CSTR general features

In this chapter, we develop the basis for design and performance analysis for a CSTR (continuous stirred-tank reactor). The general features of a CSTR are outlined in Section 2.3.1, and are illustrated schematically in Figure 2.3 for both a single-stage CSTR and a two-stage CSTR. The essential features, as applied to complete dispersion at the microscopic level, i.e., nonsegregated flow, are recapitulated as follows ... 

Three model kinetic schemes have been studied relatively intensively with periodic forcing the first-order non-isothermal CSTR of chapter 7 the Brusselator model, which is closely related to the cubic autocatalysis of chapters 2 and 3 and the surface reaction model discussed in 12.6. We will use the last of these to introduce some of the general features. 

Another important reaction supporting nonlinear behaviour is the so-called FIS system, which involves a modification of the iodate-sulfite (Landolt) system by addition of ferrocyanide ion. The Landolt system alone supports bistability in a CSTR the addition of an extra feedback chaimel leads to an oscillatory system in a flow reactor. (This is a general and powerfiil technique, exploiting a feature known as the cross-shaped diagram , that has led to the design of the majority of known solution-phase oscillatory systems in flow... 

The choice of a reactor is usually based on several factors such as the desired production rate, the chemical and physical characteristics of the chemical process, and the risk of hazards for each type of reactor. In general, small production requirements suggest batch or semi-batch reactors, while large production rates are better accommodated in continuous reactors, either plug flow or continuous stirred tank reactors (CSTR). The chemical and physical features that determine the optimum reactor are treated in books on reaction engineering and thus are not considered here. 

Therefore, we can generalize the previous discussion to say that aU qualitative features of multiple steady states in the CSTR remain unchanged for the nth-order irreversible reaction as long as is obeys positive-order kinetics. We will consider zeroth-order and negative-order kinetics in problems. 

The influence of activity changes on the dynamic behavior of nonisothermal pseudohomogeneoiis CSTR and axial dispersion tubular reactor (ADTR) with first order catalytic reaction and reversible deactivation due to adsorption and desorption of a poison or inert compound is considered. The mathematical models of these systems are described by systems of differential equations with a small time parameter. Thereforej the singular perturbation methods is used to study several features of their behavior. Its limitations are discussed and other, more general methods are developed. 

Aris et al. have primarily analyzed whether the steady-state multiplicity features in a CSTR arising from a cubic rate law also can arise for a series of successive bimolecular reactions [26]. Aris et al. have showed that the steady-state equations for a CSTR with bimolecular reactions scheme reduces to that with a cubic reaction scheme when two parameters e(=k,Cg/k j) and K(=kjC /k j) arising in system equations for the bimolecular reactions tend to zero. Aris et al. have shown that the general multiplicity feature of the CSTR for bimolecular reactions is similar to that of the molecular reactions only at smaller value of e and K. The behavior is considerably different at larger values of e and K. Chidambaram has evaluated the effect of these two parameters (e and K) on the periodic operation of an isothermal plug flow reactor [18]. 

Chaos has been observed in a number of chemical systems, but by far the most thoroughly studied is the BZ reaction. In this section, we illustrate some features of chaos in the BZ reaction in a CSTR. There appear to be two different regions of chaos in the BZ system, generally referred to as the high-flow-rate (Hudson et al., 1979 Roux et al., 1980) and the low-flow-ratc (Turner et al. 1981 Roux et al., 1983) regions. The next section lists examples of chaotic behavior in other chemical systems. 

First, a single wire problem will be considered as an introduction. It brings out essential features of the stability problem and is similar in many respects to the more familiar stability problem with a CSTR. A simple and yet realistic case of negligible internal heat transfer and external mass transfer resistances will also be treated. The general problem will then be analyzed in a limited form for the case of unit Lewis number (Le) appearing in Eq. 8.27. This considerably simplifies the problem and yet the result can be extended to a certain extent to the general case of arbitrary Lewis numbers. Readers interested in more details on stability can refer to the book by Aris (1975) and the review by Luss (1977), from which the subsequent sections are derived. 

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