Population Balance Model Predictions of the Performance of Large-Diameter Mills

Abstract

In spite of potential theoretical and economic advantages of large-diameter ball mills, many manufacturers elect not to build them owing to what is perceived as an excessively large design risk. This is because traditional predictions for mill scale-up to large diameters are not always accurate. Alternative methods of analysis and scale-up are required.

Recent studies have shown that detailed population balance models which account for important grinding subprocesses (grinding kinetics, material transport, and classification) are capable of predicting the performance of small and intermediate-diameter mills (up to 4.3 m, or 14 ft) from small-scale batch tests. These same models are used in the current study to predict the performance of large ball mill 4.7 × 5.5 m, or 15 × 18 ft) at Asarco’s Sacaton operation, a ball mill (5 × 5.8 m, or 16.4 × 19 ft) at Kennecott’s Chino operation, and one of the world’s largest ball mills (5.5 × 6.4 m, or 18 × 21 ft) at Cities Service Pinto Valley operation. Model parameters required for scale-up have been estimated in a 380-mm-diam (15-in. diam) batch mill. Predictions are compared with the results of detailed plant sampling, in the three plants. For the Sacaton and Chino operations, the error of the predictions was found to be less than 2.5%, while the corresponding error for the Pinto Valley operation was less than 2.7%.

It is concluded that proper representation of the major subprocesses of grinding in the model equations is the key to achieving accurate scale-up. Of special importance is the need to account for the size distribution of the grinding media and the influence of the size distribution environment in the mill on grinding kinetics.