A Review of the Milestones Reached by the Attainable Region Optimisation Technique in Particle Size Reduction

Abstract

The attainable region (AR) is an optimization method adopted for use in comminution to achieve different objective functions, which all converge to optimising the production of the desired particle size distributions for downstream processes. The technique has so far mostly been used to optimise the breakage of particles in tumbling mills. It achieved the desired purpose by unveiling all possible outcomes derived from a combination of operational parameters that are bound by trajectories showing the limitations of a system. The technique has given the scientific community lenses to see the behaviour of different parameters in ball mills otherwise known as the black boxes due to their concealing nature. Since its inception, the AR technique has been applied to data obtained from the laboratory tests and simulated industrial mills and the results sometimes contradict or confirm the conventional milling practices in the industry. This makes the already conservative mining industry sceptical about its adoption. This review thus assesses the milestone covered as far as the AR development in comminution is concerned. It also helps to clarify the sources of the discrepancies between the AR results and the conventional knowledge concerning the optimisation of ball mill operational parameters.