Assessment of different energy-based breakage distribution functions in population balance model of an industrial scale continuously operated wet stirred media mill

This study aimed at assessing various energy-based breakage distribution functions B_ij within the context of a population balance model (PBM) of copper ore milling in a wet stirred media mill (WSMM). First, drop weight impact tests were performed to determine the size distribution parameters, t_n. Second, various t_n models called t_n-fitted and t_n-regenerated approaches were used to fit experimental t_n, and their goodness-of-fits were compared. They were then used to construct the matrices of the cumulative breakage distributions, B_ij, of the PBM, while a power-law form of the specific breakage rate function, S_i, was assumed. By fitting the PBM to the product particle size distributions (PSDs) obtained under various rotor speeds, suspension volumetric flow rate, and solids content, we estimated the S_i parameters. Results suggest that except the Napier-Munn model, all t_n models fitted the experimental drop weight data reasonably well, which was reflected in the PBM fitting of the product PSDs. The PBM fits with B_ij constructed with the t_n-regenerated approach were more accurate than those with the t_n-fitted approach. The PBM was validated with additional tests that were not considered in the parameter estimation. Overall, we have established that the choice of t_n function and the methodology to determine B_ij can affect the PBM predictions of the WSMM process significantly.