More about Discovery Process Models
87
answer is no, for the following reason. Discovery process models are
controlled not only by physical features of deposition, but also by the
manner in which the pools are discovered. Therefore, if the pools have
been destroyed by geological processes, the discovery probabilities will
not be the same because the pools destroyed by nature are excluded
from the maximum-likelihood function (see Eq. 3.5).
Take a simple case, for example, where N = 5 with pool sizes x 1 , x 2 , x 3 ,
x 4 , and x 5 . The probability of discovering pool x 1 is x 1 /(x 1 1 x 2 1
x 3 1 x 4 1 x 5 ). Suppose x 2 has been destroyed by geological processes,
then the probability of discovering pool x 1 is x 1 /(x 1 1 x 3 1 x 4 1 x 5 ).
Note that x 2 is not included in the probability statement. This trivial
example demonstrates that nonproductive traps have no impact on
the estimates derived from discovery process models.
To illustrate the concept of a discovery process model, let us do some
“marble fi shing.” Suppose we have an urn that contains red, green, and
black marbles of different sizes. The red and green marbles represent
gas (red) and oil (green) pools, and the black marbles represent nonproductive traps. When fi shing for marbles, we cannot see or touch them,
but intend to “fi sh out” large red or green marbles and not the black
ones. What we know is that our marble-fi shing technique allows us to
fi sh out large red or green marbles with high probability. Whenever
we obtain either a red or green marble, we place it in a time sequence.
The black marbles we fi sh out are discarded as failed prospects. All the
marbles we have fi shed out are not put back in the urn. This is the statistical procedure of sampling without replacement. After several trials,
the following questions arise:
From the time sequence, can we estimate how many red and
•
green marbles are yet to be fi shed out?
What are the sizes of the remaining red and green marbles?
•
The discovery process model is designed to estimate the number and
size of the remaining red and green marbles (not the black ones).
Impact of Missing Pools
Commonly, small pools are not reported because of economic truncation. The absence of small pools from discovery sequences raises a
problem in petroleum assessment. To investigate the impact of their
absence from a discovery sequence, the lognormal population (Fig. 4.3)
is used. Suppose that pools with sizes less than 0.5 × 10
6 m
3 were not
87
answer is no, for the following reason. Discovery process models are
controlled not only by physical features of deposition, but also by the
manner in which the pools are discovered. Therefore, if the pools have
been destroyed by geological processes, the discovery probabilities will
not be the same because the pools destroyed by nature are excluded
from the maximum-likelihood function (see Eq. 3.5).
Take a simple case, for example, where N = 5 with pool sizes x 1 , x 2 , x 3 ,
x 4 , and x 5 . The probability of discovering pool x 1 is x 1 /(x 1 1 x 2 1
x 3 1 x 4 1 x 5 ). Suppose x 2 has been destroyed by geological processes,
then the probability of discovering pool x 1 is x 1 /(x 1 1 x 3 1 x 4 1 x 5 ).
Note that x 2 is not included in the probability statement. This trivial
example demonstrates that nonproductive traps have no impact on
the estimates derived from discovery process models.
To illustrate the concept of a discovery process model, let us do some
“marble fi shing.” Suppose we have an urn that contains red, green, and
black marbles of different sizes. The red and green marbles represent
gas (red) and oil (green) pools, and the black marbles represent nonproductive traps. When fi shing for marbles, we cannot see or touch them,
but intend to “fi sh out” large red or green marbles and not the black
ones. What we know is that our marble-fi shing technique allows us to
fi sh out large red or green marbles with high probability. Whenever
we obtain either a red or green marble, we place it in a time sequence.
The black marbles we fi sh out are discarded as failed prospects. All the
marbles we have fi shed out are not put back in the urn. This is the statistical procedure of sampling without replacement. After several trials,
the following questions arise:
From the time sequence, can we estimate how many red and
•
green marbles are yet to be fi shed out?
What are the sizes of the remaining red and green marbles?
•
The discovery process model is designed to estimate the number and
size of the remaining red and green marbles (not the black ones).
Impact of Missing Pools
Commonly, small pools are not reported because of economic truncation. The absence of small pools from discovery sequences raises a
problem in petroleum assessment. To investigate the impact of their
absence from a discovery sequence, the lognormal population (Fig. 4.3)
is used. Suppose that pools with sizes less than 0.5 × 10
6 m
3 were not