The content of Mr. Laherrere's article (OGJ, Apr. 17, 2000, p. 63) is interesting and useful. Especially appreciated by me (an electrical engineer) are his perceptive discussions about the various oil basins of the world and the different patterns of discovery; Lower 48, Alaska, former Soviet Union (FSU), and the UK. And, happily, I learned even more by ferreting out the errors and contradictions, not to mention the challenging typo. In brief: While I agree with many of his conclusions, I strongly disagree on three key points:
- The claim that he is using Dr. Hubbert's method.
- That the 'Shaman of Lascaux' has the true knowledge of the world's oil reserves.
- That there is only one way to progress beyond the Hubbert model.
For reasons explained later, I distinguish between the "Hubbert method" and the "Laherrere method" (i.e., what Mr. Laherrere variously labels "Hubbert," "Hubb," "Hub," or "H"). In other words, I believe that the title of his article should read, "Learn strengths, weaknesses to understand Laherrere curve." Further, although it was an important breakthrough in its day, I do not advocate the Hubbert model as an effective tool for oil forecasting. I think we can do much better, discussed later.
Mathematical Error: Mr. Laherrere (p. 64) states "But in practice it is more convenientellipse to model how annual production starts at zero and ends at zero with a peak in between" (emphasis added). But Laherrere does not "start at zero." Rather, he cobbles up his own set of equations wherein production always starts at a non-zero "effective beginning" or "cut-off," abbreviated "Pc," where Pc = 0.027*Pm ("Pm" means peak production). Consider three of Laherrere's own examples: 1. For the US Lower 48, Pc = 0.11 billion bbl in 1903 [Fig. 3]; 2. For the FSU, Pc = 0.14 billion bbl in 1940 [Fig. 8]; and 3. For the world, Pc = 1.03 billion bbl in 1930 (Fig. 13]. Clearly, none of the values of Pc are zero. Bottom line: Laherrere's method violates his own zero-peak boundary requirements. L'Hopital would turn in his grave!
Similarities and Differences: Both Hubbert and Laherrere use the same generic time-domain equations. In other words, although the equations look a bit different, they are mathematically equivalent. Mr. Laherrere confirms this fact (p. 64). So that's not the problem. Looking further, however, the production equation contains two constants that must be determined from production data. Hubbert uses a single auxiliary equation and a graphical technique to determine the values. In contrast, Laherrere uses a medley of auxiliary equations and a different technique. Different constants give different oil production curves. That's the problem.
The Hubbert constants: To determine the constants 'Q°°' and 'a' in the time-domain, Hubbert uses a linear auxiliary equation: ln N = ln N° - at. He then employs a graphical technique to get the best-fit values. For details, see pages 50-59, Hubbert (1982).
The Laherrere constants: To determine the constants 'b' and 'tm,' Laherrere uses a medley of auxiliary equations including, tc = tm-c; Pc = 0.027*Pm, and U = 4Pm/b = 0.8c*Pm. These equations, however, have no connection whatsoever to Hubbert's auxiliary equation. Proof: Laherrere's technique requires an "effective beginning" or "cut-off" year (i.e., "tc") for oil production, while the Hubbert technique does not. For details, compare pages 63-66 of Laherrere with Hubbert (1982).
En summa: Does a method have to be exactly the same as the Hubbert method to be labeled as such? (Does a lottery ticket have to have exactly the winning number to claim the prize?) The answer is an uncompromising yes. The 100 or more "Hubbert" labels in this article should all be changed to "Laherrere."
The Oil Shaman of Lascaux: Current estimates of the world's oil reserves (i.e., conventional oil + natural gas liquids) are highly contentious and vary widely. The minimum estimate is, to my knowledge, some 1,250 billion bbl by Mr. Laherrere (p. 74)-derived from the IHS/Petroconsultants database. In contrast, the maximum estimate is about 2,630 billion bbl by the US Geological Survey (Petzet, 2000). At points in between are estimates by the US Department of Energy, the International Energy Agency, BP Amoco, and others. All the databases except that of IHS/Petroconsultants are freely available to the public. Noteworthy too is that the minimum estimate (Laherrere) is less than half the maximum estimate (USGS).
Soothsayers are scarce nowadays and go out of style quickly. It is hauteur, I believe, to claim that any one database is demonstrably better than all the rest. Aptly put by geologist C. J. Campbell, "All the numbers are wrong, we just don't know how wrong." Time will tell. Meanwhile, I think the most realistic reserve estimates are derived from an amalgam of all the latest estimates, including those mentioned above. This approach was used to develop a new oil forecasting method, discussed below.
Beyond the Hubbert Model: Mr. Laherrere (p. 76) concludes, "Knowing backdated annual discovery is a must, but it has to be the annual discovery-based mean, not proved reserves. Hubbert's model derived only from production data is an insufficient tool." I agree with the latter statement but would actually prefer to bequeath the entire Hubbert model, once and for all, to the teachers of freshman geology courses! In contrast, however, I strongly disagree with Laherrere's first statement because we mortals don't know the backdated, updated, fore-shifted, F95, F50, F5, mean, or any other version of the oil discovery curve. Only the Oil Shaman knows the truth, and he won't tell.
With that in mind, I've developed a new and unique heuristic forecasting method (i.e., sans Gauss, Hubbert, Laherrere, et al.) to generate oil forecasts for the top 42 nations (any combination OK too), 7 regions, OPEC and non-OPEC, and the world. Papers on the first two world oil forecasts are published and the third is in publication. The fourth forecast includes a detailed description of the method. A draft is available on request from [email protected]. State "4th forecast" and your USPS address.
Richard C. Duncan
Seattle
