Tu ELI1 09
Assessment Performance Tracking of Multiple
Target Prospects - A Statistical Approach
G. Martinelli* (Schlumberger Information Solutions) & C.B. Stabell
(Schlumberger Information Solutions)
SUMMARY
Systematic tracking of exploration results relative to pre-drill predictions is challenging, but important. It
is a means both to motivate assessment quality and to improve the assessments produced by the
exploration team. Unbiased, accurate and consistent assessments are key for effective exploration
decisions. This paper deals with the case where a single well targets multiple zones, compartments or
reservoirs in a prospect. Most companies handle the situation as a case of multiple distinct targets.
However, while simple, this approach ignores to what extent assessment has handled estimation of risk
dependencies and volume correlations between targets. A key challenge for tracking assessments of
multiple target prospects is tracking the estimates of risk dependencies between the targets: single well
results do not give clear feedback on this estimate. We present an exploration program-level statistical
measure of the quality both at the level of aggregate risk dependency estimates and at the level of the
individual chance (risk) factor dependency estimates. The procedure is demonstrated with a hypothetical,
but illustrative drilling program. Implementation of multiple target prospect assessment performance
tracking should both improve assessments of this class of exploration ventures and stimulate more robust,
accurate and transparent estimation of prospect-scale risk dependencies.
76th EAGE Conference & Exhibition 2014
Amsterdam RAI, The Netherlands, 16-19 June 2014
Introduction
Systematic and consistent tracking and interpretation of pre-post-drill results from risked prospects
are becoming increasingly important. There are two main reasons for this increase in importance and
interest: Tracking promotes focus on accurate and consistent assessments and tracking provides a
basis for systematic learning about biases and improving future assessments. The problem has been
discussed in the literature for quite some time, starting with the seminal works of [Rose, 1987] and
[Otis and Schneidermann, 1997]. More recently, other works ([Stabell, 2006] and [Stabell, 2010])
have proposed additional screening indices to compare pre and post drill estimates, and to evaluate the
accuracy of assessments.
In the latter paper, the author discusses the issue of how to track assessment of risk dependency in
multiple segment prospects. In fact, while there exist several approaches for tracking pre/post
estimates for single targets, there is no established approach for evaluating such estimates in the case
of wells penetrating multiple targets. In this work we propose a statistically robust methodology for
tracking what pre-post drill can tells us about the accuracy of risk dependency estimates in multiple
segment prospects. The proposed methodology provides the basis for a series of diagnostic tools.
Theory and method
Let us consider a multiple segment prospect with 2 segments, such as the one presented in Figure 1.
The two segments can represent stacked reservoirs or any two kinds of accumulations that share some
geological control. During the risk assessment the G&G team needs to assess the risk dependency
between the two segments in order to generate an estimate of the chance of success and the success
case volumes if we drill both segments in the prospect. Risk dependency is due to shared geological
controls. Dependency is therefore assessed at the level of the individual risk (chance) factors, i.e. the
exploration team establish a risk dependency estimate for each risk factor (source, migration,
reservoir, trap, seal).
Figure 1 Multiple segment prospect with two segments A and B.
In [Martinelli et al., 2013] we have introduced a dependency coefficient c that provides a prospect
level measure of the risk dependency that summarizes the implication of all the dependencies defined
at the risk factor level.
Essentially, if we name the two segments A and B, we can explicitly derive the bivariate distribution
of the COS (chance of success), and compute the dependency coefficient through a simple Monte
Carlo evaluation.
A/B
B = dry
B = oil
marginal
A= dry
N00
N01
N0A
A=oil
N10
N11
N1A
marginal
N0B
N1B
N
Table 1: Bivariate distribution of a multiple segment prospect with 2 segments A and B.
76th EAGE Conference & Exhibition 2014
Amsterdam RAI, The Netherlands, 16-19 June 2014
In Table 1, N00 represent the number of Monte Carlo trials where both A and B are dry, N01 are the
cases where B alone is successful, N10 are the cases where A alone is successful, N11 are the cases
where both A and B are successful, N0A are the cases where A is dry and N are the total MC runs.
The dependency coefficient c can be then computed as:
c=
We use c in a Bayesian setting to drive our analysis. Intuitively, in a prospect with n segments, we
expect that if c is large (high risk dependency), we would get a proportion of successful segments
close to 0 (failure in all) or to n (success in all). On the other side, if the c is low, we expect a more
balanced distribution, with a peak driven by the overall COS of the prospect.
We can therefore assume that the proportion of successes p within a prospect is distributed according
to a beta distribution Beta(alpha,beta), whose alpha and beta parameters are a function of c. More
specifically, we fix alpha=beta=2*(1-c). In this way, when c is small, we get alpha=beta<1, and when
c is large we get alpha=beta>1. When c=0.5, we get a uniform distribution between 0 and 1. The three
cases are shown in Figure 2, and they are in accordance with the intuitive argument given above.
Figure 2 Beta distribution for different values of the shape parameters.
We have therefore:
Since p is the proportion of success in the prospect, it is possible to write the number of successes as a
Binomial distribution of parameters p and n, where n is the number of segments within the prospect.
Finally, thanks to the conjugation property between the beta and the binomial distribution, we can
write in closed form the posterior distribution of p given the number of observed successes. For a
reference see [Gelman et al., 2003].
Given k observed success out of n segments, we can therefore write the posterior distribution for p as:
We can further improve the methodology by incorporating a correction for the prospect COS in the
prior. In this case, the alpha parameter is corrected by a factor proportional to |COS-0.5|. The posterior
distribution follows according to the same rules for conjugate models.
76th EAGE Conference & Exhibition 2014
Amsterdam RAI, The Netherlands, 16-19 June 2014
In order to determine the quality of our assessment, we need to measure the distance between our
prior and our posterior distributions. We apply an L2 norm on the interval, in order to estimate the
distance between the density functions. Alternative distance measures are currently under
investigation.
Let us consider what happens to our original example. We assume that the exploration team has
assessed the prospect as highly dependent (c=0.8) and with a high prospect COS, COS=0.8. After the
exploration well, the outcome is that both segments are successful. We plot this situation in Figure 3,
on the top left. Had we observed 1 success and 1 failure, we would get a posterior shown in top right
in Figure 3. The computation of the distribution distance confirms our intuition: the distance is equal
to 1.36 in the case of two successes, and 5.22 in the case of 1 success and 1 failure -- in other words,
a result of two successes is more in line with our prior estimate of the risk dependency.
Now consider the opposite case, where the original assessment was of total independence between the
two segments (c=0). The corresponding posteriors are shown in the bottom layer of Figure 3. Again,
the computation of the distribution distance between prior and posterior confirms our hypothesis: the
distance is equal to 2.33 in the case of two successes and 2.06 in the case of 1 success and 1 failure,
that confirms to be the most plausible scenario for that prior. In this case the difference is less marked,
because of the large prior prospect COS, that makes the case with two successes almost equally likely
as the one with one success and one failure.
Figure 3 Prior and posterior distribution of successes for a 2-segments prospect with different
correlation coefficient. In black we show the area of largest accordance between prior and posterior.
An illustrative exploration program case
We apply the proposed methodology on an illustrative exploration program with 6 prospects, each of
them with two segments A and B. All the prospects have been assessed by two different exploration
teams and later drilled. For the sake of simplicity we assume here that the dependency refers to a
single risk factor, but as we have seen in the original statement there are no limitations, since we can
76th EAGE Conference & Exhibition 2014
Amsterdam RAI, The Netherlands, 16-19 June 2014
always compute a coefficient c that captures the overall risk dependency at the prospect level. For the
same reasons, we remove the COS issue in this example. Input and results are presented in Table 2.
Prospect
Ass. Team 1
Ass. Team 2
Result
segment A
Result
Dist.
Dist.
segment B Team 1 Team 2
Arkansas
Arizona
Georgia
Kansas
Minnesota
Oregon
Dep  c=0.8
Ind  c=0
Ind c=0
Dep c=0.7
Dep c=0.3
Dep c=0.9
Dep  c=0.7
Ind  c=0
Dep c=0.3
Ind  c=0
Indc=0
Dep c=0.6
success
failure
success
failure
failure
success
success
success
failure
failure
success
success
1.14
1.33
1.33
1.67
1.63
0.57
Average Distance 1.28
1.67
1.33
1.63
3.69
1.33
2.13
1.96
Table 2 Input and results for illustrative case study.
From this illustrative analysis, we can conclude that on the average the Team 1 has provided a better
assessment of risk dependency than Team 2. In five out of the six prospects, Team 1’s analysis of risk
dependency has led to a smaller posterior-prior distance, while just in the Minnesota prospect the
results indicate that Team 1’s estimate of c = .3 is not supported.
It is worth mentioning that a complete analysis of the assessment performance of the two teams
should consider several additional dimensions of their assessment, including volumetric assessment,
their COS estimates, and other measures discussed extensively in [Rose, 1987] and [Stabell, 2006].
The discussion of these dimensions lies outside the scope of the present work.
Future developments and conclusions
We have presented a robust statistical index for evaluating pre-post assessment of risk dependency in
multiple segment prospects. The index is based on a distance between a prior and a posterior
distribution, where the former is built on the basis of the original risk assessment, while the latter is
derived after collecting results from the exploration campaign. The method is precise in detecting any
original bias, both for what concerns the prior prospect COS, and for what concerns the prior
assessment of the risk dependency. From the posterior distribution for the proportion p of successes, it
is possible to calculate the optimal posterior dependency index for each prospect. This provides a
diagnostic tool for systematic evaluation of risk dependency between multiple targets in prospects.
The method has been presented and applied in an illustrative study with a series of binary prospects,
but it can be generalized to the case of prospects with multiple (>2) segments. A detailed
methodology for handling the general case is under further investigation. Another natural
enhancement of the presented workflow consists in evaluating single risk factor dependencies instead
of the global dependency measure used in this paper. Such an approach, though, would require more
detailed (risk factor-level success and failure) post-exploration data.
Reference
Gelman A., Carlin G.B., Stern H. S., and Rubin D.B., [2003], Bayesian Data Analysis, 2nd edition.
CRC Press
Martinelli G., Stabell C., Langlie E., [2013], Handling Seismic Anomalies in Multiple Segment
Prospects: Explicit Modeling of Anomaly Indicator Correlation, EAGE 2013
Otis, R.M and Schneidermann, N., [1997], A process for evaluating exploration prospects, AAPG
Bulletin, v. 81, no. 7, p. 1087-1109
Rose P.R., [1987], Dealing with risk and uncertainty in exploration: how can we improve, AAPG
Bulletin, v. 71, no. 1, p. 1-16
Stabell, C., [2006], A New Metric for Tracking Assessment Performance, Petex 2006
76th EAGE Conference & Exhibition 2014
Amsterdam RAI, The Netherlands, 16-19 June 2014
Stabell C., 2010, Optimal learning from pre-post drill evaluations. The case of multiple target
prospects, Petex 2010
76th EAGE Conference & Exhibition 2014
Amsterdam RAI, The Netherlands, 16-19 June 2014