Operation of a perfusive catalytic membrane with nonlinear kinetics

Abstract

Operation of a perfusive catalytic curved membrane is systematized into different transport-reaction regimes. The internal viscous permeation improves the catalyst performance, measured here by the effectiveness factor and by its enhancement relative to purely diffusive conditions. A theoretical analysis is presented for nonlinear kinetic expressions, which are suitable to describe the consumption of a reactant in many (bio)catalytic systems. The kinetic and transport parameters required to attain maximum enhancement are related by simple design rules, which depend on the form of the reaction rate law (namely on the order of reaction and dimensionless inhibition constant). For zero-order reactions, these optimum conditions correspond to attaining negligible concentration at a position inside the membrane, while may be interpreted in general as separating situations of severe mass transfer resistance from cases of high effectiveness. It is important to incorporate the correct form of the kinetic expression in the analysis, so that the predictions can be used in a quantitative manner. The results for the different regimes are compiled in enhancement plots and in Peclet-Thiele diagrams. Moreover, the study also yielded new results for the nonlinear reaction-diffusion problem in a curved membrane with its two surfaces exposed to different concentrations, a case of relevance in membrane reactors.