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## Thursday, April 27, 2006

### Reserve Peak Proven!

Stuart Staniford at The Oil Drum suggested looking at peaks in the estimated reserves of oil as another way of predicting future trends. He plotted the reserve estimates on top of the production curves for several geographic regions and noticed that reserves typically lead the production curves, showing, in general, an earlier peak for reserve estimates than for production.

I can't argue with that logic and it does add a new dimension to looking at the data. Typically, we see the famous production curve (i.e. Hubbert curve) published and occasionally see a similarly peaked discovery curve that precedes the production curve by sometimes as much as 40 years. As this relationship usually holds up pretty well, the reserve peak ends up positioning itself somewhere in between the two peaks.
Reserve = Cumulative(Discoveries) - Cumulative(Production)
Interestingly, given the above relationship, we can pinpoint the reserve peak precisely in time, and at the very least just by eyeballing the two original curves. If the reserve peak occurs when the derivative of the above relationship goes to zero, and dCumulative(x(t))/dt = x(t), then:
dReserve/dt = Discoveries - Production = 0
or the striking result that the reserve peak occurs when Discoveries/year = Production/year! We can call it the mobjectivist law for a lack of a better name (or until I can dig up whoever discovered this originally).

As an example, we can look at the Norway data, which has recently hit a peak of sorts.

I previously fit the data to this curve:

And showing the reserve peak overlayed:

Clearly, you can see the reserve peak occurring approximately where the discovery peak on its downward slope meets the production curve on its upward slope (actually you see quite a few intersections corresponding to a number of local maximum). And, like I said, you can actually -- with eyeball accuracy -- pinpoint the comparable reserve peaks occurring at 1987 and 1992.

Kind of neat, eh? ... umm, I mean, Q.E.D.