Introduction to the use of the attainable region method in determining the optimal residence time of a ball mill

• The attainable region technique has been applied and extended to continuous milling.
• Ball size was found critical in controlling the residence time of the mill.
• Using ideal flow models, boundaries of the maximum production of fines were determined.
• There exists an optimum mill speed corresponding to the lowest residence time.

The application of the attainable region (AR) technique to the analysis of ball milling is currently limited to batch data. This paper introduces the use of the technique in continuous milling.To this end, a platinum-bearing ore (less than 850 μm in size) was used and its breakage characteristics were measured by means of standard batch milling tests. The breakage parameters were scaled up to an industrial mill. This enabled the extension of the AR methodology to full-scale milling. However, the analysis was limited to two simple transport models: plug-flow and well-mixed mills without exit classification. Following this, the importance of controlling the residence time of the mill optimally was appreciated.Initial findings showed that milling conditions should be tailored to the desired product size requirements. The lower and upper limits in which the maximum production of fines should lie were also identified. Finally, mill speed was found to be pivotal in controlling the retention time of particles inside the mill.

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