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