(McGraw-Hill chemical engineering series) Robert Ewald Treybal - Mass-transfer operations-McGraw-Hill (1980)

774 INDEX

Gas(es): Gas-liquid ratio in absorption, 285, 286
Gas-solid operations, 3-4
kinetic theory of, 21, 30, 40
slurry adsorption of, 609 (See a/so Adsorption; Desorption: Drying)
Gaseous diffusion, defined,S
steady-state molecular diffusion in, 27, 28-30 Gasoline, recovery of, 322
(See also specific masS-lransfer operalions) Gelatins, drying of, 678
Gas absorption, 275-341 Geometric similarity of agitated vessels, defined,
by chemical reaction, 333
150
in continuous-contact equipment, 300-322 Glitsch Ballast Tray valve design, 177, 178
for absorption of one component, 301-304 Glues, drying of, 678, 695
height equivalent to theoretical plate, 301-307, Goodloe packings, 190
305, 307 Graesser ex,traetors, 546
overall coefficients and transfer units in, Grain boundaries, diffusion through metals along,
307-322
for dilute solutions, 308-309 95
graphical construction for transfer units, Grashof number, 68
309-31/ Grids (hurdles), 190, 259
for nonisothennal operations_ 313-322, 315, Grinding, leaching during, 731-732
3/9-321 Grosvenor humIdity (mass absolute humidity),
overall heights of transfer units, 311-313,
JI2 227

defined, 3 Heap leaching, 720
Heat:
equilibrium solubility of gases in liquids and,
275-282 of adsorption, 574-575
differential, defined, 574
choice of solvents for absorption, 281, 282 heat of wetting, 580
in multicomponent systems, 277-279
for drying operations, 661-662
in nonideal liquid solutions, 279-281, 280 in continuous direct-heat drying. 701-710
in two-component systems, 276, 277 702, 703
interfacial area for, 205 in direct driers, 664, 666
in multicomponcnt systems, 322-332, 324, in direct-heat: eocurrent-flow drying. 690
cqulhbrium solubility in, 277-279 countercurrent-flow drying, 690
multistage, in ag!lated vessels, 158 in freeze drying, 667
one component transferred, 282-300
in cocurrent flow, 286-289 humid; in adiabauc gas-liquid contact, 236-237
in countereurrent flow, 282, 283-285 in air-water systems, 235
in countercurrent multistage operations, defined. 230

289-300 for humidificat10n operations: heat balance.
absorption factor A, 291-293, 292 defined, 225
dilute gas mix,tures, 290-291
in nonisothennal operatIOns, 293-298, 294, latent heal of vaporization, defined, 222
sensible heat, defined, 222
297 of unsaturated vapor-gas mix,tures, 230
overall coeffiCIents for, 313-314 losses of, in Ponchon-Savarit distillation method,
real trays and tray effiCiency, 298-300
minimum liqUid-gas ratIO, 285, 286 400, 401, 402
Gas-adsorbent carbon (see Carbon) (See also under Thermal)
Gas bubbles (see Bubbles) Heat capacity, defined. 226
Gas-enthalpy transfer units, number of, 247 Heat eddy diffusivity, 58-59
Gas·gas operations, 3, 5 Heal transfers and heat-transfer cocfficient~, 60
Gas holdup, 143, 144, 156 analogies with mass-transfer coefficients. 66-72
Gas-liquid operations, 3
equipment for, 139-319 corresponding dimensionless groups of mass
WIth gas dispersed, 139-158 and heat transfers and, 68

agItated, for single-phase liquids, 146-/52, turbulent flow in circular pipes and, 70-72,
147, 148
71
agitated vessels for gas-liquid contact.
153-158.155 mass-transfer coefficients for simultaneous mass
and, 78-82, 79, 81
sparge vessels. 140-146, 142. /43
with liquid dIspersed, 186-211 Heatless adsorbers (pressure SWing), 628-630
Heavy components of mu]ticomponent systems,
packed towers (see Packed towers, gas.liquid
operations in) 43'
Heavy key components of multicomponent
S1eve trays (see Sieve trays and SIeve-tray
towers, gas-liquid operal1ons In) systems, 435
Height:
spray towers and chambers, 187
Venturi scrubbers, 186, 187 of slurries, in leaching, 731
of transfer units: in absorption, 311-313, 312
welled_wall towers, 187
gas-liquid contact adiabatic, 236 in adsorption, 615-616
separated by membranes. 5 Height equivalent to theoretical plate (HETP),
(See also Ad1abatic operat1ons, hum1diflcat1On
301-307,305
by; Desorption: Distillation; Gas absorpl1on: Henry's law, 93, 279, 291. 299, 300, 309, 551
HumIdIfIcation; Nonadlabalic operations) Heteroazeotropie mix,tures, 352-353

INDEX 71S

HETP (heIght equivalent to theorehcal plate), Hypersorber, 612
HystereSiS:
30/-307,305
Hickman centrifugal molecular suUs, 46/ adsorption, 571-573, 572
drying, 657, 658
HigbIe theory (penetratIon theory), 60, 61
Hlggms contactors, 6/3 Ideal-gas law, 145. 222, 279
High-purity products: Ideal solullons (see Mulucomponent systems:

with McCabe-ThIele dlsttUallon method, 422-423 Raoult's law)
with Ponchon_Savant dlstlUauon method, 402 Ideal stages (see Equihbrium st:lges)
Hlrsehfelder-Blrd-SpolZ method, WIlke-Lee modlfl' Ideal trays (theorencal trays), 289-293
ImmISCIble phases, mass_transfer operallons by
catIOn of, 31
Holdup: direct contact of twO, 2-5
Impellers;
dIspersed-phase, 522, 535, 536
gas, /43, 144, 156 for gas-liqUid contact, 154. 155-158
IIqUld; In packing towers, 202-203, 206. 207 power of, 601-602
single-phase liquids agitated by, 146-148
in tray towers versus packing towers, 210-21 I In-place leachmg {in-situ leachmg: solution

solid, 692-693 mlning),719-720
Honzontal extractors, 743 Indirect drying, 661, 666-667
Horton-Franklin equauon, 323, 326. 327, 330 IndIrect-heat, countercurrent-flow drying, 691,
HTU (.1'.... Height, of transfer umts)
692
Hu-Kintner correlation, 533 IndIrect operatIOns makmg use of surface phenolll-
Humid heat;
ena, 7
in adiabatIc gas-ltquld contact, 236-237 Induced-draft towers, 261
in air-water systems, 235 Inorganic chemIcals, punflcation of. 478
Insoluble liquids:
defined, 230
Humid volume; continuous mulustage countercurrent extraction
of,505-507
in aIr-water systems, 231
defined, 230 multistage crosscurrent extraction of, 496, 497
HumidIfIcation, 220-274 steam dlslIllauon of, 354-355
defined, 3 InsolubIlity of solvents, 488, 489
enthalpy In: evaporallve coohng, 265 Insoluble sohds, drying eqUIlibrium of, 656, 657
Intalox saddles, 189,190,199, 26!
for pure substances, 224-226, 225 Integra! heat of adsorptIon, dcfmed, 574
of unsaturated vapor-gas mixtures. 230-231 Interconnected pores of solids, diffUSIOn through,
by gas-hquld contact (s..e Admbauc operal1ons,
95
humIdIfIcatIOn by: Nonadlabahc operations) Interfacial absorption, adlabahc, 316-322, ]19-321
of vapor-gas mIxtures, 227-241
InterfaCIal area:
with absolute humidIty, 227 10 agitated vessels of stage-type extractors,
by adIabatIc operatIOns. 236, 237 522-523
in gas-liqUId operations, 144, 156,204,205,207
of aIr-water vapors, 231.232-236
of saturated vapor-gas mIxtures, 227-228 Interfacial tension in hquld extraction:
of unsaturated vapor-gas mIxtures, 228-231, and drop coalescence, 538-539
and drop tenUlnal velOCIty, 533, 534
229 emulSions and, 527
wet-bulb temperature and, 237-241. 238 in flow mIxers, 521
vapor-hqUld equlhbnum for pure substances solvents and, 489

in, 220-224. 22/ Interfacial turbulence (Marangoni effect), 113
Internal-diffUSIon controlhng m batch drymg,
HumIdIty:
absolute and mass absolute, defined, 227 681-682
relallve. defined. 228 Internal rebollers, 393
(See a/so Drying: Humidification: MOIsture: Interphase mass transfers. 104-136
Wet-bulb lemperature)
diffUSIOn between phases of, 106-117
Hurdles (gnds). 190. 259 average overall coeffICIents for, 113-117. 114
Hydrauhc(s), sIeve-tray. 532-536 local coefficients, 111-113
local overall coeffiCients for, 109-111, 113
Hydraulic head of SIeve -trays. 171-172, 176 localtwa--phase masS transfers, 107-109
Hydrocarbons:
equilibnum 10, 104-106
decolorization of, 582.583 departure of bulk-phase concentratIOns from.
JOS
as leaching solvents. 740 equllibrium-dlstnbutJon curve. 105
separatIon of; by absorplJon, 295-298. 297.
material balances in. 117 -123
327-331 in steady-state cocurrent processes, 117-121,
by adsorptIOn, 565, 570, 571, 586, 608
by distillatton, 436-439, 457-459 119,120
by extraction. 478-479, 510-514, 511-513, in steady-state continuous cocurrent processes,

519-520 12'
by fracllonation, 612
Hydrocyclones (hydroclones), leachmg 10, 738, 10 steady-state countercurrent processes,
121-124
739
HydrodynamiC movement of diffUSIOn through

porous soltds, 95, 99-100
Hydrogen from waste rdmery gases, 94
Hy-Pak rings, 189
Hyperfil packmgs, 190

776 INDEX

Interphase mass transfers: Leaching:
stages of, 123-133
in batch pr~esses, 124 under unsteady-state conditions, 719-731
cascades and, J15-130
in continuous caCUl'Tcnt processes, 124 in agitated vessels, 726-730, 731
mass-transfer rates and, 130-133 in closed vessels, 724, 725
stage defined, 123 by countercurrent multiple contact operations,

Interstitial mechanism of diffusion through melals, 723, 724, 740
95
in filter-press leaching, 725-726
Interstitialcy mechanism of diffusion through in heap leaching, 720
metals, 9S
in in-place leaching, 7 I9-720
Ions: in percolation tanks, 720-722, 723
crowd·ion mechanism, 9S ~ngth of unused bed (LUB), 639, 640
ion exchange, 641-646, 6.fS Lessing rings, 189, 190
ion exclusion, 643 Leva trays, 177-178

Isolated pores of solids, diffusion through, 9S Lewis-Matheson calculation, 434, 443-445, 447,
Isostere. defined, 574
4"
Jacketed kettle rcboilers, 393 Lewis number, 41, 240, 252
lD. 68, 70 Lewis relation, 240-241, 245
JH. 68, 70
Lewis-Whitman theory (tWO_film theory; two-resis-
Karr reciproclUing-platc extractors, 546 tance theory), 107, 110
Kennedy extractors. 741. 742
Kerr·McGee uranium extractors, 530 Light components of muiticomponent systems,
Kettle rcboilers, 392, 393 434
Key components of multicomponent systems,
Light key components of multicomponent systems,
434-435 434
Kiln action, described, 692
Kinematic similarity of agitated vessels, defined, Lightfoot theory (surface-stretch theory), 63, 64
Linde Irays, 176, 177
150 Line mixers (flow mixers), 190,521
Kinetic theory of gases, 21, 31,.d0 Linear falling-rate period of drying, 680
Kittel trays, 177 Liquid(s):
Klee-Treybal equation, 534
Knudsen's law, 97-100 boiting point of, defined, 222
Koch Flexitray, 177 diffusivity of, 35-37, 36
Koch-Sulzer packings, 190 saturated, defined, 221
Kremser-Brown-Sonders equations (Kremser steady-state molecular diffusion in, 34-35
(S~~ also sp~cific mass-transfer operations)
equations), 128,291,323,326-327,422,594
Liquid entrainment:
Laminar flow: makeup water to replace, 248
mass-transfer coefficients in, 50-54 in packing towers, eliminators of, 193
molecular diffusion in: momentum and heat in sieve-tray towers, 166, 173, 174, 176
transfers in, 38-41, 39 and tray efficiency, 182
(See also Moleeular diffusion, steady-state)
Liquid eqUilibrium:
Langmuir equation, 460, 571 in adsorption, 580, 581-584
Lalent heal of vaporization, defined, 222 (Su also Gas absorption, equilibrium solubility
Leaching, 717-764 of gases into liquids; Liquid extraction,
liquid equilibrium in)
calculation methods for, 744-761
in multistage countercurrent leaching, 751-760, Liquid extraction, 477-561
753,755-757, 759 defined,4
in multistage crosscurrent leaching, 749-751, in differential extractors, 541-553
750 centrifugal extractors, 547, 548
rate of leaching, 760-76 I design of, 548-551, 549
in single-stage leaching, 748, 749 for dilute solutions, 551-552
stage efficiency, 744 mechanically-agitated extractors, 544-547
in packed towers, 542-544, 543
defined, 5, 717 performance of, 552-553
preparation of solids for, 718-719 in spray towers, 542
under steady-state conditions, 731-744 fields of usefulness of, 478-479

in agitated vessels, 732, 7J3 liquid equilibrium in, 479-489
continuous, of coarse solids, 738-744, 740-743 choice of solvents and, 488, 489
by continuous countercurrent decantation, equilateral-triangular coordinates of, 480, 481

736-738 in mutticomponent systems, 488
during grinding, 731-732 notation scheme for, 479-480
in hydrocyc!ones, 738, 739 rectangular coordinates- of, 486, 487
in thickeners, 733-738, 734, 735, 737
in systems of three liquids: with one pair
partially soluble, 482-484

with two pairs partially soluble, 484, 485
in systems of two partialIy soluble liquids and

one solid, 485, 486
stage efficiency in, 520, 521, 537-539, 538
in stage-type extractors, 521-541

INDEX 777

Liquid elltraction: Mass-transfer coeffIcients:
in stage-type extractors: agitated vessels, analogies with heat- and momentum-transfer
521-516,524
of emulsions and dispersions, 526-527 coefficients, 66-72
mixer-settler cascades in, 529, 530 corresponding dimensionless groups of mass
settlers in, 527-529, 528
sieve-tray towers, 530-541, 531-534, 536, 538 and heat transfers, 68
by stagewise contact, 490-521 turbulent flow in circular pipes and, 70-72,
continuous countercurrent with reflux, 507-
514,509,5IJ-5J3 71
continuous multistage countercurrent extrac- eddy motions and, 45, 46
tion, 497-507, 498-501, 503-506 fractionation, in packed towers, 429-431
economic balances in, 514 in gas absorption (see Gas absorption, overall
fractional extractIOn, 514, 515-518
in multicomponent systems, 518-520, 519 coefficients· and transfer units in)
multistage crosscurrent extraction, 493-497, in gas-liquid operations, 202-209, 205, 206
495 in interphase mass transfers: average overall
single-stage elltraction, 490-493, 491, 492
stage efficiency in, 520, 521 coefficients, 113-117, 114
loca! coefficients, 111-113
Liquid films, gas into falling, mass-transfer local overall coefficients, 109-111, 113
coefficients In, SO, 51-54 stages and, 130-133
in laminar flow, 50-54
Liquid flow in tray towers, 164, 165 in liquid extraction, 536-541, 538
Liquid/gas ratio: relations between, 49
for simple situations, 72-78, 74-75
minimum, in absorption, 285, 286 for simultaneous mass and heat transfers, 78-82,
and use of tray towers, 211
Liquid holdup: 79,81
in packing towers, 202-203, 206, 207 in transfers to conflned fluids, 47, 48
in tray towers versus packing towers, 210-21 I in turbulent flow, 54-66
Liquid-liquid operations, 4, 476
phases separated by membranes, 5 boundary layers and, 64-66
(See also Liquid extraction) in circular pipes, 70-72, 71
Liquid miscibility, partial, in positive deviations eddy diffusion and, 54-59, 55
film theory of, 59, 60
from ideality, 352, 353
Liquid-solid equilibrium (see Adsorption, flow past sohds, 64-66
on fluid surfaces, 60-64, 62, 63
equilibrium in) Mass-transfer operations, 1-18
Liquid-solid operations, 4-5 choice of separation method for, 7-8
(See also specific muss-trallS!er operatiQIIS)
(See also Adsorption; Leaching) classificatIOn of, 2-7
Liquid/vapor ratio in distillation of mUlticompo- design prinCiples, 11-12

nent systems, 447-449 method of conducting, 8-10
Lixiviation, defined, 717 unit systems used, 12-18, 13-17
Loading in packing towers, 194, 195 Mass-transfer resistances in adsorption, 604,
Local mass-transfer coefficients, 48
Local two-phase mass transfers, 107-109 606-608, 607
Low-pressure distillation, 460-462 Material balances:
LUB (length of unused bed), 639, 640
Luwesta extractors, 548 in continuous drying, 699-701, 700
in Interphase mass transfers (see Interphase mass
McCabe-Thiele method (see Distillation, by
fractionation, McCabe-Thiele method of) transfers, material balances in)
Maximum boiltng azeotropism, 355-357, 356
Macropores, 95 Mechanical agitatIon (see Liquid extraction)
Marangoni effect (interfacial turbulence), 113 Mechanical-draft towers (induced-draft towers),
Marc, defined, 740
Marine-type propellers, single-phase liquids 259-261
Mechanical separation, 8
agitated by, 146, 147
Mass absolute humidity (Grosvenor humidity), by drainage, 721-723,722

227 in settlers, 527-529, 528
Mass balance in adiabatic absorption, 315 Mechanically-agitated extractors (countercurrent
Mass-action-law constant, 643
Mass eddy diffusivity, 58-59 extractors),544-547
Mass-transfer coefficients, 18-19,45-87 Membrane(s), separator, 529
Membrane operations, 5-6
in adiabatic operatIOns, 261
adiabatic absorption, 314-315 Metals:
diffusion through, 95
in agitated vessels: adsorption, 602-606 recovery of: by ion exchange, 642-646, 645
gas-liquid contact, 156-158 by leaching, 5, 717-720, 724, 727, 731, 732,
in stage-type extractors, 523, 524
7J9
by liqUid extraction, 478

by zone refining, 4
Micropores, 95
Minerals recovery:

choice of method for, 7-8
by leaching, 717

Mimmum-boiling azeotropism, 350-352, 351

778 INDEX

Minimum reflux ratio: Multicomponent systems (ideal solutions):
countercurrent extraction and, 510, 5f} steady-state molecular diffusion in, 29-30
in McCabe-Thiele method, 411-413 vapor-liquid equilibnum in, 360-363
in multicomponent systems, 435-439 (See also Raoult's law)

in Ponchon-Savarit method, 385-387, 386 Multiple downspouts, 176, 178
Multistage countercurrent opcrations:
MisceUa:
in Bollman extractors, 742, 744 adsorption by, 592-594
in fluidized beds, 610
defined, 740 Freundlich equation applied to, 594-5<>9,
Miscibility, partial liquid, in positive deviations 595-598

from ideality, 352, 353 continuous countercurrent multistage extraction,
Miscible phases, mass transfers by direct contact 497-507,498-501,503-506

of,6 gas absorption by (see Gas absorption, one
Mixco Ljghtnin CMContractor (Oldshue-Rushton component transferred, in countercurrent
multistage operations)
extractor), 544, 545
Mixer(s): leaching by, methods of calculating, 751-760,
753, 755-757, 759
static, 190
(Sec also Liquid extraction, in stage-type (See also Fractionation)
Multistage crosscurrent operations:
extractors; and specific types of mixers)
Mixer-settler(s), described, 521 adsorption by, Freundlich equation applied to,
Mixer-settler operations (contact filtration): 590-592

adsorption of liquids by, 585-599, 586, 588, extraction by, 493-497, 495
589,591-598 leaching by, 749-751, 750
Multistage operations, absorption by, in agitated
cascades in stage-type extractors, 529, 530
Mixing (see Axial mixing; Back mixing; and specific vessels, 158
Multistage tray towers (see Disti!lation, by
mass-rrfJlISjer operariollS)
Mixing length (Prandtl mixing length), 56 fractionation, McCabe-Thiele method of;
Distillation, by fractionation, Ponchon-Savarit
Moisture: method of)
critical, 669, 682 Murpnree stage efficiency, 124, 254, 423
diffusion of, 678 in adsorption, 606, 607
in cross-flow cascades, 125
types of, 660, 661 in humidification, 254
unbound, 683-684 in liquid extraction, 520, 521, 524
(See also Drying; Water) (See also Stage efficiency)
Moisture conten!. Murphree tray efficiency, 181_183
critical, dcfined, 669, 682 in absorption, 298-300
dry basis, defined, 660
wet basis, defined, 660 Natural-draft towers (natural-circulation towers),
Molal absolute humidity, defined, 227 259, 260
Molecular diffusion, 21-44
in binary solutions, 24 Navier-Stokes equation, 51, 56
equation of continuity and, 24-26, 25 Neo-Kloss packings, 190
momentum and heat transfers in laminar flow Nonadiabatic operations, 242

and, 38-4\, 39 evaporative cooling with, 263-269, 264, 265
Nondiffusing liquids:
steady-state, 26-38
applications of, 37-38 mass-transfer codficients in, 48-50
diffusivity of gases and, 31-34 steady-state molecular diffusion in, 28, 29, 34
Nonideal solutions, equilibrium solubility of gases
diffusivlty of liqUids and, 35-37, 36
in gases, 27-30, 28 in, 279-281. 280
in liquids, 34-35 Nonisotnermal operations, gas absorption by,
Molecular distmation, 460-462, 461
Molecular-screenmg activated carbon, 568 293-298, 294, 297
Molecular sieves as adsorbents, 568-569 overall coefficients in, 313-322, 315, 319-321
Nontoxicity of solvents, 489
Molecular volumes of gases, 33 Nonvortexing systems in agitated vessels, 151-153,
Momentum eddy diffusivity, 58 152
Momentum-transfer coefficients (see Mass-transfer Normal boiling point of liquids, defined, 222
Nusselt number, 67, 69
coefficients, analogies with heat- and momen- Nutter float-valves, 177
tum-transfer coefficients)
Moving-bed adsorbers (see Adsorption, by Odor removal (see Adsorption)
continuous contact, under steady-state condi- Oils:
tions)
crude, 453-455, 454
Multibeam support plates, 192 cylinder, 582, 583
Multicomponent absorbers, 324 (See also Animal oils; Fish oils; Vegetable oils)
Multicomponent strippers, 324 Oldshue-Rushton extractors (Lixco Llghtnin
Multicomponent systems (ideal solutions):
CMContrac\or),544, 545
distillation of (see Distillation, of multicompo- Open steam:

nent systems) in McCabe-Thiele distillation method, 416, 417
gas absorption in, 322-332, 324

equilibrium solubility of gases into liquids,
277-279

liquid extraction in, 518-520, $19
liquid equilibrium, 488

INDEX 779

Open steam: Partition chromatography, 632
in Ponchon-Savant distillation method, 394-397, Partition coefficient (see Equilibrium distnbution)
395, 396
Partition rings, 189, 190
Open tanks, gas_liquid surfaces and, in prevention
of vortex formation, 149 Pedet number, 68, 182
Penetration theory (Higbie theory), 60, 61
Operating line in Interphase mass transfers. Percentage saturat10n (percentage absolute humid-
lJ9-121
ity),229
Optimum renux ratio: Percolation and percolation tanks:
in McCabe-Th1ele distillation method, 412-416,
415 leaching in, 720-723, 722
in Ponchon-Savant distmation method, 387-392, liqUid adsorption in, 630-631
388,390,391 Perforated trays (see Sieve trays and sieve-tray

Ordinary binary mixtures, vapor-liquid equilibrium towers)
in, 343-344 Penneability:

Ore(s) (see Metals) diffusion and, 94
Ore slurries, adsorption of, by ion exchange, 642 leaching and, 721
Osmosis, defined, 6 Penneation separations, defined, 5
Overall gas transfer units, number and height of, Pennisstble flow rate, 11
Petroleum (see Hydrocarbons)
308,311-313,312
Overall mass-transfer coefficients (see Mass-trans- Petroleum topping plant, 454
Pharmaceuticals:
fer coefficients)
Overa!! stage efficiency (see Stage efficiency) decolorization of, 568
Overall tray efficiency (see Tray efficiency) drying of, 666, 696
leaching to obtain, 718
Pachuca tanks, 140, 726, 727, 732 liquid extraction of, 479, 547
Packed absorbers, 315 Physical adsorption (van der Waals adsorption),
Packed strippers, 315
Packed towers: 566
Pitch of impellers, defined, 146
distillation in, 426-431, 427 Pitched-blade turbines for adsorption, 599, 600
gas absorption in, 301, 302 Plait point, 482
gas-liquid operations in. 187-2\0,188 Plasticizers, defined, 92n,
Plate(s):
cocurrent flow of gas and liquid in, 209
countercurrent flow of liquid and gas in, 194 analogies between mass, heat and momentum
end effects and axial mixing in, 209-210
flooding and loading in, [94, 195 transfers in, 66-70
liquid distribution in, 192 boundary layers on nat, 64
mass-transfer coefficients for, 202-209, 205, momentum transfers in, 38, 39
(See also Slabs)
206 Plate driers, 688
packing characteristics, 189 Plate towers (see specific fO~'ers)
packing restrainers and entrainment elimin"a- Pneumatic driers (nash driers), 698, 699
Podbie1niak extractors, 547, 548
tors, 193 Point efficiency of trays, 178-181, 179
packing supports, 191,192
pressure drop in: for single-phase flow, 200 PoiseUtile's law, 99
Polymers, diffusion through, 93-95
for two-phase flow, 200-201 Ponchon-Savarit method (see Dist1l1ation, by
random packings in. 189, 190
fractionation, Ponchon-Savarit method of)
characteristics of, /96-199 Porous solids, diffusion through, 95-100
flooding and pressure drop in, 194, 195 Power:
size of, and liquid redistribution, 192, 193
regular packings in, 190,191 adsorption: batch adsorption, 605
shells of, 191 in implellers, 60 1-602
for humidification, differenhal section of, 243
leaching in, 721, 722 agitation, 150-/55,152
liquid extraction in, 542-544, 543 in stage-type e~tractors, 522
tray towers versus, 210-211
(See also Tray towers) supplied to sparge vessels, 145-146
Paint pigments, drying of, 679 Prandtl mixing length, 56
Pall rings (flexirings), 189-191, 190, /97, 261 Prandtl number, 40-41, 56, 70, 71, 73
Pan driers, agitated, 666 Preforming of solids, 663
Paper: Pressure:
chlorination of, 139
drying of, 678 constant total, and diffusion through porous
Parallel adiabatic operations, continuous drying
by, 686-687 solids, 96-99
Parallel-now trays, 176, 178 critical, of vapor-liquid equilibrium, 221
Partial condensation, flash vaporization by, 365 in cross-circulation drying, 680
Partial condensers in McCabe-Thiele distillation diffusivity of gases at standard atmospherie,
method, 417, 418
Partial liquid miscibility in positive deviations from 31
ideality, 352, 353 drop in: in packing towers, 200-201
Partial pressure of gas eqUilibrium, 277
in random packings, 194, 195

in sieve.tray towers, 170-172, 175
in tray and packing towers, 210
effects of, on equilibrium of ternary systems

with one pair partially soluble, 484
effects of change of, on adsorption equilibrium,

579, 580

780 INDEX

Pressure: Renull ratio, 373
low_pressure distillation 460-462 minimum: countercurrent elltraction and, 510,
partial, of gas equilibrium, 277
vapor-liquid equilibrium and: constant-pressure 511
vapor-liquid equilibrium, 344-346 in McCabe-Thiele distillation method, 41/-413
at increa~ed pressure, 346, 347 in multicomponent systems, 435-439
in Ponchon-Savarit distillation method,
Pressure swing (heatless adsorbers), 628-630
Pressure_temperature_concentration phase of 385-387
optimum; in McCabe-Thiele distillation method,
vapor-liquid equilibrium, 343-344
Priming in tray towers, 160 412-416,415
Products obtained by distillation: in Ponchon-Savarit distillation method,

compositions of, 440-441 387-392,388,390,391
with McCabe-Thiele method, 422-423 total; in countercurrent elltraction, 511,512
with Ponchon-Savarit method, 402
Propei!ers, single-phase liquids agitated by marine- in McCabe-Thiele distillation method. 410,
411
type propellers, 146, 147
Proprietary trays, 176-178 in multicomponent systems, 439-440
Psychometric charts for humIdification, 229, 231, in Ponchon-Savarit distillation method. 384

232-234 385
Psychometric ratio of wet-bulb temperature, 239 Regain, defined, 657
Pulsed columns, 546, 547 Regular packings (stacked packings), 190,191
Regular vapor.liquid solutions, equilibrium of.
q and q line, 407-409, 408, 412
Quiescent nuidized beds, 608-609 349
Relative adsorptivity (separation factor), 346,
Radial diffusion, 89, 91-92
Raffinate: 576-5<14
Relative saturation (relative humidity), defined,
defined, 477
(Sec also Liquid elltraction) 228
Random packings, 189,190 Repulping of sludge, 737
characteristics of, 196-199 Residual saturation in leaching, 721
nooding and pressure drop in, 194, 195 Residues (bottoms):
size of, and liquid redistribution, 192, 193
Raoult's law, 578 defined, 372
equilibrium solubility of gases in liquids and, reboiled vapor in equilibrium with, 405-406
Resins for ion exchange, 642-646, 645
278-279 Resting fluids, steady.state molecular diffusion
of vapor-liquid equilibrium, 348, 349
(See also Multicomponent systems) in (see Molecular diffusion, steady-state)
Raschig rings, 158, 189-191,203,205,206,210 Reversible adsorption, 566
Rate-of-drying curve, 667-670, 668 Reynolds number;
Rayleigh equation, 369
Rayleigh number, 157 in adsorption, 601-603
ROC (rotating-disk contactors), 545 gas-liquid operations and, 144, 149-153, 156
Reboiled absorbers, 332 in humidification, 240
Reboilers. fractionation in, 392-394, 393 mass-transfer coefficients and, 52, 56, 68-70
Recirculating llquids and gas-humidification terminal velocity of drops and, 533
Ripple trays, 177
cooling, 252-255, 253 Rising velocity (see Terminal velocity)
Recoverability of solvents, 489 Rotary-disk contactors (ROC), 545
Recovery of solvents by elltraction, 502, 503-505 Rotary driers, 689-693, 690, 691
Rectification, continuous (see DIstillation, by rate,of drying in, 704-707
through-circulation, 693, 694
fractionation) Rotary (illers (crystal-filter driers), 684
Rectifying sectiOn of fractionators (see Ellhausting Rotating fixed-bed adsorbers. 628
Rotating shelves (turbo-type driers), 687, 688
section of fractionators) Rotocel,leaching in, 740, 741,743
Recycling: Ruggles-Coles XW hot-air driers, 690

of gases, in drying, 663-664, 688-689 Saddle packings (see Berl saddles; Intalox saddles)
of liquids. 524 Sand, drying of, 679
RenUll: Saturated liquids, defined, 221
countercurrent elllraction with, 507-514, 509, Saturated vapor(s), defined, 221
Saturated vapor-gas mixtures, humidification of,
5J/-513
III McCabe-Thiele distillation method: at bubble 227-228
Saturation:
point, 404-405
cold,419 percentage, defined, 229
in multicomponent systems, 332 relative, defined, 228
Renull accumulators, 397 residual, in leaching, 721
(See also Humidification)
Scheibel correlation, 36
Scheibel elltractors, 546
Schmidt number:
in adsorption, 603

INDEX 781

Schmidt number: Slurries:
in gas-liquid operations, 151 in leaching: settling of 728, 729
settling characteristics, 746
in humidification, 240 stirring and, 729
mass-transfer coefficients and, 40, 58, 68, 73
of vegetable seeds, 743
Seal pots, 164 slurry adsorption of gases and vapors, 609
Selectivity: Soap, drying of, 678, 696
Solid(s):
of adsorbents, 567
of solvents, 488 diffusion (see Diffusion, in solids)
Semibatch operations, 9 mass-transfer coefficients in flow past,
(See also Batch operations: and speCIfic mars-
64-66
transfer operations) preparation of, for leaching, 718-719
Sensible heat, defined, 222
Separation factor (relative adsorptivity), 346, (See also Leaching)
(See also speCIfic mass-transfer operations)
576-584 Solid-fluid operations (see Adsorption; Drying;
Separator membranes, described, 529
Settlers: Leaching)

in stage-type extractors, 527-529, 528 Solid holdup, 692-693
(See also Mixer-settler operations) Solid-solid operations, 5
Shanks system of leaching, 723, 724, 740 Solid suspensions, adsorption of, 600-601
Shelf driers (see Tray driers) Solid-vapor equilibrium (see Adsorption,

Shells: eqUilibrium in)
of packing towers, 191 Solubility, equilibrium (see Gas absorption,
of tray towers, 161
equilibrium solubility of gases in liquids
Sherwood number, 52, 67, 68, 70, 72, 151 and)

SI units (Systeme International d' Unites), 12-18, Soluble solids, drying of, 658-660, 659
Solutes, 8-9
/3-17
Side streams: adsorption: from dilute solutions, 580-582
solute co!!e.!'\ions, 614-617, 615
in distillation of multicomponent systems, 433
in Ponchon-Savarit dIstillation method, 400 (See also Adsorption)
removal of, 211 separation of two, 515-518
Sieve(s), molecular, 568-569 (See also Liquid extraction, Membrane opera-
Sieve trays and sieve-tray towers:
gas-liquid operations in, 166-176,168,169,171, tions)

m Solution mining (in-place leaching: in·situ leach-
ing), 719-720
activated area of, 167-/69
efficiency of, 183,184 Solutropic systems, defined, 482
operating charactenstics of, 163 Solvents:
liquid extraction in, 530-541, 531-534, 536,
chojce of: for gas absorption, 281, 282
538 (See also Gas absorption)
Silica gel as adsorbent, 567, 568, 581, 609, 626
Simple distillation (differential distillation), 367- for liquid extraction, 488, 489
(See also Liquid extraction)
m
cost of, 282, 489
SimulatIon of moving beds, 622, 623 defined, 457, 477
leaching and, 724 recovery of, 502,503-505
Spacing of trays, 161, 162
Single DOTT classifiers, 740 Sparge vessels (bubble columns), 140-146, /41,

Single gases, adsorption eqUilibrium for, 569-575, 143
570-573 Spheres:

Single-phase liquids, mechanical agitation of, diffusion through, 89, 91
146-153, /47, 148, 152 of ion-exchange resins, 642
Split.reed treatment, 590-592, 59/
Single-stage operations: Spouted beds, continuous drying in, 698
adsorption by, 587-589, 588, 597 Spray chambers, 187
Freundlich equation applied to, 589, 590 adiabatic operations in, 262, 263
defined, 123 Spray driers, 695-697, 696
distillation by (see Flash vaporization) Spray ponds for adiabatic operations, 262-263
leaching by, 748, 749 Spray towers, 187
liquid extraction in, 542
liquid extraction by, 490-493. 49/, 492 Square pitch of impellers, defined, 146
Single vapors, adsorption eqUilibrium for, 569-575,
Stacked packings (regular packings), 190,191
570-573 Stage(s):
Slabs:
defined. 10
diffusion through, 88, 92-93 equilibrium, defined, 10, 123-124
with sealed edges, 90
(See also Equilibrium stages)
[See also Plate(s)j
Slip vehx:ity, 143 of interphase mass transfers (see Interphase mass
Slotted trays, 176, 177 transfers, stages of)

Slurries: (See also Cascade(s): Single.stage operations:
carbonation of lime, 139 Two-stage adsorption: specific mars-transfer
in leaching: effects of concentration of, 730 operations and under Multistage)
effects of height of, 731

782 INDEX

Stage efficiency: Surface stretch theory (lightfoot theory), 63, 64
in adsorption, 606, 607 Sweep diffusion, described, 6
defined, 10, 124 Synthetic polymeric adsorbenlS, 568
Sysleme In/unational d' Unius (SI units), 12-18,
in leaching, 744
13-17
in liquid extraction, 520, 521, 537-539, 538
Murphree (see Murphree stage effIciency) Tannins, recovery of, by leaching, 724, 725
(See also Tray efficiency) Teeter beds, 608-609
Te!lerettes, 190
Stage-type extractors (see liqUId extraction, in Temperature:
stage-type extractors)
adsorption equilibrium and, 573-574, 579, 580
Stagewise equipment (see Liquid extraction, in distillation: bubble-point temperature curve,
diHerential extractors: Liquid extraction, in
stage-type extractors; Liquid extraction, by 345
stagewise contact) (See also ConstanHemperature equilibrium)
dry-bulb: in adiabatic operations. 248
Stagewise operallons, 10 defined, 228
adsorption by (see Adsorption, by stagewise drying: in constant-rate drying, 675
operations) rate of drying at high, 701-707, 702, 703
ion exchange by, 642 rate of drying at low, 707-710, 708
in gas absorption, 32J, 322
liquid extraction by (see Liquid extraction, by in gas-liquid operations, fluctuations in, 21 I
stagewise contact) humidification: critical, of vapor-liquid

Stanton number, 68 equilibrium, 221
Static mixers, 190 evaporative cooling, 265
(See also AdiabatIc-saturation temperature)
Steady state, 9-10 leaching, 719
interphase mass transfers in: COCUTrent, JJ 7-121. in liqUid extraction: effects on equilibrium of
119, 120
lernary systems: with one pair partially
continuous cocurrent, 124 soluble, 483
countercurrent, 121-124 with two paIrs partially soluble, 484, 485
(See also Adsorption, by continuous contact, wet-bulb: in adiabatic operatlons, 248
in humidification of vapor-gas mixtures,
under steady-state condillortS; Continuous 237-241, 238
operatIOns; Leaching, under steady-state Lewis relatIOn and, 241
conditions; Molecular diffusion, steady-state) (See also Heat)
Terminal velocity (rising velocity):
Steady-state equlmolal counterdlffusion: of drops, 533, 534
in gases, 29, 30 of single-gas bubbles, 141,142
Ternary systems:
lfl liquids, 34-35 distillation of, 432
Steam, open: in McCabe-ThIele diSllllallon method, with one pair parually soluble, liquld equihbrium
of, 482-484
416,417 with two pairs partla!ly soluble, liqUId
eqUIlibrium of, 484, 485
In Ponchon-Savant dIstillatIOn method, Textiles, drying of, 663, 670, 678, 687, 709-710
394-397, 395, 396 Theoretical stages (see Equlhbrium stages)
TheoreHcal trays (ideal trays), 289-293
Steam disullation, 354-355 Thermal conditions for feed, in McCabe-ThIele
distillation method, 4Gb
Stills: Thermal dIffusion, described, 6
falling-film. 4<>2 Thermal-swing procedures, defmed, 626
Thermoslphon reboilers. 392-394,393
Hickman centrifugal molecular, 461 Thickeners, leaching in, 733-738,734,735,737,
Stokes' law, 142 747
Straight opeTatmg line, 119, 120 Thickness of drytng solids, effects on constant-rate
Streams (see SIde streams) drymg, 675-676
ThIele-Geddes method of distillatIOn, 433-434,
Stnppers and strippmg, 283, 284 439,442-443,445,449-455,454
in countercurrent multistage absorpllon opera- Through-circulation drying and driers_ 663, 664,
tions, 291-293 682-686, 688. 689
HETP apphed to, 304-307, 305 in rotary dners, 693, 694
material balances m, 282-289, 283, 284 Time:
number of transfer units fOf_ 310 drying, 670-672
as requirement, deslgn and, II
Stripping factor, defined. 124 Total condensers in McCabe-ThIele distillatIOn
Stripping secllon of fractlonators (see Exhaustmg method, 404-405
Total pressure, constant, diffusion through porous
section of fractlOnators) sohds and, 96-99
Subhmation, fractional. defined, 3
SublimalJon drying (freeze drymg). 666-667
Sugar and sugar beets:

drying of, 690
leaching of. 717, 718_ 725, 731. 738-739, 760

productIOn of dlnc aCId from. 139
refining of, 565, 582. 585, 631
separation of crystalhne substance In solutIons

of,5-6
Superheated vapor, defmed. 221

Surface(s), mass-transfer coeffICIents on, 60-64,

62.63
Surface diffUSIon tn porous solids, 95, 99

Surface phenomena. mass-transfer operatIOns
making use of. 6- 7

Surface-renewal theory. 6 I-62

INDEX 783

Total reflu;w; ratio (infinite n:rlu;w; ratio): Underflow in leachlllg, 747, 754
in countercurrent e;w;traction, 511, 512 Unit systems, 12-18, iJ-17
in McCabe-ThIele distillatIOn method, 4/0, 411 Universal range, defilled, 55
in multicomponent systems, 439-440 Unsaturated~surface drying, 670, 680, 681
in Ponchon-Savant distillation method, 384, Unsaturated vapor·gas mixtures, humidification

m of. 228-231, 229
Unsteady state, 9
Towers (see specific to ....ers and specific mass-trailsfer
adsorption in (see Adsorption, by continuous
operatiOlls) contact, under unsteady·state condilions)
Transfer units:
diffusion in, 89, 90, 91,92-93
in absorption (see Gas absorption, in leaching in (sec Leaching, under unsteady-state
continuous-contact equipment, overall
coefficients and transfer units in) conditions)
(See also Batch operations)
in adsorption, 619, 636, 615-616 Uranium recovery, 5b 6
in distillation, 426-431, 427 by extracllon, 478, 510
in drying, 704-707 by leachmg, 720
height of (see HeIght, of transfer units)
in humidifIcation, 247-253, 250 Vacancy mechanism of diffusion through metals,
in liqUid e;w;traction, 548-552
Tray absorbers, 282, 289, 290 95
Tray driers (shelf driers; cabinet driers: compart- Vacuum rotary driers, 666
Vacuum shelf driers, 666
ment driers), 662, 663 Valve trays, 177
vacuum shelf driers as, 666 Van der Waals adsorption (phySical adsorption),
Tray efficiency:
in distillation, 402, 423-426, 425 566
in gas-liquid operations, 159-160, 178-186, 181, Van't HoWs law, 277
Vapor(s):
184,185
Murphree, 181-183 adsorption of: adsorptLon eqUilibrium of single
vapors, 569-575, 570-571
in absorption, 298-300
Tray towers: from fluidized beds, 697, 698
by fractionation, 61 1
adiabatic operatIons, 262 under unsteady-state conditions, 625, 626-610
for gas-liquid operations: bubble-cap trays, 158, (See also Adsorption)
air-water: dehumidIfication of, 252
159, 165-167, 166 in humldlflcallon operations, 231-236, 232-
proprietary trays, 176-178
(Set! also Sieve trays and sieve-tray towers, m

gas-liquid operations m) distillation of, 405-406
general characteristics of, 161,162-165 drying of, 679-680
multistage (see Distillation, by fractionation, saturated, defined, 221
superheated, defllled, 221
McCabe-Thiele method of; Dlsli!latlon, by (Sec also Gas absorptIOn; Humidlfu;,ation)
fractionation, Ponchon-Savar;t method of) Vapor-gas mi;w;tures:
packing towers versus, 210-211 adsorption equihbrium of, 575-580, 577-579
Treyba1 extractors, 546 humidification of (sec Humidiflcalion, of
Trickle-bed reactors, 209
Truck driers, 661 vapor-gas mixtures)
Tunnel driers, 687, 704 Vapor-liquid eqUilibrium:
Turbines:
flat-bed and pitched-blade, 599, 600 for pure substances, 220-224, 221
single-phase hquids agitated by, 147 (See also Distillation, vapor-liqUid equilibnum
Turbo·Grid, 177
Turbo.type driers (rotating shelves), 687, 688 in)
Turbulence: Vapor pressure:
in circular pipes, 70-72, 71
fully-barned, in open tanks, 149 in humidification, 221, 222
interfacial, 113 solvents and, 489
mass-transfer coefficients in (see Mass-transfer Vaporization:
coefficients, in turbulent flow) flash: distillation by, 163-367, 364
Turbulent diffusion (see Eddy diffusion)
Turndown ratIO, defined, 165 freezing by, 666
Two-component systems, equilibrium solubility latent heat of, defined, 222
of gases in, 276, 277 in McCabe-Thiele distiJIation method, 402-403
TWo-feed fractionators, 397-399, 198
Two-film theory (LeWis-Whitman theory; two-resis- (See also DistIllation)
tance theory), /07, 110 Vegetable oils:
Two-stage adsorption:
countercurrent, 595, 596, 599 adsorption of, 568
crosscurrent, 598-599 decolorization of, 586, 623
Two-truck driers, 663 recovery of, by leaching, 7 17-719,726,731-732,

Unbound moisture, rate of drying of, 683-684 738-744,741-741,760
Unbound water, defined, 657 Velocity:

deviating, defined, 55
effects of gas, on constant-rate drying, 675
slip, 143
terminal: of drops, 533, 514

of single-gas bubbles, 141, 142

784 INDEX

Venturi scrubbers, 186, 187 Water-coolin8 towers, 259, 260
Vessels (su specific types oj vessels) Weber number, 151, 533
Viscosity: Weeping:

force constants of gases as determined by, 33 defined, 161
of solvents, 489 in sieve trays, 173
Weir(s):
for gas absorption, 282 of sieve-tray towers, 170,171, 175
Vitamins: of tray towers, 164
Weir.through liquid distributors, 193
from fish oils, 395 Wet-bulb approach, defined, 248
low.pressure distillation to obtain, 460 Wel·bulb depression, defined, 239
Volatility: Wet·bulb temperature:
constant relative, in differential distillation, in adiabatic operations, 248
in humidification of vapor-gas mixtures, 237-241,
369-370
in Ponchon·Savant distillation method, 384-385 238
relative, vapor.liquid equilibpum and, 346 Lewis relation and, 241
of solvents for gas absorption, 281-282 Welled·wall towers, 71, 187
Volumetric overall mass·transfer coefficients, 202 Wetting, heat of, 580
Vortex fonnation, prevention of, 147-149, 148 Wilke·Chang correlation, 35
Wilke·Lee modification of Hirschfelder.Bird.Spotz
Water:
air-cooling of, 245-252, 246, 249, 250 method,31
bound and unbound, defined, 657 Wood:
deionization of, 642
deodorization of, 565 for cooling towers, 259
desalinization of, 6, 342 drying of, 657, 663, 678
makeup fresh, in humidification, 248 leaching of, 724
(Su also Humidification) Wood grids (hurdles), 190
softening of, 641, 642
solubility of gases in, 276 Zenz correlation, 535, 536
(See also Drying) Zeolites, 641
Zone refining, described, 4