M

Macropores, 920

Macros, in spreadsheets, 8, 185–188

Magma

batch crystallization, 821–822

continuous cooling crystallizers, 780–781

crystal nucleation, 801

description, 770

MSMPR crystallizers, 806, 808, 814–815

vacuum crystallizers, 791–792

Magnesium in ion exchange, 970

Magnesium chloride (MgCl₂) solubility in water, 775

Maldistributions

McCabe-Thiele diagrams, 428

multiple-pass trays, 379

packed column design, 408

Manganese chloride (MnCl₂) solubility in water, 775

Manganese nitrate (Mn(NO₃)₂) phase diagram, 783–784

Mars Climate Orbiter program, 7–8

Mass balances

azeotropic processes, 273–274, 276, 279, 281

batch distillation, 341–343, 348, 351

binary Fickian diffusion, 633–638, 640–647

binary flash distillation, 25, 27–29, 31

binary mass transfer, 662

chemical reaction, 307–308

cocurrent cascades, 508

column distillation, 94–97, 106–112, 146

concentrated absorbers and strippers, 504–505

concentrated systems, 497–498, 500

condenser and reboiler size, 443

continuous cooling crystallizers, 777–782

countercurrent extraction cascades, 561–566

diffusion, 981

dilute absorption, 486–487

dissolving solid particles, 667

distillation tray efficiency, 738–739

evaporating liquid drops, 666

evaporative and vacuum crystallizers, 790–793

extraction, cross-flow, 543

extraction, dilute, 532–538, 541

extraction, immiscible, batch, 551–552

extraction, immiscible, concentrated, 547, 549

extraction mixers, 748

extractive distillation, 298

feed lines, 121–122

Fenske equation, 250

gas permeation, 848

ion exchange, 975–977

irreversible absorption, 508

leaching, 611, 614

matrix solutions, 221–225

McCabe-Thiele method, 117, 139, 142–143, 145

mixing calculations, 557

multicomponent distillation, 36, 191–194, 204

multicomponent VLE, 32

multistage binary batch distillation, 353, 356–357

nonlinear solute movement, 963

open steam heating, 135

partially miscible single-stage systems, 559–560

pervaporation, 887–888

prerequisites, 8

pressure-swing processes, 286–287

reboilers, 148, 151

reverse osmosis, 867

side streams, 148–149

simultaneous multicomponent convergence, 43

solute movement, 931

sorption systems, 920

steam distillation, 284–285

stripping analysis, 489

temperature swing adsorption, 941–943

ternary systems, 290–291

three-phase flash calculations, 47

total reboilers, 148

Underwood equations, 254, 257

washing, 607

Mass flux

diffusivity in dilute binary mixture, 635

Fickian diffusion, 635, 641

mass transfer, 662

membranes, 844

reverse osmosis solute, 865

reverse osmosis solvent, 863

ultrafiltration, 882

Mass reference velocity, 642

Mass transfer

binary column distillation efficiency, 154

binary systems, film theory, 657–660

binary systems, linear driving-force model, 656–670

binary systems, shrinking diameter of oxygen bubble, 664–669

binary systems, through stagnant films, 660–661

binary systems, to expanding and contracting objects, 661–664

column distillation, 88, 90

concentration polarization in reverse osmosis, 872–876

concepts, 4–5

crystallization, 770, 800–803

Fickian model of diffusivity, 632

gas permeation, 847

homework, 700–706

linear chromatography, 991

linear systems, 985–993

liquid-liquid extraction, 531

lumped parameter, 981–983

Maxwell-Stefan model, 683–698

mixer-settler design, 573–575

molecular movement, 629–631

overview, 627–629

packed beds, 978–984

packed columns, 406, 712

pressure swing adsorption, 950

references, 698–700

reverse osmosis, 866

solute movement, 932, 984

tray efficiencies, 385, 387

ultrafiltration, 879

Mass transfer analysis, 711

absorbers, 731–738

correlations for packed towers, 723–730

extraction, 741–753

HETP and HTU relationship, 720–722

homework, 758–765

HTU-NTU, 712–720

prediction of distillation tray efficiency, 738–741

rate-based, 753–756

references, 756–758

simulations, 764–768

spreadsheets, 765

strippers, 731–736

Mass transfer coefficients

based on analogies, 680–682

cocurrent absorbers, 738

correlations, 670–682

dimensionless groups, 671–672

estimation, 679–680

extraction, 742, 752–753

extraction mixers, 744, 746

film theory, 657–658

linear driving-force model, 656–657

mixer stage efficiency, 746–748

mixers, 750–753

packed distillation columns, 714, 716

packed towers, 723–730

rate-based analysis of distillation, 754

reverse osmosis, 872–875

semi-empirical and empirical, 677–679

theoretically derived, 672–677

ultrafiltration, 880

unit conversions, 1053

Mass transfer models, advantages and disadvantages, 698

Mass transfer zone (MTZ), 993–995, 1024. See also LUB

Mathematical prerequisites, 8

MATLAB, 345

Matrix solutions

component mass balances, 221–225

concentrated absorbers and strippers, 504–508

energy balances, 229–231

extraction, 572

multicomponent distillation, 219–221, 226–229

Naphtali-Sandholm method, 232–233

Maximum boiling azeotrope, 289–290

Maxwell, James Clerk, 683

Maxwell-Stefan model

difference equations, 687–688

diffusion and mass transfer, 683–698

Fickian diffusivities relationship, 688–689

film theory, 657

ideal ternary systems, 691–695

independent fluxes, 686–687

introductory development, 683–686

multicomponent solutions, 698

nonideal binary diffusion, 689–691

nonideal ternary systems, 697–698

rate-based analysis of distillation, 753

ternary mass transfer, 695–697

McCabe-Thiele diagrams

advantages, 132

applications, 604–605

azeotropic processes, 274–277, 279–280, 329

binary column distillation, 116–120, 128–132, 155–156

binary flash distillation, 25, 27–28

concentrated immiscible extraction, 547, 550

concentrated systems, 497–501

countercurrent extraction cascades, 565

cross-flow extraction, 543–546

dilute absorption, 485–489

dilute extraction, 532–538

dilute fractional extraction, 542

dilute systems, 490–492

distillation cascades, 82

equilibrium stages, 452

extractive distillation, 299–300

feed lines, 121

general procedure, 138–145

generalized, 603–604

intermediate condensers, 149, 151

intermediate reboilers, 149, 151

irreversible absorption, 509

leaching, 611–612, 615

vs. Lewis analytical method, 161–162

maldistributions, 428

minimum solvent rate, 571–572

miscellaneous separations, 617–618

multisolute absorption and stripping, 502–504

multistage binary batch distillation, 353–355, 357

open steam heating, 132–138

packed distillation columns, 715

partially miscible systems, 560, 569–570

reboilers, 148–149

side streams, 148

spreadsheets, 186

stripping analysis, 490

stripping columns, 150–151

ternary systems, 287–288

VLE, 20–22

washing, 608–610

Meal, leaching calculations, 613

Mechanical equilibrium, 3–4

Melt crystallization, 784

Melting points in eutectic systems, 783–784

Membrane extractors, 529–530

Membrane separation processes, 837–838

bulk flow pattern effects, 895–899

design problems, 897–898, 912–913

equipment, 840–843

gas permeation, 845–862

homework, 901–913

membrane concepts, 843–845

membrane thickness, 845

pervaporation, 883–895

references, 899–901

reverse osmosis, 862–877

spreadsheets, 911–912, 914–916

system properties, 839

ultrafiltration, 877–883

Mesopotamian clay distillation pots, 339

Metal cation, 923

Metastable regions

crystallization, 770, 772, 774

seeding for, 814

Methacrylic acid in ion exchange, 970

Methane (CH₄)

adsorption equilibrium constant, 926

adsorption isotherms, 924

diffusivity, 648

equilibrium data on activated carbon, 928

equilibrium in liquid ammonia, 515

gas permeation, 853–857

heat capacity, latent heat and boiling point data, 45

K values, 33–35

LUB approach, 996–998

permeability, 849

pressure swing adsorption, 951–956

Methanol

adsorbents, 924

chemical reaction, 307

diffusivity, 652

latent heat of vaporization, 134

Lennard-Jones potential parameters, 649

MTBE from, 308

Methanol-acetone separation in pressure-swing distillation processes, 287

Methanol-methyl butyrate-toluene example of distillation separation, 468–470

Methanol-water VLE, 58

Methyl acetate, manufacture of, 306

Methyl butyrate separation, 468–470

Methyl cyclohexane-toluene-ammonia LLE equilibrium, 556

Methyl ethyl ketone (MEK) separation by two-pressure distillation, 286–287

Methyl isobutyl ketone distribution ratio, 534

Methyl nitrate. See Safety

Methyl tert-butyl ether (MTBE) production, 308

Methylcyclohexane–heptane-aniline LLE equilibrium data, 593

Microfiltration, 838

Micropores in sorption systems, 920

Middle operating lines

McCabe-Thiele method, 142–145

side streams, 148

Minimum-boiling azeotropes, 24–25

Minimum reflux

binary column distillation, 151–153

Underwood equations, 254–259

Minimum solvent rate

concentrated absorber, 498–501

dilute absorber, 487–488

concentrated immiscible extraction, 548

countercurrent immiscible extraction, 535, 537

partially miscible systems, 570–572

Mixed distillate product, 342–343

Mixed suspension, mixed product removal (MSMPR) crystallizers, 799

crystal nucleation and growth, 800–804

crystal size distributions, 800–814

distribution assumptions, 800

distribution development and application, 806–809

equilibrium, 811–814

MSMPR equation, 804–805

screen analysis data, 809–810

sieve analysis, 810–811

Mixed systems, binary permeation in, 848–858

Mixer-settler systems. See also Mixers, Settlers

countercurrent extraction cascades, 567

design overview, 573–574

example, 582–586

extractors, 529–530

leaching, 610

mass transfer, 744

simulations, 600–601

Mixers

design, 574–578

flat-blade impellers, 576

mass transfer coefficients, 750–753

stage efficiency, 743–749

Mixing calculations in liquid-liquid extraction, 556–558

Molar flow rates

column diameter calculations, 392

packed distillation columns, 712

packed towers, 727

steam distillation, 284

Molar flux

diffusivity in dilute binary mixture, 634

Fickian diffusion, 634, 642

mass transfer, 667, 669

Maxwell-Stefan model, 685

membranes, 844

pervaporation, 892–893

Molar overflow. See Constant molal overflow (CMO) conditions

Molar reference velocity in Fickian diffusion, 641–642

Molar transfer rate in gas permeation, 845, 851

Molar velocity

absorbers and strippers, 731

Fickian diffusion, 643

Maxwell-Stefan model, 684

Mole and weight fractions versus mole and weight ratios

absorbers and strippers, mole fractions, 485–495

absorbers and strippers, mole ratios, 497–501

definition ratios, 497, 547, 611

leaching, 611

liquid-liquid extraction, mole fractions, 532–539

liquid-liquid extraction, mole ratios, 547–551

nomenclature, fractions and ratios, 533, 605

Molecular diffusion, 630

Molecular diffusion coefficient, 637

Molecular movement in mass transfer, 629–631

Molecular weight

Fickian diffusion, 642–643, 647–649, 651

hydrates, 773, 779–780

Knudsen diffusivity, 980

precipitation, 825

Monoethanolamine (MEA) in H₂S removal, 481

Monovalent-monovalent ion exchange, 972, 974–975

More volatile component (MVC)

azeotropic processes, 274–277

batch distillation, 342

binary flash distillation, 25

column distillation, 91–94, 106, 146

dilute absorption, 487

distillation cascades, 82–83, 85–87

equilibrium data, 18

Fenske equation, 252

McCabe-Thiele diagrams, 139, 142, 604

multicomponent distillation profiles, 197

packed distillation columns, 712

VLE, 20

Mother liquor in crystallization, 771

Motivation and confidence step in problem solving, 5

MSMPR crystallizers. See Mixed suspension, mixed product removal (MSMPR) crystallizers

Multicomponent distillation, 189. See also Aspen Plus

calculational difficulties, 189–194

CMO conditions, 199–206

homework, 206–212

ideal, 460–466

profiles, 194–199

references, 206

spreadsheets, 211–217

stage-by-stage calculations, 199–206

Multicomponent distillation approximate shortcut methods. See also FUG method

finite reflux ratios (Gilliland correlation), 259–262

homework, 263–270

minimum reflux (Underwood equations), 254–259

references, 263

simulations, 270

total reflux (Fenske equations), 250–254

Multicomponent distillation exact calculation procedures, 219. See also Aspen Plus

component mass balances, 221–225

discussion, 233–234

energy balances in matrix form, 229–231

flow rates and temperature initial guesses, 225

homework, 235–240

matrix solution, 219–221

Naphtali-Sandholm method, 232–233

references, 234–235

temperature convergence, 225–229

Multicomponent flash distillation

Aspen Plus, 67–76

overview, 36–42

spreadsheets for, 77–79

Multicomponent permeation, 858–860

Multicomponent simple batch distillation, 357–360, 372–374

Multicomponent VLE, 32–36

Multieffect distillation cascades, 462

Multieffect systems in energy conservation, 458–459

Multiple-pass trays, 378–379

Multistage batch distillation, 340, 352–353

constant reflux ratio, 353–357

variable reflux ratio, 357

Murphree efficiencies

absorption, 481

column diameter calculations, 394

column distillation, 154–156

extraction mixers, 743–745, 748

irreversible absorption, 508–509

Kremser equation with, 494

mixer-settler design, 578

stripping analysis, 489

trays, 385–387, 739–741

MVC. See More volatile component (MVC)

N

Nanofiltration, 838

Naphtali-Sandholm simultaneous convergence method, 232–233

Naphthalene

diffusivity, 648

example, elution chromatography, 936

solubility in carbon dioxide, 615–616

Narrow-boiling procedure in matrix solutions, 220–221

National Aeronautics and Space Administration (NASA), 7–8

Natural rubber membranes, 849

Newtonian convergence. See Convergence

Nickel chloride (NiCl₂) solubility in water, 775

Nitrogen (N₂)

adsorption equilibrium constant, 926

gas permeation, 895–896

molecule movement, 630

permeability, 849

purge gas systems, 934

separation from air in multieffect distillation system, 459

temperature swing adsorption, 946

VSA units, 950

Non-key (NK) components

definition, 190

Fenske equation, 252–253

multicomponent distillation, 225

Underwood equations, 257

Nonane K values, 33–35

Nonideal binary diffusion, 689–691

Nonideal ternary systems

Maxwell-Stefan model, 697–698

synthesis of distillation systems, 466–470

Nonlinear isotherms

adsorbents, 924

convergence, 1025–1027

Nonlinear solute movement, 961–962

diffuse waves, 962–965

shock waves, 965–969

Nonlinear sorption systems, 993–998

Nonrandom two-liquid (NRTL) parameters in LLE, 599–600

Nonrandom two-liquid (NRTL) procedure

multicomponent VLE, 36

nonideal ternary systems, 468–470

Nucleation in MSMPR crystallizers, 800–804

Nuclei in batch crystallization, 822

Numerical solution for variable binary diffusivity, 653–656

Nusselt number for mass transfer coefficients, 682

Nylon membranes, 849

O

O’Connell correlation

absorber efficiencies, 496

distillation tray efficiencies, 387–388

Octane

diffusivity, 648

K values, 33–35

Oldershaw design

foaming, 390

staged columns, 379

tray efficiencies, 389

Oleic acid, 535

Open steam heating, 132–138

Operating conditions in energy conservation, 455

Operating costs

changes, 454–455

packed column design, 417

Operating effects for costs, 445–454

Operating equation

analytical solutions, 161–162

binary column distillation, 111

binary flash distillation, 27–29

cocurrent absorbers, 737

concentrated immiscible extraction, 547

cross-flow extraction, 543

cross-flow permeation, 898

distillation curves, 288

feed lines, 122

gas permeation, 851, 855, 858

heterogeneous azeotropes, 274, 276–277

immiscible batch extraction, 551–552

irreversible absorption and cocurrent cascades, 509

leaching, 611

McCabe-Thiele dilute absorption, 487, 492, 503

McCabe-Thiele dilute extraction, 534

McCabe-Thiele dilute fractional extraction, 541

McCabe-Thiele dilute stripping, 489

McCabe-Thiele distillation, 117, 120, 135–136, 142–143

multicomponent stage-by-stage distillation, 204–205

multistage binary batch distillation, 353

reverse osmosis, 867

simulations of binary distillation, 157

total reflux, 152, 250

washing, 607–608

Operating lines

azeotropic processes, 274, 276, 280–281

binary column distillation, 146

binary flash distillation, 27

cocurrent absorbers, 737

concentrated immiscible extraction, 547, 549

concentrated absorbers, 500

countercurrent extraction cascades, 566

cross-flow extraction, 543–544

dilute absorption, 487–488

dilute extraction, 535–538

dilute fractional extraction, 542

feed line intersection operating lines, 121, 124

HETP and HTU relationship, 721–722

intermediate reboilers, 149

leaching, 611

McCabe-Thiele method, 116–117, 140–145

open steam heating, 135

packed distillation columns, 714–715, 718

partially miscible extraction, 569

pervaporation, 888

pinch points, 152

stripping analysis, 489

stripping columns, 151

Operating time in batch distillation, 361–362

Operating vapor velocity in column diameter calculations, 392

Operational suggestions in nonideal ternary systems, 466–468

Optimum configurations in ideal multicomponent distillation, 462–466

Optimum feed plate in distillation

binary, 91

Gilliland correlation, 260

McCabe-Thiele method, 118–120, 145

multicomponent distillation, 204–205, 246

Organic compounds, distillation drying, 277–282

Organic solvents, adsorption drying, 947–948

Orifice coefficient in sieve tray layout, 399

Osmosis. See Reverse osmosis (RO)

Outlet concentration

linear chromatography, 989–991

nonlinear sorption systems, 994–995

Outlets in staged column design, 380–384

Overall efficiency in binary column distillation, 154

Overflow liquid, washing, 607

Overflow loops in settler design, 579

Oxygen (O₂)

gas permeation, 895–896

permeability, 849

VSA units, 950

Oxygen bubbles, shrinking diameter of, 664–669

P

Packed beds for sorption systems, 918. See also Solute movement analysis

ion exchange, 919

mass and energy transfer in, 978–984

practical aspects, 998–1000

sorption systems, 918

Packed columns for distillation, absorption and stripping, 375–376

column type choices, 418–421

economic trade-offs, 417–418

flooding and diameter calculation, 411–417

homework, 425–433

HTU-NTU analysis, 712–720

introduction, 406

mass and energy transfer in, 615

packing height, 409–410

packings, 406–409

references, 421–425

Packed towers

Bolles and Fair correlation, 723–725

design, 406

H_G and H_L estimates, 725–729

mass transfer coefficients, 723–730

simple correlations, 729–730

Packing

costs, 441–442

energy conservation, 456

height, 409–410

Pall rings

HETP value, 410

size and F factors, 412–413

Parallel configuration for membrane separation processes, 840–842

Partial condensers

binary column distillation, 146, 154

flash distillation, 16

heat exchanger design, 445

matrix solutions, 223

tray efficiencies, 385

Partial pressures

batch steam distillation, 351

mass transfer coefficients, 678

Maxwell-Stefan model, 684

multicomponent VLE, 35

pervaporation, 883, 894

Partial reboilers

binary column distillation, 108–110, 115, 154

feed lines, 121

HETP method, 409

matrix solutions, 224

McCabe-Thiele method, 118

multicomponent distillation, 230–231

tray efficiencies, 385

Partially miscible extraction systems

Aspen Plus, 598–602

countercurrent extraction cascades, 561–569

extraction equilibrium, 553–556

McCabe-Thiele and triangular diagrams, 569–570

minimum solvent rate, 570–572

single-stage, 558–561

Particle density in sorption systems, 920

Particle size distribution (PSD). See also Crystal size distribution

antisolvent crystallization, 823

determining, 793

Passing streams

countercurrent extraction cascades, 563–567

distillation cascades, 85

leaching, 612

McCabe-Thiele diagrams, 117, 487

Pattern velocity in nonlinear sorption systems, 995–996

Pattern waves in nonlinear solute movement, 961–962

Payback periods

capital investments, 455

column changes, 454

costs, 449

Peclet number

linear chromatography, 990

lumped parameter mass transfer, 982

mass transfer coefficients, 672, 750

rate-based analysis of distillation, 755–756

Pellet density in sorption systems, 920

Peng-Robinson equation, 46

Penicillin manufacturing, 528

Pentane

azeotropic distillation, 303–305

diffusivity, 648

heat capacity, latent heat and boiling point data, 45

K values, 33–35

removal by absorption, 481

Permeability. See also Gas permeation

gas permeation, 847–849

membranes, 845

Permeance of membranes, 845

Permeate-in-series system, 842–843

Pervaporation, 883

basics, 883–886

experimental data, 886–892

feasibility calculation, 889–892

hybrid systems, 886

theoretical design, 892–895

Petroleum processing, 528

Petyluk columns, 460–461

Pharmaceutical industry, supercritical fluids for, 616

Phase equilibria

description, 4

eutectic systems, 785

prerequisites, 8

Phenol in extractive distillation, 298–300

Physical absorption, 481

Physical constants, 1054

Pickles, salt leaching, 611

Pinch points

binary column distillation, 152–153

profiles, 132, 195

stripping analysis, 489

Underwood equations, 254

Pinch technology in energy conservation, 456–457

Pinholes in gas permeation, 860–862

Pipe elbows in staged column design, 381

Plait points, 555

Plan step in problem solving, 6

Plant installed costs, 439

Plant operating rates changes, 454–455

Plate-and-frame system, 840–841

Platelet mass in dissolving solid particles, 668

Point efficiency

extraction mixers, 745

distillation trays, 386–387, 389, 738–739

Polarization modulus in ultrafiltration, 879

Polyamide polymers in membrane separation, 843–844

Polyethylene glycol (PEG)

antisolvent, 825

cross-flow extraction, 544–547

Polymer membranes

gas permeation, 847–848

membrane separation processes, 843–844

reverse osmosis, 862–863

ultrafiltration, 878

Polymer resins

ion exchange, 970

sorbents, 923

Polymerization effect in column type choices, 419

Polymorphic crystals, 814–815

Polystyrene membranes permeability, 849

Polystyrene resins in ion exchange, 970

Polysulfone

membrane separation processes, 843

ultrafiltration, 878

Ponchon-Savarit diagrams

binary column distillation, 110

leaching, 615

VLE, 21

Population balances in crystallization, 798–799, 813. See also Mixed suspension, mixed product removal (MSMPR) crystallizers

Porosity

sorption systems, 919–920

washing, 607

Porous particles, diffusion in, 979–980

Port switching in simulated moving beds, 958

Potassium chloride (KCl)

diffusivity, 652

MSMPR crystallizers, 811–814

solubility in water, 775

Potassium fluoride (KF), solubility in water, 775

Potassium nitrate (KNO₃)

continuous cooling crystallizers, 778

solubility in water, 775

Power-law kinetic model, 803

Power-law relationship, 801

Power number in mixer-settler design, 576–578

Prandtl number, 672, 681

Precipitation, 825

antisolvent addition, 825–826

salting out, 826–828

Prediction of distillation tray efficiency, 738–741

Preheating feeds, 473

Prerequisite material, 8–9

Pressure heads in sieve tray layout, 399–400

Pressure swing adsorption, 938, 948–956

Pressure-swing distillation processes

Aspen Plus, 326–329

azeotrope separation, 326–329

overview, 286–287

Pressures

absorption and stripping, 502

adsorption, 924

column diameter calculations, 393

column distillation, 90–91, 94, 107

cost effects, 446–448, 451

cost factor, 440–441

countercurrent extraction cascades, 561

crystallization, 772

distillation cascades, 82–83

energy conservation, 455, 457

equilibrium data, 18–20

Fickian binary gas diffusivities, 647

Fickian binary liquid diffusivities, 651

Fickian binary steady-state diffusion, 645

flash distillation, 16–17, 27, 30

gas permeation, 846–847, 851

linear driving-force model, 656

mass transfer coefficients, 678

Maxwell-Stefan model, 684–685

McCabe-Thiele method, 116

multicomponent convergence, 42–43

multicomponent distillation simulation, 243–246

packed column design, 408, 417–418

partially miscible systems, 553–554, 558

pervaporation, 883–884, 894

reverse osmosis, 862–864, 870–871

steam distillation, 282, 351

supercritical fluids, 615–617

tray design, 404–406

tray efficiencies, 387

ultrafiltration, 880

unit conversions, 1054

variable binary diffusivity, 653–654

VLE, 20, 32–35

Pretreatment for reverse osmosis, 863

Problem-solving

seven stage method, 5–7

skills prerequisites, 9

Profiles

binary column distillation, 132

composition. See Composition profiles

concentration. See Concentration profiles

multicomponent distillation, 194–199

Programming languages, learning, 184

Propane

adsorption isotherm, 924

K values, 33–35

Lennard-Jones potential parameters, 649

Propane-propylene separation, 459

Propanol diffusivity, 652

Propellers in mixer-settler design, 576

Proportional pattern waves, 961–962

Propylene K values, 33–35

Protein, salting out, 825–828

Protein alcohol dehydrogenase, 544–547

PSD (particle size distribution). See also Crystal Size Distribution

antisolvent crystallization, 823

determining, 793

Pseudo-steady state

binary mass transfer, 663

diffusion experiments with evaporation, 638

dissolving solid particles, 667–668

oxygen bubbles, 665

Pulsed-column extractors, 529–530

Pump-around distillation systems, 175

Pumps

flash distillation, 16

mixer-settler design, 576

pervaporation, 886

pressure swing adsorption, 950

subcooled reflux, 160

Punching patterns in sieve trays, 398

Pure solute crystals, 787–789

Purge step

crystallization, 771–772

elution chromatography, 935

pressure swing adsorption, 954

solute movement, 934–938

Pyridine-water-chlorobenzene LLE data, 548

Q

Quad command, 345

Quality of feed, q, 113

R

Rachford-Rice equation

flash distillation, multicomponent convergence, 43, 45–46

multicomponent flash distillation, 38–42

multicomponent gas permeation, 859

three-phase flash distillation calculations, 47–48

Raffinate phase

countercurrent extraction, 532, 562–564

equilibrium data, 548

immiscible batch extraction, 552–554

leaching, 613

mass transfer, 743

partially miscible systems, 555, 560–561

Rag layers in settler design, 579

Random packings

Bolles and Fair correlation, 723–729

correlations, 729–730

packing factors, 411–413

Raoult’s law

azeotropic processes, 278

binary flash distillation, 30

evaporating liquid drops, 665–666

multicomponent VLE, 35–36

reverse osmosis, 864

Raschig rings

packed column design, 407

size and F factors, 412–413

Rate-based distillation analysis, 753–756, 764–768

Rate transfer (RT) equation

gas permeation, 849–851, 855–857

pervaporation, 887, 889

reverse osmosis, 866

Ratings for tray design, 434

Ratio units. See Mole and weight fractions versus mole and weight ratios

Rayleigh equation

batch distillation, 341–344

batch distillation, multicomponent, 357–358

batch distillation, multistage, 352–353, 357

batch distillation, simple binary, 345–346, 349, 351

operating time, 361

Reactants in chemical reaction, 306

Reboilers

balancing calculated diameters, 397

costs, 443, 446, 449–450, 453–454

energy conservation, 459

Fenske equation, 250

heat transfer coefficients, 445

intermediate, 149

matrix solutions, 224

McCabe-Thiele method, 118

size, 443–444

tray efficiencies, 385

Reciprocating-plate columns extractors, 529–530

Recompression heat pumps, 459

Recovery analysis in concentrated absorbers, 500

Rectifying sections in distillation cascades, 86

Redistribution systems in packed column design, 408

Reference velocities

Fickian diffusion, 640–644, 647

film theory, 647

Reflux and reflux ratios

azeotropic processes, 274, 276–277, 281

batch distillation, 340

chemical reaction, 308

column distillation, 90–93, 95–96, 114–116, 146, 151–154

cost effects, 451

distillation cascades, 84–85

energy conservation, 455

extractive distillation, 298, 300

feed lines, 124

Gilliland correlation, 259–262

McCabe-Thiele method, 119, 140–142, 145

multicomponent distillation, 226, 460–461

multistage binary batch distillation, 353–357

open steam heating, 135

stripping columns, 151

subcooled, 159–161

Underwood equations, 254–259

Refrigeration costs, 447, 449, 451

Regenerable solvents in irreversible absorption, 508

Regeneration

description, 918

extraction process, 527

ion exchange, 976, 978

linear isotherms, 942–947

purge cycle, 934

solute movement analysis, 930

supercritical fluids, 616–617

temperature swing adsorption, 938–940, 947

Rejection coefficient in reverse osmosis, 868

Relative retention in chromatography, 1012

Relative volatility

azeotropic processes, 278–279, 282

binary column distillation, 154

binary flash distillation, 30–31

chemical reaction, 306–307

constant-mole batch distillation, 350

distillation cascades, 87

extractive distillation, 296

Fenske equation, 251, 253

film theory, 659–660

multicomponent distillation, 358, 360

pervaporation, 886

simple binary batch distillation, 346

ternary systems, 288–289, 293–296

tray efficiencies, 387–388

Underwood equations, 255–256, 258

Repressurization step in pressure swing adsorption, 951–953, 956

Residence times

chemical reaction, 306

crystallization, 770, 814

downcomers design, 399, 401, 404

HTU-NTU analysis, 713

mass transfer coefficients, 673–675, 679

membrane separation processes, 843

mixers, 576, 578

rate-based analysis of distillation, 755–756

solute movement, 984

stage efficiency, 740, 743–745

Residue curves

azeotropic distillation, 303–304

chemical reaction, 306–307

extractive distillation, 296–298, 301

multicomponent simple batch distillation, 358–359

spreadsheets, 336–338

ternary systems, complex, 291–296

ternary systems, nonideal, 467, 470

Residuum Oil Supercritical Extraction (ROSE) process, 616

Resins in ion exchange, 970–973

Resolution in linear chromatography, 991–993

Resources for separation process engineering, 9–11

Retentate-in-series system, 841–842

Retentate-recycle system, 843

Retrofits for energy conservation, 455–456

Retrograde phenomenon in supercritical fluids, 616

Reverse addition crystallization, 825

Reverse osmosis (RO), 862–863

analysis, 865–867

holes in membrane, 908–909

mass transfer of concentration polarization, 872–876

membrane properties, 869–871

osmosis analysis, 863–865

well-mixed modules, 867–872

Reversible reactions

absorption, 481

distillation, 306–308

methyl acetate, 306

Reynolds analogy, 680–681

Reynolds, Osborne, 680–681

Reynolds number

definition, 671–672

falling laminar liquid film, 676–677

impellers, 577

lumped parameter mass transfer, 982

mass transfer coefficients, 678–680, 750–751

reverse osmosis, 873

settler design, 580–581, 584

wetted-wall column, 678

Right triangular diagrams in LLE, 554–556

Right triangular diagrams in leaching, 612–615

Ripples in falling laminar liquid film, 677

RO. See Reverse osmosis (RO)

Roads, deicing, 783

Robeson plots, 908

Robeson’s limit in gas permeation, 848

ROSE (Residuum Oil Supercritical Extraction) process, 616

Rotary-agitation columns extractors, 529–530

Rubber membranes, 849

Runge-Kutta integration, 292

Ryff, Walter, 340

S

S-shaped breakthrough curves, 986, 989

Saddles

packed column design, 407

size and F factors, 412

Safety. See also Fires

activated carbon columns, 946–947

adsorbers, 1000

column height, 454

distillation hazardous chemicals, 463

fire prevention in distillation columns, 419, 421

nitromethane (methyl nitrate), 320

total reflux operation, 152

vacuum distillation columns, 446

Salt balance in evaporative crystallizers, 788–789

Salting out precipitation, 826–828

Salts in crystallization, 772–776

Saturated line in VLE, 20–23

Saturation of adsorbents, 924

Scale-up procedure

continuous cooling crystallizers, 777

crystallization, 800, 820

mixer-settler design, 578

packings, 408

supercritical fluids, 617

Schmidt number

definition, 672, 725

Fickian diffusivities, 650

H_G and H_L estimation, 723–729

lumped parameter mass transfer, 982

mass transfer coefficients, 672, 678, 680–682, 750

random packings correlations, 730

reverse osmosis, 873

Scraping in continuous cooling crystallizers, 776–777

Screen analysis. See also Crystal Size Distribution

crystallization data, 795–798

MSMPR crystallizers, 805, 809–810

Seal pans in staged column design, 381

Secondary nucleation in crystallization, 801

Sections in McCabe-Thiele method, 138–140

Seed crystals in crystallization, 801

Seeding

crystal size control, 818–819

crystallization, 770, 814–819, 824

CSD analysis, 815–818

Selectivity

ion exchange, 975

membranes, 844, 848

pervaporation, 886–889

reverse osmosis, 867–870

solvents, 531, 534

supercritical fluids, 616

Self-sharpening shock waves, 967–969

Semi-empirical mass transfer coefficients, 677–679

Semibatch crystallization, 820–825

Semipermeable membranes, 863

Separating agents in absorption, 481

Separation factors in pervaporation, 886–887

Separation process engineering overview

equilibrium concepts, 3–4

homework, 12–13

importance, 1–3

mass transfer concepts, 4–5

prerequisite material, 8–9

problem-solving methods, 5–7

references, 11–12

resources, 9–11

simulations, 8

units, 7–8

Separation Research Program (SRP), 418

Sequential convergence for flash distillation, 43

Sequential optimization approach, 462–466

Sequential solution procedure for flash distillation, 26–30

Settlers. See also Decanters, Mixer-settler systems

design, 578–581

simulations, 600–601

Shape factor in MSMPR crystallizers, 802–803

Sherwood number

definition, 671

falling laminar liquid film, 676–677

lumped parameter mass transfer, 982

mass transfer coefficients, 671, 750

reverse osmosis, 873

Shock waves. See also Solute movement analysis

ion exchange, 974, 976–977

nonlinear solute movement, 961, 965–969

nonlinear sorption systems, 995–996

Shrinking diameter of oxygen bubbles, 664–669

Shrinking spheres in binary mass transfer, 662–664

Side enrichers, 460–461

Side streams

binary distillation, 147–149

multicomponent distillation, 462–463

Side strippers, 460–461

Sieve analysis in crystallization, 793–798, 810–811

Sieve trays

column diameter calculations, 390, 392

column distillation, 88–89

column type choices, 419

costs, 441–442, 446

efficiencies, 386–387, 496

staged column design, 376, 398–404

Sieve-type membranes, 879

Silica gel sorbents, 923

Silicone rubber membranes

membrane separation processes, 844, 846

permeability, 849

Simpson’s rule

mathematical formulas, 345

multistage binary batch distillation, 356

packed distillation columns, 718–719

simple binary batch distillation, 345–348

variable binary diffusivity, 655

Simulated moving beds (SMB)

Aspen Chromatography, 1038–1042

overview, 956–961

Simulations. See also Aspen Chromatography and Aspen Plus

absorption and stripping, 520–525

azeotropic distillation, 304

chromatography, 1019–1023

column distillation, 93, 156–158, 179–183

complex distillation methods, 326–336

extractive distillation, 332–336

flash distillation, 67–76

liquid-liquid extraction, 572–573, 598–602

mass transfer analysis, 764–768

multicomponent distillation, 241–248, 270

overview, 8

pervaporation, 894–895

tray and downcomer design, 433–435

troubleshooting guide, 1047–1049

Simultaneous convergence

flash distillation, 42–47

Naphtali-Sandholm, 232–233

Simultaneous solutions

binary flash distillation, 30–32

evaporative and vacuum crystallizers, 790–793

Single-column binary heterogeneous azeotrope systems, 273–274, 329–331

Single-pass pervaporation systems, 886–887

Single-porosity model of adsorption, 983, 985

Single-stage LLE systems

immiscible, 543–547

partially miscible, 558–561

Six-tenths rule for capital costs, 438

Size calculation

flash distillation drums, 48–53

distillation tray design, 433–435

Size exclusion

chromatography, 931

sorption systems, 919

Skarstrom cycle for PSA, 948–950

Slope of distillation feed lines, 123, 125–126

Slot area in valve tray design, 406

Slurry adsorbents, 622

Sodium acetate (NaC₂H₃O₂), solubility in water, 775

Sodium carbonate (Na₂CO₃)

enthalpy-composition diagrams, 790–791

vacuum crystallizers, 791–793

Sodium chloride (NaCl)

crystallization, 772–776, 824–825

deicing roads, 783

diffusivity, 652

dissolution, 669–670

evaporative crystallizers, 788

ion exchange, 976–977

reverse osmosis, 876–877

solubility in water, 775

Sodium hydroxide (NaOH)

H₂S removal, 481

washing process, 609

Sodium ion exchange, 970, 972

Sodium nitrate (NaNO₃) solubility in water, 775

Sodium sulfate (Na₂SO₄) solubility in water, 775

Solid-liquid extraction (SLE), 610–612. See also Leaching

Solid particles

dissolution example, 669–670

dissolving in concentrated liquids, 668–669

dissolving in dilute liquids, 667–668

Solid solutions, 784–785

Solubility envelope in ternary LLE systems, 554–555

Solubility parameter

gas permeation, 847

liquid-liquid extraction, 531

salts, 826

Solute crystals, 777–782

Solute mass flux in ultrafiltration, 882

Solute movement analysis

chromatography applications, 930–938

derivation, 983–984

diffuse waves, 962–965

ion exchange, 973–974, 978

linear analysis, 930–961

nonlinear, 961–969

nonlinear analysis for ion exchange, 973–978

pressure swing adsorption, 938, 948–956

simulated moving beds, 956–961

shock waves, 965–969

temperature swing adsorption, 938–948

Solute velocity

elution, 988

linear chromatography, 991

nonlinear solute movement, 963

pressure swing adsorption, 953–954

simulated moving beds, 960

sorption columns, 930–932

temperature swing adsorption, 943–944

Solute waves in pressure swing adsorption, 951

Solutes

absorption and stripping, 482

countercurrent extraction, 532

crystallization, 771, 776

dilute extraction systems, 539–542

evaporative crystallizers, 787–789

immiscible batch extraction, 552–553

liquid-liquid extraction, 527–528

partially miscible systems, 554, 560

reverse osmosis, 863, 866

supercritical fluids, 616

Solution-diffusion mechanism in gas permeation, 847

Solvent flux

reverse osmosis, 866

ultrafiltration, 878–880

Solvents

absorption, 481–482

azeotropic distillation, 302–306

constant-mole batch distillation, 349–350

continuous cooling crystallizers, 778

crystallization, 770–771, 776

dilute fractional extraction flow rate, 540–542

extractive distillation, 296–302

gradients, 938

immiscible batch extraction, 551–553

irreversible absorption, 508

liquid-liquid extraction, 527–528, 531–532

minimum solvent rate, 570–572

reverse osmosis, 863–865

selecting for LLE, 531

semibatch crystallization, 820

supercritical fluids, 616

temperature swing adsorption, 946

Sorbates, 978

Sorbents and sorption equilibrium, 918–919

adsorption equilibrium behavior, 924–929

definitions, 919–922

sorbent types, 922–923

Sorel method, 110

Sorption systems, 918

homework, 1003–1018

ion exchange, 970–978

LUB approach, 993–999

mass and energy transfer in packed beds, 978–984

mass transfer linear systems, 985–993

nonlinear solute movement, 961–970

practical design and operation, 998–1000

references, 1000–1003

solute movement analysis for linear systems, chromatography, 930–938

solute movement analysis for linear systems, TSA and PSA, 938–961

sorbents and sorption equilibrium, 918–929

spreadsheets, 1018

Specific heat unit conversions, 1053

SPEEDUP solver, 984

Spherical particles in diffusion, 979–980

Spiral-wound membranes

membrane separation processes, 840–841

reverse osmosis, 863, 873

Split drawoffs in staged column design, 381

Splits in multicomponent distillation simulation, 244

Spray regime

column distillation, 90

rate-based analysis of distillation, 754

Spreadsheets

binary column distillation, 178, 183–188

crystallization, 835–836

diffusion, 707–709

flash distillation, 77–79

gas permeation, 854–855

mass transfer analysis, 765

membrane separation processes, 911–912, 914–916

multicomponent distillation, 211–217, 359–360, 372–374

overview, 8

residue curves, 336–338

sorption systems, 1018

SRP (Separation Research Program), 418

Stage-by-stage calculations

absorbers, co-current, 508–509

absorbers, concentrated, 497–501

absorbers, dilute, 485–489

absorbers, dilute, multi-solute, 502–504

batch distillation, multistage, 352–357

binary column distillation, 110–116

binary heterogeneous azeotropes, 274–277, 279–282

countercurrent extraction, concentrated, immiscible, 547–550

countercurrent extraction, partially miscible, 562–569

cross-flow extraction, dilute, 543, 546

cross-flow extraction, partially miscible, 560–561

description, 3

fractional extraction, dilute, 541–542

internal balances, distillation, 106–110

leaching, constant flow rates, 611–612

leaching, variable flow rates, 612–614

liquid-liquid extraction, dilute, 532–537

liquid-liquid extraction, dilute, multi-solute, 538

McCabe-Thiele method, 116–132

multicomponent distillation, 192–206

spreadsheets, 212–217

strippers, concentrated, 497–501

strippers, dilute, 489–490

strippers, dilute, multi-solute, 502–504

washing, 607–610

Staged column design, 375–376

balancing calculated diameters, 396–397

column diameter calculations, 390–396, 501–502

downcomers and weirs, 378–380

equipment, 376–385

height, 446

homework, 425–433

inlets and outlets, 380–384

references, 421–425

sieve tray layout and tray hydraulics, 398–404

tray and downcomer design, 433–436

tray efficiencies, 385–390

valve tray design, 404–406

Stagnant films, transfer through, 660–661

Stanton number, 672

Steady-state binary Fickian diffusion

with convection, 640–647

without convection, 633–638

Steady-state energy balance in column distillation, 95

Steady-state mass balance

concentrated immiscible extraction, 547

crystallizers, 777–781

cross-flow extraction, 543

extraction mixers, 744

falling laminar liquid film, 674

McCabe-Thiele diagrams, 498

washing, 607

Steady-state overall flux in gas permeation, 846

Steady-state population balance in crystallization, 799, 804

Steady-state solvent flux in ultrafiltration, 880

Steam

costs, 447–449

energy conservation, 457–459

heat exchanger design, 443–444

Steam distillation

batch, 350–352

steady-state, columns, 282–285

Steam heating for pervaporation, 886

Stefan, Josef, 683

Stepping off stages. See Stage-by-stage calculations

Steric exclusion in sorbents, 923

Stirred tanks

extraction, 573–578

membrane separation processes, 840

reverse osmosis, 874, 876

Stokes-Einstein equation, 651

Stokes law in settler design, 580–582, 584

Stream tearing, 326

Strippers and stripping, 481–482

analytical solutions, 490–495

column diameters, 501–502

concentrated systems, 497–501

dilute multisolute, 502–504

dilute systems, 489–490

equilibrium, 483–485

homework, 511–520

HTU-NTU analysis, 731–736

Kremser equation, 494–495

matrix solution, 504–508

McCabe-Thiele and Kremser procedures, 605

multicomponent distillation, 460–461

references, 510–511

transfer through stagnant films, 660–661

Stripping distillation columns, 150–151

Stripping sections in distillation

azeotropic processes, 275–276

binary column distillation, 108–109, 111, 150–151

distillation cascades, 87

feed lines, 121

McCabe-Thiele method, 117–119

multicomponent distillation, 204

packed distillation columns, 714–715, 718–720

simulated moving beds, 958

stage-by-stage calculations, 212–217

Underwood equations, 256

Strong resins in ion exchange, 970

Structural density

elution chromatography, 936

sorption systems, 920

Structured packings. See also Packed columns for distillation, absorption and stripping

description and photo, 407–408

F factors 412–413

fires from, 419

Subcooled reflux in binary column distillation, 159–161

Submerged objects geometry, 663

Sucrose (C₁₂H₂₂O₁₁)

diffusivity, 652

solubility in water, 775

Sugar, leaching, 622

Sulfolane in petroleum processing, 528

Sulfur dioxide (SO₂) absorption, 735–736

Sulfur in column type choices, 419

Sum-of-resistances model in film theory, 659

Supercritical fluids (SCFs), 615–617

Superficial velocity in sorption systems, 920

Superheated boilup, 159–161

Superposition

linear systems, 986–989

ultrafiltration, 881

Supersaturation

batch crystallizers, 821–822

continuous cooling crystallizers, 777

crystallization, 770–771

crystallization seeding, 814–816

evaporative crystallizers, 785

MSMPR crystallizers, 800–804

Surface diffusion, 980

Surface tension data, 431

Surfactants in settler design, 580

Symmetric breakthrough curves in LUB approach, 996–997

Synthesis of column sequences, 460–466

Synthesis of distillation systems, 466–470

T

Tangent pinch points

binary column distillation, 153

stripping analysis, 489

Temperature effects

adsorbents, 924–925

column diameter calculations, 393

crystal size control, 819

crystallization, 772–776, 820–823

diffusion, 980

diffusion experiments by evaporation, 636–638, 644–647

distillation cascades, 83–85

distillation, thermal decomposition, 90, 302, 306

energy conservation, 458–459

equilibrium data, 18–20

eutectic systems, 782

feed lines, 123

Fickian binary gas diffusivities, 647–650

Fickian binary liquid diffusivities, 651–653

flash distillation, 16–17, 30, 39

flash drum, 26, 31

gas permeation, 851

heat exchanger design, 443–444

intermediate reboilers, 149, 151

liquid-liquid extraction equilibrium, 556

matrix solutions, 220–221

Maxwell-Stefan model, 684–685

molecular movement, 629–630

MSMPR crystallizers, 814

multicomponent distillation calculations, 225

multicomponent distillation profiles, 194–195, 199–205

multicomponent distillation simulation, 244–246

multicomponent VLE, 32–34

multisolute absorption and stripping, 502

Naphtali-Sandholm method, 232

pervaporation, 884, 886–889, 892

profiles, 132, 196, 308

rate-based analysis of distillation, 754

reverse osmosis, 864–865

simultaneous multicomponent convergence, 43–46

solute movement, 938, 984

stage-by-stage calculations, 213–215

steam distillation, 282–285, 352

supercritical fluids, 615–616

temperature swing adsorption, 939

ultrafiltration, 880

Underwood equations, 256

unit conversions, 1054

VLE, 20–24

washing process, 609

Temperature-composition diagrams, 21–22

Temperature convergence in multicomponent distillation, 225–229

Temperature gradient method in chromatography, 938

Temperature programming in chromatography, 938

Temperature swing adsorption (TSA), 938–948

Ternary mass transfer in Maxwell-Stefan model, 695–697

Theoretically derived mass transfer coefficients, 672–677

Thermal conductivity in Fourier’s model, 631

Thermal cycles in solute movement, 938

Thermal equilibrium, 3

Thermal waves in temperature swing adsorption, 939–941, 944

Thermally coupled distillation systems, 460–461

Thermodynamics of osmosis, 864. See also Reverse osmosis

Thermosiphon reboilers, 381

Thomas algorithm, 224, 227–228, 506

Three-phase flash calculations, 47–48

Tie lines

partially miscible systems, 555, 571

stage-by-stage calculations, 564, 566

Time unit conversions, 1054

Toluene data, 1062–1063

Top operating lines

azeotropic processes, 273–274, 276, 280–281

binary column distillation, 146

feed lines, 124

McCabe-Thiele method, 117–119, 130, 140–145

open steam heating, 135–137

pinch points, 152

simulations, 157

stripping columns, 151

Tortuosity in sorption systems, 922

Total annual costs (TAC), 449

Total condensers

batch distillation, 344

mass and energy balance calculations, 95–96

McCabe-Thiele diagrams, 116, 138

multicomponent distillation, 229–231

Total flow

absorbers and strippers, 502, 504, 506

absorber and stripper column diameters, 502

Kremser equation, 490, 539, 541

leaching, 611

liquid-liquid extraction, 532–533

McCabe-Thiele diagrams, 497, 532, 534–535, 569, 609, 611

multicomponent distillation profiles, 194–195

washing, 607–608

Total flux in Fickian diffusion, 640–642, 644–646

Total operating costs, 446–449

Total reboilers in binary column distillation, 147–148

Total reflux

binary column distillation, 151–152

complex ternary systems, 288–290, 293–296

Fenske equation, 250–254

HETP method, 409

Total surface area in MSMPR crystallizers, 808

Total transfer rate in falling laminar liquid film, 676

Towers (columns)

casing costs, 440–441, 450–451

cost formula, 441

leaning, 425

Transfer units in HTU-NTU. See HTU-NTU analysis

Tray efficiencies. See also Murphree efficiencies

multicomponent distillation, 246

prediction of, 738–741

staged column design, 385–390

Trays. See also Bubble-cap trays, Chimney trays, Sieve trays, Valve trays

azeotrope separation, 328

column diameter calculations, 390–392

column distillation, 88–90

costs, 449–451

energy conservation, 455–456

hydraulics, 398–404

staged column design, 376–380, 433–436

Trial-and-error (guess-and-check) procedures

batch distillation, 346, 348, 353

binary column distillation, 110–111

countercurrent extraction cascades, 567

dilute systems, 494–495

liquid-liquid extraction, partially miscible, 555

membrane separation processes, 898

multicomponent convergence, 43–46

multicomponent distillation, 201–204

multisolute absorbers and strippers, 503–504

washing, 610

Triangular diagrams

countercurrent extraction cascades, 562

leaching, 612–615

mass balances, 290

partially miscible systems, 554–557, 560–563, 569–570

residue curves, 291

stage-by-stage extraction calculations, 566–567

Trichloroethane, Henry’s law constant, 485

Tridiagonal matrices. See also Thomas algorithm

concentrated absorbers and strippers, 506

distillation, 224

extraction simulations, 572

inverting, 224, 227

Triethylamine NRTL parameters, 599

True moving bed (TMB) systems

Aspen Chromatography, 1038–1042

description, 957–958

Tube-in-shell membrane system, 840–841

Turbulent tank mixing for reverse osmosis, 874

Turndown, tray, 376, 380, 386

Two-column systems

azeotrope separation, 331–332

azeotropic distillation, 274–277

Two-porosity models for diffusion, 981

Two-stage countercurrent immiscible batch extraction, 552

Tyler Screen sizes, 793–794

Type, equations solved by, 220

U

Ultrafiltration (UF), 877–883

Uncontrolled cooling in batch crystallization, 821–822

Underflow liquid, washing, 606–608

Underwood equations, 254–259

UNIFAC group contribution method, 36

UNIQUAC method, 36

Unit operation, 2

Units

conversions, 1053–1054

overview, 7–8

prerequisites, 9

Unsteady binary Fickian diffusion, 638–639

Utility costs, 447–449

V

Vacuum distillation columns

costs, 90, 446

diameters, 446

pressure drop, 414

structured packings, 408

uses, 418

Vacuum crystallizers, 785

crystallization, 776

equipment, 785–787

simultaneous calculations, 790–793

Vacuum pumps in pervaporation, 886

Vacuum swing adsorption (VSA), 948, 950

Valve trays

column diameter calculations, 390

column distillation, 90

column type choices, 419

costs, 441–442

efficiencies, 386–387, 496

pressure drop, 405

staged column design, 376, 404–406

van Laar equation. See Activity coefficients

van’t Hoff equation, 864

Vapor density

column diameter calculations, 395, 418

drum size calculations, 48, 52

ideal gas law determination, 52, 852

Vapor flow rates

absorbers and strippers, 506

binary distillation, 30, 93, 148

distillation cascades, 83, 85

drum size calculations, 48–49, 52–53

energy conservation, 455

enthalpy-composition diagrams, 31

feed lines, 122

froth regime, 88

multicomponent distillation, 194–195, 220, 225, 229–231

packed towers, 727

stripping and enriching columns, 151

tray efficiencies, 390, 392

Underwood equations, 255–256

valve trays, 376

Vapor-liquid equilibrium (VLE)

activity coefficients, 36

azeotrope separation, 327

complex ternary systems, 287–288

correlations, 36–37

data sources, 19

DePriester charts, 33–35

description, 3, 17–18

extractive distillation, 298

flash distillation, 32–36

graphical representation, 20–25

liquid-liquid extraction, 572

multicomponent distillation, 199, 245

pressure-swing processes, 286–287

Raoult’s law, 35

simulations, 71–72

Vapor mole fractions

binary flash distillation, 26

linear driving-force model, 656

Vapor permeation, 838

Vapor-phase mass transfer coefficient, 755

Vapor pressure (VP)

Antoine equation, 35–36, 60, 62, 314, 319, 368, 370

ethanol, 636–637

pervaporation, 892

Raoult’s law, 35

reverse osmosis measurements, 864

steam distillation, 282

Vapor recompression heat pumps, 459

Vapor velocity. See also Vapor flow rates

balancing calculated diameters, 396

binary column distillation, 159

column diameter calculations, 390, 392–393

operating time, 361

rate-based analysis of distillation, 755–756

regime change, 90

sieve tray layout, 398–399

tray efficiencies, 386–387, 389

valve tray design, 404

Vaporization efficiencies in batch steam distillation, 351

Variable binary diffusivity, 653–656

Variable flow rates in leaching, 612–615

Variable reflux ratio in multistage distillation, 357

Variables in Gibbs phase rule, 19

VBA. See Visual Basic for Applications (VBA)

Velocities

elution chromatography, 936

falling laminar liquid film, 674–675, 677

interstitial. See Interstitial velocity

ion exchange, 974–975

mass transfer coefficients, 671–672

solute. See Solute velocity

sorption systems, 920

thermal waves, 939, 944

vapor. See Vapor velocity

Venturi valves, 376

Vertical flash drums size calculation, 48–50

Vertical packed beds, 919–922

Vignes correlation, 653, 689

Vinyl chloride, Henry’s law constant, 485

Viscosities

binary column distillation efficiency, 154

mixer-settler design, 573, 577

resource, 430

settler design, 580

tray efficiencies, 387, 389

unit conversions, 1053

Visual Basic for Applications (VBA), 8

binary column distillation, 178, 811–814

Do loops, 185

For...Next loops, 184

functions, 184

membrane separation processes, 914–916

multicomponent distillation, 212, 359–360

overview, 183–188

residue curves, 336–338

stage-by-stage calculations, 215–217

VLE. See Vapor-liquid equilibrium (VLE)

Volatile organic compounds (VOCs), 939

Volume available in sorption systems, 919–920

Volume unit conversions, 1053–1054

Volumetric average velocity, 643

Volumetric flow rates

absorber and stripper column diameter, 502

column diameter calculations, 390

crystallization, 799

drum size calculations, 50

extraction mixers, 743

gas permeation, 845–862

membrane separation processes, 898

mixer-settler design, 575

Volumetric fluxes

gas permeation, 846, 851, 855–856

membranes, 844

pervaporation, 892

steady-state binary Fickian diffusion, 642

Volumetric fraction in mixer-settler design, 575–576

W

Wakao and Funazkri correlation, 982

Washing

equilibrium, 607

homework, 619–627

McCabe-Thiele and Kremser procedures, 605

McCabe-Thiele diagrams, 608–610

overview, 606–608

references, 618

Wastewater treatment, 947

Water

costs, 447–449, 451

diffusivity for gases, 648

diffusivity for liquids, 652–653

latent heat of vaporization, 134

Lennard-Jones potential parameters, 649

polarity, 301

solubility of solutes in, 776

Water-acetic acid-isopropyl ether, equilibrium data, 568

Water balance

continuous cooling crystallizers, 779

evaporative crystallizers, 788–789

Water-chloroform-acetone equilibrium data, 554

Water crisis, 862

Water-ethanol

azeotropic distillation, 303, 305

binary flash distillation, 27–30

extractive distillation, 296–297

pervaporation, 887–895

VLE, 18, 20–25

Water-ethanol-benzene residue curves, 293

Water of hydration in crystallization, 773–774

Water-sodium chloride mixtures, 783

Water softening, 970, 978

Watkins correlation, 49

Weak resins in ion exchange, 970

Weeping in sieve trays, 401–402, 404

Weight of seeds

batch crystallization, 822

crystal size control, 819

Weight ratios. See Mole and weight fractions versus mole and weight ratios

Weight unit conversions, 1053

Weighted average crystal length, 809

Weirs

adjustable, 380, 425

column distillation, 88–89

notched, 380, 382

sieve tray layout, 398–401, 403

staged columns, 378–382

Well-mixed modules in reverse osmosis, 867–872

Wide-boiling feeds in flash and column distillation, 43–44

Wilke-Chang theory, 651

Wilson equation, 298

Withdrawal lines in binary distillation, 148–149

X

x-intercept in McCabe-Thiele diagrams, 27

Y

y-x equilibrium graphs, 20–24

y=x line on McCabe-Thiele diagrams

flash distillation, 24–25, 28

intermediate reboilers, 149

McCabe-Thiele diagrams, 27–29, 143–144

side streams, 148

washing, 607

y=x line perfectly mixed gas permeation, 855–856

Yield in MSMPR crystallizers, 814

Z

Zeolites

adsorbents, 920

molecular sieves, 923

sorbents, 923

Zones

simulated moving beds, 958–959

solute movement, 938

Zuiderweg correlation, 754