The modelling and simulation of autogenous (ag) and semi-autogenous (sag) grinding circuits has been the subject of continuous research for over thirty years. During this period several mathematical models have been developed, mostly being steady-state varieties for design and optimisation. Much less effort has been expended in developing dynamic models. The few models which have resulted from this work have been exclusively for control purposes. The descriptions of process mechanisms in these models are non-existent or simplistic, rely on a number of empirical equations and therefore are specific to the circuits for which they were constructed. Their general applicability are therefore severely limited.
Despite the traditional approach of developing separate dynamic and steady-state models, it is asserted that a model which describes properly the process mechanisms in ag/sag mills in a life-like manner should be able to predict their operation in both dynamic and steady-state, i.e. only one model is required. As steady-state is the end-point reached following a step change in any process variable, then if the effect of a step change is modelled correctly, the result should be a correct description of the mill response with time, including its final steady-state condition. This thesis describes such a new model for ag/sag mills which can be used to accurately predict the steady-state and dynamic response in terms of power draw, grinding charge level, slurry level and product size distribution for changes in process variables such as feed rate, feed size, feed hardness, speed and water addition.
As well as being the first dynamic and steady-state model believed to have been developed, it incorporates the most up-to-date descriptions of sub-processes that occur in ag/sag mills and a number of novel ideas relating to these sub-processes. The main novel contributions and special features of the model are a new method to calculate the energy absorbed by rock particles in the mill, more realistic equations for the mass transport, on-line prediction of power draw, a relationship between mill charge composition and breakage frequency based on projected surface areas of the grinding media and target particles, and the effect of slurry content and hold-up on the mill behaviour.
To help interpret the mechanisms by which operating variables affect mill performance and the way the dynamic model should reproduce these mechanisms, a large number of industrial surveys were conducted. The resultant model is described in detail as well as validation tests based on dynamic and steady-state data collected at several industrial scale ag/sag mills.
It is expected that the model will assist with the understanding of plant dynamics, testing and implementation of control strategies, mill operator training as well as plant optimisation and circuit design.