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TABLE 1-4

Zipf predictions based on East Texas field as Rank 1 (column 1) and Rank 2 (column 2);
figures in column 3 assume that Prudhoe Bay was next discovery. Other figures are Rank
1 divided by rank number. Figures in millions of barrels
Rank Actual 1 2 3

1 5600 5600 11,200 9600
2 2500 2800 5600 4800
3 2334 1867 3733 3200
4 2100 1400 2800 2400
5 1773 1120 2240 1920
6 1683 933 1867 1600
I 1647 800 1600 1371
8 1318 700 1400 1200
9 1303 622 1244 1067
10 1205 560 1120 96 0
Total 21,463 16,402 32,804 28,118

It can hardly be said that Zipf’s law is yet a law that describes the size
distribution of oil fields very well, but it is an interesting way of looking at
the statistics. Bearing in mind that there is a tendency to rank oil fields too
highly, with too small a rank number, and to underestimate the ultimate re-
coverable reserves in them, we can perhaps improve on the estimate of the
Zipf constant. Note how the value of this constant on the 1968 information
in Table 7-3 tends to increase with increasing rank, suggesting that in the largest
fields, the rank number is too small or the reserve estimate too small, or both.
A value of 12 X lo9 bbl for this constant in North America could still prove
to be a good value.
We can extend the argument, following Folinsbee (1977), to estimate the
world’s ultimate total recoverable oil. Let us assume that the sum of the har-
monic series approaches 12, with about 100,000 accumulations that could
be produced economically. These numbers are not very sensitive: for 50,000,
it is 11.4, so Ranks 50,000 to 100,000 would only contribute about 5% to
the total. The ultimate recoverable reserves are given by the product of this
number and the Zipf constant for the world. Taking the Zipf constant to
be the largest suggested by the world’s top-ranking ten oil fields in 1968
(Table 7-5, from Halbouty et al., 1970, Table I, facing p. 504), as a conservative
figure, the indicated ultimate recoverable reserves are probably at least
120 X lo9 X 12 = 1450 X lo9 bbl. If the Zipf constant is really about 150 X
lo9 bbl, the ultimate recoverable reserves will be about 1800 X lo9 bbl.