Population balance modeling approach to determining the mill diameter scale-up factor: Consideration of size distributions of the ball and particulate contents of the mill

In the past, most of the Population Balance Model-based ball mill scale-up studies were carried out using a mono-size ball charge and a single size fraction of the particulate material as the starting feed. It was reported that the breakage distribution parameters were independent of the mill diameter, specific breakage rate parameters varied with mill diameter as Dγ, and the mill diameter exponent γ was independent of particle size. However, in the industrial grinding operations, we have significantly broad size distributions for both the grinding media and the particulate contents of the mill. Therefore, experimental data generated under these conditions were taken from the literature and analyzed. These data pertain to the dry and wet batch grinding of limestone, quartz, and ores of vanadium and pyrochlore. Our analysis of the data showed that in contrast to the findings of the earlier researchers, the breakage distribution parameters were not independent of the mill diameter, and the value of γ for the specific breakage rate parameters varied with particle size in the case of multicomponent ores. Because of these complications, a single parameter, the specific rate of production of material that is finer than a specified size, was used as the basis for scale-up. It was found that the value of the mill diameter scale-up factor varied quite significantly with the breakage properties of the material, the size distribution of the particulate contents of the mill, the size of the desired product, and the mode of grinding (dry/wet). Therefore, ball mill scale-up models presently available need to be modified in light of these new findings.