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## Tuesday, May 02, 2006

### Foot, note in mouth

In a footnote the other day, I archived what seemed like an offhand comment:
1 If you think this curve a bit far-fetched, remember that some reserve growth predictions, by the USGS no less, generate parabolic growth laws. If real, these may even have longer tails than we show above.
This leads to an incredible conundrum that peak oil deniers like Michael Lynch must face up to, based on their quotes of very large reserves. How big can these reserves get? Well, the reserve growth that some USGS analysts predict follows what looks like a parabolic growth law:

The name of the law refers to the quadratic or parabolic shape you get when plotting Amount versus Time (hint: tilt your head sideways to the right). More typical, if we plot Time on the x-axis and Amount on the y-axis, it turns into a square-root relationship. If we stopped right now and relied only on reserve growth, Q(t), then production can only proceed by at most the derivative of this number:
Q(time) = Integral (P(t)) = k*squareRoot(t)

dQ(t)/dt = P(t) = 0.5*k/squareRoot(t)

The production number shown drops off like 1/t1/2, which provides an even slower drop-off than the 1/t dependence I conjured up earlier. Like my hypothetical curve, the USGS's curve also appears to generate an infinite supply of oil.

Got that? The bureaucrats at USGS lead us to believe -- perhaps just a sin of omission -- that reserve growth will generate an infinite supply of oil. I say they "lead us to believe" this, because no where do they say a limiting factor appears. This kind of sloppy analysis gives apologists like Lynch ample ammunition to spew forth a cornucopian outlook on the population.

However, the conundrum still remains. While reserve growth could hypothetically continue to grow as a square-root against time, the production will still drop off by the reciprocal of this number. If we indeed have reached a peak, then the reserve growth will still not make up for depletion losses and we will continue to face relentlessly diminishing supplies in the future. Only lots of new discoveries, sufficiently removed from known reservoirs will prevent the decline.

As a general rule, the deniers will always insert foot into mouth and generate just enough rope to hang themselves with -- evidently they can't even win an argument with an infinite supply of oil on their side of the equation.