A theoretical model for enzymatic catalysis using asymmetric hollow fiber membranes

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).

Enzymatic membrane reactor for the kinetic resolution of racemic ibuprofen ester: modeling and experimental studies

“…Membrane as a carrier for enzyme immobilization was first reported by Rony (1972), followed by Lewis and Middleman (1974), Waterland et al (1974) and Webster and Shuler (1978). The reactor performance can be modeled by formulating differential equations on the diffusion, reactant consumption or product formation at each location.…”

Modeling of Axial-Flow Hollow Fiber Cell Culture Bioreactors

“…The most notable work is that of Waterland et al (1974). In their model, the transport in the lumen is a mass balance that includes radial diffusion and convection with fully developed parabolic profile:…”

Mathematical models for hollow‐fiber enzyme reactors

“…and Waterland et al , 9 who considered substrate concentration gra-dients in a single hollow fiber. If the recycle ratio (defined as the volumetric flow rate through the dialyzer tubes, divided by the reactant volumetric fresh feed rate to the system) is high ( a lo), our system can be modeled as a continuous-flow stirred-tank reactor,22 which maintains constant catalytic activity owing to an actively growing cell suspension being slowly circulated through the dialyzer shell side.…”