Overview of AR Construction Methods

AR construction algorithms are similar to many numerical methods in engineering in that there are often different methods for solving the same problem. There is no definitive AR construction method that is suitable for all problem types, and it is the duty of the designer to pick the best method for the problem at hand. In general, AR construction methods may be classified into two categories  

Superstructure methods. The superstructure approach was briefly mentioned in Chapter 1. A reactor superstructure is designed to approximate the performance characteristics for various scenarios. Combining the superstructure in different arrangements produces a range of outputs that is, in turn, an approximation to the AR. Superstructure methods result in a system of algebraic equations and must be solved using a non-LP method. 

Geometric methods map closer to the geometric nature of the AR itself, and therefore these methods are also often easier to understand. Within the category of geometric construction methods, we can again categorize methods into two broad subclasses  

The algorithms described in this chapter deal mostly with candidate regions in concentration space alone. At present, some of the methods discussed are able to handle nonisothermal problems, such as those given in Chapter 7. Other methods possess the ability to compute candidate regions in residence time space (unbounded problems). As further research into AR construction methods continues, a broader range of techniques for the determination of the AR may be developed. 

Hereafter, we shall assume that constructions occur in concentration space. It will also be assumed that kinetics in a functional form—for use in the reactor equations—is available, and that a known feed point from which to generate the AR from has also been specified. 

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