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On numerical modeling of reservoir geomechanical problems with non-smooth solutions using finite element method
1 Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences
2 Moscow Institute of Physics and Technology National Research University
3 Lomonosov Moscow State University
Journal: Geophysical research
Tome: 23
Number: 1
Year: 2022
Pages: 30-48
UDK: 539.3
DOI: 10.21455/gr2022.1-3
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Dubinya N.V., Vershinin A.V., Pirogova A.S., Tikhotsky S.A. On numerical modeling of reservoir geomechanical problems with non-smooth solutions using finite element method // . 2022. Т. 23. № 1. С. 30-48. DOI: 10.21455/gr2022.1-3
@article{DubinyaOn2022,
author = "Dubinya, N. V. and Vershinin, A. V. and Pirogova, A. S. and Tikhotsky, S. A.",
title = "On numerical modeling of reservoir geomechanical problems with non-smooth solutions using finite element method",
journal = "Geophysical research",
year = 2022,
volume = "23",
number = "1",
pages = "30-48",
doi = "10.21455/gr2022.1-3",
language = "English"
}
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Keywords: reservoir geomechanics, drilling risks assessment, mechanical properties, computational mechanics, Finite Element Method (FEM)
Аnnotation: The problem of numerical modeling of stress-strain state of rock masses in the cases of non-smooth rheological properties of these masses and non-smooth boundary conditions is consid-ered. The problem emerges from the need to estimate the potential drilling risks at the early stages of hydrocarbon field development. Conventionally, at the early stages of HC field development we estimate the drilling risks based on the preliminary mechanical models built from the exploration seismic data. From the interpretation of seismic data, we get either the models of continuous properties (e.g. the results of conventional seismic inversion) or the structural models that describe the configuration of layer boundaries. Estimates of the elastic and mechanical properties may be assigned to the geological layers and objects in the structural models. In that case, the models of mechanical properties of the subsurface have discontinuous boundaries. The current study is focused on such discontinuous models of mechanical properties of rocks. Usage of such models leads to the need to state boundary conditions as discontinuous functions within the framework of geomechanical modeling. Hence, standard numerical modeling techniques should be revisited so that they can incorporate discontinuous (non-smooth) mechanical models with non-smooth boundary conditions. The study presents the results of the geomechanical modeling for discontinuous models of the mechanical properties built from the reflection seismic data acquired in the Russian Arctic shelf. The estimation of stress-strain state of rocks is completed for several models that contain typical geological objects associated with potential risks for the offshore drilling in the research area. Finite element method is applied to compute the stresses in the models that contain permafrost and gas-bearing intervals in the near-surface. Numerical calculations are carried out using Fidesys computational software. It is shown that discontinuous models of mechanical properties require adjustments in the numerical modeling approach. Discontinuous spectral elements are needed to properly simulate stresses and strains fields in such models
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Pirogova A.S., Tikhotsky S.A., Tokarev M.U., Suchkova A.V., Estimation of Elastic Stress-Related Properties of Bottom Sediments via the Inversion of Very- and Ultra-High-Resolution Seismic Data, Izvestiya, Atmospheric and Oceanic Physics, 2019, no. 55, pp. 1755-1765.
Sedov L.I., Mekhanika sploshnoi sredy. Tom 2 (Continuum Mechanics, Volume 2), Moscow: Science Publishing House, 1970, 568 p. [In Russian].
Sheorey P.R., A theory for in situ stresses in isotropic and transversely isotropic rock, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1994, vol. 31, no. 1, pp. 23-34.
Wang Y., Dusseault M.B., A coupled conductive-convective thermo-poroelastic solutions and
implications for wellbore stability, Journal of Petroleum Science and Engineering, 2003, vol. 38, pp. 187-198.
Yamamoto K., Shioya Y., Uryu N., Discrete element approach for the wellbore instability of laminated and fissured rocks, Proceedings of SPE/ISRM Rock Mechanics Conference, Irving, Texas, October 2002, 2002, Paper Number: SPE-78181-MS.
Zhang J., Bai M., Roegiers J.C., On drilling directions for optimizing horizontal well stability using dual-porosity poroelastic approach, Journal of Petroleum Science and Engineering, 2006, vol. 53,
pp. 61-76.
Zienkiewicz O., Taylor R., The Finite Element Method. Volume 1: Its basis and fundamentals, Amsterdam: Elsevier, 2014, 802 p.
Zoback M.D., Reservoir Geomechanics, Cambridge: Cambridge University Press, 2007, 737 p.
Amadei B., In situ stress measurements in anisotropic rock, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1984, vol. 21, no. 6, pp. 327-338.
Biot M.A., Theory of propagation of elastic waves in a fluid-saturated porous solid, J. Acoust. Soc. Am., 1956, no. 28, pp. 179-191.
Bogoyavlensky V.I., Prospects and problems of the Arctic shelf oil and gas fields development, Burenie & Neft (Drilling and Oil), 2012, no. 11, pp. 4-9. [In Russian].
Cho D., Mutual E., Norton M., Miller D., McHarg D., Estimation of the Biot-Willis coefficient via rock-physics inversion, Proceedings of 2016 SEG International Exposition and Annual Meeting, Dallas, Texas, October 2016, 2016, pp. 3205-3209.
Coelho L.C., Soares A.C., Ebecken N.F.F., Alves J.L.D., Landau L., The impact of constitutive modeling of porous rocks on 2-D wellbore stability analysis, Journal of Petroleum Science and Engineering, 2005, vol. 46, pp. 81-100.
Delgado P., Kumar V., A stochastic Galerkin approach to uncertainty quantification in poroelastic media, Applied Mathematics and Computation, 2015, vol. 266, pp. 328-338.
Dubinya N.V., Vershinin A.V., Pirogova A.S., Tikhotsky S.A., Usage of imitational geological-petrophysical models to reduce drilling risks for offshore reservoirs exploration, Proceedings of the SPE Russian Petroleum Technology Conference, Virtual, October 2020, 2020, Paper Number: SPE-201978-MS.
Etesami D., Shahbazi K., Prediction of Uniaxial Compressive Strength of Underground Formations From Sonic Log Parameters, Petroleum Science and Technology, 2014, vol. 32, pp. 1641-1653.
Franquet J.A., Abass H.H., Experimental evaluation of Biot’s poroelastic parameter: Three different methods, Proceedings of The 37th U.S. Symposium on Rock Mechanics (USRMS), Vail, Colorado, June 1999, 1999, Paper Number: ARMA-99-0349.
Galerkin B.G., Series solution of some problems in elastic equilibrium of rods and plates, Vestnik Inzhenerov (Bulletin of engineers), 1915, vol. 1, no. 19, pp. 897-908. [In Russian].
Garagash I.A., Dubovskaya A.V., Bayuk I.O., Tikhotskiy S.A., Glubovskikh S., Korneva D.A., Berezina I.A., 3D Geomechanical Modeling of Oil Field on the Basis of a Model of the Mechanical Properties for the Task of Wells Construction, Proceedings of the SPE Russian Petroleum Technology Conference, Moscow, Russia, October 2015, 2015, Paper Number: SPE-176637-MS.
Hoek E., Brown E.T., Underground Excavations in Rock, London: Champan & Hall, 1980, 532 p.
Karatela E., Taheri A., Xu C., Stevenson G., Study on effect of in-situ stress ratio and discontinuities orientation on borehole stability in heavily fractured rocks using discrete element method, Journal of Petroleum Science and Engineering, 2015, vol. 139, pp. 94-103.
Karpenko V.S., Vershinin A.V., Levin V.A., Zingerman K.M., Some results of mesh convergence estimation for the spectral element method of different orders in Fidesys industrial package, IOP Conference Series: Materials Science and Engineering, 2016, vol. 158, Paper 012049.
Kolyubakin A.A., Mironyuk S.G., Roslyakov A.G., Rybalko A.E., Terekhina Ya.E., Tokarev M.Yu., Usage of a set of geophysical methods for detection of geohazards at Laptev Sea shelf, Inzhenernye Izyskaniya (Engineering Survey), 2016, no. 10-11, pp. 38-52. [In Russian].
Kukushkin A.V., Konovalov D.A., Vershinin A.V., Levin V.A., Numerical simulation in CAE Fidesys of bonded contact problems on non-conformal meshes, Journal of Physics: Conference Series, 2019, vol. 1158, Paper 032022.
Kwakwa K.A., Batchelor A.S., Clark R., An Assessment of the Mechanical Stability of High-Angle Wells in Block 22/11, Nelson Field Discovery, SPE Drilling Engineering, 1991, vol. 6, no. 1, pp. 25-30.
Levin V.A., Zingerman K.M., Vershinin A.V., Freiman E.I., Yangirova A.V., Numerical analysis of the stress concentration near holes originating in previously loaded viscoelastic bodies at finite strains, International Journal of Solids and Structures, 2013, vol. 50, no. 20-21, pp. 3119-3135.
Liu M., Jin Y., Lu Y., Chen M., Hou B., Chen W., Wen X., Yu X., A wellbore stability model for a deviated well in a transversely isotropic formation considering poroelastic effects, Rock Mechanics and Rock Engineering, 2016, vol. 49, pp. 3671-3686.
Lobkovskiy L.I., Nikiforov S.L., Dmitrevskiy N.N., Libina N.V., Semiletov I.P., Ananiev R.A., Meluzov A.A., Roslyakov A.G., Gas extraction and degradation of the submarine permafrost rocks on the Laptev Sea shelf, Oceanology, 2015, no. 55, pp. 283-290.
Maleki S., Gholami R., Rasouli V., Moradzedh A., Riabi R.G., Sadaghzadeh F., Comparison of different failure criteria in prediction of safe mud weigh window in drilling practice, Earth Science Reviews, 2014, vol. 136, pp. 36-58.
Moos D., Peska P., Finkbeiner T., Zoback M., Comprehensive Wellbore Stability Analysis Utilizing Quantitative Risk Assessment, Journal of Petroleum Science and Engineering, 2003, vol. 38, pp. 97-109.
Morozov E.M., Levin V.A., Vershinin A.V., Prochnostnoi analiz. Fidesis v rukakh inzhenera (Strength analysis. Fidesys in the hands of an engineer), Moscow: URSS Publishing Group, 2015, 408 p. [In Russian].
Pirogova A.S., Tikhotsky S.A., Tokarev M.U., Suchkova A.V., Estimation of Elastic Stress-Related Properties of Bottom Sediments via the Inversion of Very- and Ultra-High-Resolution Seismic Data, Izvestiya, Atmospheric and Oceanic Physics, 2019, no. 55, pp. 1755-1765.
Sedov L.I., Mekhanika sploshnoi sredy. Tom 2 (Continuum Mechanics, Volume 2), Moscow: Science Publishing House, 1970, 568 p. [In Russian].
Sheorey P.R., A theory for in situ stresses in isotropic and transversely isotropic rock, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1994, vol. 31, no. 1, pp. 23-34.
Wang Y., Dusseault M.B., A coupled conductive-convective thermo-poroelastic solutions and
implications for wellbore stability, Journal of Petroleum Science and Engineering, 2003, vol. 38, pp. 187-198.
Yamamoto K., Shioya Y., Uryu N., Discrete element approach for the wellbore instability of laminated and fissured rocks, Proceedings of SPE/ISRM Rock Mechanics Conference, Irving, Texas, October 2002, 2002, Paper Number: SPE-78181-MS.
Zhang J., Bai M., Roegiers J.C., On drilling directions for optimizing horizontal well stability using dual-porosity poroelastic approach, Journal of Petroleum Science and Engineering, 2006, vol. 53,
pp. 61-76.
Zienkiewicz O., Taylor R., The Finite Element Method. Volume 1: Its basis and fundamentals, Amsterdam: Elsevier, 2014, 802 p.
Zoback M.D., Reservoir Geomechanics, Cambridge: Cambridge University Press, 2007, 737 p.
