh and the duty for Condenser E1 is 438 MJh Because of the large effect of composition on liquidphase activ ity coefficients column profiles for azeotropic columns often show steep fronts In Figure 1136a to c stage temperatures total vapor 1 3 5 7 9 11 13 Ethanol Benzene Water II III III III II IV IV IV V V V I I 15 17 19 Top Bottom Tray number Liquid mole fraction on Tray i 21232527 29313335373941 10 09 08 07 06 05 04 03 02 01 00 Figure 1134 Five multiple solutions for a heterogeneous distillation operation From JW Kovach III and WD Seider Computer Chem Engng 11 593 1987 with permission 440 Chapter 11 Enhanced Distillation and Supercritical Extraction C11 10042010 Page 441 and liquid flow rates and liquidphase compositions for Column C1 vary only slightly from the reboiler Stage 19 up to Stage 13 In this region the liquid is greater than 99 mol ethanol whereas the npen tane concentration slowly builds up from a negligible concentration in the bottoms to just less than 002 mol at Stage 13 From Stage 13 to Stage 8 the npentane mole fraction in the liquid increases rapidly to 538 mol In the same region temperature decreases from 3856 K to 3484 K Continuing up the column from Stage 8 to 3 where feed enters the most significant change is the mole fraction of water in the liquid Rather drastic changes in all variables occur near Stage 3 Effects of nC5 concentration on the a of water to ethanol and of water on nC5 to ethanol are shown in Figure 1136d where the vari ation over the column is 10fold for each pair Table 115 Converged Material Balance for Example 117 Flowrate kmolh Stream nPentane Ethanol Water Total C1 feed 00000 136117 32059 168176 C1 overhead 225565 21298 107269 354132 C1 bottoms 00000 136117 00624 136741 C1 reflux 225565 21298 75834 322697 D1 nC5rich 225500 10637 01129 237266 D1 waterrich 00081 13326 124816 138223 C2 overhead 00081 13326 93381 106788 C2 bottoms 00000 00000 31435 31435 Feed 19 C1 Azeotropic distillation D1 Decanter Bubblepoint liquid E1 Total condenser 3411 K 3089 kPa 3446 K 00624 kmolh water C2 Splitter 3089 kPa 18 3 1 Total condenser Partial reboiler P E W 3443 K 333 kPa kmolh 00000 136117 32059 20 80 3315 kPa Ethanol product 5 4 1 Partial reboiler Water product Figure 1135 Processflow diagram for Example 117 From Perrys Chemical Engineers Handbook 6th ed RH Perry and DW Green Eds McGrawHill New York 1984 with permission 390 380 370 360 350 340 330 Temperature K 0 5 10 Stage number from the top a 15 20 60 50 40 30 20 10 0 Flow rate kmolh 0 5 10 Stage number from the top b 15 20 Liquid Vapor 1 09 08 07 06 05 04 03 02 01 0 Mole fraction in the liquid phase 0 5 10 Stage number from the top c 15 20 nPentane Ethanol Water 13 12 11 10 9 8 7 6 5 4 3 2 1 Relative volatility 0 5 10 Stage number from the top d 15 20 Water to Ethanol Pentane to Ethanol Figure 1136 Results for azeotropic distillation column of Example 117 a Temperature profile b Vapor and liquid traffic profiles c Liquidphase composi tion profiles d Relative volatility profiles 116 Heterogeneous Azeotropic Distillation 441 C11 10042010 Page 446 Flow Rate mols Component Distillate Bottoms MeOH 2832 031 IB 727 131 NB 34492 864 MTBE 012 18674 Total 38063 19700 The combined feeds contained a 103 mole excess of MeOH over IB Therefore IB was the limiting reactant and the preceding product distribution indicates that 956 of the IB or 18686 mols reacted to form MTBE The percent purity of the MTBE in the bot toms is 948 Only 24 of the inert NB and 11 of the unreacted MeOH are in the bottoms The condenser and reboiler duties are 532 and 404 MW Seven iterations gave a converged solution Figure 1138a shows that most of the reaction occurs in a narrow temperature range of 3486 to 353 K Figure 1138b shows that vapor traffic above the two feed entries changes by less than 11 because of small changes in temperature Below the two feed entries temperature increases rap idly from 353 to 420 K causing vapor traffic to decrease by about 20 In Figure 1138c composition profiles show that the liquid is dominated by NB from the top down to Stage 13 thus drastically reducing the reaction driving force Below Stage 11 liquid becomes richer in MTBE as mole fractions of other components decrease because of increasing temperature Above the reaction zone the mole fraction of MTBE quickly decreases as one moves to the top stage These changes are due mainly to the large differences between the K values for MTBE and those for the other three components The a of MTBE with any of the other components ranges from about 024 at the top stage to about 035 at the bottom Nonideality in the liquid influences mainly MeOH whose liquidphase activity coefficient varies from a high of 10 at Stage 5 to a low of 26 at Stage 17 This causes the unreacted MeOH to leave mainly with the NB in the distillate rather than with MTBE in the bottoms The rateofreaction profile in Figure 1138d shows that the forward reaction dominates in the reaction section however 56 of the reaction occurs on Stage 10 the MeOH feed stage The least amount of reaction is on Stage 11 The literature indicates that conversion of IB to MTBE depends on the MeOH feed stage In the range of MeOH feed stages from about 8 to 11 both low and highconversion solutions exists This is shown in Figure 1139 where the highconversion solutions are in the 90þ range while the lowconversion solutions are all less than 10 However if component activities rather than mole fractions are used in the rate expressions the lowconversion solutions are higher because of the large MeOH activity coefficient The results in Figure 1139 were obtained starting with the MeOH feed entering Stage 2 The resulting profiles were used as the initial guesses for the run with MeOH entering Stage 3 Subsequent runs were performed in a similar manner increasing the MeOH feed stage by 1 each time and initializ ing with the results of the previous run 450 400 350 300 250 200 150 100 50 0 Temperature K Condenser Reboiler 2 3 4 5 6 7 8 Stage number from the top a 9 10111213141516 Condenser 2 3 4 5 6 7 8 9 Stage number from the top d 10111213141516 Reboiler 120 100 80 60 40 20 0 Rate of generation of MTBE mols Vapor flow rate leaving stage mols 3500 3000 2500 2000 1500 1000 500 0 Condenser Reboiler 2 3 4 5 6 7 8 Stage number from the top b 9 10 11121314 1516 1 2 3 4 5 6 7 8 9 Stage number from the top c 10 11 12 13 MTBE NB IB MeOH 14 15 16 17 1 09 08 07 06 05 04 03 02 01 0 Liquidphase mole fraction Figure 1138 Profiles for reactive distillation in Example 119 a Temperature profile b Vapor traffic profile c Liquidphase molefraction profile d Reactionrate profile 1 2 3 4 5 6 7 8 9 Methanol feed stage from the top 10 11 12 13 14 15 16 1 09 08 07 06 05 04 03 02 01 0 Fractional conversion of isobutene Figure 1139 Effect of MeOH feedstage location on conversion of IB to MTBE 446 Chapter 11 Enhanced Distillation and Supercritical Extraction C11 10042010 Page 447 Highconversion solutions were obtained for each run until the MeOH feed stage was lowered to Stage 12 at which point conver sion decreased dramatically Further lowering of the MeOH feed stage to Stage 16 also resulted in a lowconversion solution How ever when the direction of change to the MeOH feed stage was reversed starting from Stage 12 a low conversion was obtained until the feed stage was decreased to Stage 9 at which point the conver sion jumped back to the highconversion result Huss et al 101 present a study of reactive distillation for the acidcatalyzed reaction of acetic acid and methanol to produce methyl acetate and water including the side reaction of meth anol dehydration using simulation models and experimental mea surements They consider both finite reaction rates and chemical equilibrium coupled with phase equilibrium The results include re flux limits and multiple solutions 118 SUPERCRITICALFLUID EXTRACTION Solute extraction from a liquid or solid mixture is usually accomplished with a liquid solvent at conditions of temperature and pressure substantially below the solvent critical point as discussed in Chapters 8 and 16 respectively Following extraction solvent and dissolved solute are subjected to subsequent separations to recover solvent for recycle and to purify the solute In 1879 Hannay and Hogarth 78 reported that solid potassium iodide could be dissolved in ethanol as a dense gas at supercritical conditions of T Tc ¼ 516 K and P Pc ¼ 65 atm The iodide could then be precipitated from the ethanol by reducing the pressure This process was later called supercriticalfluid extraction SFE supercriticalgas extrac tion and most commonly supercritical extraction By the 1940s as chronicled by Williams 79 proposed applications of SFE began to appear in the patent and technical literature Figure 1140 shows the supercriticalfluid region for CO2 which has a critical point of 3042 K and 7383 bar The solvent power of a compressed gas can undergo an enormous increase in the vicinity of its critical point Consider the solubility of piodochlorobenzene pICB in ethylene as shown in Figure 1141 at 298 K for pressures from 2 to 8 MPa This temperature is 105 times the critical temperature of ethylene 283 K and the pressure range straddles the criti cal pressure of ethylene 51 MPa At 298 K pICB is a solid melting point ¼ 330 K with a vapor pressure of the order of 01 torr At 2 MPa if pICB formed an idealgas solution with ethylene the concentration of pICB in the gas in equilibrium with pure solid pICB would be 000146 gL But the concen tration from Figure 1141 is 0015 gL an order of magnitude higher If the pressure is increased from 2 MPa to almost the critical pressure at 5 MPa an increase by a factor of 25 the equilibrium concentration of pICB is increased about 10fold to 015 gL At 8 MPa the concentration is 40 gL 2700 times higher than predicted for an idealgas solution It is this dra matic increase in solubility of a solute at nearcritical solvent conditions that makes SFE of interest Why such a dramatic increase in solvent power The explanation lies in the change of solvent density while the solute solubility increases A pressureenthalpy diagram for ethylene is shown in Figure 1142 which includes the 200 0 50 100 150 200 250 300 350 400 220 240 260 280 300 320 340 Temperature K Solid Liquid Triple point Pressure bar Gas Critical point Supercritical fluid region Figure 1140 Supercriticalfluid region for CO2 0 5 10 Pressure MPa Concentration of solute in gas phase gL 100 50 298 K 10 5 1 05 01 005 001 Figure 1141 Effect of pressure on solubility of pICB in supercritical ethylene 118 SupercriticalFluid Extraction 447 C11 10042010 Page 448 Figure 1142 Pressureenthalpy diagram for ethylene From KE Starling Fluid Thermodynamic Properties for Light Petroleum Systems Gulf Publishing Houston 1973 reprinted with permission 448 C11 10042010 Page 449 specific volume reciprocal of the density as a parameter The range of variables and parameters straddles the critical point of ethylene The density of ethylene compared to the solubility of pICB is as follows at 298 K Pressure MPa Ethylene Density gL Solubility of pICB gL 2 258 0015 5 95 015 8 267 40 Although far from a 11 correspondence for the increase of pICB solubility with ethylene density over this range of pres sure there is a meaningful correlation As the pressure increases closer packing of the solvent molecules allows them to surround and trap solute molecules This phenomenon is most useful at reduced temperatures from about 101 to 112 Two other effects in the supercritical region are favorable for SFE Molecular diffusivity of a solute in an ambient pressure gas is about four orders of magnitude higher than for a liquid For a nearcritical fluid the diffusivity of solute molecules is usually one to two orders of magnitude higher than in a liquid solvent thus resulting in a lower masstrans fer resistance in the solvent phase In addition the viscosity of the supercritical fluid is about an order of magnitude lower than that of a liquid solvent Industrial applications for SFE have been the subject of many studies patents and venture capital proposals How ever when other techniques are feasible SFE usually cannot compete because of high solventcompression costs SFE is most favorable for extraction of small amounts of large rela tively nonvolatile and expensive solutes as discussed in 863 on bioextraction Applications are also cited by Wil liams 79 and McHugh and Krukonis 80 Solvent selection depends on the feed mixture If only the chemicals to be extracted is are soluble in a potential sol vent then high solubility is a key factor If a chemical besides the desired solute is soluble in the potential solvent then sol vent selectivity becomes as important as solubility A number of gases and lowMW chemicals including the following have received attention as solvents Critical Temperature Critical Pressure Critical Density Solvent K MPa kgm3 Methane 192 460 162 Ethylene 283 503 218 Carbon dioxide 304 738 468 Ethane 305 488 203 Propylene 365 462 233 Propane 370 424 217 Ammonia 406 113 235 Water 647 220 322 Solvents with Tc 373 K have been well studied Most promising particularly for extraction of undesirable valu able or heatsensitive chemicals from natural products is CO2 with its moderate Pc high critical density low super critical viscosity high supercritical molecular diffusivity and Tc close to ambient Also it is nonflammable noncorrosive inexpensive nontoxic in low concentrations readily availa ble and safe Separation of CO2 from the solute is often pos sible by simply reducing the extract pressure According to Williams 79 supercritical CO2 has been used to extract caf feine from coffee hops oil from beer piperine from pepper capsaicin from chilis oil from nutmeg and nicotine from tobacco However the use of CO2 for such applications in the US may be curtailed in the future because of an April 2009 endangerment finding by the Environmental Protection Agency EPA that CO2 is a pollutant that threatens public health and welfare and must be regulated CO2 is not always a suitable solvent however McHugh and Krukonis 81 cite the energy crisis of the 1970s that led to substantial research on an energyefficient separation of ethanol and water The goal which was to break the ethanol water azeotrope was not achieved by SFE with CO2 because although supercritical CO2 has unlimited capacity to dissolve pure ethanol water is also dissolved in significant amounts A supercriticalfluid phase diagram for the ethanolwater CO2 ternary system at 3082 K and 1008 MPa based on the data of Takishima et al 82 is given in Figure 1143 These conditions correspond to Tr ¼ 1014 and Pr ¼ 1366 for CO2 For the mixture of water and CO2 two phases exist a water rich phase with about 2 mol CO2 and a CO2rich phase with about 1 mol water Ethanol and CO2 are mutually sol uble Ternary mixtures containing more than 40 mol etha nol are completely miscible If a nearazeotropic mixture of ethanol and water say 85 mol ethanol and 15 mol water is extracted by CO2 at the conditions of Figure 1143 a mixing line drawn between this composition and a point for pure CO2 does not cross into the twophase region so no separation is possible at these condi tions Alternatively consider an ethanolwater broth from a fermentation reactor with 10 wt 417 mol ethanol If this H2O CO2 C2H5OH Figure 1143 Liquidfluid equilibria for CO2C2H5OHH2O at 3083132 K and 1011034 MPa 118 SupercriticalFluid Extraction 449 C11 10042010 Page 450 mixture is extracted with supercritical CO2 complete dissolu tion will not occur and a modest degree of separation of etha nol from water can be achieved as shown in the next example The separation can be enhanced by a cosolvent eg glycerol to improve selectivity as shown by Inomata et al 83 When CO2 is used as a solvent it must be recovered and recycled Three schemes discussed by McHugh and Krukonis 81 are shown in Figure 1144 In the first scheme for separation of ethanol and water the ethanolwater feed is pumped to the pressure of the extraction column where it is contacted with supercritical CO2 The raffinate leaving the extractor bottom is enriched with respect to water and is sent to another location for further processing The top extract stream containing most of the CO2 some ethanol and a smaller amount of water is expanded across a valve to a lower pressure In a flash drum downstream of the valve Raffinate a Compressor Ethanol Ethanolwater feed Separator Extraction column Pressure reduction valve CO2 recycle b c CO2 to recovery CO2 to recovery CO2 extractant Ethanol water feed Ethanol separator CO2 vapor compressor Caffeine lean CO2 Concentrated caffeine and water Fresh water Raffinate Ethanol Stripper Distillation column Reboiler Water separator Extract phase Extractor Coffee extractor Water column Caffeine rich CO2 Caffeine rich water Decaffeinated green coffee Green moist coffee Reverse osmosis Figure 1144 Recovery of CO2 in supercritical extraction processes a Pressure reduction b Highpressure dis tillation c Highpressure absorption with water 450 Chapter 11 Enhanced Distillation and Supercritical Extraction C11 10042010 Page 453 3 Extractive distillation using a lowvolatility solvent that enters near the top of the column is widely used to sepa rate azeotropes and very closeboiling mixtures Prefera bly the solvent should not form an azeotrope with any feed component 4 Certain salts when added to a solvent reduce the solvent volatility and increase the relative volatility between the two feed components In this process called salt distilla tion the salt is dissolved in the solvent or added as a solid or melt to the reflux 5 Pressureswing distillation utilizing two columns operat ing at different pressures can be used to separate an azeo tropic mixture when the azeotrope can be made to disappear at some pressure If not it may still be practical if the azeotropic composition changes by 5 mol or more over a moderate range of pressure 6 In homogeneous azeotropic distillation an entrainer is added to a stage usually above the feed stage A mini mum or maximumboiling azeotrope formed by the entrainer with one or more feed components is removed from the top or bottom of the column Applications of this technique for difficulttoseparate mixtures are not com mon because of limitations due to distillation boundaries 7 A more common and useful technique is heterogeneous azeotropic distillation in which the entrainer forms with one or more components of the feed a minimumboiling heterogeneous azeotrope When condensed the overhead vapor splits into organicrich and waterrich phases The azeotrope is broken by returning one liquid phase as re flux with the other sent on as distillate for further processing 8 A growing application of reactive distillation is to com bine chemical reaction and distillation in one column To be effective the reaction and distillation must be feasible at the same pressure and range of temperature with reac tants and products favoring different phases so that an equilibriumlimited reaction can go to completion 9 Liquidliquid or solidliquid extraction can be carried out with a 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and SI Sandler AIChE J 38 671680 1992 87 Sandler SI H Orbey and BI Lee in SI Sandler Ed Models for Thermodynamic and Phase Equilibria Calculations Marcel Dekker New York pp 87186 1994 88 Knapp H R Doring L Oellrich U Plocker and JM Prausnitz VaporLiquid Equilibria for Mixtures of Low Boiling Substances Chem Data Ser Vol VI DECHEMA pp 771793 1982 89 Shibata SK and SI Sandler Ind Eng Chem Res 28 18931898 1989 90 Wong DSH H Orbey and SI Sandler Ind Eng Chem Res 31 20332039 1992 91 Gmehling J and U Onken VaporLiquid Equilibrium Data Compi lation DECHEMA Data Series DECHEMA Frankfurt 1977 92 SkjoldJørgensen S Ind Eng Chem Res 27 110118 1988 93 Colussi IE M Fermeglia V Galloand I Kikic Computers Chem Engng 16 211224 1992 94 Doherty MF and MF Malone Conceptual Design of Distillation Systems McGrawHill New York 2001 95 Stichlmair JG and JR Fair Distillation Principles and Practices WileyVCH New York 1998 96 Siirola JJ and SD Barnickiin RH Perry and DW Green Eds Perrys Chemical Engineers Handbook 7th ed McGrawHill New York pp 1354 to 1385 1997 97 Eckert E and M Kubicek Computers Chem Eng 21 347350 1997 98 Hoffmaster WR and S Hauan AIChE J 48 25452556 2002 99 LlanoRestrepo M and J AguilarArias Computers Chem Engng 27 527549 2003 100 Fu J AIChE J 42 33643372 1996 101 Huss RS F Chen MF Malone and MF Doherty Computers Chem Engng 27 18551866 2003 454 Chapter 11 Enhanced Distillation and Supercritical Extraction C11 10042010 Page 456 azeotropic distillation using acetone as the entrainer Can the same separation be achieved using methanol as the entrainer If not why not Ref Ratliff RA and WB Strobel Petro Refiner 335 151 1954 1117 Homogeneous azeotropic distillation Devise a separation sequence to separate 100 mols of an equi molar mixture of toluene and 25dimethylhexane into nearly pure products Include in the sequence a homogeneous azeotropic distil lation column using methanol as the entrainer and determine a feasi ble design for that column Ref Benedict M and LC Rubin Trans AIChE 41 353392 1945 1118 Homogeneous azeotropic distillation A mixture of 16500 kgh of 55 wt methyl acetate and 45 wt methanol is to be separated into 995 wt methyl acetate and 99 wt methanol Use of one homogeneous azeotropic distillation column and one ordinary distillation column has been suggested Possible entrainers are nhexane cyclohexane and toluene Deter mine feasibility of the sequence If feasible prepare a design If not suggest an alternative and prove its feasibility Section 116 1119 Heterogeneous azeotropic distillation Design a threecolumn distillation sequence to separate 150 mols of an azeotropic mixture of ethanol and water at 1 atm into nearly pure ethanol and nearly pure water using heterogeneous azeotropic distillation with benzene as the entrainer 1120 Heterogeneous azeotropic distillation Design a threecolumn distillation sequence to separate 120 mols of an azeotropic mixture of isopropanol and water at 1 atm into nearly pure isopropanol and nearly pure water using heterogeneous azeo tropic distillation with benzene entrainer Ref Pham HN PJ Ryan and MF Doherty AIChE J 35 15851591 1989 1121 Heterogeneous azeotropic distillation Design a twocolumn distillation sequence to separate 1000 kmolh of 20 mol aqueous acetic acid into nearly pure acetic acid and water Use heterogeneous azeotropic distillation with npropyl acetate as the entrainer in Column 1 Section 117 1122 Reactive distillation Repeat Example 119 with the entire range of methanol feed stage locations Compare your results for isobutene conversion with the values shown in Figure 1139 1123 Reactive distillation Repeat Exercise 1122 but with activities instead of mole frac tions in the reactionrate expressions How do the results differ Explain 1124 Reactive distillation Repeat Exercise 1122 but with the assumption of chemical equilibrium on stages where catalyst is employed How do the re sults differ from Figure 1139 Explain Section 118 1125 Supercriticalfluid extraction with CO2 Repeat Example 1110 but with 10 equilibrium stages instead of 5 What is the effect of this change 1126 Model for SFE of a solute from particles An application of supercritical extraction is the removal of sol utes from particles of porous natural materials Such applications include extraction of caffeine from coffee beans and extraction of ginger oil from ginger root When CO2 is used as the solvent the rate of extraction is found to be independent of flow rate of CO2 past the particles but dependent upon the particle size Develop a mathematical model for the rate of extraction consistent with these observations What model parameter would have to be determined by experiment 1127 SFE of bcarotene with CO2 Cygnarowicz and Seider Biotechnol Prog 6 8291 1990 present a process for supercritical extraction of bcarotene from water with CO2 using the GCEOS method of SkjoldJørgensen to estimate phase equilibria Repeat the calculations for their design using the PengRobinson EOS with the WongSandler mixing rules How do the designs compare 1128 SFE of acetone from water with CO2 Cygnarowicz and Seider Ind Eng Chem Res 28 14971503 1989 present a design for the supercritical extraction of acetone from water with CO2 using the GCEOS method of Skjold Jørgensen to estimate phase equilibria Repeat their design using the PengRobinson EOS with the WongSandler mixing rules How do the designs compare 456 Chapter 11 Enhanced Distillation and Supercritical Extraction C12 10042010 Page 467 5 10 Stage number 15 20 145 150 155 Pressure psia a 160 5 10 Stage number 15 20 160 180 200 Liquid temperature F b 220 240 5 Liquid Vapor 10 Stage number 15 20 200 0 400 600 Flows lbmolh c 800 5 10 Stage number 15 MEK Tol nC7 20 00 02 04 Vapor mole fraction d 06 08 10 00 02 04 06 08 10 5 10 Stage number 15 20 Liquid mole fraction e 5 10 Stage number 15 20 100 50 0 Mass transfer rate lbmolh f 50 100 00 02 04 06 08 10 nC7 nC7 MEK MEK Tol Tol Figure 122 Column profiles for Example 122 a pressure profile b liquidphase temperature profile c vapor and liquid flow rate profiles d vapor molefraction profiles e liquid molefraction profiles f masstransfer rate profiles continued 125 Method of Calculation 467 C12 10042010 Page 468 EXAMPLE 123 Packed Column Design Repeat Example 122 for a tower packed with FLEXIPAC1 2 struc tured packing at 75 of flooding The packing heights are as follows Section Packing Height ft Above top feed 13 Between top and bottom feeds 65 Below bottom feed 65 Solution Each 65 feet of packing was simulated by 50 segments Because of the large number of segments mixed flow is assumed for both vapor and liquid Newtons method could not converge the calculations Therefore the homotopycontinuation option was selected Then convergence was achieved in 73 s after a total of 26 iterations The predicted separation which is just slightly better than that in Exam ple 122 is as follows Component Distillate lbmolh Bottoms lbmolh nHeptane 5488 012 Toluene 040 4460 Methylethyl ketone 19972 028 The HETP profile is plotted in Figure 123 Median values for nheptane toluene and methylethyl ketone respectively are approximately 055 m 217 inches 045 m 177 inches and 05 m 197 inches The HETP values for the ketone vary widely Predicted column diameters for the three sections starting from the top are 165 175 and 185 m which are very close to the pre dicted sievetray diameters 1252 RATEFRAC Program The RATEFRAC program of Aspen Technology is designed to model absorbers distillation and reactive distillation The latest version of ChemSep can also model reactive distillation For RATEFRAC the reactions can be equili briumbased or kineticsbased including reactions among electrolytes For kinetically controlled reactions builtin powerlaw expressions are selected or the user supplies FORTRAN subroutines for the rate laws For equili briumbased reactions the user supplies a temperature dependent equilibrium constant or RATEFRAC computes reactionequilibrium constants from freeenergy values stored in its data bank The user specifies the phase in which the reaction takes place Flow rates of sidestreams and the columnpressure profile must be provided The heat duty must be specified for each intercooler or inter heater The standard specifications for the rating mode are the reflux ratio and the bottoms flow rate However these specifications can be manipulated in the design mode to achieve any of the following substitute specifications a Purity of a product or internal stream with respect to one component or a group of components b Recovery of a component or group of components in a product stream c Flow rate of a component or group of components in a product or internal stream d Temperature of a product or internal vapor or liquid stream e Heat duty of condenser or reboiler f Value of a product or internal stream physical property g Ratio or difference of any pair of product or internal stream physical properties where the two streams can be the same or different Masstransfer correlations are built into RATEFRAC for bubblecap trays valve trays sieve trays and packings Users may provide their own FORTRAN subroutines for transport 5 10 Stage number 15 20 Fractional murphee efficiency g 00 02 04 06 08 10 nC7 MEK Tol Figure 122 Continued g Murphree vaportray efficiencies 50 100 150 Stage number 00 02 Tol MEK nC7 04 06 HETP m 08 100 Figure 123 Column HETP profiles for Example 123 468 Chapter 12 RateBased Models for VaporLiquid Separation Operations C12 10042010 Page 470 2 Ratebased models incorporate rigorous procedures for componentcoupling effects in multicomponent mass transfer 3 The number of equations for a ratebased model is greater than that for an equilibriumbased model because separate balances are needed for each of the two phases In addition ratebased models are influ enced by the geometry of the column internals Corre lations are used to predict masstransfer and heat transfer rates Tray or packing hydraulics are also incorporated into the ratebased model to enable prediction of columnpressure profile Phase equili brium is assumed only at the phase interface 4 Computing time for a ratebased model is not generally more than an order of magnitude greater than that for an equilibriumbased model 5 Both the ChemSep and RATEFRAC ratebased com puter programs offer considerable flexibility in user specifications so much so that inexperienced users can easily specify impossible conditions Therefore it is best to begin simulation studies with standard specifications REFERENCES 1 Sorel E La rectification de lalcool Paris 1893 2 Smoker EH Trans AIChE 34 165 1938 3 Thiele EW and RL Geddes Ind Eng Chem 25 290 1933 4 Lewis WK and GL Matheson Ind Eng Chem 24 496498 1932 5 Lewis WK Ind Eng Chem 14 492 1922 6 Murphree EV Ind Eng Chem 17 747750 960964 1925 7 Lewis WK Ind Eng Chem 28 399 1936 8 Seader JD Chem Eng Prog 8510 4149 1989 9 Walter JF and TK Sherwood Ind Eng Chem 33 493501 1941 10 Toor HL AIChE J 3 198 1957 11 Toor HL and JK Burchard AIChE J 6 202 1960 12 Krishna R HF Martinez R Sreedhar and GL Standart Trans I Chem E 55 178 1977 13 Waggoner RC and GD Loud Comput Chem Engng 1 49 1977 14 Krishna R and GL Standart Chem Eng Comm 3 201 1979 15 Taylor R and R Krishna Multicomponent Mass Transfer John Wiley Sons New York 1993 16 Krishnamurthy R and R Taylor AIChE J 31 449 456 1985 17 Taylor R HA Kooijman and JS Hung Comput Chem Engng 18 205217 1994 18 ASPEN PLUS Reference ManualVolume 1 Aspen Technology Cam bridge MA 1994 19 Taylor R and HA Kooijman CACHE News No 41 1319 1995 20 AIChE BubbleTray Design Manual New York 1958 21 Harris IJ British Chem Engng 106 377 1965 22 Hughmark GA Chem Eng Progress 617 97100 1965 23 Zuiderweg FJ Chem Eng Sci 37 1441 1982 24 Chan H and JR Fair Ind Eng Chem Process Des Dev 23 814 827 1984 25 Chen GX and KT Chuang Ind Eng Chem Res 32 701708 1993 26 Onda K H Takeuchi and YJ Okumoto J Chem Eng Japan 1 56 62 1968 27 Bravo JL and JR Fair Ind Eng Chem Process Des Devel 21 162170 1982 28 Bravo JL JA Rocha and JR Fair Hydrocarbon Processing 641 5660 1985 29 Bravo JL JA Rocha and JR Fair I Chem E Symp Ser No 128 A489A507 1992 30 Billet R and M Schultes I Chem E Symp Ser No 128 B129 1992 31 Kooijman HA and R Taylor Chem Eng J 572 177188 1995 32 Fair JR HR Null and WL Bolles Ind Eng Chem Process Des Dev 22 5358 1983 33 Powers MF DJ Vickery A Arehole and R Taylor Comput Chem Engng 12 12291241 1988 34 Taylor R HA Kooijman and MR Woodman I Chem E Symp Ser No 128 A415A427 1992 35 Ovejero G R Van Grieken L Rodriguez and JL Valverde Sep Sci Tech 29 18051821 1994 36 Scheffe RD and RH Weiland Ind Eng Chem Res 26 228236 1987 37 Young TC and WE Stewart AIChE J 38 592602 with errata on p 1302 1993 38 Young TC and WE Stewart AIChE J 41 13191320 1995 39 Spagnolo DA EL Plaice HJ Neuburg and KT Chuang Can J Chem Eng 66 367376 1988 40 Higler A R Krishna and R Taylor AIChE J 45 23572370 1999 41 Pyhalahti A and K Jakobsson Ind Eng Chem Res 42 61886195 2003 STUDY QUESTIONS 121 For binary distillation what assumption did Smoker add to the McCabeThiele assumptions to obtain an algebraic solution 122 What assumptions did Murphree make in the development of his tray efficiency equations 123 For which situations does the Murphree efficiency appear to be adequate What are its deficiencies 124 What unusual phenomena did Toor find for diffusion in a ternary mixture Is a theory available to predict these phenomena 125 In the ratebased model is the assumption of phase equili brium used anywhere If so where Is it justified 126 The ratebased model requires component masstransfer coefficients interfacial areas and heattransfer coefficients How are the latter obtained 470 Chapter 12 RateBased Models for VaporLiquid Separation Operations C13 09292010 Page 488 Step 2 is 95 mol pure MCB The residual left in the reboiler after Step 3 is quite pure in DCB A plot of the instantaneousdistillate composition as a function of totaldistillate accumulation for all steps is shown in Figure 1312 Changes in mole fractions occur rapidly at certain times during the batch rectification indicating that relatively pure cuts may be possible This plot is useful in developing alternative schedules to obtain almost pure cuts Using Figure 1312 if relatively rich dis tillate cuts of B MCB and DCB are desired an initial benzenerich cut of say 18 lbmol might be taken followed by an intermediate cut for recycle of say 18 lbmol Then an MCBrich cut of 34 lbmol followed by another intermediate cut of 8 lbmol might be taken leaving a DCBrich residual of 22 lbmol For this series of operation steps with the same vapor boilup rate of 200 lbmolh and reflux ratio of 3 the computed results for each distillate accumula tion cut using a time step of 0005 h are given in Table 134 As seen all three product cuts are better than 98 mol pure However ð18 þ 8Þ ¼ 26 lbmol of intermediate cuts or about 14 of the origi nal charge would have to be recycled Further improvements in purities of the cuts or reduction in the amounts of intermediate cuts for recycle can be made by increasing the reflux ratio andor the number of stages 137 INTERMEDIATECUT STRATEGY Luyben 19 points out that design of a batchdistillation process is complex because two aspects must be considered 1 the products to be obtained and 2 the control method to be employed Basic design parameters are the number of trays the size of the charge to the still pot the boilup ratio and the reflux ratio as a function of time Even for a binary feed it may be necessary to take three products a distillate rich in the mostvolatile component a residue rich in the leastvolatile component and an intermediate cut contain ing both components If the feed is a ternary system more intermediate cuts may be necessary The next two examples demonstrate intermediatecut strategies for binary and ter nary feeds EXAMPLE 1310 Intermediate Cuts One hundred kmol of an equimolar mixture of nhexane C6 and nheptane C7 at 1 atm is batchrectified in a column with a total condenser It is desired to produce two products one Table 133 Results at the End of Each Operation Step for Example 139 Operation Step 1 2 3 Operation time h 0605 0805 0055 No of time increments 121 161 11 Accumulated distillate Total lbmol 3365 4196 273 Mole fractions B 0731 0009 0000 MCB 0269 0950 0257 DCB 0000 0041 0743 Reboiler holdup Total lbmol 6613 2419 2146 Mole fractions B 0006 0000 0000 MCB 0616 0044 0018 DCB 0378 0956 0982 Total heat duties 106 Btu Condenser 195 265 019 Reboiler 208 263 018 10 01 001 0001 Instantaneous mole fractions in distillate 0 20 MCB DCB B 40 Total accumulation of distillate lbmol 60 80 Figure 1312 Instantaneousdistillate composition profile for Example 139 Perrys Chemical Engineers Handbook 6th ed RH Perry and DW Green Eds McGrawHill New York 1984 with permission Table 134 Results of Alternative Operating Schedule for Example 139 Distillate Amount Composition Mole Fractions Cut lbmol B MCB DCB Benzenerich 18 0993 0007 0000 Intermediate 1 18 0374 0626 0000 MCBrich 34 0006 0994 0000 Intermediate 2 8 0000 0536 0464 DCBrich residual 22 0000 0018 0982 Total 100 488 Chapter 13 Batch Distillation C13 09292010 Page 490 Intermediate cuts and their recycle have been studied by a number of investigators including Mayur May and Jackson 20 Luyben 19 QuinteroMarmol and Luyben 21 Farhat et al 22 Mujtaba and Macchietto 23 Diehl et al 24 and Robinson 25 138 OPTIMAL CONTROL BY VARIATION OF REFLUX RATIO An operation policy in which the composition of the instanta neous distillate and therefore the accumulated distillate is maintained constant is discussed in 1322 This policy requires a variable reflux ratio and accompanying distillate rate Although not as simple as the constantrefluxratio method of 1321 it can be implemented with a rapidly responding composition or surrogate sensor and an associated reflux control system Which is the optimal way to control a batch distillation by 1 constant reflux ratio 2 constant distillate composition or 3 some other means With a process simulator it is fairly straightforward to compare the first two methods However the results depend on the objective for the optimi zation Diwekar 26 studied the following three objectives when the accumulateddistillate composition andor the residual composition is specified 1 Maximize the amount of accumulated distillate in a given time 2 Minimize the time to obtain a given amount of accu mulated distillate 3 Maximize the profit The next example compares the first two control policies with respect to their ability to meet the first two objectives EXAMPLE 1312 Two Control Policies Repeat Example 1310 under conditions of constant distillate com position and compare the results to those of that example for a con stant reflux ratio of 4 with respect to both the amount of distillate and time of operation Solution For Example 1310 from Table 135 for a reflux ratio of 4 the amount of accumulated distillate during the first operation step is 424 kmol of 95 mol C6 The time required for this cut which is not listed in Table 135 is 198 hours Using a process simulator the operation specifications for a constant composition operation are a boilup rate of 100 kmolh as in Example 1310 with a constant instantaneousdistillate composition of 95 mol C6 For the maxi mum distillate objective the stop time for the first cut is 198 hours as in Example 1310 The amount of distillate obtained is 435 kmol which is 26 higher than for operation at constant reflux ratio The variation of reflux ratio with time for constantcomposition control is shown in Figure 1314 where the constant reflux ratio of 4 is also shown The initial reflux ratio 17 rises gradually at first and rap idly at the end At 1 hour the reflux ratio is 4 while at 198 hours it is 154 For constant composition control 424 kmol of accumulated distillate are obtained in 1835 hours compared to 198 hours for refluxratio control Constant composition control is more optimal this time by almost 8 0 0 08 16 24 32 4 48 56 64 72 8 88 04 12 2 28 36 44 Time hours 52 6 68 76 84 01 02 03 04 05 06 07 08 09 1 Accumulator mole fraction First slop cut C6 cut C7 cut C7 C7 C7 C7 C6 C7 C8 C8 C8 C6 C6 C6 Second slop cut Figure 1313 Ternary batch distillation with two intermediate slop cuts in Example 1311 490 Chapter 13 Batch Distillation C13 09292010 Page 491 Studies by Converse and Gross 27 Coward 28 29 and Robinson 25 for binary systems by Robinson and Coward 30 and Mayur and Jackson 31 for ternary sys tems and Diwekar et al 32 for higher multicomponent systems show that maximization of distillate or minimiza tion of operation time as well as maximization of profit can be achieved by using an optimalrefluxratio policy Often this policy is intermediate between the constant refluxratio and constantcomposition controls in Fig ure 1314 for Example 1312 Generally the optimalreflux curve rises less sharply than that for the constantdistillate composition control with the result that savings in distil late time or money are highest for the more difficult separations For relatively easy separations savings for constantdistillatecomposition control or optimalreflux ratio control may not be justified over the use of the sim pler constantrefluxratio control Determination of optimalrefluxratio policy for complex operations requires a much different approach than that used for simpler optimization problems which involve finding the optimal discrete values that minimize or maximize some objective with respect to an algebraic function For example in 737 a single value of the optimal reflux ratio for a con tinuousdistillation operation is found by plotting as in Fig ure 722 the total annualized cost versus R and locating the minimum in the curve Establishing the optimal reflux ratio as a function of time R t f g for a batch distillation which is modeled with differential or integral equations rather than algebraic equations requires optimalcontrol methods that include the calculus of variations the maximum principle of Pontryagin dynamic programming of Bellman and non linear programming Diwekar 33 describes these methods in detail Their development by mathematicians in Russia and the United States were essential for the success of their respective space programs To illustrate one of the approaches to optimal control con sider the classic Brachistochrone Greek for shortest time problem of Johann Bernoulli one of the earliest variational problems whose investigation by famous mathematicians including Johann and Jakob Bernoulli Gottfried Leibnitz Guillaume de LHopital and Isaac Newtonwas the starting point for development of the calculus of variations a subject considered in detail by Weinstock 34 A particle eg a bead is located in the xy plane at ðx1 y1Þ where the xaxis is horizontal to the right while the yaxis is vertically down ward The problem is to find the frictionless path y ¼ ffxg ending at the point ðx2 y2Þ down which the particle will move subject only to gravity in the least time Some possi ble paths from point 1 to point 2 shown in Figure 1315 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 Reflux ratio 0 02 04 06 08 1 Time hours 12 14 16 18 2 Constant reflux ratio control Constant distillate composition control Figure 1314 Binary batch distillation under distillatecomposition control in Example 1312 02 0 2 18 16 14 12 1 08 06 04 02 0 04 06 08 1 x y 12 14 16 18 2 Point 1 Point 2 Straight line Broken line Circular arc Brachistochrone arc Figure 1315 Frictionless paths between two points 138 Optimal Control by Variation of Reflux Ratio 491 C13 09292010 Page 494 17 Carnahan B and JO Wilkes Numerical Solution of Differential EquationsAn Overview in RSH Mah and WD Seider Eds Founda tions of ComputerAided Chemical Process Design Engineering Founda tion New York Vol I pp 225340 1981 18 Varga RS Matrix Iterative Analysis PrenticeHall Englewood Cliffs NJ 1962 19 Luyben WL Ind Eng Chem Res 27 642647 1988 20 Mayur DN RA May and R Jackson Chem Eng Journal 1 1521 1970 21 QuinteroMarmol E and WL Luyben Ind Eng Chem Res 29 19151921 1990 22 Farhat S M Czernicki L Pibouleau and S Domenech AIChE J 36 13491360 1990 23 Mujtaba IM and S Macchietto Comput Chem Eng 16 S273 S280 1992 24 Diehl M A Schafer HG Bock JP Schloder and DB Leineweber AIChE J 48 28692874 2002 25 Robinson ER Chem Eng Journal 2 135136 1971 26 Diwekar UM Batch DistillationSimulation Optimal Design and Control Taylor Francis Washington DC 1995 27 Converse AO and GD Gross Ind Eng Chem Fundamentals 2 217221 1963 28 Coward I Chem Eng Science 22 503516 1967 29 Coward I Chem Eng Science 22 18811884 1967 30 Robinson ER and I Coward Chem Eng Science 24 16611668 1969 31 Mayur DN and R Jackson Chem Eng Journal 2 150163 1971 32 Diwekar UM RK Malik and KP Madhavan Comput Chem Eng 11 629637 1987 33 Diwekar UM Introduction to Applied Optimization Kluwer Aca demic Publishers 2003 34 Weinstock R Calculus of Variations McGrawHill Book Co Inc New York 1952 35 Barolo M G Guarise S Rienzi and A Macchietto Ind Eng Chem Res 35 46124618 1996 36 Phimister JR and WD Seider Ind Eng Chem Res 39 18401849 2000 STUDY QUESTIONS 131 How does batch distillation differ from continuous distillation 132 When should batch distillation be considered 133 What is differential Rayleigh distillation How does it differ from batch rectification 134 For what kinds of mixtures is differential distillation adequate 135 What is the easiest way to determine the average composi tion of the distillate from a batch rectifier 136 Which is easiest to implement 1 the constantreflux pol icy 2 the constantdistillatecomposition policy or 3 the opti malcontrol policy Why 137 What is a batch stripper 138 Can a batch rectifier and a batch stripper be combined If so what advantage is gained 139 What effects does liquid holdup have on batch rectification 1310 What are the assumptions of the rigorousbatch distillation model of Distefano 1311 Why is the Distefano model referred to as a differential algebraic equation DAE system 1312 What is the difference between truncation error and stability 1313 How does the explicitEuler method differ from the implicit method 1314 What is stiffness and how does it arise What criterion can be used to determine the degree of stiffness if any 1315 In the development of an operating policy campaign for batch distillation what is done with intermediate slop cuts 1316 What are the common objectives of optimal control of a batch distillation as cited by Diwekar 1317 What is varied to achieve optimal control EXERCISES Section 131 131 Evaporation from a drum A bottle of pure nheptane is accidentally poured into a drum of pure toluene in a laboratory One of the laboratory assistants sug gests that since heptane boils at a lower temperature than toluene the following purification procedure can be used Pour the mixture 2 mol nheptane into a simple still pot Boil the mixture at 1 atm and condense the vapors until all heptane is boiled away Obtain the pure toluene from the residue You a chemical engineer with knowledge of vaporliquid equili brium immediately realize that such a purification method will not work a Indicate this by a curve showing the composition of the material remaining in the stillpot after various quantities of the liq uid have been distilled What is the composition of the residue after 50 wt of the original material has been distilled What is the com position of the cumulative distillate b When onehalf of the hep tane has been distilled what is the composition of the cumulative distillate and the residue What weight t of the original material has been distilled Equilibrium data at 1 atm Ind Eng Chem 42 2912 1949 are Mole Fraction nHeptane Liquid Vapor Liquid Vapor 0025 0048 0448 0541 0062 0107 0455 0540 0129 0205 0497 0577 0185 0275 0568 0637 0235 0333 0580 0647 0250 0349 0692 0742 0286 0396 0843 0864 0354 0454 0950 0948 0412 0504 0975 0976 494 Chapter 13 Batch Distillation C13 09292010 Page 495 132 Differential distillation A mixture of 40 mol isopropanol in water is distilled at 1 atm by differential distillation until 70 mol of the charge has been vaporized equilibrium data are given in Exercise 733 What is the composition of the liquid residue in the stillpot and of the collected distillate 133 Differential distillation A 30 mol feed of benzene in toluene is to be distilled in a batch differentialdistillation operation A product having an average com position of 45 mol benzene is to be produced Calculate the amount of residue assuming a ¼ 25 and W0 ¼ 100 134 Differential distillation A charge of 250 lb of 70 mol benzene and 30 mol toluene is subjected to differential distillation at 1 atm Determine the compo sitions of the distillate and residue after 13 of the feed has been distilled Assume Raoults and Daltons laws 135 Differential distillation A mixture containing 60 mol benzene and 40 mol toluene is subjected to differential distillation at 1 atm under three different conditions 1 Until the distillate contains 70 mol benzene 2 Until 40 mol of the feed is evaporated 3 Until 60 mol of the original benzene leaves in the vapor Using a ¼ 243 determine for each of the three cases a number of moles in the distillate for 100 mol of feed b compositions of distil late and residue 136 Differential distillation Fifteen mol phenol in water is to be differentialbatchdistilled at 260 torr What fraction of the batch is in the stillpot when the total distillate contains 98 mol water What is the residue concentration Vaporliquid data at 260 torr Ind Eng Chem 17 199 1925 x wt H2O 154 495 687 773 1963 2844 3973 8299 8995 9338 9574 y wt H2O 4110 7972 8279 8445 8991 9105 9115 9186 9277 9419 9564 137 Differential distillation with added feed A stillpot is charged with 25 mol of benzene and toluene con taining 35 mol benzene Feed of the same composition is supplied at a rate of 7 molh and the heating rate is adjusted so that the liquid level in the stillpot remains constant If a ¼ 25 how long will it be before the distillate composition falls to 045 mol benzene 138 Differential distillation with continuous feed A system consisting of a stillpot and a total condenser is used to separate A and B from a trace of nonvolatile material The stillpot initially contains 20 lbmol of feed of 30 mol A Feed of the same composition is supplied to the stillpot at the rate of 10 lbmolh and the heat input is adjusted so that the total moles of liquid in the reboiler remain constant at 20 No residue is withdrawn from the stillpot Calculate the time required for the composition of the over head product to fall to 40 mol A Assume a ¼ 250 Section 132 139 Batch rectification at constant reflux ratio Repeat Exercise 132 for the case of batch distillation carried out in a twostage column with LV ¼ 09 1310 Batch rectification at constant reflux ratio Repeat Exercise 133 assuming the operation is carried out in a threestage column with LV ¼ 06 1311 Batch rectification at constant reflux ratio One kmol of an equimolar mixture of benzene and toluene is fed to a batch still containing three equivalent stages including the boiler The liquid reflux is at its bubble point and LD ¼ 4 What is the average composition and amount of product when the instan taneous product composition is 55 mol benzene Neglect holdup and assume a ¼ 25 1312 Differential distillation and batch rectification The fermentation of corn produces a mixture of 33 mol ethyl alcohol in water If this mixture is distilled at 1 atm by a differen tial distillation calculate and plot the instantaneousvapor compo sition as a function of mol of batch distilled If reflux with three theoretical stages including the boiler is used what is the maxi mum purity of ethyl alcohol that can be produced by batch rectification Equilibrium data are given in Exercise 729 1313 Batch rectification at constant composition An acetoneethanol mixture of 05 mole fraction acetone is to be separated by batch distillation at 101 kPa Vaporliquid equilibrium data at 101 kPa are as follows Mole Fraction Acetone y 016 025 042 051 060 067 072 079 087 093 x 005 010 020 030 040 050 060 070 080 090 a Assuming an LD of 15 times the minimum how many stages should this column have if the desired composition of the distillate is 090 mole fraction acetone when the residue contains 01 mole fraction acetone b Assume the column has eight stages and the reflux rate is varied continuously so that the top product is maintained constant at 09 mole fraction acetone Make a plot of the reflux ratio versus the stillpot composition and the amount of liquid left in the stillpot c Assume the same distillation is carried out at constant reflux ratio and varying product composition It is desired to have a resi due containing 01 and an average product containing 09 mole fraction acetone Calculate the total vapor generated Which method of operation is more energyintensive Suggest operating policies other than constant reflux ratio and constant distillate compositions that lead to equipment or operating cost savings 1314 Batch rectification at constant composition Two thousand gallons of 70 wt ethanol in water having a spe cific gravity of 0871 is to be separated at 1 atm in a batch rectifier operating at a constant distillate composition of 85 mol ethanol with a constant molar vapor boilup rate to obtain a residual waste water containing 3 wt ethanol If the task is to be completed in 24 h allowing 4 h for charging startup shutdown and cleaning determine a the number of theoretical stages b the reflux ratio when the ethanol in the stillpot is 25 mol c the instantaneous distillate rate in lbmolh when the concentration of ethanol in the stillpot is 15 mol d the lbmol of distillate product and e the lbmol of residual wastewater Vaporliquid equilibrium data are given in Exercise 729 Exercises 495 C13 09292010 Page 496 1315 Batch rectification at constant composition One thousand kmol of 20 mol ethanol in water is to undergo batch rectification at 1013 kPa at a vapor boilup rate of 100 kmolh If the column has six theoretical stages and the distillate composi tion is to be maintained at 80 mol ethanol by varying the reflux ratio determine the a time in hours for the residue to reach an ethanol mole fraction of 005 b kmol of distillate obtained when the condition of part a is achieved c minimum and maximum reflux ratios during the rectification period and d variation of the distillate rate in kmolh during the rectification period Assume con stant molar overflow neglect liquid holdup and obtain equilibrium data from Exercise 729 1316 Batch rectification for constant composition Five hundred lbmol of 488 mol A and 512 mol B with a relative volatility aAB of 20 is separated in a batch rectifier consist ing of a total condenser a column with seven theoretical stages and a stillpot The reflux ratio is varied to maintain the distillate at 95 mol A The column operates with a vapor boilup rate of 2135 lbmolh The rectification is stopped when the mole fraction of A in the still is 0192 Determine the a rectification time and b total amount of distillate produced Section 133 1317 Batch stripping at constant boilup ratio Develop a procedure similar to that of 133 to calculate a binary batch stripping operation using the equipment arrangement of Fig ure 138 1318 Batch stripping at constant boilup ratio A threetheoreticalstage batch stripper one stage is the boiler is charged to the feed tank see Figure 138 with 100 kmol of 10 mol nhexane in noctane mix The boilup rate is 30 kmolh If a constant boilup ratio VL of 05 is used determine the instan taneous bottoms composition and the composition of the accumu lated bottoms product at the end of 2 h of operation 1319 Batch distillation with a middle feed vessel Develop a procedure similar to that of 133 to calculate a com plex binary batchdistillation operation using the equipment arrangement of Figure 139 Section 135 1320 Effect of holdup on batch rectification For a batch rectifier with appreciable column holdup a Why is the charge to the stillpot higher in the light component than at the start of rectification assuming that totalreflux conditions are estab lished before rectification b Why will separation be more difficult than with zero holdup 1321 Effect of holdup on batch rectification For a batch rectifier with appreciable column holdup why do tray compositions change less rapidly than they do for a rectifier with negligible column holdup and why is the separation improved 1322 Effect of holdup on batch rectification Based on the statements in Exercises 1320 and 1321 why is it difficult to predict the effect of holdup Section 136 1323 Batch rectification by shortcut method Use the shortcut method of Sundaram and Evans to solve Exam ple 137 but with zero condenser and stage holdups 1324 Batch rectification by shortcut method A charge of 100 kmol of an equimolar mixture of A B and C with aAB ¼ 2 and aAC ¼ 4 is distilled in a batch rectifier contain ing four theoretical stages including the stillpot If holdup can be neglected use the shortcut method with R ¼ 5 and V ¼ 100 kmolh to estimate the variation of the stillpot and instantaneousdistillate compositions as a function of time after total reflux conditions are established 1325 Batch rectification by the shortcut method A charge of 200 kmol of a mixture of 40 mol A 50 mol B and 10 mol C with aAC ¼ 20 and aBC ¼ 15 is to be separated in a batch rectifier with three theoretical stages including the stillpot and operating at a reflux ratio of 10 with a molar vapor boilup rate of 100 kmolh Holdup is negligible Use the shortcut method to estimate instantaneousdistillate and bottoms compositions as a function of time for the first hour of operation after total reflux conditions are established Section 137 1326 Batch rectification by rigorous method A charge of 100 lbmol of 35 mol nhexane 35 mol n heptane and 30 mol noctane is to be distilled at 1 atm in a batch rectifier consisting of a stillpot a column and a total condenser at a constant boilup rate of 50 lbmolh and a constant reflux ratio of 5 Before rectification begins totalreflux conditions are established Then the following three operation steps are carried out to obtain an nhexanerich cut an intermediate cut for recycle an nheptane rich cut and an noctanerich residue Step 1 Stop when the accumulateddistillate purity drops below 95 mol nhexane Step 2 Empty the nhexanerich cut produced in Step 1 into a receiver and resume rectification until the instantaneousdistil late composition reaches 80 mol nheptane Step 3 Empty the intermediate cut produced in Step 2 into a receiver and resume rectification until the accumulateddistillate composition reaches 4 mol noctane For properties assume ideal solutions and the idealgas law Consider conducting the rectification in two different columns each with the equivalent of 10 theoretical stages a stillpot and a total condenser refluxdrum liquid holdup of 10 lbmol For each column determine with a suitable batchdistillation computer pro gram the compositions and amounts in lbmol of each of the four products Column 1 A plate column with a total liquid holdup of 8 lbmol Column 2 A packed column with a total liquid holdup of 2 lbmol Discuss the effect of liquid holdup for the two columns Are the results what you expected 1327 Rigorous batch rectification with holdup One hundred lbmol of 10 mol propane 30 mol nbutane 10 mol npentane and the balance nhexane is to be separated in a batch rectifier equipped with a stillpot a total condenser with a liq uid holdup of 10 ft3 and a column with the equivalent of eight theo retical stages and a total holdup of 080 ft3 The pressure in the condenser is 500 psia and the column pressure drop is 20 psi The rectification campaign given as follows is designed to produce cuts of 98 mol propane and 998 mol nbutane a residual cut of 99 mol nhexane and two intermediate cuts one of which may be a relatively rich cut of npentane All five operating steps are con ducted at a molar vapor boilup rate of 40 lbmolh Use a suitable batchdistillation computer program to determine the amounts and compositions of all cuts 496 Chapter 13 Batch Distillation PART03 07282010 2249 Page 499 Part Three Separations by Barriers and Solid Agents In recent years industrial applications of separations using barriers and solid agents have increased because of progress in producing selective membranes and adsorbents Chapter 14 presents a discussion of mass transfer rates through membranes and calculation methods for the more widely used batch and continuous membrane separations for gas and liquid feeds includ ing bioprocess streams These include gas permeation reverse osmosis dialysis electrodialysis pervapora tion ultrafiltration and microfiltration Chapter 15 covers separations by adsorption ion exchange and chromatography which use solid sepa ration agents Discussions of equilibrium and mass transfer rates in porous adsorbents are followed by design methods for batch and continuous equipment for liquid and gaseous feeds including bioprocess streams These include fixedbed pressureswing and simulatedmovingbed adsorption Electrophoresis is also included in Chapter 15 499 C14 10042010 Page 537 membrane is used for the dehydration of ethanol with water being the main permeating species The support layer is porous polyester which is cast on a microporous poly acrylonitrile or polysulfone membrane The final layer which provides the separation is dense PVA of 01 mm in thickness This composite combines chemical and thermal stability with adequate permeability Hydrophobic mem branes such as silicone rubber and Teflon are preferred when organics are the permeating species Commercial membrane modules for PV are almost exclu sively of the plateandframe type because of the ease of using gasketing materials that are resistant to organic sol vents and the ease of providing heat exchange for vaporiza tion and hightemperature operation Hollowfiber modules are used for removal of VOCs from wastewater Because feeds are generally clean and operation is at low pressure membrane fouling and damage is minimal resulting in a use ful membrane life of 24 years Models for transport of permeant through a membrane by pervaporation have been proposed based on solution diffusion 1434 They assume equilibrium between the upstream liquid and the upstream membrane surface and Pervaporation Condenser Phase separator Permeate recycle Ethanolwater feed Pump a b Water Recycle DCErich permeate Condenser Condenser Vacuum pump Ethanol product Pervaporation Preheater Watersaturated dichloroethylene feed Purified DCE Pervaporation Nearly pure water c Wastewater to treatment Vacuum pump Threephase separator Threephase separator Waterrich liquid Wastewater feed VOCrich liquid Vacuum pump Figure 1426 Pervaporation processes a Hybrid process for removal of water from ethanol b Dehydration of dichloroethylene c Removal of volatile organic compounds VOCs from wastewater 10 08 06 04 02 0 Weight fraction alcohol in vapor 0 02 04 06 Weight fraction alcohol in liquid Pervaporation Vapor composition for permeate pressure 15 mm Hg 45 line Distillation Vaporliquid equilibrium 1 atm 08 10 Figure 1427 Comparison of ethanolwater separabilities From M Wesslein et al J Membrane Sci 51 169 1990 148 Pervaporation 537 C14 10042010 Page 541 proteins Polishing with directflow deadend MF described in 1493 may be used in lieu of ultra centrifugation to remove residual insoluble particulate and precipitated impurities Sterile filtration in pharmaceutical operations uses a validatable sterilizinggrade 022 mm MF to reduce bioburden in preparation for subsequent formula tion One or more sterile buffer exchanges often follow ster ile filtration to incorporate excipients or adjuvants into the final bulk product prior to filling vials Compared to centrifu gation membrane filtration of biological products is energy efficient and less capital intensive with less product shear and less severe operating conditions 1492 Biofiltration Operating Modes MF NF UF and VF of bioproducts may be conducted by flowing feed normal to a deadend membrane surface referred to as direct flow normal flow inline or deadend filtration DEF or tangentially across the surface called crossflow or tangentialflow filtration TFF Figure 1428 compares normal and tangentialflow modes In DEF a batch of feed solution is forced under pressure through the membrane causing retained material to accumulate on and within the membrane The pressure required to maintain a desired flow rate must increase or permeate flux will decrease A combined operation as described in 1431 and illustrated in Example 143 in which constantflux operation is employed up to a limiting pressure followed by constant pressure operation until a minimum flux is reached is supe rior to either constantpressure or constantflux operation DEF has lower capital cost lower complexity and higher operating cost relative to TFF DEF is better suited for dilute solutions while TFF can be employed for concentrated solutions In TFF which is more suitable for largescale continuous filtration feed flows along the surface with only a fraction of the solvent passing through the membrane while retained matter is carried out with the retentate fluid Retentate is usu ally recycled through the filter at tangentialflow velocities parallel to the membrane surface in the 325fts range TFF gives up to 10foldhigher flux values than DEF 57 The tangentialflow mode is also used almost exclusively for RO as discussed in 146 and for UF Improvements in product yield and throughput in TFF have been demonstrated by operating to maintain flux rather than transmembrane pressure drop TMP Concentration factors up to 100fold in singlestage UF systems have been demonstrated using high membranepacking density and reduced holdup vol umes Maintaining constant retained protein concentration at the membrane surface cwall has been shown to enhance product yield and minimize membrane area for large varia tions in feed quality and membrane properties 58 Flux data at successively higher TMP values taken at multiple concen trations is fit to stagnant film and osmotic pressure models to estimate values of masstransfer coefficients osmotic virial coefficients and fouled membrane resistance to guide opera tion to maintain constant cwall a variable that is not known a priori Highperformance TFF HPTFF uses optimal values of buffer pH ionic strength and membrane charge to maximize differences in hydrodynamic volume between product and impurity to enhance mass throughput and selectivity as a function of local pressuredependent flux 59 60 Cocurrent flow on the membrane filtrate side maintains uniform TMP at or below the point at which filtrate flux becomes pressure independent HPTFF can separate equally sized proteins based on charge differences monomers from dimers and sin gleaminoacid variants in real dilute feeds significantly improving yield and purification factors Scalable UF devices are available that permit 1000fold volumetric increases with consistent protein yield and permeate flux by increasing chan nel number in hollowfiber cassettes or by decreasing channel width in flatsheet cassettes while maintaining pressure fluid flow concentration profile and channel length 61 Membrane Geometries for Bioseparations The most common membrane geometries used in bioprocess ing are flat plate spiral wound tubular internal diameter id 0635 cm capillary 01 id 0635 cm and hollow fibers 0025 id 01 cm which need clarified feed to avoid clogging Flatplate membranes are commonly used in plateandframe filterleaf Nutsch and rotating filter configurations Plateandframe and filterleaf pleated car tridges are typically used for MF In the latter the membrane is pleated and then folded around a permeate core Many module types are inexpensive and disposable A typical dis posable cartridge is 25 inches in diameter by 10 inches long with 3 ft2 of membrane area The cartridge may include a prefilter to extend filter life by removing large particles leav ing the microporous membrane to make the required separa tion For UF newer compositeregenerated cellulose membranes that are mechanically strong easily cleaned and foul less than synthetic polymers provide better permeability and retention 62 63 Covalent surface modification with quaternary amine or sulfonicacid groups improves mem brane selectivity particularly for HPTFF applications a Deadend microfiltration Membrane Particlefree permeate b Tangentialflow microfiltration Particlefree permeate Feed Particle buildup on membrane surface Membrane Retentate Feed Figure 1428 Common modes of microfiltration 149 Membranes in Bioprocessing 541 C14 10042010 Page 542 Membrane Casting Polymer membranes used widely in MF UF and RO of bio products are typically prepared by casting a polymer that has been dissolved in a mixture of solvent and highboiling non solvent as a film of precise thickness on a conveyer in an environmentally controlled chamber 64 The casting pro cess produces membranes in which pores result from inter connected openings between polyhedral cells formed by progressive evaporation of solvent that causes phase separa tion The nonsolvent coalesces into droplets surrounded by a shell of polymer which gels out of solution and concentrates at phase interfaces Further solvent evaporation deposits additional polymer that thickens swelling polymer shells which come into mutual contact as solvent disappears Area minimizing forces consolidate the shells into clusters that are distorted into polyhedral cells filled with nonsolvent Cell edges accumulate polymer thinning the walls which rupture and create interconnections between adjacent cells Metering pores of the membrane consist of the interconnected open ings between the polyhedral cells The concentration of poly mer in solution determines intersegmental separation of flexible chain segments that coil and overlap as opposing electrical attractive and repulsive forces maintain separation of long polymer molecules increasing pore size at greater dilution Membrane Requirements for Biotechnology Process filters to prepare biopharmaceutical agents described in 19like recombinant proteins or DNA vaccine anti gens or viral vectors for gene therapyhave the following unique requirements when compared with bioprocess filters used to prepare food and beverages or to purify other non pharmacological bioproducts 1 Preserve biological activity Denaturation proteolytic cleavage or misforming of protein projects must be avoided Immunogenicity of a targeted vaccine anti gen for example must be maintained 2 Satisfy cGMP requirements Depending on the appli cation these may include biocompatibility sterilizabil ity and flushout of extractables 3 Accommodate modest scales of operation Dose sizes of mg or less may be required for vaccine antigens or recombinant proteins Milligrams to grams of active agents may be recovered from just 10 to 1000 liters of broth so process scales are relatively small particularly for orphan drugs that treat rare diseases 4 Include batch operation A defined volume of phar maceutical product undergoes a battery of assays to verify activity purity sterility and other mandates in the Code of Federal Regulations CFR to be approve able by the Food and Drug Administration FDA Batch bioprocess volumes are a consequence of the volume of fermentation or cell culture required to pro duce sufficient active bioproduct to economically satisfy market demands This batch volume is processed dis cretely from inception to final release to eliminate car ryover contamination that may compromise multiple batches The batch nature and release criteria of bio pharmaceutical operations distinguish them from large scale continuous bioprocesses Challenges Unique to Filtration in Biotechnology There are also the following unique challenges to implement ing filtration in vaccine bioprocesses in the pharmaceutical industry 1 Integrated process The process may define the product particularly when complete physicochemical characterization of a biological antigen to satisfy FDA regulatory requirements is not possible Therefore fil tration cannot be implemented or optimized in isola tion but must be approached as an integral part of the entire series of fermentation purification and formula tion steps 2 Compressed development Pressing market need for biotechnology products to prevent or treat public health problems drives accelerated timelines for devel opment Consequently as little as weeks to months may be available to select and optimize filters in the lab 3 Limited raw materials Only mL to L of fermentation or cell culture broth may be initially available for filter selection characterization and optimization 4 Variable fermentation or cell culture Membrane fil ter operations must accommodate wide variations in cell culture and fermentation composition and produc tivity while providing consistent yield and purity Such variability often occurs during scaleup and in cam paigns to produce actives for clinical trials 5 Operability Filter operations that maximize the robustness of process operations must be selected to provide consistent purity and yield resulting in an eco nomical validatable process 6 Virus removal Endogenous viruslike particles in mammalian cells used to manufacture rDNA products and adventitious viruses that contaminate cell cultures eg 20nm parvovirus must be reduced to a level of less than one virus particle per 106 doses Membrane filters provide sizebased virus removal in which maximum virus resolution is obtained by optimizing pH ionic strength and membrane charge to distinguish pro teins 412 nm from virus 12300 nm by exploiting charge repulsion This complements chemical inactivation chaotropes low pH solvents or detergents physical inactivation heat or UV adsorption ionexchange chroma tography or other sizebased separations sizeexclusion chromatography Membrane bioprocessing can contribute unique bene fits to society as illustrated by membrane filtration of vaccine antigens 65 Vaccines have virtually eliminated 542 Chapter 14 Membrane Separations C14 10042010 Page 562 18 Beck RE and JS Schultz Biochim Biophys Acta 255 273 1972 19 Brandrup J and EH Immergut Eds Polymer Handbook 3rd ed John Wiley Sons New York 1989 20 Lonsdale HK U Merten and RL Riley J Applied Polym Sci 9 13411362 1965 21 Motamedian S W Pusch G Sendelbach TM Tak and T Tanioka Proceedings of the 1990 International Congress on Membranes and Membrane Processes Chicago Vol II pp 841843 22 Barrer RM JA Barrie and J Slater J Polym Sci 23 315329 1957 23 Barrer RM and JA Barrie J Polym Sci 23 331344 1957 24 Barrer RM JA Barrie and J Slater J Polym Sci 27 177197 1958 25 Koros WJ and DR Paul J Polym Sci Polym Physics Edition 16 19471963 1978 26 Barrer RM J Membrane Sci 18 2535 1984 27 Walawender WP and SA Stern Separation Sci 7 553584 1972 28 Naylor RW and PO Backer AIChE J 1 9599 1955 29 Stern SA TF Sinclair PJ Gareis NP Vahldieck and PH Mohr Ind Eng Chem 572 4960 1965 30 Hwang ST and KL Kammermeyer Membranes in Separations WileyInterscience New York pp 324338 1975 31 Spillman RW Chem Eng Progress 851 4162 1989 32 Strathmann H Membrane and Membrane Separation Processes in Ullmanns Encyclopedia of Industrial Chemistry VCH FRG Vol A16 p 237 1990 33 Chamberlin NS and BH Vromen Chem Engr 669 117122 1959 34 Graham T Phil Trans Roy Soc London 151 183224 1861 35 Juda W and WA McRae J Amer Chem Soc 72 1044 1950 36 Strathmann H Sep and Purif Methods 141 4166 1985 37 Merten U Ind Eng Chem Fundamentals 2 229232 1963 38 Stoughton RW and MH Lietzke J Chem Eng Data 10 254 260 1965 39 Spillman RW and MB Sherwin Chemtech 378384 June 1990 40 Schell WJ and CD Houston Chem Eng Progress 7810 3337 1982 41 Teplyakov V and P Meares Gas Sep and Purif 4 6674 1990 42 Rosenzweig MD Chem Eng 8824 6266 1981 43 Kober PA J Am Chem Soc 39 944948 1917 44 Binning RC RJ Lee JF Jennings and EC Martin Ind Eng Chem 53 4550 1961 45 Wesslein M A Heintz and RN Lichtenthaler J Membrane Sci 51 169 1990 46 Wijmans JG and RW Baker J Membrane Sci 79 101113 1993 47 Rautenbach R and R Albrecht Membrane Processes John Wiley Sons New York 1989 48 Rao MB and S Sircar J Membrane Sci 85 253264 1993 49 Baker R Membrane Technology and Applications 2nd ed John Wiley Sons New York 2004 50 Chisti Y Principles of Membrane Separation Processes in G Subramanian Ed Bioseparation and Bioprocessing WileyVCH Verlag GmbH Co KGaA Weinheim 2007 51 Belfort G RH Davis and AJ Zydney J Membrane Science 96 158 1994 52 Van Reis R and AL Zydney Curr Opinion Biotechnol 12 208211 2001 53 Van Reis R and AL Zydney J Membr Sci 2971 1650 2007 54 Aimar P Membranes in Bioprocessing 113139 1993 55 McGregor WC Ed Membrane Separations in Biotechnology Mar cel Dekker Inc New York 1986 56 Zeman LJ and AL Zydney Microfiltration and Ultrafiltration Principles and Applications Marcel Dekker New York 1996 57 Porter MC Ind Eng Chem Prod Res Dev 11 234 1972 58 Van Reis R EM Goodrich CL Yson LN Frautschy R Whitely and AL Zydney J Membr Sci 130 123140 1997 59 Van Reis R JM Brake J Charkoudian DB Burns and AL Zyd ney J Membr Sci 159 133143 1999 60 Zeman LJ and AL Zydney Microfiltration and Ultrafiltration Principles and Applications Marcel Dekker Inc New York 1996 61 Van Reis R EM Goodrich CL Yson LM Frautschy S Dzenge leski and H Lutz Biotechnol Bioeng 55 737746 1997 62 Tucceli R and PV McGrath Cellulosic ultrafiltration membrane US Patent 5736051 1996 63 Van Reis R and AL Zydney Protein Ultrafiltration in MC Flickinger and SW Drew Eds Encyclopedia of Bioprocess Technology Fermentation Biocatalysis and Bioseparation John Wiley Sons New York pp 21972214 1999 64 Meltzer TH Modus of Filtration in Adv Biochem EnginBio technol SpringerVerlag Heidelberg Vol 9 pp 2771 2006 65 Roper DK A Johnson A Lee J Taylor C Trimor and E Wen First International Conference on Membrane and Filtration Technology in Biopurification Cambridge UK April 79 1999 66 Harrison RG P Todd SR Rudge and DP Petrides Biosepara tions Science and Engineering Oxford University Press New York 2003 67 Grace HP Chem Eng Progr 49 303 1953 68 Ruth BF GH Montillon and RE Montanna Ind Eng Chem 25 7682 1933 69 Hermia J Trans Inst Chem Eng Lond 60 183 1982 70 Ho CC and AL Zydney J Colloid Interface Sci 232 389 2000 71 Ho CC and AL Zydney Ind Eng Chem Res 40 1412 2001 72 Zydney ALand CC Ho Biotech Bioeng 83 537 2001 73 Schweitzer P A Handbook of Separation Techniques for Chemical Engineers 2nd ed Section 21 by MC Porter McGrawHill Book Co New York 1988 74 Badmington G M Payne R Wilkins and E Honig Pharmaceut Tech 19 64 1995 75 Meltzer TH and MW Jornitz Filtration in the Biopharmaceutical Industry Marcel Dekker Inc New York 1998 76 Shuler ML and F Kargi Bioprocess Engineering 2nd ed Prentice Hall PTR Upper Saddle River NJ 2002 77 Bailey JE and DF Ollis Biochemical Engineering Fundamentals 2nd ed McGrawHill New York 1986 78 Emory S Pharm Technol 13 68 1980 79 Baker LA and CR Martin Nanotechnology in Biology and Medi cine Methods Devices and Applications Vol 9 pp 124 2007 80 Baker LA T Choi and CR Martin Current Nanoscience 23 243255 2006 81 Belfort G Membrane Separation Technology An Overview in HR Bungay and G Belfort Eds Advanced Biochemical Engineering John Wiley Sons New York p 253 1987 82 Kahn DW MD Butler GM Cohen JW Kahn and ME Winkler Biotechnol Bioeng 69 101106 2000 562 Chapter 14 Membrane Separations C14 10042010 Page 563 83 Cruz PE CC Peixoto K Devos JL Moreira E Saman and MJ T Carrondo Enzyme Microb Technol 26 6170 2000 84 Ladisch MR Biseparations Engineering WileyInterscience New York 2001 85 Scopes RK Protein Purification 2nd ed SpringerVerlag New York 1987 86 Pujar NS and AL Zydney Ind Eng Chem Res 22 2473 1994 87 Blatt WF A Dravid AS Michaels and L Nelson Solute Polar ization and Cake Formation in Membrane Ultrafiltration Causes Conse quences and Control Techniques in JE Flinn Ed Membrane Science and Technology Plenum Press New York pp 4797 1970 88 Belfort G RH Davis and AJ Zydney J Membrane Sci 96 158 1994 89 Leighton DT and A Acrivos J Fluid Mech 181 415439 1987 90 Robertson BC and AL Zydney J Colloid Interface Sci 134 563 1990 91 Winzeler HB and G Belfort J Membrane Sci 80 157185 1993 92 Sandler SI Chemical Biochemical and Engineering Thermo dynamics 4th ed John Wiley Sons New York 2006 93 Porter MC Ind Eng Chem Prod Res Dev 11 234 1972 94 Eckstein EC PG Bailey and AH Shapiro J Fluid Mech 7 191 1977 95 Zydney AL and CK Colton Chem Eng Commun 47 1 1986 96 Davis RH and JD Sherwood Chem Eng Sci 45 32043209 1990 97 Drew DA JA Schonber and G Belfort Chem Eng Sci 46 32193224 1991 98 Henry JD Cross Flow Filtration in NN Li Ed Recent Devel opments in Separation Science CRC Press Cleveland OH Vol 2 pp 205 225 1972 99 Belfort G P Chin and DM Dziewulski A New GelPolarization Model Incorporating Lateral Migration for Membrane Fouling Proc World Filtration Congress III Philadelphia PA p 91 1982 100 Taddei C P Aimar JA Howell and JA Scott J Chem Technol Biotechnol 47 365376 1990 101 Le MS J Chem Technol Biotechnol 37 5966 1987 102 Sakai K K Ozawa K Ohashi R Yoshida and H Sakarai Ind Eng Chem Res 28 5764 1989 103 Geankoplis CJ Transport Processes and Separation Process Prin ciples 4th ed Prentice Hall PTR New Jersey 2003 104 Nielsen WK Ed Membrane Filtration and Related Molecular Separation Technologies International Dairy Books Aarhus Denmark 2000 105 Cheryan M Ultrafiltration Handbook Technomic Publishing Co Lancaster PA 1986 STUDY QUESTIONS 141 What are the two products from a membrane separation called What is a sweep 142 What kinds of materials are membranes made from Can a membrane be porous or nonporous What forms pores in polymer membranes 143 What is the basic equation for computing the rate of mass transfer through a membrane Explain each of the four factors in the equation and how they can be exploited to obtain high rates of mass transfer 144 What is the difference between permeability and perme ance How are they analogous to diffusivity and the masstransfer coefficient 145 For a membrane separation is it usually possible to achieve both a high permeability and a large separation factor 146 What are the three mechanisms for mass transfer through a porous membrane Which are the best mechanisms for making a separation Why 147 What is the mechanism for mass transfer through a dense nonporous membrane Why is it called solutiondiffusion Does this mechanism work if the polymer is completely crystalline Explain 148 How do the solutiondiffusion equations differ for liquid transport and gas transport How is Henrys law used for solutiondif fusion for gas transport Why are the film resistances to mass transfer on either side of the membrane for gas permeation often negligible 149 What are the four idealized flow patterns in membrane modules Which is the most effective Which is the most difficult to calculate 1410 What is osmosis Can it be used to separate a liquid mix ture How does it differ from reverse osmosis For what type of mixtures is it well suited 1411 Can a nearperfect separation be made with gas perme ation If not why not 1412 What is pervaporation 1413 How do microfiltration and ultrafiltration differ from reverse osmosis with respect to pore size pressure drop and the nature of the permeate 1414 What is the evidence that concentration polarization and fouling are occurring during biofiltrations and what steps are taken to minimize these effects 1415 What are the four common configurations for ultrafiltration 1416 What is continuous feedandbleed ultrafiltration What are its limitations 1417 What is diafiltration How does it differ from continu ous feedandbleed ultrafiltration Under what conditions is dia filtration used in conjunction with continuous feedandbleed ultrafiltration 1418 In microfiltration why is an operation that combines con stantflux and constantpressure operations used EXERCISES Section 141 141 Differences between membrane separations and other separations Explain as completely as you can how membrane separations differ from a absorption and stripping b distillation c liquid liquid extraction d extractive distillation 142 Barrer units for permeabilities For the commercial application of membrane separators dis cussed at the beginning of this chapter calculate the permeabilities of hydrogen and methane in barrer units Exercises 563 C14 10042010 Page 567 1427 Constantpressure cake filtration Beginning with the Ruth equation 1424 obtain general expressions for timedependent permeate volume Vt and time dependent flux Jt in terms of operating parameters and charac teristics of the cake for constantpressure cake filtration 1428 Poreconstriction model Derive a general expression for the total filtration time necessary to filter a given feed volume V using the poreconstriction model From this expression predict the average volumetric flux during a filtration and the volumetric capacity necessary to achieve a given filtration time based on laboratoryscale results 1429 Minimum filter area for sterile filtration Derive a general expression for the minimum filter area re quirement per a sterility assurance limit SAL in terms of a concentration of microorganisms in the feed b volume per unit parenteral dose c sterility assurance limit and d filter capacity 1430 Cheese whey ultrafiltration process Based on the problem statement of Example 1420 calculate for just Section 1 the component material balance in pounds per day of operation the percent recovery yield from the whey of the TP and NPN in the final concentrate and the number of cartridges required if two stages are used instead of four 1431 Fourstage diafiltration section Based on the problem statement of Example 1420 design a fourstage diafiltration section to take the 55 wt concentrate from Section 1 and achieve the desired 85 wt concentrate thus elimi nating Section 3 Exercises 567 C15 09222010 Page 569 The ionexchange concept can be extended to the removal of essentially all inorganic salts from water by a twostep demineralization process or deionization In step 1 a cation resin exchanges hydrogen ions for cations such as calcium magnesium and sodium In step 2 an anion resin exchanges hydroxyl ions for strongly and weakly ionized anions such as sulfate nitrate chloride and bicarbonate The hydrogen and hydroxyl ions combine to form water Regeneration of the cation and anion resins is usually accomplished with sulfuric acid and sodium hydroxide In chromatography the sorbent may be a solid adsorbent an insoluble nonvolatile liquid absorbent contained in the pores of a granular solid support or an ion exchanger In any case the solutes to be separated move through the chromato graphic separator with an inert eluting fluid at different rates because of different sortion affinities during repeated sorption desorption cycles During adsorption and ion exchange the solid separating agent becomes saturated or nearly saturated with the mole cules atoms or ions transferred from the fluid phase To recover the sorbed substances and allow the sorbent to be reused the asorbent is regenerated by desorbing the sorbed substances Accordingly these two separation operations are carried out in a cyclic manner In chromatography regeneration occurs continuously but at changing locations in the separator Adsorption processes may be classified as purification or bulk separation depending on the concentration in the feed of the components to be adsorbed Although there is no sharp dividing concentration Keller 1 has suggested 10 wt Early applications of adsorption involved only purification Adsorption with charred wood to improve the taste of water has been known for centuries Decolorization of liquids by adsorption with bone char and other materials has been prac ticed for at least five centuries Adsorption of gases by a solid charcoal was first described by CW Scheele in 1773 Commercial applications of bulk separation by gas adsorption began in the early 1920s but did not escalate until the 1960s following inventions by Milton 2 of synthetic molecularsieve zeolites which provide high adsorptive selectivity and by Skarstrom 3 of the pressureswing cycle which made possible a fixedbed cyclic gasadsorption pro cess The commercial separation of liquid mixtures also began in the 1960s following the invention by Broughton and Gerhold 4 of the simulated moving bed for adsorption Uses of ion exchange date back at least to the time of Moses who while leading his followers out of Egypt sweet ened the bitter waters of Marah with a tree Exodus 1523 26 In ancient Greece Aristotle observed that the salt con tent of water is reduced when it percolates through certain sands Studies of ion exchange were published in 1850 by both Thompson and Way who experimented with cation exchange in soils before the discovery of ions The first major application of ion exchange occurred over 100 years ago for water treatment to remove calcium and other ions responsible for water hardness Initially the ion exchanger was a porous natural mineral zeolite containing silica In 1935 synthetic insoluble polymericresin ion exchangers were introduced Today they are dominant for watersoftening and deionizing applications but natural and synthetic zeolites still find some use Since the 1903 invention of chromatography by M S Tswett 5 a Russian botanist it has found widespread use as an analytical preparative and industrial technique Tswett separated a mixture of structurally similar yellow and green chloroplast pigments in leaf extracts by dissolving the extracts in carbon disulfide and passing the solution through a column packed with chalk particles The pigments were separated by color hence the name chromatography which was coined by Tswett in 1906 from the Greek words chroma meaning color and graphe meaning writing Chroma tography has revolutionized laboratory chemical analysis of liquid and gas mixtures Largescale commercial applica tions described by Bonmati et al 6 and Bernard et al 7 began in the 1980s A A A A A A A B Matrix with fixed charges Counterions Coions B B B B 3 2 1 4 Adsorbed layer on surfaces Fluid phase in pores Adsorbent a b Figure 151 Sorption operations with solidparticle sorbents a Adsorption b Ion exchange Adsorption Ion Exchange Chromatography and Electrophoresis 569 C15 09222010 Page 577 resin ¼ 100 þ 76 ¼ 176 g maximum ionexchange capacity or 0937 ð1761000 Þ ¼ 53 eqkg dry ð Þ Depending on the extent of crosslinking resins from copolymers of styrene and divinylbenzene are listed as having actual capacities of from 39 high degree of crosslinking to 55 low degree of cross linking Although a low degree of crosslinking favors dry capacity almost every other ionexchanger property including wet capacity and selectivity is improved by crosslinking as discussed by Dorfner 18 1513 Sorbents for Chromatography Sorbents called stationary phases for chromatographic sep arations come in many forms and chemical compositions because of the diverse ways that chromatography is applied Figure 157 shows a classification of analytical chromato graphic systems taken from Sewell and Clarke 19 The mixture to be separated after injection into the carrier fluid to form the mobile phase may be a liquid liquid chromatog raphy or a gas gas chromatography Often the mixture is initially a liquid but is vaporized by the carrier gas giving a gas mixture as the mobile phase Gas carriers are inert and do not interact with the sorbent or feed Liquid carriers sol vents can interact and must be selected carefully The stationary sorbent phase is a solid a liquid supported on or bonded to a solid or a gel With a poroussolid adsorb ent the mechanism of separation is adsorption If an ion exchange mechanism is desired a synthetic polymer ion exchanger is used With a polymer gel or a microporous solid a separation based on sieving called exclusion can be operative Unique to chromatography are liquidsupported or bonded solids where the mechanism is absorption into the liquid also referred to as a partition mode of separation or partition chromatography With mobile liquid phases the stationary liquid phase may be stripped or dissolved Accord ingly methods of chemically bonding the stationary liquid phase to the solid support have been developed In packed columns 1 mm inside diameter the sorbents are in the form of particles In capillary columns 05 mm inside diameter the sorbent is the inside wall or a coating on that wall If coated the capillary column is referred to as a wallcoated opentubular WCOT column If the coating is a layer of fine particulate support material to which a liquid adsorbent is added the column is a supportcoated open tubular SCOT column If the wall is coated with a porous adsorbent only the column is a porouslayer opentubular PLOT column Each type of sorbent can be applied to sheets of glass plas tic or aluminum for use in thinlayer or planar chromatogra phy or to a sheet of cellulose material for use in paper chromatography If a pump rather than gravity is used to pass a liquid mobile phase through a packed column the name highperformance liquid chromatography HPLC is used The two most common adsorbents used in chromatogra phy are porous alumina and porous silica gel Of lesser importance are carbon magnesium oxide and carbonates Figure 157 Classification of analytical chromatographic systems From PA Sewell and B Clarke Chromatographic Separations John Wiley Sons New York 1987 with permission 151 Sorbents 577 C15 09222010 Page 609 154 EQUIPMENT FOR SORPTION OPERATIONS A variety of configurations and operating procedures are employed for commercial sorptionseparation equipment due mainly to the wide range of sorbent particle sizes and the need in most applications to regenerate the solid sorbent 1541 Adsorption For adsorption widely used equipment and operations are listed in Table 1513 For analysis purposes the listed devices are classified into the three operating modes in Figure 1540 In 1540a a powdered adsorbent such as activated carbon of dp 1 mm is added with water to an agitated tank to form a slurry The internal resistance to mass transfer within the pores of small particles is small However even with good stirring the external resistance to mass transfer from bulk liq uid to the external surface of the adsorbent particles may not be small because small particles tend to move with the liquid Thus the rate of adsorption may be controlled by external mass transfer The main application of this operation is removal of small amounts of large dissolved molecules such as coloring agents from water Spent adsorbent which is removed from the slurry by sedimentation or filtration is discarded because it is difficult to desorb large molecules The slurry system also called contact filtration can be oper ated continuously The fixedbed cyclicbatch operating mode shown in Figure 1540b is widely used with both liquid and gas feeds Adsorbent particle sizes range from 005 to 12 cm Bed pres sure drop decreases with increasing particle size but solute transport rate increases with decreasing particle size The optimal particle size is determined mainly from these two considerations To avoid jiggling fluidizing the bed or blow ing out fines during adsorption the feed flow is often down ward For removal of small amounts of dissolved hydrocarbons from water spent adsorbent is removed from the vessel and reactivated thermally at high temperature or discarded Fixedbed adsorption also called percolation is used for removal of dissolved organic compounds from water For purification or bulk separation of gases the adsorbent is almost always regenerated inplace by one of the five methods listed in Table 1513 and considered next In thermal temperatureswingadsorption TSA the adsorbent is regenerated by desorption at a temperature higher than used during adsorption as shown in Figure 1541 Bed temperature is increased by 1 heat transfer from heating coils located in the bed followed by pulling a moder ate vacuum or 2 more commonly by heat transfer from an inert nonadsorbing hot purge gas such as steam Following desorption the bed is cooled before adsorption is resumed Because heating and cooling of the bed requires hours a typi cal cycle time for TSA is hours to days Therefore if the quan tity of adsorbent in the bed is to be reasonable TSA is practical only for purification involving small adsorption rates 0 1 09 08 07 06 05 04 03 02 01 0 500 1000 1500 2000 2500 Time a 3000 3500 4000 4500 5000 ccF 0 1 09 08 07 06 05 04 03 02 01 0 1000 2000 Time b 3000 4000 5000 6000 Fructose Glucose Sucrose 7000 ccF Figure 1539 Computed chromatograms for Example 1516 a Comparison of ideal to nonideal wave for fructose b Computed chromatogram for nonideal eluant Table 1513 Common Commercial Methods for Adsorption Separations Phase Condition of Feed Contacting Device Adsorbent Regeneration Method Main Application Liquid Slurry in an agitated vessel Adsorbent discarded Purification Liquid Fixed bed Thermal reactivation Purification Liquid Simulated moving bed Displacement purge Bulk separation Gas Fixed bed Thermal swing TSA Purification Gas Combined fluidized bedmoving bed Thermal swing TSA Purification Gas Fixed bed Inertpurge swing Purification Gas Fixed bed Pressure swing PSA Bulk separation Gas Fixed bed Vacuum swing VSA Bulk separation Gas Fixed bed Displacement purge Bulk separation 154 Equipment for Sorption Operations 609 C15 09222010 Page 610 A fluidized bed can be used instead of a fixed bed for ad sorption and a moving bed for desorption as shown in Figure 1542 provided that particles are attritionresistant In the ad sorption section sieve trays are used with raw gas passing up through the perforations and fluidizing the adsorbent The fluidized particles flow like a liquid across the tray into the downcomer and onto the tray below In the food industry this type of tray is rotated From the adsorption section the solids pass to the desorption section where as moving beds they first flow down through preheating tubes and then through desorption tubes Steam is used for indirect heating in both sets of tubes and for stripping in the desorption tubes Moving beds rather than fluidized beds on trays are used in desorption because the strippingsteam flow rate is insuffi cient for fluidizing the solids At the bottom of the unit the regenerated solids are picked up by a carrier gas which flows up through a gaslift line to the top where the solids settle out on the top tray to repeat the adsorption cycle Keller 136 reports that this configuration which was announced in 1977 is used in more than 50 units worldwide to remove small amounts of solvents from air Other applications of Powdered adsorbent Batch liquid Slurry to filtration Saturated adsorbent Feed Feed Moving beds c b a Adsorber Adsorption step Desorption step Fixed beds Regenerated adsorbent Regenerator Heavy product or desorbate Heavy product or desorbate Purge Purge Light product or raffinate Light product or raffinate Figure 1540 Contacting modes for adsorption and ion exchange a Stirredtank slurry operation b Cyclic fixedbed batch operation c Continuous countercurrent operation q qads Pdes Pads P qdes P swing T swing Isotherm at Tads Isotherm at Tdes Tads Figure 1541 Schematic representation of pressureswing and thermalswing adsorption Raw gas Steam for heating Steam for desorption Tray Clean gas Desorption section Adsorbent flow Gas flow Adsorption section Adsorbent carrier gas Gas lift line Preheating tube Desorption tube Recovered solvent Condensate Figure 1542 PurasivTM process with a fluidized bed for adsorption and moving bed for desorption From GE Keller Separations New Directions for an Old Field AIChE Monograph Series 83 17 1987 with permission 610 Chapter 15 Adsorption Ion Exchange Chromatography and Electrophoresis C15 09222010 Page 611 TSA include removal of moisture CO2 and pollutants from gas streams In an inertpurgeswing regeneration desorption is at the same temperature and pressure as the adsorption step because the gas used for purging is nonadsorbing inert or only weakly adsorbing This method is used only when the solute is weakly adsorbed easily desorbed and of little or no value The purge gas must be inexpensive so that it does not have to be purified before recycle In pressureswing adsorption PSA adsorption takes place at an elevated pressure whereas desorption occurs at nearambient pressure as shown in Figure 1541 PSA is used for bulk separations because the bed can be depressur ized and repressurized rapidly making it possible to operate at cycle times of seconds to minutes Because of these short times the beds need not be large even when a substantial fraction of the feed gas is adsorbed If adsorption takes place at nearambient pressure and desorption under vacuum the cycle is referred to as vacuumswing adsorption VSA PSA and VSA are widely used for air separation If a zeolite adsorbent is used equilibrium is rapidly established and nitrogen is preferentially adsorbed Nonadsorbed high pressure product gas is a mixture of oxygen and argon with a small amount of nitrogen Alternatively if a carbon molecu larsieve adsorbent is used the particle diffusivity of oxygen is about 25 times that of nitrogen As a result the selectivity of adsorption is controlled by mass transfer and oxygen is preferentially adsorbed The resulting highpressure product is nearly pure nitrogen In both cases the adsorbed gas which is desorbed at low pressure is quite impure For the separation of air large plants use VSA because it is more energyefficient than PSA Small plants often use PSA because that cycle is simpler In displacementpurge displacementdesorption cycles a strongly adsorbed purge gas is used in desorption to dis place adsorbed species Another step is then required to recover the purge gas Displacementpurge cycles are viable only where TSA PSA and VSA cannot be used because of pressure or temperature limitations One application is sepa ration of mediumMW linear paraffins C10C18 from branchedchain and cyclic hydrocarbons by adsorption on 5A zeolite Ammonia which is separated from the paraffins by flash vaporization is used as purge Most commercial applications of adsorption involve fixed beds that cycle between adsorption and desorption Thus compositions temperature andor pressure at a given bed location vary with time Alternatively a continuous counter current operation where such variations do not occur can be envisaged as shown in Figure 1540c and discussed by Ruth ven and Ching 137 A difficulty with this scheme is the need to circulate solid adsorbent in a moving bed to achieve steadystate operation The first commercial application of countercurrent adsorption and desorption was the moving bed Hypersorption process for recovery by adsorption on activated carbon of light hydrocarbons from various gas streams in petroleum refineries as discussed by Berg 138 However only a few units were installed because of prob lems with adsorbent attrition difficulties in regenerating the adsorbent when heavier hydrocarbons in the feed gas were adsorbed and unfavorable economics compared to distilla tion Newer adsorbents with a much higher resistance to attri tion and possible applications to more difficult separations are reviving interest in movingbed units A successful countercurrent system for commercial sepa ration of liquid mixtures is the simulatedmovingbed sys tem shown as a hybrid system with two added distillation columns in Figure 1543 and known as the UOP Sorbex pro cess As described by Broughton 139 the bed is held sta tionary in one column which is equipped with a number perhaps 12 of liquid feed entry and discharge locations By shifting with a rotary valve RV the locations of feed entry desorbent entry extract adsorbed removal and raffinate nonadsorbed removal countercurrent movement of solids is simulated by a downward movement of liquid For the valve positions shown in Figure 1543 Lines 2 entering desorbent 5 exiting extract 9 entering feed and 12 exit ing raffinate are operational with all other numbered lines closed Liquid is circulated down through and externally back up to the top of the column by a pump Ideally an infi nite number of entry and exit locations exist and the valve would continuously change the four operational locations Since this is impractical a finite number of locations are AC RV Desorbent Extract Desorbentfree extract 1 2 3 4 5 6 7 8 9 10 11 12 Desorbent Extract Feed Raffinate Desorbentfree raffinate Distillation Distillation Feed Simulated movingbed adsorption EC RC Figure 1543 Sorbex hybrid simulatedmovingbed process for bulk separation AC adsorbent chamber RV rotary valve EC extract column RC raffinate column From DB Broughton Chem Eng Progress 64 8 6065 1968 with permission 154 Equipment for Sorption Operations 611 C15 09222010 Page 612 used and valve changes are made periodically In Figure 1543 when the valve is moved to the next position Lines 3 6 10 and 1 become operational Thus raffinate removal is relocated from the bottom of the bed to the top of the bed Thus the bed has no top or bottom Gembicki et al 140 state that 78 Sorbextype commercial units were installed during 19621989 for the bulk separation of pxylene from C8 aromatics nparaffins from branched and cyclic hydro carbons olefins from paraffins p or mcymene or cresol from cymene or cresol isomers and fructose from dextrose and polysaccharides Humphrey and Keller 141 cite 100 commercial Sorbex installations and more than 50 different demonstrated separations 1542 Ion Exchange Ion exchange shown in Figure 1540 employs the same modes of operation as adsorption Although use of fixed beds in a cyclic operation is most common stirred tanks are used for batch contacting with an attached strainer or filter to sep arate resin beads from the solution after equilibrium is approached Agitation is mild to avoid resin attrition but sufficient to achieve suspension of resin particles To increase resin utilization and achieve high efficiency efforts have been made to develop continuous countercurrent contactors two of which are shown in Figure 1544 The Hig gins contactor 142 operates as a moving packed bed by using intermittent hydraulic pulses to move incremental por tions of the bed from the ionexchange section up around and down to the backwash region down to the regenerating section and back up through the rinse section to the ion exchange section to repeat the cycle Liquid and resin move countercurrently The Himsley contactor 143 has a series of trays on which the resin beads are fluidized by upward flow of liquid Periodically the flow is reversed to move incremen tal amounts of resin from one stage to the stage below The batch of resin at the bottom is lifted to the wash column then to the regeneration column and then back to the top of the ionexchange column for reuse 1543 Chromatography Operation modes for industrialscale chromatography are of two major types as discussed by Ganetsos and Barker 144 The first and most common is a transient mode that is a scaledup version of an analytical chromatograph referred to as largescale batch or elution chromatography Packed columns of diameter up to 46 m and packed heights to 12 m have been reported As shown in Figure 1545 and discussed by Wankat in Chapter 14 of a handbook edited by Rousseau 9 a recycled solvent or carrier gas is fed continuously into a sorbentpacked column The feed mixture and recycle is Contacting section Resin storage Overflow Overflow Rinse water Ω Adsorption column Wash column Regenerant column Regenerant effluent Resin flow Water Waste Rinse Resin flow Resin flow Feed Product Regenerant Backwash Feed Pulse section Pulse Regenerating section a b Product Rinse outlet Regenerant Figure 1544 Continuous countercurrent ionexchange contactors a Higgins moving packedbed process b Himsley fluidizedbed process Column Cleanup Injector Recycle Products Separators Filter Feed Pump or compressor 1 2 3 Figure 1545 Largescale batch elution chromatography process 612 Chapter 15 Adsorption Ion Exchange Chromatography and Electrophoresis C15 09222010 Page 616 absence of a purge fluid by simply vaporizing the adsorbate some readsorption of solute vapor would occur upon cool ing thus it is best to remove desorbed adsorbate with a purge The desorption temperature is high but not so high as to cause deterioration of the adsorbent TSA is best applied to removal of contaminants present at low concentrations in the feed so that nearly isothermal adsorption and desorption is achieved An ideal cycle involves four steps 1 adsorption at T1 to breakthrough 2 heating of the bed to T2 3 desorption at T2 to a low adsorbate loading and 4 cooling of the bed to T1 Practical cycles do not operate with isothermal steps Instead Steps 2 and 3 are combined with the bed being simultaneously heated and desorbed with preheated purge gas until effluent temperature approaches that of the inlet purge Steps 1 and 4 may also be combined because as dis cussed by Ruthven 10 the thermal wave precedes the MTZ front Thus adsorption occurs at feedfluid temperature The heating and cooling steps cannot be accomplished instantaneously because of the low bed thermal conductivity Although heat transfer can be done indirectly from jackets surrounding the beds or from coils within the beds tempera ture changes are more readily achieved by preheating or pre cooling a purge fluid as shown in Figure 1547 The purge fluid can be a portion of the feed or effluent or some other fluid and can also be used in the desorption step When the adsorbate is valuable and easily condensed the purge fluid might be a noncondensable gas When the adsorbate is valu able but not easily condensed and is essentially insoluble in water steam may be used as the purge fluid followed by con densation of the steam to separate it from the desorbed adsorbate When the adsorbate is not valuable fuel andor air can be used as the purge fluid followed by incineration Often the amount of purge in the regeneration step is much less than the feed in the adsorption step In Figure 1547 the feed fluid is a gas and the spent bed is heated and regenerated with preheated feed gas which is cooled to condense des orbed adsorbate Because of the time to heat and cool a fixed bed cycle times for TSA are long usually hours or days Longer cycle times require longer bed lengths which result in a greater percent bed utilization during adsorption However for a given cycle time when the MTZ width is an appreciable frac tion of bed length such that bed capacity is poorly utilized a leadtrimbed arrangement of two absorbing beds in series should be considered When the lead bed is spent it is switched to regeneration At this time the trim bed has an MTZ occupying a considerable portion of the bed and that bed becomes the lead bed with a regenerated bed becoming the trim bed In this manner only a fully spent bed is switched to regeneration and three beds are used If the feed flow rate is very high beds in parallel may be required Adsorption is usually conducted with the feed fluid flow ing downward Desorption can be either downward or upward but the upward countercurrent direction is preferred because it is more efficient Consider the loading fronts shown in Figure 1548 for regeneration countercurrent to adsorption Although the bed is shown horizontal it must be positioned vertically The feed fluid flows down entering at the left and leaving at the right At time t ¼ 0 breakthrough has occurred with a loading profile as shown at the top where the MTZ is about 25 of the bed If the purge fluid for regeneration also flows downward entering at the left the adsorbate will move through the unused portion of the bed and some desorbed adsorbate will be readsorbed in the unused section and then desorbed a second time If counter current regeneration is used the unused portion of the bed is never in contact with desorbed adsorbate During a countercurrent regeneration step the loading profile changes progressively with time as shown in Figure 1548 The rightside end of the bed where purge enters is desorbed first After regeneration residual loading may be uniformly zero or more likely finite and nonuniform as shown at the bottom of Figure 1548 If the latter then the useful cyclic capacity called the delta loading is as shown in Figure 1549 Feed adsorbate partial pressure P1 Lessadsorbed product adsorbate partial pressure P2 Adsorbate partial pressure Adsorbate loading Possible Heater Feed Adsorption Cooler direct vent Adsorbed product T1 T1 T2 T2 X1 X2 P2 P1 Regeneration Figure 1547 Temperatureswing adsorption cycle 616 Chapter 15 Adsorption Ion Exchange Chromatography and Electrophoresis C15 09222010 Page 620 gas leaving Bed 1 is routed to Bed 2 to purge that bed in a direction countercurrent to the direction of flow of feed gas during the adsorption step When moisture is to be removed from air the dryair product is produced during the adsorp tion step in each of the two beds In Figure 1552 the adsorp tion and purge steps represent less than 50 of the total cycle time In many commercial applications of PSA these two steps consume a much greater fraction of the cycle time because pressurization and blowdown can be completed rap idly Therefore cycle times for PSA and VSA are short typi cally seconds to minutes and small beds have relatively large throughputs With the valving shown in Figure 1551 the cyclic sequence can be programmed to operate automatically With some valves open and others closed as in Figure 1551 adsorption takes place in Bed 1 and purge in Bed 2 During the second half of the cycle valve openings and beds are switched Improvements have been made to the Skarstrom cycle to increase product purity product recovery adsorbent produc tivity and energy efficiency as discussed by Yang 25 and by Ruthven Farooq and Knaebel 155 Among these modi fications are use of 1 three four or more beds 2 a pres sureequalization step in which both beds are equalized in pressure following purge of one bed and adsorption in the other 3 pretreatment or guard beds to remove strongly adsorbed components that might interfere with separation of other components 4 purge with a strongly adsorbing gas and 5 use of an extremely short cycle time to approach iso thermal operation if a longer cycle causes an undesirable increase in temperature during adsorption and an undesirable decrease in temperature during desorption Separations by PSA and VSA are controlled by adsorption equilibrium or adsorption kinetics where the latter refers to mass transfer external andor internal to adsorbent particle Both types of control are important commercially For the separation of air with zeolites adsorption equilibrium is the controlling factor with N2 more strongly adsorbed than O2 and argon For air with 21 O2 and 1 argon O2 of about 96 purity can be produced When carbon molecular sieves are used O2 and N2 have almost the same adsorption iso therms but the effective diffusivity of O2 is much larger than that of N2 Consequently a N2 product of very high purity 99 can be produced PSA and VSA cycles have been modeled successfully for both equilibrium and kineticcontrolled cases Models and computational procedures are similar to those for TSA and are particularly useful for optimizing cycles Of particular importance in PSA and TSA is determination of the cyclic steady state In TSA following desorption the regenerated bed is usually clean Thus a cyclic steady state is closely approached in one cycle In PSA and VSA this is not often the case complete regeneration is seldom achieved or neces sary It is only required to attain a cyclic steady state whereby product obtained during adsorption has the desired purity and at cyclic steady state the difference between loading profiles after adsorption and desorption is equal to the solute in the feed Starting with a clean bed attainment of a cyclic steady state for a fixed cycle time may require tens or hundreds of cycles Consider an example from a study by Mutasim and Bowen 156 on removal of ethane and CO2 from nitrogen with 5A zeolite at ambient temperature with adsorption and desorption for 3 minutes each at 4 bar and 1 bar respectively in beds 025 m in length Figures 1553a and b show loading development and gas concentration profiles at the end of each adsorption step for ethane starting from a clean bed After the first cycle the bed is still clean beyond about 011 m By the end of the 10th cycle a cyclic steady state has almost been attained with the bed being clean only near the very end Experimental data points for ethane loading at the end of 10 cycles agree with the computed profile PSA and VSA cycle models are constructed with the same equations as for TSA but the assumptions of negligible axial diffusion and isothermal operation may be relaxed For each cycle the pressurization and blowdown steps are often ignored and initial conditions for adsorption and desorption become the final conditions for desorption and adsorption of 16 12 8 4 0 0 005 Cycle 1 Ethane gas concentration molm3 010 015 z m b 020 025 12 08 04 0 0 005 Cycle 1 Loading gmolkg 010 015 z m a 020 025 Figure 1553 Development of cyclic steadystate profiles a Loading profiles for first 11 cycles b Ethane gas concentration profiles for first 16 cycles 620 Chapter 15 Adsorption Ion Exchange Chromatography and Electrophoresis C15 09222010 Page 624 an aqueous solution of glucose and fructose is separated by an SMB into an extract of aqueous glucose and a raffinate of aqueous fructose In the literature SMBs are often referred to as chromatographic rather than adsorptive separations An SMB can be treated as a countercurrent cascade of sec tions or zones rather than stages where stream entry or withdrawal points bound the sections Zang and Wankat 161 review two three and four section systems for producing two products and a nine section system for three products with the foursection sys tem of Figure 1557a being the most common commercial design More recently Kim and Wankat 162 proposed SMB designs with from 12 to 32 sections for separation of quaternary mixtures An SMB is best understood by studying the two represen tations of a foursection system and accompanying fluid composition profile in Figure 1557 The schematic in Figure 1557a shows a TMB with circulation of solid adsorbent S Section III Section IV QR QS Hypothetical solid adsorbent circulation S QF QE Section I Extract Arich Makeup QD desorbent D Section II Adsorption of A Adsorption of B Desorption of A Desorption of B Feed A B QC Fluid recirculation Drich Raffinate Brich a Schematic representation of a true moving bed 10 9 8 11 12 1 3 7 6 2 5 4 Section III Section I Section IV Section II Raffinate Makeup desorbent Direction of fluid flow and port switching Feed Extract b Simulatedmovingbed system with port switching 100 0 Liquid composition Section III Section IV Section II Section I B A D Extract Arich Raffinate Brich Feed A B Solid Fluid Movement in the column c Component composition profile Figure 1557 Foursection system 624 Chapter 15 Adsorption Ion Exchange Chromatography and Electrophoresis C15 09222010 Page 639 sorbent Most commonly the overall rate of adsorption is expressed in the form of a lineardrivingforce LDF model where driving force is the difference between bulk concentration and concentration in equilibrium with the loading The coefficient in the LDF equation combines an overall masstransfer coefficient and an area for sorption 15 In ideal fixedbed operation solutesorbate equilibrium between the flowing fluid and the static bed is assumed everywhere For plug flow and negligible axial disper sion the result is a sharp concentration front that moves like a shock wave stoichiometric front through the bed Upstream of the front the sorbent is spent and in equili brium with the feed mixture Downstream the sorbent is clean of sorbate The stoichiometric front travels through the bed at a much slower velocity than the interstitial feed velocity The time for the front to reach the end of the bed is the breakthrough time 16 When masstransfer effects are included the concentra tion front broadens into an Sshaped curve such that at breakthrough only a portion of the sorbent is fully loaded When masstransfer coefficients and sorption isotherms are known these curves can be computed using Klinkenbergs equations When shapes of experi mental concentration fronts exhibit a constant pattern because of favorable adsorption equilibrium commer cialsize beds can be scaledup from laboratory break through data by the method of Collins 17 Thermalswing adsorption TSA is used to remove small concentrations of solutes from gas and liquid mix tures Adsorption is carried out at ambient temperature and desorption at an elevated temperature Because bed heating and cooling between adsorption and desorption are not instantaneous TSA cycles are long typically hours or days The desorption step starting with a par tially loaded bed can be computed by the method of lines using a stiff integrator 18 Pressureswing adsorption PSA is used to separate air and enrich hydrogencontaining streams Adsorption is carried out at an elevated or ambient pressure whereas desorption occurs at a lower pressure or vacuum the lat ter is called vacuumswing adsorption VSA Because pressure swings can be made rapidly PSA cycles are short typically seconds or minutes It is not necessary to regenerate the bed completely but if not a number of cycles are needed to approach a cyclic steadystate operation 19 Although continuous countercurrent adsorption with a moving bed is difficult to achieve successfully in prac tice a simulatedmovingbed SMB system is popular particularly for separation of solutes in dilute aqueous solutions and for bulkliquid separations Design pro cedures for SMB systems which require solution of differentialalgebraic equations DAEs are highly developed 20 Design calculations for ionexchange operations are based on an equilibrium assumption for the loading and regeneration steps 21 In the basic mode of chromatography feed is periodi cally pulsed into a column packed with sorbent Between feed pulses an elutant is passed through the column causing the less strongly sorbed solutes to move through the column more rapidly than slower solutes If the col umn is long enough a multicomponent feed can be com pletely separated with solutes eluted one by one from the column In the absence of masstransfer resistances a rectangular feed pulse is separated into individual solute rectangular pulses whose positiontime curves are readily established When masstransfer effects are important rectangular pulses take on a Gaussian distri bution predicted by analytical solutions that use a linear adsorption isotherm 22 Electrophoresis separates solutes based on relative mass and charge driven by an electricfield gradient It com monly occurs in a gel matrix of synthetic or natural poly mer developed inplace between parallel glass plates or inside a silica capillary to minimize electroosmosis and resistive Joule heating 23 Several electrophoretic modes are widely used to isolate and concentrate biomolecules They are distinguished by denaturants matrix pH and electrolyte content rela tive to the direction of the applied field gradient all of which influence the electrophoretic mobility of the biomolecule 24 Chemical stains fluorescence immunological probes and spectroscopyspectrometry are used to visualize and recover biomolecules distinguished by electrophoresis REFERENCES 1 Keller GE II in TE Whyte Jr CM Yon and EH 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Yang Ind Eng Chem Res 30 10231032 1991 155 Ruthven DM S Farooq and KS Knaebel PressureSwing Adsorption VCH New York 1994 156 Mutasim ZZ and JH Bowen Trans I Chem E 69 Part A 108 118 March 1991 157 Ruthven DM and CB Ching Chem Eng Sci 44 10111038 1989 158 Wankat PC LargeScale Adsorption and Chromatography Vols I and II CRC Press Inc Boca Raton 1986 159 Berg C Trans AIChE 42 665680 1946 160 Eagleton LC and H Bliss Chem Eng Progress 49 543548 1953 161 Zang Y and PC Wankat Ind Eng Chem Res 41 52835289 2002 162 Kim JK and PC Wankat Ind Eng Chem Res 43 10711080 2004 163 Wankat PC Ind Eng Chem Res 40 61856193 2001 164 Storti G M Masi S Carra and M Morbidelli Chem Eng Sci 44 1329 1989 165 Rhee HK R Aris and NR Amundson Phil Trans Royal Soc London Series A 269 No 1194 187215 Feb 5 1971 166 Mazzotti M G Storti and M Morbidelli AIChE Journal 40 1825 1842 1994 167 Ruthven DM and CB Ching Chem Eng Sci 44 10111038 1989 168 Zhong G and G Guiochon Chem Eng Sci 51 43074319 1996 169 Storti G M Mazzotti M Morbidelli and S Carra AIChE Journal 39 471492 1993 170 Mazzotti M G Storti and M Morbidelli J Chromatography A 769 324 1997 171 Danckwerts PV Chem Eng Sci 2 1 1953 172 Constantinides A and N Mostoufi Numerical Methods for Chemi cal Engineers with MATLAB Applications Prentice Hall PTR Upper Saddle River NJ 1999 173 Minceva M and AE Rodrigues Ind Eng Chem Res 41 3454 3461 2002 174 Gunn DJ Trans Instn Chem Engrs 47 T351T359 1969 175 Gunn DJChem Eng Sci 422 363373 1987 176 Broughton DB RW Neuzil JM Pharis and CS Brearby Chem Eng Prog 669 7075 1970 177 Tiselius A Trans Faraday Society 33 524 1937 178 Grossman PD FreeSolution Capillary Electrophoresis in PD Grossman and JC Colburn Eds Capillary Electrophoresis Theory and Practice Academic Press San Diego CA 1992 179 Ornstein L Ann N Y Acad Sci 121 321349 1964 180 Scopes RK Protein Purification SpringerVerlag New York 1982 181 Hjerten S Isoelectric Focusing in Capillaries in PD Grossman and JC Colburn Eds Capillary Electrophoresis Theory and Practice Ac ademic Press San Diego CA 1992 182 Demarest CW EA MonnotChase J Jiu and R Weinberger Separation of Small Molecules by High Performance Capillary Electropho resis in PD Grossman and JC Colburn Eds Capillary Electrophoresis Theory and Practice Academic Press San Diego CA 1992 183 Garcia AA MR Bonen J RamirezVick M Sadaka and A Vuppu Bioseparation Process Science Blackwell Science Malden MA 1999 184 Southern EM and JK Elder in AP Monaco Ed Pulsed Field Gel Electrophoresis A Practical Approach Oxford University Press Oxford UK 1995 STUDY QUESTIONS 151 How is a large surface area achieved for adsorption 152 What is meant by ion exchange How does ion exchange differ from deionization 153 In adsorption processes what distinguishes purification from bulk separation 154 What is meant by regeneration 155 Why is it easy to measure the amount of adsorption of a pure gas but difficult to measure adsorption of a pure liquid 156 What is the BET equation used for Does it assume physi cal or chemical adsorption Does it assume monomolecular or multimolecularlayer adsorption 157 How is it possible to use a liquid sorbent in chromatography 158 What is meant by loading in adsorption 159 What is an adsorption isotherm How can the heat of adsorption be determined from a series of isotherms 1510 What are the four steps that occur during the adsorption of a solute from a gas or liquid mixture How do they affect adsorptive bandwidth resolution and throughput Which step may be almost instantaneous such that equilibrium at the fluidsorbent interface can be assumed 1511 Within a porous particle why are mass and heat transfer not analogous 1512 For mass transfer outside a single spherical particle that is not close to a wall or other particles what is the smallest value of the Sherwood number What is the basis for this value 1513 What is the difference between slurry adsorption contact filtration and fixedbed adsorption percolation When should each be considered and not considered 1514 How do pressureswing and thermalswing adsorption dif fer What are inertpurge swing and displacement purge 642 Chapter 15 Adsorption Ion Exchange Chromatography and Electrophoresis PART04 09212010 85911 Page 649 Part Four Separations that Involve a Solid Phase Chapters 16 17 and 18 describe separations in which one or more components in a solid phase undergo mass transfer to or from a fluid phase Chapter 16 covers selective leaching from a solid to a liquid solvent This operation is widely used in the food industry Crystalli zation from a liquid and desublimation from a vapor are discussed in Chapter 17 where evaporation which often precedes crystallization is included Both solution crystallization to produce inorganic crystals and melt crystallization to produce organic crystals are consid ered Chapter 18 is devoted to drying of solids and the myriad types of equipment used industrially Drying is important in the pharmaceutical industry where many products are prepared in solution and sold as dry pow ders in tablet form A section on psychrometry is also included 649 C16 09212010 Page 651 porous clay plates obeys Ficks law of molecular diffusion extraction of oil from soybeans does not presumably because of the complex internal structure of soybeans Furthermore Othmer and Agarwal 1 using whole and cutinhalf soy beans found that diffusion is extremely slow After 168 hours in contact with hexane less than 008 of the oil in the whole beans and less than 019 of the oil in the half beans was extracted Such a slow diffusion rate for particles that are about 5 mm in diameter is due to the location of the oil within insoluble cell walls requiring that oil pass through the walls driven by low osmotic pressure differences The extent and rate of oil extraction is greatly enhanced by flaking the soybeans to thicknesses of 0005002inch Flaking ruptures the cell walls greatly facilitating contact of oil with solvent Using trichloroethylene 3 or nhexane 1 as the solvent with flakes of diameters from 004 to 024 inch approximately 90 of the oil can be extracted in 100 minutes The ideal solvent for commercial leaching of soybeans should have high oil solubility to minimize the amount of solvent a high volatility to facilitate recovery of solvent from oil by evaporation or distillation nonflammabil ity to eliminate fires and explosions low cost ready availa bility chemical stability low toxicity and compatibility with inexpensive materials of construction In many respects especially nonflammability trichloroethylene is an ideal solvent but it is classified as a hazardous toxic chemical The favored solvent is thus commercial hexane mostly nhexane which presents a fire hazard but has a low toxicity The pilotplant leaching unit used by Othmer and Agarwal known as the Kennedy extractor is shown in Figure 161 Soybeans enter continuously at the low end and are leached in a countercurrent cascade of tubs by hexane solvent which enters at the upper end The flakes and solvent are agitated and underflows are pushed uphill from one tub to the next by slowly rotating paddles and scrapers while overflows move downhill from tub to tub The paddles are perforated to drain the solids when they are lifted above the liquid level in the tub by the paddle Othmer and Agarwal used 15 tubs Soybean flakes of 0012inch average thickness 1067 wt moisture and 02675 g oilg dry oilfree flakes were fed to the Kennedy extractor at a rate of 6375 lbh Solvent flow was 10844 lbh Leaching took place at ambient conditions and after 11 hours of operation at steady state an extract the miscella of 7313 lbhr containing 1535 wt oil was produced The leached solids contained 00151 g oilg dry oilfree flakes thus 944 of the oil was extracted Resi dence time in each tub was 3 minutes giving a total resi dence time of 45 minutes From these data a massbalance check can be made for oil and solvent and the liquidto solids ratio in the leached solids can be estimated These cal culations are left as an exercise 161 EQUIPMENT FOR LEACHING Leachable solids generally undergo pretreatment before being fed to leaching equipment so that reasonable leaching times are obtained For example seeds and beans are dehulled cracked and flaked as described above for soy beans When vegetable and animal material cannot be flaked it may be possible to cut it into thin slices as is done with sugar beets prior to leaching of the sugar with water In this case the cell walls are left largely intact to minimize the leaching of undesirable material such as colloids and albu mens Metallurgical ores are crushed and ground to small particles because small regions of leachable material may be surrounded by relatively impermeable insoluble material When that material is quartzite leaching may be extremely slow Van Arsdale 4 cites the very important effect of parti cle size on the time required for effective leaching of a cop per ore by aqueous sulfuric acid The times for particle diameters of 150 mm 6 mm and less than 025 mm are approximately 5 years 5 days and 5 hours respectively When leachable solids contain a high of solute pretreat ment may not be necessary because disintegration of the remaining skeleton of insoluble material takes place at the sur face of the particles as leaching progresses When the entire solid is soluble leaching may be rapid such that only one stage of extraction is required as dissolution takes place Industrial equipment for solidliquid extraction is designed for batchwise or continuous processing The method of contacting solids with solvent is either by percola tion of solvent through a bed of solids or by immersion of the solid in the solvent followed by agitation of the mixture When immersion is used countercurrent multistage opera tion is common With percolation either a stagewise or a dif ferential contacting device is appropriate An extractor must be efficient to minimize the need for solvent because of the high cost of solvent recovery Paddle Solvent feed Scraper Tub Leached solids Overflows Underflows Flakedsoybeans solid Extract Figure 161 Kennedy extractor for leaching of oil from soybeans 161 Equipment for Leaching 651 C16 09212010 Page 652 1611 Batch Extractors When the solids to be leached are in the form of fine particles perhaps smaller than 01 mm in diameter batch leaching is conveniently conducted in an agitated vessel A simple config uration is the Pachuca tank 5 depicted in Figure 162a and used extensively in the metallurgical industry The tank is a tall cylindrical vessel constructed of wood concrete or metal that can be lined with an inert noncorrosive nontoxic mate rial Solvent and solids are placed in the tank and agitation is achieved by an air lift whereby air bubbles entering at the bot tom of a circular tube concentric with the tank cause upward flow and subsequent circulation of the solidliquid suspen sion During agitation air continuously enters and leaves the vessel When the desired degree of leaching is accomplished agitation stops and solids are allowed to settle into a sludge at the bottom where it is removed with the assistance of air The supernatant extract is removed by siphoning from the top of the tank Agitation can also be achieved by a paddle stirrer or by the use of a propeller mounted in a draft tube to provide upward flow and circulation of the solidliquid suspension much like that in the Pachuca tank When the solids are too coarse to be easily suspended by immersion in a stirred solvent percolation techniques can be used Again a tall cylindrical vessel is employed Solids to be leached are dumped into the vessel followed by percola tion of solvent down through the bed of solids much like in fixedbed adsorption To achieve a high concentration of sol ute in the solvent a series of vessels is arranged in a multi batch countercurrentleaching technique developed in 1841 by James Shanks and called a Shanks extraction battery This technique can be used for such applications as batch removal of tannin from wood or bark sugar from sugar beets and watersoluble substances from coffee tea and spices A typi cal vessel arrangement is shown in Figure 162b where Ves sel 1 is offline for emptying and refilling of solids Solvent enters and percolates down through the solids in Vessel 2 and then percolates through Vessels 3 and 4 leaving as final extract from Vessel 4 The extraction of solids in Vessel 2 is completed first When that occurs Vessel 2 is taken offline for emptying and refilling of solids and Vessel 1 is placed online Fresh solvent first enters Vessel 3 followed by Ves sels 4 and 1 In this manner fresh solvent always contacts sol ids that have been leached for the longest time thus realizing the benefits of countercurrent contacting Heat exchangers are Vessels with beds of solids Heaters or coolers Pumps Closed when bed 2 offline 1 2 3 4 Fresh solvent Extract Figure 162 a Pachuca tank for batch leaching of small particles From Handbook of Separation Tech niques for Chemical Engineers 2nd ed PA Schweitzer Editorinchief McGrawHill New York 1988 with permission b Shanks countercurrent multibatch battery system for leaching of large particles by percolation From CJ King Separation Pro cesses 2nd ed McGrawHill New York 1980 with permission Concrete Wood staves Air lift tube Air out Deflector Air for lift Air for loosening settled solids Sand b a 652 Chapter 16 Leaching and Washing C16 09212010 Page 654 are rotated slowly at about 1 rph to give solids residence times of 60 minutes Each basket contains approximately 350 kg of flaked solids For the 23 baskets shown in Figure 164a almost 200000 kg of solids can be extracted per day About equal mass flows of solids and solvent are fed to the extractor and full miscella is essentially solidsfree with about 25 wt oil Another widely used continuous extractor for flaked seeds and beans is the Rotocel extractor in Figure 164b In this device which resembles a carousel and simulates a Shanks system walled annular sectors called cells on a horizontal plane are slowly rotated by a motor The cells which hold solids and are perforated for solvent drainage successively pass a solidsfeed area a series of solvent sprays a final spray and drainage area and a solidsdischarge area Fresh solvent is supplied to the cell located just below the final spray and drainage area from where drained liquid is col lected and pumped to the preceding cell location The drain age from that cell is collected and pumped to the cell preceding that cell and so on In this manner a counter current flow of solids and liquid is achieved The extracted solids may contain 2530 wt liquid Rotocel extractors are typically 34113 m in diameter 6473 m in height and with bed depths of 1830 m They process up to 3 million kgday of flaked soybeans The number of cells can be varied and residence time controlled by the rate of rotation A popu lar variation of Rotocel extractors is the French stationary basket extractor in Figure 164c which has about the size and capacity of a Rotocel extractor Instead of the sectored cells moving the solidsfeed spout and solidsdischarge zone rotate with periodic switching of solvent feed and discharge connections Thus the weight of moving parts is reduced Continuous perforatedbelt extractors as shown in Figure 164d are used to process sugar cane sugar beets oil seeds Paddle conveyor Wetflake hopper Baskets Full miscella Half miscella Dry flakes Pure solvent a Bollman vertical movingbasket conveyor extractor Rotating cells Solvent oil miscella Solids bean flakes Solids discharge Spray Interstage liquid Interstage liquid solvent oil Leached solids Solvent hexane b Rotocel extractor Figure 164 Equipment for continuous leaching From Handbook of Separation Techniques for Chemical Engineers 2nd ed PA Schweitzer Editorinchief McGrawHill New York 1988 with permission From RE Treybal MassTransfer Opera tions 3rd ed McGrawHill New York 1980 with permission Continued 654 Chapter 16 Leaching and Washing C16 09212010 Page 655 c French stationarybasket extractor Solids in Solvent Extract Extracted solids d Continuous perforatedbelt extractor Cossette inlet Fresh water inlet Return water inlet Sieve Raw juice outlet Steam inlet Steam jacket Cossette outlet e DDS doublescrew slope extractor Figure 164 Continued 161 Equipment for Leaching 655 C16 09212010 Page 656 and apples for apple juice The feed solids are fed from a hopper to a slowmoving continuous and nonpartitioned perforated belt driven by motorized sprockets at either end The height of solids on the belt can be controlled by a damper at the feed hopper outlet Belt speed is automatically adjusted to maintain the desired depth of solids Extracted solids are discharged into an outlet hopper at the end of the belt by a scraper and side walls prevent solids from falling off the sides of the belt Below the belt are compart ments for collecting solvent Fresh solvent is sprayed over solids and above compartments in a countercurrent fashion starting from the discharge end of the belt in as many as 17 passes Bed depths range from 08 to 26 m and units from 7 to 37 m long with belts from 05 to 95 m wide have processed as much as 7000000 kgday of sugar cane or sugar beets The DDS De Danske Sukkerfabriker doublescrew slope extractor in Figure 164e is a very versatile unit Although used mainly for extraction of sugar beets the device has been applied successfully to a range of other feed materials including sugar cane flaked seeds and beans apples pears grapes cherries ginger licorice red beets car rots fishmeal coffee and tea The oppositeturning screws of the metal ribbons are pitched so that both screws move the solids uphill in parallel cylindrical troughs Extract flows through the screw surface downhill to achieve a differential countercurrent flow with the solids A novel feature is the ability to turn one screw slightly faster and then slightly slower than the other screw causing the solids to be periodi cally squeezed Units range in size from 237 m in diameter and 2127 m in length and have been used to process as much as 3000000 kgday of sugar beets in the form of cos settes long thin strips 1614 Continuous Countercurrent Washing When leaching is very rapid as with small particles contain ing very soluble solutes or when leaching has already been completed or when solids are formed by chemical reactions in a solution it is common to countercurrently wash the sol ids to reduce the solute concentration in the liquid adhering to the solids This can be accomplished in a series of gravity thickeners or centrifugal thickeners called hydroclones arranged for countercurrent flow of the underflows and over flows as shown in Figure 165 and sometimes called a con tinuous countercurrent decantation system A typical continuous gravity thickener is shown in detail in Figure 166a Combined feed to the thickener consists of feed solids or underflow from an adjacent thickener together with fresh solvent or overflow from an adjacent thickener The thickener must first thoroughly mix liquid and solids to obtain a uni form concentration of solute in the liquid and it must then produce an overflow free of solids and an underflow with as high a fraction of solids as possible A thickener consists of a largediameter shallow tank with a flat or slightly conical bottom The combined feed enters the tank near the center by means of a feed launder that discharges into a feed well Settling and sedimenta tion of solid particles occur by gravity due to a solid particle density that is greater than the liquid density In essence solids flow downward and liquid flows upward Around the upper inner periphery of the tank is an over flow launder or weir for continuously removing clarified liquid Solids settling to the tank bottom are moved inward toward a thick sludge discharge by a slowly rotat ing motordriven rake Thickeners as large as 100 m in diameter and 35 m high have been constructed In large thickeners rakes revolve at about 2 rpm Residence times of solids and liquids in a gravity thick ener are often large minutes or hours and as such are suffi cient to provide adequate residence time for mass transfer and mixing when small particles are involved When long residence times are not needed and the overflow need not be perfectly clear of solids the hydroclone shown in Figure 166b may be appropriate Here pressurized feed slurry enters tangentially to create by centrifugal force a downwardspiraling motion Higherdensity suspended sol ids are by preference driven to the wall which becomes conical as it extends downward and discharged as a thick ened slurry at the hydroclone bottom The liquid which is forced to move inward and upward as a spiraling vortex exits from a vortexfinder pipe extending downward from the closed hydroclone top to a location just below feed entry Underflow Underflow Overflow Wash and leaching solvent Overflow Overflow Thickeners Underflow Solids feed or reactants Conc solution 1 2 Washed solids 4 3 Figure 165 Continuous countercurrent washing system using thickeners 656 Chapter 16 Leaching and Washing C16 09212010 Page 657 162 EQUILIBRIUMSTAGE MODEL FOR LEACHING AND WASHING The simplest model for a continuous countercurrent leaching and washing system as shown in Figure 167 is similar to the model developed in 52 It assumes that the solid feed consists of a solute that is completely soluble in the solvent and an inert substance or carrier that is not soluble Leaching is assumed to be rapid such that it is completed in a single leaching stage which is followed by a series of one or more washing stages to reduce concentration of solute in the liquid adhering to the solids in the underflow All overflow streams are assumed to be free of solids In Figure 167 S ¼ mass flow rate of inert solids which is constant from stage to stage V ¼ mass flow rate of entering solvent or overflow liq uid solvent plus solute which varies from stage to stage L ¼ mass flow rate of underflow liquid solvent plus solute which varies from stage to stage y ¼ mass fraction of solute in the overflow liquid and x ¼ mass fraction of solute in the underflow liquid Alternatively V and L can refer to mass flow rates of sol vent on a solutefree basis and the symbols Y and X can be used to refer to mass ratios of solute to solvent in the over flow liquid and underflow liquid respectively Mole or vol ume flow rates can also be used Rake or scraping mechanism Feed launder Rotating mechanism Feed well Overflow launder Clear solution overflow Zone A clear Blade Thick sludge discharge a Gravity thickener Arm Solids discharge 1 Pressurized slurry enters tangentially 4 Liquid moves inward and upward as spiralling vortex 2 Slurry rotation develops high centrifugal forces throughout cyclone 3 Suspended solids driven toward wall and downward in accelerating spiral Liquid discharge b Hydroclone centrifugal thickener Figure 166 Thickeners From Handbook of Separation Techniques for Chemical Engineers 2nd ed PA Schweitzer Editorinchief McGrawHill New York 1988 with permission 162 EquilibriumStage Model for Leaching and Washing 657 C16 09212010 Page 667 model assumes that concentration of solute in the over flow leaving a stage equals that in the underflow liquid retained on the solid leaving the stage 7 When the ratio of liquid to solids in the underflow is constant from stage to stage the equilibriumstage model can be applied algebraically by a modified Kremser method or graphically by a modified McCabe Thiele method If the underflow is variable the graphi cal method with a curved operating line is appropriate 8 When leaching is slow as with food solids or low grade ores leaching calculations must be done on a rate basis In some cases the diffusion of solutes in food solids does not obey Ficks law because of com plex membrane and fiber structures 9 Leaching of lowgrade ores by reactive leaching is con veniently carried out with a shrinkingcore diffusion model using a pseudosteadystate assumption REFERENCES 1 Othmer DF and JC Agarwal Chem Eng Progress 51 372373 1955 2 DW Green and RH Perry Eds Perrys Chemical Engineers Hand book 8th ed McGrawHill New York Section 18 2008 3 King CO DJ Katz and JC Brier Trans AIChE 40 533537 1944 4 Van Arsdale GD Hydrometallurgy of Base Metals McGrawHill New York 1953 5 Lamont AGW Can J Chem Eng 36 153 1958 6 Schwartzberg HG Chem Eng Progress 764 6785 1980 7 Coulson JM JF Richardson JR Backhurstand JH Harker Chemi cal Engineering 4th ed Pergamon Press Oxford Vol 2 1991 8 Baker EM Trans AIChE 32 6272 1936 9 McCabe WL and JC Smith Unit Operations of Chemical Engineer ing McGrawHill New York pp 604608 1956 10 Ravenscroft EA Ind Eng Chem 28 851855 1936 11 Schwartzberg HG and RY Chao Food Tech 362 7386 1982 12 Karnofsky G J Am Oil Chem Soc 26 564569 1949 13 Yang HH and JC Brier AIChE J 4 453459 1958 14 Yagi S and D Kunii Fifth Symposium International on Combus tion Reinhold New York pp 231244 1955 15 Roman RJ BR Benner and GW Becker Trans Soc Mining Engi neering of AIME 256 247256 1974 16 Andueza S L Maeztu B Dean MP de Pena J Pello and C Cid J Agric Food Chem 50 74267431 2002 17 Andueza S L Maeztu L Pascual C Ibanez MP de Pena and C Cid J Sci Food Agric 83 240248 2003 18 Andueza S MP de Pena and C Cid J Agric Food Chem 51 70347039 2003 STUDY QUESTIONS 161 Is leaching synonymous with solidliquid andor liquid solid extraction 162 In a leaching operation what is the leachant the overflow and the underflow 163 Why does the underflow consist of both leached solids and liquid containing leached material 164 Why is pretreatment of the solids to be leached often necessary 165 Under what conditions would leaching be expected to be very slow 166 What is dissolution 167 What is the difference between suspension leaching and percolation leaching For what conditions is each method used 168 What are the advantages of the espresso machine over the drip method 169 Why do many leaching processes include multistage coun tercurrent washing after the leaching stage 1610 What are the assumptions for an ideal leaching or washing stage 1611 What is meant by variable underflow and what causes it 1612 How does the shrinkingcore model used for mineral leach ing differ from the simpler model used for leaching of food materials 1613 Why is an effective diffusivity that is obtained by experi ment preferred for estimating the rate of leaching of food materials 1614 What is the pseudosteadystate assumption used in the shrinkingcore leaching model EXERCISES Section 161 161 Massbalance check on leaching data Using experimental data from pilotplant tests of soybean extrac tion by Othmer and Agarwal summarized in the Industrial Example at the beginning of this chapter check mass balances for oil and hexane around the extractor assuming the moisture is retained in the flakes and compute the mass ratio of liquid oil to flakes in leached solids leaving the extractor Section 162 162 Manufacture of barium carbonate BaCO3 which is water insoluble is to be made by precipita tion from a solution containing 120000 kgday of water and 40000 kgday of BaS with a stoichiometric amount of solid Na2CO3 The reaction which produces a byproduct of water soluble Na2S will be carried out in a continuous countercurrent system of five thickeners Complete reaction will take place in Exercises 667 C17 09222010 Page 691 fine crystals that flows to a circulating pipe where it is joined by the feed and flows upward through a pump and then a heat exchanger The circulating solution is heated several degrees to provide energy for feed preheat and subsequent evaporation and to dissolve finer crystals Circulating magma reenters the main body of the crystallizer just below the bottom of the draft tube Further classification of crystals by size can be accomplished by providing an elutriation leg as shown in Figure 1716 at the bottom of the main body of thecrystallizerInthatcaseproductmagmaiswithdrawnthrough a pipe from a nozzle located near the bottom of the elutriation leg where the largest crystals are present Otherwise the product magma may be withdrawn from the lower part of the annular regionsurroundingthedrafttube 175 THE MSMPR CRYSTALLIZATION MODEL Because of the popularity of the DTB crystallizer a mathe matical model due to Randolph 14 for its design and analy sis is useful and is found in process simulators It is referred to as the MixedSuspension MixedProductRemoval MSMPR model and is based on the following assumptions 1 continuous steadyflow steadystate operation 2 per fect mixing of the magma 3 no classification of crystals 4 uniform degree of supersaturation of the magma 5 crys tal growth rate independent of crystal size 6 no crystals in the feed but seeds are added initially 7 no crystal break age 8 uniform temperature 9 mother liquor in product magma in equilibrium with the crystals 10 nucleation rate is constant uniform and due to secondary nucleation by crystal contact 11 crystalsize distribution CSD is uni form in the crystallizer and equal to that in the magma and 12 all crystals have the same shape Modifications to the model to account for classification of crystals due to settling elutriation and dissolving of fines and variable growth rate are discussed by Randolph and Lar son 15 The core of the MSMPR model is the estimation by a crystalpopulation balance of the crystalsize distribution CSD which is determined by the rpm of the drafttube pro peller and external circulation rate It is relatively easy to conduct experiments in a laboratory crystallizer that approx imates the MSMPR model and can provide crystal nucleation rate and growthrate data to design an industrial crystallizer 1751 CrystalPopulation Balance The crystalpopulation balance accounts for all crystals in the magma and with the mass balance makes possible the determi nation of the CSD Let L ¼ characteristic crystal size eg from a screen analysis N ¼ cumulative number of crystals of size L and smaller inthe magma inthe crystallizerandVML¼ volume ofthe mother liquor in the crystallizer magma A cumulativenumbers undersize plot based on these variables is shown in Figure 1717 where the slope of the curve n at a givenvalue of L is the number ofcrystalsperunitsizeperunitvolume n ¼ d NVML ð Þ dL ¼ 1 VML dN dL 1731 The limits of n as shown in Figure 1717 vary from no at L ¼ 0 to 0 at L ¼ LT the largest crystal size In the MSMPR model the cumulative plot of Figure 1717 is independent of time and location in the magma The plot is in fact the numbers cumulative CSD for productmagma crystals For a constant crystalsize growth rate independent of crystal size let G ¼ dLdt or DL ¼ GDt 1732 Cumulative number of crystals per volume of mother liquor NVML Crystal size L LT largest crystal Slope n Slope n Slope 0 Figure 1717 Typical cumulative numbers undersize distribution 175 The MSMPR Crystallization Model 691 C17 09222010 Page 698 freezing In the former crystals of a desired size distribution are grown slowly in a suspension by subcooling a seeded feed melt In the latter crystals of uncontrolled size are grown rapidly on a cooled surface wherein subcooling is supplied through the crystallized layer In suspension crystal lization the remaining melt must be separated from the crys tals by centrifugation filtration andor settling In layer crystallization the remaining melt or residual liquid is drained from the solid layer followed by melting of the solid Figure 1721 shows a twostage scrapedwallcrystallizer system used for suspension crystallization A cooling medium is used to control the surface temperatures of the two scrapedwall units causing crystals to grow which are subsequently scraped off by screws The melt mixture is cir culated through a ripening vessel The two scrapedwall units are typically 36 m long with 385 m2 of heattransfer area The screws are driven by a 10kW motor Of greater commercial importance is the fallingfilm crys tallizer in Figure 1722 developed by Sulzer Brothers Ltd This equipment produces highpurity crystals 999 at high capacity 10000 tonsyr A large pair of units each 4 m in diameter and containing 1100 12mhigh tubes can produce 100000 tonsyr of very pure crystals with typical layer growth rates of 1 inchh The feed melt flows as a film down the inside of the tubes over a crystal layer that forms and grows by progressive freezing because the wall of the tube is cooled from the outside When a predetermined crys tallayer thickness typically 520 mm is reached the feed is stopped and the tubes are warmed to cause partial melting called sweating to remove impurities that may be bonded to the crystal layer This is followed by complete melting of the remaining layer which is of high purity During the initial crystallization phase melt is circulated at a high rate com pared to the crystallization rate so that a uniform tempera ture and melt composition are approached down the length of the tube The coolant also flows as a film down along the out side surface of the tubes Consider the freezing step in a fallingfilm crystallizer for which a temperature profile is shown in Figure 1723 Melt enters at the top of the tube and flows as a film down the inside wall A coolant at a temperature below the freezing point of the melt also enters at the top and flows as a film down the Ripening vessel Scraper Screw Crystal slurry Circulation pump Feed Cooling medium Screw Figure 1721 Twostage scrapedwall melt crystallizer Melt inlet Melt outlet Coolingheating medium in Coolingheating medium out Collector Falling film melt Falling film heat carrier Distribution heat carrier Distribution melt Figure 1722 Sulzer fallingfilm melt crystallizer 698 Chapter 17 Crystallization Desublimation and Evaporation C17 09222010 Page 705 heattransfer coefficients This type of evaporator is not suitable for very viscous solutions c Longverticaltube evaporator By lengthening the vertical tubes and providing a separate vaporliquid dis engagement chamber as shown in Figure 1731c a higher liquid velocity can be achieved and thus an even higher heattransfer coefficient d Forcedcirculation evaporator To handle very viscous solutions a pump is used to force the solution upward through relatively short tubes as shown in Figure 1731d e Fallingfilm evaporator This unit shown in Figure 1731e is popular for concentrating heatsensitive solu tions such as fruit juices The solution enters at the top and flows as a film down the inside walls of the tubes Concen trate and vapor produced are separated at the bottom 17101 BoilingPoint Elevation For a given pressure in the vapor space of an evaporator the boiling temperature of an aqueous solution will be equal to that of pure water if the solute is not dissolved but consists of small insoluble colloidal material If the solute is soluble the boiling temperature will be greater than that of pure water Boiling temperature of water F Boiling temperature of solution F 0 0 50 100 150 200 250 300 350 50 100 150 200 250 300 350 400 450 x mass fraction NaOH 0 010 070 065 060 050 055 045 040 030 020 035 Figure 1732 Duhring chart for aqueous solutions of sodium hydroxide From WL McCabe JC Smith and P Harriott Unit Operations of Chemi cal Engineering 5th ed McGrawHill New York 1993 with permission NaNO3 340 320 300 280 260 240 220 200 180 160 140 120 100 120 110 100 90 80 70 60 50 40 30 20 10 0 60 5045 40 35 30 25 20 15 10 5 55 0 2 4 6 8 10 12 Boiling point rise F Solution temperature F Boiling point rise F Example At 270F a 22 CaCl2 solution has a boilingpoint rise of 97F Note Points shown based mainly on atmospheric boiling point 60 55 50 45 40 35 30 25 20 15 Weight solids Weight solids Sucrose Citric acid Kraft liquid Glycerol NH42SO4 K2CO3 HNO3 CaCl2 MgCl2 NaCl NaOH KOH LiCl LiNO3 H2SO4 KCl CaNO32 Figure 1733 Nomograph for boilingpoint elevation of aqueous solutions From Perrys Chemical Engineers Handbook 6th ed RH Perry DW Green and JO Maloney Eds McGrawHill New York 1984 with permission 1710 Evaporation 705 C17 09222010 Page 719 crystallizer with external or internal circulation 2 con tinuous cooling crystallizer and 3 continuous vac uum evaporating crystallizer 8 The MSMPR crystallization model is widely used to simulate the continuous vacuum evaporating draft tube baffled crystallizer Some of the assumptions are perfect mixing of the magma no classification of crys tals uniform degree of supersaturation throughout the magma crystal growth rate independent of crystal size no crystals in the feed no crystal breakage uniform tem perature equilibrium in product magma between mother liquor and crystals constant and uniform nucleation rate due to secondary nucleation by crystal contact uniform crystalsize distribution and uniform crystal shape 9 For a specified crystallizer feed magma density magma residence time and predominant crystal size the MSMPR model can predict the required nucleation rate and crystalgrowth rate number of crystals produced per unit time and size distribution 10 Precipitation leading to very small crystals occurs with solutes that are only sparingly soluble The precipitate is often produced by reactive crystallization from the addi tion of two soluble salt solutions producing one soluble and one insoluble salt Unlike solution crystallization which takes place at a low degree of supersaturation precipitation occurs at a high supersaturation that results in very small crystals 11 When both components of a mixture can be melted at reasonable temperatures eg certain mixtures of organic compounds melt crystallization can be used to separate the components If the components form a eutectic mixture pure crystals of one of the components can be formed However if components form a solid solution repeated stages of melting and crystallization are required for high purity 12 Many crystallizer designs have been proposed for melt crystallization Two major methods are suspension crys tallization and layer crystallization Of particular impor tance is the fallingfilm crystallizer which can be designed for high production rates when the components form eutectic mixtures For components that form solid solutions the zonemelting technique developed by Pfann can be employed to produce nearly pure compounds 13 A number of chemicals are amenable to purification by desublimation preceded perhaps by sublimation Desu blimation is almost always achieved by cooling a gas mixture at constant pressure by heat transfer quenching with a vaporizable liquid or quenching with a cold non condensable gas 14 Evaporation is used to concentrate a solute prior to solu tion crystallization Common evaporators include the horizontaltube unit shortverticaltube unit long verticaltube unit forcedcirculation unit and falling film unit For a given evaporation pressure the presence of a solute can cause a boilingpoint elevation 15 The most widely used evaporator model assumes the liquor being evaporated is wellmixed so the temperature and sol ute concentration are uniform and at exiting conditions 16 Economy of an evaporator is defined as the mass ratio of water evaporated to heating steam required It can be increased by using multiple evaporator effects that operate at different pressures such that vapor produced in one effect can be used as heating steam in a subsequent effect The solution being evaporated can progress through the effects in forward backward or mixed directions 17 Evaporators typically operate so that solutions are in the nucleateboiling regime Overall heattransfer coeffi cients are generally high because boiling occurs on one side and condensation on the other side of the tubes 18 Crystallization of bioproducts takes advantage of decreased solubility upon cooling pH adjustment or slow addition of salts and use of nonionic polymers or organic solvents to produce stable highpurity crystals in an attractive final form Sugars antibiotics enzyme inhibitors and proteins are common examples of bio products requiring crystallization 19 Primary and secondary nucleation of bioproduct crys tals followed by growth via diffusion and lattice incor poration is characterized by semiempirical powerlaw expressions Together with solubility data these expres sions are useful to obtain operating curves for cooling or solvent addition to maintain supersaturation and produce large uniform bioproduct crystals 20 Expressions for crystalsize distributions due to diffu sion or kineticcontrolled growth and dilution crystalli zation are useful for characterizing final bioproducts and selecting operating parameters to achieve targeted size distributions 21 Uniform mixing is key to maintaining constant condi tions in order to achieve targeted predicted crystalsize distributions for bioproducts and maintain performance during scaleup Jet impingement and teemixing pro vide highenergy dissipation that minimizes eddy length and mixing times in crystallization REFERENCES 1 Mullin JW Crystallization 3rd ed ButterworthHeinemann Boston 1993 2 Graber TA and ME Taboada Chem Eng Ed 25 102105 1991 3 Hougen OA KM Watson and RH Ragatz Chemical Process Principles Part I Material and Energy Balances 2nd ed John Wiley Sons 1954 4 Miers HA and F Isaac Proc Roy Soc A79 322351 1907 5 Nielsen AE Kinetics of Precipitation Pergamon Press New York 1964 6 Noyes AA and WR Whitney J Am Chem Soc 19 930934 1897 7 Nernst W Zeit fur Physik Chem 47 5255 1904 References 719 C17 09222010 Page 720 8 Miers HA Phil Trans A202 492515 1904 9 Valeton JJP Zeit fur Kristallographie 59 483 1924 10 Myerson AS Ed Handbook of Industrial Crystallization Butterworth Heinemann Boston 1993 11 Burton WK N Cabrera and FC Frank Phil Trans A243 299358 1951 12 Seavoy GE and HB Caldwell Ind Eng Chem 32 627636 1940 13 Newman HH and RC Bennett Chem Eng Prog 553 6570 1959 14 Randolph AD AIChE Journal 11 424430 1965 15 Randolph AD and MA Larson Theory of Particulate Processes 2nd ed Academic Press New York 1988 16 McCabe WL Ind Eng Chem 21 3033 and 112119 1929 17 Zumstein RC and RW Rousseau AIChE Symp Ser 83253 130 1987 18 Nielsen AE Kinetics of Precipitation Pergamon Press Oxford England 1964 19 Nielsen AE Chapter 27 in IM Kolthoffand PJ Elving Eds Trea tise on Analytical Chemistry Part 1 Volume 3 2nd ed John Wiley Sons New York 1983 20 Nielsen AE J Crys Gr 67 289310 1984 21 Fitchett DE and JM Tarbell AIChE J 36 511522 1990 22 Matsuoka M M Ohishi A Sumitani and K OhoriWorld Congress III of Chemical Engineers Tokyo Sept 21 1986 pp 980983 23 Wilcox WR Ind Eng Chem 603 1323 1968 24 Wynn N Chemical Engineering 987 149154 1991 25 Pfann WG Trans AIME 194 747 1952 26 Pfann WG Zone Melting 2nd ed John Wiley Sons New York 1966 27 Zief M and WR Wilcox Fractional Solidification Marcel Dekker New York 1967 28 Burris Jr L CH Stockman and IG Dillon Trans AIME 203 1017 1955 29 Herington EFG Zone Melting of Organic Compounds John Wiley Sons New York 1963 30 Nord M Chem Eng 589 157166 1951 31 Kudela L and MJ Sampson Chem Eng 9312 9398 1986 32 Holden CA and HS Bryant Sep Sci 41 113 1969 33 Singh NM and RK Tawney Ind J Tech 9 445447 1971 34 Poling BE JM Prausnitz and JP OConnell The Properties of Gases and Liquids 5th ed McGrawHill Book Co New York p 8191 2001 35 McCabe WL Trans AIChE 31 129164 1935 36 Geankoplis CJ Transport Processes and Unit Operations 3rd ed Prentice Hall Englewood Cliffs NJ 1993 37 Jacobsen C J Garside and M Hoare Biotechnol Bioeng 57 666 1998 38 McCabe WL JC Smith and P Harriott Unit Operations in Chemi cal Engineering 6th ed McGraw Hill New York 2000 39 Hajko P T Vesel I Radez and M Pokorny US Patent 5712130 1998 40 Harrison RG and LP NellesUS Patent 4956290 1990 41 Judge RA MR Johns and ET White Biotechnol Bioeng 48 316 1995 42 Ring TA Fundamentals of Ceramic Powder Processing and Synthe sis Academic Press San Diego 1996 43 Belter PA EL Cussler and WS Hu Bioseparations Downstream Processing for Biotechnology John Wiley Sons New York 1988 44 Nallet V D Mangin and JP Klein Mixing and Crystallization Kluwer Academic Publishers Boston 1998 45 Garcia AA MR Bonen J RamirezVick M Sadaka and A Vuppu Bioseparation Process Science Blackwell Science Malden MA 1999 46 Tavare NS J Garside and MR Chivate Ind Eng Chem Process Des Dev 19 653665 1980 47 Tosun G Ind Eng Chem Res 26 11841193 1987 48 Kamerath NR M S Thesis University of Utah 2008 49 Harrison RG P Todd SR Rudge and DP Petrides Bioseparations Science Engineering Oxford University Press New York 2003 50 de Nevers N Fluid Mechanics for Chemical Engineers 3rd ed McGraw Hill New York 2004 51 Baird CT Guide to Petroleum Product Blending HPI Consultants Inc 1989 52 Shuler ML and F Kargi Bioprocess EngineeringBasic Concepts 2nd ed Prentice Hall PTR Upper Saddle River NJ 2002 53 Tavare NS and MR Chivate J Chem Eng Jpn 13 371 1980 STUDY QUESTIONS 171 How does solution crystallization differ from melt crystallization 172 Under what conditions does precipitation occur 173 What are the two main methods used to cause crystalliza tion from an aqueous solution Which is more common and why 174 What is the difference between crystallization and desublimation 175 What is the difference between mother liquor and magma 176 Why are crystals never spherical in shape 177 What is meant by crystal habit 178 What is the difference between differential screen analysis and cumulative screen analysis 179 Does the solubility of most inorganic compounds in water increase or decrease with temperature 1710 Can an inorganic compound have more than one form of hydrate 1711 Does the commonly reported solubility of an inorganic compound in water pertain to large crystals or small crystals Why 1712 What is supersaturation Under what conditions is it possi ble to supersaturate a solution What is the metastable region 1713 In physical adsorption the resistance to the rate of adsorp tion at the solidfluid interface is negligible Is that also true for the incorporation of the solute into the crystallattice structure for solu tion crystallization If not why 1714 Why is the drafttube baffled DTB crystallizer popular What are its main features What is a draft tube 1715 What is a eutectic What is the difference between a eutec ticforming system and a solidsolutionforming system 720 Chapter 17 Crystallization Desublimation and Evaporation C18 09292010 Page 731 a Single downflow section b Multiple sections Figure 185 Perforatedbelt or bandconveyor dryer Table 182 Materials Dried in ThroughCirculation Conveyor Dryers Aluminum hydrate scored on filter Aluminum stearate extruded Asbestos fiber Breakfast food Calcium carbonate extruded Cellulose acetate granulated Charcoal briquetted Cornstarch Cotton linters Cryolite granulated Dye intermediates granulated Fluorspar Gelatin extruded Kaolin granulated Lead arsenate granulated Lithopone extruded Magnesium carbonate extruded Mercuric oxide extruded Nickel hydroxide extruded Polyacrylic nitrile extruded Rayon staple and waste Sawdust Scoured wool Silica gel Soap flakes Soda ash Starch scored on filter Sulfur extruded Synthetic rubber briquetted Tapioca Titanium dioxide extruded Zinc stearate extruded a Turbotray tower dryer b Detail of annular shelf Circular shelves Discharge Feed Turbines fans Heating elements 1 2 3 Cooling zone Drying zones Turbo fan Stationary wiper Stationary leveler Material falling to tray below Pile of material from tray above Slots Figure 186 Rotatingshelf dryer 181 Drying Equipment 731 C18 09292010 Page 732 granular solids Annular shelves mounted one above the other are slowly rotated at up to 1 rpm by a central shaft Wet feed enters through the roof onto the top shelf as it rotates under the feed opening At the end of one revolution a stationary wiper causes the material to fall through a radial slot onto the shelf below where it is spread into a pile of uni form thickness by a stationary leveler This action is repeated on each shelf until the dried material is discharged from the bottom of the unit Also mounted on the central shaft are fans that provide crosscirculation of hot gases at velocities of 2 to 8 fts across the shelves and heating elements located at the units outer periphery The bottom shelves can be used as a solidscooling zone Because solids are showered through the hot gases and redistributed from shelf to shelf drying time is less than for crosscirculation stationarytray dryers Typical turbotray dryers are from 2 to 20 m in height and 2 to 11 m in diameter with shelf areas to 1675 m2 Overall heattransfer coefficients based on shelf area of 30120 Jm2sK have been observed giving moistureevaporation rates comparable to those of throughcirculation belt or bandconveyor dryers Materials successfully handled in turbotray dryers include calcium hypochlorite urea calcium chloride sodium chloride antibiotics antioxidants and watersoluble polymers Capacities of up to 24000 lbh of dried product are quoted DirectHeat Rotary Dryers A popular dryer for evaporating water from freeflowing granular crystalline and flaked solids of relatively small size when breakage of solids can be tolerated is the direct heat rotary dryer As shown in Figure 187a it consists of a rotating cylindrical shell that is slightly inclined from the horizontal with a slope of less than 8 cmm Wet solids enter through a chute at the high end and dry solids discharge from the low end Hot gases heated air flue gas or superheated Dry solids discharge D E C B J Steam A B C D E F G J Dryer shell Shellsupporting rolls Drive gear Gasdischarge hood Exhaust fan Feed chute Lifting flights Air heater Moist air outlet Feed G A A G B F Air inlet Steam condensate a Rotary dryer b Lifting flights Radial flights 45 lip flights Hotair chambers Hotair inlet Wetfeed inlet Product outlet Exhaustgas outlet Air flowthrough louvers and material c Rotolouvre dryer Figure 187 Directheat rotary dryer From WL McCabe JC Smith and P Harriott Unit Operations of Chemical Engineering 5th ed McGraw Hill New York 1993 with permission From Perrys Chemical Engineers Handbook 6th ed RH Perry DW Green and JO Maloney Eds McGrawHill New York 1984 with permission 732 Chapter 18 Drying of Solids C18 09292010 Page 733 steam flow countercurrently to the solids but cocurrent flow can be employed for temperaturesensitive solids With cocurrent flow the cylinder may not need to be inclined because the gas will help move the solids To enhance the gas tosolids heat transfer longitudinal lifting flightsavailable in several different designs two of which are shown in Figure 187bare mounted on the inside of the rotating shell causing the solids to be lifted then showered through the hot gas during each cylinder revolution Typically the bulk solids occupy 8 18 of the cylinder volume with residence times from 5 min utes to 2 h Resulting waterevaporation rates are 550 kghm3 of dryer volume The gas blower can be located to push or pull the gas through the dryer with the latter favored if the material tends to form dust Knockers on the outside shell wall can be used to prevent solids from sticking to the inside shell wall Rotary dryers are available from 1 to 20 ft in diameter and 4 150 ft long Superficialgas velocities which may be limited by dust entrainment are 0510 fts The peripheral shell ve locity is typically 1 fts A variety of materials some of which are listed in Table 183 are dried in directheat rotary dryers The detailed mechanical designs of rotary dryers are industry specific in the sense that the standard designs are modified to accommodate starch sugar salt cement and other products each of which has unique surface and bulk properties RotoLouvre Dryers A further improvement in the rate of heat transfer from hot gas to solids in a rotating cylinder is the throughcirculation action achieved in the RotoLouvre dryer in Figure 187c A double wall provides an annular passage for hot gas which passes through louvers and then through the rotating bed of solids Because gas pressure drop through the bed may be significant both inlet and outlet gas blowers are often pro vided to maintain an internal pressure close to atmospheric These dryers range from 3 to 12 ft in diameter and 936 ft long with waterevaporation rates reported as high as 12300 lbhr They are useful for processing coarse freeflowing dustfree solids IndirectHeat SteamTube Rotary Dryers When materials are 1 free flowing and granular crystal line or flaked 2 wet with water or organic solvents andor 3 subject to undesirable breakage dust formation or con tamination by air or flue gases an indirectheat steamtube rotary dryer is often selected A version of this dryer shown in Figure 188 consists of a rotating cylinder that houses two concentric rows of longitudinal finned or unfinned tubes that carry condensing steam and rotate with the cylinder Wet sol ids are fed into one end of the cylinder through a chute or by a screw conveyor A gentle solidslifting action is provided by the tubes Dried product discharges from the other end Table 183 Materials Dried in DirectHeat Rotary Dryers Ammonium nitrate prills Sand Ammonium sulfate Sodium chloride Blast furnace slag Sodium sulfate Calcium carbonate Stone Castiron borings Polystyrene Cellulose acetate Sugar beet pulp Copper Urea crystals Fluorspar Urea prills Illmenite ore Vinyl resins Oxalic acid Zinc concentrate Wet material fed in here Dust drum Section of AA Section through steam manifold R o t a t i o n A A Dried material discharge conveyor Steam manifold Steam neck Figure 188 Indirectheat steamtube rotary dryer From Perrys Chemical Engineers Handbook 6th ed RH Perry DW Green and JO Maloney Eds McGrawHill New York 1984 with permission 181 Drying Equipment 733 C18 09292010 Page 735 bed to expand with little or no increase in gas pressure drop Typically fluidizedbed dryers are designed for gas velocities of no more than twice the minimum required for fluidization That value depends on particle size and density and gas den sity and viscosity Superficialgas velocities in fluidizedbed dryers are from 05 to 50 fts which provide stable bubbling fluidization Higher velocities can lead to undesirable slug ging of large gas bubbles through the bed The capital and operating cost of a blower to provide suffi cient gas pressure for the pressure drops across the distributor plate and the bed is substantial Therefore required solids residence time for drying is achieved by a shallow bed height and a large chamber crosssectional area Fluidizedbed heights can range from 05 to 50 ft or more with chamber diameters from 3 to 10 ft However chamber heights are much greater than fluidizedbed heights because it is desir able to provide at least 6 ft of freeboard height above the top surface of the fluidized bed unless demisters are installed so that the larger dust particles can settle back into the bed rather than be carried by the gas into the cyclone Because of intense mixing temperatures of the gas and solids in a fluid ized bed are equal and uniform at the temperature of the dis charged gas and solids There is a substantial residencetime distribution for the particles in the bed which can be mitigated by baffles multi staging and mechanical agitators Otherwise a fraction of the particles shortcircuit from the feed inlet to the discharge duct with little residence time and opportunity to dry Another frac tion of the particles spend much more than the necessary resi dence time for complete drying Thus the nonuniform moisture content of the product solids may not meet specifica tions When the final moisture content is critical it may be advisable to smooth out the residencetime distribution by using a more elaborate multistage fluidizedbed dryer such as the one shown in Figure 1810b Alternatively the stages can be arranged side by side horizontally Starch dryers have been fabricated with 20 such stages Materials that are successfully dried in fluidizedbed dryers include coal sand limestone iron ore clay granules granular fertilizer granular desiccant sodium perborate polyvinylchloride PVC starch sugar coffee sunflower seeds and salt Large fluidizedbed dryers for coal and iron ore produce more than 500000 lbh of dried material For metallurgical applications and catalyst regenera tion fluidized beds are frequently heated electrically and carry price tags of from three to six million dollars depending on the temperature and metallurgy requirements Dry product discharge Air inlet Heat source a Single bed b Multiple beds Plenum Fluidizing blower Clean gas discharge Stack Dust collector Wet feed Fluidizing chamber Feeder Distributor plate Gas Dry material Wet material To cyclone Figure 1810 Fluidizedbed dryers From WL McCabe JC Smith and P Harriott Unit Operations of Chemical Engineering 5th ed McGrawHill New York 1993 with permission 181 Drying Equipment 735 C18 09292010 Page 739 Conveyor Conveyor a Doubledrum dryer b Twindrum dryer with top feed Steamheated drum Feed pipe Steamheated drum Knife Knife Drum Drum Feed pipe Knife Knife Applicator roll Drum Drum Knife Knife c Twindrum dryer with splash feed d Singledrum dryer with applicator feed Drum Knife Manhole Drum Drum Pendulum feed Conveyor Conveyor Knife Knife Vapor outlet e Vacuum doubledrum dryer Figure 1814 Drum dryers 181 Drying Equipment 739 C18 09292010 Page 760 average moisture content at which the constantrate period ends and the fallingrate period begins is called the critical moisture content Xc In the empirical approach to the fallingrate period Xc must be known from experiment for the particular conditions because Xc is not a constant for a given material but depends on a number of factors including moisture diffusivity slab thickness initial and equilibrium moisture contents and all factors that influence moisture evaporation in the constantrate drying period A useful aspect of 1851 is that it can be used to predict Xc The basis for the prediction is the assumption that the fallingrate period will begin when the moisture content at the surface reaches the equilibriummoisture content corresponding to the conditions of the surrounding gas This prediction is facilitated as described by Walker et al 21 by replotting an extension of Curve 1 in Figure 1835a for the moisture content at the surface Xs in the form shown in Figure 1835b Use of Figure 1835b and the predicted influence of several variables on the value of Xc is illustrated in the fol lowing example a Moisture profile change 10 01 001 0001 00001 0001 001 NFoM DABta2 01 10 Xo X DAB ρsRca Constantrate drying with evaporation at surface Curve 1 surface 1 za 0 1 za 1 8 1 za 1 4 1 za 1 2 1 za Midplane 1 za 1 3 4 10 01 001 001 01 Xo XsDAB ρsRca 10 100 Xo XavgXo Xs Constantrate drying with evaporation at surface b Surface moisture change Figure 1835 Changes in moisture concentration during constantrate period while diffusion in the solid occurs From WH Walker WK Lewis WH McAdams and ER Gilliland Principles of Chemical Engineering 3rd ed McGrawHill New York 1937 with permission 760 Chapter 18 Drying of Solids C18 09292010 Page 770 Bed height To achieve the average residence time of 132 minutes ¼ 022 h the expandedbed volume and corresponding bed height must be Vb ¼ mst rb ¼ 8330 022 ð Þ 66 ¼ 278 ft3 Hb ¼ Vb pD24 ¼ 278 4 ð Þ 314 47 ð Þ2 ¼ 16 ft 186 DRYING OF BIOPRODUCTS The selection of a dryer is often a critical step in the design of a process for the manufacture of a bioproduct As discussed in several chapters of the Handbook of Industrial Drying 32 drying may be needed to preserve required properties and maintain activity of bioproducts If a proper drying method is not selected or adequately designed the bioprod uct may degrade during dewatering or exposure to elevated temperatures For example the bioproduct may be subject to oxidation and thus require drying in a vacuum or in the pres ence of an inert gas It may degrade or be contaminated in the presence of metallic particles requiring a dryer constructed of polished stainless steel Enzymes may require pH control during drying to prevent destabilization Some bioproducts may require gentle handling during the drying process Of major concern is the fact that many bioproducts are thermolabile in that they are subject to destruction decom position or great change by moderate heating Table 187 lists several examples of bioproduct degradation that can occur during drying at elevated temperatures As shown the Table 187 Examples of Degradation of Bioproducts at Elevated Temperatures Product Type of Reaction Degradation Processes Result Live microorganisms Microbiological changes Destruction of cell membranes Denaturation of protein Death of cells Lipids Enzymatic reactions Peroxidation of lipids discoloration of the product Reaction with other components including proteins and vitamins Proteins Enzymatic and chemical reactions Total destruction of amino acids Denaturation of proteins and enzymes Derivation of some individual amino acids Partial denaturation loss of nutritive value Crosslinking reaction between amino acids Change of protein functionality Enzyme reaction Polymer carbohydrates Chemical reactions Gelatination of starch Improved digestibility and energy utilization Hydrolysis Fragmentation of molecule Vitamins Chemical reactions Derivation of some amino acids Partial inactivation Simple sugars Physical changes Caramelization MaillardBrowning reaction Loss of color and flavor Melting Source Handbook of Industrial Drying 32 Table 188 Selection of Dryer for Representative Bioprocesses Bioproduct Dryer Type Comments Citric acid Fluidizedbed dryer Feed is wet cake from a rotary vacuum filter Pyruvic acid Fluidizedbed dryer Feed is wet cake from a rotary vacuum filter LLysine amino acid Spray dryer Feed is solution from an evaporator Riboflavin Vitamin B2 Spray dryer Feed is solution from a decanter aCyclodextrin polysaccharide Fluidizedbed dryer Feed is wet cake from a rotary vacuum filter Penicillin V acid Fluidizedbed dryer Feed is a wet cake from a basket centrifuge Recombinant human serum albumin protein Freezedryer Feed is from sterile filtration Recombinant human insulin protein Freezedryer Feed is wet cake from a basket centrifuge Monoclonal antibody cell No dryer Product is a phosphatebuffered saline PBS solution a1Antitrypsin protein No dryer Product is a PBS solution Plasmid DNA parasitic DNA No dryer Product is a PBS solution 770 Chapter 18 Drying of Solids C18 09292010 Page 771 result of such exposure is serious and unacceptable To avoid such degradation many bioproducts are dried at nearambient or cryogenic temperatures The most widely used dryers for sensitive bioproducts particularly solutions of enzymes and other proteins are spray dryers and freeze dryers ie lyophilizers 33 34 Heinzle et al 35 consider dryer selection for 11 different bioprocesses as listed in Table 188 The bioproducts cover more than a sevenfold range of product value and more than a sixfold range of annual production rate as shown in Figure 1839 It is interesting to note that the three most expensive bioproducts are not dried but produced as phosphate buffered saline solutions The leastexpensive and highest volume bioproducts use either fluidizedbed or spray dryers The fluidizedbed dryers are used with relatively stable bio molecules and operate at nearambient temperatures The two bioproducts at intermediate levels of price and volume use freezedryers Intermittent Drying of Bioproducts As discussed in 138 batchdistillation operations can be improved by controlling the reflux ratio Similarly batch drying operations can be improved particularly for heatsen sitive bioproducts by varying conditions during the drying operation This technique is referred to as intermittent dry ing Although the concept has been known for decades it is only in recent years that it has received wide attention as dis cussed by Chua et al 36 The intermittent supply of heat is beneficial for materials that begin drying in a constantrate period but dry primarily in the fallingrate period where the rate of drying is controlled by internal heat and mass transfer In traditional drying the external conditions are constant and the surface temperature of the material being dried can rise to unacceptable levels In intermittent drying the external con ditions are altered so that the surface temperature does not exceed a limiting value In the simplest case the heat input to the material is reduced to zero during a socalled temper ing phase while interior moisture moves to the surface so that a constantrate period can be resumed The benefits of intermittent drying have been demonstrated for a number of products including grains potatoes guavas bananas car rots rice corn clay cranberries apples peanuts pineapples sugar beans ascorbic acid and bcarotene SUMMARY 1 Drying is the removal of moisture water or another volatile liquid from wet solids solutions slurries and pastes 2 The two most common modes of drying are direct by heat transfer from a hot gas and indirect by heat trans fer from a hot wall The hot gas is frequently air but can be combustion gas steam nitrogen or any other non reactive gas 3 Industrial drying equipment can be classified by opera tion batch or continuous mode direct or indirect or the degree to which the material being dried is agitated Batch dryers include tray dryers and agitated dryers Continuous dryers include tunnel belt or band turbo tray tower rotary screwconveyor fluidizedbed spoutedbed pneumaticconveyor spray and drum Dry ing can also be accomplished with electric heaters infra red radiation radio frequency and microwave radiation and also from the frozen state by freezedrying 4 Psychrometry which deals with the properties of air water mixtures and other gasmoisture systems is use ful for making drying calculations Psychrometric humidity charts are used for obtaining the temperature at which surface moisture evaporates 5 For the airwater system the adiabaticsaturation tem perature and the wetbulb temperature are by coinci dence almost identical Thus surface moisture is evaporated at the wetbulb temperature This greatly simplifies drying calculations 6 Most wet solids can be grouped into one of two categories Granular or crystalline solids that hold moisture in open pores between particles can be dried to very low moisture contents Fibrous amorphous and gellike materials that dissolve moisture or trap it in fibers or very fine pores can be dried to low moisture contents only with a gas of low humidity The second category of materials can exhibit a significant equilibriummoisture content that depends on temperature pressure and humidity of the gas 7 For drying calculations moisture content of a solid and a gas is usually based on the bonedry solid and bonedry gas The boundmoisture content of a material in contact with a gas is the equilibriummoisture content when the gas is saturated with the moisture The excessmoisture Figure 1839 Price and production volume of representative bioproducts 35 Summary 771 C18 09292010 Page 772 content is the unboundmoisture content When a gas is not saturated excess moisture above the equilibrium moisture content is the freemoisture content Solid materials that can contain bound moisture are hygro scopic Bound moisture can be held chemically as water of hydration 8 Drying by direct heat often takes place in four periods The first is a preheat period accompanied by a rise in temperature but with little moisture removal This is fol lowed by a constantrate period during which surface moisture is evaporated at the wetbulb temperature This moisture may be originally on the surface or moisture brought rapidly to the surface by diffusion or capillary action The third period is a fallingrate period during which the rate of drying decreases linearly with time with little change in temperature A fourth period may occur when the rate of drying falls off exponentially with time and the temperature rises 9 Drying rate in the constantrate period is governed by the rate of heat transfer from the gas to the surface of the solid Empirical expressions for the heattransfer co efficient are available for different types of directheat dryers 10 The drying rate in the fallingrate period can be deter mined by using empirical expressions with experimental data Diffusion theory can be applied in some cases when moisture diffusivity is available or can be measured 11 For directheat dryer models material and energy bal ances are used to determine rates of heat transfer from the gas to the wet solid and the gas flow rate 12 A useful model for a twozone belt dryer with through circulation describes the changes in solidsmoisture con tent both vertically through the bed and in the direction of belt travel 13 A model for preliminary sizing of a directheat rotary dryer is based on the use of a volumetric heattransfer coefficient assuming that the gas flows through curtains of cascading solids 14 A model for sizing a large fluidizedbed dryer is based on the assumption of perfect solids mixing in the dryer when operating in the bubblingfluidization regime The procedure involves taking dryingtime data from batch operation of a laboratory fluidizedbed dryer and correct ing it for the expected solidparticleresidencetime dis tribution in the large dryer 15 Many bioproducts are thermolabile and thus require careful selection of a suitable dryer Most popular are fluidizedbed dryers spray dryers and freezedryers REFERENCES 1 Handbook of Industrial Drying 2nd ed AS Mujumdar Ed Marcel Dekker New York 1995 2 Perrys Chemical Engineers Handbook 8th ed DW Green and RH Perry Eds McGrawHill New York 2008 3 Walas SM Chemical Process Equipment Butterworths Boston 1988 4 vant Land CM Industrial Drying Equipment Marcel Dekker New York 1991 5 Uhl VW and WL Root Chem Eng Progress 58 3744 1962 6 McCormick PY in Encyclopedia of Chemical Technology 4th ed John Wiley Sons New York Vol 8 pp 475519 1993 7 Keey RB Introduction to Industrial Drying Operations Pergamon Press Oxford 1978 8 Lewis WK Mech Eng 44 445446 1922 9 Faust AS LA Wenzel CW Clump L Maus and LB Anderson Principles of Unit Operations John Wiley Sons New York 1960 10 Luikov AV Heat and Mass Transfer in CapillaryPorous Bodies Pergamon Press London 1966 11 Sherwood TK Ind Eng Chem 21 1216 1929 12 Sherwood TK Ind Eng Chem 21 976980 1929 13 Marshall WR Jr and OA Hougen Trans AIChE 38 91121 1942 14 Gamson BW G Thodos and OA Hougen Trans AIChE 39 135 1943 15 Wilke CR and OA Hougen Trans AIChE 41 445451 1945 16 Hougen OA HJ McCauley and WR Marshall Jr Trans AIChE 36 183209 1940 17 Carslaw HS and JC Jaeger Heat Conduction in Solids 2nd ed Oxford University Press London 1959 18 Newman AB Trans AIChE 27 310333 1931 19 Sherwood TK Ind Eng Chem 24 307310 1932 20 Gilliland ER and TK Sherwood Ind Eng Chem 25 11341136 1933 21 Walker WH WK Lewis WH McAdams and ER Gilliland Princi ples of Chemical Engineering 3rd ed McGrawHill New York 1937 22 Ceaglske NH and FC Kiesling Trans AIChE 36 211225 1940 23 Keey RB Drying Principles and Practice Pergamon Press Oxford 1972 24 Genskow LR Ed ScaleUp of Dryers in Drying Technology 121 2 1416 1994 25 Thygeson JR Jr and ED Grossmann AIChE Journal 16 749754 1970 26 Matchett AJ and MS Sheikh Trans Inst Chem Engrs 68 Part A 139148 1990 27 McCormick PY Chem Eng Progress 586 5761 1962 28 Schofield FR and PG Glikin Trans Inst Chem Engrs 40 183 190 1962 29 Langrish TAG RE Bahu and D Reay Trans Inst Chem Engrs 69 Part A 417424 1991 30 Ergun S Chem Eng Progr 48 2 8994 1952 31 Fogler HS Elements of Chemical Reaction Engineering 3rd ed PrenticeHall Upper Saddle River NJ 1999 32 Handbook of Industrial Drying 3rd ed AS Mujumdar Ed Taylor and Francis Boca Raton FL 2007 772 Chapter 18 Drying of Solids PART05 07282010 22610 Page 777 Part Five Mechanical Separation of Phases Previous chapters of this book deal with separation of chemical species in a mixture by phase creation distil lation drying phase addition absorption extraction transport through a barrier membrane addition of a solid agent adsorption and the imposition of a force field or gradient electrophoresis In previous chapters descriptions of these processes focused on the move ment of species and heat and momentum transfer from one phase to another to achieve a processing goal However for many separations transfer of species heat and momentum from one phase to another does not complete the process because the phases must then be disengaged This is done using mechanical phase separation devices such as filters precipitators settlers and centrifuges whose function and design is the sub ject of Chapter 19 Exceptions occur in distillation absorption stripping and extraction columns where phase separation takes place in the column 777 C19 10042010 Page 781 capturing a 6mm particle and a 99 efficiency for capturing a 25mm particle The nomenclature in this field is far from standardized The term aerosol for example is used to describe suspended liquid or solid particles that are slow to settle be they sub micron or 50 mm in size Mists are generally described as particles upward of 01 mm in size that arise because of vapor condensation Sprays are the result of intentional or unintentional atomization processes In developing a flowsheet for a particlecollection system it is well to remember the strongest of the process design heuristics Cheapest first In terms of the devices listed in Table 192 this means removing large particles by inexpensive settling chambers vane arrays or impingement devices and then removing the small amount of remaining particles with the highercapitalcost units like membranes centrifuges or electric precipitators 192 INDUSTRIAL PARTICLESEPARATOR DEVICES The operative mechanisms for the particle separators to be described are 1 gravity settling where the force field is ele vation 2 inertial including centrifugal impaction where the force field is a velocity gradient 3 flowline direct interception or impingement where the particle is assumed to have size but no mass and follows a streamline 4 diffu sional Brownian deposition where the force field is a con centration gradient 5 electrostatic attraction due to an electricfield gradient 6 agglomeration by particleparticle collisions and 7 sieving where the flow pathway is smaller than the particle Mechanisms 24 are depicted in Figure 192 Note that in interception the particle follows the stream line while in impaction it follows a direct path Generally devices that operate by a combination of mechanisms 2 and 3 combine impaction and interception in one empirical design equation In many devices synergistic mechanisms are used In cyclones for example gravity settling is abetted by centrif ugal force A generic consideration in collection devices is the problem of reentrainment The inertial forces that deposit a particle on a fiber can also blow the particle off the fiber Cy clones for example are more efficient for liquid droplets than for solid particles because droplets are more likely to coalesce and agglomerate at the bottom than are solid particles 1921 Gravity Settlers If the velocity of the carrier fluid is sufficiently low all parti cles whose density is above that of the carrier will eventually settle Terminal velocities of droplets and solid particles are such that the required size of the settling chamber usually Table 192 ParticleSize Ranges for Particle Capture Devices ParticleCapture Device Size Range mm Membranes 00000100001 Ultracentrifuges 00011 Electrical precipitators 000220 Centrifuge 0055 Cloth collectors 005500 Fiber panels and candles 01010000 Elutriation 1100 Air filters 250 Centrifugal separators 21000 Impingement separators 52000 Vane arrays 510000 Cyclones high efficiency 635 Filter presses 1050 Cyclones low efficiency 15250 Cloth and fibers 201000 Gravity sedimentation 4510000 Screens and strainers 501000 Sieving screens 5020000 Table 191 Typical Particle Sizes Particle Size mm Large molecules 00010004 Smoke 00051 Fume 00101 Tobacco smoke 001012 Smog 0011 Virus 00301 Mist 0110 Fog 0130 Spores 05180 Bacteria 0510 Prokaryotic cells 110 Dust 1100 Limit of visibility 1040 Liquid slurries 1050 Eukaryotic cells 10100 Drizzle 10400 Spray 101000 Pollen 2080 Mist 50100 Human hair 50200 Rain 1001400 Heavy industrial dust 1005000 Interception Diffusion Filter fiber Impaction Figure 192 Particlecollection mechanisms 192 Industrial ParticleSeparator Devices 781 C19 10042010 Page 782 becomes excessive for droplets smaller than 50 mm and for solid dusts smaller than 40 mm For solid particles air veloc ities greater than 10 fts lead to reentrainment of all but the heaviest particles In the horizontal settling chamber of Figure 193 the gas ve locity upon entering the chamber is greatly reduced The key design variable the particleresidence time computed as the length of the chamber divided by the gas velocity determines whether or not the chamber is long enough to allow the particle to fall to the bottom The width of the chamber must be such that the gas velocity is below the pickup velocity that will cause reentrainment For lowdensity materials such as starch this is 58 fts For gassolid systems settling chambers have advantages of minimal cost and maintenance rapid and simple construction low pressure drop and dry disposal of solids A crude classification of solids takes place in the sense that the first of the dustcollecting hoppers contains larger particles than the ones that follow but little use is made of that because particle sizes overlap Many variations of the simple enclosure in Figure 193 exist The height a particle has to fall can be decreased by banks of trays set within the chamber as in the Howard multitray settling chamber Baf fles can be used to direct the gas flow downward to add a momentum effect to the gravitational force Baffles and tortu ous paths also aid particle capture by inertial mechanisms but the cost in terms of pressure drop is high For solidliquid systems devices based on gravity are called sedimenting separators clarifiers thickeners flocculators and coagulators Coagulation is the precipitation of colloids by floc formation caused by addition of simple electrolytic salts which modify electrostatic forces between the particles and fluid The term flocculation is generally used to describe the action of watersoluble organic polymeric molecules that may or may not carry a charge such as polyacrylamide which promotes set tling Figure 194 depicts a liquidsettling device of the type widely used for wastewater treatment which is equipped with a slowly moving rake that revolves at about 2 rph and moves the sludge downward to promote particle agglomeration The vol ume of clear liquid produced depends primarily on the cross sectional area and is almost independent of the tank depth Liquidliquid gravity separators are important in the oil industry where mixtures of water and oil are commonplace and in the chemical industry where extractive distillations and liquidliquid extractions are carried out extensively In liquidliquid separators called decanters there is often a con tinuous phase with a discontinuous phase of dispersed drop lets The two phases must be held for a sufficient time for the droplets to settle if heavy or rise if light so that the two phases disengage cleanly A completely clean disengagement is a rarity because unless the liquids are unusually pure dirt and impurities concentrate at the interface to form a scum or worse yet an emulsion that must be drained off Figure 195 shows a continuousflow gravity decanter designed to separate an oil layer from a water layer that contains oil droplets It does not show the perforated underflow and interface baffles outlet nozzles or inlet flow distributors The unit does not run full and the design involves balanc ing the liquid heights due to the density difference of the phases and determining the settling velocities of droplets moving up or down from the dispersed to the continuous phase Needless to say rules of thumb and years of experi ence are required to design units that work well Some design methods are based on the time it takes particles to move through a semihypothetical interface between the heavy and light fluids Example 196 shows how the dimensions for a continuousflow decanter are obtained Methods for design ing a vertical decanter are given in Exercise 198 1922 Impaction and Interception Separators Inertial impaction and interception mechanisms shown above in Figure 192 consist of a particle colliding with a Gas in Gas out Dustcollecting hoppers Smaller particles Larger particles Figure 193 Horizontal settling chamber Drive Scum Trough Influent Well Skimmer Effluent Sludge DrawOff Scum DrawOff Influent Collector Arm Sludge Concentrator Figure 194 Liquid sedimentation and flocculation 782 Chapter 19 Mechanical Phase Separations C19 10042010 Page 783 target that can be anything from a screen a bed of fibers staggered channels or louvers Inertial forces accelerate large particles less than small particles and this coupled with reentrainment and variable drag coefficients due to shape make theoretical prediction of capture efficiency and velocity distributions within a cloth or mesh filter virtually impossible Instead impingement separators are designed on the basis of systemspecific constants provided by device manufacturers and used in conjunction with the Souders Brown equation 640 developed in 661 to describe droplet behavior in distillation columns 3 Also provided by the manufacturer are recommendations on allowable gas or liquid velocities and pressure drops For particlecapture devices performance parameters cannot be calculated from physical properties if the velocity is lower than what is rec ommended impingement of small particles may not take place and if it is too high reentrainment will occur In addi tion use is frequently made of generalized or devicespecific information regarding collection efficiency as a function of Reynolds number or particle size When impingement devices are used to capture liquid droplets they coalesce and the liquid must be drained from the collector device Often modern coalescence devices combine vane and channel impingements with waffled filters An endless array of governmental and industry standards and regulations apply to products manufactured for the pur pose of removing particles and contaminants from air streams Not only do public health laws with respect to the quality of the air emitted exist but there are also industry standards for how devices that impact the environment are to be tested Based on these tests products are graded and cate gorized This is typical for industrial products intended for a specific use such as filtering air for hospital operating rooms or removing oil mists generated by air compressors The Eurovent standards for flatpanel ventilation filters shown in Table 193 were set by the quasigovernmental agency the European Committee of Air Handling and Refrigeration Equipment Manufacturers and apply to both glassfiber me dia and synthetic organic fibers Parallel specifications have been set by American manufacturers and trade organizations Light phase overflow Top of light phase Light phase out Interface Heavy phase out Heavy phase Heavy phase out Light phase Drain interface Feed for emulsion Figure 195 Gravityflow decanter Table 193 CenEurovent Filter Classification Type Class Eurovent Designation Efficiency Measured by Coarse dust filter EU1 65 Synthetic dust EU2 6580 EU3 8090 EU4 90 Fine dust filter EU5 4060 Atmospheric EU6 6080 Dust spot EU7 8090 Efficiency EU8 9095 EU9 95 Highefficiency EU10 85 Sodium chloride particulate air EU11 95 or liquid filter HEPA EU12 995 aerosol EU13 9995 EU14 99995 Ultra low EU15 999995 Liquid aerosol penetration air EU16 9999995 filter ULPA EU17 99999995 192 Industrial ParticleSeparator Devices 783 C19 10042010 Page 784 such as the American Petroleum Institute API Not shown in this table are specifications regarding particle size but they do exist 4 Table 194 shows the internationally accepted grading sys tem for coalescing filter media used to capture liquid oil oil water emulsions and oil aerosols emitted by oillubricated compressors These are glass microfibers in the 05075 mm range which will trap up to 9999999 of oilwater aerosols and dirt particles in compressed air down to a size of 001 mm The mechanical sandwich construction of the twostage filter element held between stainless steel support sleeves is shown in Figure 196 Because of the coalescing filter medium the condensate is drained and the elements are self regenerative as far as removal of liquid is concerned How ever it is advisable that prefilters capable of removing parti cles down to 5 mm or less be placed in the line ahead of the coalescing filter or it will quickly be plugged In this table the coalescing efficiency was measured using 03006 mm particles based on 50 ppm maximum inlet concentration A welldesigned filtration system as shown in Figure 197 will have elements such as an inexpensive coarse particle prefilter collector like a screen filter or cyclone fol lowed by an extendedsurface filter that is effective down to the micron level and then a submicron filter where the veloc ity is lower and the particle capture is principally by Brownian motion andor sieving 1923 Fabric Collectors A very common industrial filtration device is a fabric dust col lector In industry multiple collectors are housed in enclosures called baghouses These are relatively inexpensive installations Prefilter media velocity Face velocity 25 ms Extended surface filter media velocity 011 ms HEPA filter media velocity 002 ms 13 ms 13 ms Interception diffusion Diffusion 25 ms 25 ms Viscous impingement Figure 197 Multistage filter system Figure 196 Brink fiberbed mist collector Courtesy of MECS Inc Table 194 CoalescingFilter Media Grades Pressure bar Grade Code Color Efficiency Coalescing Carryover Maximum Oil Dry Wet 2 green 99999 0001 mgm3 01 034 4 yellow 99995 0004 mgm3 0085 024 6 white 9997 001 mgm3 0068 017 8 blue 985 025 mgm3 0034 019 10 orange 95 10 mgm3 0034 005 784 Chapter 19 Mechanical Phase Separations C19 10042010 Page 785 capable of capturing particles down to 005 mm As shown in Figure 198 particles are collected on the outside of a fabric encased porous cylindrical candle The device has a vibratory or compressedair blowback system to remove the particles trapped on the outside of the filter element Liquids as well as solids are processed in units of this type For both liquids and gases as the particles on the cloth build up they form a cake that acts as a filter and often is a more effective filter than the fabric or screen This makes screen and fabric collectors sys tem specific there is no way to predict performance other than to take laboratory data because the filtering action of the cake cannot be predicted analytically 1924 Vanes and Louvers Another device that falls in the aerodynamicimpingement category is the vane or louvered particle collector Here the carrier fluid is forced through a maze changing direction frequently This type of device is most effective for collecting droplets or mists and fogs that coalesce and can then be drained from the system Most often if pressure drop allows vane units are used as prefilters for mesh filters particularly for very small droplets that coa lesce upon impingement 1925 Cyclones and Centrifuges For a centrifuge or cyclone centrifugal acceleration is substi tuted for gravitational acceleration in the appropriate fluid dynamics equations The complicating factors are that centrifu gal force depends on the distance from the axis of rotation which depends on the complex geometry and flow patterns in the device and that the concentration of particles may be so high that hindered by neighboring particlessettling equations are necessary A typical design method applied to a Podbiel niak centrifugal extractor was demonstrated in Example 811 This design strategy consists of finding the optimal conditions for the centrifuge from test runs using a small laboratory unit and then using a set of scientifically deduced semiempirical rules for scaleup to a large industrial unit This methodology as will be seen is also used to design cyclones Because cyclones are inexpensive and durable with a decent collection efficiency for particles larger than about 5 mm they are the most widely used device for industrial dust collection If the efficiency is not high enough multiple units can be placed in series The dustladen stream enters the top section of the cylindrical device tangentially which imparts a spinning motion Centrifugal force sends the particles to the wall where they agglomerate and fall to the bottom The spin ning gas also travels toward the wall but it reverses direction and leaves the device from a sleeve at the top whose bottom extends to below the inlet as shown in Figure 199 which includes standarddimension relations The path is usually axial there being an inner upflow vortex inside the downward vortex In liquid cyclones hydroclones the upward flow is separated from the downward flow by an outer jacket wherein the liquid flows up Separation depends on settling velocities particle properties and geometry of the device By directing the inlet flow tangent to the top of the cyclone centrifugal force can be utilized to greatly enhance particle collection Welldesigned cyclones can separate liquid droplets as small as 10 mm from an air stream Small cyclones are more efficient than large ones and can generate forces 2500 times that of gravity For solids reentrainment problems can be reduced by water sprays and vortex baffles at the outlet 1926 Electrostatic Precipitators Electrostatic precipitators are best suited for the collection of fine mists and submicron particles The first practical appli cation was fashioned by Cottrell in 1907 for abating sulfuric acid mists A particle suspended in an ionized gas stream within an electrostatic field will become charged and migrate to a collecting surface Care must be taken that the particles do not reentrain but are removed from the device Two types of devices are available one in which ionization and A DustLaden Air Inlet B Dust Hopper C Filter Bag TYP D Clean Air Plenum E Clean Air Outlet F Compressed Air Source G Bag Support Cage B A C G F D E Figure 198 Tubular bag filter with pulse jet cleaning 0375 DC 25 DC 15 DC 05 DC 05 DC 05 DC02 DC DC DC Collecting hopper diameter Figure 199 Standard highefficiency cyclone dimensions 192 Industrial ParticleSeparator Devices 785 C19 10042010 Page 788 delivery of the slurry to the filter cloth which is backed by a metal plate discharge of the filtrate and retention of the cake and addition of wash water with in some mod els the impurities leaving through a different port The device can have from two to four separate ports and some presses embody features such as inflatable dia phragms that enable cake dewatering by compression a process called expression After the cycle the press is dis assembled and the cakes are collected manually Figures 1915 and 1916 show the most common sim plest twoport configuration which consists of alternate plates and frames hung on a rack and pressed together with a closing and opening screw device The filter cloths which have holes to align with the inlet and outlet ports are hung over the plates and act as gaskets when the press is closed A very large plateandframe filter press may have as many as 100 plates and frames and up to 300 square meters of filter area Slurry feed enters from the bottom and feeds the cavi ties in parallel The filtrate flows through the cloth channels in the plate and out the top while the cake builds up in the frame The frame is full when the cakes which build up on both sides of the frame meet Other versions of the plate andframe filter press have three and fourport systems which facilitate washing when required because if the slurry fills the frame the wash water may be blocked if it enters through the slurry feed lines A type of filter press that competes with plateandframe devices in batchproduction processes is the pressure leaf fil ter which has the advantage of not having to be disas sembled completely after each cycle Most leaf filters resemble the baghouse device shown in Figure 198 Hori zontal and vertical versions of pressure leaf and plateand frame filters are available Choice of filter equipment is gov erned mostly by economic factors which include relative cost of labor capital energy and product loss but attention must be paid 8 to 1 fluid viscosity density and chemical reactivity 2 solid particle size size distribution shape flocculation tendency and compressibility 3 feed slurry concentration 4 throughput 5 value of the product 6 wastedisposal costs and environmental problems and 7 completeness of separation and material yields Experi mental data are required to establish these parameters and pilotplant testing is a necessity Proper choice and concen tration of filter aid and the choice and pretreatment of the Material enters under pressure Clearfiltrate outlet Fixed head Plate Frame Solids collect in frames Movable head Closing device Side raits Filter cloth Figure 1916 Plateandframe filter press Frame Inlet Outlet Plate Figure 1915 Plateandframe pair 788 Chapter 19 Mechanical Phase Separations C19 10042010 Page 804 197 MECHANICAL SEPARATIONS IN BIOTECHNOLOGY Figure 1931 is a schematic of the processing steps necessary to separate bioproducts obtained from plants and fermenta tion of bacteria molds and fungi from mammalian cells or by recombinant methods which include insertion of DNA into appropriate hosts An introduction to these methods was given in 19 When the bioproduct is produced extracellu larly the biomass is separated from the broth by vacuum or pressure filtration centrifugation or by membranes micro filtration or ultrafiltration Expression the deliquoring of the biomass by compression may be done if it is economi cally viable The filtrate is then subject to an initial purifica tion which will include precipitation from solution or methods described in previous chapters of this book The subsequent candidate purification and concentration opera tions are all described in previous chapters If the product resides intracellularly the cells must first be harvested separated from the broth Then they are subject to cell disruption a homogenization process wherein the cell walls are breached so the product can be extracted Intra cellular products include recombinant insulin and growth factors A number of recombinant products form relatively insoluble inclusion bodies others such as porcine insulin need to be removed from pig pancreas Different types of cells can be disrupted differently Grampositive bacteria have a cell wall about 03 mm thick composed of peptido glycan teichoic acid and polysaccharides which is followed by a fragile membrane made of proteins and phospholipids The cell wall of grampositive bacteria is susceptible to lysis by the enzyme lysozyme which degrades peptidoglycan Gramnegative bacteria are enveloped by multilayer mem branes significantly thinner than the walls of grampositive bacteria and cannot be lysed Osmotic shock simply immersing a cell in distilled water can be used to recover periplasmic proteins if the cell wall is breached or nonexist ing Yeast and mold cells have walls 0102 mm thick but mammalian cells do not have walls and are relatively fragile In general the fragile plasma membranes are readily destabi lized by acids alkali detergents or solvents Cell debris are removed by centrifugation microfiltration or filtration under vacuum or pressure The broth which characteristically contains very low concentrations of the tar get species then undergoes an initial purification to increase the product concentration to reduce the cost of subsequent purification steps and to prevent fouling of ion exchangers adsorbents chromatography columns etc Precipitation or extraction are possible venues Both the range of products and the media in which they are produced are enormous so generalizations are difficult Special attention must be paid to Figure 1931 Sequencing of bioseparations 804 Chapter 19 Mechanical Phase Separations C19 10042010 Page 806 Watersoluble powders of the type used in flocculation which were introduced in 192 can be used to precipitate proteins In the research stage are affinity precipitants where a conformal ligand attached to the polymer can couple with a target protein to further enhance aggregation Here as with the other precipitation processes pH is important since pro teins exhibit their lowest solubility at the isoelectric point 1972 Coagulation Flocculation Clarification and Sedimentation A precise lexicographic definition of these processes is not possible because they may be proceeding simultaneously and be viewed functionally Sedimentation in Perrys Chemical Engineers Handbook 11 is defined as the partial separa tion or concentration of suspended solid particles from a liq uid by gravity settling This process may be divided into the functional operations of thickening and clarification The purpose of thickening is to increase the concentration of sus pended solids while that of clarification is to produce a clear effluent In all aspects but one clarifiers and thickeners are identical The one difference is that clarifiers are usually ligh ter in construction because the average density and viscosity are lower because the suspended solid concentration is lower This makes the definition function specific Small particles dispersed in a suspension are stabilized by forces due to the surface charges of the particles which is why they do not agglomerate spontaneously due to Brownian motion Bacterial cells and most solids suspended in water possess negative charges at neutral pH The source of the sur face charges is the surface groups which are capable of ion ization A second source of surface charge is the preferential adsorption of ions in the solution The physical process of sedimentation is enhanced by coagulation and flocculation which may occur sequentially as in Figure 1932 but often occur simultaneously as do pre cipitation and agglomeration of proteins if a polyelectrolyte is present when the temperature of a saturated solution of proteins is lowered Flocculation is thus defined as the further agglomeration of the small slowly settling floc formed dur ing coagulation to form a larger aggregated floc particle The relative sizes of suspended particles encountered in biologi cal systems are shown in Table 1910 Organic particles below the size visible to the human eye approximately 004 mm 40 microns generally have settling times that are unreasonably long and thus coagulation and flocculation as well as mild agitation are required to achieve economically sized equipment Table 1911 provides a list of inorganic and organic coag ulants as well as some coagulantflocculant aids which are used in part because they shorten settling times by increas ing the density of the suspended microorganisms These are hydrophyllic and associated with both internal and surface bound water so their density is very close to that of the broth Inorganic coagulants are watersoluble inorganic acids bases or salts that when dissolved produce cations or hydrolyzed cations Increasing the concentration of salt com presses the electrical double layer surrounding a suspended particle and decreases the repulsive interaction between par ticles thus destabilizing them In flocculation there is further agglomeration by an organic polyelectrolyte One end of a flocculant molecule attaches itself to the surface of one parti cle at one or more adsorption sites and the other extended unadsorbed end of the same molecule bridges and adsorbs to one or more additional particles thus forming a larger aggre gate of floc particles The coagulantflocculant aids in Table 1911 are insoluble particulates generally used to enhance solidliquid separa tions where slime and gluelike interactions are troublesome It is known for example that broth cultures of actinomy cetes such as Streptomyces greisius are difficult to filter or settle and require the addition of about 23 diatomaceous filter aid to form a satisfactory cake Usually large quantities of these filter aids are required and this raises the need of recovery or wastedisposal processes In general filtration of biosystems is difficult and centrifugation is preferred Figure 1932 Coagulation flocculation sedimentation sequence Table 1910 Relative Sizes of Suspended Particles Class Diameter mm Colloids 000000010001 Dispersed 000101 Coagulated 0110 Flocculated 1010 806 Chapter 19 Mechanical Phase Separations C19 10042010 Page 809 REFERENCES 1 Tiller FM Theory and Practice of SolidLiquid Separation Chemical Engineering Department University of Houston 1978 2 Shuler ML and F Kargi Bioprocess Engineering Prentice Hall PTR Upper Saddle River NJ 2002 3 Souders M and GG Brown Ind Eng Chem 261 96 1934 4 Sutherland K Filters and Filtration Handbook 5th ed Buttersworth Heinemann Burlington MA 2008 5 Towler G and R Sinott Chemical Engineering Design Elsevier Bur lington MA 2008 6 Nonhebel G Processes for Air Pollution Control Butterworth Co Cleveland OH 1972 7 Wakeman RJ and ES Tarleton Filtration Elsevier Science New York 1999 8 Foust AS LA Wenzel CW Clump L Maus and LB Anderson Principles of Unit Operations J Wiley Sons New York 1960 9 Amistco Corporation Alvin Texas 10 Stairmand CJ Trans Inst Chem Eng 29 356 1951 11 Perrys Chemical Engineers Handbook 8th ed DW Green and RH Perry Eds McGrawHill New York 2008 12 Coker AK Chapter 6 Mechanical Separations in Ludwigs Ap plied Process Design for Chemical and Petroleum Plants 4th ed Vol 1 Elsevier Publishing New York 2007 13 Einstein A Ann Physik 174 549 1905 14 Brink J Can J Chem Eng 41 134 1963 15 McCabe WL JC Smith and P Harriott Unit Operations of Chemi cal Engineering 4th ed McGrawHill Book Co New York 1985 16 Carpenter CR Chem Eng 9023 227231 1983 17 Kula MR KH Kroner and H Hustedt Advances in Biochemical Engineering 24 73 1984 18 Schweitzer PA Handbook of Separation Techniques for Chemical Engineers McGrawHill Book Co New York 1979 19 Peters SM KD Timmerhaus and RE West Plant Design and Eco nomics for Chemical Engineers 5th ed McGrawHill New York 2003 20 Ruth BF GH Montillion and RE Montonna Ind Eng Chem 25 76 153 1933 21 Tiller FM Chem Eng 73 13 151 1966 22 Silla H Chemical Process Engineering Marcel Dekker Inc New York 2003 23 Svarovsky L SolidLiquid Filtration 3rd ed Butterworths London 1990 24 Chopey N Handbook of Chemical Engineering Calculations 3rd ed McGrawHill Book Co New York 2003 25 Aiba S AE Humphrey and NF Mills Biochemical Engineering Academic Press New York 1965 26 Blasewitz AG and BF Judson Filtration of Radioactive Aerosols by Glass Fibers Chem Eng Progress 511 6 1955 27 Stairmand CJ Trans Inst of Chem Engrs 28 131 1950 28 Walas SM Chemical Process Equipment Butterworths Boston 1988 29 Ghosh R Principles of Bioseparations Engineering World Scientific Publishing Co Hackensack NJ 2006 STUDY QUESTIONS 191 Why is particle size the main parameter used in selecting a mechanical phaseseparation device 192 At the particle settling velocity what force balances the drag force plus the buoyant force 193 Into what four regions are settling equations for particles divided 194 What form of the SoudersBrown equation is used to cor relate empirical settling data 195 What criteria have been developed for deciding which set tling equation is applicable for a given particle diameter 196 How are settling velocity equations modified to take into account particleparticle collisions and particleshape differences 197 What empirical equations with constants obtained from experimental data are frequently used to design many particlefluid separation devices 198 Why do governmental regulatory agencies and trade orga nizations set many design and performance specifications for parti cle emissions 199 Why is centrifugal force frequently applied to speed up and facilitate particlefluid separation 1910 Why have theoretical analyses that treat voids in filter cakes as flow channels not been applied industrially 1911 In a filtration cycle why does constantpressure filtration usually occur near the end of the cycle and constantrate filtration at the beginning 1912 For what particlesize and particleconcentration ranges are vacuum rotarydrum leaf and plateandframe filters generally used 1913 For what assumptions do filtration data plot as a straight line for V versus tV coordinates 1914 Why are precoat and filter aids generally used in solid liquid plateandframe or vacuum rotarydrum filtrations 1915 Why are wash periods followed by expression often part of the filtering cycle 1916 What are the assumptions in the Ruth equation for filtration 1917 How are empirical constants in filtration models determined 1918 Why are pump characteristic curves important in pressure filtration 1919 What is the sigma theory and how is it applied 1920 How do processes for separating extracellular and intra cellular bioproducts differ 1921 What steps can be taken to speed coagulation of particu lates from bioreactors 1922 How are washing cycles determined 1923 Name five methods for cell disruption Study Questions 809 BINDEX 09222010 Page 817 Index A Absorption absorber 7 8 185 equipment 207 graphical design method 213 Kremser method 185 217 minimum absorbent flow rate 214 reboiled 7 8 13 rigorous design methods 388 393 400 stage plate tray efficiency 218 Absorption factor 186 Acentric factor 45 Activity 39 Activity coefficient 39 Adiabatic flash 150 Adiabaticsaturation temperature 743 745 Adsorbate loading 589 Adsorbents 571 572 573575 595 activated alumina 572 573 activated carbon 572 574 molecularsieve carbon 572 574 molecularsieve zeolites 572 574 polymeric 572 575 silica gel 572 574 595 Adsorption adsorber 13 568 capacity 599 Freundlich isotherm 580 582 Henrys law linear isotherm 579 Langmuir isotherm 581 582 membrane 598599 pressureswing 13 609611 619 simulated movingbed 609 611 623 slurry 609 610 613 thermalswing 13 609 610 615 transport 587594 true moving bed TMB 623 Air purification 780 particle sizes in air 781 particle capture devices for air 781 Amagats law 41 Analogies 115 ChiltonColburn 115 ChurchillZajic 117 FriendMetzner 117 Prandtl 115 Reynolds 115 Aqueous twophase extractionATPE 345349 Arithmeticman diameter 678 Availability 36 Axial dispersion backmixing 338 Azeotropes 56 59 144 Azeotropic distillation 9 11 413 432 435 B Baghouse 784 Balances Availability exergy 36 energy 36 entropy 36 material mole or mass 14 Batch distillation 471 differential 471 multicomponent rapid method 487 rigorous method 481 shortcut method 479 Barrer unit 506 BET equation 572 BilletShultes correlations flooding 242 holdup 236 mass transfer 246 pressure drop 242 Binodal curve 313 436 Biocolloid interactions 6874 bond energies 68 electrostatic double layers 69 flocculation 7172 hydration forces 72 75 solvation forces 72 steric forces 73 surface force measurements 7374 van der Waals forces 70 Biomolecule reactions 7476 bioaffinity 76 348 bonding 7475 affinity interactions 75 Bioproducts 1921 biopolymers 1920 345346 cellular particulates 19 2122 extraction 340350 mechanical separations 804808 cell disruption 805 coagulation 806 extracellular products 804 intracellular products 804 precipitation 805 sequencing of bioseparations 804 proteins 1920 7376 130 345 346 548 550 557560 590 594595 601 711 sizes 540 small molecules 19 thermodynamic activity of 6476 Bioseparations 1927 activity 24 chromatography 595601 crystallization 711718 electrophoresis 632638 example 2627 extraction 340350 features of 2124 membranes 539560 purity 24 steps in 2425 540 yield 24 Blasius equation 110 Boilingpoint elevation 705 Boilup 7 264 Bond energies 68 covalent 69 hydrogen 69 hydrophilic 69 hydrophobic 69 Bowtie region 423 Brownian motion 792793 Bubble cap 208 210 Bubble point 149 Bubblepoint BP method 382 Buffers 6468 Phosphate buffered saline PBS 66 67 Bulkflow in mass transfer 85 86 C Calculus of variations 491 Candle particle collectors 785 CarmanKozeny KozenyCarman equation 510 511 795 Carrier 151 299 Cascades 180 Catalytic distillation 413 Cell disruption 807808 by freezing 808 by mechanical means 807808 by ultrasound 808 817 BINDEX 09222010 Page 818 Cell reactions 528 Centrifugal contactor 208 Centrifugation gas 14 Ultracentrifugation 130 Centrifuges 800802 basket 801 bowl 801 disk stack 801 Sigma factor 801 ChanFair correlation 229 Chaotropes 72 Chemical potential 38 39 128 vs physical potential 128 Chemsep program 465 Chromatography 13 569 577 595 606 624 affinity 597 convectiondispersion model 588 equilibrium wave pulse theory 607 equipment 609 hydrophobic interaction 596 immobilized metal affinity 7475 597 ion exchange 26 595596 598599 kinetics 587 loading 589 plate height 590 ratebased model 591594 resolving power 591 594 reversedphase 596 scaleup 597 separation efficiency 590 594 size exclusion 597 theory 587595 ChiltonColburn analogy 115 jfactors 116 592 Clarifiers 806 Cloudpoint titration 152 Coalescence and coagulation devices 782 for bioproducts 806 Coion 528 Composition measures of 16 Compressibility factor 45 Concentration polarization 524 528 532 539 549 Condenser 270 Continuity equation 227 Convergence pressure 44 51 Corresponding states theorem of 45 Counterion 528 Critical solution temperature 312 Crystals 673 711 biological 711 habits 674 675 predominant size 692 size distribution 674 space lattices 674 systems 674 Crystallization crystallizer 9 11 670 batch 713 constant supersaturation 716 dilution 714 bioproducts of 711718 cooling curve 713 equipment 688 697 growth crystal 685 712 law of McCabe 692 melt 11 697 micromixing 717 MSMPR model 691 nucleation 684 population balance crystal 715 precipitation 714 scaleup 717718 seeding 713 size distribution 714 solubility 671 672 679 supersaturation 683 716717 zone melting or refining 11 700 Cunningham correction 792 Current density 528 Cut 519 Cyclones 785 collection efficiency 786 design 790 D Daltons law 41 Darcys law 509 795 Decanter settler 300 302 303 782783 design 794 oilwater 794 Degrees of freedom analysis 139 191 Deionization 569 Demineralization 569 Desublimation 10 11 165 702 Dew point 149 Diafiltration 555 Dialysis 12 525 Diffusion 85 eddy turbulent 85 equimolar counterdiffusion EMD 87 Ficks first law 86 MaxwellStefan equations 127 462 molecular 85 128 multicomponent 458 pores in 97 shearinduced 551552 steadystate 86 101 unimolecular diffusion UMD 88 unsteady state 101 102 Newmans method 104 velocities 87 Diffusivity diffusion coefficient 90 128 biological solutes 96 effective in porous solid 97 593 electrolytes 95 gas mixture 90 liquid mixture 92 Onsagers reciprocal relations 128 solids 96 Dimensionless groups in transport 114 Eotvos number 333 Fourier number for mass transfer 104 758 Froude number 114 237 329 Lewis number 114 745 Luikov number 745 Nusselt number 114 Peclet number 114 339 Peclet number for mass transfer 114 223 Power number 329 Prandtl number 114 Rayleigh number 634 Reynolds number 114 impeller 329 Schmidt number 114 Sherwood number 114 Stanton number 114 Stanton number for mass transfer 114 Weber number 114 Distillation 79 11 258 359 378 413 457 473 equipment 208213 operating pressure selection of 361 Distillation boundary 416 Distillation curve 421 Distillation curve map 421 Distribution coefficient 39 310 DLVO theory 69 Donnan effect exclusion 68 528 Drag coefficient 110 114 791 vs Reynolds number 791 Drybulb temperature 743 745 Drying of solids 9 11 726 drying periods 751 equipment 727 models 763 belt dryer throughcirculation 764 directheat rotary dryer 766 fluidizedbed dryers 768 E Eddy diffusivities 115 Efficiency stage Murphree tray 222 Overall of Lewis 210 818 Index BINDEX 09222010 Page 819 Electrodialysis 14 Electrolysis 14 529 Electrolyte solution models 63 Electrostatic precipitators 785787 Electrophoresis 14 632 banding 637 blotting 637 detection 636637 gels 636 geometries 636 modes 632 634636 capillary 634 denaturing 634 isoelectric focusing IEF 634635 isotachophoresis 635 pulsedfield 635636 twodimensional 635 resistive heating 633 theory 637 Electrostatic double layer interactions 69 Energyseparating agent ESA 7 Enthalpyconcentration diagrams 286 682 707 Eotvos number 333 Equation of state models 40 Equation tearing 380 Ergun equation 242243 510 Espresso machine 5 653 Euler method 417 479 Eutectic point 160 671 672 697 Evaporation evaporator 9 11 704 equipment 704 model 706 multipleeffect systems 708 Exergy 36 Expression 788 Extraction factor 183 Extractive distillation 7 8 424 F Ffactor 230 244 Fabric collectors 784 Fanning friction factor 112 114 Faradays law 529 Fenske equation 362 FenskeUnderwoodGilliland method 359 Ficks first law 86 514 Ficks second law 102 Fieldflow fractionation 14 Film theory 119 filmpenetration theory 122 film theory of Nernst 119 MaxwellStefan relation to 131 penetration theory 120 surfacerenewal theory 121 Film thickness 120 Filter aid 787 Filter cake 779 cake resistance 795 compressibility 795 796 void fraction 795 Filter operation 796804 constant pressure 796799 constant rate 799 variable rate 799 wash cycles 802804 Filter selection Pc Select 787 Filters types of 781 bag 785 belt 787 Brink fiber bed 784 CENEUROVENT ULPA classification 783 coalescing 784 depth 780 HEPA 780 leaf 788 mesh 789 plate and frame 788 rotary drum vacuum 787 vanes and louvers 785 Fixedbed adsorption Percolation 601 breakthrough 601 constantpattern front 605 ideal local equilibrium 601 linear driving force LDF 603 masstransfer zone MTZ 605 stoichiometric front 601 Flash vaporization 7 8 147 adiabatic 150 isothermal 147 168 Flocculators 806 Flooding 225 packed column 240 plate column 225 Fluidization 768 Foam fractionation 10 11 Fouriers law 101 Freundlich adsorption isotherm 580 Fugacity 38 39 Fugacity coefficient 38 39 G Gibbs phase rule 139 H HendersonHasselbach equation 67 Henrys law 40 98 119 123 163 217 517 579 Heterogeneous azeotropic distillation 413 435 HETP HETS 232 244 Hofmeister series 73 348 Holdup packed columns liquidliquid 334 packed columns vaporliquid 236 Hollowfiber membrane modules 506 508 Homogeneous azeotropic distillation 413 432 HTU 234 235 Humidity 742 743 HunterNash method 312 Hybrid systems 190 522 536 Hydrates 161 681 682 Hydraulic diameter 247 Hydrogen bonds 72 75 I Impellers 302 Insideout method 400 Ion exchange 13 14 568 575 584 595 612 631 Ionic interactions 74 Ionic strength 70 Ionization 6466 Isothermal flash 147 168 J jfactors of Chilton and Colburn 114 116 Jacobian matrix 394 Janecke diagram 154 323 K Kvalues 39 40 Kelvin equation 573 749 Kicks law 808 Knudsen diffusion 509 515 593 Kosmotropes 72 KozenyCarmen equation 795 Kremser group method 185 217 371 621 L Langmuir adsorption isotherm 581 582 Leaching 10 13 158 650 equilibriumstage model 657 equipment 651 ratebased model 662 shrinkingcore model 665 Liquidliquid extraction 9 11 183 343 372 391 bioproducts of 340350 equipment 302 graphical design methods 312 reflux extract and raffinate 321 rigorous design method 391 Liquidliquid miscibility boundaries 152 Liquid membrane 1213 Liquidsolid extraction 10 13 Index 819 BINDEX 09222010 Page 820 Loading point in packed columns 236 Longitudinal axial mixing dispersion 223 224 338 Lost work 36 37 M McCabe law of 692 McCabeThiele method for binary distillation 261 McCabeThiele method for counter current adsorption 621 McCabeThiele method for leaching and washing 657 Magma 672 MaloneySchubert method 325 Marangoni interface effect 123 312 332 Margules equation 55 57 Massmean diameter 678 Massseparating agent MSA 7 Mass transfer 5 85 bulkflow effect 85 86 coefficient 107 volumetric 233 driving forces 123 droplet 331 interfacial area 229 331 laminar flow in 106 boundary layer on a flat plate 110 falling liquid film 106 fully developed flow in a tube 111 large driving force case of 125 membranes in 587 591 multicomponent 127 MaxwellStefan equations 127133 462 packed bed 232 284 591 particle for external 591 internal 593 turbulent flow in 113 twofilm theory of Whitman 123 244 Mechanical Separations 778808 Membrane cascades 189 522 Membrane materials 503 asymmetric 505 casting 542 thinlayer composite 505 transport in 508 Membrane modules 506 flow patterns in 520 deadend flow 543 tangential flow 547 Membrane separations 1113 500 MESH equations 379 Method of lines MOL 617 Microfiltration 12 543544 Micromixing 717 Minimum absorbent rate 215 Minimum equilibrium stages 266 362 Minimum reflux ratio 266 364 Minimum solvent rate 316 Minimum work of separation 36 37 Mixersettlers 302 328 Moisture content of solids 748 Moistureevaporation temperature 747 Molecularsieve carbon 572 574 Molecularsieve zeolites 572 574 575 Moment equations 692 Monolithic membrane modules 506 508 MSMPR crystallization model 691 Multiple solutions multiplicity 439 N Nanofiltration 546 NernstHaskell equation 95 Net charge 65 NewtonRaphson method 389 393 Newtons law of cooling 107 Nonequilibrium thermodynamics 127 NRTL equation 57 60 NTU Number of transfer units 234 235 340 Nusselt number 114 592 O Occlusion 208 ODEPACK 618 Oldershaw column 223 OldshueRushton column 304 305 Onsagers reciprocal relations 128 Osmosis 12 530 Osmotic pressure 531 P Packed column tower 209 diameter 240 flooding 240 height 234 HETP HETS 234 HTU 234 liquid holdup 236 loading 236 mass transfer 244 NTU 234 packings 209 211 238 pressure drop 240 Ergun correlation for dry bed 242 243 Packings 209 random dumped characteristics 238239 structured arranged ordered characteristics 240 Parachor 93 Partial condensation 7 8 Partial vaporization 7 8 Particle density 571 Particle porosity 571 Particles separation devices 781 classification 794 collection mechanisms 781 settling mechanisms 791 terminal velocity 791 Partition coefficient 39 dependence of 342343 Permeability 504 506 Permeance 504 Permeate 501 Pervaporation 12 13 535 pH 65 Phase equilibria 3841 140 gasliquid 163 gassolid 165 liquidliquid 41 151 157 solidliquid 41 158 vaporliquid 39 141 Phase splitting 57 Pinch points 215 364 Plait point 153 311 312 Plateandframe membrane modules 506508 Podbielniak centrifugal extractor 306 307 337 Poiseuille equation 795 Polymerase chain reaction 69 Polymer membranes 504 Poresize distribution 573 Power number 329 Poynting correction 40 Precipitation 695 of bioproducts 805 Pressure diffusion 130 Pressure drop packed column 240 trayed tower 228 Pressureswing adsorption PSA 13 609611 619 Pressureswing distillation 413 429 Proteins 1920 aqueous twophase extraction of 345346 chromatography 590 594595 crystallization 711 counterflow separation of 601 fouling 550 interactions 73 ligandreceptor binding 74 molecular weights 130 550 physical parameters 548 precipitation 73 Scatchard analysis 7576 820 Index BINDEX 09222010 Page 821 structure stabilization 73 ultrafiltration of 557560 Product composition region feasible 423 Pseudosteadystate assumption 665 Psychrometric ratio 745 Psychrometry 741 definitions table of 743 humidity charts airtoluene at 1 atm 716 746 airwater at 1 atm 742 Pumparounds 379 Q qline 143 264 R RachfordRice method 147 157 169 Raoults law 40 deviations from 54 modified 40 Reactive distillation 413 442 Reboiled absorption 7 8 12 Reboiled stripping 9 11 Reboiler 273 Reentrainment 781 783 Reflux 7 261 Reflux drum 261 283 Refluxed stripping 7 8 Regular solutions 53 Rejection 532 Relative volatility 39 Residencetime distribution 121 Residue curve 416 Residue curve map 416 Resins ion exchange 575 Retentate 501 Reverse micelles 344 Reverse osmosis 12 530 Reynolds number 107 114 Reynolds stress 117 Rittingers law 808 Ruth equation 796 S Salt distillation 413 428 Sauter mean diameter 331 678 Screen analysis 676 cumulative 677 differential 676 Screens US standard 676 Secondlaw analysis 36 37 Secondlaw efficiency 36 37 Separation mechanisms 5 6 Separation factor power 18 Separation specifications 1416 activity biological 24 component recoveries 1720 product purities 1720 24 split fraction 1720 split ratio 1720 yield 24 Settling of particles 792794 at intermediate Reynolds numbers792 hindered 793 Newtons law 792 Stokes law 792 velocity 791792 Shrinkingcore model 665 Sieve perforated trays 208 Sigma factor 801 Simulated movingbed adsorber 609 611 623 Singlesection cascade 180 185 193 Slop intermediate cuts 481 488 Slurry adsorption contact filtration 609 610 617 Solidliquid extraction 10 13 650 Solid solution 671 672 Solubility 681 pH effects on biological 67 Solubility parameter 53 Solubility product 680 695 Solution crystallization 670 688 Solutiondiffusion 99 509 516 517 Solutropy 156 313 Solvent selection 341 Sorption 568 SoudersBrown equation 791 Sphericity 592 675 Spiralwound membrane modules 506 508 Spray tower column 208 209 303 Stage equilibrium 192 Sterile filtration 545 Stiff differential equations 483 Stokes law 792 Stripping stripper 7 185 Kremser algebraic design method 371 rigorous design methods 388 393 400 Stripping factor 186 Sublimation 11 165 Sumrates SR method 388 Supercriticalfluid extraction 11 341 447 Superficial velocity 237 Supersaturation 683 Surface diffusion 593 Surfacemean diameter 678 T Temperature infinite surroundings 36 reference datum 41 Terminal velocity 791 Ternary liquidliquid phase diagrams 153 311 414 Thermal diffusion 14 129 Thickeners 782 Thermalswing adsorption TSA 13 609 610 615 Threephase flash 168 Tieline 143 153 Tortuosity 97 510 514 Trayed plate tower column 208 Tray spacing 226 Tubular membrane modules 506508 Turndown ratio 208 209 212 227 Twosection cascade 180 193 U Ultrafiltration 12 505 539 Underwood equations 364 UNIFAC equation 61 62 UNIQUAC equation 57 60 61 V Valve cap 208210 van der Waals interactions 68 70 van Laar equation 55 57 Vapor pressure 39 42 Velocity interstitial 588 superficial 237 terminal 791 Virus filtration 542 546 Volumemean diameter 678 W WangHenke BP method 382 Washing factor 182 Weeping 208 231 Wilson equation 57 5860 Work lost 36 37 minimum 36 37 Z Zeolites 574 575 Zeotropic system 414 Zone melting 700 Index 821