LINEAR STOCHASTIC-MODELS FOR MINERAL LIBERATION

This paper provides a clearly defined procedure for the calculation of the liberation spectrum that can be expected when any two-phase or porphyry three-phase ore is comminuted in a ball mill or an open-circuit continuous mill. All the data that are required by the model are readily obtained by suitable image analysis of the original ore. The model accommodates both random and non-random fracture patterns although, in the latter case, the model is not entirely predictive at present and requires some measurements to be made on the comminuted ore. A linear stochastic process is used to characterize the mineralogical texture of the ore. This model of the ore texture can be used to predict the liberation spectrum in particles of any size after comminution of the ore. The model is parameter-free and is not limited to textures having convex grain structures nor to convex particles. The model is extended to include the effects of different brittleness of the mineral components and fracture along the grain boundaries which lead to non-random fracture patterns. The model predicts that modest amounts of grain-boundary fracture will not increase liberation in minerals having exponentially distributed linear intercept lengths in each phase. The model is extended to multicomponent ores. Examples calculations are given for a binary ore having exponentially distributed linear intercepts through both phases. An exponentially distributed porphyry ore with two valuable mineral phases is analyzed up to the calculations of the linear grade distribution as a function of particle size. The calculated distribution of linear grades for this three-phase ore cannot be stereologically transformed to the distribution of volumetric grades because no suitable transformation kernel has yet been determined.