Kinetic approach to ball mill scale-up for dry and wet systems

In this investigation detailed experimentation has been carried out to establish a relationship for mill scale-up using a linear population balance model in dry and wet grinding systems. Data were obtained in three different sizes of mill (10, 15 and 30 inches in diameter) for limestone grinding. In each case the selection and breakage parameters of the population balance model were determined. Analysis of these data showed that the selection functions are proportional to the specific power draft of the mill (S^ = S^(P/H)) for both wet and dry grinding. In addition the breakage functions were found to be independent of mill size, the same for wet and dry grinding. For dry grinding the specific selection functions (S?) were found to be independent of fineness of grind. While for wet grinding the specific selection functions varied with fineness of grind. These relationships were found to constitute a basis for mill scale-up. By incorporating the specific selection functions and breakage functions into the linear population balance model it was possible to accurately predict dry product size distributions in the larger mills from data obtained in the 10-inch diameter mill. Equally accurate predictions were achieved for wet grinding by employing a linearization procedure termed as the "similar fineness of grind approach".