acetone, in liquid–liquid mass contactors, 124–5, 137
adiabatic reactors, 48–9, 50
adsorption
in liquid–gas mass contactors, 117
in solid–fluid mass contactors, 115
agitation nozzles, 68
Arnold cell, 225–30
binary diffusivity measurements with, in gases, 226
mole fraction profiles for, 229
in species mass conservation equations, 252
batch heat exchangers, 56–60, 63, 67, 68
equilibrium temperature in, 58–60
examples of, 56
mechanical mixers in, 57
heat load in, 60
Level I analysis of, 57–8
mixed–mixed fluid motion in, 56
mixed–plug fluid motion in, 68
model equations for, 136
pilot-scale, 66
with reactions, 111–13
batch mass contactors, 118–20, 135–7. See also two-phase mass contactors
homogenous mixing for, 118
Level I analysis of, 119–20
conservation of mass in, 119
Level II analysis of, 120
model equations for, 136
two-phase systems for, 118–19
batch reactors, 10, 11, 34
chemical equilibrium in, 25–6
chemical reactor analysis for, 21–6
model equations for, 14, 28, 136
mole balance equations for, 24–5
rates of reaction in, 23–5
biomass concentrations, 30, 31
in pilot-scale bioreactors, 347–8
bioreactors, 29–30, 31. See also semibatch reactors
air spargers in, 348–52
biomass concentrations in, 347–8
Candida utilis in, 345
gas hold-up equation in, 349
mass transfer rates in, 347
oxygen concentrations in, 346–8
pilot-scale, 345–52
plumes in, 349
semibatch, 346
Biot number, 195–9, 235
fin efficiency v., 199
in molecular diffusion, 206–8
lumped analysis of, 235
Birmingham wire gauge (BWG), 79, 101
Blasius solution, 255, 272
in tubular two-phase mass contactors, 316, 317
boundary conditions
for boundary layer equations, 258
in countercurrent double pipe heat exchangers, 91, 92
in molecular diffusion, 206
in thermal conduction, 195, 197
constant temperature, 192–3
flux, 193
mixed, 194–5
for tubular two-phase mass contactors, 161
boundary layers, 185, 260
analysis of, 254–64
in convective heat transfer, 246–7
Navier–Stokes equations and, 247
for penetration theory, 275
Prandtl analogy for, 264
bubble breakage, 323–6
experimental data for, 325
Kolmogorov–Hinze theory and, 323
Levich force balance and, 326
Weber number in, 323, 326
bubble size, 302, 303
estimation of, 304–7
gas hold-up and, 312, 313
maximum, 304
orifices and, 303, 310–11
rise velocity and, 314
BWG. See Birmingham wire gauge
Candida utilis, 29
in pilot-scale bioreactors, 345
CFSTRs. See continuous-flow stirred tank reactors
characteristic scales, 248
characteristic velocity, 248
Chemical Engineers’ Handbook, 62, 94, 122, 219, 319, 328, 343
chemical equilibrium, 5
in batch reactors, 25–6
in Level II mathematical models, 5
chemical reactor analysis, 20–51
for acetic acid/sodium acetate, 52
for batch reactors, 21–6
chemical equilibrium in, 25–6
fluid motion in, 20
mole balance equations for, 24–5
rates of reaction in, 23–5
for CFSTRs, 20, 34, 37–41
constant density system in, 38
Level III analysis of, 39
residence time in, 20, 46, 48
steady-state operations in, 38
equipment classification for, 21
fermentor analysis and, 29–32, 140
biomass concentration in, 30, 31
Candida utilis in, 29
growth in bioreactors and, 29–30, 31
Monod-type relationships in, 32
for H2SO4 concentrations, 7, 29, 51
interfacial areas in, 20
in Level I models, 21
in Level II models, 21
in Level III models, 21
rates of reactions in, 26–33
reactor energy balance in, 47–51
adiabatic reactors and, 48–9, 50
energy of activation in, 50
exothermic reactions in, 50
heat of reaction in, 48
for semibatch reactors, 20, 34–7
for tubular reactors, 21, 42–47
Chilton–Colburn transport analogy, 260, 264, 265, 272
Lewis number in, 262
Pohlhausen solution in, 261
Stanton number in, 261
cocurrent double-pipe heat exchangers, 81–8
conservation of energy in, 83
driving force for heat transfer in, 82
energy balance in, 84, 114, 148
heat load in, 82, 85–7
temperature profiles in, 82
temperature v. position for, 82
cocurrent tubular solid–fluid mass contactors, 116
coefficient of skin friction, 250
coefficients. See coefficient of skin friction; heat transfer coefficients; mass transfer coefficients
coils
in heat exchanger design, 79, 98–9
residence time in, in semibatch heat exchangers, 72, 73–4
component mass balance, 36
in tubular reactors, 44
conduction. See thermal conduction
conservation of energy
in cocurrent flow, 83
in heat exchanger analysis, 56
in Level I mathematical models, 3–5
in thermal conduction, 188, 210
conservation of mass
in batch mass contactors, 119
in continuity equations, 294
in continuous-flow two-phase mass contactors, 144
in heat exchanger analysis, 56
in Level I mathematical models, 3–5
in molecular diffusion, 202
in rate of reactions, for mass transfer, 125
in tubular reactors, 43
in tubular two-phase mass contactors, 158
constitutive equations
Fick’s constitutive equation, 202
in molecular diffusion, 200, 201–6, 211–12
in penetration theory, 276
Sherwood number and, 208
Fourier’s constitutive equation, 187–95
differential forms of, 191
in penetration theory, 276
in heat exchanger analysis, 60
in thermal conduction, 189
constitutive relationships
Fick’s “Law,” 16
Fourier’s “Law,” 16
for heat transfer, 15
in Level III mathematical models, 15
for mass transfer rates, 127
for mass transfer, 16
for momentum transfer, 16
Newton’s “Law” of viscosity, 16
in phase equilibria, 6
for rate of reaction, 16
continuity equations
in convective heat transfer, 248–9
in tubular reactions, 43
continuous-flow stirred tank reactors (CFSTRs), 20, 34, 37–41
constant density system in, 38
Level III analysis of, 39
plug flow rates in, 41
residence time in, 20, 46, 48
steady-state operations in, 38
continuous-flow tank-type heat exchangers, 74–9
heat loads in, 75
heat transfer coefficient in, 77–8
mixed–mixed fluid motions in, 74–8
mixed–plug fluid motions in, 78–9
steady-state operations in, 74
continuous-flow two-phase mass contactors, 143–56
design summary for, 168–74
evaluation/iteration of, 172
flow rate determination in, 170–1
interfacial area determination in, 171–2
mass transfer agent choice in, 169–70
mass transfer coefficient estimation in, 171
mass transfer load calculations in, 169
stage efficiency in, 171
thermodynamic property information in, 170
equilibrium stage in, 146
gas–liquid, 154
mixed–mixed fluid motion in, 144–6
conservation of mass and, 144
mixed–plug fluid motion in, 153–6
control volumes
in differential transport equations, 293
in Level III mathematical models, 12
in Level I mathematical models, 3
selection of, 12
in semibatch heat exchangers, 73
in single-phase reactors, 21
for thermal conduction, 210
in tubular reactors, 42
in word statement of conservation laws, 11
convective flux, 203, 226, 228
countercurrent double-pipe heat exchangers, 55, 81, 88–94
boundary conditions in, 91, 92
log-mean differences in, 101
steady-state operations in, 91
technically feasible design for, 92, 96, 328
temperature profiles in, 89, 90, 95
countercurrent tubular mass contactors, 117
flooding limits in, 339
flow rate determinations in, 337–42
interfacial area determination for, 343–5
liquid distributors and, 319, 344
mass transfer coefficients in, 342
mass transfer load calculations in, 336
packed towers and, 336, 344
packing in, 335
penetration theory model and, 342
Raschig rings in, 341, 342, 343
stage efficiency in, 339
technically feasible design for, 335–45
crystallinity, 190
cylindrical fin, 196
Damköhler number, 299
design, for mathematical models, 17
logic required for, 8, 10
desorption, 115
deviatoric stress, 295
diffusion. See molecular diffusion
diffusive flux, 226
distillation columns
in Level I mathematical models, 5
in Level II mathematical models, 6
distribution coefficients, in liquid-liquid mass contactors
double pipe heat exchangers, 55, 79, 80, 86
cocurrent, 81–8
conservation of energy in, 83
cross-sectional slice of, 83
driving force for heat transfer in, 82
energy balance in, 84, 114, 148
heat load in, 82, 85–7
limiting behavior for, 84
temperature profiles in, 82
temperature v. position for, 82
countercurrent, 55, 81, 88–94
boundary conditions in, 91, 92
cross-sectional slice of, 90
log-mean differences in, 101
steady-state operations in, 91
technically feasible design for, 92, 96
temperature profiles in, 89, 90, 95
plug–plug heat exchangers and, 56
technically feasible design for, 334
driving forces, for heat transfer, 66
drop breakage, 323–6
experimental data for, 325
Kolmogorov–Hinze theory and, 323
Levich force balance and, 326
Weber number in, 323
drop size, 157, 302, 303
control volume and, 306
estimation of, 304–7
maximum stable size, 304
surface tension force and, 304
Weber number and, 304
efficiency of separation, 147
energy balance
in cocurrent double-pipe heat exchangers, 84, 114, 148
constant volume and, 110
in heat exchanger analysis, 109–10
in semibatch heat exchangers, 70
energy conservation equations
in convective heat transfer, 250–2
Fourier’s constitutive equation and, 251–81
heat transfer coefficients in, 251
Nusselt number in, 251
Prandtl number in, 251, 252
Reynolds number in, 251, 252
in Navier–Stokes equations, 251
energy of activation, 50
enthalpy, 58
in heat exchanger analysis, 61, 111
in thermal conduction, 210
equilibrium stage, 146
equilibrium temperature
in batch heat exchangers, 58–60
in heat transfer, 65
equimolar counterdiffusion, 273
exothermic reactions, 50
Fanning friction factor, 255
fermentor analysis, 29–32, 140
biomass concentration in, 30, 31
Candida utilis in, 29
equilibrium values in, 32–3
exponential growth in, 32
glucose in, 30
growth in bioreactors and, 29–30, 31
Monod-type relationships in, 32
substrates in, 30–1
Fick, Adolf, 201
Fick’s “Law” constitutive equation, 17, 185, 202
control volume for analysis of, 202
in molecular diffusion, 200, 201–6, 211–12
in penetration theory, 276
Sherwood number and, 208
species mass conservation equations and, 252
film theory, in fluid–fluid systems, 273
equimolar counterdiffusion in, 273
fin efficiency, 198
Biot number v., 199
temperature profile in, 197
flooding limits, 339
in packed towers, 340
flow of complex mixtures in pipes, 156
fluid motion. See also mixed–mixed fluid motion; mixed–plug fluid motion; plug-flow fluid motion; well-mixed fluid motion
in batch heat exchangers, 56, 68
in batch reactors, 20
cocurrent double-pipe heat exchangers, 81
in continuous-flow two-phase mass contactors, 144–6, 153–6
countercurrent flow, 81
equipment classification for, 115
in Level III mathematical models, 7
in Level IV mathematical models, 7
plug flow, 81
in semibatch heat exchangers, 68, 69–74
in semibatch mass contactors, 138–9
tubular–tubular plug flow, 81
in tubular two-phase mass contactors, 156
fluid velocity gradients, 247
fouling, 219
Fourier, Jean-Baptiste-Joseph, 190
Fourier number, Biot number v., in transient conduction/diffusion, 232
Fourier’s constitutive equation, 187–95
through composite layered materials, in thermal conduction, 214
differential forms of, 191
energy conservation equations and, 251–81
Nusselt number v., 199, 201–9
for one-dimensional thermal conduction, 210
in penetration theory, 276
Fourier’s “Law”, 16, 185, 190
Fourier’s “Second Law”, 192, 195
in molecular diffusion, 204
Frössling equation, 267
gas flow rates
in countercurrent mass contactor design, 339
for molar gases, 165
in tubular two-phase mass contactors, 319
gas hold-up, 312, 313
in pilot-scale bioreactors, 349
gas phase reactions, 27
gas plumes. See plumes
Gilliland’s equation, 269
Handbook of Industrial Mixing, 309
heat capacity
for batch heat exchangers, 58
in heat exchanger analysis, 61
in heat exchanger design, 96
heat exchanger analysis, 55–102
for batch heat exchangers, 56–60, 63, 67, 68
equilibrium temperature in, 58–60
heat load in, 60
Level I analysis of, 57–8
mixed–mixed fluid motion in, 56
pilot-scale, 66
with reactions, 111–13
for continuous-flow tank-type exchangers, 74–9
heat transfer coefficient in, 77–8
mixed–mixed fluid motions in, 74–8
mixed–plug fluid motions in, 78–9
steady-state operations in, 74
for CSTR, 113
for double pipe heat exchangers, 55, 79, 80, 86
energy balance in, 109–10
enthalpy in, 61, 111
law of conservation of energy/mass an, 56
mixture approximations in, 110–11
for rate of heat transfer, 60–7
for semibatch heat exchangers, 67, 68–74
agitation nozzles in, 68
coil residence time in, 72, 73–4
control volumes in, 73
energy balance in, 70
heat load for, 70
mixed–mixed fluid motion in, 69–72
mixed–plug fluid motion in, 68, 72–4
well-mixed fluid motion in, 68
for tubular heat exchangers, 79–94
cocurrent, 81
double pipe, 55, 79, 86
plate and frame, 80–1
shell and tube, 79–80
steady-state operations for, 84
heat exchangers, 67–79. See also batch heat exchangers; cocurrent double-pipe heat exchangers; countercurrent double-pipe heat exchangers; shell and tube heat exchangers
analysis of, 55–102
for batch exchangers, 56–60, 63, 68
for continuous-flow tank-type exchangers, 74–9
for semibatch exchangers, 67, 68–74
for tubular, 79–94
batch, 56–60, 63, 68
equilibrium temperature in, 58–60
heat load in, 60
Level I analysis of, 57–8
mixed–mixed fluid motion in, 56
pilot-scale, 66
continuous-flow tank type, 74–9
heat loads in, 75
heat transfer coefficient in, 77–8
mixed–mixed fluid motions in, 74–8
mixed–plug fluid motions in, 78–9
steady-state operations in, 74
convective transport coefficient estimations for, 281–4
for mixed–mixed tank type, 282–3
for mixed–plug tank type, 284
for tubular tank type, 284
designs of
double pipe, 55, 79, 80, 86
cocurrent, 81–8
countercurrent, 55, 81, 88–94
plug–plug heat exchangers and, 56
model equations for, 15
plate and frame, 80–1
semibatch, 67, 68–74
agitation nozzles in, 68
coil residence time in, 72, 73–4
control volumes in, 73
energy balance in, 70
heat load for, 70
mixed–mixed fluid motion in, 69–72
mixed–plug fluid motion in, 68, 72–4
well-mixed fluid motion in, 68
technically feasible design for, 94–102, 328–34
coils in, 98–9
double-pipe exchangers, 334
local heat transfer coefficients in, 330
log-mean differences in, 98
overall heat transfer coefficients in, 330
pipe diameter/velocities in, 99, 102
pipe schedule in, 332
Prandtl numbers in, 330
Reynolds number in, 328, 330
tubular, 79–94
BWG measurements for, 79
cocurrent flow in, 81
cross section of, 217
double pipe, 55, 79
plate and frame, 80–1
shell and tube, 79–80
steady-state operations for, 84
heat load
in batch heat exchangers, 60
in cocurrent double-pipe heat exchangers, 82, 85–7
in continuous-flow tank-type heat exchangers, 75
for semibatch heat exchangers, 70
heat of reaction, 48
heat transfer coefficients
in cocurrent double-pipe heat exchangers, 87
through composite layered materials, 212–17
in continuous-flow tank-type heat exchangers, 77–8
Nusselt number and, 200, 201–6
in shell and tube heat exchanger design, 332–4
for tubular exchangers, 217
Heat Transfer Research Institute (HTRI), 94
design procedures of, for shell and tube heat exchangers, 331
heat transfer. See also boundary layers; transport analogies; transport coefficient models, in fluid–fluid systems
area available for, 55
in batch heat exchangers, properties for, 63
in batch reactors, 15
Biot number for, 195–9
constitutive relationships for, 15–16
convective, 246
boundary layers in, 246–7, 248, 254–64
central hypothesis in, 246
coefficient of skin friction in, 250
continuity equations in, 248–9
energy conservation equations in, 250–2
friction factors for, 256, 267
Frössling equation in, 267
Gilliland’s equation in, 269
in heat exchangers, 281–4
in mass contactors, 284–5
Navier–Stokes equations in, 249–50, 251
transport analogies in, 247, 254–60, 264, 265, 272
transport coefficient models in, 273
in wet bulb experiment, 261
in wetted wall column, 269
heat exchanger analysis for, 60–7
mathematical models for, 8, 15
plug-flow fluid motion in, 7
in thermal conduction, 194
Henry’s “Law”, 6
constants, for gases, 122
in countercurrent mass contactor design, 337
in liquid–gas mass contactors, 122
liquid–liquid mass contactors and, 123
in semibatch mass contactors, 142
horizontal mass contactors, 158
HTRI. See Heat Transfer Research Institute
impeller diameter, 307
Reynolds number for, 309
Weber number for, 308
interfacial areas, 301–20
in chemical reactor analysis, 20
in continuous-flow two-phase mass contactors, 171–2
in countercurrent mass contactor design, 343–5
experimental technique summary for, 324
for mass transfer, 130
for plumes, 312, 315
in tank-type mass contactors, 306, 307–15
separators in, 309
in tubular two-phase mass contactors, 162, 316–20
cocurrent area estimation, 316
cocurrent Km estimation, 318
interphase mass transfer, in fluid-fluid systems, 279–81
oxygenation of water in, 281
Introduction to Chemical Engineering Analysis (Denn/Russell), 8, 9, 18, 20, 114
Kolmogorov–Hinze theory, 316
bubble/drop breakage and, 323
laminary boundary layer, 248, 254–6, 259
Blasius solution in, 255, 272
Fanning friction and, 255
Reynolds number and, 256
leaching, 115, 116
Level I (mathematical) models
chemical reactor analysis in, 21
component balance relations in, 5
conservation of mass and/or energy, 3–5
control volumes in, 3
definitions within, 4
distillation columns in, 5
simple mass balance in, 3
in single-phase reactors, 14
tubular reactors and, analysis through, 43–4
in two-phase reactors, 14
Level II (mathematical) models, 5–6
chemical equilibrium in, 5
chemical reactor analysis in, 21
distillation columns in, 6
Henry’s “Law” in, 6
Nernst’s “Law” in, 6
phase equilibrium in, 5, 6
thermal equilibrium in, 5
transport phenomena in, 5
Level III (mathematical) models, 6–7
CFSTRs and, analysis through, 39
chemical reactor analysis in, 21
constitutive relationships in, 15
control volumes in, 11–12
fluid motion in, 6–7
rate of reactions in, 15
transport rates for mass and/or energy in, 6–7
Level IV (mathematical) models, 7
fluid motion in, 7
Level V (mathematical) models, 7
Level VI (mathematical) models, 8–9
time constraints in, 8
Levich force balance, 326
Lewis number, 239
liquid distributors, 319, 344
liquid–gas mass contactors, 117, 121–2
adsorption in, 117
contactor/separators in, 135
Henry’s “Law” in, 122
oxygen concentration in, 122, 143
partial pressure in, 122
photograph of, 154
scrubbing in, 117
stripping in, 117
liquid–liquid mass contactors, 116–17, 122–5, 135–7
acetone in, 124–5, 137
continuous flow, 144
distribution coefficients in
equilibrium in, 133–4
Henry’s “Law” and, 123
ideal behavior in, 123
mixer–settlers in, 116
log-mean differences, 178–80
in countercurrent double-pipe heat exchangers, 101
in heat exchanger design, 98
in tubular two-phase mass contactors, 167
mass, word statements of conservation laws for, 13–14
mass balance. See also component mass balance
in tubular reactors, 43
mass contactor analysis, 114, 148, 173
for batch mass contactors, 118–20, 135–7
homogenous mixing for, 118
Level I analysis of, 119–20
Level II analysis of, 120
two-phase systems for, 118–19
for liquid–gas systems, 117, 121–2, 135
adsorption in, 117
contactor/separators in, 135
Henry’s “Law” in, 122
oxygen concentration in, 122
for liquid–liquid systems, 116–17, 122–5, 135–7
acetone in, 124–5, 137
continuous flow, 144
distribution coefficients in
equilibrium in, 133–4
Henry’s “Law” and, 123
ideal behavior in, 123
mixer–settlers in, 116
for rate of mass transfer, 125–34
approach to equilibrium and, 132–4
conductivity probes for, 129
conservation of mass in, 125
constitutive relationships in, 127
expression rates in, 127–32
interfacial area in, 130
overall resistance in, 128
reaction rate expression in, 114
for single-phase systems, 114
for solid–fluid systems, 115–16, 135
cocurrent tubular, 116
countercurrent tubular, 117
unit operations for, 115
for solid–liquid systems, 121, 132
surface to volume factors in, 131
for tank-types,
mixed–mixed, 117
mixed–plug mass contactors, 117
semibatch mixed–plug contactors, 116
for two-phase systems, 114, 134–56
batch contactors as, 118, 134–5
continuous flow, 143–56, 168–74
isothermal, 114
semibatch contactors as, 134–5, 137–43
tubular contactors, 156–68
mass contactors, See also batch mass contactors; cocurrent tubular solid–fluid mass contactors; continuous-flow two-phase mass contactors; countercurrent tubular mass contactors; liquid–gas mass contactors; liquid–liquid mass contactors; semibatch mass contactors; single-phase contactors; solid–fluid mass contactors; solid–liquid mass contactors; tank-type mixed–mixed mass contactors; tank-type mixed–plug mass contactors; tank-type semibatch mixed–plug contactors; two-phase mass contactors
analysis of, 114, 148, 173
for batch mass contactors, 118–20, 135–7
for liquid–gas systems, 117, 121–2, 135
for liquid–liquid systems, 116–17, 122–5, 135–7
for rate of mass transfer, 125–34
reaction rate expression in, 114
for single-phase systems, 114
for solid–fluid systems, 115–16, 135
for solid–liquid systems, 121, 132
for tank-types, 116, 117
for two-phase systems, 114, 134–56
continuous-flow two-phase, 143–56, 168–74
design summary for, 168–74
equilibrium stage in, 146
mixed–mixed fluid motion in, 144–6
mixed–plug fluid motion in, 153–6
convective transport coefficient estimations for, 284–5
Chilton–Colburn analogy in, 284
for mixed–mixed tank type, 285
for mixed–plug tank type, 285
for tubular tank type, 285
interfacial area estimation for, 306, 307–15
for mixed–mixed Km systems, 309
for mixed–mixed systems, 307–9
for mixed–plug systems, 309–13
mixed–mixed, 146–52
efficiency of separation in, 147
feasible design for, 146–52
stage efficiency in, 147, 148
TCE in, 149
model equations for, 15
semibatch, 134–5, 137–43
mixed–mixed fluid motion in, 138–9
mixed–plug fluid motion in, 139–42
Penicillin production in, 139, 141
technically feasible design for
countercurrent systems, 335–45
tubular two-phase, 156–68
cocurrent flow in, 158–9
countercurrent flow in, 157–8, 159–64
drop size in, 157
fluid motion systems in, 156, 157
as membrane contactor, 156
mass transfer coefficients, 171, 301–20
in species mass conservation equations, 253
mass transfer. See also boundary layers; transport analogies; transport coefficient models, in fluid–fluid systems
in batch reactors, 15
constitutive relationships for, 16
convective, 246–85
boundary layers in, 246–7, 248
continuity equations in, 248–9
dimensional analysis of, 247
energy conservation equations in, 250–2
Frössling equation in, 267
Gilliland’s equation in, 269
in mass contactors, 284–5
Navier–Stokes equations in, 249–50, 251
species mass conservation equations in, 252–4, 298–9
transport analogies in, 247, 254–60, 264, 265, 272
transport coefficient models in, 273
vector notations for, 299–300
in wetted wall column, 269
mathematical models for, 8, 15
in pilot-scale bioreactors, 347
plug-flow fluid motion in, 7
rate of reactions for, 16, 125–34
Material Safety Data Sheets (MSDS), 125
mathematical models, 3
laboratory scale experiments, 12
Level I, 3–5
component balance relations in, 5
conservation of mass and/or energy, 3–5
control volumes in, 3
definitions within, 4
distillation columns in, 5
simple mass balance in, 3
mathematical models (cont.)
Level II, 5–6
chemical equilibrium in, 5
distillation columns in, 6
Henry’s “Law” in, 6
Nernst’s “Law” in, 6
phase equilibrium in, 5, 6
thermal equilibrium in, 5
transport phenomena in, 5
Level III, 6–7
constitutive relationships in, 15
control volumes in, 11–12
fluid motion in, 6–7
rate of reactions in, 15
transport rates for mass and/or energy in, 6–7
Level IV, 7
fluid motion in, 7
Level V, 7
Level VI, 8–9
for mass transfer, 8, 15
technically feasible designs for, 17–18
mechanical mixers, 57
membrane contactors. See tubular two-phase mass contactors
membrane diffusion. See sorption–diffusion model
mixed–mixed fluid motion
in batch heat exchangers, 56
in continuous-flow tank-type heat exchangers, 74–8
in continuous-flow two-phase mass contactors, 144–6
in semibatch heat exchangers, 69–72
in semibatch mass contactors, 138–9
mixed–mixed heat exchangers, 55
reactor jackets in, 55, 62
mixed–mixed mass contactors, 146
efficiency of separation in, 147
feasible design for, 146
stage efficiency in, 147, 148
TCE in, 149
mixed–plug fluid motion
in continuous-flow tank-type heat exchangers, 78–9
in continuous-flow two-phase mass contactors, 153–6
Henry’s “Law” in, 142
in semibatch heat exchangers, 72–4
in semibatch mass contactors, 139–42
mixed–plug heat exchangers, 55
mixer–settlers, 116
molar flux, 202, 203, 205, 226
mole balance equations, for batch reactors, 24–5
molecular diffusion, 199, 201–9
Arnold cell and, 225–30
Biot number in, 232
through composite layered materials, 212–22
Fick’s constitutive equation in, 200, 201–6, 211–12
geometric effects on, 209–212
one-dimensional, 211
molar flux in, 202, 203, 205, 226
sorption–diffusion model, 231
transient, 231–9
Fourier number v. Biot number in, 232
short time penetration solution for, 233–5
in various gases, 204
momentum transfer, equations for, 13, 294–6
MSDS. See Material Safety Data Sheets
multiple phase transport phenomena, in Level VI models, 8–9
multistage agitator towers, 337
Navier–Stokes equations, 296
boundary layers and, 247
in convective heat transfer, 249–50, 251
energy conservation equations and, 251
Reynolds number and, 249, 250
in Reynolds transport analogy, 257
Nernst’s “Law,” 6
Newton’s “Law” of cooling, 190, 194, 199
Newton’s “Law” of viscosity, 16
Nusselt number, 186, 238
in energy conservation equations, 252
Fourier’s constitutive equation v., 199, 201–9
heat transfer coefficient and, 200, 201–6
heat transfer correlation and, 200, 201–6
Prandtl number and, 270
Reynolds number v., 268
in shell and tube heat exchanger design, 333
in thermal conduction, 199–201
transport correlations for, 264
Ohm’s “Law,” 128
orifices
bubble size and, 303, 310–11
gas flow power input in, 307, 311
in gas spargers, 303
oxidation units, 154
oxygenation of water, 281
oxygen concentrations
in liquid–gas mass contactors, 122, 143
in mixed–plug fluid motion, 142
in pilot-scale bioreactors, 346–8, 350, 351
stripping of, 117
in water in contact with air, 121
packed towers, 336, 338
flooding/pressure drops in, 340
height of, 344
operability limits for, 339
technically feasible design for, 335, 344
volume of, 344
packing, 335
random, 341
partial pressure, in liquid–gas mass contactors, 122
PDF model. See probability distribution function model
penetration theory, in fluid–fluid systems, 273–8
in countercurrent mass contactor design, 342
Fick’s constitutive equation in, 276
Fourier’s constitutive equation in, 276
local boundary layer for, 275
surface renewal theory and, 278
surface renewal time in, 274
penetration time, 274
penicillin, 139, 141
permeance, 231
phase equilibrium, 6
pilot-scale batch heat exchangers, 66
pilot-scale bioreactors, 345–52
air spargers in, 348–52
biomass concentrations in, 347–8
Candida utilis in, 345
gas hold-up equation in, 349
mass transfer rates in, 347
oxygen concentrations in, 346–8, 350, 351
plumes in, 349
pipe schedules, 332
plate and frame heat exchanger, 80–1
plug-flow fluid motion, 81
in CFSTRs, 41
in Level III mathematical models, 7
in Level IV mathematical models, 7
in mass and/or heat transfer, 7
plug-flow rates, for CFSTRs, 41
plug-flow reactors (PFRs), 42
heat exchanger analysis and, 113
plug-flow velocity, 42, 43
plug–plug heat exchangers, double pipe exchangers and, 56
plumes, 302
diameter of, 313
in gas spargers, 311
interfacial areas for, 312, 315
liquid circulation model and, 312
in pilot-scale bioreactors, 349
volume equation of, 313
Pohlhausen solution, 261
Poisson process, 278
power input, 307, 311
Prandtl analogy, 264
Prandtl number, 186, 239
in energy conservation equations, 251, 252
in heat exchanger design, 330
Nusselt number and, 270
transport correlations for, 264
pressure drops, 340
probability distribution function (PDF) model, 301
raffinates, 116
Raoult’s “Law,” 165
Raschig rings, 341, 342, 343
rates of reaction
in batch reactors, 23–5
in chemical reactor analysis, 26–33
rate expression of, 26–8
constants for, 20, 29
constitutive relationships for, 16
for gas phases, 27
in Level III mathematical models, 15
for mass transfer, 16
in semibatch reactors, 36
in tank type reactors, 33–41
reactor energy balance, 47–51
adiabatic reactors and, 48–9, 50
energy of activation in, 50
exothermic reactions in, 50
heat of reaction in, 48
reactors. See adiabatic reactors; batch reactors; bioreactors; chemical reactor analysis; continuous-flow stirred tank reactors; continuous mode tank reactors; pilot-scale bioreactors; semibatch reactors; single-phase reactors; tank types, for reactors; tubular reactors; two-phase reactors
residence time
in CFSTRs, 20, 46, 48
in coils, in semibatch heat exchangers, 73–4
Reynolds number, 186
in energy conservation equations, 251, 252
in heat exchangers design, 328
laminary boundary layer and, 256
in Navier–Stokes equations, 249, 250
Nusselt number v., 268
in shell and tube heat exchanger design, 332, 333
in species mass conservation equations, 253
transport correlations for, 264
in tubular two-phase mass contactors, 317
Reynolds transport analogy, 257–60
Sauter mean diameter, 302
schedule. See pipe schedules
Schmidt number, 186, 236–9
in species mass conservation equations, 253
transport correlations for, 264
semibatch bioreactors, 346
semibatch heat exchangers, 67, 68–74
agitation nozzles in, 68
coil residence time in, 72, 73–4
energy balance in, 70
heat load for, 70
mixed–mixed fluid motion in, 69–72
mixed–plug fluid motion in, 68, 72–4
well-mixed fluid motion in, 68
semibatch mass contactors, 134–5, 137–43
mixed–mixed fluid motion in, 138–9
mixed–plug fluid motion in, 139–42
penicillin production in, 139, 141
semibatch reactors, 20, 34–7
component mass balance equations for, 36
model behavior for, 36
rate expression in, 36
reactants’ introduction into, 34
species concentrations in, 34
separators
in liquid–gas systems, 135
in liquid–liquid systems, 135
shell and tube heat exchangers, 79–80
technically feasible design for, 331, 334
heat transfer coefficients in, 332–4
HTRI procedures in, 331
Nusselt number in, 333
Reynolds number in, 332, 333
shell diameter in, 331–2
velocity factors in, 333
Sherwood number, 186, 238
Fick’s constitutive equation and, 208
in molecular diffusion, 208–9
transport correlations for, 264
short time penetration solution
for thermal conduction/diffusion, 233–5
thermal penetration depth in, 233, 234
sieve tray towers, 337
single-phase contactors, isothermal, 114
single-phase reactors
control volume in, 21
Level I analysis for, 14
single-phase transport phenomena, in Level V models, 7
sodium acetate, 52
solid–fluid mass contactors, 115–16, 135
cocurrent tubular, 116
unit operations for, 115
adsorption, 115
desorption, 115
leaching, 115, 116
washing, 115, 116
solid–liquid mass contactors, 121, 132
sorption–diffusion model, 231
geometry in, 230
permeance in, 231
spargers, 303, 311
in pilot-scale bioreactors, 348–52
plumes and, 311
species mass conservation equations, 298–9
in convective heat transfer, 252–4
spray towers, 336
stage efficiency
in continuous-flow two-phase mass contactors, 171
in countercurrent mass contactor design, 339
in mixed–mixed mass contactors, 147, 148
Stanton number, 239, 261
steady-state operations
in CFSTRs, 38
in continuous-flow tank-type heat exchangers, 74
in continuous-flow two-phase mass contactors, 144
in countercurrent double pipe heat exchangers, 91
for thermal conduction, 192
for tubular heat exchangers, 84
in tubular two-phase mass contactors, 159
stripping, in liquid–gas mass contactors, 117
Sturm–Liouville Problem, 195
surface reaction, 299
surface renewal theory, in fluid–fluid systems, 273–8, 279
penetration theory and, 278
Poisson process in, 278
surface renewal time, 274
surface tension force, 304
tank-type mixed–mixed mass contactors, 117
tank-type mixed–plug mass contactors, 117
tank-type semibatch mixed–plug contactors, 116
tank types, for heat exchangers, 67–79
batch, 56–60, 63, 67, 68
continuous-flow, 74–9
fluid motion in, 55
mixed–mixed, 55
mixed–plug, 55
plug–plug, 55
semibatch, 67, 68–74
temperature controls in, 68
tank types, for reactors, 22
batch, 10, 11, 34
in chemical reactor analysis, 21–6
fluid motion in, 20
heat transfer in, 15
mass transfer in, 15
model equations for, 14, 28
CFSTRs, 20, 34, 37–41
constant density system in, 38
Level III analysis of, 39
residence time in, 20, 46, 48
steady-state operations in, 38
height to diameter ratio for, 34
rates of reactions in, 33–41
semibatch, 20, 34–7
component mass balance equations for, 36
model behavior for, 36
rate expression in, 36
reactants’ introduction into, 34
species concentrations in, 34
tubular, 21, 42–7
conservation of mass in, 43
continuity equations in, 43
control volume in, 42
Level I analysis in, 43–4
mass balance in, 43
plug-flow velocity in, 42, 43
TCE. See trichloroethane
technically feasible design, 327–52
for cocurrent double-pipe heat exchangers, 83
for countercurrent double-pipe heat exchangers, 92, 96, 328
for countercurrent mass contactors, 335–45
flooding limits in, 339
flow rate determinations in, 337–42
for gases, 339
interfacial area determination for, 343–5
liquid distributors, 319, 344
mass transfer coefficients in, 342
mass transfer load calculations in, 336
packed towers and, 336, 344
packing in, 335
penetration theory model and, 342
Raschig rings in, 341, 342, 343
stage efficiency in, 339
for heat exchangers, 94–102, 328–34
area estimation as part of, 98
coils in, 79, 98–9
density in, 96
double pipe, 334
feed temperature in, 96
heat capacity in, 96
heat transfer coefficient in
local heat transfer coefficients in, 330
log-mean differences in, 98
overall heat transfer coefficients in, 330
pipe diameter/velocities in, 99, 102
Prandtl numbers in, 330
procedures for, 96–102
resources for, 96
Reynolds number in, 328, 330
viscosity in, 328
for multistage agitator towers, 337
for packed towers, 335, 344
procedures in, 345
for pilot-scale bioreactors, 345–52
air spargers in, 348–52
biomass concentrations in, 347–8
Candida utilis in, 345
gas hold-up equation in, 349
mass transfer rates in, 347
oxygen concentrations in, 346–8
plumes in, 349
for shell and tube heat exchangers, 331, 334
heat transfer coefficients in, 332–4
HTRI procedures in, 331
Nusselt number in, 333
Reynolds number in, 332, 333
shell diameter in, 331–2
velocity factors in, 333
for sieve tray towers, 337
for spray towers, 336
for tray towers, 335
for wetted wall columns, 336
thermal conduction, 187
composite layered materials, 212–22
Fourier’s constitutive equation and, 214
heat transfer coefficients for, 212–17
one-dimensional, with convection, 215–20
temperature profiles in, 216
tubular exchangers, 217
constant temperature boundary conditions in, 192–3
constitutive equations in, 189
definition of, 188
experimental determination of, 187–95
Fourier’s constitutive equation in, 187–95
differential forms of, 191
for one-dimensional non-planar geometries, 210
transient heat flow measurements for, 191
flux boundary conditions in, 193
general boundary conditions, 195, 197
with generation, 222–5
geometric effects on, 209–212
heat transfer coefficient in, 195, 220, 225, 230
heat transfer rates in, 194
mathematical considerations in, 195
measurement of, 191
mixed boundary conditions in, 194–5
Newton’s “Law” of cooling in, 190, 194, 199
Nusselt number in, 186, 199–201
permeability values in, 231
Sturm–Liouville Problem and, 195
temperature profile in, 188
transient, 231–9
Fourier number v. Biot number in, 232
short time penetration solution for, 233–5
thermal conductivity
crystallinity and, 190
of liquids, 190
material property definitions for, 189–90
of solids, 190
thermal diffusivity, 192
thermal equilibrium, 5
in Level II mathematical models, 5
thermodynamic property information, 170
time constraints, in Level VI mathematical models, 8
transient heat flow, 191
transport analogies, 247, 254–64
Chilton–Colburn, 260, 264, 265, 272
Lewis number in, 262
Pohlhausen solution in, 261
Stanton number in, 261
Reynolds, 257–60
Navier–Stokes equation in, 257
transport coefficient models in fluid–fluid systems. See also film theory, in fluid–fluid systems; interphase mass transfer, in fluid–fluid systems; penetration theory, in fluid–fluid systems; surface renewal theory, in fluid–fluid systems
for heat/mass transfer, 273
film theory, 273
interphase mass transfer, 279–81
penetration theory, 273–8
surface renewal theory, 273–8, 279
transport correlations, 186
transport equations, 247–54
boundary layer analysis in, 254–64
for laminar boundary layer, 254–6, 258
derivation of, 293–9
for conservation of mass, 294
for energy, 296–8
for momentum, 294–6
for species mass, 298–9
differential, 259
control volume in, 293
for specific geometries, 264–73
transport phenomena, 5
multiple phase, in Level VI models, 8–9
single phase, in Level V models, 7
tray towers, technically feasible design for, 335
trichloroethane (TCE), 149
tubular cocurrent extractors, 117
tubular heat exchangers, 79–94. See also cocurrent double-pipe heat exchangers; countercurrent double-pipe heat exchangers; shell and tube heat exchangers
BWG measurements for, 79, 101
cocurrent flow in, heat load in, 85–7
cross section of, 217
design procedures for, 334
double pipe, 55, 79
cocurrent, 81–8
countercurrent, 55, 81, 88–94
plug–plug heat exchangers and, 56
tubular–tubular plug flow in, 81
plate and frame, 80–1
shell and tube, 79–80
steady-state operations for, 84
thermal conduction/diffusion in, 217
tubular reactors, 21, 42, 47
conservation of mass in, 43
continuity equations in, 43
control volume in, 42
Level I analysis in, 43–4
mass balance in, 43
PFRs in, 42
plug-flow velocity in, 42, 43
tubular–tubular plug flow, 81
tubular two-phase mass contactors, 156–68
cocurrent flow in, 158–9
concentration profiles in, 163
conservation of mass in, 158
cross-sectional slice of, 158
Level II analysis for, 158
steady-state operations in, 159
countercurrent flow in, 157–8, 159–64
boundary conditions for, 161
concentration profiles in, 163
contactors in, 159–60
cross-sectional slice of, 161
equilibrium analysis for, 161–2
fluid velocity in, 159
for gas–liquid systems, 164
interfacial area in, 162
Level I analysis for, 160
Level II analysis for, 160
log-mean differences in, 167
molar gas flow rates in, 165
oil flow rates in, 167–8
operating diagram for, 153–74
Raoult’s “Law” in, 165
technically feasible design for, 335–45
drop size in, 157
fluid motion systems in, 156, 157
interfacial areas in, 162, 316–20
Blasius solution and, 316, 317
cocurrent area estimation, 316
cocurrent Km estimation, 318
continuous phase turbulent flow for, 317
countercurrent estimation, 318–19
countercurrent Km estimation, 320
equilibrium bubble/drop distribution in, 317
gas flow rates in, 319
Kolmogorov–Hinze theory and, 316
low dispersed phase concentrations in, 317
Reynolds number in, 316
as membrane contactor, 156
turbulence, 302
two-phase mass contactors, 114, 118–19
batch, 118, 134–5
agitation in, 134–5
as continuous, 119
as dispersed, 119, 155
isothermal, 118
nonisothermal, 118
continuous flow, 143–56
design summary for, 168–74
isothermal, 114
semibatch, 134–5
tubular, 156–68
cocurrent flow in, 158–9
countercurrent flow in, 157–8, 159–64
drop size in, 157
fluid motion systems in, 156, 157
as membrane contactor, 156
two-phase reactors
Level I analysis for, 14
unit operations, for solid–fluid mass contactors, 115
velocity, in shell and tube heat exchanger design, 333
vertical mass contactors, 160
viscosity
in heat exchanger design, 328
Newton’s “Law” of viscosity, 16
of water, 329
water bath batch heat exchangers, 57
Weber number, 304
in bubble/drop breakage, 323
for impeller diameter, 308
modified, 304
well-mixed fluid motion
in Level III mathematical models, 6–7
in Level IV mathematical models, 7
in semibatch heat exchangers, 68
wetted wall columns, 336
wind-chill factors, 246
word statement of conservation laws, 13
for batch heat exchangers, 57
control volumes in, 11
in heat exchanger analysis, 60
for mass, 13–14
in tubular reactors, 44