A theoretical analysis of transport phenomena in a hollow fiber membrane bioreactor with immobilized biocatalyst

The behavior of a hollow fiber (HF) membrane bioreactor with entrapped biocatalyst is analyzed and characterized from a theoretical point of view. The model is based on the numerical solution of the dimensionless balance equations governing mass transfer within the regions that can be defined for this reacting system, namely the fiber lumen, the membrane dense and spongy layers. The chemical reaction is supposed to take place solely in the last two regions (skin and sponge) where the biocatalyst is confined by entrapment and distributed according to the ratio E-3/E-2. The evaluation of the significant transport mechanisms of the substrate consumption rates, and more generally of the reactor performance have been carried out by analyzing two representative parameters, i.e. the effectiveness factor and the performance index, as functions of the operating conditions, expressed in terms of a set of characteristic dimensionless groups. The enzyme distribution ratio, E-3/E-2, its overall loading, the applied trans-membrane pressure (TMP) difference, the substrate feed concentration were investigated as the system key parameters. The reaction kinetics have been modeled with reference to Michaelis-Menten rate equation, modified to account for possible substrate and product inhibition. The results of the theoretical analysis enable to predict an optimal value of TMP and, therefore, of the permeate flux, as a trade-off between the necessity of reducing the transfer resistances in the substrate access to enzyme and that of allowing suitable residence time. The bioreactor performances are no longer affected by the distribution ratio E-3/E-2, once that this parameter has reached almost unity value: this means that the enzyme can be effectively immobilized just in the membrane spongy region, with the advantage of a significant system simplification from both a technological and an economic standpoint. The model, however, is quite general and can be applied also to different reacting systems, in order to evaluate how the catalyst position within a specific support can affect their performances. A comparison between the theoretical model predictions and some literature experimental data has been also attempted, showing a good agreement for some typical operating conditions. (C) 2002 Elsevier Science B.V. All rights reserved.