this work examines the application of the hlavacek lumping technique to the substrate mass balance formulated within the cell suspension region of the hollow fiber immobilized whole cell biochemical reactor. in this ractor 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. 23 refs