More about Discovery Process Models
73
the drilling is conducted randomly on a trend, then C = 1. If the drilling
decision is based on geological and geophysical leads, then C = 2. The
third class lies between one and two. Drew et al. (1980) and Drew (1990)
adopted the Arps and Roberts method and used past exploration
effi ciency for predictions of the immediate future in the study of the
Denver Basin and the Permian Basin of West Texas and southeastern
New Mexico.
Drew (1990; Drew et al., 1980) used the following approach for selecting a C value for a particular depth interval. The procedure is to carry
out a retrospective study. For example, in the 1961 to 1974 forecasts,
the total oil and gas combined equals the actual discoveries within the
same period, so that the C value obtained equals two. In the Gulf of
Mexico offshore study, Drew et al. (1982) used a nonlinear regression
method to estimate simultaneously the number of fi elds and the effi -
ciency of exploration for each size class. The effi ciency of exploration
ranged from 2.55 to 5.35. This method was used by Arps and Roberts
(1958) and by Drew (1990; Drew et al., 1980, 1982) to forecast the future
discovery rate based on the C value obtained.
Bloomfi eld et al. (1979) used the Monte Carlo procedure to estimate discoverability for a Kansas data set and obtained a discoverability coeffi cient of 0.3. Forman and Hinde (1985) found an empirical
straight-line relationship between the logarithmic hydrocarbon volume
and the number of fi elds, N, as
log V = a 1 b N
(4.5)
where a is the intercept and b is a negative value for the slope of the fi tted line. The ability of the explorationist to discover larger pools fi rst
is specifi ed by the slope, b. The greater the degree to which larger pools
are discovered fi rst, the steeper the slope.
The purpose of using PETRIMES to estimate the β value is to
account for other factors that are not included in the likelihood function of Equation 3.5 and to obtain the mean and variance of the poolsize distribution. Two procedures can be used: (1) with LDSCV, N can
be obtained by the maximized β value; and (2) with LDSCV or NDSCV,
a specifi c value can be assigned to β and the log likelihood is computed.
By selecting the highest log-likelihood value, the plausible value of β
can then be chosen.
For the lognormal case, both LDSCV and NDSCV can predict the
β values correctly (Fig. 4.3, tables 4.1 through 4.4). For the Weibull
case, LDSCV overestimates the β value (Fig. 4.4, tables 4.1 and 4.2)
73
the drilling is conducted randomly on a trend, then C = 1. If the drilling
decision is based on geological and geophysical leads, then C = 2. The
third class lies between one and two. Drew et al. (1980) and Drew (1990)
adopted the Arps and Roberts method and used past exploration
effi ciency for predictions of the immediate future in the study of the
Denver Basin and the Permian Basin of West Texas and southeastern
New Mexico.
Drew (1990; Drew et al., 1980) used the following approach for selecting a C value for a particular depth interval. The procedure is to carry
out a retrospective study. For example, in the 1961 to 1974 forecasts,
the total oil and gas combined equals the actual discoveries within the
same period, so that the C value obtained equals two. In the Gulf of
Mexico offshore study, Drew et al. (1982) used a nonlinear regression
method to estimate simultaneously the number of fi elds and the effi -
ciency of exploration for each size class. The effi ciency of exploration
ranged from 2.55 to 5.35. This method was used by Arps and Roberts
(1958) and by Drew (1990; Drew et al., 1980, 1982) to forecast the future
discovery rate based on the C value obtained.
Bloomfi eld et al. (1979) used the Monte Carlo procedure to estimate discoverability for a Kansas data set and obtained a discoverability coeffi cient of 0.3. Forman and Hinde (1985) found an empirical
straight-line relationship between the logarithmic hydrocarbon volume
and the number of fi elds, N, as
log V = a 1 b N
(4.5)
where a is the intercept and b is a negative value for the slope of the fi tted line. The ability of the explorationist to discover larger pools fi rst
is specifi ed by the slope, b. The greater the degree to which larger pools
are discovered fi rst, the steeper the slope.
The purpose of using PETRIMES to estimate the β value is to
account for other factors that are not included in the likelihood function of Equation 3.5 and to obtain the mean and variance of the poolsize distribution. Two procedures can be used: (1) with LDSCV, N can
be obtained by the maximized β value; and (2) with LDSCV or NDSCV,
a specifi c value can be assigned to β and the log likelihood is computed.
By selecting the highest log-likelihood value, the plausible value of β
can then be chosen.
For the lognormal case, both LDSCV and NDSCV can predict the
β values correctly (Fig. 4.3, tables 4.1 through 4.4). For the Weibull
case, LDSCV overestimates the β value (Fig. 4.4, tables 4.1 and 4.2)