Rating cumulative grade recovery curve data

"Evaluation of inequalities of the partial sums defining cumulative grade and recovery prove that cumulative grade has an upper bound not dependent on the bank number and cumulative recovery possesses an upper bound proportional to the bank number. This explains one observed characteristic of cumulative grade versus cumulative recovery curves. The existence of such maxima combined with the observed shape of cumulative grade-recovery curves leads us to postulate that these curves can be well described by rectangular hyperbolae. Rectangular hyperbolae are characterized by asymptotes at right angles to each other. It is proven that this property can be used to derive an equation for the cumulative mass flow of the concentrate in terms of the asymptotic values of cumulative grade and cumulative recovery. Fitting hyperbolae to experimental cumulative grade cumulative recovery plant data then results in estimates of the maximum grade, the maximum recovery and a constant which may be taken as a performance coefficient of a row. Normalization of the cumulative grade and the cumulative recovery by their respective maxima gives rise to a graphical representation that can be used to evaluate the operating performance of a row of floatation bank cells. The normalization procedure removes the bias that is introduced by inevitable variation in mass flow of the feed and variation in feed mineralogy or feed particle size distribution. Reduction of the normalized data collapses all cumulative grade-recovery data onto one and the same curve. This removes the differences caused by the variation in row performance. The reduced cumulative grade-recovery data scatters around a common hyperbola. This can be used to gauge the validity of the assumptions made. Normalized cumulative mass pull is determined from the fitted values of the maximum recovery and maximum grade. This may serve as an alternative performance indicator of the floatation row."