Upscaling the microscopic processes in charged porous media which are responsible for pore pressure evolution and swelling is a topic of ongoing research. Current theories assume homogeneous media with uniform pore sizes and the impact of microscopic heterogeneity is neglected. This is a preliminary study to determine the significance of such pore-scale heterogeneity on the pressure evolution in charged porous media, where we neglect deformation of the solid phase. We present a pore-network model to simulate salt transport and pressure evolution in a charged porous medium. Results show that, for pore radii following a log-normal distribution, the average pressure in heterogeneous networks are significantly lower than in homogeneous networks with the same mean pore size. This is expressed by lower average pressures, as well as lower streaming potentials and faster ion transport rates in heterogeneous networks. These results indicate that heterogeneity in charged porous media should be investigated further.