The Hubbert Curve: Enabling Students To Meaningfully Model Energy Resource Depletion

Courses in Energy Systems (alternatively named “Applied Energy Conversion,” “Energy Conversion Systems,” or some variant) often discuss the idea of energy resource depletion in terms of the exponential growth model. A typical problem is: given the current growth rate of oil production, in what year will known reserves be depleted? The exponential growth model, although offering reasonable results initially, becomes less accurate in the later stages of resource exploitation as issues of scarcity, cost, and technological hurdles become important. It grossly under predicts how long a given resource will last. A better model introduced in some textbooks is the “Hubbert curve,” a bell-shaped curve resulting from the solution to the logistic equation. Textbook coverage of the Hubbert model, however, is usually limited to a brief allusion and perhaps presentation of a graph of actual vs. predicated production a fossil fuel such as oil or natural gas. This paper describes how a thorough analytical treatment of the Hubbert curve was explored in one energy systems class. Coverage includes mathematical and physical bases for the exponential and Hubbert models, comparisons of exponential and Hubbert model results, and application of the Hubbert curve to various nonrenewable fuels. Through comparisons with actual production data, students are made aware of the uncertainties associated with energy production modeling. The topic is contextualized through inclass discussions regarding the current controversy over “Hubbert’s peak” for world oil production.