Reactor network synthesis problem

AR theory is hence a set of ideas in chemical reactor design that aims to understand the reactor network synthesis problem. But to understand this problem will ultimately require us to understand a broader problem of what it means to be the best, for various designs within the block may achieve the same outcome. This is our primary concern in AR theory. It is related to the reactor network synthesis problem, but it is also distinct. 

In Section 1.2, we described how Sam, Alex, and Donald approached the BTX problem from an experimental perspective. How might our approach change if we are given mathematical expressions for the rates of reaction In the following sections, we wish to describe some common ideas and approaches in theoretically designing a network of reactors (the reactor network synthesis problem), and also describe a central challenge faced in reactor network synthesis, even when mathematical and optimization techniques are available. For example, suppose that kinetics is also available for the BTX reaction and assumed to follow the data in Table 1.4 ... 

We find that methods such as AR theory are required not because of problems involving multiple reactors, but because of problems involving multiple reactions. Many of these methods are unnecessary when the reactions are inherently simple. The reactor network synthesis problem arises often as a result of complexities in the system from multiple reactions. 

Description A popular approach to solving the reactor network synthesis problem is by use of reactor superstructures. A reactor superstructure is a reactor configuration... 

In AR theory, we have an interest in the reactor network synthesis problem, but it is not our chief interest. It is sometimes not possible to generate an optimal reactor structure using AR theory, but it is still possible to generate important information that may help to understand what the optimal reactor structure might be. Let us refer back to the following two points from Section 1.4.1.2 ... 

This example, although simple, illustrates a fundamental challenge often encountered in reactor network synthesis problems. Each exit in the maze could be considered a final objective. An answer is achieved from an initial state, but various outcomes may be realized from a single starting point. When attempting to solve reactor network synthesis problems, we often do not... 

In previous chapters, we developed a theoretical framework for interpreting concentration, mixing, and reaction from a geometric perspective. Although these concepts are simple in nature, they form the foundations of AR theory. We are now ready to begin applying these concepts to address reactor network synthesis problems. 

The use of AR theory is somewhat different from many other optimization techniques, and hence it is useful to provide a guideline for how to approach reactor network synthesis problems from this viewpoint. This framework outlines five key steps, with the level of difficulty involved in each step placed in parentheses. 

Figure 5.10 shows a generalized representation of the reactor network synthesis problem. It is assumed that a single feed is available. The volumetric flow rate of the feed is given by Q. On the other end of the network, a combined product stream of concentration C exits the network, which may be composed of potentially many mixtures of product streams within the network. Since the constant density assumption is enforced, the volumetric flow rate of the product stream is also Q. The goal is to determine the specific reactor configuration within the box that optimizes C. 

On reflection, we have come a long way to understanding the nature of the reactor network synthesis problem, and by extension the problem that Sam, Alex, and Donald originally faced. In this chapter, we have finally answered the BTX problem initially posed in Chapter 1, by computing the true AR for this system. 

Introduction In contrast to the total connectivity model, where a superstmcture representation is formulated specifically for the determination of the AR, the IDEAS framework (Burri et al., 2002) caters to the solution of more generalized reactor network synthesis problems. Candidate AR construction is one of many outputs that the IDEAS framework is capable of performing. 

Basic Idea The IDEAS framework describes a generahzed reactor superstructure that may be used for addressing many reactor network synthesis problems. Construction of a candidate AR occurs by successive solution of a number of LP subproblems for different objective functions. The solution corresponding to each LP problem results in a different point on the AR boundary. Therefore, the computation of candidate ARs is resolved in a point-wise manner. The accuracy of the constraction is determined by the number of unknown variables used in each LP problem, whereas the number of points computed for the AR boundary depends on the number of individual LPs solved. 

AR theory is not restricted to constant density systems. The use of mass fractions allows one to compute the AR, even for variahle density problems. This feat is possible because mass fractions always obey a Unear mixing law. With an appropriate equation of state, it is possible to express common process variables (including residence time) in terms of species mass fractions, and thus the AR for systems involving molar concentration and mole fraction may stUl be computed. This theory allows for the investigation of a wider range of realistic reactor network synthesis problems, such as reactions occurring in the gas phase or heterogeneous reactions. 

A number of three-dimensional adiabatic reactor network synthesis problems were described in Chapter 7. A paper by Nicol et al. (1997) looks at extending these principles to include heating and cooling utilities. In effect, heat transfer equipment may be incorporated into the optimal reactor structure on the AR boundary. The results are dependent on a number of ideas developed by Godorr et al.(1994). Aspects of this work also involve finding conditions for optimality in four-dimensional space. Further details may be found in the PhD theses of Love (1995) and Nicol (1998). 

Chapter 1 In this chapter, we introduce the idea of the reactor network synthesis problem and performance targeting. Ultimately, we attempt to articulate two important messages how do you know you have achieved the best You cannot fix what you don t know. 

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