Evaluating Conceptual Plays
121
Resources Conservation Board [1989, Table 2–5].) From Table 5.5 we
can see that because the pool area contributes most to the values of μ
and s
2 , it is the most important random variable contributing to the
pool-size equation. Correlation and covariance for the three random
variables are also given in Table 5.5. The pool area and average net pay
random variables (Fig. 2.11B), as well as porosity and pool area, have
high correlation coeffi cients of 0.682 and 0.641 respectively. In this
example, if the covariances are incorporated, the mean of the pool size
will be 151 × 10
6 m
3 of oil. In contrast, if they are all ignored, the mean
is reduced to 46 × 10
6 m
3 of oil. Similarly, if negative correlations are
omitted, then the mean will be overestimated.
The advantages of using Equation 5.8 are that (1) we can gain a better
understanding of the variables, their interdependence, and their infl uence on pool-size distribution; and (2) geological random variables
for an undiscovered pool, such as pool area and average net pay, can
also be regenerated for a given pool size (see “Generation of Reservoir
Parameters” later in this chapter).
Moreover, because we usually do not have suffi cient data to compute covariances of geological random variables for conceptual
plays, the variance of pool-size distribution can be under- or overestimated. Furthermore, correlations of random variables can change
from population to population. For example, log–log relationships
between porosity and water saturation for the Bashaw reef (Fig. 5.5A)
and Cardium marine sandstone (Fig. 5.5B) display distinct correlation
patterns. Examining possible correlations might lead to justifying the
Table 5.5. Lognormal Parameters and Correlations of Geological Variables for
the Beaverhill Lake Play
Variable
Sample
mean ˆ
m
Variance
ˆ
s
2
Correlation*
Pool area
Average
net pay
Average
porosity
Pool area
7.869
0.721
1.000
Average net pay
2.211
0.422
0.682 (0.731) 1.000
Average porosity –2.674
0.068
0.641 (0.275) 0.452 (0.077)
1.000
*Covariance in parentheses.
Constant = 0.681 2
2.164,
ij
i
j
i j
=
<
∑∑ s
Scale factor = 0.001
ˆ
m = 2.408, s ˆ
2 = 3.211 + 2.164 = 5.375
121
Resources Conservation Board [1989, Table 2–5].) From Table 5.5 we
can see that because the pool area contributes most to the values of μ
and s
2 , it is the most important random variable contributing to the
pool-size equation. Correlation and covariance for the three random
variables are also given in Table 5.5. The pool area and average net pay
random variables (Fig. 2.11B), as well as porosity and pool area, have
high correlation coeffi cients of 0.682 and 0.641 respectively. In this
example, if the covariances are incorporated, the mean of the pool size
will be 151 × 10
6 m
3 of oil. In contrast, if they are all ignored, the mean
is reduced to 46 × 10
6 m
3 of oil. Similarly, if negative correlations are
omitted, then the mean will be overestimated.
The advantages of using Equation 5.8 are that (1) we can gain a better
understanding of the variables, their interdependence, and their infl uence on pool-size distribution; and (2) geological random variables
for an undiscovered pool, such as pool area and average net pay, can
also be regenerated for a given pool size (see “Generation of Reservoir
Parameters” later in this chapter).
Moreover, because we usually do not have suffi cient data to compute covariances of geological random variables for conceptual
plays, the variance of pool-size distribution can be under- or overestimated. Furthermore, correlations of random variables can change
from population to population. For example, log–log relationships
between porosity and water saturation for the Bashaw reef (Fig. 5.5A)
and Cardium marine sandstone (Fig. 5.5B) display distinct correlation
patterns. Examining possible correlations might lead to justifying the
Table 5.5. Lognormal Parameters and Correlations of Geological Variables for
the Beaverhill Lake Play
Variable
Sample
mean ˆ
m
Variance
ˆ
s
2
Correlation*
Pool area
Average
net pay
Average
porosity
Pool area
7.869
0.721
1.000
Average net pay
2.211
0.422
0.682 (0.731) 1.000
Average porosity –2.674
0.068
0.641 (0.275) 0.452 (0.077)
1.000
*Covariance in parentheses.
Constant = 0.681 2
2.164,
ij
i
j
i j
=
<
∑∑ s
Scale factor = 0.001
ˆ
m = 2.408, s ˆ
2 = 3.211 + 2.164 = 5.375