Sensitivity analysis of Austin's scale-up model for tumbling ball mills – Part 3. A global study using the Monte Carlo paradigm

Abstract

The scale-up of batch grinding data is an attractive option for the modelling of industrial milling circuits. However, little is known in terms of the expected uncertainty attached to the predictions. This paper attempts to estimate this.For simulation purposes, coarse and fine feeds were considered in the context of an open ball milling circuit and for three predefined feed flow-rates. Realistic fluctuations were allocated to the 25 input parameters making up the simulation model. The Monte Carlo approach was then used to simultaneously process the randomly generated input parameter values. Finally, average values and standard deviations on the 50% and 80% passing sizes of the mill product were calculated in order to obtain estimates of prediction uncertainties.Global errors on the predicted full-scale mill product size were found to be as high as 70%. However, with appropriate assumptions on the scale-up correction factors, they were reduced to approximately 40%. It was also demonstrated that well planned batch tests and accurately determined batch data can further drop the error to as low as 20%. Finally, the scale-up model was found to work well when finer feeds were considered for milling at high flow-rates.