Applications of Markov Chains in Chemical Reactions

Chemical reactions occur due to collisions between similar or dissimilar species. The collision process requires, first of all, the coming together of molecules, which is of probabilistic or stochastic nature. Thus, chemical reactions may be looked upon as probabilistic or stochastic processes and more specifically as a Markov chain. According to this model, concentration of the species at time (n+1) depends only on their concentration at time n and is independent on times prior to n. Therefore, the governing equations for treating chemical reactions, as elaborated later, are Eqs.(2-23) and (2-24) below, derived in Chapter 2  

The application of the equations to chemical reactions requires the proper definition of the above quantities as well as correctly defining the transition probabilities pjj and pjk this is established in the following. It should also be noted that the models derived below for numerous chemical reactions, are applicable to chemical reaction occurring in a perfectly-mixed batch reactor or in a single continuous plug-flow reactor. Other flow systems accompanied with a chemical reaction will be considered in next chapters. 

Throughout this chapter it has been decided to apply Markov chains which are discrete in time and space. By this approach, reactions can be presented in a unified description via state vector and a one-step transition probability matrix. Consequently, a process is demonstrated solely by the probability of a system to occupy or not to occupy a state. In addition, complicated cases for which analytical solutions are impossible are avoided. 

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