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Mass and Heat Transfer

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  • 130 b/w illus. 66 tables 80 exercises
  • Page extent: 404 pages
  • Size: 253 x 177 mm
  • Weight: 0.91 kg

Library of Congress

  • Dewey number: 621.402/2
  • Dewey version: 22
  • LC Classification: TP363 .R87 2008
  • LC Subject headings:
    • Heat exchangers
    • Chemical engineering--Equipment and supplies

Library of Congress Record

Hardback

 (ISBN-13: 9780521886703)




Index



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


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