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.

中文翻译：

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工业规模连续运行湿搅拌介质磨机种群平衡模型中不同基于能量的破损分布函数的评估


本研究旨在湿搅拌介质磨机 （WSMM） 中铜矿石研磨的种群平衡模型 （PBM） 的背景下评估各种基于能量的破损分布函数 Bij。首先，进行落锤冲击试验以确定尺寸分布参数 tn。其次，使用各种称为 tn 拟合和 tn 再生方法的 tn 模型来拟合实验 tn，并比较它们的拟合优度。然后，它们被用来构建 PBM 的累积破损分布矩阵 Bij，同时假设特定破损率函数 Si 的幂律形式。通过将 PBM 拟合到在不同转子速度、悬浮液体积流速和固体含量下获得的产品粒度分布 （PSD），我们估计了 Si 参数。结果表明，除 Napier-Munn 模型外，所有 tn 模型都很好地拟合了实验落锤数据，这反映在产品 PSD 的 PBM 拟合中。使用 tn 再生方法构建的 Bij 的 PBM 拟合比使用 tn 拟合方法构建的 PBM 拟合更准确。PBM 通过参数估计中未考虑的额外测试进行了验证。总体而言，我们已经确定 tn 函数的选择和确定 Bij 的方法会显着影响 WSMM 过程的 PBM 预测。