Batch Distillation: Simulation, Optimal Design, and Control

391 Pages·2011·3.543 MB·English

by  Urmila Diwekar

K12825 Cover 12/5/11 10:14 AM Page 1
C M Y CM MY CY CMY K
Materials Science
S e c o n d E d i t i o n S e c o n d E d i t i o n
Diwekar
BATCH DISTILLATION BATCH
B
Simulation, Optimal Design, and Control
A DISTILLATION
T
Urmila Diwekar
C
Simulation, Optimal Design,
Most available books in chemical engineering mainly pertain to
continuous processes, with batch distillation relegated to a small H
and Control
section. Filling this void in the chemical engineering literature,
Batch Distillation: Simulation, Optimal Design, and Control,
D
Second Edition helps readers gain a solid, hands-on background in
batch processing. The second edition of this bestseller explores numerous
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new developments in batch distillation that have emerged since the
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publication of the first edition.
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NEW TO THE SECOND EDITION
• Special sections on complex column configurations and azeotropic, I
extractive, and reactive distillation L
• A chapter on various kinds of uncertainties in batch distillation
L
• A chapter covering software packages for batch distillation
simulation, design, optimization, and control A
• Separate chapters on complex columns and complex systems T
• Up-to-date references and coverage of recent research articles
I
O
This edition continues to explain how to effectively design, synthesize,
and make operations decisions related to batch processes. Through
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careful treatments of uncertainty analysis, optimization, and optimal
control methods, the author gives readers the necessary tools for
making the best decisions in practice.
K12825
Second
Edition
Urmila Diwekar
6000 Broken Sound Parkway, NW
Suite 300, Boca Raton, FL 33487
711 Third Avenue
an informa business New York, NY 10017
2 Park Square, Milton Park
Abingdon, Oxon OX14 4RN, UK
S e c o n d E d i t i o n
BATCH
DISTILLATION
Simulation, Optimal Design,
and Control
Urmila Diwekar
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
K12825_FM.indd 1 11/22/11 12:37:40 PM
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does
not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MAT-
LAB® software or related products does not constitute endorsement or sponsorship by The MathWorks
of a particular pedagogical approach or particular use of the MATLAB® software.
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Taylor & Francis Group
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Version Date: 20111109
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To my parents, who taught me how to face challenges.
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Contents
List of Figures ix
List of Tables xv
Preface to Second Edition xix
Preface to First Edition xvii
Notations xxiii
1 Introduction 1
1.1 Simple Distillation . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Why Batch Distillation? . . . . . . . . . . . . . . . . . . . . 7
2 Basic Modes of Operation 15
2.1 Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Constant Reflux . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Variable Reflux . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Optimal Reflux . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Column Dynamics 35
3.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Error and Stability . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Numerical Integration Techniques . . . . . . . . . . . . . . . 44
3.3.1 One-Step Methods . . . . . . . . . . . . . . . . . . . . 45
3.3.2 Multistep Methods . . . . . . . . . . . . . . . . . . . . 46
3.3.3 Stiff Equations and Implicit Methods. . . . . . . . . . 48
3.4 Solution of Column Dynamics . . . . . . . . . . . . . . . . . 51
3.4.1 Batch Distillation Startup . . . . . . . . . . . . . . . . 56
3.4.2 Low-Holdup Semirigorous Model . . . . . . . . . . . . 58
4 Simplified Models 67
4.1 Need for Simplification . . . . . . . . . . . . . . . . . . . . . 67
4.2 Shortcut Method . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3 Modified Shortcut Method . . . . . . . . . . . . . . . . . . . 83
4.4 Collocation-Based Model . . . . . . . . . . . . . . . . . . . . 90
4.5 Hierarchy of Models and BATCH-DIST . . . . . . . . . . . . 102
v
vi
5 Optimization 107
5.1 Objective Functions . . . . . . . . . . . . . . . . . . . . . . . 108
5.2 Degrees of Freedom Analysis . . . . . . . . . . . . . . . . . . 111
5.3 Feasibility Considerations . . . . . . . . . . . . . . . . . . . . 113
5.4 Problem Solution . . . . . . . . . . . . . . . . . . . . . . . . 118
6 Complex Columns 127
6.1 Inverted Column . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.1.1 Shortcut Method . . . . . . . . . . . . . . . . . . . . . 131
6.1.2 Rigorous Model . . . . . . . . . . . . . . . . . . . . . . 135
6.1.3 Semirigorous Model . . . . . . . . . . . . . . . . . . . 139
6.2 Middle Vessel Column . . . . . . . . . . . . . . . . . . . . . . 139
6.2.1 Shortcut Method . . . . . . . . . . . . . . . . . . . . . 144
6.2.2 Rigorous Model . . . . . . . . . . . . . . . . . . . . . . 148
6.2.3 Semirigorous Model . . . . . . . . . . . . . . . . . . . 154
6.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7 Complex Systems 163
7.1 Azeotropic Systems . . . . . . . . . . . . . . . . . . . . . . . 163
7.1.1 Qualitative Analysis of Azeotropic Systems . . . . . . 165
7.1.2 Extending the Shortcut Method to Azeotropic Systems 173
7.1.3 Separation Synthesis . . . . . . . . . . . . . . . . . . . 178
7.2 Extractive Distillation . . . . . . . . . . . . . . . . . . . . . . 189
7.2.1 Entrainer Selection Rules for Homogeneous Batch
Distillation . . . . . . . . . . . . . . . . . . . . . . . . 189
7.2.2 Entrainer Selection Rules for Heterogeneous Batch
Distillation . . . . . . . . . . . . . . . . . . . . . . . . 195
7.2.3 Feasibility of Extractive Batch Distillation . . . . . . . 209
7.3 Reactive Distillation . . . . . . . . . . . . . . . . . . . . . . . 212
7.3.1 Simplified Model . . . . . . . . . . . . . . . . . . . . . 212
7.3.1.1 Reaction in Liquid Phase . . . . . . . . . . . 214
7.3.1.2 Reaction in Vapor Phase . . . . . . . . . . . 224
7.3.2 Rigorous Model . . . . . . . . . . . . . . . . . . . . . . 229
7.3.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . 233
8 Batch Distillation Control 257
8.1 Optimal Control in Batch Distillation . . . . . . . . . . . . . 257
8.2 Closed-Loop Control . . . . . . . . . . . . . . . . . . . . . . . 286
9 Consideration Of Uncertainty 293
9.1 Static Uncertainties and Stochastic Modeling . . . . . . . . . 294
9.1.1 Uncertainty Quantification . . . . . . . . . . . . . . . 295
9.1.2 Sampling Techniques . . . . . . . . . . . . . . . . . . . 296
9.1.3 Output Analysis . . . . . . . . . . . . . . . . . . . . . 297
9.2 Optimization under Uncertainty . . . . . . . . . . . . . . . . 299
9.2.1 Here and Now Problems . . . . . . . . . . . . . . . . . 300
vii
9.2.2 Wait and See . . . . . . . . . . . . . . . . . . . . . . . 304
9.3 Uncertainty in Batch Distillation . . . . . . . . . . . . . . . . 304
9.3.1 Dynamic Uncertainties . . . . . . . . . . . . . . . . . . 306
9.3.1.1 Stochastic Processes . . . . . . . . . . . . . . 308
9.3.2 Relative Volatility: An Ito Process . . . . . . . . . . . 312
9.4 Optimal Control under Uncertainty . . . . . . . . . . . . . . 315
9.4.1 Stochastic Optimal Control . . . . . . . . . . . . . . . 315
9.4.2 Problems in Batch Distillation . . . . . . . . . . . . . 320
9.4.3 The Worst-Case Robust Optimization Formulation . . 327
10 Batch Distillation Software Programs 335
10.1 CHEMCAD Batch Distillation . . . . . . . . . . . . . . . . . 335
10.2 ASPEN TECH: BATCHSEP . . . . . . . . . . . . . . . . . . 341
10.3 BPRC: MultiBatchDS . . . . . . . . . . . . . . . . . . . . . . 341
10.4 Comparison of Software Packages . . . . . . . . . . . . . . . 346
Index 361
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List of Figures
1.1 Schematic of a Simple Distillation Operation . . . . . . . . . 2
1.2 Equilibrium Curve for the CS and CCl Mixture at 1 Atmo-
2 4
sphere Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Equilibrium Stage Processes . . . . . . . . . . . . . . . . . . . 5
1.4 The Continuous Distillation Column . . . . . . . . . . . . . . 6
1.5 The Batch Distillation Column . . . . . . . . . . . . . . . . . 7
1.6 Sequence of Continuous Columns for Separation of Benzene–
Toluene–Xylene System . . . . . . . . . . . . . . . . . . . . . 8
1.7 A Multifraction Batch Distillation Column for Separation of
Benzene–Toluene–Xylene System . . . . . . . . . . . . . . . . 9
1.8 Examples of Ways to Configure the Column . . . . . . . . . 12
2.1 Schematic of a Batch Distillation Column . . . . . . . . . . . 16
2.2 McCabe–Thiele Method for Plate-to-Plate Calculations . . . 18
2.3 McCabe–Thiele Method for the Constant Reflux Mode . . . . 20
2.4 Graphical Integration for Example 2.1 . . . . . . . . . . . . . 22
2.5 McCabe–Thiele Method for the Variable Reflux Mode . . . . 24
2.6 GraphicalIntegrationforCalculationofBatchTimeforExam-
ple 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.7 GraphicalIntegrationforCalculationofReboilerHeatDutyfor
Example 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.8 McCabe–Thiele Procedure for the Third Mode of Operation . 27
2.9 Graphical Integration for the Rayleigh Equation for the Third
Mode of Operation . . . . . . . . . . . . . . . . . . . . . . . . 28
2.10 Graphical Integration for Calculation of Batch Time for the
Third Mode of Operation . . . . . . . . . . . . . . . . . . . . 29
2.11 The Pole Height Concept . . . . . . . . . . . . . . . . . . . . 32
3.1 Schematic of a Batch Distillation Column . . . . . . . . . . . 37
3.2 Transient Composition Profiles for Example 3.1a . . . . . . . 53
3.3 Transient Composition Profiles for Example 3.1b . . . . . . . 54
3.4 Transient Composition Profiles for Example 3.1c . . . . . . . 55
3.5 TransientCompositionProfilesforExample3.2UsingDifferent
Startup Models . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.6 Transient Composition Profiles for Example 3.3 . . . . . . . . 59
ix