Journal of the Southern African Institute of Mining and Metallurgy
On-line version ISSN 2411-9717
Print version ISSN 0038-223X
MARQUES, D.M. and COSTA, J.F.. Analysis of the dispersion variance using geostatistical simulation and blending piles. J. S. Afr. Inst. Min. Metall. [online]. 2014, vol.114, n.8, pp.587-599. ISSN 2411-9717.
SYNOPSIS The additive property of dispersion variances was found experimentally by D.G. Krige using data from the gold deposits of the Witwatersrand. In this property, called 'Krige's relationship', the dispersion of a small unit, v, within the deposit is equal to the sum of the dispersion of v within a bigger unit, V, and the dispersion of these units, V, within the deposit, D. It is known that the variance of the grades decreases as the support increases, the so-called volume-variance relationship. To analyse volume-variance and Krige's relationship, the methodology herein proposed combines blending piles and geostatistical simulation to simulate the in situ and the pile grade variability. Variability reduction in large piles is based on the volume-variance relationship, i.e. the larger the support, the smaller the variability (assuming perfect mix). Based on a pre-defined mining sequence to select the blocks that will form each pile for each simulated block model, the statistical fluctuation of the grades derived from real piles can be simulated. Using this methodology, one can evaluate within a certain time period the expected grade variability for various pile sizes, and also calculate the Krige's relationship between the small blocks and the piles of different sizes. A real case study using a large Brazilian iron ore deposit illustrates the methodology and demonstrates the validity of the results.
Keywords : dispersion variance; blending piles; simulation; Krige's relationship.