The Search for a Sufficiency Condition

The absence of a sufficiency condition— which will signify when the true AR has been determined—presents a large theoretical challenge for both AR theorists and practitioners who employ AR theory to solve reactor synthesis problems. Without a sufficiency condition, there is no certainty that the regions produced are the true AR. This is true even if the region computed has been generated from an automated AR construction method, such as those described in Chapter 8. Only for systems of a simplified or unique nature (i.e., when a rate field contains completely convex PFR trajectories), or for systems that have been well studied (i.e.. Van de Vusse kinetics), is one confident that the true AR has been foimd. 

Although Chapter 6 discusses how precise conditions exist for computing critical DSRs and CSTRs, the complex nature of the resulting equations not only provides a rigid set of constraints but also brings about uncertainty related 

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In this chapter, we wish to touch on a number of automated AR construction schemes. At the time of writing, research in AR theory has witnessed a shift toward the development of numerical AR constmction algorithms, with less emphasis placed on general AR theory. These developments have arisen primarily out of a practical need to determine candidate regions for complex, higher dimensional problems, which are not easily computed by hand, but which are still important for practical problems of interest. AR construction methods provide a numerical basis wherefrom theoretical predictions may be compared with in the search for a sufficiency condition. Inasmuch as how... 

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