Infinite URR?

I posted on this topic awhile back, but it deserves another look because the idea provides a strong talking point to use against the cornucopians who like to play with numbers. In particular, Michael Lynch provides a foil to test the argument against. I pulled the following from disinformation he spouted on DemocracyNow last Friday:

MICHAEL LYNCH: Actually, I think the problem here is that Julian and a lot of the people making these arguments are not that familiar with the technical terms in the oil industry. The estimates that there's about two trillion barrels of oil resource are actually done by some very simplistic models, which have not always failed, but almost always failed on both the national and a global level. The oil conventional oil resource base, the oil in place, is about eight to ten trillion barrels. And right now, most estimates are that about 40% of that will be recovered, in other words, about three, three-and-a-half trillion. But the amount we'll recover will grow over time. So we're not -- we're really not even close to halfway through the conventional oil resource base.

Here, Lynch claims that we have no worries as the global economy has over 3 trillion barrels left in reserves, i.e. a relatively healthy URR.

Well, I can do him one better and claim that we can have an infinite supply left, yet we will still have to face a peak in production.

To create such a scenario, we need only to create a production profile that -- when integrated from now to eternity -- tends to an infinite cumulative value. Simple enough, the following curve¹ does this quite nicely:

Production(Time) = A/(B + C*abs(Time-T0))

The curve, for a T0=2007, looks like the following:

It looks innocent enough on the way up, and then goes through what looks like a precipitous drop, a sure sign that we have entered a doomster realm. Right? Well, not quite. The long tail that this curve contains actually contains a huge bonanza of future returns, why, a veritable cornucopia of oil!

Too bad it completely trashes Lynch's rosy assessment, which he clearly built off a dodgy initial premise. In reality, we have no idea how that purported 3 trillion, or infinite amount, in reserve will play out. On the bright side, we should have lots of time to find an alternative source to keep our productivity and life-style moving forward.

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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.