A Consistent Probabilistic Definition of Reserves

Abstract

Summary Uncertainty begs for a probabilistic treatment, and I know of almost no business filled with more uncertainty than that of the petroleum technologist in quest of oil and gas volume estimates. As in most uncertain endeavors, no single number captures the range that describes our lack of knowledge. Fortunately, the petroleum business has a mathematical ally, the central limit theorem. We know when we multiply variables (reservoir thickness, reservoir length, reservoir width, porosity, saturation, percent of hydrocarbon in place that can be produced with present technology and prices), we very quickly approach the log-normal distribution. We can make our estimates of proved, probable, and possible reserves all consistent if we make sure that each lies on the same log-normal probability distribution. We make still other improvements if we take these distributions for wells (or the basic unit on which we estimate reserves) and add the entire distribution to get reservoir, field, or company reserves. Simply adding proved reserves has never been a mathematically legal operation and ought to cease as quickly as possible. By striving for a distribution answer, we will find that we supply the kinds of numbers from "very safe" to "this is a dream" that will satisfy the various constituencies requiring volume information—governments, management, explorationists, bankers, and others. Still better, when estimates have probabilistic definitions, it is also possible to generate performance measures that hold the estimators to their promises.