Development of an Approach to the Simulation of Size Reduction/Mineral Liberation for Magnetic Taconite Ore in Tumbling Mills and Its Implementation in a BASIC Computer Program

Abstract

In late '98, the Iron Ore Cooperative Research Committee decided to fund a math modeling/simulation center for magnetic taconite concentrator applications at the Coleraine Minerals Research Laboratory of the University of Minnesota. In a previous association with the iron ore industry, the writer was actively involved in early attempts at modeling and simulating the magnetic taconite beneficiation process. After returning to the University of Minnesota and the iron ore industry in 1997, I attempted to play "catch up" on developments over the past twenty years related to magnetic taconite process modeling and simulation. Based on that review, it was evident that two items that are of particular importance for magnetic taconite process simulation were still missing from the tools available in the software packages for mineral process modeling/simulation. These are: (1) a suitable technique for handling the description of mineral liberation as a function of changes in particle size resulting from size reduction steps in the process and (2) the prediction of the performance of rotating drum magnetic separators as a function of their design and their operating conditions. It was therefore decided that steps should be taken to begin to address these deficiencies very early in the life of the Taconite Concentrator Modeling Center. The more complex of these two problem areas is the development of a technique for describing how mineral liberation, and the resultant possible early rejection of minerals to waste, can be related to particle size changes resulting from crushin~ and grinding size reduction. There have been numerous approaches to this subject, 10 • 1 but none have taken it to a useful conclusion. Lacking a model of the simultaneous mineral liberation/size reduction operation, some investigators have resorted to the assumption of complete mineral liberation, that is, all mineral species are totally free of other mineral species. This is certainly not appropriate for magnetic taconite, where rejection is dependent on grinding. The approach reported here begins with an early conceptual model of a binary mineral system's liberation by size reduction, as described by A. M. Gaudin in his 1939 text "Principles of Mineral Dressing." Relationships have previously been obtained to describe the amount of liberation of either component and the quantity/composition of unliberated or "locked" middlings as a function of the "effective" mineral grain size, particle size and the original ore's volumetric composition. The new developments described in this report make use of mathematically derived "directional coefficients" to follow the gradual transfer of material from locked assemblages of dissimilar mineral grains of one composition to other locked particle compositions and eventually to liberated particles of value or waste, as particle size is reduced. Finally, a BASIC program has been developed and is presented, which permits one to calculate the simultaneous liberation/size reduction phenomena for multi-stage, perfectly mixed, tumbling mills in series. The liberation parameters of a particular crude magnetic taconite ore sample are obtained by collecting Davis tube data for individual particle size fractions and subjecting these to a "best fit" program described in an earlier report. Once the liberation parameters are defined, appropriate breakage rates of the liberated and locked middling particles can be used in combination with the geometric effects of the resultant size reduction on mineral liberation to simulate in a relatively simple and understandable way the complex operation of size reduction/liberation. This BASIC program must now be translated into an appropriate FORTRAN program for use with the BRGM USIMPAC mineral processing simulation software. It can then be used in concert with other models to simulate the entire magnetic taconite beneficiation process.