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, Ep_X, 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 Ep_X 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 Ep_X. 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.