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The data set, taken from an article in Forbes magazine, shows discovery statistics for oil and gas deposits on the continental shelf of the US by BP, the second largest petroleum producer in the world (the former British Petroleum company). The data mostly represent Gulf of Mexico deposits, and include both oil and gas; the latter has been converted to barrels of equivalent oil (1 billion cubic feet of natural gas is equivalent to 6.29 million barrels of oil). The data show discoveries of undersea petroleum and presumably include both petroleum from producing wells and proven (but untapped) reserves. The data probably exclude unproven reserves; petroleum deposits that are likely present, but have not been tested or "proven" by actual drilling.

Exploration and discovery of hydrocarbons on the Gulf of Mexico's continental shelf shows a very well behaved pattern, which may seem surprising at first. A more random pattern might be expected, given the complexity of finding oil and gas in buried (and inaccessible) undersea rocks. One might expect each successive well to hit or miss the crude oil or gas. Part of the good behavior of this graph is due to the way in which the data are being presented. The Y-axis shows the cumulative discoveries for this region, not the size of individual discoveries at each well. Because the Y-axis is cumulative, each new discovery is added to the previous, producing an ever-increasing series of discovery volumes, though obviously not at a constant rate. The volume per discovery clearly decreases with time (with number of wells drilled), presumably related to the finite nature of this resource. Early wells are typically drilled into the "fat" deposits, to generate product and revenue to cover the up-front costs of the very expensive exploration program.

The student can model the data using both linear, power law and logarithmic functions. All regressions give high correlation coefficients, though the logarithmic function clearly matches the "shape" of the data much better. Why do the other two regressions return high correlation coefficients? Students can also model the economics of this trend, by assigning monetary values to the hydrocarbons and the wells. Students should be asked whether the data are asymptotic or not (are hydrocarbons in an area truly finite?), and whether their mathematical models show asymptotic behavior or not.

BP is well aware of the declining rate of return of drilling new wells in the same old oil patch, and has begun drilling in deep waters of the Gulf of Mexico (at very high risk and high expense). The first 60 wells in this new region show a similar pattern as the shallow water discoveries, though at somewhat higher yields per well.

Source: BP, published in Forbes, 2 April 2001, pp. 111-116.

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 Oil and Gas Discoveries by BP Amoco on the US continental shelf Source: BP Amoco and Forbes Magazine Gbarrels = billions of barrels of oil equivalent # of wells Gbarrels oil 46 5 101 10 157 15 201 18 237 20 301 22.7 337 25 401 28.8 439 30 501 32.1 601 34.1 657 35 701 36 801 37.5 901 38.4 1001 39.2 1101 39.5
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