Modeling solution mining technique has recently received much attention in order to estimate metal recovery rates. We studied the acid leaching of Cu minerals found in mine tailings using a mathematical transport model and lab-scale experiments on both batches and saturated soil columns. The model is a one-dimensional macroscopic solute transport model that considers simultaneously (i) the convection, dispersion, and consumption of H2SO4, and (ii) the convection, dispersion, solubilization, and adsorption-desorption of Cu. Time-dependent batch experiments were carried out to understand the relationship between H2SO4 consumption and Cu extraction in tailing Cu materials under stagnant conditions. Additionally, miscible-displacement experiments were conducted to obtain empirical data on Cu recovery in saturated soil columns that receive a constant pulse of H2SO4 and were designed to check the model's capability to simulate the transport phenomena. This was done by estimating the model parameters independently from the batch experiments. Since some findings from both experiments were consistent with each other, modeling assumptions, such as a second-order kinetic relationship for Cu dissolution (by H2SO4) and a first-order equilibrium isotherm for Cu, were appropriate in order to simulate the Cu recovery concentration at the outlet of each column. Finally, model equations were solved using finite differences and analytical solutions for Cu and H2SO4 transport equations, respectively, and model parameters were estimated using least squares techniques.