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Geostatistics Applied to Geometallurgical Modeling
R. S. Leal, R. L. Peroni, J. F. C. L. Costa, S. G. Pereira, R. M. Martins and L. N. Capponi
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Personal Information
Ronald Scheffer Leal
• MSc candidate at Federal University of Rio Grande do Sul (UFRGS); • Mining Engineer at Vale Fertilizantes (Araxá – MG).
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Agenda
• Introduction • Objective • Case Study
– Dataset – Univariate Analysis – Estimative Methods
• Reconciliation – Average Difference Results – Estimated Grades Vs. Real Grades Results
• Conclusion • Future Works
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Introduction
PREDICTION
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Objective
• Build an accurate model capable to predict the geometallurgical response in the processing plant.
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Objective
• Comparison between Ordinary Kriging and Indicator Kriging to estimate a geometallurgical model.
Indicator Kriging
Ordinary Kriging
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Additive Variables
• Grade
8% 12%
10%
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Non-Additive Variables
• Metallurgical Recovery
50% 60%
?
50%
60%
55%
30%
80%
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Case Study
• The methodology was applied into a phosphate deposit.
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Dataset
• Total of 5369 samples obtained from a pilot plant; – Apatite Concentrate (P2O5CON); – Metallurgical Recovery (RECTOT); – Mass Recovery (RMTOT).
• The dataset was separated into domains for estimation purposes, since its metallurgical response is directly associated with the weathering zones.
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Univariate Statistics
Variable Name Number of Data Minimum Maximum Mean Standard
Deviation
P2O5CON (%) 2434 11.50 38.00 34.59 2.70
RECTOT (%) 5369 1.77 99.32 56.49 14.10
RMTOT (%) 5369 0.78 55.10 14.98 6.32
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Indicator Kriging
• Estimates a probability of a block to be above or below a determined cut-off
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Indicator Kriging
• Cut-Off selection (based on the deciles of the distribution) • Dataset transformation (0 or 1) • Spatial Analysis for each dataset • Estimative of the probability to be above or below a determined cut-off • Model validation (swath plots)
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Average Difference Analysis
• Measure of discrepancy between the estimative methods.
Indicator Kriging
Ordinary Kriging
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Average Difference Analysis
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Average Difference – P2O5CON
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Average Difference - RECTOT
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Average Difference - RMTOT
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Estimated Grades vs. Real Grades
• Comparison between the grades estimated by the kriged models and the grades obtained from the processing plant.
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Estimated Grades vs. Real Grades
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Estimated Grades vs. Real Grades
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Estimated Grades vs. Real Grades
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Estimated Grades vs. Real Grades
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Discrepancies With Real Grades
• Upscaling effect from pilot plant to the processing plant; • Estimation error associated to the interpolation method; • Lack of geometry adherence between the planned blocks and the ones
really extracted for each pile; • Sampling error at processing and pilot plants.
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Conclusion
• The error analysis showed a significant difference between the estimation methods in some variables;
• The indicator kriged model proved to be more accurate to predict the geometallurgical response in the processing plant, even considering the discrepancies between the planned and the real.
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Future Works
• Representation of a blending pile in the pilot plant, and not isolated samples;
• Reconciliation with the blending pile sample;
• Construction of a correlation equation to estimate only the additive variables and obtain the of geometallurgical variables, instead directly estimate the non-additive variables.
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Acknowledgements
• Thanks for your attention
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References
• Braga, S. A., Costa, J. F. C. L., Silva, F. Krigagem dos Indicadores Aplicada à Modelagem das Tipologias de Minério Fosfatados da Mina F4. Encontro Nacional de Tratamento de Minérios e Metalurgia Extrativa, XXVI, 2015. Poços de Caldas – Brazil. 793-802.
• Mendonça, A., Vieira, M., Costa, J. F. C. L. Métodos Geoestatísticos Aplicados à Modelagem Geometalúrgica. Encontro Nacional de Tratamento de Minérios e Metalurgia Extrativa, XXVI, 2015. Poços de Caldas – Brazil. 813-820
• Gibson, S. A., Thompson, R. N., Leonardos, O. H., Dickin, A. P. & Mitchell, J. G. (1995). The Late Cretaceous Impact of the Trindade Mantle Plume - Evidence from Large - Volume, Mafic, Potassic Magmatism in Se Brazil. Journal of Petrology 36, 189-229.
• Brod, J. A., Gibson, S. A., Thompson, R. N., Junqueira-Brod, T. C., Seer, H. J., Moraes, L. C. & Boaventura, G. R. (2000). The kamafugite-carbonatite association in the Alto Paranaíba igneous province, southeasthern Brazil. Revista Brasileira de Geociências 30, 408-412.
• Matheron, G. 1963. Principles of Geostatistics. Economic Geology, N° 58. • Journel, A. G. 1983. Nonparametric Estimation of Spatial Distributions. Journal of the International Association for
Mathematical Geology, Vol. 15, N° 3, p 445- 468.
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