Amplification in the Uncertainty of the Yield and Recovery for a Steady-State Mineral Separator calculated using the Two-Product Formula

This paper presents a simple relationship for estimating the uncertainty in the overall yield (Y) and species recovery (Ri) when the two-product formula is applied to assays of the feed, product and tailings streams of a steady-state mineral separator. The non-linearity of the two-product formula means the reliability of these yield and recovery values can vary significantly. Monte Carlo simulations were used to investigate the uncertainty in the yield and recovery relative to the uncertainty in the raw assay data, referred to as the yield error amplification and recovery error amplification respectively. All assays were assumed to have the same relative uncertainty. We used a transformation of the data set to produce a simple analytical expression to describe these two error amplifications, which are ~ sqrt(2)(1 – Y)/|Ri – Y| and sqrt(2)(1 – Ri)/|Ri – Y| respectively for the yield and recovery. These equations enable practitioners to estimate the uncertainty in the yield and recovery values calculated using the two-product formula.