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An approximate solution for the problem of diffusion-reaction in an isothermal catalyst pellet when coke deposition occurs was developed. The approximation is based on the linearization of reaction terms, producing analytical expressions to evaluate concentration profiles inside the pellet and the effectiveness factor. The approximate solution can be extended to any form of reaction rate functionalities for the main and coking reactions. Coke formation from reactants (parallel coking) or products (consecutive coking) and deactivation functions dependent on the coke content are considered in pellets with slab, cylindrical and spherical geometry.In this work, first-order kinetics for the main and coking reactions and linear and exponential deactivation functions were evaluated. The approximate predictions of the concentration profiles and the effectiveness factors were compared with results obtained by the complete numerical solution. A good agreement was found for both parallel and consecutive coking, including the cases when low and high intra pellet diffusion resistances are present.

An Approximate Analytical Solution for the Diffusion and Reaction Problem in a Catalyst Pellet in the Presence of Coke Formation