Stochastic Process Optimization using Aspen Plus®

Juan Gabriel Segovia-Hernández, Fernando Israel Gómez-Castro

• Publisher: CRC Press
• Year: 2017
• ISBN:
  9781351651783
• Edition: 1
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

Stochastic Process Optimization using Aspen® Plus

Bookshop Category: Chemical Engineering

Optimization can be simply defined as "choosing the best alternative among a set of feasible options". In all the engineering areas, optimization has a wide range of applications, due to the high number of decisions involved in an engineering environment. Chemical engineering, and particularly process engineering, is not an exception; thus stochastic methods are a good option to solve optimization problems for the complex process engineering models.

In this book, the combined use of the modular simulator Aspen ® Plus and stochastic optimization methods, codified in MATLAB, is presented. Some basic concepts of optimization are first presented, then, strategies to use the simulator linked with the optimization algorithm are shown. Finally, examples of application for process engineering are discussed.

The reader will learn how to link the process simulator Aspen ® Plus and stochastic optimization algorithms to solve process design problems. They will gain ability to perform multi-objective optimization in several case studies.

Key Features:

• The book links simulation and optimization through numerical analyses and stochastic optimization techniques

• Includes use of examples to illustrate the application of the concepts and specific guidance on the use of software (Aspen ® Plus, Excel, MATLB) to set up and solve models representing complex problems.

• Illustrates several examples of applications for the linking of simulation and optimization software with other packages for optimization purposes.

• Provides specific information on how to implement stochastic optimization with process simulators.

• Enable readers to identify practical and economic solutions to problems of industrial relevance, enhancing the safety, operation, environmental, and economic performance of chemical processes.

1

Introduction to Optimization

1.1 What Is Optimization?

The term “optimization” may immediately lead us to a mathematical definition, given the background of any person related with science and/or engineering. Nevertheless, “optimization” can be defined from a more general point of view as “select the best alternative among a set of possibilities.” This, certainly, implies that optimization procedures may occur for any person every day, even in an unconscious way. Moreover, since decisions are mainly taken by human beings, optimization should have definitely occurred from the beginning of mankind. It has been reported that one of the first registered optimization problems is the isoperimetric problem, which was solved by Queen Dido around 1000 BC, whereas the beginning of the systematic optimization procedures started with the solution of the brachistochrone problem, around 1694 (Diwekar, 2010). Nowadays, the size of optimization problems is considerably large, existing from considerably small scales to problems involving countries or even continents. The search of the best configuration for a polymer molecule may be performed through optimization algorithms (Venkatasubramanian et al., 1994). Finding the best alternative for production scheduling of a chemical plant is an optimization problem (Lin and Floudas, 2002). Moreover, selecting the best alternative for supply chain for the production of biofuels in a country (Leao et al., 2011) or an entire continent (Wetterlund et al., 2012) is also an optimization problem. As novel optimization problems are becoming more and more complex, the development of robust optimization algorithms is necessary. Such solution methods should be able to deal with a high number of continuous and discrete variables, nonconvex search spaces, multiple objectives, and other complexities shown by modern optimization problems.

1.2 Mathematical Modeling and Optimization

Although optimization may occur by trial-and-error procedures, such strategy can be quite expensive or even dangerous. In other cases, the number of possible solutions is considerably high; therefore, it is unpractical to test each of them. When those situations occur, rigorous optimization techniques are necessary. Moreover, such methods require, in several cases, counting with a mathematical model, which properly represents the phenomena or system of interest. A mathematical model is an abstract representation of the system under study, and it relates the important variables through mathematical expressions. Such mathematical equations can be expressed as equalities (A = B), inequalities (A ≤ B or A ≥ B), or logical expressions (A → B). Furthermore, relationships between the variables can be merely algebraic, which happens for static systems, or can be differential or integro-differential, which is observed in dynamic systems. Despite the type of mathematical equations and relationships conforms to the model, it should be used for better understanding the system under study, and obtaining information about the relationship between the different components of the system. Furthermore, the model will be beneficial for examining the effects of manipulating the input variables on the entire performance of the case of study. Moreover, it allows avoiding the high costs of multiple experiments and the risks of manipulating a not well understood system. Certainly, experimentation is necessary to obtain the unknown information required for the model or to validate the results obtained, but the required number of tests will be small.

An important concept, which is the first link between mathematical modeling and optimization, is the number of degrees of freedom. Let us assume a mathematical model with M independent equations and N variables. The number of degrees of freedom, F, is then defined as follows:

$$F=N–M$$(1.1)

Thus, the degrees of freedom can be defined as a set of variables in excess, which avoids the model to be solved in a direct way. To solve the model, an M×M matrix should be obtained. Consequently, additional equations are required, which can be obtained by fixing F variables in a given value. Three situations can be observed when analyzing the number of degrees of freedom:

• Case I. The number of equations is greater than the number of variables (M > N), and thus, the number of degrees of freedom is negative. This situation commonly implies that there are some errors in the model, and it is said that the problem is overspecified. Another possibility for the existence of this situation is that there are some dependent equations in the model, which should not be considered for computing M.
• Case II. The number of equations is equal to the number of variables (M = N); thus, the number of degrees of freedom is zero. This implies that the system is an M×M matrix, and, if it consists of linear equations, there is only one solution to the problem. If the equations are nonlinear, multiple solutions can exist, but they are due to the roots of the nonlinear equations.
• Case III. The number of variables is greater than the number of equations (M > N); thus, the number of degrees of freedom is positive. This is the case where we have variables whose values cannot be obtained using the model. Moreover, they should be assumed in a manner that the M×M matrix is completed and the model can be solved. Nevertheless, there is the problem of selecting proper values for those F variables. This implies that we can have a set of possible solutions, depending on the values of the degrees of freedom. As we mentioned previously, optimizing is selecting the bes...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Acknowledgement
• Editor
• Contributors
• 1. Introduction to Optimization
• 2. Deterministic Optimization
• 3. Stochastic Optimization
• 4. The Simulator Aspen Plus®
• 5. Direct Optimization in Aspen Plus®
• 6. Optimization using Aspen Plus® and Stochastic Toolbox
• 7. Using External User-Defined Block Model in Aspen Plus®
• 8. Optimization with a User Kinetic Model
• 9. Optimization of a Biobutanol Production Process
• 10. Optimization of a Silane Production Process
• Index