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# Computational Techniques for Chemical Engineers

## International Series of Monographs in Chemical Engineering

- 1st Edition - January 1, 1966
- Authors: C. Storey, H. H. Rosenbrock
- Editor: P. V. Danckwerts
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 5 7 1 3 - 9

Computational Techniques for Chemical Engineers offers a practical guide to the chemical engineer faced with a problem of computing. The computer is a servant not a master, its… Read more

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Request a sales quoteComputational Techniques for Chemical Engineers offers a practical guide to the chemical engineer faced with a problem of computing. The computer is a servant not a master, its value depends on the instructions it is given. This book aims to help the chemical engineer in the right choice of these instructions. The text begins by outlining the principles of operation of digital and analogue computers and then discussing the difficulties which arise in formulating a problem for solution on such a machine. This is followed by separate chapters on digital computers and their programming; the use of digital computers in chemical engineering design work; optimization techniques and their application in the selection of optimum designs; the solution of sets of non-linear algebraic equations via hill-climbing; and determination of equilibrium compositions by minimization of Gibbs free energy. Subsequent chapters discuss the solution of partial or simultaneous differential equations; parameter estimation in differential equations; continuous systems; and analogue computers.

Foreword

Preface

Chapter 1. The Use of Analogue and Digital Computers

1. Pilot Plants, Analogues, and Digital Computers

2. The Analogue Computer

3. The Digital Computer

4. Hybrid Machines

5. Large Digital Machines

6. Setting up a Problem

6.1 An Example

7. Mathematics and Engineering

8. Further Reading

9. References

Chapter 2. Digital Computers

1. Introduction

2. Technical Details

2.1 Input

2.2 Store or Memory

2.3 Arithmetic Unit

2.4 Control Unit

2.5 Output

3. Programming

3.1 Machine Programming

3.2 Flow Diagrams

3.3 Automatic Programming

4. Recent Developments

5. Further Reading

6. References

Chapter 3. Design Problems

1. Introduction

2. Simple Routine Design Calculations

2.1 Flange Design

2.2 Orifice Plate Design

2.3 Tube Sheet Thickness

3. Design Calculations of Intermediate Complexity

3.1 Heat Exchanger Design

3.2 Plate-by-Plate Distillation Calculations

3.3 Piping Flexibility Calculations

4. Flowsheet Calculations by Computer

5. Further Reading

6. References

Chapter 4. Optimizing I — Hill-Climbing Methods

1. Scope of the Optimizing Problem

2. Hill-Climbing

2.1 Successive Variation of Parameters

2.2 Ways of Regarding the Hill-Climbing Problem

2.3 Steepest Ascent

2.4 Modified Steepest Ascent

2.5 The Gradient Method

2.6 Generalized Newton-Raphson

2.7 Modified Newton-Raphson

2.8 Methods of Comparison

2.9 A General-Purpose Optimizing Program

3. Some Comparisons of Different Methods

3.1 Discussion of the Results

4. Boundaries

4.1 Modification of F

5. A General-Purpose Optimizing Program with Constraints

6. Status of Hill-Climbing Methods

7. Linear Programming

8. Non-Linear Programming

9. Further Reading

10. References

Chapter 5. Optimization in Design

1. Introduction

2. Tonnage Oxygen Plant

3. Heavy Water Plant

4. Kinetic Problem

5. Further Reading

6. References

Chapter 6. Solution of Algebraic Equations Using Hill-Climbing

1. Introduction

2. Solution of Sets of Non-Linear Algebraic Equations

2.1 Simple Example

2.2 More Realistic Example

3. High Temperature Equilibrium

4. Other Variational Problems

4.1 Example 1. Torsion in a Bar

4.2 Example 2. Velocity Profiles

5. Further Reading

6. References

Chapter 7. Solution of Partial or Simultaneous Differential Equations

1. Relation between Simultaneous and Partial Differential Equations

2. Classification of Partial Differential Equations

2.1 Physical Consideration of Hyperbolic Equations

3. Reduction of Hyperbolic to Parabolic Equations

3.1 Example: Heat Exchanger

3.2 Example: Distillation

3.3 Scope of the above Method

4. Representation of Diffusion

4.1 Example: Regenerator

5. Boundary Conditions

6. Numerical Methods for Parabolic Equations

6.1 Stability: General Considerations

6.2 Stability: an Example

6.3 Stability and Parabolic Equations

6.4 Implicit Processes: Crank and Nicolson's Process

6.5 Computation of the Steady State

6.6 Numerical Precautions

6.7 Application: Distillation

7. Alternative Methods for Solving Parabolic Equations

7.1 Runge-Kutta Processes

7.2 Predictor-Corrector Methods

7.3 Implicit Methods of Successive Substitution

7.4 Methods Which Avoid Difference Equations

8. Status of Numerical Methods

9. Further Reading

10. References

Chapter 8. Estimation of Parameters in Differential Equations

1. Statement of the Problem

1.1 Inherent Difficulties

2. Confidence Intervals for Parameters

2.1 Analytical Development

2.2 Choice of W

2.3 Statement of Formula; Computation

2.4 Discussion of the Assumptions

3. Example

4. Further Reading

5. References

Chapter 9. Optimizing II — Stage-Wise and Continuous Systems

1. Continuous and Discrete Systems

2. Dynamic Programming

2.1 Scope and Significance of the Dynamic Programming Argument

3. Variational Methods

3.1 The "Problem of Mayer"

3.2 Pontryagin's "Maximum Principle"

4. Gradient Method in Function Space

5. Analytical Relations between Results

6. Comparison of Numerical Methods—Continuous Systems

6.1 Hill-Climbing on Parameters

6.2 Gradient Method in Function Space

6.3 Pontryagin's Method

6.4 Dynamic Programming

7. Comparison of Numerical Methods—Stage-Wise Systems

7.1 Hill-Climbing on Parameters

7.2 Gradient Method

7.3 Calculus of Variations

7.4 Dynamic Programming

8. Some Generalizations

8.1 Integral Performance Criteria

8.2 Right-Hand End Conditions

8.3 Variable End Time

8.4 Time-Dependent Systems

9. Further Reading

10. References

Chapter 10. Optimal Temperature Profiles

1. The Problem and its Mathematical Formulation

2. Best Isothermal Yield

3. First Method of Solution: Discrete Approximation

4. Second Method of Solution: Parametric Expansion

5. Third Method of Solution: Pontryagin's Maximum Principle

6. Fourth Method of Solution: Gradient Method in Function Space

7. Fifth Method of Solution: Dynamic Programming

7.1 Discrete Methods

7.2 Continuous Methods

8. Comparison of the Methods

9. Further Reading

10. Appendix. The Trapezoidal Rule for Integration

11. References

Chapter 11. Analogue Computers

1. General-Purpose Analogues

2. Computing Circuits

2.1 Multiplication by a Constant

2.2 Addition

2.3 Integration

2.4 Multiplication of Variables

2.5 Function Generators

2.6 Other Devices

3. Setting up Differential Equations

3.1 Scaling

4. Physical Equipment

5. Example: Distillation

5.1 Passive Analogue for Distillation

6. Applications of Analogue Computers

7. Further Reading

8. References

Chapter 12. Process Control

1. Scope for Computers in Process Control

2. Study of an Existing or Proposed System

2.1 Example: Electrolyser

2.2 Example: Distillation

3. Approaches to the Design of a Control Structure

3.1 Modal Analysis

3.2 Lyapunov Functions

3.3 Optimal Control Theory

4. On-Line Control of Processes by Computer

4.1 Examples

5. Adaptive and optimizing Control

6. Further Reading

7. References

Author Index

Subject Index

Other Titles in the Series

- No. of pages: 346
- Language: English
- Edition: 1
- Published: January 1, 1966
- Imprint: Pergamon
- eBook ISBN: 9781483157139

PD

### P. V. Danckwerts

Affiliations and expertise

University of Cambridge, UKRead

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