MULTISTAGESEPARATIONPROCESSES

Fourth Edition

FOUAD M. KHOURY

@CRC PressTaylor &. Francis CroupBoca Raton London New York

CRC Press is an imprint of the

Taylor & Francis Croup, an informa business

Contents

Preface xvii

Author xx i

Chapter 1 Thermodynamics and Phase Equilibria 1

1.1 Thermodynamic Fundamentals 1

1.1.1 Laws of Thermodynamics 2

1.1.1.1 Carnot Engine 2

1.1.1.2 Entropy 4

1.1.2 Thermodynamic Functions 5

1.1.3 Conditions for Equilibrium 7

1.2 PVT Behavior of Flu ids 9

1.2.1 Ideal Gas 10

1.2.2 Real Fluids 11

1.2.2.1 Qualitative PVT Behavior of Pure

Substances 11

1.2.3 Principle of Corresponding States 12

1.2.4 Equations of State 14

1.2.4.1 van der Waals Equation 14

1.2.4.2 Virial Equation 14

1.2.4.3 Redlich-Kwong Equation 15

1.2.4.4 Soave Equation 16

1.2.4.5 Peng-Robinson Equation 18

1.2.4.6 Benedict-Webb-Rubin (BWR)

Equation 19

1.2.4.7 Lee-Kesler-Plocker Equation 19

1.3 Phase Equilibria 21

1.3.1 Fugacity 21

1.3.1.1 Pure Substances 23

1.3.1.2 Mixtures 24

1.3.1.3 Application to Equations of State 25

1.3.2 Phase Equilibrium in an Ideal System 29

1.3.2.1 Raoult'sLaw 30

1.3.2.2 Binary Ideal Solutions 30

1.3.2.3 Henry's Law 31

1.3.3 Phase Equilibrium in Non-Ideal Systems 32

1.3.3.1 Activity Coefficients 32

1.3.3.2 Thermodynamic Consistency of

VLE Data 35

1.3.3.3 Margules Equation 36

1.3.3.4 van Laar Equation 37

,\ Contents

1.3.3.5 Wilson Equation 38

1.3.3.6 Non-Random Two-Liquid (NRTL)

(Renon) Equation 39

1.3.3.7 Universal Quasi-Chemical

(UNIQUAC) Equation 39

1.3.4 Vapor-Liquid Equilibria: Applications 43

1.3.4.1 Azeotropes 48

1.3.5 Liquid-Liquid and Vapor-Liquid-Liquid Equilibria... 52

1.3.5.1 Binary Systems 52

1.3.5.2 Ternary Systems 53

1.4 Enthalpy 54

1.4.1 Enthalpy Balances Involving Phase Change 59

1.5 Characterizing Petroleum Fractions 60

1.5.1 True Boiling Point (TBP) 61

1.5.2 Generating Pseudocomponents 61

1.5.3 Laboratory Data 63

1.5.4 Pseudocomponent Properties 63

1.5.5 Blending Streams 64

Nomenclature 66

Subscripts 66

Superscripts 66

Problems 66

References 72

Chapter 2 The Equilibrium Stage 73

2.1 Phase Behavior 74

2.1.1 Degrees of Freedom 74

2.1.2 Phase Diagrams 75

2.1.2.1 The Phase Envelope 75

2.1.2.2 T-Z Diagram 77

2.1.2.3 Y-X Diagram 78

2.1.3 Distribution Coefficients 79

2.1.4 Flash Operations 80

2.1.4.1 Isothermal Flash 81

2.1.4.2 Adiabatic Flash 81

2.1.4.3 Bubble Point 81

2.1.4.4 Dew Point 82

2.1.4.5 General-Type Flash 82

2.2 Performance of the Equilibrium Stage 82

2.2.1 Single-Feed Systems 83

2.2.2 Single-Stage Absorption/Stripping 87

2.2.3 Close Boilers and Azeotropes 88

2.3 Solution Methods 91

2.3.1 Isothermal Flash Method 93

2.3.1.1 Basic Algorithm 93

Contents vii

2.3.1.2 Extension to General Flush Calculations 96

2.3.2 Phase Boundary Calculations 106

2.3.2.1 Bubble Point-Dew Point Calculations

for Composition-Independenl Values.... 107

2.3.2.2 Iterative Method for Composition-Dependent /f-Values 110

2.3.2.3 Simultaneous Method 110

2.3.2.4 Bubble Point Temperature 112

2.3.2.5 Dew Point Temperature 113

2.3.3 Liquid-Liquid and Vapor-Liquid-Liquid

Equilibria 114

2.3.3.1 Rigorous VLLE Model 117

2.3.3.2 K-Value Computations 117

2.3.3.3 Application to an Equilibrium Stage 119

2.3.3.4 Iterative Solution 121

2.3.3.5 VLLE in Hydrocarbon-Water Systems.... 122

Nomenclature 126

Subscripts : 127

Superscripts 127

Problems 127

References 136

Chapter 3 Fundamentals of Multistage Separation 137

3.1 Cascaded Stages 138

3.1.1 Graphical Representation 138

3.1.2 Equilibrium Relationships 139

3.1.3 Parameter Relationships 141

3.2 Distillation Basics 147

3.2.1 Temperature Effect on Separation 148

3.2.2 Mathematical Representation 148

3.2.3 Parameter Relationships 149

3.3 Absorption/Strippi ng Basics 154

3.3.1 Ternary Systems 154

3.3.2 Multistage Absorption 158

3.3.3 Operating Parameters and Mathematical

Formulation 159

Nomenclature 160

Subscripts 161

Superscripts 161

Problems 161

Chapter 4 Material Balances in Multi-Component Separation 165

4.1 Mathematical Model 165

4.2 Types of Column Specifications 166

4.2.1 Primary Variable Specifications 166

viji Contents

4.2.2 Derived Variable Specifications 170

4.2.3 General Specifications 173

Nomenclature 177

Subscripts 177

Superscripts 177

Problems 177

Chapter 5 Binary Distillation: Principles 181

5.1 Column Section 181

5.1.1 Development of the Model 182

5.1.1.1 Assumptions and Simplifications 184

5.1.2 Analytical Solution 186

5.1.3 Graphical Representation on the Y-X Diagram 186

5.1.3.1 Constructing Equilibrium Stages 188

5.2 Total Column 189

5.2.1 Mathematical Model 190

5.2.1.1 Rectifying Section Operating Line 191

5.2.1.2 Stripping Section Operating Line 191

5.2.1.3 Feed Stage 191

5.2.1.4 Analytical Solution 193

5.2.1.5 The Description Rule 194

5.2.2 Graphical Solution on the Y-X Diagram 195

5.2.2.1 Representing a Total Column 197

5.2.2.2 Separation and Reflux Ratio Specified 198

5.2.2.3 Distillate Composition, Reflux Ratio,

and Number of Stages Specified 199

5.2.2.4 Separation and Number of Stages

Specified 199

5.2.2.5 Reflux Ratio, Product Rates, and

Number of Stages Specified 199

5.2.2.6 Columns with Multiple Feeds, Side

Draws, and Side Heaters/Coolers 199

5.2.2.7 Columns with Stripping Vapor Feed 203

5.2.3 Tray Efficiency 203

5.3 Column Solution with Material and Enthalpy Balances 204

5.3.1 Single-Stage Mass and Energy Balances 205

5.3.2 Binary H-X Diagrams 206

5.3.3 Solving Distillation Columns on the

H-X Diagram 207

5.3.4 Other Column Features Represented on the

H-X Diagram 211

5.3.4.1 Condenser Types 211

5.3.4.2 Multiple Feeds, Side Draws 212

5.3.4.3 Side Coolers, Heaters 214

5.3.4.4 Tray Efficiency 214

Contents 'x

Nomenclature 215

Subscripts 216

Superscripts 216

References 216

Chapter 6 Binary Distillation: Applications 217

6.1 Parameters Affecting Column Performance 217

6.1.1 Effect of Reflux Ratio and Product Rates 218

6.1.1.1 Product Rates 220

6.1.2 Effect of Number of Stages and Feed Location 222

6.1.3 Number of Stages versus Reflux Ratio 224

6.2 Parameter Interactions in Fixed Configuration Columns 226

6.2.1 Column Operable Ranges 227

6.2.2 Feasible Ranges of Product Rates and Reflux

Ratios 228

6.2.3 Feasible Ranges of Distillate and Bottoms

Compositions 229

6.2.4 Feasible Ranges of Distillate Composition and

Reflux Ratio 230

6.2.5 Feasible Ranges of Distillate Composition and

Bottoms Rate 230

6.3 Design Strategies Guided by Graphical Representation 231

6.3.1 Analytical Method 241

Nomenclature 242

Subscripts 243

Problems 243

References 246

Chapter 7 Multi-Component Separation: Conventional Distillation 247

7.1 Characteristics of Multi-Component Separation 247

7.2 Factors Affecting Separation 248

7.3 Specifying Column Performance 251

7.3.1 Variation in Dependent Variables with Reflux

Ratio and Product Rate 252

7.3.2 Parameter Feasible Ranges 256

7.3.2.1 Product Temperature as the

Independent Variable 259

7.4 Number of Trays and Feed Location 262

7.4.1 Minimum Reflux and Minimum Trays 262

7.4.2 Feed Location 262

7.4.3 Effect of Feed Thermal Conditions 264

7.4.4 Rectifiers and Reboiled Strippers 264

Nomenclature 264

x Contents

Subscripts 265

Problems 265

Chapter 8 Absorption and Stripping 267

8.1 Thermal Effects 267

8.2 Liquid-to-Vapor Ratios 270

8.3 Number of Stages 273

8.4 Performance Specifications 274

8.5 Graphical Representation 277

8.6 Analytical Solution 281

Nomenclature 282

Subscripts 282

Problems 282

Chapter 9 Complex Distillation and Multiple Column Processes 285

9.1 Multiple Feeds 286

9.1.1 Columns with a Reboiler and No Condenser 286

9.1.2 Columns with a Condenser and No Reboiler 293

9.1.3 Columns with a Condenser and a Reboiler 297

9.2 Multiple Products 299

9.2.1 Column Sections 299

9.2.2 Degrees of Freedom 300

9.2.2.1 Modular Representation 300

9.2.2.2 General Column Performance

Considerations 301

9.2.3 Partial and Total Condensers 303

9.2.3.1 Performance of Multi-Product

Columns 304

9.3 Side Heaters/Coolers and Pumparounds 310

9.3.1 Applications 310

9.3.1.1 Temperature Levels 310

9.3.1.2 Heat of Absorption 311

9.3.1.3 Column Vapor and LiquidFlows 311

9.3.2 Pumparounds 313

9.4 Multiple Column Processes 315

Nomenclature 318

Subscripts 319

Problems 319

Reference 322

Chapter 10 Special Distillation Processes 323

10.1 Azeotropic and Extractive Distillation 323

Contents Xl

10.1.1 Separating Azeotropes with Pressure-Sensitive

Composition 325

10.1.1.1 Graphical Representation 328

10.1.2 Separating Heterogeneous Minimum-BoilingAzeotropes 330

10.1.2.1 Graphical Representation 331

10.1.3 Separation by Forming an Azeotrope with One

Component 333

10.1.4 Separation by Forming Two Binary Azeotropes 335

10.1.5 Separation by Forming a Ternary Azeotrope 338

10.1.6 Separation by Extractive Distillation 341

10.1.6.1 Graphical Representation 342

10.1.6.2 Sample Equilibrium Calculations 346

10.1.6.3 Determining the Number of Stages 347

10.1.6.4 Benzene Recovery Section 348

10.2 Three-Phase Distillation 348

10.3 Reactive Multistage Separation 350

10.3.1 Separation of Close Boilers 351

10.3.2 Esterification of Acetic Acid 351

10.3.3 Other Applications 351

Problems 352

References 354

Chapter 11 Liquid-Liquid Extraction and Supercritical Extraction 355

11.1 Extraction Fundamentals and Terminology 356

11.1.1 Simple Extractors 356

11.1.2 Multiple Feeds 358

11.1.3 Refluxed Extractors 359

11.2 Graphical Representation 360

11.2.1 Generating Equilibrium Diagrams 361

11.2.2 Single-Stage Calculations 361

11.2.3 Countercurrent Multistage Calculations 364

11.2.4 Multiple Feed and Refluxed Extractors 369

11.2.5 LLE Rectilinear Representation 371

11.2.5.1 Analytical Approach 371

11.3 Extraction Equipment 374

11.4 Supercritical Extraction 375

Nomenclature 377

Subscripts 377

Problems 377

Reference 380

Chapter 12 Shortcut Methods 381

12.1 Columns at Total Reflux 381

xjj Contents

12.1.1 Model Description 382

12.1.2 Mathematical Representation 383

12.1.3 Degrees of Freedom 387

12.1.4 Solution Methods 388

12.1.4.1 General Specifications 390

12.1.5 Multiple Products 392

12.2 Minimum Reflux Ratio 398

12.3 Column Design and Performance Analysis 400

12.4 Modular Shortcut Methods 403

12.4.1 Column Sections 404

12.4.2 Reduced Model 411

12.4.3 Complex Configurations 417

12.4.3.1 Reboiled Stripper 418

12.4.3.2 Distillation Column with a Partial

Condenser 420

12.4.3.3 Multi-Column System 421

12.4.4 Liquid-Liquid Extraction by the Shortcut

Column Section Method 422

Nomenclature 424

Subscripts 425

Superscript 425

Problems 425

References 434

Chapter 13 Rigorous Equilibrium Methods 435

13.1 Model Description 435

13.1.1 Model Equations 437

13.2 Steady-State Solution Methods 439

13.2.1 Method of Thiele and Geddes 440

13.2.2 Modified Thiele-Geddes Method 443

13.2.3 Method of Wang and Henke 448

13.2.4 Method of Tomich 448

13.2.5 Method of Naphtali and Sandholm 450

13.2.6 Method of Wang and Oleson 453

13.2.7 Two-Tier Methods 453

13.2.7.1 Inner Loop Property Models 456

13.2.7.2 Outer Loop Property Models 457

13.2.7.3 Two-Tier Algorithm 457

13.2.7.4 Tridiagonal Matrix Algorithm 459

13.2.8 Stage Efficiencies 464

13.3 Chemical Reactions in Multistage Separation 465

13.4 Three-Phase Distillation 467

13.4.1 Hydrocarbon-Water Systems 468

13.5 Liquid-Liquid Extraction 468

13.6 Convergence by Dynamic Iteration 469

Contents X,M

13.7 Column Dynamics 474

13.7.1 Dynamic Model Definition 475

13.7.2 Solving the Dynamic Model Equations 477

13.7.2.1 Euler's Method 478

13.7.2.2 Two-Point Implicit Method 479

13.7.2.3 Runge-Kutta Method 480

Nomenclature 484

Subscripts 485

Superscripts 485

Problems 485

References 486

Chapter 14 Tray Hydraulics, Rate-Based Analysis, Tray Efficiency 489

14.1 Tray Hydraulics 491

14.1.1 Types of Trays 492

14.1.1.1 Bubble Cap Trays 493

14.1.1.2 Sieve or Perforated Trays 493

14.1.1.3 Valve Trays 493

14.1.2 Factors Affecting Tray Performance 493

14.1.2.1 Foaming 493

14.1.2.2 Vapor Entrainment 494

14.1.2.3 Liquid Entrainment 494

14.1.2.4 Liquid Gradient 494

14.1.2.5 Weeping 494

14.1.2.6 Flooding 494

14.1.2.7 Pressure Drop 495

14.1.2.8 Operable Ranges 496

14.1.3 Steps in the Analysis of Tray Hydraulics 497

14.1.4 General Tray Hydraulics Correlations 498

14.1.4.1 Tray Diameter 498

14.1.4.2 Tray Pressure Drop 501

14.1.4.3 Downcomer Backup 503

14.1.4.4 Weeping 504

14.1.4.5 Liquid Holdup 504

14.2 Rate-Based Analysis 509

14.3 Tray Efficiency 514

14.3.1 Murphree Efficiency 514

14.3.2 Overall Column Tray Efficiency 517

14.3.2.1 Theoretical Model 517

14.3.2.2 Empirical Methods 518

Nomenclature 520

Subscripts 522

Superscripts 522

Problems 522

References 528

xiv Contents

Chapter 15 Packed Columns 529

15.1 Continuous Differential Mass Transfer 530

15.1.1 Nonparallel, Straight Operating Line, and

Equilibrium Curve 532

15.2 Rate of Mass Transfer 536

15.2.1 Mass Transfer Correlations 541

15.3 Mass Transfer in Packed Columns 541

15.3.1 General Rate-Based Model 546

15.4 Packed Column Design 548

15.4.1 Estimating the HETP 548

15.4.2 Packed Column Capacity 549

15.4.3 Packed Column Design Outline 550

15.4.3.1 Packed Columns versus

Trayed Columns 551

15.4.4 Packed Column Design by the Group Method 554

Nomenclature 556

Subscripts 557

Superscripts 557

Problems 557

References 559

Chapter 16 Control and Optimization of Separation Processes 561

16.1 Multiloop Controllers 562

16.1.1 Pairing the Manipulated and Controlled Variables.. 562

16.2 Dynamic Predictive Multivariable Control 569

16.2.1 Model-Based Control and Optimization 569

Nomenclature 570

Subscripts 570

Superscripts 570

Problems 570

References 571

Chapter 17 Batch Distillation 573

17.1 Principles of Batch Distillation 574

17.1.1 Effect of Holdup 575

17.1.2 Operating Strategies 575

17.1.2.1 Constant Reflux 575

17.1.2.2 Constant Distillate Composition 576

17.1.2.3 Cycling Operation 576

17.1.3 Conceptual Control and Degrees of Freedom 576

17.2 Solution Methods 577

17.2.1 Graphical and Shortcut Methods: Binary Systems ..577

17.2.1.1 Differential Distillation 581

Contents xv

17.2.2 Shortcut Methods: Multi-ComponentDistillation 586

17.2.3 Rigorous Methods 590

17.2.4 Optimization 594

Nomenclature 595

Subscripts 596

Superscripts 596

Problems 596

References 598

Chapter 18 Membrane Separation Operations 599

18.1 General Membrane Separation Process 599

18.1.1 Possible Consistent Sets of Units 602

18.2 Performance of Membrane Separators 606

18.2.1 Perfect Mixing Model 606

18.2.2 Cross-Flow Model 613

18.2.3 Countercurrent and Cocurrent Flow Models 617

18.3 Applications 618

18.3.1 Gas Permeation 619

18.3.2 Dialysis 619

18.3.3 Reverse Osmosis 622

Nomenclature 626

Subscripts 627

Problems 627

References 630

Chapter 19 Fluid-Solid Operations 631

19.1 Fluid-Solid Interaction Models 631

19.1.1 Adsorbents 631

19.1.2 Ion Exchangers 632

19.1.3 Chromatographic Processes 634

19.2 Phase Equilibrium 634

19.2.1 Isotherms 634

19.2.1.1 Gas Adsorption 635

19.2.2 Ion-Exchange Equilibrium 637

19.3 Applications 640

19.3.1 Single-Stage Batch Equilibrium 640

19.3.2 Nonequilibrium Processes 642

19.3.3 Fixed-Bed Adsorption Columns 642

References 644