(694j) Mathematical Modelling of the Heap Leaching Process

This work is focused on the development of a simple mathematical model of copper heap leaching, able to predict the concentrations profiles of sulphate ion (SO4-2), as the leaching agent, and copper ion (Cu+2), both as a function of time. The model is based on the conservation equations applied in the heap, neglecting temperature and deformation effects. The system is considered as an isotropic porous media with porosity homogeneously distributed. An exact solution to this problem will be of utility if the optimal operational parameters are needed. Specifically, the system is considered as a three phase problem, with liquid, solid and gaseous phases, in which the transport problem is modelled considering the components sulphuric acid in liquid phase and copper's ions in liquid and solid phase. The main transport mechanism of Cu+2 through heap is advection through liquid phase. However the small amounts of Cu+2 in the leaching solution do not affect the liquid flow. Therefore, the model assumes that it is possible to uncouple the transport equations to solve the liquid flow independently. Analytical solutions for the liquid phase flow are based on the solution of the Richards' equation, Gardner retention curves, and exponential dependence of the heap permeability with liquid content. This configuration is useful to describe the liquid flow in saturated or unsaturated conditions. In order of achieving an exact solution, techniques, such as linearization, variable transformations, and perturbation analysis are useful in the development of the model. The second part of this work is focused on the study of the effects of several operational parameters (temperature, pH of the leaching agent, heap granulometry, etc.) on the amounts of recovered copper. These experimental data were used for validating the model predictions. Results agree with experiments and other works previously reported.