**Energy-based
Selection Function Model**

The alternative model for the rate of breakage is based on the idea that the amount of breakage that is achieved in a ball mill is proportional to the amount of energy that the mill has delivered to the mill charge. The rate of breakage is therefore proportional to the power drawn by the tumbling charge in the mill. This leads to a formulation of the population balance model that does not require the residence time of the solids in the mill to be specified as the primary capacity parameter. It is necessary only to specify the net power drawn by the mill.

The variation of the selection function with particle size is usually modeled using a slightly different relationship to that used by Austin. The alternative model is used in exercise 6-2 which illustrates the use of the closed circuit ball mill to grind limestone.

Exercise 6-4 illustrates the model when applied to the grinding of taconite and exercise 6-6 illustrates its application to the tough porphyry ore.