This paper dealt with the development of a two-dimensional (2D) mathematical model for column leaching and confirmed the important simulation parameters through experiment. The unsaturated state of the variably saturated flow column and the solute transport of copper ions were studied during leaching. The fluid flow problem was handled using the Richards equation on the premise of an ambient pressure column air, where the van Genuchten formulas were applied to define the nonlinear relationships of pressure head with the retention and permeability properties. The ore column permeability test gave a varied hydraulic conductivity, which was analyzed in the model. In the solute transport problem, the copper ion concentration was solved using the advection-diffusion-reaction equation whose reaction term was determined by the joint analysis of experimental copper leaching rate and the shrinking core model. Particle- and column-scale leaching tests were carried out to illustrate the difference and connection of copper extraction in both processes. This fluid flow and solute transport coupled model was determined through the finite element method using the numerical simulation software, COMSOL Multiphysics.