Heterarchical comminution model for SAG mills

Semi-autogenous grinding (SAG) mills are commonly used in the mineral processing industry to effectively grind large particles into finer ones suitable for further processing. Despite their effectiveness in comminution, these mills are highly inefficient in terms of energy consumption. Understanding this inefficiency using population-balance models is challenging, as those are not informed by granular interactions and physics involving the interplay of crushing, segregation, and mixing. Conversely, using discrete-element simulation models to study SAG mills is also limited in scope since at any given time these mills can contain eight orders of magnitude more particles than those models can handle. Here, we address these challenges by developing a new comminution approach based on heterarchy. Expanding upon the previously developed heterarchical model for comminution in rotary mills, we incorporate the dynamics of grinding media consisting of steel balls, offering a comprehensive understanding of comminution within a SAG mill. Employing this new comminution model, we further analyse the effect of the different mill operating parameters — mill speed, fill fraction, and ball-to-charge ratio — on the comminution behaviour. This model brings us one step closer to understanding energy consumption in SAG mills. • A comminution model for SAG mills based on novel stochastic heterarchical concept. • The model is independent of the quantity of particles. • Provides particle size distribution across space and time within the mill domain. • Insight into dynamics of grinding media within the mill charge.