50
Statistical Methods for Estimating Petroleum Resources
(indicated by triangles). The reason for this change is that the pool-size
distribution for the Beaverhill Lake play has the largest variance of all.
The reserves from the fi rst 10 pools amount to 91%, 68%, and 46% of
their total resources respectively. This phenomenon demonstrates that
the magnitude of σ
2 allocates the resources to individual pools.
Distribution of pool-size-by-rank should be computed from either
the number of pools, N, or the number-of-pools distribution, and the
superpopulation pool-size distribution. The previous discussion may
be summarized as follows.
The size of the largest pool increases as the number of pools,
1.
N,
increases. The amount of increase depends on the magnitude
of μ and σ
2 . For example, pool size increases rapidly when σ
2
is large.
In resource evaluation, as we will discuss in Chapter 5,
2.
μ dominates σ
2 for the mean of a pool size when the constant is not
scaled (see Eqs. 5.8 and 5.9). Therefore, parameters μ and N can
be thought of as indicators of the richness of the play, whereas
σ
2 and N are indicators of the degree of proneness for having
outliers.
For each hydrocarbon-bearing play, there is a set of
3.
μ, σ
2 , and
N values associated with the geological model that produced
the play. Different geological models can have different values for σ
2 , μ, and N, and correspondingly distinct pool sizes.
Various play examples are presented in Table 3.2.
If a play has a pool-size distribution with a large
4.
σ
2 , then most
of the play’s resources will be in the fi rst few largest pools. On
the other hand, if σ
2 is relatively small, the pool sizes of the
play will be almost equal.
Factors that distort estimations of pool-size-by-rank include
5.
the problem of mixed populations, errors in estimating the
number-of-pools and/or pool-size distributions, and errors in
measuring pool sizes. The problem of mixed populations is the
most severe one, and causes either under- or overestimation
of undiscovered pool sizes when prior distributions are specifi ed. Revisions to the play defi nition might solve the mixedpopulation problem. Chapter 4 discusses the impact by mixed
populations from simulated data sets.
With respect to the signifi cance of changes in the values of
6.
N, μ,
and σ
2 , and their impact on the estimation of individual pool
sizes, the largest pool size is sensitive to the following factors
(in decreasing importance): σ
2 , N, and/or μ.
Statistical Methods for Estimating Petroleum Resources
(indicated by triangles). The reason for this change is that the pool-size
distribution for the Beaverhill Lake play has the largest variance of all.
The reserves from the fi rst 10 pools amount to 91%, 68%, and 46% of
their total resources respectively. This phenomenon demonstrates that
the magnitude of σ
2 allocates the resources to individual pools.
Distribution of pool-size-by-rank should be computed from either
the number of pools, N, or the number-of-pools distribution, and the
superpopulation pool-size distribution. The previous discussion may
be summarized as follows.
The size of the largest pool increases as the number of pools,
1.
N,
increases. The amount of increase depends on the magnitude
of μ and σ
2 . For example, pool size increases rapidly when σ
2
is large.
In resource evaluation, as we will discuss in Chapter 5,
2.
μ dominates σ
2 for the mean of a pool size when the constant is not
scaled (see Eqs. 5.8 and 5.9). Therefore, parameters μ and N can
be thought of as indicators of the richness of the play, whereas
σ
2 and N are indicators of the degree of proneness for having
outliers.
For each hydrocarbon-bearing play, there is a set of
3.
μ, σ
2 , and
N values associated with the geological model that produced
the play. Different geological models can have different values for σ
2 , μ, and N, and correspondingly distinct pool sizes.
Various play examples are presented in Table 3.2.
If a play has a pool-size distribution with a large
4.
σ
2 , then most
of the play’s resources will be in the fi rst few largest pools. On
the other hand, if σ
2 is relatively small, the pool sizes of the
play will be almost equal.
Factors that distort estimations of pool-size-by-rank include
5.
the problem of mixed populations, errors in estimating the
number-of-pools and/or pool-size distributions, and errors in
measuring pool sizes. The problem of mixed populations is the
most severe one, and causes either under- or overestimation
of undiscovered pool sizes when prior distributions are specifi ed. Revisions to the play defi nition might solve the mixedpopulation problem. Chapter 4 discusses the impact by mixed
populations from simulated data sets.
With respect to the signifi cance of changes in the values of
6.
N, μ,
and σ
2 , and their impact on the estimation of individual pool
sizes, the largest pool size is sensitive to the following factors
(in decreasing importance): σ
2 , N, and/or μ.