Published:January 01, 2001
Methods for Calculating the Mean of a Lognormal Distribution
All of the following methods are based upon a distribution in which n = 9, and the constituent values are:
NOTE: Upper truncation is also discussed on pages 14 and 20.
NOTE: The statistical mean is theoretically the preferred expression. However, I recommend against its general use, for the following reasons:
For field-size distributions, we do not ordinarily anticipate that a given trend or basin will have an infinite number of fields; instead we generally find tens to perhaps a few hundreds of fields. Accordingly, the continuous distribution, when η = °°, seems inappropriate, and leads to an inflated mean field size.
For prospect parameters such as Area, Average Net Pay, Gross Rock Volume, HC-recovery in barrels per acre-foot (bbl/af) or thousand cubic feet per acre-foot (mcf/af), Prospect Reserves, Initial Production Rates, etc., the recommended probabilistic estimating connotations of P99%, P90%, P50%, P10%, and Pl% treat those very large outcomes greater than Pl% as practically and geologically impossible. Because the statistical mean includes contributing values larger than Pl%, such untruncated means are unrealistically large. The P99% and Pl% estimates then become very useful as lower and upper plausibility or credibility checks that encourage iterations leading to greatly improved estimates.
When such distributions are truncated at Pl% and the truncated mean is calculated by incremental summing and averaging, such truncated mean values approach values obtained by using Swanson's Mean. Truncation at the small end of reserves distributions, reflecting commercial or economic thresholds, reinforces the practical utility of Swanson's Mean.
Risk Analysis and Management of Petroleum Exploration Ventures
During the 1990s, many international petroleum companies improved their exploration performance significantly by using principles of risk analysis and portfolio management, in combination with new geotechnologies. While exploration risk cannot be eliminated, it can certainly be reduced substantially, on a portfolio scale. And the widespread adoption of standardized risk analysis methods during the 1990s brought badly needed discipline to petroleum exploration. By the mid-1980s, most well-informed major international petroleum firms that were engaged in exploration recognized that, globally, the average size of new discoveries was diminishing. Not coincidentally, the class of exploratory prospects categorized as “high risk/high-potential” was showing marked signs of underperformance. For major companies, when all such ventures, which averaged around a 10% perceived probability of success, were considered, less than 1% actually discovered profitable oil and gas reserves, and the sizes of these discoveries were generally far smaller than predicted. All in all, such exploration for new giant fields destroyed value, rather than creating it, in the 1980s and early 1990s. Consequently, exploration, as a corporate function, lost credibility. It badly needed to begin delivering on its corporate promises. It needed to become more efficient, and thereby more profitable. To optimize the allocation of exploration capital, concepts of portfolio management began to be considered.