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A numerical model for predicting diffusivity in a biocatalyst particle with heterogeneous reactions



Determination of effective diffusivity of a substrate in biocatalyst particles is a key requirement in modeling heterogeneous reactions. The diffusivity is mainly controlled by the molecular-diffusion characteristics of the substrate, the tortuousness of the diffusion path within the biocatalyst, and the void fraction of particle volume available for diffusion. A general numerical model describing reactions in a biocatalyst particle following zero-order, first-order, and Michaelis-Menten kinetics was developed. Finite volume method was used to discretize the nonlinear second-order differential equation, and tridiagonal matrix algorithm was applied to solve the algebraic equation iteratively after discretization. Computer codes were written for calculating the diffusivity under specified boundary conditions. The numerical solution of the diffusion-reaction equations was validated against the experimental data from literatures. The model was further calibrated with experimental data obtained from fungal pellet experiments and then verified using additional data. The results show that the inverse methodology developed in this study was capable of predicting diffusivity in biocatalyst particles. Based on the predicted diffusivity, oxygen consumption by an individual pellet was simulated, oxygen consumptions by small versus large pellets were compared, and the effect of reaction rate on oxygen consumption was evaluated. © 2008 American Institute of Chemical Engineers AIChE J, 2008

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