Principles and Applications of Mass Transfer The Design of Separation Processes for Chemical and Biochemical Engineering

Core textbook teaching mass transfer fundamentals and applications for the design of separation processes in chemical, biochemical, and environmental engineering

Principles and Applications of Mass Transfer teaches the subject of mass transfer fundamentals and their applications to the design of separation processes with enough depth of coverage to guarantee that students using the book will, at the end of the course, be able to specify preliminary designs of the most common separation process equipment.

Reflecting the growth of biochemical applications in the field of chemical engineering, the fourth edition expands biochemical coverage, including transient diffusion, environmental applications, electrophoresis, and bioseparations. Also new to the fourth edition is the integration of Python programs, which complement the Mathcad programs of the previous edition.

On the accompanying instructor’s website, the online appendices contain a downloadable library of Python and Mathcad programs for the example problems in each chapter. A complete solution manual for all end-of-chapter problems, both in Mathcad and Python, is also provided.

Some of the topics covered in Principles and Applications of Mass Transfer include:

• Molecular mass transfer, covering concentrations, velocities and fluxes, the Maxwell-Stefan relations, and Fick’s first law for binary mixtures
• The diffusion coefficient, covering diffusion coefficients for binary ideal gas systems, dilute liquids, and concentrated liquids
• Convective mass transfer, covering mass-transfer coefficients, dimensional analysis, boundary layer theory, and mass- and heat-transfer analogies
• Interphase mass transfer, covering diffusion between phases, material balances, and equilibrium-stage operations
• Gas dispersed gas-liquid operations, covering sparged vessels, tray towers, diameter, and gas-pressure drop, and weeping and entrainment

Principles and Applications of Mass Transfer is an essential textbook for undergraduate chemical, biochemical, mechanical, and environmental engineering students taking a core course on Separation Processes or Mass Transfer Operations, along with mechanical engineers and mechanical engineering students starting to get involved in combined heat- and mass-transfer applications.

Jaime Benítez attended the School of Engineering of the University of Puerto Rico where he received a BS in Chemical Engineering in 1970 and a MS in Nuclear Engineering in 1972. He earned his PhD in Chemical and Environmental Engineering at Rensselaer Polytechnic Institute in 1976. That year, he joined the faculty of the Chemical Engineering Department of the University of Puerto Rico where he taught continuously until 2014. He is now an adjunct lecturer at the University of Florida at Gainesville.

Preface to the Fourth Edition xvii

Preface to the Third Edition xix

Preface to the Second Edition xxi

Preface to the First Edition xxiii

Nomenclature xxv

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 12

1.2.4 Fick’s First Law for Binary Mixtures 15

1.3 The Diffusion Coefficient 16

1.3.1 Diffusion Coefficients for Binary Ideal Gas Systems 17

1.3.2 Diffusion Coefficients for Dilute Liquids 22

1.3.3 Diffusion Coefficients for Concentrated Liquids 26

1.3.4 Effective Diffusivities in Multi component Mixtures 28

1.4 Steady-state Molecular Diffusion in Fluids 34

1.4.1 Molar Flux and the Equation of Continuity 34

1.4.2 Steady-State Molecular Diffusion in Gases 35

1.4.3 Steady-State Molecular Diffusion in Liquids 47

1.5 Steady-state Diffusion in Solids 50

1.5.1Steady-State Binary Molecular Diffusion in Porous Solids 51

1.5.2 Knudsen Diffusion in Porous Solids 52

1.5.3 Hydrodynamic Flow of Gases in Porous Solids 55

1.5.4“DustyGas”Model for Multi component Diffusion 57

1.6 Transient Molecular Diffusion in Solids 58

1.7 Diffusion with Homogeneous Chemical Reaction 62

1.8 Analogies Among Molecular Transfer Phenomena 66

Problems 68

References 83

Appendix 1.1 84

Appendix 1.2 85

Appendix 1.3 86

Appendix 1.4 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 (NB=0,ΨA=1) 92

2.2.2 Equimolar Counter diffusion (NB=–NA,ΨA=undefined) 95

2.3 Dimensional Analysis 96

2.3.1 The Buckingham Method 97

2.4 Flow Past Flat Plate in Laminar Flow; Boundary Layer Theory 101

2.5 Mass- and Heat-transfer Analogies 108

2.6 Convective Mass-transfer Correlations 116

2.6.1 Mass-Transfer Coefficients for Flat Plates 116

2.6.2 Mass-Transfer Coefficients for a Single Sphere 118

2.6.3 Mass-Transfer Coefficients for Single Cylinders 122

2.6.4 Turbulent Flow in Circular Pipes 122

2.6.5 Mass Transfer in Packed and Fluidized Beds 128

2.6.6 Mass Transfer in Hollow-Fiber Membrane Modules130

2.7Multi component Mass-transfer Coefficients 133

Problems 135

References 149

Appendix 2.1 152

Appendix 2.2 153

3. Interphase Mass Transfer 155

3.1Introduction 155

3.2 Equilibrium Considerations in Chemical and Biochemical Systems 155

3.2.1 Chemical Phase Equilibria 156

3.2.2 Biochemical Equilibrium Concepts (Seaderetal.,2011) 160

3.3 Diffusion Between Phases 166

3.3.1 Two-Resistance Theory 166

3.3.2 Overall Mass-Transfer Coefficients 168

3.3.3 Local Mass-Transfer Coefficients: General Case 172

3.4 Material Balances 180

3.4.1 Counter current Flow 180

3.4.2 Co current Flow 194

3.4.3 Batch Processes 195

3.5 Equilibrium-stage Operations 196

Problems 204

References 216

Appendix 3.1 217

Appendix 3.2 218

Appendix 3.3 219

Appendix 3.4 220

Appendix 3.5 221

4. Equipment for Gas–liquid Mass-transfer Operations 225

4.1 Introduction 225

4.2 Gas–liquid Operations :Liquid Dispersed 225

4.2.1 Types of Packing 226

4.2.2 Liquid Distribution 229

4.2.3 Liquid Holdup 230

4.2.4 Pressure Drop 237

4.2.5 Mass-Transfer Coefficients 239

4.3 Gas–liquid Operations : Gas Dispersed 243

4.3.1 Sparged Vessels (Bubble Columns) 244

4.3.2 Tray Towers 249

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 258

Problems 264

References 274

5. Absorption and Stripping 277

5.1 Introduction 277

5.2 Counter current Multi stage Equipment 278

5.2.1 Graphical Determination of the Number of IdealTrays 278

5.2.2 Tray Efficiencies and Real Traysby Graphical Methods 279

5.2.3 Dilute Mixtures279

5.3 Counter current Continuous-contact Equipment285

5.3.1 Dilute Solutions; Henry’s Law290

5.4 Thermal Effects During Absorption and Stripping 292

5.4.1 Adiabatic Operation of a Packed-Bed Absorber 296

Problems 300

References 311

Appendix 5.1 312

6. Distillation 315

6.1Introduction 315

6.2 Single-stage Operation—flash Vaporization 316

6.3 DifferentialDistillation320

6.4ContinuousRectification—binarySystems322

6.5 Mc CABE–Thiele method for trayed towers324

6.5.1 Rectifying Section 325

6.5.2 Stripping Section 326

6.5.3 Feed Stage 328

6.5.4 Number of Equilibrium Stages and Feed-Stage Location 330

6.5.5 Limiting Conditions 332

6.5.6 Optimum Reflux Ratio 333

6.5.7 Large Number of Stages 339

6.5.8 Use of Open Steam 342

6.5.9 Tray Efficiencies 343

6.6 Binary Distillation in Packed Towers350

6.7 Multi component Distillation 354

6.8 Fenske–underwood–Gillil and Method 357

6.8.1 Total Reflux : Fenske Equation 357

6.8.2 Minimum Reflux : Underwood Equations 361

6.8.3 Gillil and Correlation for Number of Stages at Finite Reflux 366

6.9 Rigorous Calculation Procedures for Multi component Distillation 368

6.9.1 Equilibrium Stage Model368

6.9.2 Non equilibrium, Rate-Based Model 370

6.10 Batch Distillation 371

6.10.1 Binary Batch Distillation with Constant Reflux 372

6.10.2 Batch Distillation with Constant Distillate Composition 375

6.10.3 Multicomponent Batch Distillation 377

Problems 378

References 389

Appendix 6.1 390

Appendix 6.2 391

Appendix 6.3 392

7. Liquid–liquid Extraction 393

7.1 Introduction 393

7.2 Liquid Equilibria 394

7.3 Stage wise Liquid–liquid Extraction 399

7.3.1 Single-Stage Extraction 400

7.3.2 Multistage Crosscurrent Extraction 403

7.3.3 Counter current Extraction Cascades4 04

7.3.4 Insoluble Liquids 409

7.3.5 Continuous Countercurrent Extraction with Reflux 412

7.4 Equipment for Liquid–liquid Extraction 419

7.4.1Mixer-Settler Cascades 419

7.4.2 Multi compartment Columns 428

7. Liquid–liquid Extraction of Bio products 430

Problems 437

References 446

8. Humidification Operations447

8.1 Introduction 447

8.2 Equilibrium Considerations 448

8.2.1 Saturated Gas–Vapor Mixtures 448

8.2.2 Unsaturated Gas–Vapor Mixtures 451

8.2.3 Adiabatic-Saturation Curves 452

8.2.4 Wet-Bulb Temperature 454

8.3 Adiabatic Gas–liquid Contact Operations 457

8.3.1 Fundamental Relationships 458

8.3.2 Water Cooling with Air 460

8.3.3 Dehumidification of Air–Water Vapor 466

Problems 468

References 472

Appendix 8.1 473

Appendix 8.2 474

9. Membranes and other Solid: Sorption  Agents 477

9.1 Introduction 477

9.2 Mass Transfer in Membranes 478

9.2.1 Solution-Diffusion for Liquid Mixtures479

9.2.2 Solution-Diffusionfor Gas Mixtures 481

9.2.3 Module Flow Patterns 484

9.3 Equilibrium Considerations in Porous Sorbents 489

9.3.1 Adsorption and Chromatography Equilibria 489

9.3.2 Ion-Exchange Equilibria 494

9.4 Mass Transfer in Fixed Beds of Porous Sorbents 497

9.4.1 Basic Equations for Adsorption 499

9.4.2 Linear Isotherm 500

9.4.3 Langmuir Isotherm 501

9.4.4 Length of Unused Bed 505

9.4.5 Mass-Transfer Rates in Ion Exchangers506

9.4.6 Mass-Transfer Rates in Chromatographic Separations507

9.4.7 Electrophoresis 510

9.5 Applications of Membrane-separation Processes512

9.5.1 Dialysis 513

9.5.2 Reverse Osmosis 515

9.5.3 Gas Permeation 518

9.5.4 Ultrafiltration and Microfiltration 518

9.5.5 Bio separations 522

9.6 Applications of Sorption-separation Processes524

Problems 529

References 535

Appendix9.1 536

Appendix 9.2 538

Appendix 9.3 540

Appendix 9.4 542

Appendix 9.5 544

Appendix 9.6 546

Appendix 9.7  548

Appendix A Binary Diffusion Coefficients  551

Appendix B Lennard-Jones Constants 555

Appendix C-1 Maxwell-Stefan Equations (Mathcad) 557

Appendix C-2 Maxwell-Stefan Equations (Python) 559

Appendix D-1 Packed-Column Design (Mathcad) 563

Appendix D-2 Packed-Column Design (Python) 569

Appendix E-1 Sieve-Tray Design (Mathcad) 573

Appendix E-2 Sieve-Tray Design (Python) 579

Appendix F-1 McCabe-Thiele Method : Saturated Liquid Feed(Mathcad) 583

Appendix F-2 McCabe-Thiele Method : SaturatedLiquid Feed(Python) 587

Appendix G-1 Single-Stage Extraction (Mathcad) 591

Appendix G-2 Single-Stage Extraction (Python) 593

Appendix G-3 Multi stage Crosscurrent Extraction (Mathcad) 595

Appendix G-4 Multi stage Crosscurrent Extraction (Python) 598

Appendix H Constants and Unit Conversions 601

Index 603

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