The whole cell hollow fiber reactor—III: Comparison of reactor efficiencies using a Hlavác̆ek lumping technique

Abstract

This work examines the application of the Hlavác̆ek lumping technique to the substrate mass balance formulated within the cell suspension region of the hollow fiber immobilized whole cell biochemical reactor. In this reactor whole cells (the biocatalysts) are entrapped on the shell side of a hollow fiber dialyzer reactor unit. Substrate solution flows through the dialyser tube side from where it diffuses across the hollow fiber wall into the stagnant cell suspension and reacts irreversibly to form product. Products then back-diffuse to the tube side. The lumping technique allows the dimensionality of the differential substrate balance to be reduced, thereby allowing it to be directly compared with the substrate balance formulated around the entire reactor system. In this way, dimensionless equivalent continuous flow stirred tank reactor holding times are computed for a single hollow fiber surrounded by a cylindrical catalytic cell suspension annulus. Ratios of these dimensionless holding times provide a measure of the relative efficiencies of different sizes of hollow fiber reactor systems. This information may be of use in the optimal design of hollow fiber reactors. The application of the method to porous catalyst pellets is briefly discussed.