Optimal design of continuously stirred membrane reactors in series using Michaelis-Menten kinetics with competitive product inhibition: theoretical analysis

Analytical expressions were derived for the optimal design (based on the minimum of the volume of the total number of reactors) of N continuously stirred membrane reactors (CSMRs) performing the enzyme-catalyzed reaction described by Michaelis-Menten kinetics with competitive product inhibition. The influence of membrane selectivity for both substrate and product on the total dimensionless residence time of the reactors (overall volume) was determined. The optimal design of N CSMRs (variable volume reactors) was compared with equal volume membrane reactors required to achieve the same degree of substrate conversion. The effect of kinetic and operating parameters on the performance of membrane reactors was determined. Optimization results show that membrane reactors are superior to continuously stirred tank reactors (CSTRs) in series at a high substrate rejection coefficient and low product rejection coefficient, high substrate conversion and using a small number of reactors. Also a high dimensionless Michaelis-Menten constant, high dimensionless inhibition constant and low substrate concentration in the feed to the first reactor improved the performance of the membrane reactors vs. CSTRs in series. The reduction in total volume of the optimal membrane reactors compared to CSTRs in series was up to 86% for the conditions in this work. A comparison between the optimum and equal volume design of membrane reactors in series showed no major difference in total volume between the two design criteria at a practical range of operating conditions. A volume reduction up to 16% was observed for the conditions in this work.