Analysis of autocatalytic reactions with Michaelis-Menten kinetics in an isothermal continuous stirred tank reactor

Abstract

A systematic analysis of the behavior of autocatalytic reactions obeying Michaelis-Menten kinetics and taking place in an isothermal continuous stirred tank reactor is presented. The mathematical model is solved for general nth-order autocatalysis and the dimensionless steady-state conversion as a function of dimensionless residence time, the local stability of the stationary states and the instability type and region in parameter space bifurcation diagrams are determined. The stability-instability diagrams are very different for n > 1 compared to n = 1 (quadratic autocatalysis). The simulations are extended over five decades of dimensionless residence time to characterize in detail the wealth of dynamic behavior exhibited by such systems. Analytical expressions are also derived for the maximum autocatalyst concentration obtained in such systems with both linear and Michaelis-Menten kinetics. Finally, some qualitative connections are drawn between the autocatalytic model employed here and the varied patterns of behavior observed in the biological process of glycolysis.