Prediction of grinding mill performance, throughput and product size distribution in full 3D SAG mills with feed and discharge is now possible using a multi-physics, particle-scale model which combines charge and slurry behaviour, breakage and attrition of resolved coarse particulates, and grinding of unresolved fines in the slurry phase. This uses a fully two-way coupled DEM+SPH model to represent the behaviour of the coarse solids (DEM) and fine slurry (SPH) phases as well as the interactions between these phases. Size reduction of feed material is included in the DEM sub-model through four inter-related comminution mechanisms. These include body breakage and surface attrition (via chipping, rounding and abrasion) which create explicit size and shape modification of the resolved coarse (DEM) particles. Body breakage makes use of a particle-replacement method and breakage characterisation data to pack super-quadric progeny into each fracturing parent particle. Fine unresolved fragments either in the feed or resulting from coarse fracture are transferred to the SPH slurry phase where the viscosity then spatially varies with fines content. Collisions and shear due to the motion and stressing load of the coarse DEM particles generate local energy dissipation. which is used to calculate size-dependent grinding rates. The slurry size distribution and its time evolution are then predicted by solving a coupled set of population balance equations for each SPH particle. This allows prediction of mass transfer between size classes due to grinding. Dispersive fluid phase transport of unresolved fines (in the SPH fluid) is represented as diffusion whilst advection is automatically treated by the SPH.

The ability of this particle scale model to predict SAG mill performance is explored for an industry standard 1.8 m diameter by 0.6 m long pilot SAG mill. The model demonstrates that rock with a size invariant elastic threshold E0 for incremental damage accumulation leads to a coarsening of the rock charge as smaller particles are preferentially broken. The flow inside the grinding chamber is complex and fully three dimensional with strong axial flow away from both the feed end and the grate as well as the traditional cascading and cataracting flows from the belly lifters. These mixing and transport behaviours interact with the breakage and grinding to give a complex spatial distribution for both the coarse rocks and for the slurry phase fine rocks. Flow of both smaller resolved rocks and slurry through the grates into the pulp chamber is predicted by the model. The model is able to show which parts of the grate allow flow into the pulp chamber and which parts have retrograde flow back into the grinding chamber. Finally, discharge flow from the mill and a final product size and throughput are predicted.