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oil fields ranked according to initial recoverable reserves, rather than oil in
place. This is very different from the demonstrable validity of Zipf‘s law to
the flow rate of the world’s major rivers, all of which are known. The distinc-
tion between oil in place and recoverable reserves is probably not significant
for oil fields, because great precision is not to be expected, and the variation
of recovery factor in giants may not be great. But the very large tar-sand
deposits are oil accumulations even if the recovery factor is very small.
Zipf’s law has also been applied on different scales - the world, a continent,
by countries (which imposes a rather artificial subdivision on the geological
distribution) and by oil provinces. The reader may care to try this on the
ranking of countries by reserves in Tables 7-7-7-9. The fact that Zipf’s
law seems to work quite well under these modified conditions means that it
must be used and interpreted with caution.
The statistics of Moody et al. (1970) given above can be used as OUT
example. On the information available to them, 26,250 oil fields contained
132 X lo9 bbl of recoverable oil; and of these, 45 fields collectively contain-
ed 46 X lo9 bbl of recoverable oil. Zipf‘s law predicts the following statistics
from these figures:
- The sum of the harmonic series to n = 45 is 4.3950 and to n = 26,250 is
10.7526, so the accumulations ranked 1-45 should contain nearly 41% of
the total reserves, or 54 X lo9 bbl recoverable oil for an average of about
1.2 X lo6 bbl each.
- Rank 45 will contain about 273 X lo6 bbl of oil initially, and only 24
would contain more than 500 X lo6 bbl each (which was the criterion for
listing the first 45).
-Ranks 1 to 10 of the accumulations would be as given in Table 7-2, first

TABLE 7-2

Comparison of Zipf prediction of size of largest ten oil fields in North America on basis
of 132 X lo9 bbl ultimate recoverable oil from 26,250 fields with actual ranking and sizes
in 1968, and possible future ranking of these fields. Figures in millions of barrels

Zipf Actual, 1968 Possible
1 12,276 5600 E. Texas
2 6138 2500 Wilmington 5600 E. Texas
3 4092 2334 Eunice
4 3069 2100 Poza Rica 2500 Wilmington
5 2455 1773 Pembina 2334 Eunice
6 2046 1683 Kelly-Snyder 2100 Poza Rica
7 1754 1647 Panhandle 1773 Pembina
8 1535 1318 Swan Hills 1683 Kelly -Sny der
9 1364 1303 Elk Hills 1647 Panhandle
10 1228 1205 Golden Lane 1318 Swan Hills