A new process is introduced for saturated steam generation in porous media. The process consists of applying an electrical potential between two electrodes in contact with a porous medium (rockwool) impregnated with an ionic solution (water and mineral salts) resulting in a Joule-effect heating. Tap water is fed into the system, introducing soluble salts which increase the conductivity and insoluble salts which modify the porosity. The coupled partial differential equations, derived from the simplified balance equations of energy, motion and diffusion, have been written and solved using a centered finite difference method and are compared favorably to experimental results. The movement of the liquid is modeled using a capillary diffusion of the liquid phase.