SPATIAL CORRELATION FUNCTION AND SPECIFIC PROBLEMS OF RESERVOIR STRUCTURE
Gassiyev, Aslan 1986-
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The spatial correlation function has been introduced to the specific geophysical problem of theoretical characterization of effective elastic properties of gas shales. The spatial correlation function has been described in the form of pair correlation approximation (PCA), meaning that only binary interactions are considered and interactions of higher order are omitted (Shermergor, 1977). The theoretically built model was based on the mineralogical composition of the rock sample with which our calculations have been compared. The model consists of a matrix and gas- filled inclusions. The matrix is composed of 70 percent quartz and 30 percent illite, while the gas concentration varies from zero to ten percent. PCA has an advantage over other averaging techniques like Voigt-Reuss-Hill (Voigt, 1928; Reuss, 1929; Hill, 1963), Eshelby's method (Eshelby, 1957), Backus (Backus, 1962) due to the presence of an additional variable called fluctuation component that is responsible for interactions between end-members. The theoretical results for the isotropic medium with inclusions show that the difference between PCA and VRH techniques in terms of e ective elastic sti ness tensor is about 7 percent, and between PCA and Eshelby's methods is around 22 percent when the aspect ratio of inclusions is 0.03. The aspect ratio of 0.02-0.03 is common for these types of inclusions (Brodov, Tikhonov, Chesnokov, Tertychnyi, & Zatsepin, 1991). Theoretical results for anisotropic medium with inclusions show dramatical increase in differences between these methods. The di erence between PCA and VRH is 25 percent, and between PCA and Eshelby is 30 percent. It has been observed that keeping the aspect ratio constant at a value of 0.03, and increasing the gas volume concentration in anisotropic medium, tends to reduce anisotropy. This phenomenon is explained by random orientation of inclusions, and the fact that keeping the aspect ratio and the length of inclusion constant, the crack density increases with the increase of gas content. As gas content increases the crack density increases from 0.08 at one percent of gas to 0.796 at 10 percent of gas at constant aspect ratio value of 0.03. Comparison with experimental data shows that PCA has more solid physical background, as the result tend to match well compared to other methods presented in this work.