16
Statistical Methods for Estimating Petroleum Resources
enough to represent the population. In fact, neither of these
assumptions is valid.
During the exploration–discovery process, large pools are normally
discovered at an early stage. This implies that smaller pools remain
to be discovered. Thus, the population mean would be overestimated
by the sample mean obtained here, whereas the population variance
would be underestimated by the sample variance. Therefore, we believe
that the discovery process can be viewed as a sampling process whereby
pool discovery probability is proportional to pool size and sampling
without replacement.
Let us consider the patch reef model as an example of how statistical
methods can be developed to evaluate a reef play. First, a reef model
(Fig. 2.7, top) is defi ned as a collection of geologically analogous reef
pools, and a reef play or population (upper right-hand corner of Fig. 2.7)
contains some members of the reef model. In other words, a reef play
consists of a fi nite number of reef pools, whereas a reef model contains
an infi nite number of reef pools with similar geological characters.
Second, a reef model can be described in terms of its geological
random variables, such as pool size, pool area, net pay, porosity, and
number of pools. The range of all possible values for each variable
exhibits a continuous probability distribution because of the infi nite
number of reef pools, except that the number of pools has a discrete
distribution expressed as an integer (Fig. 2.7, upper left-hand corner).
Third, for a specifi c play, the values of a variable are considered to be
taken as a random sample from its probability distribution—in other
words, they are independently derived from a common (or identical)
distribution (written as i.i.d. in statistical literature). The following two
statistical assumptions, which can be verifi ed from basin analysis, are
the following:
A play is defi ned as a single and natural population.
1.
All pools are deposited under similar geological conditions.
2.
Fourth, pool sizes obtained from discoveries of a play (lower righthand corner of Fig. 2.7) can be used as a sample to estimate the two
population distributions (continuous pool-size distribution and the
discrete number-of-pools distribution).
In summary, two statistical assumptions are required: (1) all pools of
a play have been deposited under similar geological conditions and (2)
all pools within a specifi c play boundary form a single, natural geological
Statistical Methods for Estimating Petroleum Resources
enough to represent the population. In fact, neither of these
assumptions is valid.
During the exploration–discovery process, large pools are normally
discovered at an early stage. This implies that smaller pools remain
to be discovered. Thus, the population mean would be overestimated
by the sample mean obtained here, whereas the population variance
would be underestimated by the sample variance. Therefore, we believe
that the discovery process can be viewed as a sampling process whereby
pool discovery probability is proportional to pool size and sampling
without replacement.
Let us consider the patch reef model as an example of how statistical
methods can be developed to evaluate a reef play. First, a reef model
(Fig. 2.7, top) is defi ned as a collection of geologically analogous reef
pools, and a reef play or population (upper right-hand corner of Fig. 2.7)
contains some members of the reef model. In other words, a reef play
consists of a fi nite number of reef pools, whereas a reef model contains
an infi nite number of reef pools with similar geological characters.
Second, a reef model can be described in terms of its geological
random variables, such as pool size, pool area, net pay, porosity, and
number of pools. The range of all possible values for each variable
exhibits a continuous probability distribution because of the infi nite
number of reef pools, except that the number of pools has a discrete
distribution expressed as an integer (Fig. 2.7, upper left-hand corner).
Third, for a specifi c play, the values of a variable are considered to be
taken as a random sample from its probability distribution—in other
words, they are independently derived from a common (or identical)
distribution (written as i.i.d. in statistical literature). The following two
statistical assumptions, which can be verifi ed from basin analysis, are
the following:
A play is defi ned as a single and natural population.
1.
All pools are deposited under similar geological conditions.
2.
Fourth, pool sizes obtained from discoveries of a play (lower righthand corner of Fig. 2.7) can be used as a sample to estimate the two
population distributions (continuous pool-size distribution and the
discrete number-of-pools distribution).
In summary, two statistical assumptions are required: (1) all pools of
a play have been deposited under similar geological conditions and (2)
all pools within a specifi c play boundary form a single, natural geological