Optimization of Chemical Processes

by Edgar, Thomas F.; Himmelblau, D. M.

• ISBN13: 9780070189911
• ISBN10: 0070189919
• Format: Hardcover
• Copyright: 1988-01-01
• Publisher: McGraw-Hill College

Table of Contents

Preface	xv
Part I Problem Formulation	1	(120)
1 The Nature and Organization of Optimization Problems	3	(31)
1.1 What Optimization Is All About	4	(1)
1.2 Why Optimize?	4	(1)
1.3 Scope and Hierarchy of Optimization	5	(4)
1.4 Examples of Applications of Optimization	9	(5)
1.5 The Essential Features of Optimization Problems	14	(4)
1.6 General Procedure for Solving Optimization Problems	18	(8)
1.7 Obstacles to Optimization	26	(1)
References	27	(1)
Problems	28	(6)
2 Fitting Models to Data	34	(35)
2.1 Classification of Models	36	(5)
2.2 How to Build a Model	41	(2)
2.3 Fitting Functions to Empirical Data	43	(7)
2.3.1 How to Determine the Form of a Model	43	(7)
2.4 The Method of Least Squares	50	(7)
2.5 Factorial Experimental Designs	57	(3)
2.6 Fitting a Model to Data Subject to Constraints	60	(2)
References	62	(1)
Problems	63	(6)
3 Formulation of Objective Functions	69	(52)
3.1 Investment Costs and Operating Costs in Objective Functions	70	(8)
3.2 Consideration of the Time Value of Money	78	(5)
3.3 Measures of Profitability	83	(5)
3.4 Optimizing Profitability	88	(5)
3.5 Project Financial Evaluation	93	(12)
3.6 Cost Estimation	105	(8)
References	113	(1)
Problems	114	(7)
Part II Optimization Theory and Methods	121	(318)
4 Basic Concepts of Optimization	123	(34)
4.1 Continuity of Functions	124	(3)
4.2 Unimodal Versus Multimodal Functions	127	(2)
4.3 Convex and Concave Functions	129	(5)
4.4 Convex Region	134	(4)
4.5 Necessary and Sufficient Conditions for an Extremum of an Unconstrained Function	138	(7)
4.6 Interpretation of the Objective Function in Terms of Its Quadratic Approximation	145	(6)
References	151	(1)
Problems	152	(5)
5 Optimization of Unconstrained Functions: One-Dimensional Search	157	(31)
5.1 Numerical Methods for Optimizing a Function of One Variable	160	(1)
5.2 Scanning and Bracketing Procedures	161	(1)
5.3 Newton, Quasi-Newton, and Secant Methods of Unidimensional Search	162	(9)
5.3.1 Newton's Method	163	(1)
5.3.2 Quasi-Newton Method	164	(1)
5.3.3 Secant Method	164	(7)
5.4 Region Elimination Methods	171	(4)
5.5 Polynomial Approximation Methods	175	(6)
5.5.1 Quadratic Interpolation	175	(3)
5.5.2 Cubic Interpolation	178	(3)
5.6 How the One-Dimensional Search is Applied in a Multidimensional Problem	181	(2)
5.7 Evaluation of Unidimensional Search Methods	183	(1)
References	184	(1)
Problems	184	(4)
6 Unconstrained Multivariable Optimization	188	(62)
6.1 Direct Methods	190	(12)
6.1.1 Random Search	190	(1)
6.1.2 Grid Search	190	(1)
6.1.3 Univariate Search	190	(2)
6.1.4 Simplex Method	192	(2)
6.1.5 Conjugate Search Directions	194	(3)
6.1.6 Powell's Method	197	(5)
6.1.7 Summary	202	(1)
6.2 Indirect Methods--First Order	202	(6)
6.2.1 Gradient Method	202	(4)
6.2.2 Conjugate Gradient	206	(2)
6.3 Indirect Methods--Second Order	208	(11)
6.3.1 Newton's Method	208	(6)
6.3.2 Forcing the Hessian Matrix to be Positive Definite	214	(2)
6.3.3 Movement in the Search Direction	216	(1)
6.3.4 Termination	217	(1)
6.3.5 Summary of Newton's Method	218	(1)
6.3.6 Relation Between Conjugate Gradient Methods and Quasi-Newton Methods	219	(1)
6.4 Secant Methods	219	(11)
6.4.1 Determination of the Approximate Hessian Matrix	220	(7)
6.4.2 Movement in the Search Direction	227	(1)
6.4.3 Termination	228	(1)
6.4.4 Summary of Secant Methods	228	(1)
6.4.5 Summary of Indirect Methods	229	(1)
6.5 Finite Difference Approximations as Substitutes for Derivatives	230	(3)
6.6 Sources of Computer Codes for Unconstrained Optimization	233	(3)
6.7 Evaluation of Codes for Unconstrained Optimization	236	(3)
6.8 Diagnosis of Optimization Code Failure to Solve a Problem	239	(1)
References	239	(2)
Problems	241	(9)
7 Linear Programming and Applications	250	(49)
7.1 Basic Concepts in Linear Programming	254	(5)
7.2 Degenerate LP's--Graphical Solution	259	(2)
7.3 Natural Occurrence of Linear Constraints	261	(2)
7.4 The Simplex Method of Solving Linear Programming Problems	263	(7)
7.5 Standard LP Form	270	(3)
7.6 Obtaining a First Feasible Solution	273	(6)
7.7 The Revised Simplex Method	279	(3)
7.8 Sensitivity Analysis	282	(2)
7.9 Duality in Linear Programming	284	(3)
7.10 The Karmarkar Algorithm	287	(3)
7.11 LP Applications	290	(1)
References	290	(1)
Problems	291	(8)
8 Nonlinear Programming with Constraints	299	(96)
8.1 The Lagrange Multiplier Method	302	(7)
8.2 Necessary and Sufficient Conditions for a Local Minimum	309	(10)
8.3 Quadratic Programming	319	(3)
8.4 The Generalized Reduced-Gradient Method	322	(12)
8.4.1 Concept of the Reduced Gradient	323	(4)
8.4.2 The Generalized Reduced Gradient Algorithm	327	(7)
8.4.3 Sources of Computer Codes	334	(1)
8.5 Penalty Function and Augmented Lagrangian Methods	334	(8)
8.6 Successive (Sequential, Recursive) Quadratic Programming	342	(16)
8.6.1 Form of the Quadratic-Programming Subproblem	343	(5)
8.6.2 Successive Quadratic-Programming Algorithm	348	(10)
8.6.3 Successive Quadratic-Programming Codes	358	(1)
8.7 Random Search Methods	358	(3)
8.8 Comparative Evaluation of General Nonlinear Programming Codes	361	(2)
8.9 Successive Linear Programming	363	(1)
8.10 Optimization of Dynamic Processes	364	(8)
8.11 Diagnosis of the Failure of Optimization Codes to Solve Problems	372	(1)
References	373	(6)
Problems	379	(16)
9 Optimization of Staged and Discrete Processes	395	(44)
9.1 Dynamic Programming	397	(9)
9.2 Integer and Mixed Integer Programming	406	(18)
9.2.1 Implicit Enumeration	411	(2)
9.2.2 The Branch and Bound Technique	413	(9)
9.2.3 Nonlinear Mixed-Integer Programming Algorithms	422	(2)
References	424	(2)
Problems	426	(13)
Part III Applications of Optimization	439	(160)
10 Heat Transfer and Energy Conservation	443	(31)
10.1 Optimizing Recovery of Waste Heat	447	(2)
10.2 Optimum Shell and Tube Heat Exchanger Design	449	(8)
10.3 Optimization of Heat Exchanger Networks	457	(5)
Example 10.1 Optimal Allocation of Temperatures in a Sequence of Heat Exchangers	458	(4)
10.4 Optimization of Evaporator Design	462	(5)
Example 10.2 Optimization of a Multistage Evaporator	463	(4)
10.5 Boiler/Turbo Generator System Optimization	467	(4)
References	471	(3)
11 Separation Processes	474	(28)
11.1 Optimization of Liquid-Liquid Extraction Processes	475	(5)
Example 11.1 Optimization of Liquid Extraction Column Flowrates	475	(5)
11.2 Optimal Design and Operation of Staged Distillation Columns	480	(21)
Example 11.2 Optimal Design and Operation of Conventional Staged Distillation Columns	486	(5)
Example 11.3 Nonlinear Regression to Fit Vapor-Liquid Equilibrium Data	491	(4)
Example 11.4 Determination of the Optimum Reflux Ratio for a Staged Distillation Column	495	(3)
Example 11.5 Use of Linear Programming to Optimize a Separation Train	498	(3)
References	501	(1)
12 Fluid Flow Systems	502	(22)
Example 12.1 Optimal Pipe Diameter	503	(3)
Example 12.2 Minimum Work Compression	506	(4)
Example 12.3 Economic Operation of a Fixed-Bed Filter	510	(3)
Example 12.4 Optimal Design of a Gas Transmission Network	513	(9)
References	522	(2)
13 Chemical Reactor Design and Operation	524	(27)
13.1 Formulation of Chemical Reactor Optimization Problems	525	(3)
13.1.1 Modeling of Chemical Reactors	525	(1)
13.1.2 Objective Functions for Reactors	526	(2)
13.2 Use of Differential Calculus in Reactor Optimization	528	(6)
Example 13.1 Optimal Residence Time for Maximum Yield in an Ideal Isothermal Batch Reactor	531	(1)
Example 13.2 One-Dimensional Search for Optimum Residence Time of a Chemostat	532	(2)
13.3 Use of Linear Programming to Optimize Reactor Operations	534	(4)
Example 13.3 Optimization of a Thermal Cracker	534	(4)
13.4 Nonlinear Programming Applied to Chemical Reactor Optimization	538	(12)
Example 13.4 Maximum Yield With Respect to Reactor Volume	541	(1)
Example 13.5 Optimal Design of an Ammonia Reactor	542	(4)
Example 13.6 Solution of an Alkylation Process by Sequential Quadratic Programming	546	(4)
References	550	(1)
14 Optimization in Large-Scale Plant Design and Operation	551	(48)
14.1 General Methods of Meshing Optimization Procedures with Process Models/Simulators	556	(3)
14.2 Equation-Based Large-Scale Optimization	559	(13)
Example 14.1 Equation-Based Optimization for a Refrigeration Process	561	(9)
Example 14.2 Application of ASCEND-II to the Optimization of a Distillation Column	570	(2)
14.3 Large-Scale Optimization Using Sequential Modular Flowsheeting	572	(16)
14.3.1 Feasible Path Strategies	575	(3)
Example 14.3 Application of the Feasible Path Method to a Process for the Chlorination of Propylene	578	(9)
14.3.2 Infeasible Path Strategies	587	(1)
Example 14.4 Application of the Nonfeasible Path Method to a Process for the Chlorination of Propylene	588	(1)
14.4 Large-Scale Optimization Incorporating Simultaneous Modular Flowsheeting Strategies	588	(6)
14.4.1 Calculation of the Elements in the Jacobian Matrix that Represent the Process	591	(2)
14.4.2 Nonlinear Programming Algorithm	593	(1)
14.4.3 Scaling of the Objective Function and Variables	593	(1)
14.5 Conclusions Regarding Combining Optimization with Flowsheeting Codes	594	(1)
14.6 Treatment of Large-Scale Problems with Integer-Valued Variables	594	(1)
References	595	(4)
Appendixes	599	(34)
A Nomenclature	599	(5)
B Mathematical Summary	604	(19)
B.1 Definitions	605	(1)
B.2 Basic Matrix Operations	606	(7)
B.3 Linear Independence and Row Operations	613	(3)
B.4 Solution of Linear Equations	616	(3)
B.5 Eigenvalues, Eigenvectors	619	(2)
References	621	(1)
Problems	621	(2)
C Range Space and Null Space and Relation to Reduced Gradient and Projection Methods	623	(9)
References	632	(1)
Name Index	633	(9)
Subject Index	642