This work is intended for the development of a numerical method to simulate flows and solute transport in multiphasical porous medium taking into consideration the interaction of solid/solute. More precisely, the studied problem is modeled by a coupled system composed of an elliptical equation (for the flow) and an equation convection-diffusion-reaction (for the transfer). Numerical simulations were realistic for two-dimensional problems confirming the stability and efficiency of the combined scheme in the characterization of a pollutant transport through an unsaturated zone of an industrial site.