A model for the reactive transport of matter through porous media induced by an externally applied electric field is discussed. The Nernst–Planck–Poisson system of equations is used for modeling multi-species electro-diffusion transport phenomena, assuming chemical equilibrium during the process. The system of equations includes the transport of water and the resulting advective flow of the aqueous species. The model takes into account transient change in porosity and its impact on transport. Test examples were performed and compared to experimental data for electrokinetic desalination treatment of yellow bricks contaminated with chloride salts.