Mill Scaleup: Ball Collision Frequency and Collision Energy Density in Laboratory and Plant-Scale Mills

The traditional method of scale-up uses the population-balance model. In particular, the selection function values for a material are determined in a laboratory mill and a variety of correlations are used to scale these values to plant scale mills. For example, the factor D2-5L (D-mill diameter, L-mill length) appears in many power correlations. The number of collisions is proportional to the number of balls (aD2L), the frequency of mill rotation ((x 1/4D-) and effectiveness of impact ((XD), which gives rise to the 'D2.5L' expression. However, what is lacking in this expression is that it does not throw light on the intensities of collisions. In other words, the collision intensities in both laboratory and plant scale mills are implied to be identical. This fact has been very limiting. Alternatively, the collision frequencies and intensity of impacts can be computed with the discrete element code. This code computes the motion and collision of each individual ball in the ball charge. Therefore the number of collisions and the fraction of collisions in the energy range Et, E2.òòE. (collision energy density) are calculated for a given mill size and operating conditions. Then, using the breakage function determined in drop-weight experiments, the evolution of size distribution is computed for a lab mill. The collision frequency and energy density for larger mill sizes are shown. The fundamental theory outlined for the calculation of size distribution is equally applicable for the large mill, which is the basis for scale-up.