Effect of nutrient momentum and mass transport on membrane gradostat reactor efficiency

Abstract

Since the first uses of hollow-fiber membrane bioreactors (MBR’s) to immobilize whole cells were reported in the early 1970’s, this technology has been used in as wide ranging applications as enzyme production to bone tissue engineering. The potential of these devices in industrial applications is often diminished by the large diffusional resistances of the membranes. Currently, there are no analytical studies on the performance of the MBR which account for both convective and diffusive transport. The purpose of this study was to quantify the efficiency of a biocatalytic membrane reactor used for the production of enzymes. This was done by developing exact solutions of the concentration and velocity profiles in the different regions of the membrane bioreactor (MBR). The emphasis of this study was on the influence of radial convective flows, which have generally been neglected in previous analytical studies. The efficiency of the MBR was measured by means of the effectiveness factor. An analytical model for substrate concentration profiles in the lumen of the MBR was developed. The model was based on the solution of the Navier-Stokes equations and Darcy’s law for velocity profiles, and the convective-diffusion equation for the solute concentration profiles. The model allowed for the evaluation of the influence of both hydrodynamic and mass transfer operating parameters on the performance of the MBR. These parameters include the fraction retentate, the transmembrane pressure, the membrane hydraulic permeability, the Reynolds number, the axial and radial Peclet numbers, and the dimensions of the MBR. The significant findings on the hydrodynamic studies were on the influence of the fraction retentate. In the dead-end mode it was found that there was increased radial convective flow, and hence more solute contact with the enzymes/biofilm immobilised on the surface of the membrane. The improved solute-biofilm contact however was only limited to the entrance half of the MBR. In the closed shell mode there was uniform distribution of solute, however, radial convective flows were significantly reduced. The developed model therefore allowed for the evaluation of an optimum fraction retentate value, where both the distribution of solutes and radial convective flows could be maximised.