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Innovative methods in geostatistics from studies in Chilean copper deposits - Serge Séguret

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Drawing on hands-on experience and theoretical contributions Serge will encourage attendees to consider innovative approaches to problems across the mining logic chain, with examples including:
• Porphyry unit modelling - Simulations
• Integrating grade control and resource drilling data – Co-kriging
• Modelling geotechnical characteristics - Directional Concentration
• Predicting metallurgical recovery & sampling – non additivity

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Innovative methods in geostatistics from studies in Chilean copper deposits - Serge Séguret

  1. 1. 1serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits Innovative methods in geostatistics from studies in Chilean copper deposits CONSULTANT OFFICE UNIVERSITY Research for money Money for Research Research for … … research ? Serge Antoine Séguret – Geostatistician - MINES ParisTech, Fontainebleau, France serge.seguret@mines-paristech.fr Since 2003 Serge Séguret has been heavily involved in the application of geostatistics in the mining industry for partners including Codelco (Chile, copper), Vale (Brazil, iron) and Ma’aden (Saudi Arabia, phosphate) and more recently on South America lithium deposits. Serge completed his PhD under the supervision of Georges Matheron at the Centre for Geostatistics in Fontainebleau in 1991. For more than 30 years Serge has contributed to the dissemination of Geostatistics through theoretical works and applications in various domains including Marine Geophysics, Petroleum and Environment Application of the Truncated Gaussian Simulation Method to the MM deposit at Codelco Norte, Chile. EAGE Madrid, Spain, 2005. Analysis and Estimation of Multi-unit Deposits - Application to a Porphyry Copper Deposit. Mathematical Geosciences, 2013. Geostatistical comparison between blast and drill holes in a porphyry copper deposit. 7th world conference on sampling and blending, Bordeaux, France, 2015. Fracturing, Crushing and Directional Concentration. Mathematical Geosciences, 2016. Geostatistical Evaluation of Rock-Quality Designation and its link with Linear Fracture Frequency. IAMG, Freiberg, Germany. 2015. Additivity, metallurgical recovery, and grade. 8th international Geostatistics Congress, Santiago, Chile, 2008 Spatial sampling effect of laboratory practices in a porphyry copper deposit. 5th World Conference on Sampling and Blending, Santiago, Chile, 2011.
  2. 2. 2serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits 3 Mining Drill & Blast Recovery Sampling Geotechnique Geological units Intrusive object Units & Grades ProductionBefore production 1 2 3 4 5 6 7 8 5  T G S MM fault Unit simulations (MM)1
  3. 3. 3serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits 7 Dyke (El Teniente) 4 500 drill holes 2 10 Block Modelling (Chuqui’, MM(H), R&T) Current practices Geological interpretation Drilhole 1 Drilhole 2 Drillholes Data Block gradesProportions by block 3
  4. 4. 4serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits 11 Modelling the problem n units {i}  i1 (x) 1 grade  Cu(x) i1 (x) Cu(x) = Cu (x)i  Partial grades x, 1 (x) 1 x, Cu(x) Cu (x)i i n n       x, Cu (x) Cu (x)COK COK i n     Simplifying ?Cu (x)COK i n partial grades i ( ) ( Metal)Cu x n unit indicators i1 ( ) ( Geometry)x ij i (h) (h)   = p(x+h j | x i, x+h i)   iiZ i (h) (h)   = E[Z(x+h) | x+h i, x i]  Probabilistic interpretation 12
  5. 5. 5serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits iiZ i (h) (h)   = E[Z(x+h) | x+h i, x i]  Application (Chuqui, MM, R&T) /ix, i Cu (x) m 1 (x) R (x)i i i    Simplifying ,yes Cu (x)COK i /iCu (x) m 1 (x) R (x)COK COK K i i i   /iCu (x) m 1 (x) R (x)S COS S i i i  TGS 13 14 Also Chuqui (cross validation) R&T (blast holes) Cu Geol Cu Geol Cu Geol Cu Blast Cu Blast Cu Blast Cu Partial Grades Cu Partial Grades Cu Partial Grades 0.67  0.63  0.69 
  6. 6. 6serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits 15 Conclusions Combining ≠ approaches: @ Resource classification level By geologist By geostat. 122 000 samples 12 000 samples 16 /ix, i Cu (x) m 1 (x) R (x)i i i   
  7. 7. 7serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits Blast holes Drill holes • Few • Long term planning (month, year, decade) • Large scale strategy • “Good” quality • Many • Short-term planning (day, week,) • Small-scale selectivity • Bad quality Question: how to combine the two types of measurements? Blast & Drill Holes (R&T) 17 4 ( )Drill h int ( )Po h3 m deconvolution 15 m // convolution 15 m  convolution // ( )Blast h ( )Blast h  18
  8. 8. 8serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits 19 15( , , ) ( , , ) ( ) ( , , )blast m blastY x y z Y x y z p z R x y z   3( , , ) ( , , ) ( ) ( , , )drill m drillY x y z Y x y z p z R x y z   15( ) ( ) ( )blastblast m Rh h h     3( ) ( ) ( )drilldrill m Rh h h     Blast sampling error Drill sampling error 20
  9. 9. 9serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits 21 1. Filtering the blast error 2. Blast deconvolution 3. Block modelling using blasts & drills fract NC N ( ) FF( ) L ( ) x x x  Geotechnique, FF (Chuqui, R&T) 29 5
  10. 10. 10serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits • Not additive • How estimating at block scale? fract 1 fract 2 1 2 NC 1 NC 2 fract 1 fract 2 NC 1 NC 2 N ( ) N ( ) FF( ) L ( ) L ( ) 1 N ( ) N ( ) 2 L ( ) L ( ) x x x x x x x x x x           Measures FF(x1) FF(x2) FF(x5)FF(x3) FF(x5) FF*(V)? FF(x1) FF(x2) Additivity 30 Observation of a natural phenomenon 31
  11. 11. 11serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits • Chuqui, 13,000 samples • 1,5 m length • Underground mine, Codelco • 1000x2300x1000 m3 32 33
  12. 12. 12serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits (1) (2) (3) 34 fract NC * N ( ) FF ( ) L ( ) K x x K x V V V  Measures FF(x1) FF(x2) FF(x5)FF(x3) FF(x5) FF*(V)? 35
  13. 13. 13serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits 36 Understanding this link 37
  14. 14. 14serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits Directional Classes 1 ( ) ( , ) n totN x N x     Terzagui Correction 38 Directional Concentration 1 ( ) ( , ) n totN x N x     2 2 ,( ) [ ( , )] [( ( , ) ( )) ]meanx Var N x E N x N x         , ( ) ( ) tot mean N x N x n    2 2 , 1 ( ) 1 ( ( , ) ( )) n meanx N x N x n         39
  15. 15. 15serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits 2 ( ) 0x  full directional isotropy, all the fractures are equally distributed over the directions 2 2 ,max( )x    2 2 2 ,max ,0 ( ) ( ) ( ) ( 1)meanx x N x n         full directional anisotropy, all the fractures lie along one direction 2 2 2 2 1,max , ( ) ( ) 1 ( , ) ( 1) ( ) ( 1) ( ) n mean x x N x R x n n N x                40 41
  16. 16. 16serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits Directional Concentration Classes 42 Another deposit (R&T) 43
  17. 17. 17serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits 44 Deposit 1 Deposit 2 45
  18. 18. 18serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits Residual model  2 , , ,( ) ( ( )) ( ) 1 ( ) ( ) ( ( ))Ntot tot N Lc C N Lc N Lc Lc N x x L x x RSD x C x         , (x)= (x) + (x)tot corr indx N N N 46 Independent fractures - Deposit 1 47
  19. 19. 19serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits Independent fractures - Deposit 2 48 Geotechnique, RQD (Chuqui) 49 6
  20. 20. 20serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits * i i aR bS  * * * i i i CuR R CuT  Oxide Copper 66 Metallurgy, recovery (Andina, Gaby)7 71 Sampling (Andina) CAUSES •Spatial restriction •Regularization •Sampling density •Grade selection 8
  21. 21. 21serge.seguret@mines-paristech.fr Innovative methods in geostatistics from studies in Chilean copper deposits 81 Serge Antoine Séguret – Geostatistician - MINES ParisTech, Fontainebleau, France

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