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

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2006 Annual Conference & Exposition


Chicago, Illinois

Publication Date

June 18, 2006

Start Date

June 18, 2006

End Date

June 21, 2006



Conference Session

Energy Resources, Efficiency, and Conservation

Tagged Division

Energy Conversion and Conservation

Page Count


Page Numbers

11.1297.1 - 11.1297.13



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Paper Authors


Mark Schumack University of Detroit Mercy

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Mark Schumack is Professor of Mechanical Engineering at the University of Detroit Mercy. He teaches courses in heat transfer, thermodynamics, fluid mechanics, and energy systems. His research interests include thermal/fluid modeling using computational techniques, with applications in the automotive, manufacturing, and energy fields. Dr. Schumack earned his BS, MS, and Ph.D. degrees in Mechanical Engineering from the University of Michigan.

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

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.


The term “peak oil” refers to the period in history when humankind reaches the point of maximum oil production. After that time, many experts and observers warn of economic and political turmoil as countries transition to an uncertain energy future. Geologist Kenneth Deffeyes states:

There will be chaos in the oil industry, in governments, and in national economies. Even if governments and industries were to recognize the problems, it is too late to reverse the trend.1

James Howard Kunstler, author of The Long Emergency and other books predicting the gloom of a post-peak world, is arguably the most rabid, yet most eloquent, proponent of the peak oil crisis:

Many of my readers, I sense, wonder why things aren't falling apart across America right now, given the hallucinatory nature of our economy. The answer is that Peak Oil is not the end of anything, it's the peak of everything. We're getting more oil now than ever before or ever again, and it is making us crazy. It makes it possible for me to succumb to the invitation to fly across North America for a one-day meeting. It keeps feeding the spreading tumors of suburbia. It supports the illusion that burning liquid hydrocarbons results in the creation of wealth2.

Schumack, M. (2006, June), The Hubbert Curve: Enabling Students To Meaningfully Model Energy Resource Depletion Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--373

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