Requirements for estimating the volume of rocks and balls in a grinding mill

Abstract

This study aims to indicate which measurements are required in order to estimate the volume of rocks and balls in a semi-autogenous grinding mill as two separate states. The nonlinear observer model used here includes the following process states: water, solids, rocks, and balls in the mill, where solids are all ore small enough to discharge through the end-discharge grate, and rocks are all ore too large to discharge. The model includes the discharge rate, abrasion rate of rocks and the abrasion rate of balls as parameters. The available measurements are the total mill filling, the discharge flow-rate, and the discharge density. As seen from an observability analysis, the states and parameters become observable from the second-order time-derivatives of the measurements. The minimum set of measurements required for observability of all states and parameters is the mill filling, the discharge density, and the first and second-order time-derivatives of the discharge density. However, modelling the second-order time-derivative of the discharge density is problematic, as it assumes constant model parameters. Although the combined volume of rocks and balls can be estimated using measurements of the mill filling, the discharge flow-rate, the discharge density, and the first-order time-derivative of the discharge density, these measurements remain insufficient to distinguish between rocks and balls. To reliably distinguish between the rocks and balls in the mill, an additional measurement apart from the ones mentioned above is required. Since power draw models introduce large parameters sets of their own, another viable and reliable option is required.