Geoscience Reference
In-Depth Information
estimation uncertainties. Within these, issues related to di-
lution should be emphasized, as well as an assessment of
the information effect. The resulting model of uncertainty
should be checked against actual production, if available, or
against some resource model taken as reference or base case.
Risk assessments should be fully developed, validated, and
documented, with clearly stated objectives.
Best practice consists of, in addition to the above, full
modeling of all recognized and quantifiable uncertainties, in-
cluding those attached to the data, to the sampling and assay-
ing procedures, to the geologic model and simulation domain
definition (as above), and the modeling of grade. Conditional
simulations should thus be used to provide both global and
local uncertainty measures, and a full description of the re-
source model. However, the exclusive use of probabilities
for resource classification is not recommended. An arbitrary
choice of probabilistic criteria will often lead to unreason-
ably large or small volumes in each category. It is however
advisable to apply geometric criteria for resource classifica-
tion, with or without smoothing out the zones with mixing
of resource classes, and provide further support through a
probabilistic analysis. The probabilistic analysis may cause
the competent person to reconsider their geometric criteria,
but the geometric criteria are used for disclosure.
If, however, the possibility exists of reliably validating
the uncertainty model obtained from the conditional simula-
tions through mine production, then it is reasonable to use
the probabilistic intervals as basic definition for resource
classification.
two features in varying degrees. Consider a simple calcula-
tion of oil in place (OIP) that depends only on a few input
parameters:
OIP
=
6.2898
*
GRV
**
ϕ
(1
−
Sw) / FVF
where GRV is the gross rock volume, φ is the porosity, Sw is
the water saturation, and FVF is the formation volume factor.
The constant 6.2898 is a metric conversion factor to relate
cubic metres to stock tank barrels. Suppose that each of the
input variables can be described as a random variable: All
variables are normally distributed with the following mean
and variance values:
Va r i a b l e
Mean
Variance
GRV
79 million cubic meters
5 million cubic meters
17 %
5 %
2
φ
9 %
2
S
W
11 %
FVF
1.3
0.2
Question 1:
Using Monte Carlo simulation, draw 100 real-
izations for each input parameter and then
calculate the corresponding OIP for each real-
ization. Plot the distribution of uncertainty
about OIP.
Question 2:
Consider now partitioning each of the input
distributions into ten different partitions (you
can set the thresholds at the deciles). Apply
latin hypercube sampling (LHS) and calculate
OIP (you should only need to draw 10 realiza-
tions for each input and ensure that you only
draw from each partition once). Plot and com-
ment on this distribution of OIP.
Question 3:
Suppose now that there is a relationship
between φ and Sw, which can be described
as bivariate Gaussian with correlation of 0.5.
Given that there is no longer independence
between all the input variables, describe
how you would implement a Monte Carlo
approach (similar to Question 1) to account
for the impact this relationship has on uncer-
tainty in OIP. If you have time, you may wish
to implement this and compare against the
distribution in Question 1.
Question 4:
Perhaps the most common approach to sen-
sitivity analysis is the vary one at a time
approach. This requires keeping all the input
variables at the base case value (usually the
mean), and then for one input variable, choose
say the p10 and p90 of that input variable and
12.5
Exercises
The objective of this exercise is to review aspects of uncer-
tainty and risk assessment together with loss functions and
decision making. Some specific (geo)statistical software
may be required. The functionality may be available in dif-
ferent public domain or commercial software. Please acquire
the required software before beginning the exercise. The data
files are available for download from the author's website—
a search engine will reveal the location.
12.5.1
Part One: Sampling Uncertainty
The objective of this exercise is to experiment with different
uncertainty sampling and sensitivity assessment approaches.
Available methods for these two purposes can vary great-
ly depending on whether one is interested in sampling ef-
ficiency and/or realistic uncertainty assessment accounting
for dependency structures. The set of tools we will explore
in this exercise applies different methods that satisfy these
