Modeling the RTD of an industrial overflow ball mill as a function of load volume and slurry concentration

The role of residence time distribution (RTD) in the accuracy of milling simulation is well appreciated in literature. Accordingly, the development of models that can accurately predict the RTD at various mill operating conditions would be of considerable benefit to the milling industry. In this paper, a 3-parameter RTD model has been derived using the concept of serial stirred mixers with a dead zone. The model parameters were optimized by minimizing the error between experimental tracer response data and model predictions using a MATLAB algorithm. Based on the optimum values of the model parameters, the mean residence time of slurry was evaluated and the effects of ball load volume and slurry concentration examined. The results revealed that the mean residence time of slurry inside the mill is affected to a larger extent by slurry concentration than the ball load volume. An empirical correlation was developed to predict the mean residence time as a function of slurry concentration, ball load volume and slurry feed rate. Over the range of conditions investigated, the mean residence time was observed to vary linearly with slurry concentration and ball load volume but inversely with feed flow rate. Lastly, a test case of the simulated mill product size distribution using the predicted RTD is presented displaying a close match with experimental data.