A stochastic treatment of unimolecular reactions in an unsteady state continuous flow system

A stochastic approach, namely a continuous time Markov chain (Markov process), is employed to analyze and model, in a unified fashion, both the kinetics of unimolecular reactions and mixing accompanied by flow in a continuous flow reactor under an unsteady state operation; the results reduce to those under the corresponding steady state operation in the limit as t→∞. This approach can be applied to both the time homogeneous and heterogeneous processes. The transitional distributions of the number of molecules of each type inside the reactor as well as at the exit are formulated. The treatment leads to the general expressions for the transient internal and exit age distributions of molecules in the flow reactor. The life time distribution of molecules under steady state is also derived. The statistical basis of the residence time distribution theory for flow reactors is clarified. The approach is illustrated with two examples.