Grinding Mills: How to Accurately Predict Their Power Draw

"The first 90 years of the last century generated a considerable volume of technical literature on the subject of grinding mill power and its prediction. It is therefore surprising that during this time there were no published models for predicting grinding mill power draw which were validated using a wide range of comprehensive industrial scale data.Notwithstanding this lack of data, the majority of models placed limited emphasis on the internal dynamics of mills and relied on simple assumptions which considered the charge to take up a fixed position and shape.Laboratory based studies (Liddell, 1986), and industrial data (Morrell, 1993), showed that these assumptions did not hold over a wide range of operating conditions, and brought into doubt the ability of the (then) existing models to accurately predict grinding mill power draw. Furthermore no model treated AG,SAG and ball mills as a single class of devices whose power draw could be predicted with the same equations.Through a detailed investigation of the charge dynamics, coupled with a large data base of industrial mill power draws, this situation was rectified by the end of the century, by which time a model had been developed and validated, which accurately predicted the power draw of all wet tumbling mills. This paper describes this model and reviews some of the earlier attempts at mill power modelling.INTRODUCTIONThe early 1900?s saw the beginnings of published papers which tackled the problem of what influenced the power draw of tumbling mills and what equations (models) were suitable for predicting power draw. This interest continued for the rest of the 20th century and the literature contains many papers that attempted to satisfactorily answer these questions. A common and disappointing theme in the majority of them, however, is the distinct lack of suitable experimentally derived power draw data. This deficiency consequently limited the practical application of many of the attempts at modelling mill power draw. Prior to the early 1990?s some limited data on the power draw of grinding mills in the literature can be found, but as Harris et al (1985) remarked they are ?... too frequently unusable simply because one or more essential variables have been omitted?. The absence of published results, from vigorous experimental testing of the various models, has resulted in a general lack of evaluation of the validity of assumptions and hypotheses that such models contain. Harris et al (1985) however, did make some efforts in attempting to evaluate the performance of various power prediction equations and in so doing further developed a semi-empirical one of their own. However, in using manufacturers? published data, which themselves were undoubtedly generated by proprietary equations of unproven validity, they probably succeeded in generating little more than a consensus of the various errors in these models."