A spherical model catalyst with a diameter of 4 mm and a granular model catalyst of 10-20 mesh were prepared by ordered packing of 22-293 nm monodisperse SiO2 Particles, which were prepared through hydrolysis and condensation of alkoxysilanes, and then calcinned at 800 degrees C. A mathematical model of oil diffusing in the spherical model catalyst was established according to the material balance. Through Laplace transform an analytical solution of the model was obtained. By using the prepared model catalysts, the diffusion coefficient of Dagang vacuum residue fractions separated by supercritical fluid extraction and fractionation was determined with the mathematical model and was found to be 10(-10)-10(-11) m(2)/S. The diffusion coefficient increases with increasing pore diameter of the model catalysts and decreases with average molecular weight of the oil fractions. The diffusion is restricted for the oil fractions with an average molecular diameter of more than 2 nm in catalyst pores of less than 8 nm.