Whole‐cell hollow‐fiber reactor: Effectiveness factors

Abstract

AbstractAnalytical expressions, which allow the generation of effectiveness factor graphs for a reactor system employing immobilized whole cells a biocatalyst, are presented. In particular hollow‐fiber devices (such as dialysis or ultrafiltration units) are considered. Such devices are analogs to a shell‐and‐tube heat exchanger. Whole cells are entrapped on the shell side: a nutrient solution is circulated through the tubes, substrate diffuses from the tube side, across the fiber, and into the cell mass on the shell side, where it irreversibly reacts to form product. The product back‐diffuses into the circulating nutrient solution. The overall substrate mass‐transfer process is hypothesized to be either diffusion limited in the hollow‐fiber tube wall and/or the shell‐side cell suspension and/or reaction limited at the enzyme sites within the whole cells. The first‐ and zero‐order limits of the Michaelis‐Menten rate law are used in generating effectiveness factor expressions. The effectiveness factor is a function of reaction order, Thiele modulus, diffusion coefficient ratio (defined as the effective substrate diffusivity in the hollow‐fiber membrane wall divided by the effective substrate diffusivity in the cell suspension), partition coefficient, volume of the cell suspension, and hollow‐fiber width. Equations for the effectiveness factor are also detailed when the hollow‐fiber mass‐transfer resistance is far greater than the cell suspension mass‐transfer resistance. An effectiveness factor chart is presented specifically for the commercially available C‐DAK 4 dialyzer (Cordis Dow Co., Miami, Florida). In general terms the effectiveness factor expressions are applicable for characterizing diffusion and reaction within a catalytically active cylindrical annulus, Whose inner surface offers a diffusional resistance and whose outer surface is impermeable to reactants. Some generalization of the Thiele modulus is undertaken which serves to draw the asymptotes on the effectiveness factor charts together. Comment is made on the variation of the slope of the effectiveness factor graph and its relation to the change in the observed reaction activation energy. Possible application of the model to the catalytic tube wall reactor is discussed.