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 and species recovery 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. Formal treatment of the problem provides a generalized, albeit complex, expression for the uncertainty (Wills, 1997), limited to relatively small input disturbances. This paper explores the problem further using Monte Carlo simulations, covering the effects of relatively small through to relatively large input disturbances. Assay values for the feed, GF, product, GP, and tailings, GT, were assumed to have the same relative uncertainty. The work focussed on the amplification in the uncertainty of the yield, AY, and recovery, AR, resulting in very simple expressions, AY ∼ 2 GF/|GF – GT| and AR ∼ 2 GT/|GF – GT|.