I agree with some of your points Halfin. I wouldn't generally expect a model this simple for a phenomenon as complex as the global oil industry to be more than qualitatively right. If anything, the mystery is why it's done so incredibly well at fitting the US data (but it has, at least after circa 1958). It is mysterious why the data look crazy on these plots at the beginning and settle down later. Only time will tell if the upjog in the actuals of the last couple of years is just noise, or the start of a fundamentally different regime than we saw over the last two decades. At this point, it doesn't look out of the noise regime yet.

At least in the US data (which I guess I should make another post of some day), if you plot price on the same graph as the overall production, you can pretty clearly see that price causes the second order wiggles around the basic logistic form of the graph. Global peak might cause larger price excursions and be able to distort the graph more than the US graph got distorted.

I have seen a few of these types of graphs from Jean Laherrere in his Lisbon talk and they all seem to spike at the beginning, whether they are for individual fields, US states, or even countries.  It is probably the nature of an oil field itself.  Initially the gushers at the beginning force high production with their high pressure, but then things settle down into a steady pumping 'rhythm'.

Remember, the graph is not a graph of time, and the 'early' values depend heavily on accumulated production, so small 'inaccuracies' at the beginning are heightened.

It is not unlike the 'estimated time left' calculation that is done when you download a file.  In the first few seconds the estimate can go all over the place, but then it settles down to a fairly steady rate.

"I also think that the theoretical justification for the model's end-state behavior is pretty weak. While it might make sense for a given oil field (and I have seen such curves look pretty good for individual fields), running out of oil on a world-wide basis is a very different phenomenon, especially if there are no good replacements. With prices rising through the roof the incentive to find more oil and increase productivity will plausibly move us considerably above the logistics curve. The very fact that prices are higher towards the end of the curve than at the beginning is going to bias most production towards that end state. That means that extrapolating behavior during the low-price regime is going to underestimate total production levels. That makes the CERA curve not look so bad to me."

Bingo!  This is a point that I've been meaning to bring up here.  Worldwide PO is a very different phenomenon than an individual well, field, or even country reaching peak.  The reason is simple: Incentives.

Halfin correctly points out the effect rising prices have as we approach the world peak, but let's also look at what happens when a country reaches peak.  Assume it's 1970-ish, and you run an oil company.  You have the rights to some fields in the US (onshore or off) that can be profitably exploited only at a ridiculously high market price, say >= $20/barrel.  Of course you don't extract and market that oil, as it would be a money losing operation.  The fact that the US just reached peak is irrelevant--there's enough production from the rest of the world to keep the price below your magic threshold.

Fast forward to 2005, and not only have market prices increased, but improved technology has likely reduced your cost of production by anywhere from a little to a lot.  It could very well be a financially sound move to produce oil from that field now.

Similarly, as market prices rise there will be some demand response, as we've seen very recently from China.

And on top of that, we have public policy, in which those of us lucky enough to have enlightened leaders can look ahead and take actions now to further reduce consumption.  Plus infrastructure bottlenecks, supply constraints caused by natural and man-made phenomena, etc.

Any model that's based solely on geology and ignores these other factors will inevitably predict a quicker arrival of the peak, with a sharper decline.  I have no idea how to adjust the model to take all these issues into account; if I did, I would be on the short list to replace Alan Greenspan.

I'm not anti-model, by any means; hell, when I was (briefly) in economics grad school one of my planned areas of specialization was econometrics.  IMO, as useful as models are, they're most useful when we're aware of both their strengths and weaknesses.