Cascading reactor-separator sets reduces total processing time for low yield Michaelis-Menten reactions: model predictions

Integration of reaction with separation has often been claimed to provide enhanced processing due to alleviation of processing constraints which, like equilibrium limitation or product inhibition, are common in enzyme-catalyzed reactions. In this paper, a mathematical model is developed to assess the effect of cascading sets of enzyme reactors and physical separators (which, when the number of sets tends to infinity, is equivalent to full integration of reaction and separation), when compared with the classical unit operation approach, in terms of total time required to effect reaction and separation for a given overall conversion. The analysis is laid out using several relevant reactional parameters [final conversion of substrate (χ(f)), equilibrium constant (K(eq) and dimensionless dissociation constants of substrate and product (K*(m,S), and K*(m,P))] and separational parameters [extent of separation in a single step (ζ) and ratio of time scales for molecular transport and chemical reaction (Ξ)]. Cascading provides a gain in processing time, up to an optimum at a finite degree of cascading, only for reaction-controlled processes (typified by low ζ, low Ξ, low K(eq), low K*(m,P), high χ(f) and high K*(m,S)); hence, full integration is not necessarily the best processing solution. Lengthening of the cascade leads to a decrease in the maximum substrate conversion while permitting higher degrees of product recovery.