Creamed again

One of peak-oil denier Michael Lynch's favorite arguments to counter the oil depletion pessimists out there (Campbell and Laherrere, et al) has to do with questionable interpretation of the so-called "creaming curves" from mature fields. Since I did some real honest-to-goodness Monte Carlo simulations fairly recently, I think I have a handle on what Lynch has gone half-cocked over. Bottom-line: nothing to get excited about -- just Lynch practicing his highly refined art of attacking the model and not the reality of the situation.

Lynch essentially states that the creaming curves that get published have a tendency to creep up over time, implying that more oil exists than anyone currently realizes. I have thought about this for awhile, found his arguments somewhat intriguing myself, until the trickery finally popped into my head. Unfortunately, Lynch has mistaken the asymptotic properties of finite regions with the semi-infinite scope that some creaming curves occur under.

As an example, consider this Lynch curve:

Note that one curve gets plotted according to time progression. From the looks of it, it doesn't appear to have any asymptotic properties. On the other hand, when ordered by size (i.e. sorted), it shows a clear asymptote. Lynch likes to point out that people shouldn't look at the purple curve because the other one keeps climbing. What Lynch fails to point out, and many people have gotten taken by, constitutes a rather serious sin of omission on his part. He doesn't state his assumptions. If he did, then you would see the flaw in his argument rather quickly.

1. Within a finite field area, the asymptote gets truncated artificially. The geologists or petroleum engineers declare the field "dry" when they stop finding strikes, go back and order the numbers, and figure out the creaming value. Ordering the values high to low and doing a cumulative sum gives the curve a filtered look that shows a horizontal asymptote. Graphically displaying the integration works out as a nice PowerPoint slide for management. The men in the suits agree, nodding their heads, and go on to the next field. And the engineers and scientists don't have to try to suck blood from a turnip.
2. Within a quasi-infinite or continuously expanding field, the asymptote continues to creep upward. You can't make any assumptions on asymptotic behavior because the big discovery occasionally occurs, pushing the curves inexorably upward. In reality, only when you hit the limits of your quasi-infinite world can you make any serious interpretations on creaming.

The moral: Unless the field has hit the end of its lifetime, don't read too much into a creaming curve. If the discoveries do follow an ordering according to size, big to small, you might have an argument to stand on. (The unsorted curve should show show a noisy but quite straight linear upward trend if the sizes show independence with respect to time) However, in the quasi-infinite situations, the big discoveries will likely still occur where you haven't looked, thus invalidating any asymptotic trend that you may have counted on.

This exercise in Lynch de-debunking helped me see another interesting property of the creaming curve. When ordered according to size, a histogram of the individual slope values gives the probability density function. Which means you can easily check against a log-normal distribution. If I could find a creaming curve for the entire world, we should get a good distribution to work with.