Applications of Markov Chains in Chemical Reactors

The major aim of the present chapter is to demonstrate how Markov chains can be applied to determine the behavior of a complicated system with respect to the residence time of fluid elements flowing through it. In other words, to obtain the response of the system to some tracer input, usually in the form of a pulse. 

It is well-known that fluid elements entering simultaneously a continuous reactor, do not, in general, leave together, owing to the complex flow pattern inside the reactor. Because of this reason, there is a spread of the residence time of the flowing elements, i.e. the time each element resides in the reactor the latter can be represented by the so-called age distribution function. Thus, if a chemical reaction is carried out in a reactor, the resulting products depend on the length of time each element of the reactants spends within the reactor, which affects the overall conversion. 

Several models have been suggested to simulate the behavior inside a reactor [53, 71, 72]. Accordingly, homogeneous flow models, which are the subject of this chapter, may be classified into (1) velocity profile model, for a reactor whose velocity profile is rather simple and describable by some mathematical expression, (2) dispersion model, which draws analogy between mixing and diffusion processes, and (3) compartmental model, which consists of a series of perfectly-mixed reactors, plug-flow reactors, dead water elements as well as recycle streams, by pass and cross flow etc., in order to describe a non-ideal flow reactor. 

In the following, approach (3) above was adopted. Stimulating the resulting flow configuration by some input, yields the residence time distribution of fluid elements in the flow system. In the present chapter, the flow system was treated 

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