A distributed parameter model for downward percolation leaching

Abstract

The first mathematical dissolution models were developed as early as 1846 for very simple and idealised situations. Since then, many other models have been developed, generally using semiempirical relationships. A new mathematical model totally based on the phenomenology of leaching is proposed. Formally, the model is a distributed parameter system where all the parameters have a precise physical sense which allows to measure them physically in a laboratory. The model consists of a three first order partial differential equations system, the first describing the space-time evolution of the concentration of the leaching agent. The second one outlines the behaviour of the metal in the solid phase in the same domain, and the last one describes the variation of the concentration in metal transferred from solid phase to liquid as a consequence of the depletion in the leaching agent. The physical reality undoubtedly defines both the initial and the boundary conditions. It also suggests a chained integration sequence and the applicability of numerical methods. Because there is not a known analytical solution for the system of PDE, numerical methods - finite differences were used. The stability of the solution was studied in detail as a function of discretization of the domain. The simulations performed using the model showed a high agreement when compared to experimental data, proving its robustness.