Page 247 - Geology and Geochemistry of Oil and Gas

214 MATHEMATICAL MODELING IN PETROLEUM GEOLOGY

system (range of variation, scattering, variations coefficient, etc.) have no upper
limit, so that the use of relative entropy makes it possible to rate the heterogeneity of
a rock without resorting to comparisons with the other parameters of heterogeneity.
As an example of application of the relative entropy in rating the heterogeneity of
rocks, the grain-size composition of rocks of the Kala Formation of the Absheron oil
and gas region of Azerbaijan was analyzed. The most homogeneous portion of this
formation was found in the Gum Deniz and Turkyany areas, whereas the least
homogeneous portion was present in the Karachukhur–Zykh area and in the south-
eastern part of the Absheron Archipelago. As determined from cores, the grain-size
heterogeneity (or microheterogeneity) of the various rock types (see Fig. 11.5) in-
dicates that the relative entropy is increasing with heterogeneity increase. A general
increase of the relative entropy, however, has no significant effect on variations in
the relative entropy of the whole area.
Heterogeneity in individual deposits can be extended to the areal variations in
lithology. Entropy contours are plotted on the map and then interpreted to decipher
the paleogeography of the area, sedimentation scenario, and subsequent diagenetic
and catagenetic alterations of sediments and rocks. For example, the homogeneity of
the Kala Formation increases with increasing depth of sediment deposition (under a
calm hydrodynamic regime) (Table 11.1).
With increasing burial depth in the Karachukhur–Zykh–Gousany–Gum
Deniz–Turkyany anticlinal trend, the relative entropy progressively decreases.
The entropy increases along the Gyurgyany Deniz–Chalov Adasi–Palchygh
Pilpilasi–Neft Dashlary anticlinal trend. The relative entropy progressively decreas-
es with burial depth in the offshore oil and gas fields of Absheron Archipelago. There
is an inverse depth–entropy relationship between individual areas.
As far as the basic relationship in spatial distribution of H r as a criterium of
heterogeneity of the rocks is concerned, there is a decrease in H r and a better sorting

TABLE 11.1
Evaluation of heterogeneity entropy for the Kala Formation of the Absheron Archipelago, Azerbaijan
(after Buryakovsky et al., 2001)
Area Number of Average Entropy Relative entropy
reservoirs depth (m)
Without With
microheterogeneity microheterogeneity
Gyurgyany Deniz 56 2160 1.580 0.72 0.83
Chalov Adasi 120 720 1.933 0.88 0.92
Palchygh Pilpilasi 59 1130 1.699 0.77 0.87
Neft Dashlary 170 1010 1.904 0.87 0.90
Karachukhur–Zykh 64 2790 1.816 0.83 0.91
Gousany 180 4010 1.597 0.73 0.80
Gum Deniz 25 3500 1.410 0.64 0.65
Tyurkyany 65 3760 1.423 0.65 0.67
Kala Formation as a 746 — — 0.71 0.76
whole