Population ? Balance Models for Predicting Grinding Mill Performance

Comminution represents one of the major costs of mineral recovery from low-grade ores. Efficient mineral recovery in a typical low-grade ore grinding-flo¬tation process depends on grinding the ore small enough to liberate mineralization without producing excessive slimes, which would result in higher power and flotation reagent costs. Size criteria for efficient grinding should be stated in terms of the distribution of mineralization sizes, but as the mineralization-size distribution is difficult to determine, less desirable criteria of absolute particle-size distribution (PSD) are used in practice. Thus, there is considerable incentive to be able to analyze and predict the PSD performance of grinding circuits for control and optimization of the process. Any realistic model of a grinding circuit must account for recycle of oversize material; such oversize recycle adds to the total mill load and limits total production rate. Simulation of such closed-circuit operation to study grind factors affecting total throughput can be done in a straightforward fashion provided recycle calculations can be added to an accurate input-output model of PSD in the grinding mill itself. Such a total simulation of mill performance is of obvious practical value in assessing the practicality and benefits of various over-all mill control schemes and/or modes of operation. For example, considerable interest has been shown in the development of continuous on-line particle-size sensors and such instruments should be an operating reality in a few years. A total closed-circuit PSD model of this type would be invaluable in the utilization of, and in predicting the pay-out from, such an on-line particle-size sensor. The purpose of this paper is to present a new approach to the development of an input-output PSD model of a grinding mill. The model is continuous in the par¬ticle size coordinate, L, and is based on the principle of a particle population balance along the particle size coordinate. Most previous studies of the grinding unit operation attempt to relate power