30
Statistical Methods for Estimating Petroleum Resources
where x 1 , … , x N represents the pool size in the play, and N is total
number of pools in the play.
Take the example of N = 3 and n = 2 to illustrate the discovery process model. Let the sizes of the three pools be x 1 = 50, x 2 = 300, and
x 3 = 100 MMbbls. The probabilities for all possible discovery sequences
are graphed in Figure 3.3, which indicates that the most likely sequence
is (x 2 , x 3 , x 1 ), even though other sequences are also possible. This is the
concept adopted by the discovery process model to characterize the
exploration process. In other words, the probabilities for discovery of
each pool of a play are set according to their volumes, and the probabilities for discovery of the remaining pools change as exploration
continues. This concept allows us to formulate the discovery process
likelihood function to be discussed in the following sections.
In Equation 3.2, the probability is completely proportional to pool
size, but in reality pool size might be only one of many controlling factors. Thus, Equation 3.2 is generalized by adding an exponent to the
equation as follows (Lee and Wang, 1985):
∞
+ +
+ +
b
b
b
b
1
P
···
···
j
j
j
N
X
X
X
X
(3.3)
Figure 3.3. Examples of discovery sequence. W N = (100, 300, 50) and N = 3, n = 2.