Multistationarity in kinetic models of continuous flow stirred tank reactors

3 Multistationarity in kinetic models of continuous flow stirred tank reactors 

In this field, as in any other part of reaction kinetics, there are two approaches investigation of simple, but possibly realistic models see, for example, Caram Scriven (1976), Othmer (1976), Luss (1980, 1981) Gray Scott (1983a, b) or the example of Horn Jackson (1972, cited here as Exercise 1) or a search for general criteria that ensure or exclude multistationarity in large classes of mechanisms. This second approach was initiated by Rumschitzky Feinberg (in preparation Rumschitzky, 1984). Here we present results of this second approach, and some of the Problems contain results on specific models derived using the first approach. 

The theorems by Feinberg, Horn, Jackson and Vol pert provide sufficient conditions to exclude multistationarity. These theorems can be applied in the case of homogeneous systems, and in the case of inhomogeneous systems, if the system can be modelled by formal elementary reactions as shown several times above. An especially important case of an inhomogeneous systems is the isothermal continuous (flow) stirred tank reactor (CSTR). By a CSTR we mean one in which there is perfect mixing and in which, at each instant, every component within the reaction vessel is also contained in the effiuent stream. 

Investigation of several examples shows that the deficiency of the models of these reactors is usually more than zero, and their Vol pert graph is usually cyclic. The authors mentioned above started another approach to avoid these problems. Their results belong to two different classes some of them come from the direct investigation of formally homogeneous models of CSTRs and others of them come from the application of the deficiency one theory. Before applying this theory it must (and can) be shown that chemically relevant assumptions define a class of models with deficiency one. 

Now let us turn to the simplest results in the first class to the theory specifically devised to treat reactions in CSTRs. It turns out that it is only the structure of the mechanism in the reactor that counts. 

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