On the Joint Multi Point Simulation of Discrete and Continuous Geometallurgical Parameters

Abstract

Geometallurgical parameters are descriptions of the mineralogy and microstructure of the ore determining its mineralogical and microstructural char- acteristics. From a conditional geostatistical simulation of such properties, a pro- cessing model can compute recovery, equipment usage, processing costs, and thus the monetary value for mining and processing a block with certain processing parameters. The output can be used for optimising mining sequences or finding optimal processing parameters by solving the corresponding stochastic optimisation problem. The approach requires two properties of the simulation not provided by established geostatistical techniques: (1) Many relevant geometallurgical parameters are from non-Euclidean statistical scales such as (mineral) compositions, (grain size) distribution, (grain) geom- etry, and (stratigraphic type) categorical which might produce nonsensical values (for example, negative proportions, negative facies probabilities, planar grains) when simulated with standard geostatistical techniques. (2) Due to the nonlinearity of processing, the entire conditional distribution of the geometallurgical parameters is relevant, not only its mean and variance. The geostatistical simulation needs to reproduce the joint conditional distributions of all the geometallurgical parameters. The multi-point conditional geostatistical simulation technique discussed here allows for jointly simulating dependent spatial variables from various sample spaces. The technique combines an infill simulation, similar to the one used in multi-point geostatistics (MPS), with a new form of distributional regression to estimate conditional distributions of arbitrary scales from different information sources, including training images, training models and observed data. The distri- butional regression is based on a generalisation of logistic regression and is related to both Bayesian Maximum Entropy (BME) geostatistics and high order cumulants. The method ensures that simulated data reside in the set of possible values and honour the characteristics of the joint distribution to be reproduced. The compu- tational effort is substantial, but affordable for a useful application with standard problems: from processing-aware block value prediction and block processing optimisation as shown in the test application to a mathematically completely defined simulated model situation with a complex processing model.