WIlllAM 1. LUYBENWILLIAM 1. LUYBEN I PROCESS MODELING,PROCESS MODELING, l SIMULATION AND SIMULATION AND \ CONTROL iOR 5 CONTROL FlitI m CHEMICAL ENGINEERS m SECOND EDITION- I a I 1 L McGraw-Hill Chemical Engineering Series ’ Editorial Advisory Board James J. Carberry, Profissor of Chemical Engineering, University of Notre Dame James R. Fair, Professor of Chemical Engineering, University of Texas, Austin WilUum P. Schowalter, Professor of Chemical Engineering, Princeton University Matthew Tirrell, Professor of Chemical Engineering, University of Minnesota James Wei, Professor of Chemical Engineering, Massachusetts Institute of Technology Max S. Petem, Emeritus, Professor of Chentical Engineering, University of Colorado Building the Literature of a Profession Fifteen prominent chemical engineers first met in New York more than 60 years ago to plan a continuing literature for their rapidly growing profession. From industry came such pioneer practitioners as Leo H. Baekeland, Arthur D. Little, Charles L. Reese, John V. N. Dorr, M. C. Whitaker, and R. S. McBride. From the universities came such eminent educators as William H. Walker, Alfred H. White, D. D. Jackson, J. H. James, Warren K. Lewis, and Harry A. Curtis. H. C. Parmelee, then editor of Chemical and Metallurgical Engineering, served as chair- man and was joined subsequently by S. D. Kirkpatrick as consulting editor. After several meetings, this committee submitted its report to the McGraw- Hill Book Company in September 1925. In the report were detailed specifications for a correlated series of more than a dozen texts and reference books which have since become the McGraw-Hill Series in Chemical Engineering and which became the cornerstone of the chemical engineering curriculum. From this beginning there has evolved a series of texts surpassing by far the scope and longevity envisioned by the founding Editorial Board. The McGraw- Hill Series in Chemical Engineering stands as a unique historical record of the development of chemical engineering education and practice. In the series one finds the milestones of the subject’s evolution: industrial chemistry, stoichio- metry, unit operations and processes, thermodynamics, kinetics, and transfer operations. Chemical engineering is a dynamic profession, and its literature continues to evolve. McGraw-Hill and its consulting editors remain committed to a pub- lishing policy that will serve, and indeed lead, the needs of the chemical engineer- ing profession during the years to come. The Series Bailey and OUii: Biochemical Engineering Fundamentals Bennett and Myers: Momentum, Heat, amd Mass Transfer Beveridge and Schechter: Optimization: Theory and Practice Brodkey and Hershey: Transport Phenomena: A Unified Approach Carberry: Chemical and Catalytic Reaction Engineering Constantinides: Applied Numerical Methods with Personal Computers Cougbanowr and Koppel: Process Systems Analysis and Control Douglas: Conceptual Design ofchemical Processes Edgar and Himmelblau: Optimization ofchemical Processes Fabien: Fundamentals of Transport Phenomena Finlayson: Nonlinear Analysis in Chemical Engineering Gates, Katzer, and Scbuit: Chemistry of Catalytic Processes Holland: Fundamentals of Multicomponent Distillation Holland and Liapis: Computer Methods for Solving Dynamic Separation Problems Katz, Cornell, Kobayaski, Poettmann, Vary, Elenbaas, aad Weinaug: Handbook of Natural Gas Engineering King: Separation Processes Luyben: Process Modeling, Simulation, and Control for Chemical Engineers McCabe, Smitb, J. C., and Harriott: Unit Operations of Chemical Engineering Mickley, Sberwood, and Reed: Applied Mathematics in Chemical Engineering Nelson: Petroleum Refinery Engineering Perry and Cbilton (Editors): Chemical Engineers’ Handbook Peters: Elementary Chemical Engineering Peters and Timmerbaus: Plant Design and Economics for Chemical Engineers Probstein and Hicks: Synthetic Fuels Reid, Prausnitz, and Sherwood: The Properties of Gases and Liquids Resnick: Process Analysis and Design for Chemical Engineers Satterfield: Heterogeneous Catalysis in Practice Sberwood, Pigford, aad Wilke: Mass Transfer Smith, B. D.: Design of Equilibrium Stage Processes Smith, J. M.: Chemical Engineering Kinetics Smith, J. M., and Van Ness: Zntroduction to Chemical Engineering Thermodynamics Treybal: Mass Transfer Operations VaUe-Riestra: Project Evolution in the Chemical Process Industries Van Ness and Abbott: Classical Thermodynamics of Nonelectrolyte Solutions: with Applications to Phase Equilibria Van Winkle: Distillation Volk: Applied Statistics for Engineers -/ Walas: Reaction Kinetics for Chemical Engineers .J J Wei, Russell, and Swartzlander: The Structure of the Chemical Processing Industries WbitweU and Toner: Conservation of Mass and E -’ . / / Also available from McGraw-Hill Schaum’s Outline Series in Civil Engineering Each outline includes basic theory, definitions, and hundreds of solved problems and supplementary problems with answers. Current List Includes: Advanced Structural Analysis Basic Equations of Engineering Descriptive Geometry Dynamic Structural Analysis Engineering Mechanics, 4th edition Fluid Dynamics Fluid Mechanics & Hydraulics Introduction to Engineering Calculations Introductory Surveying Reinforced Concrete Design, 2d edition Space Structural Analysis Statics and Strength of Materials Strength of Materials, 2d edition Structural Analysis Theoretical Mechanics . - Available at Your College Bookstore PROCESS MODELING, SIMULATION, AND CONTROL FOR CHEMICAL ENGINEERS Second Edition William L. Luyben Process Modeling and Control Center Department of Chemical Engineering Lehigh University McGraw-Hill Publisbing Company New York St. Louis San Francisco Auckland Bogota Caracas Hamburg Lisbon London Madrid Mexico Milan Montreal New Delhi Oklahoma City Paris San Juan SHo Paul0 Singapore Sydney Tokyo Toronto PROCESS MODELING, SIMULATION, AND CONTROL FOR CHEMICAL ENGINEERS INTERNATIONAL EDITION 1996 Exclusive rights by McGraw-Hill Book Co Singapore for manufacture and export. This book cannot be m-exported from the country to which it is consigned by McGraw-Hill. 567690BJEPMP9432 Copyright e 1999, 1973 by McGraw-Hill, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, u without the prior written permission of the publisher. This book was set in Times Roman. The editors were Lyn Beamesderfer and John M. Morris.% The production supervisor was Friederich W. Schulte. The cover was designed by John Hite. Project supervision was done by Harley Editorial Services. Ubrury of Congress Cataloging-in-Publlcatlon Data William L. Luyben 2nd ed. p. cm. Bibliography: p. Includes index. ISBN 6-67-639159-9 1. Chemical process-Math data processing., 3. Chemica TP155.7.L66 1969 , 669.2’61-dc19 When ordering this title use ISBN 1 process No.DEADQUiSICION ABOUT THE AUTHOR William L. Luyben received his B.S. in Chemical Engineering from the Penn- sylvania State University where he was the valedictorian of the Class of 1955. He worked for Exxon for five years at the Bayway Refinery and at the Abadan Refinery (Iran) in plant. technical service and design of petroleum processing units. After earning a Ph.D. in 1963 at the University of Delaware, Dr. Luyben worked for the Engineering Department of DuPont in process dynamics and control of chemical plants. In 1967 he joined Lehigh University where he is now Professor of Chemical Engineering and Co-Director of the Process Modeling and Control Center. Professor Luyben has published over 100 technical papers and has authored or coauthored four books. Professor Luyben has directed the theses of over 30 graduate students. He is an active consultant for industry in the area of process control and has an international reputation in the field of distillation column control. He was the recipient of the Beckman Education Award in 1975 and the Instrumqntation Technology Award in 1969 from the Instrument Society of America. f r , .,y<i ‘., Overall, he has devoted ove$? 3$,years to, his profession as a teacher, researcher, author, and practicing en&eer: :.: ’ ! 1. I’ vii This book is dedicated to Robert L. Pigford and Page S. Buckley, two authentic pioneers in process modeling and process control CONTENTS 1 1.1 1.2 1.3 1.4 1.5 1.6 Part I Preface Introduction 1 Examples of the Role of Process Dynamics and Control Historical Background Perspective Motivation for Studying Process Control General Concepts Laws and Languages of Process Control 1.6.1 Process Control Laws 1.6.2 Languages of Process Control 1 6 7 8 8 11 11 12 Mathematical Models of Chemical Engineering Systems Xxi 2 Fundamentals 2.1 Intreduction 2.1.1 Uses of Mathematical Models 2.1.2 Scope of Coverage 2.1.3 Principles of Formulation 2.2 Fundamental Laws 2.2.1 Continuity Equations 2.2.2 Energy Equation 2.2.3 Equations of Motion 2.2.4 Transport Equations 2.2.5 Equations of State 2.2.6 Equilibrium 2.2.7 Chemical Kinetics Problems 15 15 15 16 16 17 17 23 27 31 32 33 36 38 xi I 4 Xii CONTENTS 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 Part II Examples of Mathematical Models of Chemical Engineering Systems Introduction Series of Isothermal, Constant-Holdup CSTRs CSTRs With Variable Holdups Two Heated Tanks Gas-Phase, Pressurized CSTR Nonisothermal CSTR Single-Component Vaporizer Multicomponent Flash Drum Batch Reactor Reactor With Mass Transfer Ideal Binary Distillation Column Multicomponent Nonideal Distillation Column Batch Distillation With Holdup pH Systems 3.14.1 Equilibrium-Constant Models 3.14.2 Titration-Curve Method Problems Computer Simulation 40 40 41 43 44 45 46 51 54 57 62 64 70 72 74 74 75 77 4 Numerical Methods 89 4.1 Introduction 89 4.2 Computer Programming 90 4.3 Iterative Convergence Methods 91 4.3.1 Interval Halving 93 4.3.2 Newton-Raphson Method 96 4.3.3 False Position 100 4.3.4 Explicit Convergence Methods 101 4.35 Wegstein 103 4.3.6 Muller Method 103 4.4 Numerical Integration of Ordinary Differential Equations 105 4.4.1 Explicit Numerical Integration Algorithms 106 4.4.2 Implicit Methods 113 Problems 114 5 Simulation Examples 5.1 Gravity-Flow Tank 5.2 Three CSTRs in Series 5.3 Nonisothermal CSTR 5.4 Binary Distillation Column 5.5 Multicomponent Distillation Column 5.6 Variable Pressure Distillation 5.6.1 Approximate Variable-Pressure Model 5.6.2 Rigorous Variable-Pressure Model 116 116 119 124 129 132 141 141 142 [...]... controller) and feed the difference (the error) into a feedback controller that will change a manipulated variable to drive the controlled variable back to the desired value Information is thus “fed back” from the controlled variable to a manipulated variable, as sketched in Fig 1.7 4 Feedforward control The basic idea is shown in Fig 1.8 The disturbance is detected as it enters the process and an appropriate... time for a second edition In the area of process control, new methods of analysis and synthesis of control systems have been developed and need to be added to the process control engineer’s bag of practical methods The driving force for much of this development was the drastic increase in energy costs in the 1970s This led to major redesigns of many new and old processes, using energy integration and. .. have indeed been blessed Alhamdulillahi! William L Luyben PROCESS MODELING, SIMULATION, AND CONTROL FOR CHEMICAL ENGINEERS CHAPTER 1 INTRODUCTION This chapter is an introduction to process dynamics and control for those students who have had little or no contact or experience with real chemical engineering processes The objective is to illustrate where process control fits into the picture and to indicate... Control Systems and Hardware Control Instrumentation 7.1.1 Sensors 7.1.2 Transmitters 7.1.3 Control Valves 7.1.4 Analog and Digital Controllers 7.1.5 Computing and Logic Devices Performance of Feedback Controllers 7.2.1 Specifications for Closedloop Response 7.2.2 Load Performance Controller Tuning 7.3.1 Rules of Thumb 7.3.2 On-Line Trial and Error 7.3.3 Ziegler-Nichols Method Problems 8 Advanced Control. .. Sampled-Data Control of Processes With Deadtime Sampled-Data Control of Openloop Unstable Processes Problems Xix 702 705 709 Appendix Instrumentation Index Hardware 711 721 PREFACE The first edition of this book appeared over fifteen years ago It was the first chemical engineering textbook to combine modeling, simulation, and control It also was the first chemical engineering book to present sampled-data... compositions and temperatures on all the trays Note that one physical stream may be considered to contain many variables: Feed flow rate fi Load disturbances Feed composition z w Distillate composition xg Bottom composition x,, 1 Level reflux drum ~ MR Controlled variables Manipulated variables Uncontrolled variables i i FIGURE 1.6 10 PROCESS MODELING, Disturbance SIMULATION, AND CONTROL FOR CHEMICAL ENGINEERS. .. costs and with the development of more severe, higher-capacity, higher-performance equipment and processes in the 1940s and early 195Os, it became uneconomical and often impossible to run plants without automatic control devices At this stage feedback controllers were added to the plants with little real consideration of or appreciation for the dynamics of the process itself Rule-of-thumb guides and. .. Manipulated variable Controlled variable c Process I Measurement device 7 Control valve +* FIGURE 1.7 Feedback control loop flow rate, its composition, its temperature, etc., i.e., all its intensive and extensive properties its 3 Feedback control The traditional way to control a process is to measure the variable that is to be controlled, compare its value with the desired value (the setpoint to the controller)... this book exploring this important design and operating problem All our studies of mathematical modeling, simulation, and control theory are aimed at understanding the dynamics of processes and control systems so that we can develop and design better, more easily controlled plants that operate more efficiently and more safely For now let us say merely that the control system shown in Fig 1.5 is a typical... simplest control system that will do the job is the best Complex elegant control systems look great on paper but soon end up on “manual” in an industrial environment Bigger is definitely not better in control system design (2) SECOND LAW You must understand the process before you can control it 12 PROCESS MODELING, SIMULATION, AND CONTROL FOR CHEMICAL ENGINEERS No degree of sophistication in the control . 1. LUYBEN I PROCESS MODELING ,PROCESS MODELING, l SIMULATION AND SIMULATION AND CONTROL iOR 5 CONTROL FlitI m CHEMICAL ENGINEERS m SECOND EDITION- I a I 1 L McGraw-Hill Chemical Engineering. Your College Bookstore PROCESS MODELING, SIMULATION, AND CONTROL FOR CHEMICAL ENGINEERS Second Edition William L. Luyben Process Modeling and Control Center Department of Chemical Engineering Lehigh. Handbook of Natural Gas Engineering King: Separation Processes Luyben: Process Modeling, Simulation, and Control for Chemical Engineers McCabe, Smitb, J. C., and Harriott: Unit Operations of Chemical