Principles and Modern Applications of Mass Transfer Operations

• New edition has a stronger emphasis on membrane separations, chromatography and other adsorptive processes, ion exchange
• Discusses many developing topics in more depth in mass transfer operations, especially in the biological engineering area
• Covers in more detail phase equilibrium since distillation calculations are completely dependent on this principle
• Integrates computational software and problems using Mathcad
• Features 25-30 problems per chapter

Preface to the Third Edition xvii

Preface to the Second Edition xix

Preface to the First Edition xxi

Nomenclature xxiii

1. Fundamentals of Mass Transfer 1

1.1 Introduction 1

1.2 Molecular Mass Transfer 3

1.2.1 Concentrations 4

1.2.2 Velocities and Fluxes 10

1.2.3 The Maxwell–Stefan Relations 13

1.2.4 Fick’s First Law for Binary Mixtures 16

1.3 The Diffusion Coefficient 17

1.3.1 Diffusion Coefficients for Binary Ideal Gas Systems 18

1.3.2 Diffusion Coefficients for Dilute Liquids 24

1.3.3 Diffusion Coefficients for Concentrated Liquids 30

1.3.4 Effective Diffusivities in Multicomponent Mixtures 31

1.4 Steady-State Molecular Diffusion in Fluids 37

1.4.1 Molar Flux and the Equation of Continuity 37

1.4.2 Steady-State Molecular Diffusion in Gases 38

1.4.3 Steady-State Molecular Diffusion in Liquids 53

1.5 Steady-State Diffusion in Solids 56

1.5.1 Steady-State Binary Molecular Diffusion in Porous Solids 57

1.5.2 Knudsen Diffusion in Porous Solids 59

1.5.3 Hydrodynamic Flow of Gases in Porous Solids 62

1.5.4 “Dusty Gas” Model for Multicomponent Diffusion 64

1.6 Diffusion with Homogeneous Chemical Reaction 65

1.7 Analogies Among Molecular Transfer Phenomena 71

Problems 73

References 89

2. Convective Mass Transfer 91

2.1 Introduction 91

2.2 Mass-Transfer Coefficients 92

2.2.1 Diffusion of A Through Stagnant B (N_B = 0, Ψ_A = 1) 93

2.2.2 Equimolar Counterdiffusion (N_B = –N_A , Ψ_A = undefined) 95

2.3 Dimensional Analysis 97

2.3.1 The Buckingham Method 97

2.4 Flow Past Flat Plate in Laminar Flow; Boundary Layer Theory 103

2.5 Mass- and Heat-Transfer Analogies 110

2.6 Convective Mass-Transfer Correlations 119

2.6.1 Mass-Transfer Coefficients for Flat Plates 120

2.6.2 Mass-Transfer Coefficients for a Single Sphere 121

2.6.3 Mass-Transfer Coefficients for Single Cylinders 126

2.6.4 Turbulent Flow in Circular Pipes 127

2.6.5 Mass Transfer in Packed and Fluidized Beds 133

2.6.6 Mass Transfer in Hollow-Fiber Membrane Modules 136

2.7 Estimation of Multicomponent Mass-Transfer Coefficients 140

Problems 142

References 156

3. Interphase Mass Transfer 158

3.1 Introduction 158

3.2 Equilibrium 158

3.3 Diffusion Between Phases 163

3.3.1 Two-Resistance Theory 164

3.3.2 Overall Mass-Transfer Coefficients 166

3.3.3 Local Mass-Transfer Coefficients–General Case 171

3.4 Material Balances 179

3.4.1 Countercurrent Flow 179

3.4.2 Cocurrent Flow 194

3.4.3 Batch Processes 197

3.5 Equilibrium-Stage Operations 198

Problems 206

References 220

4. Equipment for Gas–Liquid Mass-Transfer Operations 221

4.1 Introduction 221

4.2 Gas–Liquid Operations: Liquid Dispersed 221

4.2.1 Types of Packing 222

4.2.2 Liquid Distribution 225

4.2.3 Liquid Holdup 227

4.2.4 Pressure Drop 234

4.2.5 Mass-Transfer Coefficients 237

4.3 Gas–Liquid Operations: Gas Dispersed 242

4.3.1 Sparged Vessels (Bubble Columns) 242

4.3.2 Tray Towers 248

4.3.3 Tray Diameter 252

4.3.4 Tray Gas-Pressure Drop 255

4.3.5 Weeping and Entrainment 257

4.3.6 Tray Efficiency 259

Problems 266

References 279

5. Absorption and Stripping 281

5.1 Introduction 281

5.2 Countercurrent Multistage Equipment 282

5.2.1 Graphical Determination of the Number of Ideal Trays 282

5.2.2 Tray Efficiencies and Real Trays by Graphical Methods 283

5.2.3 Dilute Mixtures 284

5.3 Countercurrent Continuous-Contact Equipment 290

5.3.1 Dilute Solutions; Henry’s Law 296

5.4 Thermal Effects During Absorption and Stripping 299

5.4.1 Adiabatic Operation of a Tray Absorber 299

5.4.2 Adiabatic Operation of a Packed-Bed Absorber 302

Problems 306

References 318

6. Distillation 319

6.1 Introduction 319

6.2 Single-Stage Operation–Flash Vaporization 320

6.3 Differential Distillation 325

6.4 Continuous Rectification–Binary Systems 328

6.5 Mccabe–Thiele Method for Trayed Towers 328

6.5.1 Rectifying Section 330

6.5.2 Stripping Section 331

6.5.3 Feed Stage 333

6.5.4 Number of Equilibrium Stages and Feed-Stage Location 335

6.5.5 Limiting Conditions 336

6.5.6 Optimum Reflux Ratio 339

6.5.7 Large Number of Stages 345

6.5.8 Use of Open Steam 349

6.5.9 Tray Efficiencies 350

6.6 Binary Distillation in Packed Towers 358

6.7 Multicomponent Distillation 363

6.8 Fenske-Underwood-Gilliland Method 366

6.8.1 Total Reflux: Fenske Equation 366

6.8.2 Minimum Reflux: Underwood Equations 370

6.8.3 Gilliland Correlation for Number of Stages at Finite Reflux 377

6.9 Rigorous Calculation Procedures for Multicomponent Distillation 379

6.9.1 Equilibrium Stage Model 379

6.9.2 Nonequilibrium, Rate-Based Model 381

6.10 Batch Distillation 383

6.10.1 Binary Batch Distillation with Constant Reflux 383

6.10.2 Batch Distillation with Constant Distillate Composition 387

6.10.3 Multicomponent Batch Distillation 390

Problems 391

References 404

7. Liquid–Liquid Extraction 406

7.1 Introduction 406

7.2 Liquid Equilibria 407

7.3 Stagewise Liquid–Liquid Extraction 413

7.3.1 Single-Stage Extraction 413

7.3.2 Multistage Crosscurrent Extraction 417

7.3.3 Countercurrent Extraction Cascades 418

7.3.4 Insoluble Liquids 425

7.3.5 Continuous Countercurrent Extraction with Reflux 427

7.4 Equipment for Liquid–Liquid Extraction 435

7.4.1 Mixer-Settler Cascades 435

7.4.2 Multicompartment Columns 445

Problems 448

References 456

8. Humidification Operations 457

8.1 Introduction 457

8.2 Equilibrium Considerations 458

8.2.1 Saturated Gas–Vapor Mixtures 459

8.2.2 Unsaturated Gas–Vapor Mixtures 461

8.2.3 Adiabatic-Saturation Curves 462

8.2.4 Wet-Bulb Temperature 464

8.3 Adiabatic Gas–Liquid Contact Operations 468

8.3.1 Fundamental Relationships 468

8.3.2 Water Cooling with Air 471

8.3.3 Dehumidification of Air–Water Vapor 479

Problems 479

References 484

9. Membranes and Other Solid Sorption Agents 485

9.1 Introduction 485

9.2 Mass Transfer in Membranes 486

9.2.1 Solution-Diffusion for Liquid Mixtures 488

9.2.2 Solution-Diffusion for Gas Mixtures 489

9.2.3 Module Flow Patterns 492

9.3 Equilibrium Considerations in Porous Sorbents 498

9.3.1 Adsorption and Chromatography Equilibria 498

9.3.2 Ion-Exchange Equilibria 503

9.4 Mass Transfer in Fixed Beds of Porous Sorbents 507

9.4.1 Basic Equations for Adsorption 509

9.4.2 Linear Isotherm 510

9.4.3 Langmuir Isotherm 511

9.4.4 Length of Unused Bed 514

9.4.5 Mass-Transfer Rates in Ion Exchangers 517

9.4.6 Mass-Transfer Rates in Chromatographic Separations 518

9.5 Applications of Membrane–Separation Processes 520

9.5.1 Dialysis 522

9.5.2 Reverse Osmosis 524

9.5.3 Gas Permeation 528

9.5.4 Ultrafiltration and Microfiltration 528

9.6 Applications of Sorption–Separation Processes 532

Problems 537

References 544

Appendix A Binary Diffusion Coefficients 545

Appendix B Lennard–Jones Constants 548

Appendix C Maxwell–Stefan Equations 550

Appendix D Packed-Column Design Program 552

Appendix E Sieve-Tray Design Program 558

Appendix F-1 McCabe–Thiele: Liquid Feed 564

Appendix F-2 McCabe–Thiele: Vapor Feed 568

Appendix G-1 Single-Stage Extraction 572

Appendix G-2 Multistage Crosscurrent Extraction 574

Appendix H Constants and Unit Conversions 578

Index 581

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