In this paper a two-dimensional solute transport model is considered to simulate the leaching of copper ore tailing using sulfuric acid as the leaching agent. The mathematical model consists in a system of differential equations: two diffusion-convection-reaction equations with Neumann boundary conditions, and one ordinary differential equation. The numerical scheme consists in a combination of finite volume and finite element methods. A Godunov scheme is used for the convection term and an P1-FEM for the diffusion term. The convergence analysis is based on standard compactness results in L2. Some numerical examples illustrate the effectiveness of the scheme.