Part 2: A Micro Peak Oil Model
I want to hammer a few points home on the Micro Peak Oil Model. The characteristic asymmetry of the consumption curves (i.e. steeper rise than fall-off) arises due to the first-order assumption that humans extract petroleum at a rate proportional to the amount left in the ground. I can't say that this follows precisely the real world, but as a fan of Occam, I normally try to use the simplest explanation for phenomenon that I can get away with. For a good example of the proportionality principle, consider the rise and decay of U.S. wildcat operations. At one time, each gusher generated a large flow, but over time the reservoir contents became depleted enough that the contents reduces to the much smaller stripper well flow. The latencies involved in collecting and delivering the oil extracted from stripper wells contribute to the extended tails we see in the post-Hubbert-peak of U.S. oil production.
A commenter pointed me to this extended abstract from the ASPO 2005 conference. The researchers do a good job in empirically fitting various distributions to the global production profile (something that I didn't even attempt to try my hand at) but do raise the same point I made:
Contrary to popular belief, Gaussians are not good models for time series. The Central Limit Theorem applies to random walks through controllable dimensions. To apply to oil production, the theory would have to be that God dropped 2 trillion barrels directly above the year 2008, and the barrels scattered forwards and backwards through time from there. ThatÂs obviously silly.I wish the authors would have tried fitting to the regional oil production numbers (i.e. U.S., Europe, etc.). With the laws of self-similarity applying, they might have gotten some more insight into the asymmetry. However, as they wanted to concentrate on the global scene, the tails have not yet emerged for them to easily fit any of the standard distributions to.
But do you know what gets me spooked? Natural gas depletion. I have seen many references in various forums that depletion in natural gas reservoirs does not follow the "rate-proportional-to-contents" empiricism. Like the nitrous oxide left in the whipping cream container, it maintains a steady flow of output while the can continues to hold pressure. After that, nada. The analogy: No stripper wells, No tails to the curve -- the production of natural gas drops off the table much more quickly than petroleum1. Gulp.
Thanks to MonkeyGrinder and ProfGoose for taking an interest in this math-intensive topic and recommending it to the EnergyBulletin memory hole.
1Except for oil production drop-off aided by water injection recovery techniques. This not only maintains a high rate, it apparently spoils much of the contents as well. Double Gulp.