Page 294 - Geology and Geochemistry of Oil and Gas

256 MATHEMATICAL MODELING IN PETROLEUM GEOLOGY

Fig. 11.28. Comparison of actual porosity and that obtained from nomogram (after Buryakovsky et al.,
1990). (a) Venezuela, (b) Pre-Caucasus Region, (c) Absheron Peninsula and Archipelago. 1 – Actual
porosity, 2 – calculated porosity.

11.3.3. Combination of analytical and statistical approaches

11.3.3.1. Sediment compaction
The rate of compaction of sediments depends on the lithology, rate of sedimen-
tation, and the tectonic regime of the sedimentation basin. One of the most impor-
tant properties determining the degree of compaction of sediments is the ease of
release (expulsion) of interstitial waters: sand gives up pore waters easier than clay.
The presence of thick strata of water-saturated clays in a sedimentary section retards
the compaction. A rapid rate of sedimentation also retards the compaction process.
On the other hand, intensive tectonic activity may result in rapid lithification.
An attempt was made by Buryakovsky et al. (1982) to describe systematically the
process of sediment compaction. The curves showing changes in the porosity with
depth may be described by the so-called ‘‘organism-growth model’’, equivalent to the
‘‘model of proportional effects’’.
The difference between the ‘‘model of organism growth’’ and the ‘‘model of pro-
portional effects’’ is as follows: the former is based on the equality of the rate of change
in variable y to the value of this variable reached by a certain moment of time t, i.e.,
dy=dt ¼ cy (11.82)

which leads to an exponential dependence of the variable y on time t:

y ¼ y e ct (11.83)
o
where c is the factor of proportionality.