Optimum design of a series of CSTRs performing reversible Michaelis-Mentenkinetics: a rigorous mathematical study

The optimum design of a given number of CSTRs in series performing reversib le Michaelis-Menten kinetics in the liquid phase assuming constant activity of the enzyme is studied. In this study, the presence of product in the fe ed stream to the first reactor, as well as the effect of the product interm ediate concentrations in the downstream reactors on the reaction rate are i nvestigated. For a given number of N CSTRs required to perform a certain de gree of substrate conversion and under steady state operation and constant volumetric flow rate, the reactor optimization problem is posed as a constr ained nonlinear programming problem (NLP). The reactor optimization is base d on the minimum overall residence time (volume) of N reactors in series. W hen all the reactors in series operate isothermally, the constrained NLP is solved as an unconstrained NLP. And an analytical expression for the optim um overall residence time is obtained. Also, the necessary and sufficient c onditions for the minimum overall residence time of N CSTRs are derived ana lytically. In the presence of product in the feed stream, the reversible Mi chaelis-Menten kinetics shows competitive product inhibition. And this is, because of the increase in the apparent rate constant K-m' that results in a reduction of the overall reaction rate. The optimum total residence time is found to increase as the ratio (psi(0)) of product to substrate concentr ations in the feed stream increases. The isomerization of glucose to fructo se, which follows a reversible Michaelis-Menten kinetics, is chosen as a mo del for the numerical examples.