Mathematical modeling of the acoustic and elastic anisotropy of the shale reservoir rocks of the Dnipro-Donetsk depression
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.
Downloads
References
Wojtacki, K., Daridon, L., Monerie Computing, Y., Wojtacki K. (2017). Тhe elastic properties of sandstone submit-ted to progressivedissolution. International Journal of Rock Mechanics and Mining Sciences. Montpellier, France, 16-25. http://doi.org/10.1016/j.ijrmms.2016.12.015
Guéry, A., Cormery, F., Suet K. et al. (2008). A micromechanical model for the elasto-viscoplastic and damage be-havior of a cohesive geomaterial. Phys. Chem. Earth, 33, 416-421.
Weng, M., Tsai, L., Hsieh, Y., Jeng F. (2010). An associated elastic–viscoplastic constitutive model for sandstone involving shear-induced volumetric deformation. Int. J. Rock Mech. Min. Sci, 47, 1263-1273.
Atkinson, B.K. (1982). Subcritical crack propagation in rocks: theory, experimental results and applications. J. Struct. Geol, 4, 41-56.
Grgic, D. (2001). Modelling of the short and long-term behavior of rocks of Lorraine (France) ferriferous for-mation. PhD Thesis. INPL, Nancy.
Guliyev, I.S., Kerimov, V.YU., Mustayev, R.N., Bondarev, A.V. (2018). The estimation of the generation potential of the low permeable shale strata of the Maikop Caucasian series. SOCAR Proceedings, 1, 4-20. DOI: 10.5510/OGP20180100335
Johnson, D. (2003). Reservoir characterization of the Barnett Shale. Barnett Shale Symposium, Ellison Miles Ge-otechnology Institute at Brookhaven College, Dallas, Texas. 12–13 November 2003. http://www.energyconnect.com/pttc/archive/barnettshalesym /2003barnettshalesymp.pdf.
Lopatin, N.V., Zubairaev, S.L., Kos, I.M., Emets. T.P., Romanov, E.A., Malchikhina, O.V. (2003). Unconventional Oil Accumulations in the Upper Jurassic Bazhenov Black Shale Formation, West Siberian Basin: A Self-Sourced Res-ervoir System. Journal of Petroleum Geology, 26, 225–244. doi.org/10.1111/j.1747-5457.2003.tb00027.x
Arutyunov, Т.V. (2015). Shale gas as perspective type fossilized fuel. Science. Engineering. Technology (polytechnical bulletin), 2, 27–35.
Arutyunov, Т.V., Arutyunov, А.А., Savenok, O.V. (2015). Problem definition of physical and chemical modeling of slate breeds. Scientific and technical magazine «Inzhener-neftyanik», 1, 42–47.
Bayuk, I.O., Beloborodov, D.Ye., Berezina I.A. et al. (2015). Elastic properties of core samples under confining pressure. Tekhnologii seysmorazvedki, 2, 36-45. http://ts.sbras.ru doi:10.18303/1813-4254-2015-2-36-45
Prodayvoda, G., Vyzhva, S., Bezrodna, I., Prodayvoda, T. (2011). Geophysical methods for estimation the perfor-mance of oil and gas collectors. K.: VPTS "Kyyivsʹkyy universytet".
Aleksandrov, K.S., Prodayvoda, G.T. (2000). Anisotropy of the elastic properties of minerals and rocks. N.: Izd. SO RAN.
Bezrodna, I., Bezrodnyy, D., Holyaka, R. (2016). Mathematical modelling of influence of the mineral composition and porosity on elastic anisotropic parameters of complex sedimentary rocks of Volyn-Podolia area. Visnyk Taras Shevchenko National University of Kyiv. Geology, 73, 27-32. http://doi.org/10.17721/1728-2713.73.04.
Vyzhva, S.A., Onyshchuk, I.I., Bezrodna, I.M. et al. (2017). Complex analytical laboratory researches of core from wells of the Runovshchyna region. Report, Kyiv.
Bezrodna, I., Bezrodnyy, D., Kozionova, O. (2017). Analysis of impact of mineral matrix of Runovshchinska area reservoir rocks on the elastic and acoustic parameters (based on the results of mathematical modelling). Visnyk Taras Shevchenko National University of Kyiv. Geology, 2 (77), 52-58 http://doi.org/10.17721/1728-2713.77.06
Prodayvoda, G.T., Bezrodnyy, D.A., Bezrodna, I.M. (2012). Investigation of the influence of tectonic deformations on the parameters of elastic and acoustic anisotropy of ferruginous quartzite of Krivoy Rog ultra-deep well ac-cording to mathematical modeling. Visnyk Taras Shevchenko National University of Kyiv. Geology, 57, 8-12.
Prodayvoda, G.T., Bezrodna, I.M., Kuzmenko, T.M. (2010). Mathematical modeling of influence of fluid saturation and saline’s on the elastic and acoustic properties of volyno-podillya limestone’s. Materials of the IXth Interna-tional Conference “Geoinformatics: Theoretical and Applied Aspects”, 11-14 May 2010, Kiev, Ukraine.
Prodayvoda, G.T. (2004). Acoustics of rocks texture. K.: VGL “Obriyi”.
Mori, T., Tanaka, K. (1973). Average Stress in Matrix and Average Elastic Energy of Materials with misfitting in-clusions. Acta Metallurgica, 21, 4, 571-574.
Thomsen, L. (1986). Weak elastic anisotropy. Geophysics, 51 (10), 1954-1966. doi:10.1190/1.1442051.
Mykhaylov, V.A., Stavytsʹkyy, E.A., Proskuryakov, O.A. et al. (2013). Unconventional sources of hydrocarbons of Ukraine. B. 1. Unconventional sources of hydrocarbons of Ukraine: review of the problem. K.: Nika-Tsentr.
