The classical equations of two-phase flow in a porous media are solved together with two transport equations representing the leaching process. For the two-phase flow we use the pressure-saturation formulation, where the principal variables are the total pressure, the total flux and the saturation of the liquid phase. For the transport equations the variables of interest are the sulfuric acid and the copper concentration. The numerical method combines a mixed finite element method with a finite volume method. The first one is used to approximate the total pressure and flux, while the second is used to calculate the saturation and both concentrations. The advantage of this approach is its capacity to completely characterize the dynamics of the liquid and gaseous phase, and treat with the same model acid and bio-leaching processes. Several examples show the application of the method. (c) 2005 Elsevier B.V. All rights reserved.