Page 167 - Petroleum Geology

144

Fig. 7-1. Harmonic size distribution, 1 + 1/2 + 1/3 t . . . + 1/30.

TABLE 7-1
Expected distribution of reserves in the eight
largest of 400 giant accumulations according
to Zipf’s law
Rank % Cumulative (%)

1 15.2 15.2
2 7.6 22.8
3 5.1 27.9
4 3.8 31.7
5 3.0 34.8
6 2.5 37.3
7 2.2 39.5
8 1.9 41.4

. . . t l/n, the sum of which for large n (> 50, for example) is very closely
approximated by In n + (1/2n) + 0.5772 (the last number being Euler’s Con-
stant). From these it is a simple matter to compute the expected distribution
of accumulations by size, as a proportion of the total. For example, if the
world actually contains 400 giant oil accumulations, Zipf’s law predicts that
the proportional distribution of their total reserves will be as in Table 7-1,
and 40% of the total reserves of these 400 giants will be in only 8 accumula-
tions.
This is a plausible result, and may one day be found to be accurate; but
only about 300 of these accumulations have so far been discovered. We can
rank these according to size, but we do not know the true rank of these ac-
cumulations.
In practice, Zipf’s law has come to be applied more to the distribution of