Developing A Simulator For Ball Mill Scale-Up - A Case Study

INTRODUCTION Recent research has shown that popu- lation balance models hold considerabl e promise as a basis for accurate mill scale-up from laboratory batch grinding tests. It has been shown that entire product size distributions from large ball mills can be predicted from data obtained in tests in small mills with errors of less than one or two percent. This level of accuracy has been demonstrated for batch grinding scale-up (Herbst and Fuerstenau, 1980; Austin, 1973; and Malghan and Fuerstenau, 1976) and for continuous grinding scale-up (Herbst, et a1., 1976; Herbst, Rajamani and Sanchez, 1982; and Herbst, Rajamani and Lo, 1982) in commercial mills up to 14.5 x 32 feet. A procedure which has been proposed for commercial mill design using the population balance approach and specific power information is shown in Figure 1 (Herbst and Fuerstenau, 1980). Here batch grinding data (size distributions for various energy inputs) obtained in a small batch mill is input to an estimation program which determines the "best" set of breakage rate parameters from the data provided. In turn, these breakage rate parameters are input to a scale-up program along with traditional inputs such as: a) desired circuit throughput and product size b) circuit operating conditions including fraction of critical speed and fractional ball load, size distribution and % solids in feed and circulating load (if closed circuit). In addition, since the population balance approach relies on more detailed models of the grinding circuit sub- processes than the classical design methods do, it is necessary to provide input to the scale-up program on the nature of material transport through the mill (e.g. residence time distribution information) and classifier performance characteristics (e .g. selectivity functions). The scale-up program will make the design calculations including the selection of mill dimensions and drive requirements, will predict product size distributions throughout the commercial circuit and will provide information on the sensitivity of the design to errors in the design assumptions. In order to implement such a scale- up scheme it is necessary to have a computer program for parameter estimation and a program for scale-up prediction. A program which is suitable for parameter estimation, ESTIMILL, has been developed and tested on a wide variety of ores at the University of Utah. This program has been in use in