PurposeThe purpose of this paper is to apply the numerical methods to study the heap leaching process in a bed of porous and spherical ore particles. This study is performed in two stages: first, modeling the leaching process of a soluble mineral from a spherical and porous ore particle to obtain the distribution of mineral concentrations, leaching solvent concentration and dissolved mineral in the particles (the particle model), and second, modeling the heap leaching of the mineral from a porous bed consisting of spherical and porous ore particles to obtain the distribution of mineral concentrations, leaching solvent concentration and dissolved mineral in the bed (the bed model).Design/methodology/approachThe governing equations are derived for the particle model, and then converted into non‐dimensional form using reference quantities. The non‐dimensional equations are discretised on a uniform spherical grid fitted to the particle using finite difference method. The resulting algebraic equations are solved using Tri‐Diagonal Matrix Algorithm, and the governing equations are derived for the bed model, and then converted into non‐dimensional form using reference quantities. The non‐dimensional equations are discretised explicitly on a one‐dimensional and uniform grid fitted to the bed. The unknown quantities are evaluated using the corresponding values at the previous time interval.FindingsThe results obtained from numerical modeling show that, when the particle has a low diffusion resistance or a high chemical resistance, the reaction takes place slowly and homogeneously throughout the ore particle. On the other hand, when the bed has a low convection resistance, the reaction takes place homogeneously throughout the bed. As the convection resistance increases, the non‐homogeneous (local) behavior predominates. It is also noticed that, when the chemical reaction resistance is high, the reaction takes place homogeneously throughout the bed.Research limitations/implicationsThe dynamic diffusion and movement of solution in the ore particles and ore bed are not modeled and volumetric ratio of solution in the particles and the bed and also vertical velocity of solution in the bed are assumed to be fixed constants.Practical implicationsThis study shows that the reaction takes place homogeneously throughout the bed when the convection resistance is low, the diffusion resistance is high, the concentration resistance is low, and the chemical reaction resistance is high.Originality/valueHomogeneous reaction conditions being suitable for heap leaching operations are identified. Thus, it is recommended to approach the above conditions when preparing ore heaps and designing the relevant operation.