A model to predict the transport of ionic species within the pore solution of porous materials, under the effect of an external electric field has been developed. A Finite Elements method was implemented and used for the integration of the Nernst-Plank equations for each ionic species considered. Electrical neutrality was continuously assured in the model by the inclusion of the Poisson-Boltzmann equation to the system of governing equations. Voltage differences were applied across the sample as boundary conditions in order to evaluate the competition between diffusion and electromigration terms in the transport process. As a modification of a previous work, water equilibrium was reestablished between iterations in the numerical method and the pH value monitored. Simulations were conducted in order to visualize the acid and basic fronts advance, and to evaluate the use of a buffer substance in the electrode compartments. Simulations were compared with lab scale results for desalination experiments, where an inert matrix of sandstone was used to minimize the effect of chemical reactions in the process.