Continuum models for copper leaching incorporating intra-ore diffusion–reaction interaction

Accurate prediction of field-scale percolation leaching systems requires capturing essential intra-ore diffusion–reaction interactions while remaining computationally efficient. This study proposes and assesses two continuum models based on one-dimensional and zero-dimensional approximate solutions (AS1D and AS0D) to the three-dimensional intra-ore diffusion–reaction process, enabling efficient upscaling to field-scale leaching simulations. The two models are first presented and assessed with spherical- and cubic-shaped ore fragments and mineral grains across reaction-controlled, mixed-controlled, and diffusion-controlled regimes. Both models are then further tested in single-mineral and multi-mineral systems for copper sulphide leaching, including chalcocite and chalcopyrite. To improve computational efficiency for complex multi-mineral systems, further approximation of the intra-ore diffusion process was made to both models, resulting in four models in total. The results show that all four models demonstrate good agreement with the baseline reference obtained from directly solving intra-ore diffusion–reaction in three-dimensional ore fragments, with the overall root-mean-square errors all below 5%. In general, both versions of AS1D are more computationally demanding than AS0D, as AS1D solves for the actual diffusion–reaction process, whereas AS0D adopts the pseudo-steady approximation. This work provides effective approaches to incorporate ore-scale properties for continuum leaching simulations, with key model features discussed in detail to inform model selection and application.