More about Discovery Process Models
103
pool area of the Cardium sandstone (Fig. 4.27A), porosity (Fig. 4.27B),
and net pay (Fig. 4.27C) of the Lower Mannville sandstone, and the net
pay of the Devonian clastics (Fig 4.27D) can be approximated by the
families of the lognormal distribution. Figure 4.27A displays a peculiar pattern. The large steps between 60 and 100 ha are the result of the
assignment of 64 ha to some of the small pools. In these cases, a prior
distribution such as the lognormal can provide a framework for estimating the population distribution.
If a pool-size distribution is computed from the products and divisions of several dependent or independent lognormal distributions,
then the end product is lognormal. According to the central limit theorem, the end product also tends to be a normal or lognormal distribution, regardless of the original probability distribution types. These
probability distributions can be area of pool, net pay, formation thickness, porosity, water saturation, and others.
Oil and gas pools form as the result of the following processes. First,
organic matter is deposited in a bed to form the source rock, after which
it is transformed into oil and/or gas when the source rock is buried deep
enough to generate oil or gas. Oil and gas migrate from the source rock
and are trapped in the fi nal reservoir. Countless minute oil drops and
gas bubbles accumulate in tiny traps and may leak to the surface as
seepage or gas bubbles. If we use a probability distribution to express
the quantities of the result of each process, then the end product of all
geological processes can be equivalent to the multiplication of these
distributions together as a single distribution. The law of proportionate effect (Aitchison and Brown, 1969, pp. 22–23) supports the deduction that the end products of the geological processes, oil and/or gas
pools, are lognormally distributed.
Advantages of Using a Lognormal Distribution
For the immature or conceptual plays, probability distributions for all
geological variables are constructed from interpretations of geological
information. The distributions constructed refl ect current knowledge.
In these cases, if the assumption of lognormality is used, then geologists
will be able to examine the sizes of the largest few pools without predetermination by assessors. Lognormal distributions adequately approximate the distributions recognized by geologists (Lee and Wang, 1983b).
In addition, correlation among variables can be conveniently handled with a lognormal distribution. Refer to the section on lognormal
approximation in Chapter 5 for details.
103
pool area of the Cardium sandstone (Fig. 4.27A), porosity (Fig. 4.27B),
and net pay (Fig. 4.27C) of the Lower Mannville sandstone, and the net
pay of the Devonian clastics (Fig 4.27D) can be approximated by the
families of the lognormal distribution. Figure 4.27A displays a peculiar pattern. The large steps between 60 and 100 ha are the result of the
assignment of 64 ha to some of the small pools. In these cases, a prior
distribution such as the lognormal can provide a framework for estimating the population distribution.
If a pool-size distribution is computed from the products and divisions of several dependent or independent lognormal distributions,
then the end product is lognormal. According to the central limit theorem, the end product also tends to be a normal or lognormal distribution, regardless of the original probability distribution types. These
probability distributions can be area of pool, net pay, formation thickness, porosity, water saturation, and others.
Oil and gas pools form as the result of the following processes. First,
organic matter is deposited in a bed to form the source rock, after which
it is transformed into oil and/or gas when the source rock is buried deep
enough to generate oil or gas. Oil and gas migrate from the source rock
and are trapped in the fi nal reservoir. Countless minute oil drops and
gas bubbles accumulate in tiny traps and may leak to the surface as
seepage or gas bubbles. If we use a probability distribution to express
the quantities of the result of each process, then the end product of all
geological processes can be equivalent to the multiplication of these
distributions together as a single distribution. The law of proportionate effect (Aitchison and Brown, 1969, pp. 22–23) supports the deduction that the end products of the geological processes, oil and/or gas
pools, are lognormally distributed.
Advantages of Using a Lognormal Distribution
For the immature or conceptual plays, probability distributions for all
geological variables are constructed from interpretations of geological
information. The distributions constructed refl ect current knowledge.
In these cases, if the assumption of lognormality is used, then geologists
will be able to examine the sizes of the largest few pools without predetermination by assessors. Lognormal distributions adequately approximate the distributions recognized by geologists (Lee and Wang, 1983b).
In addition, correlation among variables can be conveniently handled with a lognormal distribution. Refer to the section on lognormal
approximation in Chapter 5 for details.