Embedded fracture model in numerical simulation of the fluid flow and geo-mechanics using Generalized Multiscale Finite Element Method
In this work, we consider a pororelasticity problem in fractured porous media. Mathematical model contains a coupled system of equations for pressure and displacements, for which we use an embedded fracture model. The fine grid approximation is constructed based on the finite volume approximation fo...
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| Vydáno v: | Journal of physics. Conference series Ročník 1392; číslo 1; s. 12075 - 12080 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Bristol
IOP Publishing
01.11.2019
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| ISSN: | 1742-6588, 1742-6596 |
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| Abstract | In this work, we consider a pororelasticity problem in fractured porous media. Mathematical model contains a coupled system of equations for pressure and displacements, for which we use an embedded fracture model. The fine grid approximation is constructed based on the finite volume approximation for the pressure in fractured media and finite element method for the displacements. Multiscale approximation is developed using a structured coarse grid and is based on the Generalized Multiscale Finite Element Method for pressures and displacements. The performance of the method is tested using a two-dimensional model problem with different number of the multiscale basis functions. |
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| AbstractList | In this work, we consider a pororelasticity problem in fractured porous media. Mathematical model contains a coupled system of equations for pressure and displacements, for which we use an embedded fracture model. The fine grid approximation is constructed based on the finite volume approximation for the pressure in fractured media and finite element method for the displacements. Multiscale approximation is developed using a structured coarse grid and is based on the Generalized Multiscale Finite Element Method for pressures and displacements. The performance of the method is tested using a two-dimensional model problem with different number of the multiscale basis functions. |
| Author | Vasilyeva, Maria Tyrylgin, Aleksei Chung, Eric T. |
| Author_xml | – sequence: 1 givenname: Aleksei surname: Tyrylgin fullname: Tyrylgin, Aleksei email: aa.tyrylgin@mail.ru organization: Multiscale model reduction laboratory, North-Eastern Federal University – sequence: 2 givenname: Maria surname: Vasilyeva fullname: Vasilyeva, Maria organization: Institute for Scientific Computation, Texas A&M University – sequence: 3 givenname: Eric T. surname: Chung fullname: Chung, Eric T. organization: Department of Mathematics, The Chinese University of Hong Kong (CUHK), Hong Kong SAR |
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| Cites_doi | 10.1016/j.jcp.2017.10.023 10.1016/j.jngse.2017.02.040 10.1137/S1064827503429363 10.1029/2000WR900340 10.2118/103901-PA 10.2118/146422-PA 10.1016/0021-8928(60)90107-6 10.1016/j.jcp.2008.06.013 10.1137/030600795 10.1016/j.jcp.2013.04.045 10.1051/m2an/2013132 |
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| References_xml | – volume: 353 start-page: 356 year: 2018 ident: JPCS_1392_1_012075bib5 article-title: Multiscale model reduction for shale gas transport in poroelastic fractured media publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2017.10.023 – volume: 48 start-page: 65 year: 2017 ident: JPCS_1392_1_012075bib1 article-title: Multiscale model reduction for shale gas transport in a coupled discrete fracture and dual-continuum porous media publication-title: Journal of Natural Gas Science and Engineering doi: 10.1016/j.jngse.2017.02.040 – volume: 26 start-page: 1667 year: 2005 ident: JPCS_1392_1_012075bib3 article-title: Modeling fractures and barriers as interfaces for flow in porous media publication-title: SIAM Journal on Scientific Computing doi: 10.1137/S1064827503429363 – volume: 37 start-page: 443 year: 2001 ident: JPCS_1392_1_012075bib8 article-title: Hierarchical modeling of flow in naturally fractured formations with multiple length scales publication-title: Water resources research doi: 10.1029/2000WR900340 – volume: 4 year: 2009 ident: JPCS_1392_1_012075bib13 publication-title: Multiscale Finite Element Methods: Theory and Applications – volume: 11 start-page: 750 year: 2008 ident: JPCS_1392_1_012075bib6 article-title: Efficient field-scale simulation of black oil in a naturally fractured reservoir through discrete fracture networks and homogenized media publication-title: SPE Reservoir Evaluation & Engineering doi: 10.2118/103901-PA – year: 2006 ident: JPCS_1392_1_012075bib9 – year: 2015 ident: JPCS_1392_1_012075bib10 – volume: 17 start-page: 1 year: 2012 ident: JPCS_1392_1_012075bib2 article-title: Multiscale gas transport in shales with local kerogen heterogeneities publication-title: SPE journal doi: 10.2118/146422-PA – volume: 24 start-page: 1286 year: 1960 ident: JPCS_1392_1_012075bib11 article-title: Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata] publication-title: Journal of applied mathematics and mechanics doi: 10.1016/0021-8928(60)90107-6 – volume: 227 start-page: 8604 year: 2008 ident: JPCS_1392_1_012075bib15 article-title: Iterative multiscale finite-volume method publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2008.06.013 – year: 2003 ident: JPCS_1392_1_012075bib7 – volume: 3 start-page: 50 year: 2005 ident: JPCS_1392_1_012075bib14 article-title: Adaptive multiscale finite-volume method for multiphase flow and transport in porous media publication-title: Multiscale Modeling & Simulation doi: 10.1137/030600795 – volume: 251 start-page: 116 year: 2013 ident: JPCS_1392_1_012075bib12 article-title: Generalized multiscale finite element methods publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2013.04.045 – volume: 48 start-page: 1089 year: 2014 ident: JPCS_1392_1_012075bib4 article-title: A reduced model for darcy’s problem in networks of fractures publication-title: ESAIM: Mathematical Modelling and Numerical Analysis doi: 10.1051/m2an/2013132 |
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| SubjectTerms | Approximation Basis functions Computational fluid dynamics Displacement Finite element analysis Finite element method Fluid flow Mathematical analysis Physics Porous media Two dimensional models |
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| Title | Embedded fracture model in numerical simulation of the fluid flow and geo-mechanics using Generalized Multiscale Finite Element Method |
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