Fitting Of Liberation Model Parameters To Davis Tube Test Data

Abstract

After studying the direction work in mineral liberation has taken for the past twenty years, and in particular the more recent five to ten years, it has become apparent to me that at least for the magnetic taconite process, the use of the Davis tube ideal magnetic separator on individual size fractions of process feed can provide useful data on liberation. A study made by the writer1 of process feed samples to twelve magnetite concentrators indicated a reasonable conformity between Davis tube concentrate magnetite grade and size fraction mean particle size relationships and what was predicted using the idealized "random liberation model" formulation2 with appropriate specific gravities for magnetite and waste minerals. This then suggests that the magnetic taconite liberation behavior can be characterized by three parameters (given the two specific gravities): (1) magnetite ore feed grade; (2) an average mineral grain size; and (3) an average size fraction particle size. Of the twelve sample sets noted above, only two indicated significant deviations from the shape of the concentrate grade-particle size relationships displayed by the "random model." A BASIC computer program (LIBFIT.BAS) has therefore been written to obtain the best fit of the two parameters: magnetite feed grade of the ore and average mineral grain size for the "random model," to Davis tube data on size fractions of ground taconite. The program is relatively simple in concept, in that it first seeks a value of average mineral grain size, which minimizes the sum of squares of differences in the measured and calculated Davis tube concentrate grades for an estimated magnetite feed grade of the ore. It then holds the optimum average mineral grain size constant and searches for the optimum magnetite feed grade for that mineral grain size. It continues to switch back and forth, looking at first mineral grain size and then magnetite ore feed grade for some 18 iterations, which then provides a best fit estimate of the two parameters.