Over the last 10 years the design of catalyst particles and porous structures has made considerable progress. Due to the complicated interaction of diffusion and reaction in catalysts, more detailed models of porous structures are needed. We have based our model on a three-dimensional network of interconnected cylindrical pores as pore model, although the treatment is applicable to alternative pore geometries, e.g., slit pores. The network assumed has predefined distributions of pore radii, connectivity, and porosity. Mass transport in the individual pores of the network is described by the dusty-gas model. In contrast to 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 mass balances within the entire network, the mass balances for individual pores have to be solved simultaneously, since these mass balances are coupled by the boundary conditions at the nodes of the network. The system of differential equations has been solved by the finite-difference method. To solve the resulting large nonlinear system, a Schur complement method was employed. Due to a decoupling technique, the Schur complement method has relatively small computer storage requirements. The use of the algorithm is demonstrated for a complex reaction network.