Study of intraparticle diffusionreaction of substrate for Michaelis–Menten kinetics in a porous slab catalyst

The effect of internal diffusion on the overall reaction rate in a biocatalyst having slab geometry containing an immobilized enzyme or cells have been investigated theoretically. Zero-order, first-order and Michaelis-Menten kinetics were studied. The exact solutions for zero-order and first- order reactions were studied to verify our numerical algorithm which was later used to obtain solution for the Michaelis-Menten kinetic. The concentration profiles within the catalyst slab were obtained as a function of Thiele modulus which in turn were used to evaluate effectiveness factor. The exact solutions for zero and first order reactions can be obtained analytically. However one has to resort to numerical solution for Michaelis Menten kinetics as the resulting nonlinear differential equation cannot be solved analytically for the exact solution. Thus, for the Michaelis–Menten kinetics, the diffusion-reaction equation is solved using numerical method employing an explicit finite difference scheme which proved to be stable and accurate. A simple third order polynomial solution to the differential equation is also proposed. The approximate solution shows close agreement (error about less than 10%) with the numerical solution within the range of parameters of practical significance such as Thiele modulus values up to 8. Thus the approximate solution obtained in this work gives quite satisfactory results for a wide range of Thiele modulus compared to that reported in the literature. The nutrients diffuse deeper into the pellet with decreasing Thiele moduli for the three rate kinetics studied. The effectiveness factor decreases with increasing Thiele moduli which is in agreement with the trend in concentration profile for all the cases investigated and the range of parameters studied. Keywords: Diffusion-reaction; Michaelis–Menten kinetics; Immobilized slab biocatalyst; Finite difference method; Approximate solutio