**Time-based
Selection Function Model**

The population balance is based on the idea that grinding can be described as a simple kinetic process and that the rate at which a particular type of particle is destroyed in the mill is proportional to the mass of that type of particle in the mill charge. The constant in this simple rate law is, however, a complicated function of the environment in the mill and of the mechanical operation of the mill. Some of the internal mill parameters that influence the rate constant are the slurry density, the size of the grinding media, the speed of rotation of the mill, the mill diameter and the lifter and liner geometry.

The kinetic model implies that the longer the small material stays in the mill, the more finely it is ground. The parameter that determines the amount of grinding and therefore the fineness of grind in the product is the average residence time of the solid material in the mill.

Exercise 6-1 illustrates the simulation of a closed ball milling circuit using the time-based breakage-selection function model when an easily-ground material (limestone) is processed.

Exercise 6-3 illustrates the use of the same circuit to grind a tougher material, taconite.

Exercise 6-5 illustrates how the circuit must change to deal with a very tough porphyry ore.