Mass Transfer Processes: Modeling, Computations, and Design

Title Page......Page 2
Copyright Page......Page 3
Contents......Page 4
Preface......Page 15
About the Author......Page 20
Notation......Page 21
1.1.1 What Is Interfacial Mass Transfer?......Page 34
1.2.2 Concentration: Mole Units......Page 35
1.3.1 Molar and Mass Flux: Definition......Page 36
1.3.3 Diffusion Flux......Page 37
1.4.1 Gas…Liquid Interface: Henrys Law......Page 38
1.4.5 Nonlinear Equilibrium Models......Page 40
1.5.2 Unit Operations......Page 41
1.5.4 Semiconductor and Solar Devices......Page 42
1.5.8 Electrochemical Processes......Page 43
1.7 CONSERVATION PRINCIPLE......Page 44
1.8 DIFFERENTIAL MODELS......Page 45
1.9.2 Sublimation of a Solid Sphere: Mass Transfer Coe......Page 46
1.10 MESOSCOPIC OR CROSS-SECTION AVERAGED MODELS......Page 47
1.10.1 Solid Dissolution from a Wall......Page 48
1.10.2 Tubular Flow Reactor......Page 49
1.11 COMPARTMENTAL MODELS......Page 50
REVIEW QUESTIONS......Page 51
PROBLEMS......Page 52
2.1.1 Steady State Diffusion across a Slab......Page 54
2.1.2 Steady State Diffusion with Reaction in a Slab......Page 56
2.1.3 Transient Diffusion in a Slab......Page 59
2.1.4 Diffusion with Convection......Page 60
2.2.1 Steady State Radial Di......Page 62
2.2.2 Steady State Mass Transfer with Reaction......Page 63
2.3.1 Steady State Diffusion across a Spherical Shell......Page 64
2.3.2 Diffusion and Reaction......Page 65
SUMMARY......Page 66
PROBLEMS......Page 67
3.1 MACROSCOPIC BALANCE......Page 73
3.1.1 In and Out Terms from Flow......Page 75
3.1.2 Wall or Interface Transfer Term......Page 77
3.1.4 Accumulation Term......Page 79
3.2.1 Differential Equations for the Reactor......Page 80
3.2.2 ODE45 with CHEBFUN......Page 84
3.3 REACTOR…SEPARATOR COMBINATION......Page 89
3.4 SUBLIMATION OF A SPHERICAL PARTICLE......Page 95
3.4.1 Correlation for Mass Transfer Coe......Page 98
3.5 DISSOLVED OXYGEN CONCENTRATION IN A STIRRED TANK......Page 100
3.6 CONTINUOUS STIRRED TANK REACTOR......Page 103
3.6.1 First-Order Reaction......Page 105
3.6.2 Second-Order Reaction......Page 106
3.7 TRACER EXPERIMENTS: TEST FOR BACKMIXED ASSUMPTION......Page 111
3.7.1 Interconnected Cells Model......Page 112
3.8 LIQUID…LIQUID EXTRACTION......Page 114
3.8.1 Mass Transfer Rate......Page 116
3.8.2 Backmixed…Backmixed Model......Page 117
3.8.3 Equilibrium Stage Model......Page 118
3.8.4 Stage Efficiency......Page 120
SUMMARY......Page 122
REVIEW QUESTIONS......Page 125
PROBLEMS......Page 126
4.1 SOLID DISSOLUTION FROM A WALL......Page 135
4.1.1 Model Details......Page 136
4.1.2 Mass Transfer Correlations in Pipe Flow......Page 137
4.2 TUBULAR FLOW REACTOR......Page 138
4.2.2 Dispersion Closure......Page 139
4.3.1 Single Stream......Page 140
4.3.2 Two Streams......Page 141
4.3.3 NTU and HTU Representation......Page 144
REVIEW QUESTIONS......Page 145
PROBLEMS......Page 146
5.1.1 Mole Basis......Page 149
5.2.1 Mass Fraction Averaged Velocity......Page 150
5.2.2 Mole Fraction Averaged Velocity......Page 151
5.3 PROPERTIES OF DIFFUSION FLUX......Page 153
5.4 PSEUDO-BINARY DIFFUSIVITY......Page 154
5.5.3 Overall Continuity: Mass Basis......Page 155
5.5.6 Common Simplifications......Page 156
5.6 COMMON BOUNDARY CONDITIONS......Page 157
5.7 MACROSCOPIC MODELS: SINGLE-PHASESYSTEMS......Page 158
5.8 MULTIPHASE SYSTEMS: LOCAL VOLUMEAVERAGING......Page 159
REVIEW QUESTIONS......Page 161
PROBLEMS......Page 162
6.1 STEADY STATE DIFFUSION: NO REACTION......Page 164
6.1.3 Determinancy Condition......Page 165
6.1.4 Low Flux Model: The Laplace Equation......Page 166
6.2.1 Conditions for the Validity of the Low Flux Model......Page 167
6.2.3 Drift Flux Correction Factor......Page 168
6.2.4 Mole Fraction Profiles in UMD......Page 169
6.3.1 Boundary Layer Concept for Fluid…Solid Mass Transfer......Page 170
6.3.2 Film Model Approximation......Page 171
6.3.3 Film Model: Determinancy Correction Factor......Page 172
6.4.1 Low Flux Model: First-Order Reaction......Page 173
6.4.3 High Flux Model: EÀwect of Product Counter-DiÀwusion......Page 175
6.5.1 Mass Transfer CoeÀwicients......Page 176
6.5.2 Overall Mass Transfer CoeÀwicient......Page 177
SUMMARY......Page 178
PROBLEMS......Page 179
7.1 DIFFUSION COEFFICIENTS IN GASES......Page 181
7.1.1 Model Based on Kinetic Theory......Page 182
7.1.2 Frictional Interpretation......Page 185
7.2 DIFFUSION COEFFICIENTS IN LIQUIDS......Page 187
7.2.1 Stokes-Einstein Model......Page 188
7.2.2 Wilke-Chang Equation......Page 189
7.3.2 Activity Coefficient Models......Page 190
7.4.1 Vacancy Diffusion......Page 191
7.5.1 Single-Pore Gas Diffusion: Effect of Pore Size......Page 192
7.5.2 Liquid-Filled Pores: Hindered Diffusion......Page 193
7.5.3 Porous Catalysts: Effective Diffusivity......Page 194
7.6 HETEROGENEOUS MEDIA......Page 195
7.8 OTHER COMPLEX EFFECTS......Page 196
SUMMARY......Page 197
PROBLEMS......Page 198
8.1 TRANSIENT DIFFUSION PROBLEMS IN 1-D......Page 201
8.2.1 Dimensionless Representation......Page 202
8.2.3 Evaluation of the Series Coe......Page 203
8.2.4 Illustrative Results......Page 204
8.3 SOLUTIONS FOR SLAB: ROBIN CONDITION......Page 205
8.4.2 Sphere......Page 207
8.4.3 One-Term Approximation......Page 208
8.5.2 Transient Di......Page 209
8.6 2-D PROBLEMS: PRODUCT SOLUTION METHOD......Page 210
8.7.1 Constant Surface Concentration......Page 211
8.7.3 Pulse Response......Page 213
8.9 TRANSIENT DIFFUSION WITH VARIABLEDIFFUSIVITY......Page 214
8.10 EIGENVALUE COMPUTATIONS WITH CHEBFUN......Page 215
8.11 COMPUTATIONS WITH PDEPE SOLVER......Page 216
8.11.1 Sample Code for 1-D Transient Di......Page 217
SUMMARY......Page 218
PROBLEMS......Page 219
9.1 DEFINITIONS FOR EXTERNAL AND INTERNALFLOWS......Page 221
9.2 RELATION TO DIFFERENTIAL MODEL......Page 222
9.3.1 Other Derived Dimensionless Groups......Page 223
9.5.2 Turbulent Flow......Page 224
9.6.2 Gas to Liquid......Page 225
9.8 MASS TRANSFER FROM A GAS BUBBLE......Page 226
9.8.1 Bubble Swarms and Bubble Columns......Page 227
9.9 MASS TRANSFER IN MECHANICALLY AGITATEDTANKS......Page 228
9.10.2 Gas Side Coe......Page 229
REVIEW QUESTIONS......Page 230
PROBLEMS......Page 231
10.1 MASS TRANSFER IN LAMINAR FLOW IN A PIPE......Page 233
10.1.1 Dimensionless Form......Page 234
10.1.2 Constant Wall Concentration: The Dirichlet Problem......Page 235
10.1.3 Concentration, Wall Mass Flux, and Sherwood Number......Page 236
10.2.1 Solution Using CHEBFUN......Page 237
10.3 ENTRY REGION ANALYSIS......Page 238
10.4 CHANNEL FLOWS WITH MASS TRANSFER......Page 239
10.5 MASS TRANSFER IN FILM FLOW......Page 240
10.5.1 Solid Dissolution at a Wall in Film Flow......Page 241
10.5.2 Gas Absorption from Interface in Film Flow......Page 242
SUMMARY......Page 243
PROBLEMS......Page 244
11.1 FLAT PLATE WITH LOW FLUX MASS TRANSFER......Page 246
11.1.2 Velocity Equations......Page 247
11.1.4 Exact or Blasius Analysis......Page 248
11.2.1 Integral Momentum Balance......Page 251
11.2.3 Solution for No Reaction Case......Page 252
11.2.4 Solution for Homogeneous Reaction......Page 253
11.3.2 Integral Balance Method......Page 254
11.3.3 Blasius Approach......Page 255
11.4.1 Pressure Variation Term......Page 256
11.4.2 Integral Balance Method for Inclined and Curved Surfaces......Page 257
11.4.4 Wedge Flow: Falkner-Skan Equation......Page 258
11.5.1 Rigid Bubbles......Page 259
SUMMARY......Page 260
REVIEW QUESTIONS......Page 261
PROBLEMS......Page 262
12.1.1 Transition Criteria......Page 263
12.2 PROPERTIES OF TIME AVERAGING......Page 264
12.3.1 Turbulent Mass Flux......Page 265
12.4.1 Turbulent Schmidt Number......Page 266
12.5 VELOCITY AND TURBULENT DIFFUSIVITY PROFILES......Page 267
12.5.2 Eddy Diffusivity Profiles......Page 268
12.6.1 Simplified Analysis: Constant Wall Flux......Page 269
12.6.3 Analogy with Momentum Transfer......Page 271
12.6.4 Stanton Number for Pipe Flows......Page 272
12.7 VAN DRIEST MODEL FOR LARGE SC......Page 273
12.8.1 Damping of Turbulence......Page 274
SUMMARY......Page 275
PROBLEMS......Page 276
13.2.1 Step Input......Page 279
13.2.3 Age Distribution Functions......Page 280
13.2.4 Tracer Response for Tanks in Series Model......Page 281
13.3 MOMENT ANALYSIS OF TRACER DATA......Page 282
13.3.1 Moments from Laplace Transform of Response......Page 283
13.4 TANKS IN SERIES MODELS: REACTOR PERFORMANCE......Page 284
13.5.1 Second-Order Reaction......Page 285
13.6 VARIANCE-BASED MODELS FOR PARTIAL MICROMIXING......Page 286
13.7.1 Matrix Representation......Page 287
13.8.2 Level I or Equilibrium Model......Page 289
13.9.1 Backmixed…Backmixed Model......Page 290
13.9.3 Mixing Cell Model......Page 291
13.10.1 Equilibrium Model......Page 292
SUMMARY......Page 293
PROBLEMS......Page 294
14.1 PLUG FLOW IDEALIZATION......Page 296
14.2 DISPERSION MODEL......Page 297
14.2.2 Solution for a First-Order Reaction......Page 298
14.2.5 Criteria for Negligible Dispersion......Page 299
14.3.2 Moments of the Response Curve......Page 300
14.4 TAYLOR MODEL FOR DISPERSION IN LAMINARFLOW......Page 301
14.5 SEGREGATED FLOW MODEL......Page 303
14.6 DISPERSION COEFFICIENT VALUES FOR SOME COMMON CASES......Page 304
14.7.1 Plug-Backmixed Model......Page 305
14.7.2 Non-Idealities in Two-Phase Flow......Page 306
14.8 TRACER RESPONSE IN TWO-PHASE SYSTEMS......Page 308
14.8.1 Single Flowing Phase......Page 309
SUMMARY......Page 310
REVIEW QUESTIONS......Page 311
PROBLEMS......Page 312
15.1.1 Binary Revisited......Page 315
15.2 COMPUTATIONS FOR A REACTING SYSTEM......Page 316
15.3 HETEROGENEOUS REACTIONS......Page 318
15.4.1 Evaporation of a Liquid in a Ternary Mixture......Page 319
15.4.2 Evaporation of a Binary Liquid Mixture......Page 321
15.4.3 Equimolar Counter-Di......Page 322
15.5.1 D Matrix Relation to Binary Pair Diffusivity......Page 323
PROBLEMS......Page 325
16.1.1 Mobility and Di......Page 327
16.2 CHARGE NEUTRALITY......Page 328
16.3.1 Laplace Equation for the Potential......Page 329
16.4 ELECTROLYTE TRANSPORT ACROSS UNCHARGED MEMBRANE......Page 330
16.5.1 Interfacial Jump: Donnan Equation......Page 331
16.5.2 Transport Rate......Page 332
16.6 TRANSFER RATE IN DIFFUSION FILM NEAR ANELECTRODE......Page 333
SUMMARY......Page 334
PROBLEMS......Page 335
17.1.1 Dimensionless Model Equations......Page 338
17.2.1 Small B: Pure Convection Model......Page 340
17.3 MESOSCOPIC DISPERSION MODEL......Page 341
17.4.2 Non-Newtonian Fluids......Page 342
17.4.5 Axial Dispersion Model for the Turbulent Case......Page 343
PROBLEMS......Page 344
18.1 CATALYST PROPERTIES AND APPLICATIONS......Page 346
18.2 DIFFUSION-REACTION MODEL......Page 347
18.2.1 First-Order Reaction......Page 348
18.2.2 Zero-Order Reaction......Page 352
18.2.3 nth-Order Reaction......Page 354
18.3 MULTIPLE SPECIES......Page 355
18.4.1 Application Examples......Page 356
18.5.1 Equations for Heat and Mass Transport......Page 357
18.5.3 Dimensionless Boundary Conditions......Page 358
18.6.1 Basis of the Method......Page 359
18.6.2 Two-Point Collocation......Page 360
18.7.2 Zero-Order Reaction......Page 361
18.8 LINKING WITH REACTOR MODELS......Page 362
18.8.2 Second-Order Reaction......Page 363
SUMMARY......Page 364
PROBLEMS......Page 365
19.1.1 No Solid Product......Page 370
19.1.2 Solid Product: Ash Layer Effects......Page 373
19.2.1 Kinetic Model......Page 375
19.2.3 First-Order Reaction in B......Page 376
19.2.4 Zero-Order Reaction......Page 378
19.3.1 Effect of Structural Changes......Page 379
19.4.1 Classical Models......Page 381
SUMMARY......Page 382
PROBLEMS......Page 384
20.1 FIRST-ORDER REACTION OF DISSOLVED GAS......Page 387
20.1.2 Dimensionless Version......Page 388
20.1.4 Enhancement Factor......Page 389
20.2.1 Bulk Concentration......Page 390
20.2.2 Absorption Rate Calculation for Ha < 0.2......Page 391
20.3.1 Dimensionless Representation......Page 392
20.3.2 Invariance Property of the System......Page 393
20.3.4 Analysis for Instantaneous Asymptote......Page 394
20.3.5 Second-Order Case: An Approximate Solution......Page 395
20.3.6 Instantaneous Case: Effect of Gas Film Resistnace......Page 396
20.4.1 Model Equations......Page 397
20.4.3 CHEBFUN Solution......Page 398
20.5.1 Semibatch Reactor......Page 399
20.5.2 Packed Column Absorber......Page 400
20.6.1 Particle Size Effect......Page 401
20.6.2 Instantaneous Reaction Case......Page 402
SUMMARY......Page 403
REVIEW QUESTIONS......Page 404
PROBLEMS......Page 405
21.1.1 First-Order or Pseudo-First-Order Reaction......Page 407
21.1.2 Laplace Transform Method......Page 408
21.1.4 Relation between Film Theory and Penetration Theory......Page 409
21.2.2 Illustrative Results......Page 410
21.3 INSTANTANEOUS REACTION CASE......Page 411
21.4.1 Laminar Jet Apparatus......Page 412
21.4.3 Wetted Sphere......Page 413
SUMMARY......Page 414
PROBLEMS......Page 415
22.1.2 Dimessionless Representaion......Page 419
22.1.4 Instantaneous Reaction Asymptote......Page 420
22.1.5 Pseudo-First-Order Reaction Asymptote......Page 421
22.2.1 Model for Counter-Transport......Page 422
22.3 EQUILIBRIUM MODEL: A COMPUTATIONALSCHEME......Page 423
22.4.1 Emulsion Liquid Membranes (ELM)......Page 424
SUMMARY......Page 425
PROBLEMS......Page 426
23.1.2 Transport Steps for Oxygen Uptake......Page 429
23.2 TRANSPORT IN TISSUES: KROGH MODEL......Page 431
23.2.1 Oxygen Variation in the Capillary......Page 432
23.3.2 Physiologically Based Compartments......Page 433
23.4.1 Model Formulation......Page 434
SUMMARY......Page 435
PROBLEMS......Page 436
24.1.1 Anodic and Cathodic Reactions......Page 439
24.1.3 Classification of Electrode Reactions......Page 440
24.2 THERMODYNAMIC CONSIDERATIONS: NERNSTEQUATION......Page 441
24.2.1 Equilibrium Cell Potential......Page 443
24.3.1 Butler-Volmer Equation......Page 444
24.4.1 Concentration Overpotential......Page 446
24.5 VOLTAGE BALANCE......Page 447
24.6.2 Voltage Balance......Page 448
24.7 HYDROGEN FUEL CELL......Page 449
24.8.1 Charging......Page 450
SUMMARY......Page 451
PROBLEMS......Page 452
25.1 WET AND DRY BULB TEMPERATURE......Page 455
25.1.1 The Lewis Relation......Page 456
25.2.2 General Design Considerations......Page 457
25.3.2 Enthalpy Balance Equations......Page 458
25.3.3 Merkel Equation......Page 459
25.4 CROSS-FLOW COOLING TOWERS......Page 461
25.5.1 Types of Dryers......Page 462
25.6 CONSTANT RATE PERIOD......Page 463
25.7 FALLING RATE PERIOD......Page 464
25.7.2 Diffusion Type of Models......Page 465
SUMMARY......Page 467
PROBLEMS......Page 468
26.1 CONDENSATION OF PURE VAPOR......Page 470
26.1.1 Laminar Regime: Nusselt Model......Page 471
26.2.2 Heat Transfer Rate and Ackermann Correction Factor......Page 472
26.2.3 Interface Temperature Calculations......Page 473
26.3 FOG FORMATION......Page 474
26.4 CONDENSATION OF BINARY GAS MIXTURE......Page 475
26.4.1 Condensation Rates: Unmixed Model......Page 476
26.5.1 Liquid and Vapor Phase Balances......Page 477
SUMMARY......Page 479
PROBLEMS......Page 480
27.1 GAS SEPARATION MEMBRANES......Page 482
27.1.2 Transport Rate: Permeability......Page 483
27.1.4 Selectivity......Page 484
27.2 GAS TRANSLATION MODEL......Page 485
27.3.1 Flux Relations......Page 486
27.3.3 Backmixed-Backmixed Model......Page 487
27.3.4 Countercurrent Flow......Page 488
27.3.5 Cross-Flow Pattern......Page 489
27.4 REACTOR COUPLED WITH A MEMBRANE SEPARATOR......Page 490
REVIEW QUESTIONS......Page 491
PROBLEMS......Page 492
28.1 CLASSIFICATION BASED ON PORE SIZE......Page 493
28.2.1 Osmotic Pressure......Page 494
28.2.2 Reverse Osmosis......Page 495
28.2.3 Concentration Polarization Effects......Page 496
28.3 FORWARD OSMOSIS......Page 497
28.4.1 Illustrative Applications......Page 498
28.4.3 Local Permeate Composition......Page 499
REVIEW QUESTIONS......Page 500
PROBLEMS......Page 501
29.1 APPLICATIONS AND ADSORBENT PROPERTIES......Page 503
29.2.2 Competitive Adsorption Isotherm......Page 504
29.3.2 Particle-Level Model......Page 505
29.3.3 Linear Driving Force Model......Page 506
29.3.5 Simulation Using the Collocation Method......Page 507
29.4 FIXED BED ADSORPTION......Page 508
29.4.2 Axial Dispersion E......Page 509
29.4.4 Klinkenberg Equation......Page 510
29.5 CHROMATOGRAPHY......Page 511
REVIEW QUESTIONS......Page 512
PROBLEMS......Page 513
30.1 TECHNOLOGICAL ASPECTS......Page 514
30.1.2 Membranes......Page 515
30.1.4 Electrodialysis with Bipolar Membranes......Page 516
30.2.1 Current and Voltage......Page 517
30.3 PRINCIPLE OF ELECTROPHORESIS......Page 518
30.4.1 Philpot Design......Page 519
30.4.2 Hannig Design......Page 520
SUMMARY......Page 521
PROBLEMS......Page 522
References......Page 524