A great deal of the literature on U.S. crude-oil supply claims that supplies are rapidly depleting. Newer prediction models have become fairly sophisticated but still lack adequate treatment of the physics of oil production and effects of technology. This paper addresses these issues and develops a model that is much less pessimistic and broader in range.
Hubbert,1 who first began publishing his ideas in the 1950's, probably initiated the trend of claiming that supplies are rapidly depleting with the notion that U.S. crude-oil production would behave like a bell-shaped curve (Fig. 1). In spite of his lack of defensible theory, Hubbert used this reasoning to conclude the conterminous U.S. (e.g., not including Alaska) would produce no more than 170 billion bbl. Other, more contemporary, analysts perpetuate this notion with forecasts founded on similar principles.2,3
Four basic factors affect oil production:
physics,
economics,
technology, and
the oil still in the ground.
The model developed here incorporates these factors by use of basic production theory and multivariate regression analysis.
The laws of physics require oil production to decline over time. Eq. 1, which can be derived from these laws, is commonly used to model this decline.4
Equation (1)
Proved reserves, Q, are calculated by determining the area beneath this curve over the anticipated life of the production, T. This relationship is shown by
Equation (2a)
for large T, and
Equation (2b)
for the general case. Note that proved reserves can be approximated by dividing the initial production, qi, by the decline rate, di, if a sufficiently long time interval, T, is assumed. Eq. 2b, for the general case, has been rearranged by solving for the decline rate. This relationship between production, decline rates, and proved reserves is powerful for several reasons.
