A random three-dimensional pore network of interconnected pores was taken as a model of the porous structure of catalyst supports. Multicomponent Knudsen, molecular and surface diffusion were modelled according to the dusty gas model. In contrast to most previous publications, the present network model can be applied to any common reaction kinetics. This becomes quite inevitable in order to make three-dimensional network models applicable to practical problems in industry. To solve the model equations a globally convergent solver for nonlinear equations is introduced which may be transfered to many other problems in chemical engineering. The computations are compared with measurements in a single-pellet diffusion reactor. It turned out that surface diffusion may contribute significantly to the fluxes in a catalyst support.