Abstract
André Journel joined Stanford University in 1978, and his program grew quickly to include a dozen students from the USA, Canada, Europe, and South Africa. He was instrumental in organizing the Second International Geostatistical Conference (Tahoe ’83), during which 13 papers were presented that can be linked to his group. Out of these 13 papers, 9 were mining-related, with 7 on recoverable reserves, 2 on uncertainty, 2 on conditional simulation, and 3 on nonparametric geostatistics. A significant research effort at the time was therefore directed at change of support, global and local recoveries, and uncertainty, but future trends could also be identified, such as nonparametric geostatistics and conditional simulation. This paper is a practical review of conditional simulation as a tool to improve mineral resource estimation in the areas of uncertainty, classification, and mining selectivity or dilution, based on the authors’ experience. Some practical considerations for conditional simulation are briefly discussed. Four case studies from the early 1990s to the late 2010s are presented to illustrate some solutions and challenges encountered when dealing with real-world commercial projects.
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References
Abzalov MZ (2006) Localised uniform conditioning (LUC): a new approach for direct modelling of small blocks. Math Geol 38(4):393–411. https://doi.org/10.1007/s11004-005-9024-6
Armstrong M, Ndiaye A, Razanatsimba R, Galli A (2013) Scenario reduction applied to geostatistical simulations. Math Geosci 45(2):165–182. https://doi.org/10.1007/s11004-012-9420-7
Benndorf J, Buxton M, Shishvan MS (2014) Sensor-based real-time resource model reconciliation for improved mine production control—a conceptual framework. In: Dimitrakopoulos R (ed) Orebody Modelling and Strategic Mine Planning: Integrated mineral investment and supply chain optimisation. AUSIMM Publication Series No 13/2014, pp 223 – 233
Benndorf J (2020) Closed loop management in mineral resource extraction: turning online geo-data into mining intelligence. Springer, Berlin
Boucher A, Dimitrakopoulos R, Vargas-Guzman JA (2004) Joint simulations optimal drillhole spacing and the role of the stockpile. In: Leuangthong O, Deutsch CV (eds) Geostatistics Banff 2004. vol. 1, pp 35–44, Springer, Dordrecht
Boucher A, Dimitrakopoulos R (2009) Block simulation of multiple correlated variables. Math Geosci 41(2):215–237. https://doi.org/10.1007/s11004-008-9178-0
Cáceres A, Emery X, Aedo L, Gálvez O (2011) Stochastic geological modelling using implicit boundary simulation. In: Proceedings of the 2nd International Seminar on Geology for the Mining Industry, GEOMIN 2011, p 10
Chica-Olmo M, Laille JP (1983) Simulation of a brown coal deposit. In: Verly G, David M, Journel AG, Marechal A (eds) Geostatistics for Natural Resource Characterization, vol 2. Reidel, Dordrecht, pp 1001–1014
Chilès JP (1983) Simulation of a nickel deposit: problems encountered and practical solution. In: Verly G, David M, Journel AG, Marechal A (eds) Geostatistics for Natural Resource Characterization, vol 2. Reidel, Dordrecht, pp 1015–1030
Coombes J, Thomas G, Glacken I, Snowden V (2000) Conditional simulation—which method for mining? In Kleingeld WJ, Krige DG (eds) Geostatistics 2000, vol. 2, pp 677–691, Cape Town
Davis B (1997) Some methods of producing interval estimates for global and local resources. In: SME Preprint 97–5, p 4
Deraisme J, de Fouquet C (1983) Recent and future developments of “downstream” geostatistics. In: Verly G, David M, Journel AG, Marechal A (eds) Geostatistics for Natural Resource Characterization, vol 2. Reidel, Dordrecht, pp 979–1000
Dimitrakopoulos R, Farelly CT, Godoy M (2002) Moving forward from traditional optimization: grade uncertainty and risk effects in open-pit design. Mining Technol 111(2):A82–A88
Dimitrakopoulos R (2011) Stochastic optimization for strategic mine planning: A decade of developments. J Min Sci 47(2):138–150
Dimitrakopoulos R, Godoy MC (2014) Grade control based on economic ore/waste classification functions and stochastic simulations – examples, comparisons and applications. In: Mineral Resource and Ore Reserve Estimation, The AusIMM Guide to Good Practice, Second Edition. AusIMM Monograph 30, pp 685–699
Dimitrakopoulos R (ed) (2018) Advances in applied strategic mine planning. Springer, Berlin
Dowd P (1983) Conditional simulation of inter related beds in an oil deposit. In: Verly G, David M, Journel AG, Marechal A (eds) Geostatistics for Natural Resource Characterization, vol 2. Reidel, Dordrecht, pp 1031–1044
Glacken IM (1997) Change of support and use of economic parameters for block selection. In: Baafi EY, Schofield NA (eds) Geostatistics Wollongong, vol 2. Kluwer Academic, Dordrecht, pp 811–821
Godoy MC, Dimitrakopoulos R, Costa, JF (2001) Economic functions and conditional simulation applied to grade control. In: Mineral Resource and Ore Reserve Estimation—The AusIMM Guide to Good Practice. AusIMM Monograph 23, pp 591–599
Godoy M, Dimitrakopoulos R (2011) A risk quantification framework for strategic mine planning: method and application. J Min Sci 47(2):235–246
Goodfellow R, Dimitrakopoulos R (2016) Global optimization of open pit mining complexes with uncertainty. Appl Soft Comput 40:292–304. https://doi.org/10.1016/j.asoc.2015.11.038
Goodfellow R, Dimitrakopoulos R (2017) Simultaneous stochastic optimization of mining complexes and mineral value chains. Math Geosci 49(3):341–360. https://doi.org/10.1007/s11004-017-9680-3
Helwick SJ, Luster GR (1983) Fluid-flow modeling using a conditional simulation of porosity and permeability. In: Verly G, David M, Journel AG, Marechal A (eds) Geostatistics for natural resource characterization, vol 1. Reidel, Dordrecht, pp 635–650
Isaaks EH (1983) Indicator simulation: application to the simulation of a high grade uranium mineralization. In: Verly G, David M, Journel AG, Marechal A (eds) Geostatistics for Natural Resource Characterization, vol 2. Reidel, Dordrecht, pp 1046–1057
Isaaks EH (1990) The application of Monte Carlo methods to the analysis of spatially correlated data. Ph.D. Thesis, Stanford University, p 213
Isaaks E (2004) The Kriging oxymoron: a conditionally unbiased and accurate predictor (2nd Edition). In: Leuangthong O, Deutsch CV (eds) Geostatistics Banff 2004, vol 1. Springer, Dordrecht, pp 363–374
Jewbali A, Perry R, Allen L, Inglis R (2014) Applicability of categorical simulation methods for assessment of mine plan risk. In: Dimitrakopoulos R (ed) Orebody Modelling and Strategic Mine Planning: Integrated mineral investment and supply chain optimisation. pp 85–97, AUSIMM Publication Series No 13/2014,
Journel AG (1974) Geostatistics for conditional simulation of ore bodies. Econ Geol 69(5):673–687
Journel AG (1975) Ore grade distributions and conditional simulations – two geostatistical approaches. In: Guarascio M, David M, Huijbregts C (eds) Advanced geostatistics in the mining industry. Springer, Dordrecht, pp 195–202
Journel AG (1983) The place of non-parametric geostatistics. In: Verly G, David M, Journel AG, Marechal A (eds) Geostatistics for natural resource characterization, vol 1. Reidel, Dordrecht, pp 307–335
Journel AG, Kyriakidis PC (2004) Evaluation of mineral reserves: a simulation approach. Oxford University Press, New York, p 216
Le Loc’h G, Galli A (1996) Truncated pluriGaussian method: theoretical and practical points of view. In: Baafi EY, Schofield NA (eds) Geostatistics Wollongong’96, vol 1. Kluwer Academic, Dordrecht, pp 211–222
Lyster S, Deutsch CV (2004) Short Note: sequential indicator simulation with local probabilities derived from a deterministic rock type model. CCG Paper 2004–305. Centre for Computational Geostatistics, University of Alberta
Marcotte D (1993) Direct simulation of block grades. In: Dimitrakopoulos R (ed) Geostatistics for the Next Century, pp 245–252
Montiel L, Dimitrakopoulos R, Kawahata K (2014) Globally optimising open pit and underground mining operations under geological uncertainty. In: Dimitrakopoulos R (ed) SMP Symposium 2014 Orebody Modelling and Strategic Mine Planning: Integrated mineral investment and supply chain optimisation. AUSIMM Publication Series No 13/2014, pp 201–211
Montiel L, Dimitrakopoulos R (2017) A heuristic approach for the stochastic optimization of mine production schedules. J Heuristics 23(5):397–415. https://doi.org/10.1007/s10732-017-9349-6
Montiel L, Dimitrakopoulos R (2018) Simultaneous stochastic optimization of production scheduling at Twin Creeks Mining Complex. Nevada Mining Eng 70(12):48–56
Murphy M, Parker HM, Ross A, Audet MA (2004) Ore-thickness and nickel grade resource confidence at the Koniambo nickel laterite (a conditional simulation voyage of discovery). In: Leuangthong O, Deutsch CV (eds) Geostatistics Banff 2004, vol 1. Springer, Dordrecht, pp 469–478
Neufeld C, Deutsch CV (2007) Why choosing one realization for mine planning is a bad idea. CCG Paper 2007–310. Centre for Computational Geostatistics, University of Alberta
Parker HM, Dohm C (2014) Evolution of Mineral Resource classification from 1980 to 2014 and current best practice. Finex 2014 Julius Wernher Lecture
Parker HM (2014) Reconciliation principles for the mining industry. In: Mineral Resource and Ore Reserve Estimation, The AusIMM Guide to Good Practice, Second Edition. AusIMM Monograph 30, pp 721–737
Parker HM, Hill E, Morgan R (2015) Comparison of Fort Knox gold deposit resources from pre-feasibility study (1991) to production (1997 to 2015), 37th APCOM Presentation
Pasti HA, Leite Costa JFC, Boucher A (2012) Multiple-point geostatistics for modeling lithological domains at a Brazilian iron ore deposit using the single normal equations simulation algorithm. In: Abrahamsen P, Hauge R, Kolbjørnsen O (eds) Geostatistics Oslo 2012. Springer, Dordrecht, pp 397–407
Ramazan S, Dimitrakopoulos R (2004) Stochastic optimisation of long-term production scheduling for open pit mines with a new integer programming formulation. In Dimitrakopoulos R (ed) Orebody Modelling and Strategic Mine Planning: Uncertainty and Risk Management. AUSIMM Publication Series No 7/2004, pp 353 – 359
Ravenscroft PJ (1992) Risk analysis for mine scheduling by conditional simulation. Trans. Inst. Min. Metall. (Sec. A: Min. Industry), vol. 101
Remacre AZ (1989) Uniform conditioning versus indicator kriging. In: Armstrong M (ed) Geostatistics: Proceeding of the Third International Geostatistics Congress), vol 2. Kluwer, Dordrecht, pp 947–960
Schofield N, Rolley P (1997) Optimisation of ore selection in mining: Method and Case Studies. In: Third International Mining Geology Conference. AusIMM-AIG, Series 6.97, pp 93–97
Schofield NA (2001) Determining optimal drilling densities for near mine resources. In: Mineral Resource and Ore Reserve Estimation—The AusIMM Guide to Good Practice. AusIMM Monograph 23, pp 293–298
Searston S, Smith LB, Verly G (2020) Farewell to Harry Parker (1946–2019). Math Geosci 52:447–450. https://doi.org/10.1007/s11004-020-09865-2
Silva DSF, Boisvert JB (2014) Mineral Resource classification: a comparison of new and existing techniques. J Southern African Instit Min Metall 114:265–273
Snowden V (2001) Practical interpretation of mineral resource and ore reserve classification guidelines. In: Mineral Resource and Ore Reserve Estimation—The AusIMM Guide to Good Practice. AusIMM Monograph 23, pp 643–652
Strebelle S (2002) Conditional simulation of complex geological structures using multiple-point statistics. Math Geol 34(1):1–21. https://doi.org/10.1023/A:1014009426274
Strebelle S, Remy N (2005) Post-processing of multiple-point geostatistical models to improve reproduction of training patterns. In: Leuangthong O, Deutsch CV (eds) Geostatistics Banff 2004, vol 2. Springer, Dordrecht, pp 979–988
Verly G (2005) Grade control classification of ore and waste: a critical review of estimation and simulation based procedures. Math Geol 37(5):471–475. https://doi.org/10.1007/s11004-005-6660-9
Verly G, Brisebois K, Hart W (2008) Simulation of geological uncertainty, Resolution porphyry copper deposit. In: Ortiz JM, Emery X (eds) Proceedings of the Eight International Geostatistics Congress, pp 31–40
Verly G, Postolski T, Parker HM (2014) Assessing uncertainty with drill hole spacing studies—applications to Mineral Resources. In: Dimitrakopoulos R (ed) Orebody Modelling and Strategic Mine Planning Symposium 2014, AUSIMM Publication Series No 13/2014, pp 109–118
Verly G., Parker HM, Artica C, Kim H, Bortoletto Machado EL (2017) Classification and dilution study by simulation of a large copper deposit, Peru. In: Dagdelen K (ed) Proceedings of the 38th APCOM International Symposium, pp K-11-K-18
Wambeke T, Benndorf J (2018) A Study of the influence of measurement volume, blending ratios and sensor precision on real-time reconciliation of grade control models. Math Geosci 50(7):801–826
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The authors would like to thank the John Wood Group plc for permission to publish this paper. They also thank the reviewers whose comments and suggestions helped improve the paper.
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Verly, G., Parker, H.M. Conditional Simulation for Mineral Resource Classification and Mining Dilution Assessment from the Early 1990s to Now. Math Geosci 53, 279–300 (2021). https://doi.org/10.1007/s11004-021-09924-2
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DOI: https://doi.org/10.1007/s11004-021-09924-2