For the reaction of ethylene catalytic oxidation to ethylene oxide over a gear-shaped catalyst particle

a three-dimensional reaction-mass transfer-heat transfer model is developed to calculate effectiveness factor of the catalyst. Effective diffusivities and effective thermal conductivity are the function of temperature and concentration distribution in catalyst particle. The finite element method is employed to solve the set of highly nonlinear partial differential equations

and the values obtained agree well with those given by literatures. Geometric external surface area is a key parameter for the effectiveness factor. The effectiveness factor is 0.1804 for gear-shaped catalyst with geometric external surface area of 1862 m2·m-3

and 0.0993 for cylindrical catalyst with geometric external surface area of 924 m2·m-3. The quantitative calculation for reaction-transport phenomena in a single catalyst particle could be a guide for catalyst design and a basis for multi-scale simulation of coupling hydromechanics and catalytic reaction-transport phenomena.