Hubbert peak

The Hubbert Peak theory posits that for any given geographical area, from an individual oil field to the planet as a whole, the rate of oil production tends to follow a bell-shaped curve. Early in the curve (pre-peak), production increases due to the addition of infrastructure. Late in the curve (post-peak), production declines due to resource depletion.

"Peak Oil" as a proper noun, also known as Hubbert's peak, refers to a singular event in history: the peak of the entire planet's oil production. After Peak Oil, according to the Hubbert Peak Theory, the rate of oil production on Earth will enter a terminal decline. The theory is named after American geophysicist Marion King Hubbert, who created a model of known oil reserves, and proposed, in a paper he presented to the American Petroleum Institute in 1956 [3], that production of oil from conventional sources would peak in the continental United States between 1965 and 1970, and worldwide within "about half a century" from publication.

In 1956, Hubbert proposed that crude oil production in a given region over time would follow a bell-shaped curve without giving a precise formula; he later used the Hubbert curve, the derivative of the logistic curve, for estimating future production.

Hubbert assumed that after oil reserves are discovered, oil production at first increases approximately exponentially, as wells are drilled and more efficient facilities are installed. At some point, a peak output is reached, and oil production begins declining until it approximates an exponential decline.

The Hubbert curve satisfies these constraints. Furthermore, it is symmetrical, with the peak of production reached when half of the oil that will ultimately be produced has been. It also has a single peak.

Given past oil production data, a Hubbert curve may be constructed that attempts to approximate past data, and used to provide estimates for future production. In particular, the date of peak oil production and the total amount of oil ultimately produced can be estimated that way.

The standard Hubbert curve is a real-valued function of one real variable; in order to apply it to the real world, scales have to be chosen, one for time and one for oil production, based on the observed data. They are usually given implicitly by specifying the integral of the Hubbert curve, the ultimate total oil production Q∞, with a unit of billions of barrels, and the initial growth rate asymptotically reached for very early times, a, often expressed in percent per year.

Hubbert also proposed a method for determining the values for Q∞ and a based on empirical data, by considering the ratio of production at a given time and cumulative production to that point as a function not of time but of the cumulative production itself; if production followed a Hubbert curve, this function would have the form, a straight line. Thus, by considering the best linear fit to the function actually observed, estimates for a and Q∞ can be obtained.