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

Abstract

This study aimed at assessing various energy-based breakage distribution functions Bij 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, tn. Second, various tn models called tn-fitted and tn-regenerated approaches were used to fit experimental tn, and their goodness-of-fits were compared. They were then used to construct the matrices of the cumulative breakage distributions, Bij, of the PBM, while a power-law form of the specific breakage rate function, Si, 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 Si parameters. Results suggest that except the Napier-Munn model, all tn models fitted the experimental drop weight data reasonably well, which was reflected in the PBM fitting of the product PSDs. The PBM fits with Bij constructed with the tn-regenerated approach were more accurate than those with the tn-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 tn function and the methodology to determine Bij can affect the PBM predictions of the WSMM process significantly.