The development of cumulative rates models for metalliferous ores

摘要

Grinding circuits treating metalliferous ores usually comprise rotary tumbling mills operating in open circuit or in closed circuit with screens or hydrocyclones. Mill types usually include AG (autogenous grinding) or SAG (semi-autogenous grinding) mills with grate discharge arrangements for primary milling duties and ball mills with overflow discharge arrangements for secondary milling. This paper reviews the development of the so-called cumulative rates model, which is applicable to a wide range of comminution devices. The attractive feature of a cumulative basis model is that it requires only one function to quantify grinding kinetics. Conventional phenomenological models require both a specific breakage rate function and a separate breakage distribution function to perform this task. The characterisation of the material transport behaviour of the ore particles and water as they pass through the mill is also an important modelling consideration. It is shown that a simple but effective way of doing this is to treat the mill as a single fully mixed reactor and invoke the concept of a specific discharge rate function that can quantify classification effects for both overflow and grate discharge mills. Details are given of the mathematical structure of these simple models. It is also shown how they can be used to guide the design, control and optimisation of milling circuit using data generated from laboratory and pilot scale tests.