Chapter 1 Separation Processes 1
1.1 Industrial Chemical Processes 1
1.2 Mechanism of Separation 5
1.3 Separation by Phase Addition or Creation 7
1.4 Separation by Barrier 14
1.5 Separation by Solid Agent 16
1.6 Separation by External Field or Gradient 18
1.7 Component Recoveries and Product Purities 19
1.8 Separation Power 22
1.9 Selection of Feasible Separation Processes 23
Summary 27
References 28
Exercises 28
Chapter 2 Thermodynamics of Separation Operations 31
2.1 Energy, Entropy, and Availability Balances 31
2.2 Phase Equilibria 36
Fugacities and Activity Coefficients 37
K-Values 38
2.3 Ideal Gas, Ideal Liquid Solution Model 42
2.4 Graphical Correlations of Thermodynamic Properties 47
2.5 Nonideal Thermodynamic Property Models 51
P-v-T Equation-of-State Models 54
Derived Thermodynamic Properties from P-v-T Models 58
2.6 Activity Coefficient Models for the Liquid Phase 63
Activity Coefficients from Gibbs Free Energy 63
Regular Solution Model 64
Chao-Seader Correlation 66
Nonideal Liquid Solutions 68
van Laar Equation 72
Margules Equations 72
Local Composition Concept and Wilson Equation 74
NRTL Equation 78
UNIQUAC Equation 79
UNIFAC Equation 80
Liquid-Liquid Equilibria 82
Summary 83
References 83
Exercises 84
Chapter 3 Mass Transfer and Diffusion 90
3.1 Steady-State Ordinary Molecular Diffusion 91
Fick s Law of Diffusion 92
Velocities in Mass Transfer 92
Equimolar Counterdiffusion 93
Unimolecular Diffusion 95
3.2 Diffusion Coefficients 99
Diffusivity in Gas Mixtures 99
Diffusivity in Liquid Mixtures 101
Diffusivity in Solids 109
Steady State 117
3.3 One-Dimensional Steady-State and Unsteady-State Molecular Diffusion 117
Unsteady State 118
3.4 Molecular Diffusion in Laminar Flow 126
Falling Liquid Film 127
Boundary-Layer Flow on a Flat Plate 133
Fully Developed Flow in a Straight, Circular Tube 136
3.5 Mass Transfer in Turbulent Flow 140
Reynolds Analogy 141
Chilton-Colburn Analogy 142
Prandtl Analogy 143
3.6 Models for Mass Transfer at a Fluid-Fluid Interface 144
Film Theory 145
Penetration Theory 146
Surface Renewal Theory 147
Film-Penetration Theory 149
3.7 Two-Film Theory and Overall Mass Transfer Coefficients 150
Gas-Liquid Case 150
Liquid-Liquid Case 153
Case of Large Driving Forces for Mass Transfer 154
Summary 157
References 158
Exercises 159
Chapter 4 Single Equilibrium Stages and Flash Calculations 163
4.1 The Gibbs Phase Rule and Degrees of Freedom 163
Degrees-of-Freedom Analysis 164
4.2 Binary Vapor-Liquid Systems 166
4.3 Azeotropic Systems 173
4.4 Multicomponent Flash, Bubble-Point, and Dew-Point Calculations 176
Isothermal Flash 178
Bubble and Dew Points 181
Adiabatic Flash 184
4.5 Ternary Liquid-Liquid Systems 186
4.6 Multicomponent Liquid-Liquid Systems 195
4.7 Solid-Liquid Systems 198
Leaching 198
Crystallization 201
Liquid Adsorption 204
4.8 Gas-Liquid Systems 207
Sublimation and Desublimation 211
4.9 Gas-Solid Systems 211
Gas Adsorption 212
4.10 Multiphase Systems 213
Approximate Method for a Vapor-Liquid-Solid System 214
Approximate Method for a Vapor-Liquid-Liquid System 215
Rigorous Method for a Vapor-Liquid-Liquid System 218
Summary 220
References 221
Exercises 222
5.1 Cascade Configurations 232
Chapter 5 Cascades 232
5.2 Solid-Liquid Cascades 234
5.3 Single-Section Liquid-Liquid Extraction Cascades 237
Cocurrent Cascade 238
Crosscurrent Cascade 239
Countercurrent Cascade 239
5.4 Multicomponent Vapor-Liquid Cascades 241
Single-Section Cascades by Group Methods 242
Two-Section Cascades 246
5.5 Degrees of Freedom and Specifications for Countercurrent Cascades 253
Stream Variables 254
Adiabatic or Nonadiabatic Equilibrium Stage 254
Single-Section Countercurrent Cascade 255
Two-Section Countercurrent Cascades 257
Summary 263
References 264
Exercises 264
Chapter 6 Absorption and Stripping of Dilute Mixtures 270
6.1 Equipment 273
6.2 General Design Considerations 281
6.3 Graphical Equilibrium-Stage Method for Trayed Towers 282
Minimum Absorbent Flow Rate 284
Number of Equilibrium Stages 285
6.4 Algebraic Method for Determining the Number of Equilibrium Stages 289
6.5 Stage Efficiency 292
Performance Data 293
Empirical Correlations 294
Semitheoretical Models 299
Scale-up from Laboratory Data 303
6.6 Tray Capacity, Pressure Drop, and Mass Transfer 305
Tray Diameter 306
Tray Vapor Pressure Drop 310
Mass Transfer Coefficients and Transfer Units 312
Weeping, Entrainment, and Downcomer Backup 315
6.7 Rate-Based Method for Packed Columns 317
6.8 Packed Column Efficiency, Capacity, and Pressure Drop 325
Liquid Holdup 325
Capacity and Pressure Drop 330
Mass Transfer Efficiency 335
6.9 Concentrated Solutions in Packed Columns 342
Summary 346
References 347
Exercises 348
Chapter 7 Distillation of Binary Mixtures 355
7.1 Equipment and Design Considerations 358
7.2 McCabe-Thiele Graphical Equilibrium-Stage Method for Trayed Towers 359
Rectifying Section 362
Stripping Section 365
Feed-Stage Considerations 366
Limiting Conditions 369
Determination of Number of Equilibrium Stages and Feed-Stage Location 369
Column Operating Pressure and Condenser Type 374
Subcooled Reflux 376
Reboiler Type 380
Condenser and Reboiler Duties 381
Feed Preheat 382
Optimal Reflux Ratio 382
Large Number of Stages 384
Use of Murphree Efficiency 386
Multiple Feeds, Side Streams, and Open Steam 387
Performance Data 391
7.3 Estimation of Stage Efficiency 391
Empirical Correlations 392
Semitheoretical Models 395
Scale-up from Laboratory Data 396
7.4 Capacity of Trayed Towers and Reflux Drums 397
Reflux Drums 397
7.5 Rate-Based Method for Packed Columns 398
HETP Method 399
HTU Method 400
7.6 Ponchon-Savarit Graphical Equilibrium-Stage Method for Trayed Towers 404
Summary 406
References 407
Exercises 408
Chapter 8 Liquid-Liquid Extraction with Ternary Systems 419
8.1 Equipment 423
Mixer-Settlers 424
Spray Columns 426
Packed Columns 426
Plate Columns 426
Columns with Mechanically Assisted Agitation 427
8.2 General Design Considerations 432
8.3 Hunter and Nash Graphical Equilibrium-Stage Method 438
Number of Equilibrium Stages 440
Minimum and Maximum Solvent-to-Feed Flow-Rate Ratios 444
Use of Right-Triangle Diagrams 448
Use of an Auxiliary Distribution Curve 451
Extract and Raffinate Reflux 453
8.4 Maloney and Schubert Graphical Equilibrium-Stage Method 459
Mixer-Settler Units 465
8.5 Theory and Scale-up of Extractor Performance 465
Multicompartment Columns 475
Axial Dispersion 480
Summary 484
References 485
Exercises 486
Chapter 9 Approximate Methods for Multicomponent, Multistage Separations 492
9.1 Fenske-Underwood-Gilliland Method 492
Selection of Two Key Components 493
Column Operating Pressure 495
Fenske Equation for Minimum Equilibrium Stages 497
Distribution of Nonkey Components at Total Reflux 500
Underwood Equations for Minimum Reflux 501
Gilliland Correlation for Actual Reflux Ratio and Theoretical Stages 508
Feed-Stage Location 511
Distribution of Nonkey Components at Actual Reflux 512
9.2 Kremser Group Method 514
Strippers 514
Liquid-Liquid Extraction 518
References 521
Summary 521
Exercises 522
Chapter 10 Equilibrium-Based Methods for Multicomponent Absorption, Stripping, Distillation, and Extraction 526
10.1 Theoretical Model for an Equilibrium Stage 526
10.2 General Strategy of Mathematical Solution 530
10.3 Equation-Tearing Procedures 531
Tridiagonal Matrix Algorithm 531
Bubble-Point Method for Distillation 534
Sum-Rates Method for Absorption and Stripping 544
Isothermal Sum-Rates Method for Liquid-Liquid Extraction 551
10.4 Simultaneous Correction Procedures 555
10.5 Inside-Out Method 569
MESH Equations 571
Rigorous and Complex Thermodynamic Property Models 571
Approximate Thermodynamic Property Models 572
Inside-Out Algorithm 573
Summary 577
References 578
Exercises 579
Chapter 11 Enhanced Distillation and Supercritical Extraction 586
11.1 Use of Triangular Graphs 587
Residue-Curve Maps 591
Distillation-Curve Maps 599
Product-Composition Regions at Total Reflux 602
11.2 Extractive Distillation 604
11.3 Salt Distillation 611
11.4 Pressure-Swing Distillation 612
11.5 Homogeneous Azeotropic Distillation 616
11.6 Heterogeneous Azeotropic Distillation 621
Multiplicity 627
11.7 Reactive Distillation 631
11.8 Supercritical-Fluid Extraction 641
Summary 650
References 651
Exercises 653
Chapter 12 Rate-Based Models for Distillation 655
12.1 Rate-Based Model 658
12.2 Thermodynamic Properties and Transport-Rate Expressions 662
12.3 Methods for Estimating Transport Coefficients and Interracial Area 667
ChemSep Program 668
12.5 Method of Calculation 668
12.4 Vapor and Liquid Flow Patterns 668
RATEFRAC Program 674
Summary 677
References 677
Exercises 677
Chapter 13 Batch Distillation 681
13.1 Differential Distillation 681
13.2 Binary Batch Rectification with Constant Reflux and Variable Distillate Composition 685
13.3 Binary Batch Rectification with Constant Distillate Composition and Variable Reflux 688
13.4 Batch Stripping and Complex Batch Distillation 689
13.5 Effect of Liquid Holdup 691
13.6 Shortcut Method for Multicomponent Batch Rectification with Constant Reflux 691
13.7 Stage-by-Stage Methods for Multicomponent Batch Rectification 695
Rigorous Model 695
Rigorous Integration Method 698
Rapid Solution Method 705
Summary 708
References 708
Exercises 709
Chapter 14 Membrane Separations 713
14.1 Membrane Materials 718
14.2 Membrane Modules 722
14.3 Transport in Membranes 725
Porous Membranes 725
Bulk Flow 726
Liquid Diffusion 728
Gas Diffusion 729
Nonporous Membranes 731
Solution-Diffusion for Liquid Mixtures 731
Solution-Diffusion for Gas Mixtures 733
Module Flow Patterns 738
Cascades 741
Concentration Polarization 745
14.4 Dialysis and Electrodialysis 747
Electrodialysis 750
14.5 Reverse Osmosis 755
14.6 Gas Permeation 761
14.7 Pervaporation 765
Summary 771
Exercises 773
References 773
Chapter 15 Adsorption, Ion Exchange, and Chromatography 778
15.1 Sorbents 781
Adsorbents 782
Ion Exchangers 789
Sorbents for Chromatography 792
15.2 Equilibrium Considerations 794
Pure Gas Adsorption 794
Liquid Adsorption 802
Ion Exchange Equilibria 806
Equilibria in Chromatography 810
15.3 Kinetic and Transport Considerations 811
External Transport 812
Internal Transport 816
Mass Transfer in Ion Exchange and Chromatography 818
15.4 Sorption Systems 820
Adsorption 820
Ion Exchange 824
Chromatography 825
Slurry Adsorption (Contact Filtration) 827
Fixed-Bed Adsorption (Percolation) 831
Thermal-Swing Adsorption 843
Pressure-Swing Adsorption 848
Continuous Countercurrent Adsorption Systems 856
Ion-Exchange Cycle 861
Chromatographic Separations 863
Summary 870
References 872
Exercises 873
Index 881