Models for apparent reaction kinetics in heap leaching: A new semi-empirical approach and its comparison to shrinking core and other particle-scale models

Abstract

Particle-scale effects are critically important to the performance of heap leaching operations. In a heap-scale simulation, the transport of fluid phases and reactive species external to the ore particles might be modelled with thousands of grid elements by the finite volume or finite element method. The inter- and intra-particle diffusions and reactions are usually parametrised by a deterministic model, such as the shrinking core model (SCM), that translates the external conditions into an effective product extraction rate. However, the rate equation takes the form of an implicit or partial differential equation for all but the simplest models and kinetic regimes, becoming expensive to solve on large grids. We instead propose an economical, easily calibrated semi-empirical approach in which the dependencies on external conditions and the current state of the ore are considered to be mathematically separable. We show that the standard SCM does not suffer greatly from this approximation even when there is a mixed control regime with nonlinear kinetics. The dependency on the state of the ore is derived empirically, inherently capturing heterogeneous features and cluster-scale effects. We demonstrate that this method scales correctly when fitted to data from physical column leaching experiments.