growth curves

The logistic function has been used to describe the discovery and production of oil and natural gas at the national level. This type of functional representation provides a direct approach for estimating the available supply of the resource and the time at which that supply will be essentially depleted. The mathematical characteristics of the function imply restrictions, which are not necessarily applicable to natural resource-production patterns. We examine these restrictions in the context of crude-oil production at a regional level. We attempt to show that statistical estimates of the functional parameters based on actual crude-oil production could satisfy the mathematical restrictions inherent in the logistic function.

Published in: Energy, Volume 9, Issue 7, July 1984, Pages 565-570
Available from: ScienceDirect

Hubbert predicted the time of U.S. peak production and the ultimate recovery of crude oil
by analysing smoothed growth curves derived from discovery and production data. Early work’
depended on independent recovery quantity estimates and predicted the production peak to be
about 1965-1970. Later, growth curves were used to predict both the year (1967) of the peak
more precisely and the quantity (170 billion bbl). A recent survey of growth curves describes their use as a well-established tool. However, the effect on ultimate oil production quantity due to social, political, economic, and technological effects has not been well addressed. Energy growth curves generally assume that future production will reflect previous production, which limits the recovery efficiency, for example, to an average of past values.

The amount of ultimately recoverable crude oil is found to be 181.1 billion bbl for the conterminous U.S. (including offshore). Inclusion of Alaska raises the total to 217.2 billion bbl.

Published in: Energy, Volume 19, Issue 7, July 1994, Pages 813-815
Available from: ScienceDirect