Modeling, Analysis and Optimization of Process and Energy Systems

485 Pages·2011·51.709 MB·English

by  F. Carl Knopf

Modeling, Analysis and
Optimization of Process
and Energy Systems

Modeling, Analysis and
Optimization of Process
and Energy Systems
F. Carl Knopf
Louisiana State University
Baton Rouge, LA
A JOHN WILEY & SONS, INC., PUBLICATION
Copyright © 2012 by John Wiley & Sons, Inc. All rights reserved.
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Library of Congress Cataloging-in-Publication Data:
Knopf, F. Carl, 1952-
Modeling, analysis and optimization of process and energy systems / F. Carl Knopf.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-470-62421-0 (hardback)
1. Factories–Energy conservation. 2. Manufacturing industries–Energy conservation. 3. Industrial efficiency–Simulation
methods. 4. Manufacturing processes–Evaluation. 5. Electric power-plants–Efficiency. I. Title.
TJ163.5.F3K66 2012
658.2'6–dc23
2011015221
Printed in the United States of America.
10 9 8 7 6 5 4 3 2 1
I dedicate this book to my wife Donna and our daughter Megan.

Contents
Preface    xiii References    39
Conversion Factors    xvii Problems    39
List of Symbols    xix
3. Computer-Aided Solutions of Process
Material Balances: The Sequential
Modular Solution Approach 42
1. Introduction to Energy Usage, Cost,
and Efficiency 1 3.1  Elementary Material Balance  
Modules    42
1.1  Energy Utilization in the United States    1 3.1.1  Mixer    43
1.2  The Cost of Energy    1 3.1.2  Separator    43
1.3  Energy Efficiency    4 3.1.3  Splitter    44
1.4  The Cost of Self-Generated versus Purchased  3.1.4  Reactors    45
Electricity    10 3.2  Sequential Modular Approach: Material 
1.5  The Cost of Fuel and Fuel Heating  Balances with Recycle    46
Value    11 3.3  Understanding Tear Stream Iteration  
1.6  Text Organization    12 Methods    49
1.7  Getting Started    15 3.3.1  Single-Variable Successive  
Substitution Method    49
1.8  Closing Comments    16
3.3.2  Multidimensional Successive  
References    16
Substitution Method    50
Problems    17
3.3.3  Single-Variable Wegstein  
Method    52
3.3.4  Multidimensional Wegstein 
2. Engineering Economics with VBA Procedures 19
Method    53
3.4  Material Balance Problems with  
2.1  Introduction to Engineering Economics    19 Alternative Specifications    58
2.2  The Time Value of Money: Present Value 
3.5  Single-Variable Optimization  
(PV) and Future Value (FV)    19 Problems    61
2.3  Annuities    22 3.5.1  Forming the Objective Function  
2.4  Comparing Process Alternatives    29 for Single-Variable Constrained  
2.4.1  Present Value    31 Material Balance Problems    61
2.4.2  Rate of Return (ROR)    31 3.5.2  Bounding Step or Bounding Phase: 
2.4.3  Equivalent Annual Cost/Annual Capital  Swann’s Equation    61
Recovery Factor (CRF)    32 3.5.3  Interval Refinement Phase: Interval 
2.5  Plant Design Economics    33 Halving    65
2.6  Formulating Economics-Based Energy  3.6  Material Balance Problems with Local 
Optimization Problems    34 Nonlinear Specifications    66
2.7  Economic Analysis with Uncertainty: Monte  3.7  Closing Comments    68
Carlo Simulation    36 References    69
2.8  Closing Comments    38 Problems    70
vii
viii Contents
4. Computer-Aided Solutions of Process 6. Introduction to Data Reconciliation and Gross
Material Balances: The Simultaneous Error Detection 132
Solution Approach 76
6.1  Standard Deviation and Probability Density 
4.1  Solution of Linear Equation Sets: The  Functions    133
Simultaneous Approach    76 6.2  Data Reconciliation: Excel Solver    136
4.1.1  The Gauss–Jordan Matrix Elimination  6.2.1  Single-Unit Material Balance:  
Method    76 Excel Solver    136
4.1.2  Gauss–Jordan Coding Strategy for Linear  6.2.2  Multiple-Unit Material Balance: Excel 
Equation Sets    78 Solver    138
4.1.3  Linear Material Balance Problems:  6.3  Data Reconciliation: Redundancy and Variable 
Natural Specifications    78 Types    138
4.1.4  Linear Material Balance Problems:  6.4  Data Reconciliation: Linear and Nonlinear 
Alternative Specifications    82
Material and Energy Balances    143
4.2  Solution of Nonlinear Equation Sets: The 
6.5  Data Reconciliation: Lagrange 
Newton–Raphson Method    82
Multipliers    149
4.2.1  Equation Linearization via Taylor’s Series 
6.5.1  Data Reconciliation: Lagrange  
Expansion    82
Multiplier Compact Matrix 
4.2.2  Nonlinear Equation Set Solution  
Notation    152
via the Newton–Raphson  
6.6  Gross Error Detection and 
Method    83
Identification    154
4.2.3  Newton–Raphson Coding Strategy for 
6.6.1  Gross Error Detection: The Global Test 
Nonlinear Equation Sets    86
(GT) Method    154
4.2.4  Nonlinear Material Balance  
6.6.2  Gross Error (Suspect Measurement) 
Problems: The Simultaneous 
Identification: The Measurement Test 
Approach    90
(MT) Method: Linear Constraints    155
References    92
6.6.3  Gross Error (Suspect Measurement) 
Problems    93
Identification: The Measurement Test 
Method: Nonlinear Constraints    156
6.7  Closing Remarks    158
References    158
5. Process Energy Balances 98 Problems    158
5.1  Introduction    98 7. Gas Turbine Cogeneration System
5.2  Separator: Equilibrium Flash    101 Performance, Design, and Off-Design
5.2.1  Equilibrium Flash with Recycle:  Calculations: Ideal Gas Fluid Properties 164
Sequential Modular Approach    103
5.3  Equilibrium Flash with Recycle: Simultaneous 
7.1  Equilibrium State of a Simple Compressible 
Approach    109
Fluid: Development of the T ds 
5.4  Adiabatic Plug Flow Reactor (PFR) Material 
Equations    165
and Energy Balances Including Rate 
7.1.1  Application of the T ds Equations to an 
Expressions: Euler’s First-Order  Ideal Gas    166
Method    112 7.1.2  Application of the T ds Equations 
5.4.1  Reactor Types    112 to an Ideal Gas: Isentropic 
5.5  Styrene Process: Material and Energy  Process    166
Balances with Reaction Rate    117 7.2  General Energy Balance Equation for an  
5.6  Euler’s Method versus Fourth-Order Runge– Open System    167
Kutta Method for Numerical  7.3  Cogeneration Turbine System  
Integration    121 Performance Calculations: Ideal Gas  
5.6.1  The Euler Method: First-Order  Working Fluid    167
ODEs    121 7.3.1  Compressor Performance 
5.6.2  RK4 Method: First-Order   Calculations    167
ODEs    122 7.3.2  Turbine Performance 
5.7  Closing Comments    124 Calculations    168
References    125 7.4  Air Basic Gas Turbine Performance 
Problems    125 Calculations    169