SEPARATION PROCESSES SEPARATION PROCESSES McGraw-Hill Chemical Engineering Series Editorial Advisory Board James J Carberry, Professor of Chemical Engineering, University of Notre Dame James R Fair, Professor of Chemical Engineering, University of Texas, Austin Max S Peters, Professor of Chemical Engineering, University of Colorado McGraw-Hili Chemical Engineering Series William R Schowalter, Professor of Chemical Engineering, Princeton University James Wei, Professor of Chemical Engineering, Massachusetts Institute of Technology BUILDING THE LITERATURE OF A PROFESSION Editorial Advisory Board Fifteen prominent chemical engineers first met in New York more than 50 years ago to plan a continuing literature for their rapidly growing profession From industry came such pioneer practitioners as Leo H Baekeland, Arthur D Little, Charles L Reese, John V N Dorr, M C Whitaker, and R S McBride From the universities came such eminent educators as William H Walker, Alfred H White, D D Jackson, J H James, Warren K Lewis, and Harry A Curtis H C Parmelee, then editor of Chemical and Metallurgical Engineering, served as chairman and was joined subsequently by S D Kirkpatrick as consulting editor After several meetings, this committee submitted its report to the McGraw-Hill Book James J Carberry, Professor of Chemical Engineering V"il'ersity of Notre Dante James R Fair, Professor of Chemical Engineering University of Texas, Austin Max s Peters, Professor C?f Chemical Engineering University of Colorado William R Schowalter, Professor of Chemical Engineering, Princeton llnil'ersity James Wei, Professor of Chemical Engineering, Massachusetts Institute of Technology Company in September 1925 In the report were detailed specifications for a correlated series of more than a dozen texts and reference books which have since become the McGraw-Hill Series in Chemical Engineering and which became the cornerstone of the chemical engineering curriculum From this beginning there has evolved a series of texts surpassing by far the scope and longevity envisioned by the founding Editorial Board The McGraw-Hill Series in Chemical Engineering stands as a unique historical record of the development of chemical engineering education and practice In the series one finds the milestones of the subject's evolution: industrial chemistry, stoichiometry, unit operations and processes, thermodynamics, kinetics, and transfer operations BUILDING THE LITERATURE OF A PROFESSION Chemical engineering is a dynamic profession, and its literature continues to evolve McGraw-Hill and its consulting editors remain committed to a publishing policy that will serve, and indeed lead, the needs of the chemical engineering profession during the years to come Fifteen prominent chemical engineers first met in New York more than 50 years ago to plan a continuing literature for their rapidly growing profession From industry came such pioneer practitioners as Leo H Baekeland, Arthur D Little, Charles L Reese, John V N Dorr, M C Whitaker, and R S McBride From the universities came such eminent educators as William H Walker, Alfred H White, D D Jackson, J H James, Warren K Lewis, and Harry A Curtis H C Parmelee then editor of Chemical and Metallurgical Engineering, served as chairman and was joined subsequently by S D Kirkpatrick as consulting editor After several meetings, this committee submitted its report to the McGraw-Hill Book Company in September 1925 In the report were detailed specifications for a correlated series of more than a dozen texts and reference books which have since become the McGraw-Hill Series in Chemical Engineering and which became the cornerstone of the chemical engineering curriculum From this beginning there has evolved a series of texts surpassing by far the scope and longevity envisioned by the founding Editorial Board The McGraw-Hili Series in Chemical Engineering stands as a unique historical record of the development of chemical engineering education and practice In the series one finds the milestones of the subject's evolution: industrial chemistry, stoichiometry, unit operations and processes, thermodynamics, kinetics, and transfer operations Chemical engineering is a dynamic profession and its literature continues to evolve McGraw-Hili and its consulting editors remain committed to a publishing policy that will serve, and indeed lead, the needs of the chemical engineering profession during the years to come The Series Bailey and Ollis: Biochemical Engineering Fundamentals Bennett and Myers: Momentum, Heat, and Mass Transfer Beveridge and Schechter: Optimization: Theory and Practice Carberry: Chemical and Catalytic Reaction Engineering The Series Churchill: The Interpretation and Use of Rate Data—The Rate Concept Clarke and Davidson: Manual for Process Engineering Calculations Coughanowr and Koppel: Process Systems Analysis and Control Danckwerts: Gas Liquid Reactions Gates, Katzer, and Schuit: Chemistry of Catalytic Processes Harriott: Process Control Johnson: Automatic Process Control Johnstone and Hiring: Pilot Plants, Models, and Scale-up Methods in Chemical Engineering Katz, Cornell, Kobayashi, Poettmann, Vary, Ellenbaas, and Weinaug: Handbook of Natural Gas Engineering King: Separation Processes Knudsen and Katz: Fluid Dynamics and Heat Transfer Lapidus: Digital Computation for Chemical Engineers Luyben: Process Modeling, Simulation, and Control for Chemical Engineers VlcCabe and Smith, J C.: Unit Operations of Chemical Engineering Mickley, Sherwood, and Reed: Applied Mathematics in Chemical Engineering Nelson: Petroleum Refinery Engineering Perry and Chilton (Editors): Chemical Engineers' Handbook Peters: Elementary Chemical Engineering Peters and Timmerhaus: Plant Design and Economics for Chemical Engineers Reed and Gubbins: Applied Statistical Mechanics Reid, Prausnitz, and Sherwood: The Properties of Gases and Liquids Satterfield: Heterogeneous Catalysis in Practice Sherwood, Pigford, and Wilke: Mass Transfer Slattery: Momentum, Energy, and Mass Transfer in Continua Smith, B D.: Design of Equilibrium Stage Processes Smith, J M.: Chemical Engineering Kinetics Smith, J M., and Van Ness: Introduction to Chemical Engineering Thermodynamics Thompson and Ceckler: Introduction to Chemical Engineering Treybal: Mass Transfer Operations Van Winkle: Distillation Volk: Applied Statistics for Engineers YValas: Reaction Kinetics for Chemical Engineers Wei, Russell, and Swartzlander: The Structure of the Chemical Processing Industries Whit well and Toner: Conservation of Mass and Energy Bailey and Ollis: Biochemical Engineering Fundamentals Bennett and Myers: Momentum, Heat, and Mass Transfer Beveridge and Schechter: Optimization: Theory and Practice Carberry: Chemical and Catalytic Reaction Engineering Churchill: The Interpretation and Use of Rate Data- The Rate Concept Clarke and Davidson: Manual for Process Engineering Calculations CoughanoWl' and Koppel: Process Systems Analysis and Control Danckwerts: Gas Liquid Reactions Gates, Katzer, and Schuit: Chemistry of Catalytic Processes Harriolt: Process Control Johnson: Automatic Process Control Johnstone and Thring: Pilot Plants, Models, and Scale-up Methods in Chemical Engineering Katz, Cornell, Kobayashi, Poettmann, Vary, Ellenbaas, and Weinaug: Handbook of Natural Gas Engineering King: Separation Processes Knudsen and Katz: Fluid Dynamics and Heat Transfer Lapidus: Digital Computation for Chemical Engineers Luyben: Process Modeling, Simulation, and· Control for Chemical Engineers McCabe and Smith, J C.: Unit Operations of Chemical Engineering Mickley, Sherwood, and Reed: Applied Mathematics in Chemical Engineering Nekon: Petroleum Refinery Engineering Perry and Chilton (Editors): Chemical Engineers' Handbook Peters: Elementary Chemical Engineering Peters and Timmerhaus: Plant Design and Economics for Chemical Engineers Reed and Gubbins: Applied Statistical Mechanics Reid, Prausnitz, and Sherwood: The Properties of Gases and Liquids Satterfield: H eterogeneous Catalysis in Practice Sherwood, Pigford, and Wilke: Mass Transfer Slattery: Momentum, Energy, and Mass Transfer in Continua Smith, B D.: Design of Equilibrium Stage Processes Smith, J M.: Chemical Engineering Kinetics Smith, J M., and Van Ness: Introduction to Chemical Engineering Thermodynamics Thompson and Ceckler: Introduction to Chemical Engineering Treybal: Mass Transfer Operations Van Winkle: Distillation Volk: Applied Statistics for Engineers Walas: Reaction Kinetics for Chemical Engineers Wei Russell, and Swartzlander: The Structure of the Chemical Processing Industries Whitwell and Toner: Conservation of Mass and Energy -~~ SEPARATION PROCESSES Second Edition C JtidsonJKing Professor of Chemical Engineering -_ _ _ ~ ~ _ 'WjIC.·~~ SEPARATION PROCESSES University of California, Berkeley McGraw-Hill Book Company New York St Louis San Francisco Auckland Bogota Hamburg Johannesburg London Madrid Mexico Montreal New Delhi Second Edition Panama Paris Sao Paulo Singapore Sydney Tokyo Toronto c Judso~ing Professor of Chemical Engineering University of California, Berkeley McGraw-Hili Book Company New York St Louis San Francisco Auckland Bogota Hamburg Johannesburg London Madrid Mexico Montreal New Delhi Panama Paris Sao Paulo Singapore Sydney Tokyo Toronto •• · I This book was set in Times Roman The editors were Julienne V Brown and Madelaine Eichberg; the production supervisor was Leroy A Young The drawings were done by Santype International Limited This book was set in Times Roman The editors were Julienne V Brown and Madelaine Eichberg; the production supervisor was Leroy A Young The drawings were done by San type International Limited R R Donnelley & Sons Company was printer and binder R R Donnelley & Sons Company was printer and binder SEPARATION PROCESSES Copyright © 1980, 1971 by McGraw-Hill, Inc All rights reserved SEPARATION PROCESSES Printed in the United States of America No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without (he prior written permission of the publisher 1234567890 DODO 7832109 Library of Congress Cataloging in Publication Data King, Cary Judson, date Separation processes Copyright © 1980 1971 by McGraw-Hill, Inc All rights reserved Printed in the United States of America No part of this publication may be reproduced stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying recording, or otherwise, without the prior written permission of the publisher (McGraw-Hill chemical engineering series) Includes bibliographies and index 1234567890 DODO 7832109 Separation (Technology) I Title TP156.S45K5 1981 660'.2842 79-14301 ISBN 0-07-034612-7 Library of Congress Cataloging in Publication Data King Cary Judson, date Separation processes (McGraw-Hili chemical engineering series) Includes bibliographies and index Separation (Technology) I Title TP156.S45K5 1981 660'.2842 79-14301 ISBN 0-07-034612-7 To MY PARENTS TO MY PARENTS and and TO MY WIFE, JEANNE, for inspiring, encouraging, and sustaining To MY WIFE, JEANNE, for inspiring, encouraging, and sustaining INDEX Absorber, reboiled 163-164 Absorber-stripper, 341, 683 Absorption, 22 with chemical reaction, 268-270, 304-307, 456-466 energy conservation, 720-721 energy consumption, 682-684 examples, 311-313, 321-324, 408-109 fractional, 682-684 multicomponent, calculation of, 498-499 patterns of change: binary, 311-313, 317-318 multicomponent 321-324 temperature profiles, 311-313, 317-318, 321-324 yx diagram for, 264-270 Absorption factor, 73 optimum value, 367 Acetic acid, extraction from water, 762-763 Activity coefficients, 31 influence on extraction processes, 758-761 Addition of resistances, 538-539, 542-545 Adductive crystallization, 23, 745 Adiabatic flash, 80-89, 93-% Adiabatic-saturation temperature, 549 Adsorbing-colloid flotation, 27-28 Adsorption 22 charcoal, 5, 6, chromatography, 179 cycling-zone, 193-195 drying of gases by, 128-130, 136 heatless 130 for separation of xylenes, 745-746 zeolites, 745-746 Adsorptive bubble separation methods, 27 Agitated column for extraction, 765-770 AIChE method for stage efficiencies in plate columns, 609-626 summarized, 621-622 Air, separation of, 16, 307-308 697-698 Alumina, activated, water-sorption equilibrium 129 Amines as solvents, 762-763 ASTM distillation 436 Available energy, 664, 689 Axial dispersion: analytical solutions, 575-577 defined, 556, 570-571 effect upon operating diagram, 571-572 graphical solution, 576 837 838 INDEX Axial dispersion: mechanisms, 570-571 models of, 572-575 numerical solutions, 577-580 Taylor dispersion, 570 Azeotropes, 34-35, 250 Azeotropic distillation, 345-349, 352-354, 455, 745 Baffle-column extractors, 765-770 BAND program for block-tridiagonal matrices, 811-815 Batch distillation, 115-123, 243-248, 501 Batch processes, 115-130, 243-248 Berl saddles, 153 Binary distillation, 206-250 group methods 393-406 Binary flash, 72 Binary multistage separations (general), calculation of, 259-295, 361-398, 556-583 Binary systems, defined, 206-208 Binomial distribution, 378 Biot number, 541 Block-tridiagonal matrix 480-481, 566-568, 577-579,811-815 Blowing on distillation plates, 601-602 Boiling curves 436 438 Bond energies suitable for chemical complexing, 737 Borax, manufacture of, 54-57 Boric acid, manufacture of, 54, 57 BP arrangement, 483-485 Breakthrough curves, 126-127 (See also Fixed-bed processes) Brine processing, 54-57 Bubble-cap trays 147, 149, 150 entrainment with, 597-598, 620-621 flooding in, 594-5% Bubble caps 147 149, 150 Bubble fractionation 23 27-28 164-166 Bubble point 61-68 acceleration of calculation within distillation problems, 474 Bubble-point (BP) arrangement for calculation of multicomponent distillation 483-J85 Caffeine removal from coffee, 516-518, 541-542, 775-776 Capacity of separation equipment (flows), 591-608 contrasted with stage efficiency, 641-642 Cascade trays, 602-604 Cascades: of distillation columns, 692-695 multiple-section, 371-376 one-dimensional, 140-144, 189-190 two-dimensional, 195-197 Centrifugal extractors, 767-770 Centrifugation, 2, 5, filtration-type, 26 gravity-type, 25 Chemical absorption, 268-270, 304-307, 456-466 Chemical complexing, 27, 735-738, 746 761-763 Chemical derivitization, 27 Chemical reaction, effect of: on mass- transfer coefficient, 528 INDEX 839 Chromatography: polarization, 187-188 scale-up, 191 sieving, 179 temperature programming, 186-187, 384 thin-layer, 185-186 uses, 188-189 Citrus processing: peel liquor, 690-692 {See also Fruit juices) Clarification, Clathration, 23, 744, 755 Cocurrent contacting, compared with countercurrent, 157-160, 642-643 Coffee: decaffeination of, 516-518, 541-542, 775-776 extraction of, 173-174 instant, manufacture of, 775-776 Colburn equation, 563-564 Complexing, chemical, 27, 735-738, 746, 761-763 Composition profiles: absorption, 311-313 321-324 distillation 313-315 325-331 extraction, 319-321 336-343 Computer methods: multistage processes 446-503 single-stage processes 64-90 Computer programs for separation processes, 503 Concentration polarization, 534-535, 586-589 Condensation, partial, as separation process, 667-672 Condenser: optimum temperature difference, 807-308 partial: defined, 145 versus total, specification variables, 795 total, defined, 145 Constant molal overflow, 216-218 Constant-rate period in drying, 552-553 Contacting devices (see specific types; e.g Packed towers, Plate towers, etc.) Continuous contactors: cocurrent, 580-583 Continuous contactors: countercurrent, 556-580 crosscurrent 583 Continuous countercurrent contactors, 556-583 minimum height, 566 sources of data, 583 Control schemes, 770-771 Convection, 508 Convergence methods, 65-68, 404, 777-784 review of, 777-784 Cooling tower, 549 Costs, references, 798 Counter-double-current distribution (CDCD), 189 Countercurrent contacting, 150-154 contrasted with cocurrent contacting, 157-160 642-643 840 INDEX Density gradients, effect upon mass- transfer rates and stage efficien- cies, 630-633 Derivitization, 27 Desalination of seawater, 16, 155-157, 171, 199-200, 723-725, 785-790 Description rule, 69-71, 791-797 Design problems, 70, 225-226, 448 49M96 Design successive approximation (DSA) method, 491^*94 Desublimation, 21 Deuterium, separation from hydrogen (see Heavy water, distillation) Dew point, 61-68 Dialysis 24, 45, 172, 753 Diameter, optimum, for column, 807 Dielectric constant, relation to intermolecular forces, 734-736 Difference point, 275-278 286-291 Differential migration, 179 Differential model of axial dispersion, 572-573 Diffuser for extraction and leaching of solids, 172 Diffusion: in cylinder, 516 gaseous, for separation, 23, 43-45, 119-121, 166-168,687 Knudsen, 44 513 molecular (kinetic theory), 508-514 multicomponent, 511 nozzle, 25 in slab, 516 in solids 513.514 in sphere, 516, 540-541 sweep, 23 thermal, 24 Diffusion equations, solutions, 515-518 Diffusional separation processes, 18 Ditfusivity: definition of, 509-510 prediction of: gases, 511-513 liquids, 513-514 Dimensionless groups, 524-525 Biot number, 541 Fourier number, 523, 525 Grashof number, 524 Lewis number, 549 Nusselt number, 524 Dimensionless groups: Peclet number, 573, 576 Prandtl number, 525 Rayleigh number, 524 Reynolds number, 524 Schmidt number, 524 Sherwood number, 523 Dipole moment, 734, 736, 740-741 Direct substitution (convergence), 78-79, 777-779 Displacement chromatography, 176-177 Distillation, 21 allowable operating conditions, 233-234 ASTM 436 azeotropic (see Azeotropic distillation) batch: multistage, 243-248 single-stage, 115-123 binary, 206-250 INDEX 841 Distillation: Rayleigh, 115-123 reverse, 333-337 reversible, 703-704 sequencing, 710-719 specification, 791-797 stage efficiencies, allowance for, 237-239 steam, 248-250 TBP, 436 temperature profiles, 313-316, 325-337 ternary mixtures, 710-713 thermodynamic efficiency, 681-682 Underwood equations, 393^406 vapor-recompression in, 726-727 varying molar flows, 273-283 Distributing nonkeys (minimum reflux), 334,418-423 Distribution of nonkey components, 433^36 effect of reflux ratio, 434-436 Distribution ratio (DR), defined, 426 Downcomer, 146, 148 liquid back-up in, 595-596 Drying: of gases: absorption, 298-299 solid desiccants, 128-130 136 of solids, 21 550-556 freeze drying, 554 rates, 552-556 Dual-solvent extraction 163 Dual-temperature exchange processes 21, 52-53,204, 302-304,410 Dumping in plate columns, 602 Duo-sol process, 163 Dynamic behavior of separation processes 501 Efficiency (see specific types; e.g., Murphree efficiency, Stage efficiency, Thermodynamic efficiency, etc.) Effusion, gaseous (see Diffusion, gaseous) EFV (equilibrium flash vaporization) curve, 436 Electrochromatography, 190-191 Electrodialysis, 24, 168-171, 199-200 Electrolysis, 24 Electrophoresis, 20, 24, 179 Electrostatic precipitation, 26 Elution chromatography, 176-177 Empirical correlations (stages versus reflux), 428-432 Energy, available, 664, 689 Energy conservation, 687-721 Energy requirements, 660-721 multistage processes, 678-687 reduction of, 687-721 reversible separations, 661-666 Energy separating agent, defined, 18 Enthalpies: of hydrocarbons, 82 index of data, 826 "virtual," partial molar, 481, 485 Enthalpy-balance restrictions: in absorption and stripping, 317-318 in distillation, 315-316, 318 Enthalpy-concentration diagram, 93-96, 273-283 Entrainer in azeotropic distillation, 346 842 INDEX Ethanolamines, absorption of acid gases by, 456-466 equilibrium data, 457-459 Ethylbenzene, separation from styrene, 643-651 Ethylene manufacture, 699-700, 708-710, 717-719,725-727 Eutectic point, 39-40 Evaporation, 2, 8, 21 flash, 200-201 forward feed versus backward feed, 789-790 of fruit juices, 748-750 multieffect, 155-157, 785-790 preheat, 789-790 simultaneous heat and mass transfer, 546-549 vacuum, 749 Evaporative crystallization, 2-9 Evaporators: fouling of, 749 multieffect, 155-157 preheat, 789-790 Expression (separation process), 8, 26, 690-691 External resistance, 550-552 Extract reflux, 161-162, 291-292 Extraction, 22 chemical complexing in, 762-763 complex, computation of 499-501 equilibrium data, 36-37, 42-43 758-761 equipment for, 13, 162 765-770 examples, 15, 318-321, 336-343, 762-763 flooding, in packed column, 596 fractional, 163, 333-335 graphical approaches, 96-97, 283-293 multistage, graphical analysis, 283-293 patterns of change: binary, 318-321 multicomponent, 336-343, 499-501 process configuration, 763-765 process selection 757-770 reflux in, 162-164 single-stage, 96-97 of solids, 172-174 solvent selection, 757-763 staging of, 160-163 unsaturates from saturates, 729-731 yx diagram for 259-262 Extractive crystallization, 745 Extractive distillation, 20 23, 344-345, 350-352, 455 saturates/unsaturates, 729-731 solvent selection, 761 Extractors, types of, 765-770 Falling-rate period in drying, 552-554 False position (convergence method), 778-780 Feasibility as selection criterion, 728-731 Feed, thermal condition, allowance for in distillation 221-223 Feed stage in distillation 228-233 effect of nonkeys, 294 optimum, 230-231, 494-4% selection 454, 494-496 Feeds, multiple, in distillation, 223-224, 423^24 Fenske-Underwood equation (minimum INDEX 843 Fog formation in distillation columns, 635 Formaldehyde, purification of, 505-506 Fouling of evaporators, 749 Fourier number, defined, 523 Fractional extraction, 163, 338-341 Fractionation index, 433-434 Fragrances, purification of, 412-413 Free energy of separation, 661-666 Freeze concentration, 104-109, 724-725, 755 Freeze drying, 21, 554, 589-590, 755 Freezing (see Crystallization) Frontal analysis, 178-179 Froth regime, 600-601, 627-628 Fruit juices: concentration and dehydration, 747-756 essence recovery, 250-251, 750-751 evaporation, 748-750 freeze concentration, 104-109, 755 volatiles loss, 748-756 Functions, choice of, 75-81, 784 Gas chromatography, 183-185 (See also Chromatography) Gas permeation, 24, 138-139 Gas-phase control, 538-539 Gaseous diffusion, 23, 43-45, 119-121 687 staging of, 166-168 Gases, solubility in water, 266 Gaussian distribution 381 Geddes fractionation index, 433-434 Gel electrophoresis, 191 Gel filtration, 25, 179 Gibbs free energy, 663-664 Gibbs phase rule, 32, 61 Gilliland correlation, 428-432 GLC (see Gas chromatography) Gradient, hydraulic, 595, 599, 601-604 Gradient solvent in liquid chroma- tography, 384 Graesser raining-bucket contactor, 767 Graetz solution, 525 Graphical approaches: absorption, 264-270 adiabatic flash, 93-% binary distillation, 206-250, 270-283 Graphical approaches: extraction: multistage, 283-293 single-stage, 96-97 multicomponent distillation, 331-333 Grid-type packing, 153 Group methods of calculation, 360-406 defined, 360 KSB equations, 361-376, 564-565 Martin equations, 387-393 Underwood equations, 393-406, 418-424 Hausen (stage) efficiency, 640-641 Heat pumps in distillation 695-697, 707, 726-727 Heat transfer combined with mass transfer, 545-556, 634-636 Heatless adsorption, 130 Heavy water, distillation, 622-626, 704-706 Height equivalent to theoretical plate (HETP), 569-570 844 INDEX Inert flows, 264 Initial values for successive-approxima- tion methods, 497, 781 Intalox saddles, 153 Intermediate condensers and reboilers, 699-708 Internal flows, 216-218 282 Internal reflux, 218, 282 Internal resistance, 550-552 Interphase mass transfer, 536-545 Intersection of operating lines 220-223 Ion exchange 22, 124-127 rotating beds, 174 Ion exclusion, 22 Ion flotation, 27-28 Irreversible processes 678, 684-687 Isenthalpic flash, 80-89, 93-% Isoelectric focusing, 19, 23 lsopycnic centrifugation, 25 Isopycnic ultracentrifugation, 23 Isotachophoresis, 179 Isothermal distillation 708-710 Isotope-exchange processes, 21 52-53 204, 302-304,410 Isotope separation (see Heavy water, distillation; Lasers, separation by; Uranium isotopes separation) Iteration methods (see Convergence methods) Janecke diagram, 284-285, 293 Key components, defined 325 Kinetic theory of gases, 511-514 Knudsen diffusion, 44 513 Kremser-Souders-Brown (KSB) equations, 361-376, 564-565 KSB equations 361-376 564-565 Lagrange multipliers 787-788 Lasers, separation by 27 Latent-heat effects: in absorption and stripping 317-318 in distillation 315-316 Leaching 22, 106-109 172-174 v.v diagram for 162-163 Leakage in rate-governed separation processes, 109 Lennard-Jones parameters, 511-513 Lessing rings, 153 Leveque solution, 525 Lever rule 90-94 Lewis-Matheson method, 450 Lewis number, 549 Limiting component, defined 367 Limiting flows 414—424 in energy-separating-agent processes, 415-425 in mass-separating-agent processes, 367.414-415.424-425 of nonkeys, 328-330 401-402 Linde double column 697-698 Linear equations (tridiagonal) method of solution, 466-471 Liquid chromatography, 183-185 (See also Chromatography) Liquid extraction (see Extraction) Liquid ion exchange, 204-205 Liquid-liquid extraction (see Extraction) Liquid membranes, 25, 763-764 Liquid-phase control, 538-539 Loading in packed columns, 593-594 INDEX 845 Mass transfer coefficients: film model, 519, 531-532 gas-phase control, 538-539 high concentration, effect, 528-533 high flux, effect, 528-533 near leading edge of flat plate, 526, 532 liquid-phase control, 538-539 multicomponent systems, 533 in packed beds, 527-528 penetration model 520-522, 531-532 for sphere, 523-524 surface-renewal model, 521-522 in turbulent field 527 Mechanical separation process, 18 for energy conservation, 687-688, 753 Mechanically-agitated columns for extraction, 765-770 Membrane processes, 24-25, 45^18, 138-139, 533-536 586-589, 676-677, 752-754 775 energy requirements, 684-687, 720-721 Membranes, 25, 48 Methane, Mollier diagram for, 671 Microencapsulation, 179 Minimum energy consumption, 661-666 Minimum flows in mass-separating-agent processes, 367 Minimum reflux, 233-235, 333-336 415-424 all components distributing, 415-417 binary systems, 233-235, 415-117 for distillations: with multiple feeds, 423-424 with sidestreams, 424 exact solution, 421 tangent pinch 234-235 Underwood equations 418-424 with varying molal overflow, 421 Minimum solvent flow, 286-287, 414-415 Minimum stages in distillation, 235-237, 424-427 binary systems, 235-237, 424-426 multicomponent systems, 427 Minimum work of separation, 661-666 Mixer-settler, equipment for extraction, 767-770 Mixing: within phases, 110-112 Mixing: on plates, 613-620 longitudinal 618-620 transverse, 619-620 (See also Axial dispersion) Mixtures, minimum (reversible) work of separation, 661-666 MLHV method, 270-273 for minimum reflux, 421 with Underwood equations, 403 Mobile phase in chromatography, 175-176 Modified-latent-heat of vaporization method (see MLHV method) Mole-average velocity, 509 Mole ratio, defined, 264 Molecular distillation, 25 Molecular flotation, 27-28 Molecular properties, influence on separation factor, 733-736 846 INDEX Net work consumption 665-666 distillation, 679-682 fractional absorption, 682-684 membrane processes, 684-687 Newman method: for converging temperature profile, 47^476 for implementing simultaneous- convergence method, 480-481 Newton convergence methods: for continuous countercurrent contactors: axial dispersion, 577-579 plug flow, 566-568 defined, 780-784 for multistage processes, 474-476, 480-483, 813-822 for single-stage equilibria 59-90 Nickel, production of, 202-204 Nomenclature, list of, 825-834 Nondistributing nonkeys (minimum reflux), 334,418-423 Nonideality, allowance for, 89-90, 480-481,499 Nonkey components: defined, 325-327 distributing versus nondistributing, 334, 415,418-423 distribution of, 433-436 limiting flows of, 328-330, 401-402 Nozzle diffusion, 25 NTU (number of transfer units), 558-566 Nuclear-material processing {see Heavy water, distillation; Uranium isotopes separation) Number of transfer units (NTU) 558-566 Numerical analysis 777-784 Nusselt number, 524 O'Connell correlation (stage efficiencies), 609-610 Oldshue-Rushton column for extraction, 767-770 Operating lines, 218-220 intersection of, 220-223 making straight, 259-273 Operating problems, 70, 239-243, 448 Optimum value of absorption, stripping or extraction factor, 367 Ore flotation, 27-28 Osmosis, 45 {See also Dialysis) Osmotic pressure, 45-46 Overall (stage) efficiency, 609-610 639 Overdesign, optimum, 808-810 Packed towers: capacity of, 593-594 comparison of performance, 604-606 contrasted with plate towers, 150-154, 604-606 effect of surface-tension gradients, 630 effect of surfactants, 633-634 for extraction, 765-770 flooding, 593-594 liquid-liquid contacting 594 loading point, 593-594 598-599 pressure drop, 598-599 vapor-liquid contacting, 151-154 Packing, types of, 153 Pairing functions and variables 86-88 INDEX 847 Phase conditions of mixture, 68 Phase equilibrium: allowance for uncertainty in, 808-810 index of values, 825-826 prediction methods, 43 sources of data, 42-43 Phase-miscibility restrictions in extraction, 318-321 Phase rule, Gibbs, 32, 61 Phosphine oxides as solvents 762-763 Pinch zones at minimum reflux, 333-336 Plait point, 36 Plasma chromatography, 27 Plate efficiency (see Stage efficiencies) Plate towers, 144-150 capacity of, 594-608 comparison of performance, 604-606 contrasted with packed towers, 150-154, 604-606 entrainment in 597-598, 601-602, 620-621 for extraction, 765-770 flooding in, 594-5%, 601-602 flow configuration, 613-620 mixing on plates, 613-620 range of operation, 601-603 (See also Trays) Plug flow, defined, 556 Podbielniak extractor, 767-770 Point efficiency, 612-613 Poisson distribution, 380 Polarizability, 734, 736, 740-741 Polarization chromatography, 187-188 Polyester fibers, Ponchon-Savarit method, 273-283 Positive deviations from ideality, 34-35 Positive systems (surface-tension gradients), 627-633 Potentially reversible processes, 678-682 Poynting effect, 662 Prandtl number, 525 Precipitate flotation 27-28 Precipitation, 8, 22 electrostatic, 26 Pressure, choice of, in distillation, 248, 803-807 Pressure drop: packed columns, 598-599 plate columns, 599-600 Process specification, 69-71 Product purities, optimum, 801-803 Pseudomolecular weight, 270-273 Pulsed-column extractors, 765-770 Pumparounds, 437, 439, 440, 706 Rachford-Rice method (equilibrium flash), 75-77 Raffmate reflux, 306-307 Raining-bucket contactor, 767 Raschig rings, 153 Rate-governed processes: defined, 18 energy requirements, 675-677, 684-687, 720-721 selection criteria, 732-733 systematic generation of, 751-755 Rate-limiting factor, 550-552 Rayleigh distillation: binary, 115-121 multicomponent, 122-123 848 INDEX Regula-falsi (convergence method), 778-780 Regular-solution theory, 758-761 Relative humidity, defined, 547 Relative volatility: defined, 31 selection of average value, 397 Relaxation factor, 489 Relaxation methods, 489-490, 568 Residence time versus efficiency, 600 Retention volume in chromatography, 185, 381-383 Reverse fractionation (minimum reflux), 334-336 Reverse osmosis, 24, 45-48, 510-511, 533-536, 586-587 energy consumption, 723 Reversible processes, 661-666 Reynolds number, 524 Richmond convergence method, 79 Ricker-Grens method, 491-494 Right-triangular diagram, 284-285 Rotating-disk contactor, 12, 13, 162, 766-770 Rotating feeds to fixed bed, 174-175 Rotating positions of fixed beds, 172-174 Safety factors in design, 808-810 Salt brines, processing, 54-57 Saturated-liquid feed, 221-222 Saturated-vapor feed, 222 SC method 480-481, 491^*94, 500-501, 566-568, 577-579, 813-822 Scatchard-Hildebrand equation, 758-761 Scheibel column for extraction, 766-770 Schildknecht crystallizer, 172 Schmidt number, 524 Screening, Searles lake brine, processing, 54-57 Seawater desalination (see Desalination of seawater) Secant methods (convergence), 778-780 Selection of separation processes, 728-771 Semibatch processes, 115-130 Sensible-heat effects: in absorption and stripping, 317-318 in distillation, 315-316 Separating agent: defined, 17-18 Separating agent: energy, 18 mass, 18 reduction of consumption of, through staging, 155-163 Separation factor: 29-48 actual (a,' ), defined 29 infinite, 41-42 inherent (a,,), defined, 29 molecular properties, dependence upon 733-736 solvents, influence of, 757-763 Separation index, 132« Separation processes: categorization, 18-28 computation of: multistage: binary, 208-250, 258-297, 361-398, 556-583 multicomponent, 331-336, 398-406, 446-503 INDEX 849 Simultaneous convergence: multistage separations, 480-481, 491-494, 500-501, 813-822 single-stage separations, 87-89 Simultaneous heat and mass transfer, 545-556 Single-stage processes (see Simple- equilibrium processes) Single-theta method, 487, 499-501 Sink-float separation, 25 Soda ash (Na,CO,), manufacture by Solvay process, 352-358 Solid solution 41-42 Solubilities of gases in water, 266 Solubility parameter, 758-761 Solvay process, 352-358 Solvent extraction (see Extraction) Solvent-free basis, 37-38, 286-287 Solvent selection, 757-763 Solvent sublation, 27-28 Sorel, E., analysis of distillation by, 208 Specifying variables, 69-71, 215-216, 791-797 Split-flow trays, 602-603 Spray columns: axial dispersion in, 571 for extraction, 765-770 Spray drying, 755 Spray regime, 600-601, 613, 628 SR arrangement, 485^89 Stage efficiencies, 131-134, 608-641 AIChE method of prediction, 621-626 allowance for uncertainty in, 808-810 chemical reaction, effect of, 626-627 contrasted with capacity, 641-642 Hausen 640-641 heat transfer, effect of, 634-636 multicomponent systems, 636-637 Murphree (see Murphree efficiency) overall, 639 surface-tension gradients, effect of, 627-633 vaporization, 639-640 Stage requirements (see individual separation processes; e.g., Distillation, Extraction, etc.) Stage-to-stage methods, 449-466 absorption, 456-466 distillation, 449-456 (See also Graphical approaches) Stagewise-backmixing model of axial dispersion, 573-575 Staging: countercurrent, 140-157 crosscurrent, 157-159 reasons for, 140-157 Stationary phase in chromatography, 175-176 Steam distillation 248-250 Straight operating and equilibrium lines, computational methods, 361-376 Streptomycin, purification of 373-376 Stripping 22, 110-112, 141-144 multicomponent, exact computation of, 498-499 sidestream, 358-359 Stripping factor, 73 optimum value 367 Stripping section, 144-145 850 INDEX Temperature profiles: correction and convergence of, 413-479, 484-485, 488-489 in distillation, 314-316, 331 Temperature programming in chromatography, 384 Thermal diffusivity, defined, 510 Thermodynamic efficiency, 666 distillation, 681-682 Theta method for converging tempera- ture profile in distillation, 473-474 Thiele-Geddes method, 473, 506 Thin-layer chromatography (TLC), 185-186 Thomas method to solve tridiagonal matrices, 468-469 Tolerance (convergence), 781 Tomich method, 482^t83 Total condenser, 145 Total flows, correction and convergence of, 485-488 Total reflux, 235-237 Transfer units, 558-566 Transient diffusion, 515-518, 540-542 Tray efficiency (see Stage efficiencies) Tray hydraulics, 594-601 Trays: bubble-cap, 147, 149, 150, 604-606 cascade, 602-604 comparison of performance, 604-606 flow configuration, 613-620 mixing 613-620 sieve, 147-149, 600, 602, 604-606 split-flow 602-603 valve, 147, 149, 151,603-606 (See also Plate towers) Triangular diagram, 36-37, 60-61, 283-293 Tridiagonal matrices, 466-471 Turbulent transport, 508 Turndown ratio, 603 UNIFAC method for activity coefficients, 43, 481 Uranium isotopes separation, 16, 44, 166-168 Valve trays, 147, 149, 151 Vapor-liquid phase separation, 15 Vapor recompression in distillation 696-697, 726-727 Vaporization (stage) efficiencies, 639-640 Variables, specification of, 69-71, 215-216,791-797 Volatiles loss from fruit juices, 748-756 Volatility of absorbent liquid, effect of, 317 Volume-average velocity, 509-510 Volume ratio, defined, 264 Washing, 2, 8, 22 106-109 xy diagram for, 262-263 Water softening, 124-127, 136-137 Weeping in plate columns, 602, 651 Weight ratio, defined, 264 Weir on a plate, 146, 148 Wet-bulb temperature, 546-549 Wetted-wall columns, effect of surface- tension gradients, 630 Wilke-Chang correlation, 513-514 Winn equation (minimum stages), 426 Work of separation 661-666 ... Variety of Separations Economic Significance of Separation Processes Characteristics of Separation Processes Separating Agent Categorizations of Separation Processes Separation Factor I nherent Separation. .. fixed-bed processes and control of separation processes, treated briefly in the first edition, are covered much better and more thoroughly elsewhere, these sections have been largely removed... fixed-bed processes and control of separation processes treated briefly in the first edition, are covered much better and more thoroughly elsewhere, these sections have been largely removed In