Evaluating Conceptual Plays
119
numbers were then multiplied as PS 1 . If one repeats this step many
times, then all the PS’s can be used to construct a pool-size distribution
(Fig. 5.4, left side of the equation).
The Lognormal Approximation
Lognormal approximation also can be applied to solve Equation 5.8. In
PETRIMES, the geological random variables are jointly approximated
through the use of a multivariate lognormal distribution. Because the
result of the product and/or division of lognormal random variables
is again a lognormal variable (Aitchison and Brown, 1973), it follows
that the pool-size distribution is lognormal. If we let μ i , s
2
i
, and s ij , i,
j = 1, 2, … , denote the mean, variance, and covariance of the natural
logarithms of the geological variables, then the mean and variance of
the pool-size distribution are given by
Mean = e
( m + s 2 / 2)
(5.9)
+
=
×
−
2
2
(2
)
Variance
(
1)
e
e
m s
s
(5.10)
RECOVERABLE POOL-SIZE DISTRIBUTION
POOL AREA
DISTRIBUTION
NET PAY
DISTRIBUTION
1.0
CUMULATIVE FREQUENCY
GREATER THAN
0
POOL SIZE, 10
6 m
3
POROSITY DISTRIBUTION
HYDROCARBON SATURATION
DISTRIBUTION
RECOVERY FACTOR
DISTRIBUTION
0
1000
1.0
R 3
P 1
POROSITY, dec
HYDROCARBON SATURATION, dec
RECOVERY FACTOR, dec
0
.01
.1
.1
H 1
F 1 1
1
.4
1.0
1.0
0
1.0
R 5
0
1.0
0
0
1
NP 1
NET PAY, m
100
ϫ
ϫ
ϫ
ϫ
ϫ
0
1000
POOL AREA, ha
R 2
R 1
R 4
A 1
= Constant
Figure 5.4. Diagram illustrating the Monte Carlo procedure for computing
pool-size distribution.