A numerical model has been developed to describe the transport and reaction processes in a porous medium in an electrical field. The model discretizes the one-dimensional porous medium by a number of compartments. The governing equations are formulated by material balance over each compartment. The model describes transport processes of advection, dispersion, ionic migration and electroosmosis. Various reactions such as aqueous complexation, precipitation/dissolution, and electrochemical reactions are treated by kinetic approaches. For fast fluid-phase reactions such as complexation, local equilibrium assumption may be applied in the model, which reduces the number of primary components and hence the number of governing equations. The sorption processes occurring at the surfaces of the porous medium are at the moment treated only by a single-component linear isotherm. Numerical solution to the model gives concentration and electrical potential distributions in the porous medium at different times and gives as well the electrical current history. Modelling results for three sample cases are reported to demonstrate the application of the model. In the first sample case, the removal of copper from sand by an electrical field is simulated. The second case concerns an electrokinetic soil remediation process with cathode rinsing. The third case models the selective filtering function of the ion exchange membranes.