A theoretical model for enzymatic catalysis using asymmetric hollow fiber membranes

TLDR: A numerical finite difference solution for nonlinear Michaelis-Menten reaction kinetics is shown to agree with the analytic solution, as Km/C0, the ratio of the Michaelis constant to the initial substrate concentration, becomes large (> 100).

Abstract: The behavior of an immobilized enzyme reactor utilizing asymmetric hollow fibers is simulated using a theoretical model. In this reactor, an enzyme solution contained within the annular open-cell porous support structure of the fiber is separated from a substrate flowing through the fiber lumen by an ultrathin dense membrane impermeable to enzyme but permeable to substrate and product. The coupled set of model equations describing the behavior of this reactor represents an extended Graetz problem in the fiber lumen, with diffusion through the ultrathin fiber skin and reaction in the microporous sponge region. Exact analytic expressions for substrate concentration profiles throughout an idealized fiber which incorporate the membrane and hydrodynamic mass transfer resistances are obtained for a first-order enzyme reaction, and numerical techniques for their evaluation are given. This analysis is extended to yield a numerical finite difference solution for nonlinear Michaelis-Menten reaction kinetics, which is shown to agree with the analytic solution, as Km/C0, the ratio of the Michaelis constant to the initial substrate concentration, becomes large (> 100).