Batch grinding simulation—population balance models and self-similar size distributions

It has been observed that batch grinding of ore samples for different grinding times will sometimes produce a series of products that have approximately self-similar size distributions. Furthermore, it has been claimed that self-similar particle size distributions cannot be generated by the population balance method (PBM) of simulating ore grinding processes. That claim is not valid. Several methods for generating self-similar size distributions to any degree of precision using PBMʹs are presented. Firstly it is shown that a single self-similar product size distribution can be generated from any set of breakage parameters by an appropriate choice of feed size distribution, and that with some restrictions on the breakage parameters multiple self-similar product size distributions can be generated. It is also shown that for any feed size distribution which is a straight line when plotted on log scales, it is possible to find breakage parameters which generate multiple self-similar product size distributions. A practical example is solved to illustrate the method.