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.

Introduction

This paper breaks no new ground in its call for using practical probabilistic methods for defining reserves. In fact, the problem has always begged for a probabilistic solution. The bigger surprise is that an industry that prides itself on its use of science, technology, and frontier risk assessment methodologies finds itself in the 1990's with a reserves definition more reminiscent of the 1890's. The petroleum industry uncovers uncertainty at virtually every stage. Its definitions need to reflect that fact. I hope this paper provides a provocation or two for future debate on this important topic.

When presenting some of these ideas during a panel discussion at the SPE 1991 Annual Technical Meeting, I half jokingly remarked that had the Society been charged with describing the probability of a fair coin, it could not have agreed on a method of quantification:

The Society suggests the following guidelines. Heads: A likely event or an event that may occur with some certainty. Tails: An entirely possible event or perhaps even a probable event. We would not recommend further quantification since having to attach actual numbers to heads or tails would prove confusing to the membership and will add nothing of value.

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