Prediction of slurry grinding due to media and coarse rock interactions in a 3D pilot SAG mill using a coupled DEM + SPH model

Abstract

A coupled DEM + SPH model can be used to predict the motion and breakage of resolved coarser particles within a SAG mill. The fine product from coarse particle fracture can then be included in the slurry phase modelled using SPH. This allows, in principle, the prediction of the breakage and transport of coarser material and the transport of the finer material within the grinding and pulp chambers of a SAG mill including discharge performance of the mill. It also allows the effect of the changing solids loading on the slurry rheology to be included. In this paper we will explore the development of an extension of this model that also allows prediction of the grinding of the finer particles embedded in the slurry phase due to the collisions and shear of the coarser particles (rocks and grinding media). The size distribution of the slurry fines is discretised into a set of size fractions so that its change due to grinding can be tracked at each point in the slurry. This is formulated as a system of coupled advection-diffusion equations. An SPH discretisation of this system is then developed. The resulting coupled SPH ODE’s are solved using the SPH method in a way that is fully coupled to the DEM and SPH parts of the model. The proposed model includes a diffusive component that allows for the shear induced dispersion of the slurry size fractions and allows prediction of the spatial distribution of these fine size fractions within the slurry phase. The advection of the slurry is automatically accounted for by the motion of the SPH particles which is an important benefit of using the SPH method for such wet mill modelling. The local fine grinding behaviour arising from the coarse DEM resolved components of the charge are characterised at each location in terms of the local energy dissipation rate. This information is used in conjunction with a first order grinding law to predict the grinding of each slurry size fraction at each location in the mill due to the collisional action of the coarser particles. The ability of this new model to predict fine particle grinding and transport within the slurry phase is demonstrated for an industry standard 1.8 m diameter by 0.6 m long AG/SAG pilot mill.