Problems in population balance modeling of wet grinding

Abstract

The Population Balance Model, PBM, contains flaws making its use for effective simulation and control of milling circuits questionable. Presented is an analysis, based on published experimental wet grinding data, showing that the assumption of linearity, used in solving the PBM, is certainly wrong in many grinding mills and wrong for most commercial wet grinding circuits. Several solutions to a typical PBM are given to demonstrate nonuniqueness of solution. The differences obtained during matrix multiplication using different solutions to the same PBM problem were quantified. It appears that significantly different mill products can be obtained with the PBM using the same feed. A stuffing matrix S was identified as the only PBM solution to any Inverse Problem for wet grinding with parallel or near parallel straight line product curves observed for wet ball mills. Some dry grinding feed matrices can be inverted, because the product size distributions curve bends sufficiently to the right in the larger particle sizes, showing that the larger particles are not broken instantaneously.