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Spatial Modeling of Geometallurgical Properties: Techniques and a Case Study

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Abstract

High-resolution spatial numerical models of metallurgical properties constrained by geological controls and more extensively by measured grade and geomechanical properties constitute an important part of geometallurgy. Geostatistical and other numerical techniques are adapted and developed to construct these high-resolution models accounting for all available data. Important issues that must be addressed include unequal sampling of the metallurgical properties versus grade assays, measurements at different scale, and complex nonlinear averaging of many metallurgical parameters. This paper establishes techniques to address each of these issues with the required implementation details and also demonstrates geometallurgical mineral deposit characterization for a copper–molybdenum deposit in South America. High-resolution models of grades and comminution indices are constructed, checked, and are rigorously validated. The workflow demonstrated in this case study is applicable to many other deposit types.

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References

  • Aitchison, J. (1982). The statistical analysis of compositional data. Journal of the Royal Statistical Society: Series B (Methodological), 44(2), 139–177.

    Google Scholar 

  • Alabert, F. G. (1987). Stochastic imaging of spatial distributions using hard and soft information. Master’s Thesis, Stanford University, Stanford, CA.

  • Babak, O., Cuba, M. A., & Leuangthong, O. (2013). Direct upscaling of semivariograms and cross semivariograms for scale-consistent geomodeling. Transactions of the Society for Mining, Metallurgy, and Exploration, 334(1), 544–552.

    Google Scholar 

  • Babak, O., & Deutsch, C. (2009a). Accounting for parameter uncertainty in reservoir uncertainty assessment: The conditional finite-domain approach. Natural Resources Research, 18(1), 7–17.

    Article  Google Scholar 

  • Babak, O., & Deutsch, C. (2009b). Collocated cokriging based on merged secondary attributes. Mathematical Geosciences, 41(8), 921–926.

    Article  Google Scholar 

  • Barnett, R., & Deutsch, C. (2012). Practical implementation of nonlinear transforms for modeling geometallurgical variables. In P. Abrahamsen, R. Hauge, & O. Kolbjørnsen (Eds.), Geostatistics Oslo 2012 (Vol. 17, pp. 409–422). Netherlands: Springer.

    Chapter  Google Scholar 

  • Barnett, R. M., & Deutsch, C. V. (2013). Imputation of geologic data. Centre for Computational Geostatistics, 15(102).

  • Barnett, R. M., & Deutsch, C. V. (2015). Multivariate imputation of unequally sampled geologic variables. Mathematical Geosciences,. doi:10.1007/s11004-014-9580-8.

    Google Scholar 

  • Barnett, R. M., Manchuk, J. G., & Deutsch, C. V. (2013). Projection pursuit multivariate transform. Mathematical Geosciences, 46(3), 337–359.

    Article  Google Scholar 

  • Bliss, C. I. (1934). The method of probits. Science, 79(2037), 38–39.

    Article  Google Scholar 

  • Boisvert, J. B., Rossi, M. E., Ehrig, K., & Deutsch, C. V. (2013). Geometallurgical modeling at Olympic Dam Mine, South Australia. Mathematical Geosciences, 1–25.

  • Carrasco, P., Chiles, J., & Seguret, S. (2008). Additivity, metallurgical recovery and grade. Paper presented at the Geostats 2008, Santiago, Chile.

  • Chilès, J. P., & Delfiner, P. (2012). Geostatistics: Modeling Spatial Uncertainty (2nd ed.). New York: Wiley.

    Book  Google Scholar 

  • Coward, S., Vann, J., Dunham, S., & Stewart, M. (2009). The primary-response framework for geometallurgical variables. Paper presented at the Seventh International Mining Geology Conference 2009, Perth, Western Australia.

  • Davis, B., & Greenes, K. (1983). Estimation using spatially distributed multivariate data: An example with coal quality. Journal of the International Association for Mathematical Geology, 15(2), 287–300.

    Article  Google Scholar 

  • Desbarats, A. J., & Dimitrakopoulos, R. (2000). Geostatistical simulation of regionalized pore-size distributions using min/max autocorrelation factors. Mathematical Geology, 32(8), 919–942.

    Article  Google Scholar 

  • Deutsch, J. L., & Deutsch, C. V. (2010). Some geostatistical software implementation details. Centre for Computational Geostatistics, 12(412).

  • Deutsch, C. V., & Journel, A. G. (1998). GSLIB: Geostatistical software library and user’s guide (2nd ed.). New York: Oxford University Press.

    Google Scholar 

  • Deutsch, C. V., & Wilde, B. J. (2013). Modeling multiple coal seams using signed distance functions and global kriging. International Journal of Coal Geology, 112, 87–93.

    Article  Google Scholar 

  • Dimitrakopoulos, R., & Jewbali, A. (2013). Joint stochastic optimization of short- and long- term mine production planning: Method and application in a large operating gold mine. IMM Transactions, Mining Technology, 122(2), 110–112.

    Article  Google Scholar 

  • Efron, B. (1982). The jackknife, the bootstrap and other resampling plans. Society for Industrial and Applied Mathematics.

  • Enders, C. K. (2010). Applied missing data analysis. Guilford Press.

  • Everett, J. E., & Howard, T. J. (2011). Predicting finished product properties in the mining industry from pre-extraction data. Paper presented at the The First AusIMM International Geometallurgy Conference, Brisbane, Queensland.

  • Fedkiw, S. O. R. (2003). Level set methods and dynamic implicit surfaces. New York: Springer.

    Google Scholar 

  • Galli, A., Beucher, H., Leloch, G., & Doligez, B. (1994). The pros and cons of the truncated Gaussian method. Geostatistical Simulations: Proceedings of the Geostatistical Simulation Workshop, 7, 217–233.

    Article  Google Scholar 

  • Goovaerts, P. (1997). Geostatistics for natural resources evaluation. New York: Oxford University Press.

    Google Scholar 

  • Isaaks, E. H. (1990). The application of Monte Carlo methods to the analysis of spatially correlated data. PhD Thesis, Stanford University, Stanford, CA.

  • Journel, A., & Xu, W. (1994). Posterior identification of histograms conditional to local data. Mathematical Geology, 26(3), 323–359.

    Article  Google Scholar 

  • Keeney, L., & Walters, S. (2011). A methodology for geometallurgical mapping and orebody modelling. Paper presented at the The First AusIMM International Geometallurgy Conference, Brisbane, Queensland.

  • Kuhar, L. L., Jeffrey, M. I., McFarlane, A. J., Benvie, B., Botsis, N. M., Turner, N. & Robinson, D. J. (2011). The development of small-scale tests to determine hydrometallurgical indices for orebody mapping and domaining. Paper presented at the The First AusIMM International Geometallurgy Conference, Brisbane, Queensland.

  • Leuangthong, O., Hodson, T., Rolley, P., & Deutsch, C. V. (2006). Multivariate geostatistical simulation at Red Dog mine, Alaska, USA. CIM Bulletin, 99(1094), 10.

    Google Scholar 

  • Lozano, C., & Bennett, C. (2003). Geometallurgical modeling applied to production forecasting, plant design and optimisation. SGS Metallurgical Services Technical Report.

  • Lund, C., Lamberg, P., & Lindberg, T. (2014). A new method to quantify mineral textures for geometallurgy. Cape Town: Paper presented at Process Mineralogy.

    Google Scholar 

  • Manchuk, J. G., & Deutsch, C. V. (2012). A flexible sequential Gaussian simulation program: USGSIM. Computers & Geosciences, 41, 208–216.

    Article  Google Scholar 

  • Marchant, B. P., & Lark, R. M. (2004). Estimating Variogram Uncertainty. Mathematical Geology, 36(8), 867–898.

    Article  Google Scholar 

  • Moyeed, R. A., & Papritz, A. (2002). An empirical comparison of kriging methods for nonlinear spatial point prediction. Mathematical Geology, 34(4), 365–386.

    Article  Google Scholar 

  • Newton, M. J., & Graham, J. M. (2011). Spatial modelling and optimisation of geometallurgical indices. Paper presented at the The First AusIMM International Geometallurgy Conference, Brisbane, Queensland.

  • Ortiz, J., & Deutsch, C. (2002). Calculation of uncertainty in the variogram. Mathematical Geology, 34(2), 169–183.

    Article  Google Scholar 

  • Pardo-Igúzquiza, E., & Dowd, P. (2001). Variance-covariance matrix of the experimental variogram: Assessing variogram uncertainty. Mathematical Geology, 33(4), 397–419.

    Article  Google Scholar 

  • Pawlowsky-Glahn, V., & Olea, R. A. (2004). Geostatistical analysis of compositional data. USA: Oxford University Press.

    Google Scholar 

  • Powell, M. S. (2013). Utilising orebody knowledge to improve comminution circuit design and enery utilisation. Paper presented at the The Second AusIMM International Geometallurgy Conference, Brisbane, Australia.

  • Pyrcz, M. J., & Deutsch, C. V. (2014). Geostatistical reservoir modeling. Oxford: Oxford University Press.

    Google Scholar 

  • Pyrcz, M. J., Gringarten, E., Frykman, P., & Deutsch, C. V. (2006). Representative input parameters for geostatistical simulation. In T. C. Coburn, J. M. Yarus, & R. L. Chambers (Eds.), Stochastic modeling and geostatistics: Principles, methods, and case studies, volume II: AAPG Computer Applications in Geology (Vol. 5, pp. 123–137). New York: Wiley.

    Google Scholar 

  • Rossi, M. E., & Deutsch, C. V. (2013). Mineral resource estimation. New York: Springer Science & Business Media.

    Google Scholar 

  • Silva, D. A., & Deutsch, C. V. (2013). Correcting distance function models to correct proportions. Centre for Computational Geostatistics, 15(116), 1–10.

    Google Scholar 

  • Switzer, P., & Green, A. A. (1984). Min/max autocorrelation factors for multivariate spatial imagery. In L. Billard (Ed.), Computer Science and Statistics: The Interface (Vol. 16). Amsterdam: Elsevier.

    Google Scholar 

  • van den Boogaart, K. G., Konsulke, S., & Tolosana Delgado, R. (2013). Non-linear geostatistics for geometallurgical optimisation. Paper presented at the The Second AusIMM International Geometallurgy Conference, Brisbane, Australia.

  • Van Tonder, E., Deglon, D. A., & Napier-Munn, T. J. (2010). The effect of ore blends on the mineral processing of platinum ores. Minerals Engineering, 23(8), 621–626.

    Article  Google Scholar 

  • Vargas-Guzmán, J. A., & Dimitrakopoulos, R. (2003). Computational properties of min/max autocorrelation factors. Computers & Geosciences, 29(6), 715–723.

    Article  Google Scholar 

  • Yan, D., & Eaton, R. (1994). Breakage properties of ore blends. Minerals Engineering, 7(2–3), 185–199.

    Article  Google Scholar 

Download references

Acknowledgments

Many discussions on best practices in multivariate geostatistical modeling with Ryan Barnett and other colleagues at the Centre for Computational Geostatistics are gratefully acknowledged. The input of Bryan Rairdan, Rodrigo Marinho, the editor of Natural Resources Research, and three anonymous reviewers is also much appreciated.

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Correspondence to Jared L. Deutsch.

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Deutsch, J.L., Palmer, K., Deutsch, C.V. et al. Spatial Modeling of Geometallurgical Properties: Techniques and a Case Study. Nat Resour Res 25, 161–181 (2016). https://doi.org/10.1007/s11053-015-9276-x

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