Show simple item record

dc.contributor.authorAkkutlu, I. Y.
dc.contributor.authorEfendiev, Yalchin
dc.contributor.authorVasilyeva, Maria
dc.date.accessioned2016-11-03T08:28:29Z
dc.date.available2016-11-03T08:28:29Z
dc.date.issued2016-05-18
dc.identifier.citationAkkutlu, I. Y., Efendiev, Y., & Vasilyeva, M. (2016). Multiscale model reduction for shale gas transport in fractured media. Computational Geosciences, 20(5), 953–973. doi:10.1007/s10596-016-9571-6
dc.identifier.issn1420-0597
dc.identifier.issn1573-1499
dc.identifier.doi10.1007/s10596-016-9571-6
dc.identifier.urihttp://hdl.handle.net/10754/621404
dc.description.abstractIn this paper, we develop a multiscale model reduction technique that describes shale gas transport in fractured media. Due to the pore-scale heterogeneities and processes, we use upscaled models to describe the matrix. We follow our previous work (Akkutlu et al. Transp. Porous Media 107(1), 235–260, 2015), where we derived an upscaled model in the form of generalized nonlinear diffusion model to describe the effects of kerogen. To model the interaction between the matrix and the fractures, we use Generalized Multiscale Finite Element Method (Efendiev et al. J. Comput. Phys. 251, 116–135, 2013, 2015). In this approach, the matrix and the fracture interaction is modeled via local multiscale basis functions. In Efendiev et al. (2015), we developed the GMsFEM and applied for linear flows with horizontal or vertical fracture orientations aligned with a Cartesian fine grid. The approach in Efendiev et al. (2015) does not allow handling arbitrary fracture distributions. In this paper, we (1) consider arbitrary fracture distributions on an unstructured grid; (2) develop GMsFEM for nonlinear flows; and (3) develop online basis function strategies to adaptively improve the convergence. The number of multiscale basis functions in each coarse region represents the degrees of freedom needed to achieve a certain error threshold. Our approach is adaptive in a sense that the multiscale basis functions can be added in the regions of interest. Numerical results for two-dimensional problem are presented to demonstrate the efficiency of proposed approach.
dc.description.sponsorshipWe are grateful to Tat Leung for helpful discussions and suggestions regarding to online basis constructions. MV's work is partially supported by the grant of the President of the Russian Federation MK-9613.2016.1 and RFBR (project N 15-31-20856). YE would like to thank the partial support from the DOE, Army, the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-FG02-13ER26165, and National Priorities Research Program grant NPRP grant 7-1482-1278 from the Qatar National Research Fund (a member of The Qatar Foundation).
dc.publisherSpringer Science and Business Media LLC
dc.relation.urlhttp://link.springer.com/10.1007/s10596-016-9571-6
dc.relation.urlhttp://arxiv.org/pdf/1507.00113
dc.rightsArchived with thanks to Springer Science and Business Media LLC
dc.rightsThis file is an open access version redistributed from: http://arxiv.org/pdf/1507.00113
dc.subjectCoarse grid
dc.subjectFinite element method
dc.subjectFractured media
dc.subjectMultiscale
dc.subjectReduced model
dc.subjectShale gas transport
dc.titleMultiscale model reduction for shale gas transport in fractured media
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)
dc.identifier.journalComputational Geosciences
dc.eprint.versionPre-print
dc.contributor.institutionDepartment of Petroleum Engineering, Texas A & M University, College Station, TX, United States
dc.contributor.institutionDepartment of Mathematics, Texas A&M University, College Station, TX, United States
dc.contributor.institutionDepartment of Computational Technologies, Institute of Mathematics and Informatics, North-Eastern Federal University, Yakutsk, Republic of Sakha (Yakutia), Russian Federation
dc.contributor.institutionInstitute for Scientific Computation, Texas A&M University, College Station, TX, United States
dc.identifier.volume20
dc.identifier.issue5
dc.identifier.pages953-973
dc.identifier.arxivid1507.00113
kaust.personEfendiev, Yalchin R.
dc.identifier.eid2-s2.0-85032070085
refterms.dateFOA2021-05-03T11:34:04Z
dc.date.published-online2016-05-18
dc.date.published-print2016-10


Files in this item

Thumbnail
Name:
Articlefile1.pdf
Size:
3.652Mb
Format:
PDF
Description:
Pre-print

This item appears in the following Collection(s)

Show simple item record