Deconvolution of fractionation data to deduce consistent washability and partition curves for a mineral separator

A density partition curve for a hypothetical steady-state separator is applied to a known feed density distribution to give the density distributions of the product and reject. Density fractionation of each of these streams is then simulated, with the fractionator Ecarte Probable, EpX, set at a specific level, to produce a set of seven or more fractions of varying mass and increasing average density. This study then describes a new algorithm that attempts to recover the partition curve of the original steady-state separator, using only the three sets of limited fractionation data and the assumption that the form of the partition curve equation is known. The algorithm first uses a simple interpolation rule to convert each set of fractionation data into a cumulative density distribution. Then the feed density distribution and the partition curve parameters are simultaneously adjusted until a consistent set of feed, product and reject density distributions is found with minimum variation from the raw fractionation data. The algorithm was applied to a simple rectangular feed distribution, and then a more realistic distribution. In both cases the algorithm accurately determined the density cut point (D50) of the separator, even for poor quality fractionations. The accuracy of the determined separator Ep value depended on the fractionator EpX and the amount of near-density material. For the simple rectangular distribution, the algorithm under predicted the separator Ep, with the error being about 34% of the fractionator EpX. For the more realistic feed distribution, there was more scatter in the Ep values, but still the same general trend. The error increased when there was little near-density material. Increasing the number of flow fractions from 7 to 11 brought some improvement in accuracy. However, above 11 fractions there was no further significant improvement. Expressing the partition function in terms of D75 and D25 (instead of D50 and Ep) reduced the sensitivity of the algorithm to the initial guess values