| This study introduces a new specification of oil and gas exploration as a sampling process, in order to estimate the number and sizes of undiscovered oil and gas pools by statistical inference from discovered pools as a sample. Oil and gas exploration is quite unlike drawing samples at random in that actual sampling is size-biased, subject to truncation of uneconomic pools, and to censorship of discovered pool sizes. The method of estimating the number and sizes of undiscovered pools proposed in this study specifically accounts for these non-random components of exploration as a sampling process, and can be easily implemented using the Expectation-Maximization algorithm. The method allows for choices between single and multiple point truncation of uneconomic pool sizes, and generalizes quite easily to the bivariate case necessary to analyze plays with pools that contain oil with associated gas. Its usefulness is enhanced by the introduction of powerful tests of fit of the lognormal distribution to the distribution of discovered pool sizes, and of meaningful measures of the uncertainty of estimates of the number and sizes of undiscovered pools. Application of the method to oil and gas plays in the San Juan basin of northwest New Mexico show that it yields quite reasonable and useful results. The method, when applied to data analyzed using other methods of estimating the number and sizes of undiscovered pools, confirms that failure to account for truncation of uneconomic pools will result in an overestimate of the average size of pools in a play. By avoiding this, and other, problems, the proposed estimation procedure should lead to better assessments of a play's potential for future discoveries of economically recoverable oil and gas. |
