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42 comments on The limit of the statistic R/P in models of oil discovery and production

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Dudley_Stark on January 23, 2008 - 2:38pm Permalink | Subthread | Parent | Comments top

Hi Dave,

I used probability theory language because it's what I'm used to, because it seemed natural to express a shifted rescaled function using random variables, and because having amount of discovered oil at least as much as amount of produced oil for any time t corresponds to a property of random variables called stochastic domination. It was not necessary for me to use probability theory language and I did not use any limit theorems from probability theory.

It's fascinating that the normal curve fits oil production, but it's not at all clear how the central limit theorem applies. It's not even clear why the logistic distribution should fit the data. Deffeyes waves his hands a little about applying the logistic equation to finding oil, but, as he says, it's not convincing.

Bentley has a model described in the Strahan book which results in asymmetric depletion curves. I've written a paper about it which has been submitted to a journal. At a Parliamentary meeting on peak oil last week a BP representative said that Hubbert uses a bell shaped curve because of the central limit theorem. Bentley objected to that as well as many other things the BP rep said.

I think looking at simple models can clarify the reasons for a peak and why something like the R/P statistic is nonsense. At the same time, it would be interesting to apply ideas developed for simpler models to more complicated models.

Sorry, I can't help you out with the coal reserves!

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DaveR on January 23, 2008 - 3:32pm Permalink | Subthread | Parent | Comments top

Hi Dudley,

Thanks for your comments. Does anyone recall Hubbert mentioning the Central Limit Theorem in his work? My sense is that Hubbert was more comfortable with the logistic function than the normal curve. In his earlier work, he thought in terms of exponential growth, and this made it natural to progress to a logistic function, because the beginning of a logistic function is exponential. Also, before the development of personal computers, the logistic function was much more tractable mathematically than a normal curve.

Dave

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westexas on January 23, 2008 - 4:07pm Permalink | Subthread | Parent | Comments top

It's not even clear why the logistic distribution should fit the data. Deffeyes waves his hands a little about applying the logistic equation to finding oil, but, as he says, it's not convincing.

We tend to find and--far more importantly--we tend to develop the largest oil fields first. When the large oil fields start declining in a given region, we can't offset the declines with new smaller oil fields.

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