About oil and gas discoveries:
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.