Calculation of Effectiveness Factors in Spherical Shells

Abstract

The calculation of reaction rates in biofilm shells is needed for the design of biological fixed-film reactors. Most biological reactions are nonlinear and require a numerical solution of the material balance equations. The method of orthogonal collocation is successfully adapted to spherical-shell geometry to calculate effectiveness factors with a small number of trial functions. New trial functions were developed that are superior to those used previously for problems extending to the particle center. The formulation is able to accommodate varying degrees of curvature and film thickness, and diverse boundary conditions on the inner surface. Examples of the accuracy of the numerical solutions are given for Michaelis-Menten kinetics.