Modelling Of Crumbling And Mineral Liberation During Crushing Using ?Natural Grain Size Distribution? For Friable Ores

Sedimentary deposits such as sandstone are formed by the aggregation of cemented sand grains. Phosphates and laterite present similar aggregation of mineral grains. Grains and cement have different mineralogy and chemical characteristics. During size reduction through crushing or coarse grinding, the rocks are crumbled. Mineral grains and cement are then liberated, and the produced size distribution reflects their ?natural size distribution?. Mathematical modelling of these concomitant effects of crumbling and mineral liberation necessitates a specific material description and the adaptation of the commonly used theories of breakage kinetics and population balance. The coarse particles are mainly agglomerates made of mineral grains and cement particles whereas the fine particles are grains and cement with a natural grain size distribution. The population balance between the different particle size and particle types during size reduction takes into account the breakage rate and the progeny size distribution. The breakage rate can be described by a simple probability function or by a first order kinetics whereas the progeny size distribution is described by a breakage matrix. The model proposed here considers that the agglomerates will produce other agglomerated particles, liberated grains and cement particles; the two latter having their natural size distribution. The liberated grains and cement particles are subject to size reduction and follow the most commonly used theory of breakage. The present paper describes the theoretical approach of the concomitant crumbling and liberation effects. The application to a mathematical model for the cone crusher is presented. The advantage of such approach is then demonstrated through a simulation study for the optimisation of a crushing plant. Keywords: mineral liberation, modelling, crushing, sedimentary ore