The Oil Drum

22 comments on Linearizing a Gaussian

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ericy on January 11, 2006 - 11:49am

This is more or less the same type of plot that Deffeyes had in his 2005 book.

I too am uncomfortable with the fact that there isn't a solid theoretical underpinning for what type of curve to fit - there are too many variables, including population growth, changes in extraction technology, market forces and all of the rest. Then again, it is hard to deny that this does fit the data quite well. I suppose the next step would be to try the same sort of thing for the North Sea oil and see if we get similar results. You could do the same thing for Prudhoe bay by itself I imagine, but both of these cases are essentially just one oilfield, so we aren't quite modelling the same thing.

Something else that would be interesting I suppose would be to plot the predicted depletion rates as a function of time. The first couple of years after a peak, production won't go down much at all. It could be 5-10 years after peak before we start to get into some of the steeper depletion, so it isn't just a matter of predicting the steepest depletion, but in having a guess as to how long it will be before we get there.

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Luis de Sousa on January 11, 2006 - 12:05pm

Fitting the North Sea Oil with just one Gaussian curve is quite impossible, you have a twin peak.

Using two logistic curves, one for each discovery cycle, the fit is nearly perfect. I don't know what you'd get fitting two gaussians in this case...

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ericy on January 11, 2006 - 5:30pm

I just played with these numbers a little bit. The main question I had was how do the depletion rates vary with time.

There is one oddity in the graph though - the 'peak' happens in 1983 or thereabouts...

For US production, 10 years from the peak (year 1993), the production was dropping at about 1.1%/year.

20 years from the peak (year 2003), it was dropping at about 2.1%/year.

30 years from the peak (year 2013), it ought to be dropping at about 3.2%/year.

40 years from the peak (year 2023), it ought to be dropping at about 4.2%/year.

50 years from the peak (year 2033), it ought to be dropping at about 5.2%/year.

My point here is that at least in this model, the steeper depletion (which is relatively modest compared to some of the worst case numbers) is something that you slowly ease into. If we assume that the world peaked this year for example, production for the first 10 years or so is likely to be fairly flat with a fairly small decrease from year to year. Once you get 20 or 30 years out, then you are in the thick of it - that is where you are forced to make larger changes on an annual basis.

No guarantee of course that world production will follow a nice gaussian though...