M. King Hubbert, a former Shell geologist and university professor, originally developed the peak oil model, which came to be known as “Hubbert’s Peak” or “Hubbert’s Curve.” Essentially, Hubbert observed and theorized that oil production follows a bell curve shape some years after the bell curve of oil discovery, and that the peak of the production curves typically occur somewhere around the halfway point of total production. This offered a way to model the production curve for a given assumed ultimate recovery volume.
In 1956, Hubbert correctly predicted that US oil production would peak between 1965 and 1970. In 1976, Hubbert also correctly predicted that the worldwide peak of conventional crude would happen in the 2005 timeframe (plus or minus geopolitical uncertainty), as you can see in this video. Hubbert was one of the first to suggest that the fossil fuel era would be of very short duration (see: “Energy from Fossil Fuels,” Science, February 4, 1949).
The peak oil theory does not state that conventional oil production will peak and decline when exactly half the assumed global endowment has been used up. That notion assumes that we know with some certainty what the world’s recoverable reserve volumes actually are, and that the producing countries will extract their oil in an unconstrained way. The halfway mark supposition comes from applying the derivative of a symmetric logistic function to estimate future oil production, as Hubbert did. This mathematical method was first employed in 1838 by Pierre Verhulst to model exponential growth in finite systems. A mathematical variant called a Hubbert Linearization is used to estimate remaining recoverable reserves.
Analysts use these methods, and others, to estimate the total global amount of recoverable oil. In 2010, a group of Kuwait researchers applied a multi-cyclic Hubbert model with excellent results.