Many computer program packages are available to utilize in geostatistical interpretation. These include VULCAN, PETRA, GEOGRAPHIX, and in the case of this example I will be using SGEMS - a freeware program. Kriging : Derives the best linear estimate of the variable over a given surface. Smoothing properties of interpolation algorithms replace local detail and replace with a good average. Geologists and reservoir engineers / mining conditions require finer scaled details of reservoir heterogeneity – Kriging is the average of numerous realizations, we may want to see these iterations to determine best fit scenarios

1. COMPUTER BASED FACIES
SIMULATIONS IN OREBODIES:
BENEFITS, DRAWBACKS AND
PRACTICAL EXAMPLES
Geological Society of America Rocky Mountain Section
Friday, 22 May 2015
Mike Bingle-Davis
Kirkwood Oil and Gas
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2. Reservoir or Deposit Simulations/Modeling
• End goal is to construct a gridded model
• Contains properties including, porosity, permeability, capillary pressure,
grade, redox. state, etc.
• Wells widely spaced with auxiliary information to enhance model
output values
• Dependent on stage of field development
• Primary : optimize location of new wells or drilling
• Secondary : infilling of data, increasing resolution of modeling
• Tertiary : historical matching becomes possible
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3. Gaussian or Normal Distribution /
Plurigaussian Approach
• The Central Limit Theorem
states that the arithmetic mean
of a sufficiently large number of
independent random variables
with be approximately normally
distributed, regardless of
underlying distribution
• Plurigaussian is an approach
where there are multiple
normally distributed attributes
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4. SGeMS data formatting
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5. 5
Example 1 : Reservoir Porosity

6. Variogram Computational Parameters
• Reduction of the estimation
• Weights placed on each
measurement are spatially
dependent
• Variogram tool allow for fitting
of the function
• Finding the best fitted variogram
can replicate trends within the
dataset
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7. 7

8. Sequential Gaussian Simulation of Porosity
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• Constructs iterative possibilities
• Depending on model stage, each
iteration should be considered

9. Example 2: Sequential Indicator of Facies
Portion of the facies sequence
1. Continental SS
2. Continental SLTS
3. Mud supported LS
4. Grain supported LS and
DOL
5. Marine SS
Determined as though a
transgressive-regressive
sequence on a very broad
shelf
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10. 10
Variogram Analysis – Each facies

11. 11
Kriged block diagram result of facies analysis

12. Example 3: Simulation of a Porphyry Copper
Deposit: Bajo de la Alumbrera, Argentina
Minera Alumbrera Ltd., Argentina
Northern Orion Explorations Ltd.
*thank you SEC
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14. Geology: Close-up
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15. Kriging Zones and Variogram Parameters
Model type Spherical
Nugget 0.1
Sill 0.5
Range along major axis 450 m
Range along minor axis 170 m
Range along vertical
axis
650 m
Direction of major axis
in Grade Zone = 93
150 o
Direction of major axis
in Grade Zone = 94
170 º
Plunge of major axis 0
Dip easterly 0
Distance along major
axis
225 m (Half variogram
range along major axis)
Distance along minor
axis
85 m (Half variogram
range along minor axis)
Distance along vertical
axis
325 m (Half variogram
range along vertical axis)
Anisotropic distances Yes
Block discretization 4 x 4 x 1
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16. Copper Block Model based on kriging
algorithm for copper and gold (October 2001)
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ULTIMATE PIT
BOREHOLES
JUNE 1999 SURFACE
0-0.15% Cu
0.15-0.30% Cu
0.30-0.60% Cu
0.60-1.20% Cu
>1.20% Cu

17. Block Model with Category
CATEG Category Comments
= 1 Waste All blocks outside the 0.15 %Cu Envelope and Low Grade Halo
(Grade Zone = 93 & 94) or within these domains but with an
undefined kriging variance.
= 2 Measured All blocks with a kriging variance ranged between 0.00 and
0.159 and within the 0.15% Cu Envelope and Low Grade Halo
(Grade Zone = 93 & 94).
= 3 Indicated All blocks with kriging variance ranging between 0.16 and
0.239 and within the 0.15 % Cu Envelope and Low Grade Halo
(Grade Zone = 93 & 94).
= 4 Other All blocks with a kriging variance ranging between 0.24 and
0.319 and within the 0.15 % Cu Envelope and Low Grade Halo
(Grade Zone = 93 & 94).
= 5 Waste All blocks with a kriging variance greater than 0.32 and within
the 0.15 % Cu Envelope and Low Grade Halo (Grade Zone =
93 & 94).
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Original topo 1996
Topo 2003
Pit Final 2006
0.15% Cu boundary
Low Grade halo
Core
<0.15
0.15
0.45
0.75
0.8
0.6
0.3
% Cu

18. Works Cited
Abzalov M., Drobov S., Gorbatenko O., Vershkov A., Bertoli O., et al. 2014, Resource estimation of in situ leach uranium projects, Applied Earth Science, Maney Publishing, pp. 71-85, 2014.
Allard D., D’Or D., Biver P., Froidevaux R. 2012, Non-parametric diagrams for pluri-Gaussian simulations of lithologies, 9th International Geostatistical Congress, Oslo, Norway 2012.
Armstrong M., Galli A., Beucher H., LeLoc’h G., Renard D., Doligez B., Eschard R., Geffroy F. 2011, Plurigaussian simulations in geosciences, New York, Springer.
Betzhold J. and Roth C. 2000, Characterizing the mineralogical variability of a Chilean copper deposit using plurigaussian simulations, The Journal of the South African Institute of Mining
and Metallurgy, pp. 111-120, March-April 2000.
Bohling G. 2007, S-GeMS Tutorial Notes, presented in Hydrogeophysics: Theory, Methods and Modeling, Boise State University, June 2007.
Caceres A. 2010, Conditional co-simulation of copper grades and lithofacies in the Rio Blanco – Los Bronces copper deposit, Proceedings of the 4th Annual Conference on Mining Innovation,
2010.
Cherubini C., Giasi C., Musci F., Pastore N. 2009, Application of truncated plurigaussian method for the reactive transport modeling of a contaminated aquifer, Proceedings of the 4th
IASME/WSEAS International Conference on Water Resources, Hydraulics, & Hydrology, 2009.
Deraisme J., Farrow D.
Godbey, K.,Angola, O., 2009, Constraining 3D facies modeling by seismic derived facies probabilities: example from Jonah Field tight gas, The Leading Edge, in press 2009
Hosseini S., Asghari O. 2014, Simulation of geometallurgical variables through stepwise conditional transformation in Sungun copper deposit, Iran, Saudi Society for Geoscientists, 2014.
John A. (ed.) 2010, Porphyry Copper Deposit Model, USGS Scientific Investigations Report 2010-5070-B
Langlais V., Beucher H., Renard D. 2008, In the shade of the truncated gaussian simulation, Proceedings of the Eighth International Geostatistics Congress, 2008.
Remacre A., Zapparolli L. 2003 Application of the plurigaussian simulation technique in reproducing lithofacies with double anisotropy, Brazillian Journal of Geology, pp. 37-42, 2003.
Remy N., Boucher A., Wu J. 2009, Applied geostatistics with SGeMS, New York, Cambridge University Press.
Renard D., Beucher H. 2012 3-D representations of a uranium roll-front deposit, Applied Earth Science, Maney Publishing, pp. 84-88, 2012.
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