What theory for peak oil?

I do realize that we have a workman-like "theory" of peak oil, but no one else has ever formally quantified -- correctly -- the theory through some basic math. Several times on this blog and elsewhere I have demonstrated how the current explanations for the Logistics sigmoid of the classic Hubbert peak rest on a premise that never made any sense from the start. Having showed that a simple yet perfectly valid math model does exist, working both on the discovery level as well as the production stage, we conceivably should start making some real headway.

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Yet, it will take some effort to get this real theory to overcome inertia of the prevailing common knowledge and conventional wisdom presented just about everywhere we look now (note that these quotes all come from the same article referenced from TOD):

Every non-renewable resource coming from a finite storage can be exhausted, this exhaustion process can be described through a mathematical function and represented by a depletion curve. This theory of depletion of non-renewable natural resources was first put forward in the 1950s by King Hubert, a US geologist, based on actual observation of oil wells' production.

1. How many people realize that this version of peak oil theory largely rests on an intuitive gut-check (however brilliant) by Hubbert? Clearly, Hubbert never presented a mathematical model, and came well short of using any formality.

Peak oil theory is well grounded in physics and mathematics, and there is little controversy that peak oil production for the world will eventually be reached at some point in the current century.

2. What math? The mathematical equations used for useful analyses such as Hubbert Linearization work essentially as heuristics based on previous empirical evidence¹. I would not call this well-grounded in physics and mathematics.

This discussion is really a reprise, to a large extent, of the Malthus theory on the evolution of population and the evolution of resources to sustain it, particularly production of food resources.

3. To explain the profile of oil depletion, not even close. Although we can give credit to Malthus, this point-of-view strays afar from the fundamentals of the life-cycle of oil itself.

(Brian Pursley comments) This article is wrong in so many ways I don't even know where to begin. Oil is renewable. Hydrocarbons do not take millions of years to form and whoever taught you that should go take a highschool level chemstry class. I can make hydrocarbons in the lab using only iron oxide, marble, and water (no fossils required), and it doesn't take millions of years. Why is the amount of oil a given? Do you really think you are omniscient? Yes we can increase reserves and we do so every year.

"Peak Oil theory is garbage as far as we’re concerned." -- Robert W. Esser, geologist, 2006

4. This comment on the article goes to the extreme in the other direction. I looked at the commenter's blogging profile and he claims to work as a hedge fund operator in investment banking. Although a good theory will do nothing to dissuade someone from pursuing a clear agenda of greed at all costs, we certainly can work on educating others who welcome new ideas.

So I contend that we need now, more than ever, to mathematically understand at a deep fundamental level the flow of physical resources (and monetary funds) on a global basis. If you look at the current USA fiscal crisis, you realize that mathematical charlatans had a big hand in this week's debacle. Without some counter-math, what can we do to stop the next Phil Gramm (who not only failed grade school once, but twice and then three times!) from spouting nonsense and basically laying waste to any common sense that a nation of logical citizens should bring to the table. If we can compare Al Franken (perfect math SAT score and brilliant analogist) vs. Phil Gramm (who the hell gave him a PhD?), we can potentially get on the right track.

We have nearly nailed the formal theory for peak oil and depletion (keep your eyes out for a new TheOilDrum.com post courtesy of Khebab), and I can't wait to start looking at how we can apply similar pragmathematics to other issues.

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¹ Even a theory like the Export Land Model, which I think has a sound fundamental basis does not get at the underling depletion behavior. It works mainly as a diagnostic tool to help people understand in terms of a zero-sum game the direction of a downturn.