Electrokinetic processes are known as the mobilization of species within the pore solution of porous materials under the effect of an external electric field. A finite elements model was implemented and used for the integration of the coupled Nernst-Plank-Poisson system of equations in order to simulate the transport process of ionic species and the modeling of electrokinetic remediation techniques. The electrode half-reactions were included in the model. The charge unbalance produced was used for satisfying the voltage differences applied as boundary conditions in the system. In addition to this, water equilibrium was continuously assured and the pH value monitored. Results from a test example simulation of the desalination of a sample of porous material contaminated with NaCl are shown.