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

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.

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

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

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

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 

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   

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

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

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

• 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

• Chuqui, 13,000 samples
• 1,5 m length
• Underground mine, Codelco
• 1000x2300x1000 m3
32
33

(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

36
Understanding this link
37

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

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

Directional Concentration Classes
42
Another deposit (R&T)
43

44
Deposit 1 Deposit 2
45

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

Independent fractures - Deposit 2
48
Geotechnique, RQD (Chuqui)
49
6

*
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

81
Serge Antoine Séguret – Geostatistician - MINES ParisTech, Fontainebleau, France

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

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