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
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
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
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
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
Fenske equation, 250
gas permeation, 848
irreversible absorption, 508
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
prerequisites, 8
pressure-swing processes, 286–287
reverse osmosis, 867
simultaneous multicomponent convergence, 43
solute movement, 931
sorption systems, 920
stripping analysis, 489
temperature swing adsorption, 941–943
three-phase flash calculations, 47
total reboilers, 148
washing, 607
Mass flux
diffusivity in dilute binary mixture, 635
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
concentration polarization in reverse osmosis, 872–876
Fickian model of diffusivity, 632
gas permeation, 847
linear chromatography, 991
liquid-liquid extraction, 531
pressure swing adsorption, 950
reverse osmosis, 866
ultrafiltration, 879
Mass transfer analysis, 711
correlations for packed towers, 723–730
HETP and HTU relationship, 720–722
prediction of distillation tray efficiency, 738–741
spreadsheets, 765
Mass transfer coefficients
cocurrent absorbers, 738
linear driving-force model, 656–657
mixer stage efficiency, 746–748
packed distillation columns, 714, 716
rate-based analysis of distillation, 754
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
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
diffusion and mass transfer, 683–698
Fickian diffusivities relationship, 688–689
film theory, 657
ideal ternary systems, 691–695
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
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
countercurrent extraction cascades, 565
cross-flow extraction, 543–546
dilute fractional extraction, 542
distillation cascades, 82
equilibrium stages, 452
extractive distillation, 299–300
feed lines, 121
intermediate condensers, 149, 151
intermediate reboilers, 149, 151
irreversible absorption, 509
vs. Lewis analytical method, 161–162
maldistributions, 428
miscellaneous separations, 617–618
multisolute absorption and stripping, 502–504
multistage binary batch distillation, 353–355, 357
packed distillation columns, 715
partially miscible systems, 560, 569–570
side streams, 148
spreadsheets, 186
stripping analysis, 490
Meal, leaching calculations, 613
Melt crystallization, 784
Melting points in eutectic systems, 783–784
Membrane separation processes, 837–838
bulk flow pattern effects, 895–899
design problems, 897–898, 912–913
membrane thickness, 845
spreadsheets, 911–912, 914–916
system properties, 839
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
heat capacity, latent heat and boiling point data, 45
permeability, 849
pressure swing adsorption, 951–956
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
side streams, 148
Minimum-boiling azeotropes, 24–25
Minimum reflux
binary column distillation, 151–153
Minimum solvent rate
concentrated absorber, 498–501
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
Mixed systems, binary permeation in, 848–858
Mixer-settler systems. See also Mixers, Settlers
countercurrent extraction cascades, 567
leaching, 610
mass transfer, 744
flat-blade impellers, 576
mass transfer coefficients, 750–753
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
Maxwell-Stefan model, 685
membranes, 844
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
Knudsen diffusivity, 980
precipitation, 825
Monoethanolamine (MEA) in H2S removal, 481
Monovalent-monovalent ion exchange, 972, 974–975
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
references, 206
stage-by-stage calculations, 199–206
Multicomponent distillation approximate shortcut methods. See also FUG method
finite reflux ratios (Gilliland correlation), 259–262
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
energy balances in matrix form, 229–231
flow rates and temperature initial guesses, 225
Naphtali-Sandholm method, 232–233
temperature convergence, 225–229
Multicomponent flash distillation
Multicomponent permeation, 858–860
Multicomponent simple batch distillation, 357–360, 372–374
Multieffect distillation cascades, 462
Multieffect systems in energy conservation, 458–459
Multistage batch distillation, 340, 352–353
constant reflux ratio, 353–357
variable reflux ratio, 357
absorption, 481
column diameter calculations, 394
extraction mixers, 743–745, 748
irreversible absorption, 508–509
Kremser equation with, 494
mixer-settler design, 578
stripping analysis, 489
MVC. See More volatile component (MVC)
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
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
multicomponent distillation, 225
Underwood equations, 257
Nonideal binary diffusion, 689–691
Nonideal ternary systems
synthesis of distillation systems, 466–470
Nonlinear isotherms
adsorbents, 924
Nonlinear solute movement, 961–962
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’Connell correlation
absorber efficiencies, 496
distillation tray efficiencies, 387–388
Octane
diffusivity, 648
Oldershaw design
foaming, 390
staged columns, 379
tray efficiencies, 389
Oleic acid, 535
Operating conditions in energy conservation, 455
Operating costs
packed column design, 417
Operating effects for costs, 445–454
Operating equation
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
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
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 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)
permeability, 849
VSA units, 950
Oxygen bubbles, shrinking diameter of, 664–669
Packed beds for sorption systems, 918. See also Solute movement analysis
ion exchange, 919
mass and energy transfer in, 978–984
sorption systems, 918
Packed columns for distillation, absorption and stripping, 375–376
flooding and diameter calculation, 411–417
introduction, 406
mass and energy transfer in, 615
Packed towers
Bolles and Fair correlation, 723–725
design, 406
mass transfer coefficients, 723–730
Packing
energy conservation, 456
Pall rings
HETP value, 410
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
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
countercurrent extraction cascades, 561–569
extraction equilibrium, 553–556
McCabe-Thiele and triangular diagrams, 569–570
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
removal by absorption, 481
Permeability. See also Gas permeation
membranes, 845
Permeance of membranes, 845
Permeate-in-series system, 842–843
Pervaporation, 883
feasibility calculation, 889–892
hybrid systems, 886
Petroleum processing, 528
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
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
membrane separation processes, 843–844
ultrafiltration, 878
Polymer resins
ion exchange, 970
sorbents, 923
Polymerization effect in column type choices, 419
Polystyrene membranes permeability, 849
Polystyrene resins in ion exchange, 970
Polysulfone
membrane separation processes, 843
ultrafiltration, 878
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
washing, 607
Porous particles, diffusion in, 979–980
Port switching in simulated moving beds, 958
Potassium chloride (KCl)
diffusivity, 652
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
Precipitation, 825
Prediction of distillation tray efficiency, 738–741
Preheating feeds, 473
Pressure heads in sieve tray layout, 399–400
Pressure swing adsorption, 938, 948–956
Pressure-swing distillation processes
Pressures
absorption and stripping, 502
adsorption, 924
column diameter calculations, 393
column distillation, 90–91, 94, 107
countercurrent extraction cascades, 561
crystallization, 772
Fickian binary gas diffusivities, 647
Fickian binary liquid diffusivities, 651
Fickian binary steady-state diffusion, 645
flash distillation, 16–17, 27, 30
linear driving-force model, 656
mass transfer coefficients, 678
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
reverse osmosis, 862–864, 870–871
tray efficiencies, 387
ultrafiltration, 880
unit conversions, 1054
variable binary diffusivity, 653–654
Pretreatment for reverse osmosis, 863
Problem-solving
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
Lennard-Jones potential parameters, 649
Propane-propylene separation, 459
Propanol diffusivity, 652
Propellers in mixer-settler design, 576
Proportional pattern waves, 961–962
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
Purge step
elution chromatography, 935
pressure swing adsorption, 954
Pyridine-water-chlorobenzene LLE data, 548
Quad command, 345
Quality of feed, q, 113
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
Raoult’s law
azeotropic processes, 278
binary flash distillation, 30
evaporating liquid drops, 665–666
reverse osmosis, 864
Raschig rings
packed column design, 407
Rate-based distillation analysis, 753–756, 764–768
Rate transfer (RT) equation
gas permeation, 849–851, 855–857
reverse osmosis, 866
Ratings for tray design, 434
Ratio units. See Mole and weight fractions versus mole and weight ratios
Rayleigh equation
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
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
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
Refrigeration costs, 447, 449, 451
Regenerable solvents in irreversible absorption, 508
Regeneration
description, 918
extraction process, 527
purge cycle, 934
solute movement analysis, 930
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
constant-mole batch distillation, 350
distillation cascades, 87
extractive distillation, 296
multicomponent distillation, 358, 360
pervaporation, 886
simple binary batch distillation, 346
ternary systems, 288–289, 293–296
Underwood equations, 255–256, 258
Repressurization step in pressure swing adsorption, 951–953, 956
Residence times
chemical reaction, 306
downcomers design, 399, 401, 404
HTU-NTU analysis, 713
mass transfer coefficients, 673–675, 679
membrane separation processes, 843
rate-based analysis of distillation, 755–756
solute movement, 984
stage efficiency, 740, 743–745
Residue curves
azeotropic distillation, 303–304
extractive distillation, 296–298, 301
multicomponent simple batch distillation, 358–359
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
mass transfer of concentration polarization, 872–876
Reversible reactions
absorption, 481
methyl acetate, 306
Reynolds number
falling laminar liquid film, 676–677
impellers, 577
lumped parameter mass transfer, 982
mass transfer coefficients, 678–680, 750–751
reverse osmosis, 873
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-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
Saturation of adsorbents, 924
continuous cooling crystallizers, 777
mixer-settler design, 578
packings, 408
supercritical fluids, 617
Schmidt number
Fickian diffusivities, 650
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
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
crystallization, 770, 814–819, 824
Selectivity
ion exchange, 975
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
simulations, 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
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
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 streams
multicomponent distillation, 462–463
Sieve analysis in crystallization, 793–798, 810–811
column diameter calculations, 390, 392
column type choices, 419
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
Simulations. See also Aspen Chromatography and Aspen Plus
absorption and stripping, 520–525
azeotropic distillation, 304
column distillation, 93, 156–158, 179–183
complex distillation methods, 326–336
extractive distillation, 332–336
liquid-liquid extraction, 572–573, 598–602
mass transfer analysis, 764–768
multicomponent distillation, 241–248, 270
overview, 8
tray and downcomer design, 433–435
troubleshooting guide, 1047–1049
Simultaneous convergence
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
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
Sodium chloride (NaCl)
crystallization, 772–776, 824–825
deicing roads, 783
diffusivity, 652
evaporative crystallizers, 788
solubility in water, 775
Sodium hydroxide (NaOH)
H2S removal, 481
washing process, 609
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
dissolving in concentrated liquids, 668–669
dissolving in dilute liquids, 667–668
Solubility envelope in ternary LLE systems, 554–555
Solubility parameter
gas permeation, 847
liquid-liquid extraction, 531
salts, 826
Solute mass flux in ultrafiltration, 882
chromatography applications, 930–938
nonlinear analysis for ion exchange, 973–978
pressure swing adsorption, 938, 948–956
simulated moving beds, 956–961
temperature swing adsorption, 938–948
elution, 988
linear chromatography, 991
nonlinear solute movement, 963
pressure swing adsorption, 953–954
simulated moving beds, 960
temperature swing adsorption, 943–944
Solute waves in pressure swing adsorption, 951
Solutes
absorption and stripping, 482
countercurrent extraction, 532
dilute extraction systems, 539–542
evaporative crystallizers, 787–789
immiscible batch extraction, 552–553
liquid-liquid extraction, 527–528
partially miscible systems, 554, 560
supercritical fluids, 616
Solution-diffusion mechanism in gas permeation, 847
Solvent flux
reverse osmosis, 866
Solvents
azeotropic distillation, 302–306
constant-mole batch distillation, 349–350
continuous cooling crystallizers, 778
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
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
Sorel method, 110
Sorption systems, 918
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
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
Split drawoffs in staged column design, 381
Splits in multicomponent distillation simulation, 244
Spray regime
column distillation, 90
rate-based analysis of distillation, 754
binary column distillation, 178, 183–188
mass transfer analysis, 765
membrane separation processes, 911–912, 914–916
multicomponent distillation, 211–217, 359–360, 372–374
overview, 8
sorption systems, 1018
SRP (Separation Research Program), 418
absorbers, co-current, 508–509
absorbers, concentrated, 497–501
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
multicomponent distillation, 192–206
strippers, concentrated, 497–501
strippers, dilute, multi-solute, 502–504
balancing calculated diameters, 396–397
column diameter calculations, 390–396, 501–502
height, 446
sieve tray layout and tray hydraulics, 398–404
tray and downcomer design, 433–436
Stagnant films, transfer through, 660–661
Stanton number, 672
Steady-state binary Fickian diffusion
Steady-state energy balance in column distillation, 95
Steady-state mass balance
concentrated immiscible extraction, 547
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
heat exchanger design, 443–444
Steam distillation
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
membrane separation processes, 840
Stokes-Einstein equation, 651
Stokes law in settler design, 580–582, 584
Stream tearing, 326
Strippers and stripping, 481–482
McCabe-Thiele and Kremser procedures, 605
multicomponent distillation, 460–461
transfer through stagnant films, 660–661
Stripping distillation columns, 150–151
Stripping sections in distillation
binary column distillation, 108–109, 111, 150–151
distillation cascades, 87
feed lines, 121
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
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
Superposition
ultrafiltration, 881
Supersaturation
continuous cooling crystallizers, 777
crystallization seeding, 814–816
evaporative crystallizers, 785
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
Tangent pinch points
binary column distillation, 153
stripping analysis, 489
Temperature effects
column diameter calculations, 393
crystal size control, 819
crystallization, 772–776, 820–823
diffusion, 980
diffusion experiments by evaporation, 636–638, 644–647
distillation, thermal decomposition, 90, 302, 306
eutectic systems, 782
feed lines, 123
Fickian binary gas diffusivities, 647–650
Fickian binary liquid diffusivities, 651–653
flash distillation, 16–17, 30, 39
gas permeation, 851
heat exchanger design, 443–444
intermediate reboilers, 149, 151
liquid-liquid extraction equilibrium, 556
MSMPR crystallizers, 814
multicomponent distillation calculations, 225
multicomponent distillation profiles, 194–195, 199–205
multicomponent distillation simulation, 244–246
multisolute absorption and stripping, 502
Naphtali-Sandholm method, 232
pervaporation, 884, 886–889, 892
rate-based analysis of distillation, 754
simultaneous multicomponent convergence, 43–46
stage-by-stage calculations, 213–215
steam distillation, 282–285, 352
temperature swing adsorption, 939
ultrafiltration, 880
Underwood equations, 256
unit conversions, 1054
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
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
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
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
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
Trays. See also Bubble-cap trays, Chimney trays, Sieve trays, Valve trays
azeotrope separation, 328
column diameter calculations, 390–392
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
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
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
Triethylamine NRTL parameters, 599
True moving bed (TMB) systems
Aspen Chromatography, 1038–1042
Tube-in-shell membrane system, 840–841
Turbulent tank mixing for reverse osmosis, 874
Two-column systems
azeotropic distillation, 274–277
Two-porosity models for diffusion, 981
Two-stage countercurrent immiscible batch extraction, 552
Type, equations solved by, 220
Uncontrolled cooling in batch crystallization, 821–822
Underflow liquid, washing, 606–608
UNIFAC group contribution method, 36
UNIQUAC method, 36
Unit operation, 2
Units
prerequisites, 9
Unsteady binary Fickian diffusion, 638–639
Vacuum distillation columns
diameters, 446
pressure drop, 414
structured packings, 408
uses, 418
Vacuum crystallizers, 785
crystallization, 776
simultaneous calculations, 790–793
Vacuum pumps in pervaporation, 886
Vacuum swing adsorption (VSA), 948, 950
column diameter calculations, 390
column distillation, 90
column type choices, 419
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
absorbers and strippers, 506
binary distillation, 30, 93, 148
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
valve trays, 376
Vapor-liquid equilibrium (VLE)
activity coefficients, 36
azeotrope separation, 327
complex ternary systems, 287–288
data sources, 19
extractive distillation, 298
graphical representation, 20–25
liquid-liquid extraction, 572
multicomponent distillation, 199, 245
pressure-swing processes, 286–287
Raoult’s law, 35
Vapor mole fractions
binary flash distillation, 26
linear driving-force model, 656
Vapor permeation, 838
Vapor-phase mass transfer coefficient, 755
Antoine equation, 35–36, 60, 62, 314, 319, 368, 370
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
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
mass transfer coefficients, 671–672
solute. See Solute velocity
sorption systems, 920
vapor. See Vapor velocity
Venturi valves, 376
Vertical flash drums size calculation, 48–50
Vinyl chloride, Henry’s law constant, 485
Viscosities
binary column distillation efficiency, 154
mixer-settler design, 573, 577
resource, 430
settler design, 580
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
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
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
Wakao and Funazkri correlation, 982
Washing
equilibrium, 607
McCabe-Thiele and Kremser procedures, 605
McCabe-Thiele diagrams, 608–610
references, 618
Wastewater treatment, 947
Water
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
Water-ethanol-benzene residue curves, 293
Water of hydration in crystallization, 773–774
Water-sodium chloride mixtures, 783
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
sieve tray layout, 398–401, 403
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-intercept in McCabe-Thiele diagrams, 27
y=x line on McCabe-Thiele diagrams
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
Zeolites
adsorbents, 920
molecular sieves, 923
sorbents, 923
Zones
simulated moving beds, 958–959
solute movement, 938
Zuiderweg correlation, 754