Fundamental reactor types

Next we consider how the three fundamental reactor types found in AR theory may be expressed in terms of the mass fraction vector z. These expressions are derived directly from the molar versions of the same expression, and converted using the mass fraction formulae given in Sections 9.2.1-9.2.4. 

Invoking the definition of mass fi action residence time r and recognizing that r,(C) = r,(C(z)) results in 

2 CSTR The CSTR expression operating in mass fraction space is derived in a manner similar to the traditional CSTR expression in molar concentration space. A species molar balance around the CSTR operating at steady state 

V is the volume of the CSTR. The volumetric flow rate of the feed and effluent streams are no longer equal, and thus mass fractions must be employed instead. Using Equation 9.4, the molar CSTR expression may be written in terms of G, W, and z, to give 

Rearranging for the species mass fraction Zj in the CSTR product stream results in 

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Understanding the fundamental reactor types requires knowledge of the design equations of reaction engineering, which will be treated in short form here. Details can be foimd in text books dealing with chemical reaction engineering [6, T26]. 

A summary of fundamental reactor types is provided in Appendix A. 

In Chapter 4, we shall expand our knowledge of the geometric viewpoint to include reaction, and describe the function of three fundamental reactor types that are used in AR theory. With this knowledge, we will be in a position to generate candidate ARs efficiently, and use this information to form optimal reactor networks, which may be applied to optimize complex reactive systems. 

In much the same way that concentration can be viewed as a vector, it is possible to view a system of reactions as a vector as well. We now wish to explain how well-known reactor models, often studied in undergraduate chemical reaction engineering courses, can also be interpreted geometrically. In this section, we would like to describe the behavior of three fundamental reactor types PER, CSTR, and DSR. 

PFRs are the simplest of all three fundamental reactor types in AR theory. This is clear when the close link between the kinetics and PFR solutions trajectories can be shown. In Chapter 6, we will discuss why almost all optimal reactor structures must terminate with a PFR. 

Now that the physical, mathematical, and geometric nature of all three fundamental reactor types used in AR theory has been detailed, it is usehil to provide a summary of the results. Table 4.5 may be used as a point of reference for the problems that are described in later chapters. The ideas described in previous sections form the foundations of AR theory, and hence it is important that these concepts are understood well. 

THE THREE FUNDAMENTAL REACTOR TYPES USED IN AR THEORY... 

CONCEPT Three fundamental reactor types " V used in AR theory... 

When reaction and mixing are the only two processes present, the AR may be constructed using reactor combinations involving PFRs, CSTRs, DSRs and mixing only. There is no requirement to devise new (perhaps novel) reactor types that might serve to extend the AR boundary further. Instead, we can focus our attention on arranging combinations of these three fundamental reactor types in an optimal arrangement. 

A number of different reactor structures are given in Figure 6.7. Each structure is composed of different fundamental reactor types. Can you identify which reactor structure would form part of an optimal structure that resides on an exposed point of the AR boundary ... 

Structures (c) and (e) are both similar, as both structures involve combinations of a CSTR and PFR in series. It is known that the final approach to the extreme points of the AR take place as a result of the union of PFR trajectories, and thus we should expect that final fundamental reactor type of any optimal reactor structure on the AR boundary is a PFR. We may conclude that structure (e) does not produce an effluent concentration that is an exposed point on the AR boundary (although the effluent concentration may still lie on the AR boundary, the point will not be exposed). The CSTR feeding the PFR in (c) must therefore produce a concentration that is a point on the AR boundary. 

Note that given the correct kinetics and feed point, it is possible for all three fundamental reactor types to produce an effluent concentration that resides on the AR boundary. However, it is only the PFR that is able to produce exposed points on the AR boundary. 

The three-dimensional Van de Vusse system is considered a complete system in AR theory. The AR for the system is well understood and can be generated with confidence. This construction allows us to demonstrate (geometrically) the role that all three fundamental reactor types play in the formation of the AR boundary. It is not always easy to identify, beforehand, whether the true AR has been found or not, and thus this example is convenient because the true AR is guaranteed by theory. 

The properties of fed-batch reactors are such that they may assume several functions, corresponding to the continuous fundamental reactor types discussed in Chapter 4. This is easily understood by way of an illustrative example. 

Introduction In Chapter 7, under the context of batch reaction, it is demonstrated how the fed-batch reactor may be used to approximate the behavior of both the PFR and CSTR, and how the fed-batch reactor is the batch analogue of a DSR. It is therefore possible to construct a candidate AR, composed of all three fundamental reactor types, using only DSR trajectories. This is the basic premise behind the recursive constant control (RCC) policy algorithm (Seodi-geng et al., 2009). 

The Total Connectivity Model The connectivity model is a reactor superstructure formulation that attempts to approximate different reactor types using a network of small CSTRs. Combination of CSTRs in series and parallel allows for the approximation of different fundamental reactor types, specificdly ... 

Chapter 4 extended our understanding of the geometric viewpoint to include reaction. Systems of reactions, together with reaction stoichiometry, may be interpreted geometrically in the form of rate vectors, which allows us to view fundamental reactor types as geometric processes. 

Reaction may also be interpreted geometrically. Rate vectors are nsed to describe how reactions can be used to move through concentration space. Three fundamental reactor types are employed in AR theory the PFR, the CSTR, and the DSR. No other reactor type is required to generate the AR. Each reactor type exhibits its own characteristic geometric interpretation and each performs a crucial function in bnilding different parts of the AR bonndary. 

In Chapter 4, we discuss the role of three fundamental reactor types in attainable region (AR) theory. Many readers may already be familiar with these reactors, for they are common in chemical reaction engineering. A small, qualitative, summary of these reactors is provided in the following text. 

Chapter 4 In this chapter, we discuss how reaction may also be viewed from a geometric perspective. We introduce the three fundamental reactor types used in AR theory, and we also discuss additional properties of the AR related to reaction. 

There are three fundamental reactor types (1) a gasifier reactor, (2) a devolatilizer, and (3) a hydrogasifier (Figure 20.4) with the choice of a particular design depending on the ultimate product gas desired. 

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