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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
Personal Information
Ronald Scheffer Leal
• MSc candidate at Federal University of Rio Grande do Sul (UFRGS); • Mining Engineer at Vale Fertilizantes (Araxá – MG).
Agenda
• Introduction • Objective • Case Study
– Dataset – Univariate Analysis – Estimative Methods
• Reconciliation – Average Difference Results – Estimated Grades Vs. Real Grades Results
• Conclusion • Future Works
Introduction
PREDICTION
Objective
• Build an accurate model capable to predict the geometallurgical response in the processing plant.
Objective
• Comparison between Ordinary Kriging and Indicator Kriging to estimate a geometallurgical model.
Indicator Kriging
Ordinary Kriging
Additive Variables
• Grade
8% 12%
10%
Non-Additive Variables
• Metallurgical Recovery
50% 60%
?
50%
60%
55%
30%
80%
Case Study
• The methodology was applied into a phosphate deposit.
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.
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
Indicator Kriging
• Estimates a probability of a block to be above or below a determined cut-off
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)
Average Difference Analysis
• Measure of discrepancy between the estimative methods.
Indicator Kriging
Ordinary Kriging
Average Difference Analysis
Average Difference – P2O5CON
Average Difference - RECTOT
Average Difference - RMTOT
Estimated Grades vs. Real Grades
• Comparison between the grades estimated by the kriged models and the grades obtained from the processing plant.
Estimated Grades vs. Real Grades
Estimated Grades vs. Real Grades
Estimated Grades vs. Real Grades
Estimated Grades vs. Real Grades
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.
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.
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.
Acknowledgements
• Thanks for your attention
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.