Process Dynamics Modeling, Analysis and Simulation

by Bequette, B. Wayne

• ISBN13: 9780132068895
• ISBN10: 0132068893
• Edition: 1st
• Format: Paperback
• Copyright: 1998-01-05
• Publisher: PEARSO
• More Book Details

Summary

Modeling, analysis and simulation of chemical processes is increasingly central to the work of chemical engineers -- but it is rarely covered in depth in process design guides. This book fills that gap. It is a comprehensive introduction to process modeling and dynamics using the powerful MATLAB and SIMULINK analysis tools.Start by understanding the rationale for process modeling, and why it is becoming so critically important. Then, review all the fundamental numerical techniques involved, including algebraic equations and numerical integration. Walk through linear systems analysis in detail, learning how to linearize non-linear models, solve linear nth Order ODE models, work with Laplace transforms and transfer function analysis, and much more. Finally, learn how to use today's increasingly-important non-linear techniques, such as phase plane analysis, quadratic maps bifurcation behavior, and analysis of chaotic behavior via Lorenz equations.For all chemical engineers, from Ph.D. professionals to non-degreed technicians and students.

Table of Contents

Preface	xvii
SECTION I PROCESS MODELING	1	(48)
1 Introduction	3	(13)
1.1 Motivation	3	(1)
1.2 Models	4	(6)
1.2.1 How Models Are Used	5	(5)
1.3 Systems	10	(2)
1.3.1 Simulation	10	(1)
1.3.2 Linear Systems Analysis	11	(1)
1.3.3 A Broader View of Analysis	11	(1)
1.4 Background of the Reader	12	(1)
1.5 How To Use This Textbook	12	(1)
1.5.1 Sections	12	(1)
1.5.2 Numerical Solutions	13	(1)
1.5.3 Motivating Examples and Modules	13	(1)
1.6 Courses Where This Textbook Can Be Used	13	(1)
Summary	14	(1)
Further Reading	14	(1)
Student Exercises	15	(1)
2 Process Modeling	16	(33)
2.1 Background	17	(1)
2.2 Balance Equations	17	(3)
2.2.1 Integral Balances	18	(2)
2.2.2 Instantaneous Balances	20	(1)
2.3 Material Balances	20	(7)
2.3.1 Simplifying Assumptions	25	(2)
2.4 Constitutive Relationships	27	(3)
2.4.1 Gas Law	27	(1)
2.4.2 Chemical Reactions	27	(1)
2.4.3 Equilibrium Relationships	28	(1)
2.4.4 Flow-through Valves	29	(1)
2.5 Material and Energy Balances	30	(4)
2.5.1 Review of Thermodynamics	31	(3)
2.6 Distributes Parameter Systems	34	(1)
2.7 Dimensionless Models	35	(1)
2.8 Explicit Solutions to Dynamic Models	36	(1)
2.9 General Form of Dynamic Models	37	(3)
2.9.1 State Variables	37
2.9.2 Input Variables
2.9.3 Parameters	38	(1)
2.9.4 Vector Notation	38	(2)
Summary	40	(1)
Further Reading	40	(1)
Student Exercises	41	(8)
SECTION II NUMERICAL TECHNIQUES	49	(54)
3 Algebraic Equations	51	(29)
3.1 Notations	51	(1)
3.2 General Form for a Linear System of Equations	51	(3)
3.3 Nonlinear Functions of a Single Variable	54	(9)
3.3.1 Convergence Tolerance	55	(1)
3.3.2 Direct Substitution	55	(3)
3.3.3 Interval Halving (Bisection)	58	(2)
3.3.4 False Position (Reguli Falsi)	60	(1)
3.3.5 Newton's Method (or Newton-Raphson)	60	(3)
3.4 MATLAB Routines for Solving Functions of a Single Variable	63	(1)
3.4.1 fzero	63	(1)
3.4.2 roots	64	(1)
3.5 Multivariable Systems	64	(6)
3.5.1 Newton's Method for Multivariable Problems	66	(3)
3.5.2 Quasi-Newton Methods	69	(1)
3.6 MATLAB Routines for Systems of Nonlinear Algebraic Equations	70	(1)
Summary	71	(1)
Further Reading	72	(1)
Student Exercises	73	(5)
Appendix	78	(2)
4 Numerical Integration	80	(23)
4.1 Background	80	(1)
4.2 Euler Integration	81	(7)
4.2.1 Explicit Euler	81	(1)
4.2.2 Implicit Euler	82	(1)
4.2.3 Numerical Stability of Explicit and Implicit Methods	83	(5)
4.3 Runge-Kutta Integration	88	(6)
4.3.1 Second Order Runge-Kutta	89	(4)
4.3.2 Fourth-Order Runge-Kutta	93	(1)
4.4 MATLAB Integration Routines	94	(3)
4.4.1 ode23 and ode45	95	(2)
Summary	97	(1)
Further Reading	97	(1)
Student Exercises	98	(5)
SECTION III LINEAR SYSTEMS ANALYSIS	103	(198)
5 Linearization of Nonlinear Models: The State-Space Formulation	105	(37)
5.1 State Space Models	106	(3)
5.5.1 General Form of State Space Models	108	(1)
5.2 Linearization of Nonlinear Models	109	(8)
5.2.1 Single Variable Example	109	(1)
5.2.2 One State Variable and One Input Variable	110	(2)
5.2.3 Linearization of Multistate Models	112	(2)
5.2.4 Generalization	114	(3)
5.3 Interpretation of Linearization	117	(2)
5.4 Solution of the Zero-Input Form	119	(8)
5.4.1 Effect of Initial Condition Direction (Use of Similarity Transform)	120	(7)
5.5 Solution of the General State-Space Form	127	(1)
5.6 MATLAB Routines step and initial	127	(3)
5.6.1 The MATLAB step Function	129	(1)
5.6.2 The MATLAB initial Function	129	(1)
Summary	130	(1)
Further Reading	131	(1)
Student Exercises	131	(11)
6 Solving Linear nth Order ODE Models	142	(26)
6.1 Background	143	(2)
6.2 Solving Homogeneous, Linear ODEs with Constant Coefficients	145	(7)
6.2.1 Distinct Eigenvalues	146	(2)
6.6.2 Repeated Eigenvalues	148	(4)
6.6.3 General Result for Complex Roots	152	(1)
6.3 Solving Nonhomogeneous, Linear ODEs with Constant Coefficients	152	(2)
6.4 Equations with Time-Varying Parameters	154	(3)
6.5 Routh Stability Criterion -- Determining Stability Without Calculating Eigenvalues	157	(3)
6.5.1 Routh Array	157	(3)
Summary	160	(1)
Further Reading	161	(1)
Student Exercises	161	(7)
7 An Introduction to Laplace Transforms	168	(22)
7.1 Motivation	168	(1)
7.2 Definition of the Laplace Transform	169	(1)
7.3 Examples of Laplace Transforms	170	(7)
7.3.1 Exponential Function	170	(2)
7.3.3 Time-Delay (Dead Time)	172	(1)
7.3.4 Derivations	173	(1)
7.3.5 Integrals	173	(1)
7.3.6 Ramp Function	174	(1)
7.3.7 Pulse	174	(2)
7.3.8 Unit Impulse	176	(1)
7.3.9 Review	177	(1)
7.4 Final and Initial Value Theorems	177	(1)
7.5 Application Examples	178	(7)
7.5.1 Partial Fraction Expansion	179	(6)
7.6 Table of Laplace Transforms	185	(2)
Summary	187	(1)
Further Reading	187	(1)
Student Exercises	187	(3)
8 Transfer Function Analysis of First-Order Systems	190	(25)
8.1 Perspective	191	(1)
8.2 Responses of First-Order Systems	191	(9)
8.2.1 Step Inputs	193	(5)
8.2.2 Impulse Inputs	198	(2)
8.3 Examples of Self-Regulating Processes	200	(6)
8.4 Integrating Processes	206	(2)
8.5 Lead-Lag Models	208	(3)
8.5.1 Simulating Lead-Lag Transfer Functions	209	(2)
Summary	211	(1)
Student Exercises	211	(4)
9 Transfer Function Analysis of Higher-Order Systems	215	(32)
9.1 Responses of Second-Order Systems	216	(10)
9.1.1 Step Responses	217	(4)
9.1.2 Underdamped Step Response Characteristics	221	(1)
9.1.3 Impulse Responses	222	(2)
9.1.4 Response to Sine Inputs	224	(2)
9.2 Second-Order Systems with Numerator Dynamics	226	(2)
9.3 The Effect of Pole-Zero Locations on System Step Responses	228	(2)
9.4 Pade Approximation for Deadtime	230	(2)
9.5 Converting the Transfer Function Model to State-Space Form	234	(2)
9.6 MATLAB Routines for Step and Impulse Response	234	(2)
9.6.1 step	234	(2)
9.6.2 impulse	236	(1)
Summary	236	(1)
Student Exercises	237	(10)
10 Matrix Transfer Functions	247	(14)
10.1 A Second-Order Example	248	(3)
10.2 The General Method	251	(1)
10.3 MATLAB Routine ss2tf	252	(5)
10.3.1 Discussion of the Results from Example 10.2	255	(2)
Summary	257	(1)
Student Exercises	257	(4)
11 Block Diagrams	261	(21)
11.1 Introduction to Block Diagrams	262	(1)
11.2 Block Diagrams of Systems in Series	262	(1)
11.3 Pole-Zero Cancellation	263	(4)
11.4 Systems in Series	267	(2)
11.4.1 Simulating Systems in Series	267	(2)
11.5 Blocks in Parallel	269	(4)
11.5.1 Conditions for Inverse Response	271	(2)
11.6 Feedback and Recycle Systems	273	(3)
11.7 Routh Stability Criterion Applied to Transfer Functions	276	(2)
11.7.1 Routh Array	277	(1)
11.8 SIMULINK	278	(1)
Summary	279	(1)
Student Exercises	280	(2)
12 Linear Systems Summary	282	(19)
12.1 Background	283	(1)
12.2 Linear Boundary Value Problems	283	(3)
12.3 Review of Methods for Linear Initial Value Problems	287	(3)
12.3.1 Linearization	187	(101)
12.3.2 Direction Solution Techniques	288	(1)
12.3.3 Rewrite the State-Space Model as a Single nth Order Ordinary Differential Equation	289	(1)
12.3.4 Use Laplace Transforms Directly on the State-Space Model	290	(1)
12.4 Introduction to Discrete-Time Models	290	(5)
12.4.1 Discrete Transfer Function Models	291	(4)
12.5 Parameter Estimation of Discrete Linear Systems	295	(2)
Summary	297	(1)
References	297	(1)
Student Exercises	298	(3)
SECTION IV NONLINEAR SYSTEMS ANALYSIS	301	(112)
13 Phase-Plane Analysis	303	(28)
13.1 Background	304	(1)
13.2 Linear System Examples	304	(7)
13.3 Generalization of Phase-Plane Behavior	311	(5)
13.3.1 Slope Marks for Vector Fields	313	(2)
13.3.2 Additional Discussion	315	(1)
13.4 Nonlinear Systems	316	(8)
13.4.1 Limit Cycle Behavior	323	(1)
Summary	324	(1)
Further Reading	324	(1)
Student Exercises	324	(7)
14 Introduction Nonlinear Dynamics: A Case Study of the Quadratic Map	331	(29)
14.1 Background	332	(1)
14.2 A Simple Population Growth Model	332	(2)
14.3 A More Realistic Population Model	334	(5)
14.3.1 Transient Response Results for the Quadratic (Logistic) Map	335	(4)
14.4 Cobweb Diagrams	339	(3)
14.5 Bifurcation and Orbit Diagrams	342	(2)
14.5.1 Observations from the Orbit Diagram (Figure 14.14)	342	(2)
14.6 Stability of Fixed-Point Solutions	344	(4)
14.6.1 Application of the Stability Theorem to the Quadratic Map	344	(2)
14.6.2 Generalization of the Stability Results for the Quadratic Map	346	(1)
14.6.3 The Stability Theorem and Qualitative Behavior	346	(2)
14.7 Cascade of Period-Doublings	348	(6)
14.7.1 Period-2	348	(3)
14.7.2 Period-4	351
14.7.3 Period-n
14.7.4 Feigenbaum's Number	353	(1)
14.8 Further Comments on Chaotic Behavior	354	(1)
Summary	354	(1)
References and Further Reading	355	(1)
Student Exercises	356	(2)
Appendix: Matlab M-Files Used in This Module	358	(2)
15 Bifurcation Behavior of Single ODE Systems	360	(21)
15.1 Motivation	360	(1)
15.2 Illustration of Bifurcation Behavior	361	(1)
15.3 Types of Bifurcations	362	(14)
15.3.1 Dynamic Responses	365	(11)
Summary	376	(1)
References and Further Reading	376	(1)
Student Exercises	377	(2)
Appendix	379	(2)
16 Bifurcation Behavior of Two-State Systems	381	(14)
16.1 Background	381	(1)
16.2 Single-Dimensional Bifurcations in the Phase-Plane	382	(2)
16.3 Limit Cycle Behavior	384	(4)
16.4 The Hopf Bifurcation	388	(4)
16.4.1 Higher Order Systems (n greater than 2)	391	(1)
Summary	392	(1)
Further Reading	392	(1)
Student Exercises	392	(3)
17 Introduction to Chaos: The Lorenz Equations	395	(18)
17.1 Introduction	396	(1)
17.2 Background	396	(1)
17.3 The Lorenz Equations	397	(2)
17.3.1 Steady-State (Equilibrium) Solutions	398	(1)
17.4 Stability Analysis of the Lorenz Equations	399	(3)
17.4.1 Stability of the Trivial Solution	399	(1)
17.4.2 Stability of the Nontrivial Solutions	400
17.4.3 Summary of Stability Results	301
17.5 Numerical Study of the Lorenz Equations	402	(5)
17.5.1 Conditions for a Stable Trivial (No Flow) Solution	402	(1)
17.5.2 Stable Nontrivial Solutions	403	(2)
17.5.3 Chaotic Conditions	405	(2)
17.6 Chaos in Chemical Systems	407	(2)
17.7 Other Issues in Chaos	409	(1)
Summary	410	(1)
References and Further Reading	410	(1)
Student Exercises	411	(1)
Appendix	412	(1)
SECTION IV REVIEW AND LEARNING MODULES	413	(204)
Module 1 Introduction to MATLAB	415	(20)
M1.1 Background	416	(1)
M1.2 Using This Tutorial	416	(1)
M1.3 Entering Matrices	417	(2)
M1.4 The MATLAB Workspace	419	(2)
M1.5 Complex Variables	421	(1)
M1.6 Some MATLAB Operations	421	(1)
M1.7 Plotting	422	(4)
M1.8 More Matrix Stuff	426	(1)
M1.9 FOR Loops and IF-THEN Statements	427	(1)
M1.10 m-files	428	(2)
M1.11 Diary	430	(1)
M1.12 Toolboxes	430	(1)
M1.13 Limitations to Student MATLAB	431	(1)
M1.14 Contacting Mathworks	431	(1)
Student Exercises	432	(3)
Module 2 Review of Matrix Algebra	435	(17)
M2.1 Motivation and Notation	436	(1)
M2.2 Common Matrix Operations	436	(4)
M2.3 Square Matrices	440	(8)
M2.4 Other Matrix Operations	448	(2)
Summary	450	(1)
Student Exercises	450	(2)
Module 3 Linear Regression	452	(12)
M3.1 Motivation	452	(2)
M3.2 Least Squares Solution for a Line	454	(1)
M3.3 Solution for the Equation of a Line Using Matrix-Vector Notation	455	(1)
M3.4 Generalization of the Linear Regression Technique	456	(2)
M3.5 MATLAB Routines polyfit and polyval	458	(6)
Module 4 Introduction to SIMULINK	464	(7)
M4.1 Introduction	464	(2)
M4.2 Transfer Function-Based Simulation	466	(3)
M4.3 Printing SIMULINK Windows	469	(2)
Module 5 Stirred Tank Heaters	471	(19)
M5.1 Introduction	471	(1)
M5.2 Developing the Dynamic Model	472	(3)
M5.3 Steady-State Conditions	475	(1)
M5.4 State-Space Model	475	(2)
M5.5 Laplace Domain Model	477	(1)
M5.6 Step Responses: Linear versus Nonlinear Models	478	(5)
M5.7 Unforced System Responses: Perturbations in Initial Conditions	483	(7)
Module 6 Absorption	490	(16)
M6.1 Background	490	(1)
M6.2 The Dynamic Model	491	(4)
M6.3 Steady-State Analysis	495	(1)
M6.4 Step Responses	496	(5)
M6.5 Unforced Behavior	501	(5)
Module 7 Isothermal Continuous Stirred Tank Chemical Reactors	506	(23)
M7.1 Introduction	506	(1)
M7.2 First-Order Irreversible Reaction	507	(9)
M7.3 Van de Vusse Reaction	516	(13)
Module 8 Biochemical Reactors	529	(30)
M8.1 Background	529	(1)
M8.2 Modeling Equations	530	(4)
M8.3 Steady-State Solution	534	(1)
M8.4 Dynamic Behavior	535	(1)
M8.5 Linearization	536	(3)
M8.6 Phase-Plane Analysis	539	(1)
M8.7 Understanding Multiple Steady-States	540	(9)
M8.8 Bifurcation Behavior	549	(10)
Module 9 Diabatic Continuous Stirred Tank Reactors	559	(38)
M9.1 Background	560	(1)
M9.2 The Modeling Equations	561	(2)
M9.3 Steady-State Solution	563	(2)
M9.4 Dynamic Behavior	565	(2)
M9.5 Linearization of Dynamic Equations	567	(4)
M9.6 Phase-Plane Analysis	571	(1)
M9.7 Understanding Multiple Steady-State Behavior	572	(8)
M9.8 Further Complexities	580	(4)
M9.9 Dimensionless Model	584	(13)
Module 10 Ideal Binary Distillation	597	(20)
M10.1 Background	597	(2)
M10.2 Conceptual Description of Distillation	599	(2)
M10.3 Dynamic Material Balances	601	(2)
M10.4 Solving the Steady-State Equations	603	(2)
M10.5 Solving the Nonlinear Dynamic Equations	605	(1)
M10.6 State-Space Linear Distillation Models	606	(2)
M10.7 Multiplicity Behavior	608	(9)
Index	617

Excerpts

Preface An understanding of the dynamic behavior of chemical processes is important from both process design and process control perspectives. It is easy to design a chemical process, based on steady-state considerations, which is practically uncontrollable when the process dynamics are considered. The current status of computational hardware and software has made it easy to interactively simulate the dynamic behavior of chemical processes. It is common for process dynamics to be included as the introductory portion of a process control textbook, however, there are a number of limitations to this approach. Since the emphasis of most of the textbooks is on process control, there is too little space to give adequate depth to modeling, analysis, and simulation of dynamic systems. The focus tends to be on transfer function-based models that are used for control system design. The prime motivation for my textbook is then to provide a more comprehensive treatment of process dynamics, including modeling, analysis, and simulation. This textbook evolved from notes developed for a course on dynamic systems that I have been teaching at Rensselaer since 1991. We have been fortunate to have a two-semester sequence in dynamics and control, allowing more depth to the coverage of each topic. Topics covered here that are not covered in a traditional text include nonlinear dynamics and the use of MATLAB for numerical analysis and simulation. Also, a significant portion of the text consists of review and learning modules. Each learning module provides model development, steady-state solutions, nonlinear dynamic results, linearization, state space and transfer function analysis and simulation. The motivation for this approach is to allow the student to "tie-together" all of the concepts, rather than treating them independently (and not understanding the connections between the different methods). An important feature of this text is the use of MATLAB software. A set of m-files used in many of the examples and in the learning modules is available via the world wide web at the following locations: http:/www/rpi.edu/-bequeb/Process_Dynamicshttp:/www.mathworks.com/education/thirdparty.htmlAdditional learning modules will also be available at the RPI location. A few acknowledgments are in order. A special thanks to Professor Jim Turpin at the University of Arkansas, who taught me the introductory course in process dynamics and control. His love of teaching should be an inspiration to us all. Many thanks to one of my graduate students, Lou Russo, who not only made a number of suggestions to improve the text, but also sparked an interest in many of the undergraduates that have taken the course. The task of developing a solutions manual has been carried out by Venkatesh Natarajan, Brian Aufderheide, Ramesh Rao, Vinay Prasad, and Kevin Schott. Preliminary drafts of many chapters were developed over cappuccinos at the Daily Grind in Albany and Troy. Bass Ale served at the El Dorado in Troy promoted discussions about teaching (and other somewhat unrelated topics) with my graduate students; the effect of the many Buffalo wings is still unclear. Final revisions to the textbook were done under the influence of cappuccinos at Cafe Avanti in Chicago (while there is a lot of effort in developing interactive classroom environments at Rensselaer, my ideal study environment looks much like a coffee shop). Teaching and learning should be dynamic processes. I would appreciate any comments and suggestions that you have on this textbook. I will use the WWW site to provide updated examples, additional problems with solutions, and suggestions for teaching and studying process dynamics. B. Wayne Bequette