The truth about population balance modelling

Abstract

Early researchers hoped to describe ball milling as a series of particle breakage and re-breakage events. This review revealed that a needed input of population balance modeling (PBM), the “breakage function”, was never intended to be taken literally. One was arbitrarily assigned in order to solve the matrix calculations. Along with liquid-tracer based residence time, breakage rates of each size class (the “selection function”) could then be back-calculated, given measured mill feed and product size distributions. This wet ball mill model, comprised of the assumed breakage function, residence time assumed to be that of liquid, and back-calculated breakage rates, works quite well in circuit simulations. All three individual elements, however, are false. It cannot be used to assess changes to the mill itself. The wrongly assumed validity of a fixed breakage function, and that particles of all sizes equally follow the liquid, misled some researchers towards falsehoods regarding effects of mill design and operating variables and scale-up. While shrouded from proper vetting by complexity, lack of progress in industry eventually resulted in discontinuation of almost all PBM research. The cumulative grinding rates model provides a very practical replacement.