# Mathematical modeling of the acoustic and elastic anisotropy of the shale reservoir rocks of the Dnipro-Donetsk depression

Keywords: unconventional shale reservoir rock, mathematical modeling, elastic and acoustic anisotropy, Thomsen parameters

### Abstract

The purpose of the work is to analyze the parameters of elastic and acoustic anisotropy in the study of a multicomponent reservoir rock model, which is represented by shale.

Research theory To solve this problem, the methods of conditional moment functions using the Mori-Tanaka calculation scheme, as well as the ordinary least squares were used. The technique of effective elastic invariables mathematical modelling of unconventional shale reservoir rocks has been developed.

Justification of the mathematical model Eight varieties of mathematical models that characterize the mineral composition, the structure of the void space and elastic properties that are characteristic for shale reservoir rocks of the Dnipro-Donetsk depression in Ukraine were substantiated and developed. The models are based on previous publications by the authors and the results of petrographic studies at the Institute of Geology.

Results The authors for the first time carried out an analysis of elastic constant rock models, acoustic tensor components, linearity and shale parameters, isolines stereo projections of index surfaces of nine elastic anisotropy parameters, as well as Thomsen parameters.

Acoustic data can be used to trace the change in the structure of the reservoir rock void space, the concentration of rock-forming minerals in the rock. Fracturing has a greater effect on rock structure than granular voids and mineral structure. The orientation of inclusions has the greatest influence on the coefficient of acoustic anisotropy, anisotropy coefficients in rocks, where the voids are oriented in the plane perpendicular to the borehole axis have the largest values (more than 20%).

When calculating the Thomsen parameters, the parameters of elastic anisotropy were obtained. They characterize not only the mineral composition of the rocks but also the qualitative structure of the void space, the orientation of minerals and voids in the rocks. Thomsen parameters correlate with acoustic anisotropy parameters for shale reservoir models.

The parameters of acoustic and elastic anisotropy are indicators in the studies of similar-type rocks with different types of mineral inclusions and the structure of the void space.

The mathematical modelling of elastic and acoustic parameters which characterizes their anisotropy and was carried out by the authors is an important step in substantiating mathematical models of shale reservoir rocks. Such models can be used in the interpretation of geophysical data (seismic surveys and well logging) to make corrections for elastic anisotropy in prospecting and exploration of oil, gas and water saturated unconventional shale reservoir rocks of complex structure, and also to compile a database of mathematical models of reservoir rocks in the given region.

### Author Biographies

Ирина Николаевна Безродная, Taras Shevchenko National University of Kyiv

PhD (Geology), Senior Researcher, Deputy Director of Institute of Geology

Дмитрий Анатолиевич Безродный, Taras Shevchenko National University of Kyiv

PhD (Geology), Associate Professor of the Department of Geophysics

Олеся Александровна Козионова, Taras Shevchenko National University of Kyiv

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Published
2019-07-10
Cited
How to Cite
Безродная, И. Н., Безродный, Д. А., & Козионова, О. А. (2019). Mathematical modeling of the acoustic and elastic anisotropy of the shale reservoir rocks of the Dnipro-Donetsk depression. Visnyk of V. N. Karazin Kharkiv National University, Series "Geology. Geography. Ecology&quot;, (50), 42-53. https://doi.org/10.26565/2410-7360-2019-50-03
Section
Geology