74
Statistical Methods for Estimating Petroleum Resources
when n = 30 and 50, whereas NDSCV overestimates its value when
n = 30 (Fig. 4.4, Table 4.3), and yields a correct estimate when n = 50
(Fig. 4.4, Table 4.4). For the Pareto example, LDSCV overestimates
the β value when n = 30 and yields a correct estimate when n = 50. On
the other hand, NDSCV presents the correct estimates when n = 30
and 50. For the mixed lognormal population case, LDSCV overestimates the β value when n = 30 and presents a correct estimate when
n = 50 (Fig. 4.6, tables 4.1 and 4.2), whereas NDSCV overestimates the
β values when n = 30 and 50 (Fig. 4.6, Tables 4.3 and 4.4). For the mixed
population of lognormal, Weibull, and Pareto populations, LDSCV
gives the correct estimates when n = 30 and 50 (Fig. 4.7, tables 4.1 and
4.2), whereas NDSCV presents a correct estimate when n = 30, and
overestimates its value when n = 50 (Fig. 4.7, tables 4.3 and 4.4).
Pool-Size-by-Rank
The point estimates derived by LDSCV and the empirical distributions
derived by NDSCV were used to compute the pool-size-by-rank for all
cases. We shall examine the plots for each case. For the lognormal cases,
LDSCV (Fig. 4.8A, B) and NDSCV (Fig. 4.8C, D) can predict all pools
within the 0.9 probability prediction intervals. For the Weibull case,
both LDSCV and NDSCV can predict the largest six pools (Fig. 4.9A,
C), but cannot predict the rest of the pools when n = 30. When n = 50,
LDSCV can predict the fi rst 20 pools (Fig. 4.9B), and NDSCV can predict all pools (Fig. 4.9D) when n = 50. For the Pareto case, when n = 30,
both LDSCV and NDSCV can predict the fi rst eight largest pools (Fig.
4.10A) and the fi rst 14 largest pools (Fig. 4.10C) respectively. When
n = 50, both LDSCV (Fig. 4.10B) and NDSCV (Fig. 4.10D) can predict
all pools within the 0.9 probability prediction interval.
For the mixed population cases, LDSCV predicts all pools when
n = 30 and 50 (Fig. 4.11A, B), but NDSCV can only predict the fi rst 17
pools when n = 50 (Fig. 4.11C, D). It is obvious that LDSCV performs
better than NDSCV if the mixed population is made up of lognormal
distributions. For the mixed population of lognormal, Weibull, and
Pareto populations, both LDSCV and NDSCV can predict all pools
when n = 30 and 50 (Fig. 4.12).
Play Resource Distribution
Play resource distributions for all cases derived by LDSCV and
NDSCV were computed (tables 4.1 through 4.4). The 0.9 probability
Statistical Methods for Estimating Petroleum Resources
when n = 30 and 50, whereas NDSCV overestimates its value when
n = 30 (Fig. 4.4, Table 4.3), and yields a correct estimate when n = 50
(Fig. 4.4, Table 4.4). For the Pareto example, LDSCV overestimates
the β value when n = 30 and yields a correct estimate when n = 50. On
the other hand, NDSCV presents the correct estimates when n = 30
and 50. For the mixed lognormal population case, LDSCV overestimates the β value when n = 30 and presents a correct estimate when
n = 50 (Fig. 4.6, tables 4.1 and 4.2), whereas NDSCV overestimates the
β values when n = 30 and 50 (Fig. 4.6, Tables 4.3 and 4.4). For the mixed
population of lognormal, Weibull, and Pareto populations, LDSCV
gives the correct estimates when n = 30 and 50 (Fig. 4.7, tables 4.1 and
4.2), whereas NDSCV presents a correct estimate when n = 30, and
overestimates its value when n = 50 (Fig. 4.7, tables 4.3 and 4.4).
Pool-Size-by-Rank
The point estimates derived by LDSCV and the empirical distributions
derived by NDSCV were used to compute the pool-size-by-rank for all
cases. We shall examine the plots for each case. For the lognormal cases,
LDSCV (Fig. 4.8A, B) and NDSCV (Fig. 4.8C, D) can predict all pools
within the 0.9 probability prediction intervals. For the Weibull case,
both LDSCV and NDSCV can predict the largest six pools (Fig. 4.9A,
C), but cannot predict the rest of the pools when n = 30. When n = 50,
LDSCV can predict the fi rst 20 pools (Fig. 4.9B), and NDSCV can predict all pools (Fig. 4.9D) when n = 50. For the Pareto case, when n = 30,
both LDSCV and NDSCV can predict the fi rst eight largest pools (Fig.
4.10A) and the fi rst 14 largest pools (Fig. 4.10C) respectively. When
n = 50, both LDSCV (Fig. 4.10B) and NDSCV (Fig. 4.10D) can predict
all pools within the 0.9 probability prediction interval.
For the mixed population cases, LDSCV predicts all pools when
n = 30 and 50 (Fig. 4.11A, B), but NDSCV can only predict the fi rst 17
pools when n = 50 (Fig. 4.11C, D). It is obvious that LDSCV performs
better than NDSCV if the mixed population is made up of lognormal
distributions. For the mixed population of lognormal, Weibull, and
Pareto populations, both LDSCV and NDSCV can predict all pools
when n = 30 and 50 (Fig. 4.12).
Play Resource Distribution
Play resource distributions for all cases derived by LDSCV and
NDSCV were computed (tables 4.1 through 4.4). The 0.9 probability