OPTIMIZATION OF CHEMICAL PROCESSES McGraw-Hill Chemical Engineering Series EDITORIAL ADVISORY BOARD Eduardo D. Glandt, Professor of Chemical Engineering, University of Pennsylvania Michael T. Klein, Professor of Chemical Engineering, Rutgers University Thomas E Edgar, Professor of Chemical Engineering, University of Texas at Austin Bailey and Ollis: Biochemical Engineering Fundamentals Bennett and Myers: Momentum, Heat, and Mass Transfer Coughanowr: Process Systems Analysis and Control deNevers: Air Pollution Control Engineering deNevers: Fluid Mechanics for Chemical Engineers Douglas: Conceptual Design of Chemical Processes Edgar, Himmelblau, and Lasdon: Optimization of Chemical Processes Gates, Katzer, and Schuit: Chemistry of Catalytic Processes King: Separation Processes Luyben: Essentials of Process Control Luyben: Process Modeling, Simulation, and Control for Chemical Engineers Marlin: Process Control: Designing Processes and Control Systems for Dynamic Pe$ormance McCabe, Smith4nd Harriott: Unit Operations of Chemical Engineering Middleman and Hochberg: Process Engineering Analysis in Semiconductor Device .. Fabrication . 1 , Perry and Green: Perry's Chemical Engineers' Handbook Peters and Timmerhaus: Plant Design and ~conomicfso f chemical Engineers Reid, Prausnitz, and Poling: Properties of Gises and Liquids Smith, Van Ness, and Abbott: Introduction tg~&micblE ngineering Thermodynamics Treybal: Mass Transfer Operations - . ', McGraw-Hill Higher Education A Bvision of The McGraw-His Companies OPTIMIZATION OF CHEMICAL PROCESSES, SECOND EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright O 2001, 1988 by The McGraw-Hill Companies, Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw- Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or trans- mission, lor broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on acid-free paper. ISBN 0-07-039359-1 Publisher: Thomas E. Casson Executive editor: Eric M. Munson ~ditoriacl oordinator: Zumna Borciuch Senior marketing manager: John Wannemacher Project manager: Vicki Kmg Media technology senior producer: Phillip Meek Senior production supervisor: Sandra Hahn Coordinator of freelance design: Michelle D. WhitcOker Cover designer: JoAnne Schopler Cover image: Corbis Supplement producer: Jodi K. Banowetz Compositor: Lachina Publishing Services 'Qpeface: 10.5/12 Times Roman Printer: R. R. Donnelley & Sons Company/Crawfordsville, IN ' Library of Congress Cataloging-in-PublicationD ata Edgar, Thomas F. Optimization of chemical processes / Thomas F. Edgar, David M. Himmelblau, Leon S. Lasdon.-2nd ed. p. cm.--(McGraw-Hill chemical engineering series.) Includes bibliographical references and index. ISBN 0-07-039359- 1 1. Chemical processes. 2. Mathematical optimization. I. Himmelblau, David Mautner, 1923- . 11. Lasdon, Leon S., 1939- . 111. Title. IV. Series. TP155.7 .E34 2001 660t.28-dc21 00-06Z468 CIP & CONTENTS Preface xi About the Authors xiv PART I Problem Formulation 1 The Nature and Organization of Optimization Problems 1.1 What Optimization Is All About l.2 Why Optimize? 1.3 Scope and Hierarchy of Optimization 1.4 ~xarn~loefs A pplications of Optimization 1.5 The Essential Features of Optimization Problems 1.6 General Procedure for Solving Optimization Problems 1.7 Obstacles to Optimization References Supplementary References Problems 2 Developing Models for Optimization 2.1 Classification of Models 2.2 How to Build a Model 2.3 Selecting Functions to Fit Empirical Data 2.3.1 How to Determine the Form of a Model / 2.3.2 Fitting Models by Least Squares 2.4 Factorial Experimental Designs 25 Degrees of Freedom 2.6 Examples of Inequality and Equality Constraints in Models References Supplementary References Problems vi Contents 3 Formulation of the Objective Function 3.1 Economic Objective Functions 3.2 The Time Value of Money in Objective Functions 3.3 Measures of Profitability References Supplementary References Problems Part I1 Optimization Theory and Methods 4 Basic Concepts of Optimization 4.1 Continuity of Functions 4.2 NLP Problem Statement 4.3 Convexity and Its Applications 4.4 Interpretation of the Objective Function in Terms of its Quadratic Approximation 4.5 Necessary and Sufficient Conditions for an Extremum of an Unconstrained Function References Supplementary References Problems Optimization of Unconstrained Functions: One-Dimensional Search 9.1 Numerical Methods for Optimizing a Function of One Variable 5.2 Scanning and Bracketing Procedures 5.3 Newton and Quasi-Newton Methods of Unidimensional Search 5.3.1 Newton's Method / 5.3.2 Finite ~flerenceA pproximations to Derivatives / 5.3.3 Quasi-Newton Method 5.4 Polynomial Approximation Methods 5.4.1 Quadratic Interpolation / 5.4.2 Cubic Interpolation 5.5 How One-Dimensional Search Is Applied in a Multidimensional Problem 5.6 Evaluation of Unidimensional Search Methods References Supplementary References Problems 6 Unconstrained Multivariable Optimization 18 1 6.1 Methods Using Function Values Only 183 6.1.1 Random Search / 6.1.2 Grid Search / 6.1.3 Univariate Search / 6.1.4 Simplex Search Method / 6.1.5 Conjugate Search Directions / 6.1.6 Summary 6.2 Methods That Use First Derivatives 6.2.1 Steepest Descent / 6.2.2 Conjugate ~radienMt ethods Contents vii 6.3 Newton's Method 6.3.1 Forcing the Hessian Matrix to Be Positive-Definite / 6.3.2 Movement in the Search Direction / 6.3.3 Termination / 6.3.4 Safeguarded Newton's Method / 6.3.5 Computation of Derivatives 6.4 Quasi-Newton Methods References Supplementary References Problems 7 Linear Programming (LP) and Applications 7.1 Geometry of Linear Programs 7.2 Basic Linear Programming Definitions and Results 7.3 Simplex Algorithm 7.4 Barrier Methods 7.5 Sensitivity Analysis 7.6 Linear Mixed Integer Programs 7.7 LP Software 7.8 A Transportation Problem Using the EXCEL Solver Spreadsheet Formulation 7.9 Network Flow and Assignment Problems References Supplementary References Problems 8 Nonlinear Programming with Constraints 8.1 Direct Substitution 8.2 First-Order Necessary Conditions for a Local Extremum 8.2.1 Problems Containing Only Equality Constraints / 8.2.2 Problems Containing Only Inequality Constraints / 8.2.3 Problems Containing both Equality and Inequality < Constraints 8.3 Quadratic Programming 8.4 Penalty, Barrier, and Augmented Lagrangian Methods 8.5 Successive Linear Programming 8.5.1 Penalty Successive Linear Programming 8.6 Successive Quadratic Programming 8.7 ' The Generalized Reduced Gradient Method 8.8 Relative Advantages and Disadvantages of NLP Methods 8.9 Available NLP Software 8.9.1 Optimizers for Stand-Alone Operation or Embedded Applications / 8.9.2 Spreadsheet Optimizers / 8.9.3 Algebraic Modeling Systems 8.10 Using NLP Software 8.10.1 Evaluation of Derivatives: Issues and Problems / 8.10.2 What to Do When an NLP Algorithm Is Not "Working " Contents References Supplementary References Problems 9 Mixed-Integer Programming 9.1 Problem Formulation 9.2 Branch-and-Bound Methods Using LP Relaxations 9.3 Solving MINLP Problems Using Branch-and-Bound Methods 9.4 Solving MINLPs Using Outer Approximation 9.5 Other Decomposition Approaches for MINLP 9.6 Disjunctive Programming References Supplementary References Problems 10 Global Optimization for Problems with Continuous and Discrete Variables 10.1 Methods for Global Optimization 10.2 Smoothing Optimization Problems 10.3 Branch-and-Bound Methods 10.4 Multistart Methods 10.5 Heuristic Search Methods 10.5.1 Heuristic Search / 10.5.2 Tabu Search / 10.5.3 Simulated Annealing / 10.5.4 Genetic and Evolutionary Algorithms / 10.5.5 Using the Evolutionary Algorithm in the Premium Excel Solver / 10.5.6 Scatter Search 10.6 Other Software for Global Optimization References Supplementary References Part I11 Applications of Optimization 11 Heat Transfer and Energy Conservation Example 11.1 Optimizing Recovery of Waste Heat Example 11.2 Optimal Shell-and-Tube Heat Exchanger Design Example 11.3 Optimization of a Multi-Effect Evaporator Example 11.4 Boiler~Turbo-GeneratorS ystem Optimization References Supplementary References 12 Separation Processes Example 12.1 Optimal Design and Operation of a Conventional Staged-Distillation Column Contents ix Example 12.2 Optimization of Flow Rates in a Liquid-Liquid Extraction Column 448 Example 12.3 Fitting Vapor-Liquid Equilibrium Data Via Nonlinear Regression 45 1 Example 12.4 Determination of the Optimal Reflux Ratio for a Staged-Distillation Column 453 References 45 8 Supplementary References 458 13 Fluid Flow Systems 460 Example 13.1 Optimal Pipe Diameter 46 1 Example 13.2 Minimum Work of Compression 464 Example 13.3 Economic Operation of a Fixed-Bed Filter 466 Example 13.4 Optimal Design of a Gas Transmission Network 469 References 478 Supplementary References 478 14 Chemical Reactor Design and Operation 480 Example 14.1 Optimization of a Thermal Cracker Via Linear Programming 484 Example 14.2 Optimal Design of an Ammonia Reactor 488 Example 14.3 Solution of an Alkylation Process by Sequential Quadratic Programming 492 Example 14.4 Predicting Protein Folding 495 Example 14.5 Optimization of Low-Pressure Chemical Vapor Deposition Reactor for the Deposition of Thin Films 500 Example 14.6 Reaction Synthesis Via MINLP 508 References 513 Supplementary References 5 14 15 Optimization in Large-Scale Plant Design and Operations 515 15.1 Process Simulators and Optimization Codes 518 15.2 Optimization Using Equation-Based Process Simulators 525 15.3 Optimization Using Modular-Based Simulators 537 15.3.1 Sequential Modular Methods / 15.3.2 Simultaneous Modular Methods / 15.3.3 Calculation of Derivatives 15.4 Summary 546 References 546 Supplementary References 548 i 16 Integrated Planning, Scheduling, and Control in the Process Industries 549 16.1 Plant Optimization Hierarchy 550 16.2 Planning and Scheduling 553 16.2.1 Planning / 16.2.2 Scheduling x Contents 16.3 Plantwide Management and Optimization 16.4 Unit Management and Control 16.4.1 Formulating the MPC Optimization Problem 16.5 Process Monitoring and Analysis References Supplementary References Appendixes 583 A Mathematical Sunimary 583 A.1 Dejinitions / A.2 Basic Matrix Operations / A.3 Linear Independence and Row Operations / A.4 Solution of Linear Equations / A.5 Eigenvalues, Eigenvectors / References / Supplementary References / Problems B Cost Estimation 603 B.1 Capital Costs / B.2 Operating Costs / B.3 Taking Account of Infation / B.4 Predicting Revenues in an Economic-Based Objective Function / B.5 Project Evaluation / References Nomenclature Name Index Subject Index