An analytical approximation of the distribution of total hydrocarbon discoveries as a function of discovery number

Recently, Manly's method has been successfully applied to hydrocarbon exploration modeling in order to approximate the expected value and the standard deviation of the total amount of hydrocarbons discovered. This method is much faster than running prolonged simulations normally required by the probabilistic model of the hydrocarbon discovery process, and the results are very accurate. This paper extends the usefulness of the approximation method by developing an approximate analytical model of the whole probability distribution of the total volume of hydrocarbons discovered. The mean and the standard deviation from Manly's approximation are used to help set the parameters of a family of beta distributions, to represent the distributions of the total amount of hydrocarbons discovered from the beginning to the end of the exploration process in an area. Three real datasets—the Nova Scotian Shelf from offshore northeastern Canada, the Bistcho Play, and the Zama Play from northwestern Canada—are chosen to verify the methodology developed. Confidence intervals of the forecast for each number of discovered fields are constructed from the analytical approximation and compared with confidence intervals generated by the simulation. Sensitivity analyses are performed to show that the idea of using a family of beta distributions is a robust approximation.