advanced geostatistics, simulations and environmental applications roussos dimitrakopoulos dept of...
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Advanced Geostatistics, Simulations
and Environmental Applications
Roussos Dimitrakopoulos
Dept of Mining and Materials EngineeringMcGill University, Canada
Email: [email protected]
URL: http://www.iamg.org/
International Association for Mathematical Geosciences
Distinguished Lecturer - 2009 & 2010
Seminar - May 28, 2009, U of Athens, Greece
CONTENT – Part 1
Introduction
Stochastic Models and Simulation
An introduction to Monte Carlo simulation
Sequential simulation (Gaussian)
CONTENT – Part 2
Quantification of Mine Spoil Variability and Rehabilitation Decision Making
Classification and Remediation of Mercury Contaminated Soils
The examples are all available in text - see materials provided
GEOSTATISTICAL TEXTBOOKS• An Introduction to Applied Geostatistics
Isaaks, EH and RM Srivastava, Oxford University Press, 1989
• Geostatistics for the Next Century Dimitrakopoulos, R, Kluwer, 1994
• Fundamentals of Geostatistics in Five Lessons Journel, AG Short Course in Geology, v. 8, AGU, 1989
• GSLIB Geostatistical Software Library and User's Guide Deutsch, CV and Journel, AG, 2nd Edition, Oxford, 1997
• Geostatistics for Natural Resources Evaluation Goovaerts, P, Oxford, 1997
• Geostatistics – Modelling Spatial Uncertainty Chiles, J-P and Delfiner, P, Wiley, 1999
Geostatistical Glossary and Multilingual Dictionary, Olea, R, Oxford, 1991
GEOSTATISTICAL TEXTBOOKS
• Applied Geostatistics with SGeMS: A User’s Guide Remy, N, Boucher, A, and Wu, J, Oxford, 2009
• Geostatistics for Environmental Scientists Webster, R and Oliver, MA, Wiley, 2007
Many managers believe that uncertainty is a problem and should be avoided…..
… you can take advantage of uncertainty. Your strategic investments will be sheltered from its adverse effects while remaining exposed to its upside potential. Uncertainty will create opportunities and value.
Once your way of thinking explicitly includes uncertainty, the whole decision-making framework changes.
Martha Amram and Nalin Kulatilakain “Real Options”
UNCERTAINTY IS NOT A “BAD THING”
Real Option Theory•Derived from the Nobel Prize-winning work of Black, Merton and Scholes
–What is the value of a contract that gives you the right, but not the obligation, to purchase a share of ‘GoldMin’ for $30 six months from now?
–Separates risk from expected return on investment and includes timing
• Applications to real (non-financial) assets
-What is the value of starting a project that gives you the right, but not the obligation, to commence production for a cost of $7M six months from now?
-What is the value of delaying production to get additional information to reduce uncertainty?
–What is the value of building in flexibility to manage uncertainty?
Options vs DCF view of ValueC
urr
en
t A
sset
Valu
e
FutureGold Price
$0
$-
$+ Real Options View:Current Value ofOption to Produce
Traditional DCF View(now or never)
No productionNPV = 0
ProductionNPV > 0
Contingent Decision Payoff Function
(future price known)
Accurate Uncertainty Assessment Needed
Unknown,trueanswer
Reserves
Accurateuncertaintyestimation
Single,oftenprecise,wronganswer
Reserves
Pro
bab
ility
1
“The goal of technical evaluation should be to strive for an accurate assessment of uncertainty, not a single precise answer”
Information about the deposit or
contaminated site or aquifer
Actual but unknown mineral deposit or contaminated site or aquifer …
Probable models of the deposit or
contaminated site or aquifer or …
Describing the Uncertainty about Spatially Distributed Phenomena
Probable models of .....
Process/Model
Parameters of interest
Transfer Function
Response 1
Response Parameter
Response Distribution
Response 2
Response m
Diagrammatic Representation of the Proposed Simulation Framework
Two Important Points
• Transfer functions are generally non-linear. As a consequence,
(i) an average type “block” model may not provide an average map of the space of response uncertainty; and
(ii) a criterion for generating possible models may be defined: the simulation technique selected for modelling must be evaluated in for its mapping of the response uncertainty
Uncertainly in Orebody Modelling
All models have identical:data, stats, continuity, information
A laterite nickel deposit
Probability Maps and Site Rehabilitation
Nor
th
East
EC>0.6(dS/M) EC>0.8 EC>1.0
1.0
0.8
0.6
0.4
0.2
0.0
0
200
100
RedRed:: Over 80% chance to be above a contaminant concentration
PurplePurple: Over 80% chance below the contaminant concentration
BlueBlue: Additional drilling would probably be needed
Map of the probability of being above a contaminant concentration provides a possible basis for deciding on additional sampling, evaluation and rehabilitation decisions . . . .
Additional Sampling
Uncertainty at Various Selectivity
The higher the degree of selectivity the greater the uncertainty of the grade-tonnage information
0
50 000
100 000
150 000
200 000
0.9 1.0 1.1 1.2 1.3 1.4
Cut-off Grade (% Ni)
Con
tain
ed M
etal
(t)
OK Model 25x25x1
Min 25x25x1
Max 25x25x1
Min 15x15x1
Max 15x15x1
Min 10x10x5
Max 10x10x1
Min 5x5x1
Max 5x5x1
Flaws in Traditional Modelling have been Known
Nor
mal
ized
Oil
Rec
over
y
Injected Pore Volume
The expected oil production has little chance to be realized
Traditional
Stochastic Simulations