Design of a cellular automaton to determine the particle size distribution exiting a SAG mill

Modelling ore comminution processes have been a highly fruitful scientific topic. The models have been proved to be largely dependent on the selected comminution technology. Among them, semiautogenous (SAG) mill technology has been widespread implemented in plants but no complete understanding of the mechanisms involved in the process is available. Tracing back in history, SAG models considered only some granulometric cut sizes such as the t10 and attempted to relate these parameters with the energy involved in the impact between particles. Other models evolved towards incorporating physical properties of the material being ground and the mill operating conditions. These material properties have assisted to obtain a more comprehensive description of the breakage mechanisms; nevertheless, the gathering of all known parameters still have not delivered a model able to describe the process. This may be a result of emergent properties or phenomena originated from interactions inside the process which are hard to predict turning the size reduction operation into a complex system. Cellular automata provide one answer to describe complex systems by following simple rules. The aim of this research work is to establish the preliminary rules of thumbs enabling the implementation of cellular automata able to predict the particle size distribution at the exit of a SAG mill. The methodology involved developing a simple 2D model of a ROM sample. Plant data from two mine sites were correctly described by a set of three rules: two rules describing the particle reduction and one rule associated with material transport across the mill. Further analysis related with expanding this model to 3D and its impact on the liberation of valuable material is also discussed.