Modelling metal recovery by co-kriging the feed and concentrate masses of metal

Geometallurgical modelling is increasingly being incorporated into mineral resource modelling and estimation as a means of increasing efficiency, decreasing operating costs and reducing risk in mining operations. Traditional geostatistical workflows for geometallurgical modelling face several difficulties, in particular, related to the non-additivity of process response variables, to highly heterotopic data sets and/or to preferential sampling designs, all of which may explain why most attempts to estimate geometallurgical response variables from assay data and mineralogy are still based on statistics and machine learning. The aim of the work presented here is to demonstrate the applicability of geostatistics to estimate copper recovery from copper sulfide ores at the Prominent Hill Iron Oxide Copper-Gold (IOCG) deposit in Australia. As recovery is non-additive, the preferred workflow is the joint estimation of the masses of metal in the feed and in the concentrate, both of which are additive variables. While the mass of metal in the feed can be estimated from abundant online assay analyses, the mass of metal in the concentrate can only be estimated from a very limited number of laboratory-scale batch flotation tests. Traditional approaches to estimating the masses of metal in the feed and in the concentrate, such as simple and ordinary co-kriging, are described and discussed. A modified version of co-kriging is introduced, which incorporates linear relationships between the mean values of the input variables, in addition to a spatial correlation model. Co-kriging with related means is shown to outperform traditional simple and ordinary co-kriging in terms of precision, accuracy and consistency of the estimates, and offers a practical and efficient tool to deal with highly heterotopic and preferential sampling designs.