Improving processing by adaptation to conditional geostatistical simulation of block compositions

Improving processing by adaptation to conditional geostatistical simulation of block compositions

Tolosana-Delgado, R.; Mueller, U.; van den Boogaart, K. G.; Ward, C.; Gutzmer, J.

Theoretically, exploitation of an ore deposit could be optimized by adapting the beneficiation processes to the properties of each individual ore block being extracted. Such an adaptation can involve switching on and off certain processes, or setting their controlling parameters. These decisions depend typically on physical and chemical attributes. Physical parameters are relevant both at macroscopic and microscopic scale, whereas chemical attributes include both the concentration of the value element, and the presence and abundance of penalty elements. As a first step towards adaptive processing, this contribution explores mapping those adaptive decisions which are based on the composition in value and penalty elements of the selective mining unit or mining block.

Cokriging and geostatistical simulation are reasonable tools to provide information about the concentration of these elements, both in expected value and uncertainty. However, when the sum of total penalty and value elements approaches 100%, it is mandatory that geostatistical results do not exceed that sum. Moreover, some processing techniques work by applying a filter to the composition of material that is being processed, so that their partial output concentration can be taken as a known portion of their input concentration. In such a context, the use of geostatistics on the raw data will deliver inconsistent results, which can be avoided via log-ratio methods: a one-to-one log-ratio transformation is applied to the raw data, followed by modelling via classical multivariate geostatistical tools, and subsequent back-transform of predictions and simulations. Results satisfy the constant sum constraints by construction, even in simulations. Furthermore, filtering processes behave linearly if expressed in terms of log-ratios.

To illustrate the approach, a toy example is used, where a 4-component system (consisting of a value element, two penalty elements and some liberable material, each representing a material type or a set of minerals) is beneficiated through a chain of technical processes. A sequence of milling, desliming and flotation is applied to separate most of the value element, and the product is classified in three qualities. Knowing all processing costs and selling prices, a compositional geostatistical simulation framework can be run to map the best processing choices and qualities as a function of the available measurements of the percentages of the four components, instead of mapping these percentages themselves. In doing so, the uncertainty about gains can be quantified at the same time.

Keywords: Change of support; compositional data analysis; geometallurgy; stochastic optimisation

  • Open Access Logo The Journal of the Southern African Institute of Mining and Metallurgy 115(2015), 13-26