118
Statistical Methods for Estimating Petroleum Resources
For this simple example, the Monte Carlo method proves cumbersome.
In the second example (Fig. 5.3B), the area under the Y = X
2 curve is
calculated from the integration of the curve as follows:
1
2
0
1 3
Y
X dx
=
=
∫
Here, the Monte Carlo method can be applied N times where n points
are located under the curve. Therefore, the area will be 34 / 100 = 0.340
units. The integration method is more effi cient than the Monte Carlo
method.
The third example (Fig. 5.3C) is used to calculate the polygonal area,
which can be calculated by Green’s theorem. In this particular case,
the Monte Carlo method (the area = 7 / 100 units, the actual area =1 / 12
units) is the most effi cient.
We can assess the accuracy of the Monte Carlo method by increasing the number of random numbers to 1000, and fi nd that the three
areas are equal to 0.509, 0.329, and 0.076 units respectively. It can be
observed that the accuracy for each example increases but varies. This
is why the Monte Carlo method requires a large sample size to reduce
the measurement error.
Atwater (1956) calculated success ratios and average pool sizes from
onshore Louisiana, and then estimated the number of prospects in the
adjacent offshore. He claimed that the petroleum resources of offshore
Louisiana could be approximated from the product of the success ratio,
the average pool size, and the number of prospects. The assumptions
for this approach are that the average pool size and the success ratio are
the same for both offshore and onshore Louisiana. This approach was
the basis for the logic of the petroleum resource assessment procedure
using the Monte Carlo method.
In the late 1960s, the petroleum industry began to use the computer
as a tool for evaluating hydrocarbon plays. For many years, the Monte
Carlo procedure has been used in play estimation (Energy, Mines and
Resources, 1977; White and Gehman, 1979), and has been widely used
in petroleum resource evaluation articles since then.
Figure 5.4 illustrates how to use the Monte Carlo method to compute
pool-size distribution. Geological variables (right side of the equation)
are expressed by their own probability distributions. Random numbers were independently generated as R 1 , R 2 , … , R 5 , because there was
no information on relationships between variables. These fi ve random
Statistical Methods for Estimating Petroleum Resources
For this simple example, the Monte Carlo method proves cumbersome.
In the second example (Fig. 5.3B), the area under the Y = X
2 curve is
calculated from the integration of the curve as follows:
1
2
0
1 3
Y
X dx
=
=
∫
Here, the Monte Carlo method can be applied N times where n points
are located under the curve. Therefore, the area will be 34 / 100 = 0.340
units. The integration method is more effi cient than the Monte Carlo
method.
The third example (Fig. 5.3C) is used to calculate the polygonal area,
which can be calculated by Green’s theorem. In this particular case,
the Monte Carlo method (the area = 7 / 100 units, the actual area =1 / 12
units) is the most effi cient.
We can assess the accuracy of the Monte Carlo method by increasing the number of random numbers to 1000, and fi nd that the three
areas are equal to 0.509, 0.329, and 0.076 units respectively. It can be
observed that the accuracy for each example increases but varies. This
is why the Monte Carlo method requires a large sample size to reduce
the measurement error.
Atwater (1956) calculated success ratios and average pool sizes from
onshore Louisiana, and then estimated the number of prospects in the
adjacent offshore. He claimed that the petroleum resources of offshore
Louisiana could be approximated from the product of the success ratio,
the average pool size, and the number of prospects. The assumptions
for this approach are that the average pool size and the success ratio are
the same for both offshore and onshore Louisiana. This approach was
the basis for the logic of the petroleum resource assessment procedure
using the Monte Carlo method.
In the late 1960s, the petroleum industry began to use the computer
as a tool for evaluating hydrocarbon plays. For many years, the Monte
Carlo procedure has been used in play estimation (Energy, Mines and
Resources, 1977; White and Gehman, 1979), and has been widely used
in petroleum resource evaluation articles since then.
Figure 5.4 illustrates how to use the Monte Carlo method to compute
pool-size distribution. Geological variables (right side of the equation)
are expressed by their own probability distributions. Random numbers were independently generated as R 1 , R 2 , … , R 5 , because there was
no information on relationships between variables. These fi ve random