In this paper, a theoretical framework is presented for the design of hollow fiber membrane bioreactors (HFMBs) operated in closed-shell mode in the presence of high recirculation flows in the cell compartment. Navier–Stokes and Brinkman equations were used to describe fluid transport, and the convection-diffusion-reaction equations to describe transport of dissolved oxygen and glucose to cells. Numerical solutions were sought with the finite element method for the high permeability typical of n