The truth about population balance modeling

Abstract

ABSTRACT Early researchers hoped to describe ball milling as a series of particle breakage and re-breakage events. This review reveals that a needed input of population balance modeling (PBM), the “breakage function,” was never intended to be taken literally but was assumed 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, comprising the assumed breakage function, solids 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. The model cannot be used to assess changes to the mill itself. 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 practical replacement.