MATHEMATICAL MODELLING OF INFLUENCE OF THE MINERAL COMPOSITION AND POROSITY ON ELASTIC ANISOTROPIC PARAMETERS OF COMPLEX SEDIMENTARY ROCKS OF VOLYN-PODOLIA AREA

The purpose of this paper is to analyze parameters of acoustic and elastic anisotropy registered at studying multi-species model of sedimentary reservoir. According to the results of mathematical modeling of complexly structured sandstones, the parameters of acoustic and elastic anisotropy of developed models have been received and analyzed depending on lithology, concentration and type of inclusions. Methods of moment functions with using a calculated Mori-Tanaka scheme and the method of least squares are used to solve this problem. The model is based on previous publications of the authors and the results of petrographic studies carried out at ESI 'Institute of Geology'. Rhombic type axial symmetry texture is typical for the majority of models of complex reservoir rocks. Slaty texture motif is characteristic for the models of pure quartz sandstone and sandstone with inclusions of clay cement. As a result of increasing the concentration of voids density of models decreases. At presence of montmorillonite density value becomes smaller. Muscovite flakes and calcite grains present in mineral composition of rocks increase the density with increasing concentrations of the latter. However, at presence of clay mineral inclusions density decreases, but in a small range. It is established that the developed models might be described as low, medium and high anisotropic ones. At increasing concentration of voids coefficient of integrated acoustic anisotropy decreases at about tenth of percent, with sharp decrease (3 %) being observed at presence of montmorillonite. In models with quartz, calcite, mica minerals the decrease of coefficient of the acoustic anisotropy is observed at calcite grains concentrations of 1-10 %, and in case of 10?20 % of their concentration it is gradually increase. With increasing the size of cracks value of integral factor of anisotropy mainly rise within 0.5-0.7 %. Gradual reduction of the calculated values of elastic constants is observed at increasing concentration of voids, and vice-versa, their values are increased at presence of inclusions of minerals. The most large changes are observed in the values of non-diagonal components. As the result of the modeling, acoustic and elastic characteristics of the proposed models were described depending on the type and concentration of inclusions represented by minerals (montmorillonite, calcite and muscovite) and voids of different formats.