Finite Population Sampling Methods for Oil and Gas Resource Estimation1
Some recent developments in finite population sampling methods are applicable to oil and gas resource assessment. The objective of these methods is to provide an estimate of the empirical frequency function of magnitudes of undiscovered deposits in a petroleum play when the only observable data are deposit magnitudes in the order of discovery (observation). Our theme is the conceptual similarity of the well-known Arps and Roberts (1958) model for magnitudes of discoveries as a function of exploratory wells drilled to a finite population sampling scheme called “successive sampling” by statisticans. There are two types of approximately unbiased estimators for parameters of successively sampled finite populations: Gordon’s (1983) moment matching estimator and Andreatta and Kaufman’s (1983) anchored estimator. Both are similar in functional form to Arps and Roberts original estimator for the number of deposits of a given magnitude ultimately discoverable in a play, but arise from different assumptions about the nature of the sampling scheme. Using Western Gulf Miocene-Pliocene data and North Sea data, some estimates of empirical field size distributions generated by the three above-mentioned estimators are presented. When applied to Western Gulf Miocene-Pliocene data, the moment-matching estimator appears sensitive to how the sample is split. The anchored estimator replicates Smith and Ward’s (1981) maximum likelihood estimates reasonably well.
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There is a continual need to update estimates of oil and gas resources remaining to be discovered, and also to refine the methodologies for making these assessments. In 1974, AAPG sponsored a research conference dealing with the above topics, and many of the papers presented there were published in AAPG Studies in Geology 1. As a follow-up to that volume, a U.S. Geological Survey workshop was held in 1983, and many papers from talks presented there, in addition to several other papers, are contained within this volume. The 22 papers have been grouped into two types: those describing methodologies for evaluating resources and those presenting assessments of both conventional and unconventional resources.