A critique of Hubbert’s model for peak oil

In 1956, Shell Oil Company geologist M. King Hubbert published a model for the growth and decline over time of the production rates of oil extracted from the land mass of the continental US. Employing an estimate for the amount of ultimately recoverable oil and a logistic curve for the oil production rate, he accurately predicted a peak in US oil production for 1970. His arguments and the success of his prediction have been much celebrated, and the original paper has 1400 publication citations to date. The theory of “peak oil” (and subsequently, of natural resource scarcity in general) has consequently become associated with Hubbert and “Hubbert” curves and models. However, his prediction for the timing of a world peak oil production rate and the subsequent predictions of many others have proven inaccurate. We revisit the Hubbert model for oil extraction and provide an analysis of it and several variants in the language of (time) autonomous differential equations.