88
Statistical Methods for Estimating Petroleum Resources
reported. After this economic truncation process, the fi nal number of
pools equals 183 instead of 300.
The resultant sequence was subjected to analysis by LDSCV and
NDSCV. The relationships between the values of N and the log likelihood are summarized as follows. In the case of missing small pools,
LDSCV predicts that the value of N = 200, whereas NDSCV plateaus
at 220. Although both models do not predict the truncated value of N
exactly, the estimated N’s are close to the true value, 183. If more small
pools were missed from the discovery sequence, then the log L versus N
relationship would degenerate into either a negative exponential or no
pattern at all. This confi rms that the missing pools affect the quality of
the assessments.
Testing the Adequacy of Probability Distributions
Essentially, probabilistic statistical analysis is based on the assumption
that a set of data arises as a sample from some class of probability distribution. Tests of distributional assumptions have been an important
subject in petroleum resource evaluation procedures. Kaufman (1965)
used a lognormal pool-size distribution to describe oil and gas pools.
McCrossan (1969) plotted the discovered oil and gas pools from the
Western Canada Sedimentary Basin on logarithmic probability paper
and found that the plots tended to be straight lines. Power (1992) applied
the Anderson–Darling test to several plays assessed by Podruski et al.
(1988) from the Western Canada Sedimentary Basin and concluded
that they follow a lognormal distribution, whereas others follow a
Weibull distribution. The statistical assumption of this test is that all
oil pools are randomly discovered by geologists. This assumption is
incorrect. The test of a data set, which is a biased population sample, is
an unsolved problem.
This section attempts to solve this problem and presents an informal
quantile–quantile (Q–Q) plot to assess distributional assumptions.
The information required is based on the results of the nonparametric
estimates, p ˆ i (refer to “Nonparametric Discovery Process Model” in
Chapter 3). The advantage of the procedure is that it is not based on any
assumption about the shape of a probability distribution. However, the
procedure assigns mass only to the observed data and assumes that
the largest pool in the population is no larger than the largest pool
in the sample, and that the smallest undiscovered pool is no smaller
than the smallest discovered one. This is an unrealistic situation. To
Statistical Methods for Estimating Petroleum Resources
reported. After this economic truncation process, the fi nal number of
pools equals 183 instead of 300.
The resultant sequence was subjected to analysis by LDSCV and
NDSCV. The relationships between the values of N and the log likelihood are summarized as follows. In the case of missing small pools,
LDSCV predicts that the value of N = 200, whereas NDSCV plateaus
at 220. Although both models do not predict the truncated value of N
exactly, the estimated N’s are close to the true value, 183. If more small
pools were missed from the discovery sequence, then the log L versus N
relationship would degenerate into either a negative exponential or no
pattern at all. This confi rms that the missing pools affect the quality of
the assessments.
Testing the Adequacy of Probability Distributions
Essentially, probabilistic statistical analysis is based on the assumption
that a set of data arises as a sample from some class of probability distribution. Tests of distributional assumptions have been an important
subject in petroleum resource evaluation procedures. Kaufman (1965)
used a lognormal pool-size distribution to describe oil and gas pools.
McCrossan (1969) plotted the discovered oil and gas pools from the
Western Canada Sedimentary Basin on logarithmic probability paper
and found that the plots tended to be straight lines. Power (1992) applied
the Anderson–Darling test to several plays assessed by Podruski et al.
(1988) from the Western Canada Sedimentary Basin and concluded
that they follow a lognormal distribution, whereas others follow a
Weibull distribution. The statistical assumption of this test is that all
oil pools are randomly discovered by geologists. This assumption is
incorrect. The test of a data set, which is a biased population sample, is
an unsolved problem.
This section attempts to solve this problem and presents an informal
quantile–quantile (Q–Q) plot to assess distributional assumptions.
The information required is based on the results of the nonparametric
estimates, p ˆ i (refer to “Nonparametric Discovery Process Model” in
Chapter 3). The advantage of the procedure is that it is not based on any
assumption about the shape of a probability distribution. However, the
procedure assigns mass only to the observed data and assumes that
the largest pool in the population is no larger than the largest pool
in the sample, and that the smallest undiscovered pool is no smaller
than the smallest discovered one. This is an unrealistic situation. To