Limitations of Statistical Methods for Predicting Petroleum And Natural Gas Reserves and Availability
Authors: Ryan J.M. 
Published: December 2007

Abstract
In recent years M. King Hubbert, C. L. Moore and the Energy Policy Staff (EPS) of the United States Department of the Interior have published estimates of the nation's resources or ultimate recoveries. The Hubbert and Moore methods, are similar in that they involve fitting analytic functions to historical data and projecting these into the future. There is no logical basis for assuming that future activities will be constrained to follow these or any other functions, so the Hubbert and Moore projections should be rejected as inadequate guides to policy. The EPS approach involves estimation of the extent to which the nation's potentially productive sediments have been explored and the extrapolation of the results achieved in explored areas to the unexplored. There is a logical basis to this approach that the resulting estimates are subject to two counter-balancing errors of large but unknown magnitude. Hence, this estimate should be used with caution.

Introduction
It is widely recognized that a reliable estimate of the amount of oil and gas in place by geographical areas would be of great value in formulating governmental and corporate policies. To be thoroughly credible, however, such an estimate would require detailed subsurface studies and exploratory drilling on a massive scale. An accurate appraisal of ultimate recoveries would be even more valuable. Such an estimate would be complicated further by the fact that it would depend not only on total resources but also on the future technology and economics of production transportation and consumption of all forms of energy. Clearly, detailed subsurface studies and accurate long term projections of future prices and technology are not available or even feasible today. Hence, most estimates of resources or ultimate recoveries do not utilize these fundamental factors but rely instead on some method of statistical projection. In the last few years three studies which can be described as essentially statistical have received publicity. These are the work of Hubbert, Moore and the EPS of the U. S. Department of the Interior. The statistical techniques of each of these studies will be reviewed to ascertain the reliability of the projections.

The Hubbert Estimates
Perhaps the best known projection of ultimate recovery of domestic oil and gas in recent years is that made by Hubbert for the National Academy of Sciences, National Research Council. In this study, Hubbert fits a particular mathematical function (the logistic curve) to historical data on cumulative gross additions to crude oil reserves on an API basis, and uses this equation to estimate total ultimate recovery. I have analyzed the Hubbert approach in some detail elsewhere, so the present paper will be restricted to a brief review of the weaknesses of the Hubbert method and the reasons for my conclusion that it is an inadequate guide to policy. Fig. 1 shows an idealized plot of Hubbert's conception of cumulative gross additions (or in his terminology, which will be used here, cumulative discoveries) and cumulative production. Both functions are logistic curves in the figure. The curve for cumulative production is identical to that for cumulative discoveries except that it is shifted t units to the right.