Optimization of cut-off grades considering grade uncertainty in narrow, tabular gold deposits

Abstract

Mineral reserve statements as well as optimizing mine planning require a block model with grades for each mining block. A cut-off grade is determined by considering the mining costs as well as the expected revenue for each block. These grades are estimated using various techniques, but in reality there is uncertainty in the grade values. These uncertainties result in two types of error. A type I error is where material is classified as ore and mined, but the true value is below the cut-off grade and the material is therefore waste. This material constitutes dilution. The type II error is where material is estimated to be below the cut-off grade and is classified as waste, whereas the true grade is actually above the cut-off grade. This material is not mined and the value is lost. This research considers the value of the lost ore and the costs of dilution under various degrees of uncertainty. Simulation using @Risk and mixed integer linear programing (Excel Solver) is used in a financial optimizer model to maximize either profit or net present value. This is applied to four Witwatersrand tabular gold deposits to investigate the impact of block grade uncertainty on cut-off grades. When optimizing for profit, value may be added by adjusting the cutoff grade slightly downwards. When optimizing for NPV, value may be added by lowering the cut-off grade significantly for the lower discounting rates. At higher discount rates, the lowering of the cut-off grades should be reduced, and in some cases an increase in cut-off grade may be required. Each mine reacted differently to the optimization and thus there is no single rule that can be applied across all tabular Witwatersrand gold deposits.