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

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