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The Derivation of "Logistic-shaped" Discovery

Posted by Nate Hagens on June 26, 2008 - 9:00am
Topic: Geology/Exploration
Tags: gaussian, logistic, m. king hubbert, original, verhulst, webhubbletelescope [list all tags]

This is a guest post from WebHubbleTelescope. The post addresses the origins and relevance (or lack thereof) of the logistic equation as it is commonly used in projecting/modeling oil production forecasts. As far as I can see, this is the first time anyone has succeeded in deriving the Logistic oil model from first principles. I will follow this with a post on the Maximum Power Principle next week, which in my opinion may shed light on the logistic curve from the perspective of oil 'demand' (as opposed to supply).

Many people believe that the Logistic equation adequately models the Hubbert peak. This comes about for a few reasons:

  1. We can (often/occasionally) get an adequate heuristic fit to the shape of the production data by matching it to a logistic sigmoid curve.
  2. The logistic-growth formula dU/dt = U(U0-U) carries some sort of physical significance.
  3. The logistic has hung around for a long time, in modern terms, therefore it must have some practical value.

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