Применение сеточно-характеристического метода для моделирования распространения упругих волн в геологических средах с наличием трещин с использованием наложенных сеток

Автор: Митьковец И.А.

Журнал: Труды Московского физико-технического института @trudy-mipt

Статья в выпуске: 3 (59) т.15, 2023 года.

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Исследование зон геологических разломов важно для определения запасов нефти и газа в месторождениях. Для моделирования рассеяния волн в зонах трещиноватости используют численные методы на структурированных вычислительных сетках для оптимизации вычислительных ресурсов. Однако эти методы позволяют рассчитать рассеяние волн на трещинах только в направлении координатных осей. Чтобы моделировать более реалистичные трещиноватые поля, используют численные методы на неструктурированных вычислительных сетках или структурированных криволинейных вычислительных сетках, требующих больших вычислительных мощностей и важных при решении обратных задач. В данной работе предлагается численный метод с использованием наложенных сеток, где расчеты проводятся на структурированных регулярных вычислительных сетках с наложенными сетками, повернутыми вдоль трещин. Основным фактором является аналитическое задание якобиана вращения объектов, описывающих трещину, и малый локальный размер наложенных вычислительных сеток для экономии вычислительных ресурсов.

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Наложенные сетки, сеточно-характеристический метод, упругие волны, распространение волн, сейсморазведка, трещины, геологические разломы, рассеяние волн

Короткий адрес: https://sciup.org/142239990

IDR: 142239990

Список литературы Применение сеточно-характеристического метода для моделирования распространения упругих волн в геологических средах с наличием трещин с использованием наложенных сеток

Cui X., Lines L.R., Krebes E.S. Seismic modelling for geological fractures // Geophysical Prospecting. 2017. V. 66(1). P. 157–168.
Schoenberg M. Elastic wave behaviour across linear slip interfaces // Journal of the Acoustical Society of America. 1980. V. 68. P. 1516–1521.
Pyrak-Nolte L.J., Myer L.R., Cook N.G.W. Anisotropy in seismic velocities and amplitudes from multiple parallel fractures // Journal of Geophysical Research. 1990. V. 95. P. 11345–11358.
Hsu C.-J., Schoenberg M. Elastic waves through a simulated fractured medium // Geophysics. 1993. V. 58(7). P. 964–977.
Backus G.E. Long-wave elastic anisotropy produced by horizontal layering // Journal of Geophysical Research. 1962. V. 67. P. 4427–4440.
Zhang J. Elastic wave modeling in fractured media with an explicit approach // Geophysics. 2005. V. 70(5). P. T75–T85.
Slawinski R.A., Krebes E.S. Finite-difference modeling of SH-wave propagation in nonwelded contact media // Geophysics. 2002. V. 67. P. 1656–1663.
Slawinski R.A., Krebes E.S. The homogeneous finite difference formulation of the P-SV wave equation of motion // Studia Geophysica et Geodaetica. 2002. V. 46. P. 731–751.
Zhang J., Gao H. Elastic wave modelling in 3-D fractured media: an explicit approach // Geophys. J Int. 2009. V. 177. N 3. P. 1233–1241.
Lan H.Q., Zhang Z.J. Seismic wavefield modeling in media with fluid-filled fractures and surface topography // Applied Geophysics. 2012. V. 9(3). P. 301–312.
Favorskaya A.V., Zhdanov M.S., Khokhlov N.I., Petrov I.B. Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid characteristic method // Geophysical Prospecting. 2018. V. 66(8). P. 1485–1502.
Guo J., Shuai D., Wei J., Ding P., Gurevich B. P-wave dispersion and attenuation due to scattering by aligned fluid saturated fractures with finite thickness: Theory and experiment // Geophysical Journal International. 2018. V. 215(3). P. 2114–2133.
Chen T., Fehler M., Fang X., Shang X., Burns D. SH wave scattering from 2-D fractures using boundary element method with linear slip boundary condition // Geophysical Journal International. 2012. V. 188(1). P. 371–380.
Cho Y., Gibson R.L., Vasilyeva M., Efendiev Y. Generalized multiscale finite elements for simulation of elastic-wave propagation in fractured media // Geophysics. 2018. V. 83(1). P. WA9-WA20.
Chung E.T., Efendiev Y., Gibson R.L., Vasilyeva M. A generalized multiscale finite element method for elastic wave propagation in fractured media // GEM-International Journal on Geomathematics. 2016. V. 7(2). P. 163–182.
Vasilyeva M., De Basabe J.D., Efendiev Y., Gibson Jr.R.L. Multiscale model reduction of the wave propagation problem in viscoelastic fractured media // Geophysical Journal International. 2016. V. 217(1). P. 558–571.
Franceschini A., Ferronato M., Janna C., Teatini P. A novel Lagrangian approach for the stable numerical simulation of fault and fracture mechanics // Journal of Computational Physics. 2016. V. 314. P. 503–521.
Khokhlov N., Stognii P. Novel Approach to Modeling the Seismic Waves in the Areas with Complex Fractured Geological Structures // Minerals. 2020. V. 10(2). P. 122.
Bosma S., Hajibeygi H., Tene M., Tchelepi H.A. Multiscale finite volume method for discrete fracture modeling on unstructured grids (MS-DFM) // Journal of Computational Physics. 2017. V. 351. P. 145–164.
Kvasov, I., Petrov, I. Numerical Modeling of Seismic Responses from Fractured Reservoirs by the Grid-characteristic Method // Society of Exploration Geophysicists. 2019.
Leviant V.B., Petrov I.B., Chelnokov F.B., Antonova I.Y. Nature of the scattered seismic response from zones of random clusters of cavities and fractures in a massive rock // Geophysical prospecting. 2017. V. 55(4). P. 507–524.
De Basabe J.D., Sen M.K., Wheeler M.F. Elastic wave propagation in fractured media using the discontinuous Galerkin method // Geophysics. 2016. V. 81(4). P. T163–T174.
Mollhoff M., Bean C.J. Validation of elastic wave measurements of rock fracture compliance using numerical discrete particle simulations // Geophysical Prospecting. 2009. V. 57(5). P. 883–895.
Lisitsa V., Tcheverda V., Botter C. Combination of the discontinuous Galerkin method with finite differences for simulation of seismic wave propagation // Journal of Computational Physics. 2016. V. 311. P. 142–157.
Novikov M.A., Lisitsa V.V., Kozyaev A.A. Numerical modeling of wave processes in fractured porous fluid-saturated media // Numerical methods and programming. 2018. V. 19. P. 130–149.
Wang K., Peng S., Lu Y., Cui X. The velocity-stress finite-difference method with a rotated staggered grid applied to seismic wave propagation in a fractured medium // Geophysics. 2020. V. 85(2). P. T89–T100.
Cho Y., Gibson R.L., Lee J., Shin C. Linear-slip discrete fracture network model and multiscale seismic wave simulation // Journal of Applied Geophysics. 2019. V. 164. P. 140–152.
Vamaraju J., Sen M.K., De Basabe J., Wheeler M. Enriched Galerkin finite element approximation for elastic wave propagation in fractured media // Journal of Computational Physics. 2018. V. 372. P. 726–747.
Hou X., Liu N., Chen K., Zhuang M., Liu Q.H. The Efficient Hybrid Mixed Spectral Element Method With Surface Current Boundary Condition for Modeling 2.5-D Fractures and Faults // IEEE Access. 2020. V. 8. P. 135339–135346.
Li J., Khodaei Z.S., Aliabadi M.H. Spectral BEM for the analysis of wave propagation and fracture mechanics // Journal of Multiscale Modelling. 2017. V. 8(03n04). P. 1740007.
Ponomarenko R., Sabitov D., Charara M. Spectral element simulation of elastic wave propagation through fractures using linear slip model: microfracture detection for CO2 storage // Geophysical Journal International. 2020. V. 223, I. 3. P. 1794–1804.
Ruzhanskaya A., Khokhlov N. Modelling of Fractures Using the Chimera Grid Approach // In 2nd Conference on Geophysics for Mineral Exploration and Mining. European Association of Geoscientists & Engineers. — 2018, September. V. 2018. N 1. P. 1–5.
Berger M.J., Joseph E.O. Adaptive mesh refinement for hyperbolic partial differential equations // Journal of Computational Physics. 1984. V. 53(3). P. 484–512.
Steger J.L. A chimera grid scheme: advances in grid generation // Am. Mech. Eng. Fluids Eng. 1983. V. 5. P. 55–70.
Steger J.L., Benek J.A. On the use of composite grid schemes in computational aerodynamics // Computer Methods in Applied Mechanics and Engineering. 1987. V. 64(1–3). P. 301–320.
English R.E., Qiu L., Yu Y., Fedkiw R. Chimera grids for water simulation // Proceedings SCA 2013: 12th ACM SIGGRAPH / Eurographics Symposium on Computer Animation. 2013. P. 85–94.
Pena D., Deloze T., Laurendeau E., Hoarau Y. Icing modelling in NSMB with chimera overset grids // AIP Conference Proceedings. 2015. 1648. 030034.
Chesshire G., Henshaw W.D. Composite overlapping meshes for the solution of partial differential equations // Journal of Computational Physics. 1990. V. 90(1). P. 1–64.
Storti B., Garelli L., Storti M., D’Elia J. A matrix-free Chimera approach based on Dirichlet–Dirichlet coupling for domain composition purposes // Computers & Mathematics with Applications. 2020. V. 79(12). P. 3310–3330.
Brezzi F., Lions J.L., Pironneau O. Analysis of a Chimera method // Comptes Rendus de l’Academie des Sciences-Series I-Mathematics. 2001. V. 332(7). P. 655–660.
Chan W. Overset grid technology development at NASA Ames Research Center // Computers & Fluids. 2009. V. 38. P. 496–503.
Mayer U.M., Popp A., Gerstenberger A., Wall W.A. 3D fluid–structure-contact interaction based on a combined XFEM FSI and dual mortar contact approach // Computational Mechanics. 2010. V. 46(1). P. 53–67.
Zhang Y., Yim S.C., Del Pin F. A nonoverlapping heterogeneous domain decomposition method for three-dimensional gravity wave impact problems // Computers & Fluids. 2015. V. 106. P. 154–170.
Nguyen V.T., Vu D.T., Park W.G., Jung C.M. Navier–Stokes solver for water entry bodies with moving Chimera grid method in 6DOF motions // Computers & Fluids. 2016. V. 140. P. 19–38.
Formaggia L., Vergara C., Zonca S. Unfitted extended finite elements for composite grids // Computers & Mathematics with Applications. 2018. V. 76(4). P. 893–904.
Zhdanov M.S. Inverse theory and applications in geophysics // Elsevier. 2015. V. 36.
Riemann B. Ueber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite // Abhandlungen der Koniglichen Gesellschaft der Wissenschaften zu Gottingen. 1860. V. 8. P. 43–66.
Kholodov A.S., Kholodov Ya.A. Monotonicity criteria for difference schemes designed for hyperbolic equations // Computational Mathematics and Mathematical Physics. 2006. V. 46(9). P. 1560–1588.
Favorskaya A., Khokhlov N. Types of elastic and acoustic wave phenomena scattered on gas- and fluid-filled fractures // Procedia Computer Science. 2020. V. 10(5). P. 307–314.
Favorskaya A., Petrov I. A novel method for investigation of acoustic and elastic wave phenomena using numerical experiments // Theoretical and Applied Mechanics Letters. 2020. V. 10(5). P. 307–314.
Malovichko M., Khokhlov N., Yavich N., Zhdanov M. Approximate solutions of acoustic 3D integral equation and their application to seismic modeling and full-waveform inversion // Journal of Computational Physics. 2017. V. 346. P. 318–339.
Malovichko M., Khokhlov N., Yavich N., Zhdanov M.S. Incorporating known petrophysical model in the seismic full waveform inversion using the Gramian constraint // Geophysical Prospecting. 2020. V. 68(4). P. 1361–1378.

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