A mathematical model to simulate Heap (bio)-leaching process: An exact conceptual model, Homotopy theory and comparative insights with conventional methods

This paper attempts to address some nonlinear differential equations which describe main mechanisms governing heap (bio) leaching process as an important metallurgical facility in mining and mineral processing industries. The Homotopy Perturbation Method (HPM), Finite Volume Method and Analytical (Laplace) Method have been employed to provide proper solutions for these equations. Comparison was made between the methods and agreement was close; considering the fact that the proposed solution in comparison with the others provided a remarkable accuracy in dealing with nonlinear problems associated with mining and mineral processing industries. The maximum error of HPM in relation to the analytical solution was 0.02. The numerical finite volume method incorporating a computational fluid dynamics model termed PHOENICS provided rational and accurate results; describing that many chemical and biological processes extremely affect the transportation mechanism of the aqueous compounds in a heap structure and subsequently on the process efficiency. Besides, all solution methods presented to simulate heap leaching process provided valuable information related to the time dependence concentrations of dissolved compounds. The results obtained from this study can be effectively applied to manage the heap leaching costs to make the process feasible.