Numerical methods and HPC
Open Access
Issue
Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles
Volume 74, 2019
Numerical methods and HPC
Article Number 41
Number of page(s) 17
DOI https://doi.org/10.2516/ogst/2019008
Published online 12 April 2019
  • Berre I., Boon W., Flemisch B., Fumagalli A., Gläser D., Keilegavlen E., Scotti A., Stefansson I., Tatomir A. (2018) Call for participation: Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Technical report, arXiv:1710.00556 [math.AP]. [Google Scholar]
  • Mourzenko V.V., Thovert J.-F., Adler P.M. (Sep 2011) Permeability of isotropic and anisotropic fracture networks, from the percolation threshold to very large densities, Phys. Rev. E 84, 036307. https://doi.org/10.1103/PhysRevE. URL https://link.aps.org/doi/10.1103/PhysRevE.84.036307. [Google Scholar]
  • Sævik P.N., Berre I., Jakobsen M., Lien M. (Oct 2013) A 3d computational study of effective medium methods applied to fractured media, Transp. Porous Media, 100, 115–142. ISSN 1573-1634. https://doi.org/10.1007/s11242-013-0208-0. [Google Scholar]
  • Ssvik P.N., Jakobsen M., Lien M., Berre I. (2014) Anisotropic effective conductivity in fractured rocks by explicit effective medium methods, Geophys. Prospect. 62, 6, 1297–1314. ISSN 1365-2478. https://doi.org/10.1111/1365-2478.12173. [CrossRef] [Google Scholar]
  • Fumagalli A., Pasquale L., Zonca S., Micheletti S. (2016) An upscaling procedure for fractured reservoirs with embedded grids, Water Resour. Res. 52, 8, 6506–6525. ISSN 1944-7973. https://doi.org/10.1002/2015WR017729. [Google Scholar]
  • Karimi-Fard M., Durlofsky L.J. (Oct 2016) A general gridding, discretization, and coarsening methodology for modeling flow in porous formations with discrete geological features, Adv. Water Res. 96, 354–372. ISSN 03091708. https://doi.org/10.1016/j.advwatres.2016.07.019. URL http://linkinghub.elsevier.com/retrieve/pii/S0309170816302950. [CrossRef] [Google Scholar]
  • Karimi-Fard M., Gong B., Durlofsky L.J. (2006) Generation of coarse-scale continuum flow models from detailed fracture characterizations, Water Resour. Res. 42, 10. ISSN 1944-7973. https://doi.org/10.1029/2006WR005015. [Google Scholar]
  • Alboin C., Jaffré J., Roberts J.E., Wang X., Serres C., Chen Z., Ewing R. E., Shi Z.-C. (2000) Domain decomposition for some transmission problems in flow in porous media. Numerical treatment of multiphase flows in porous media (Beijing, 1999), Springer, pp. 22–34. [CrossRef] [Google Scholar]
  • Amir L., Kern M., Martin V., Roberts J.E. (2005) Décomposition de domaine et préconditionnement pour un modèle 3D en milieu poreux fracturé, in: Proceeding of JANO 8, 8th Conference on Numerical Analysis and Optimization, December 2005. [Google Scholar]
  • Boon W.M., Nordbotten J.M., Yotov I. (2018) Robust discretization of flow in fractured porous media, SIAM J. Numer. Anal. 56, 4, 2203–2233. https://doi.org/10.1137/17M1139102. [Google Scholar]
  • Faille I., Fumagalli A., Jaffré J., Roberts J.E. (2016) Model reduction and discretization using hybrid finite volumes of flow in porous media containing faults, Comput. Geosci. 20, 2, 317–339. ISSN 15731499. https://doi.org/10.1007/s10596-016-9558-3. [Google Scholar]
  • Knabner P., Roberts J.E. (2014) Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy-Forchheimer flow in the fracture, ESAIM: Math. Model. Numer. Anal. 48, 1451–1472. ISSN 1290-3841. https://doi.org/10.1051/m2an/2014003. URL http://www.esaim-m2an.org/article_S0764583X1400003X. [CrossRef] [Google Scholar]
  • Martin V., Jaffré J., Roberts J.E. (2005) Modeling fractures and barriers as interfaces for flow in porous media, SIAM J. Sci. Comput. 26, 5, 1667–1691. ISSN 1064-8275. https://doi.org/10.1137/S1064827503429363. URL http://scitation.aip.org/getabs/servlet/GetabsServlet?prog= normal&id=SJ0CE3000026000005001667000001&idtype= cvips&gifs=yes. [Google Scholar]
  • Schwenck N., Flemisch B., Helmig R., Wohlmuth B.I. (2015) Dimensionally reduced flow models in fractured porous media: crossings and boundaries, Comput. Geosci. 19, 6, 1219–1230. ISSN 1420-0597. https://doi.org/10.1007/s10596-015-9536-1. [Google Scholar]
  • Tunc X., Faille I., Gallouet T., Cacas M.C., Havé P. (2012) A model for conductive faults with non-matching grids, Comput. Geosci. 16, 277–296. ISSN 1420-0597. https://doi.org/10.1007/s10596-011-9267-x. [Google Scholar]
  • Angot P. (2003) A model of fracture for elliptic problems with flux and solution jumps, C. R. Math. 337, 6, 425–430. ISSN 1631-073X. https://doi.org/10.1016/S1631-073X(03)00300-5. URL http://www.sciencedirect.com/science/article/pii/S1631073X03003005. [CrossRef] [Google Scholar]
  • Angot P., Boyer F., Hubert F. (2009) Asymptotic and numerical modelling of flows in fractured porous media, M2AN Math Model. Numer. Anal. 43, 2, 239–275. ISSN 0764-583X. https://doi.org/10.1051/m2an/2008052. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  • Chave F.A., Di Pietro D., Formaggia L. (2017) A Hybrid High-Order method for Darcy flows in fractured porous media, Technical report, HAL archives, 2017. URL https://hal.archives-ouvertes.fr/hal-01482925. [Google Scholar]
  • Karimi-Fard M., Firoozabadi A. (2003) Numerical simulation of water injection in fractured media using the discrete-fracture model and the Galerkin method, SPE Reserv. Eval. Eng. 6, 2, 117–126. [CrossRef] [Google Scholar]
  • Ahmed R., Edwards M.G., Lamine S., Huisman B.A.H., Pal M. (2015) Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model, J. Comput. Phys. 284, 462–489. ISSN 0021-9991. https://doi.org/10.1016/jjcp.2014.12.047. http://www.sciencedirect.com/science/article/pii/S0021999114008705. [Google Scholar]
  • Brenner K., Hennicker J., Masson R., Samier P. (September 2016) Gradient discretization of hybrid-dimensional Darcy flow in fractured porous media with discontinuous pressures at matrix-fracture interfaces, IMA J. Numer. Anal. https://doi.org/10.1093/imanum/drw044. URL https://hal.archives-ouvertes.fr/hal-01192740. [Google Scholar]
  • Brenner K., Hennicker J., Masson R., Samier P. (2018) Hybrid-dimensional modelling of two-phase flow through fractured porous media with enhanced matrix fracture transmission conditions, J. Comput. Phys. 357, 100–124. ISSN 0021-9991. https://doi.org/10.1016/j.jcp.2017.12.003. http://www.sciencedirect.com/science/article/pii/S0021999117308781. [Google Scholar]
  • Brenner K., Groza M., Guichard C., Masson R. (2015) Vertex approximate gradient scheme for hybrid dimensional two-phase Darcy flows in fractured porous media, ESAIM: Math. Model. Numer. Anal. 49, 2, 303–330. https://doi.org/10.1051/m2an/2014034. [CrossRef] [Google Scholar]
  • Antonietti P.F., Formaggia L., Scotti A., Verani M., Verzotti N. (2016) Mimetic finite difference approximation of flows in fractured porous media, ESAIM: M2AN 50, 3, 809–832. https://doi.org/10.1051/m2an/2015087. [CrossRef] [EDP Sciences] [Google Scholar]
  • Scotti A., Formaggia L., Sottocasa F. (2017) Analysis of a mimetic finite difference approximation of flows in fractured porous media, ESAIM: M2AN. https://doi.org/10.1051/m2an/2017028. [Google Scholar]
  • Benedetto M.F., Berrone S., Pieraccini S., Scialò S. (2014) The virtual element method for discrete fracture network simulations, Comput. Methods Appl. Mech. Eng. 280, 0, 135–156. ISSN 0045-7825. https://doi.org/10.1016/j.cma.2014.07.016. [Google Scholar]
  • Benedetto M.F., Berrone S., Borio A., Pieraccini S., Scialò S. (2016) A hybrid mortar virtual element method for discrete fracture network simulations, J. Comput. Phys. 306, 148–166. ISSN 0021-9991. https://doi.org/10.1016/jjcp.2015.11.034. http://www.sciencedirect.com/science/article/pii/S0021999115007743. [Google Scholar]
  • Fumagalli A., Keilegavlen E. (2018) Dual virtual element method for discrete fractures networks, SIAM J. Sci. Comput. 40, 1, B228–B258. https://doi.org/10.1137/16M1098231. [Google Scholar]
  • da Veiga L.B., Brezzi F., Cangiani A., Manzini G., Marini L.D., Russo A. (2013) Basic principles of virtual element methods, Math. Models Methods Appl. Sci. 23, 1, 199–214. https://doi.org/10.1142/S0218202512500492. [Google Scholar]
  • da Veiga L.B., Brezzi F., Marini L.D., Russo A. (2014) The hitchhiker’s guide to the virtual element method, Math. Models Methods Appl. Sci. 24, 8, 1541–1573. https://doi.org/10.1142/S021820251440003X. [Google Scholar]
  • da Veiga L.B., Brezzi F., Marini L.D., Russo A. (Jun 2014) H(div) and H(curl)-conforming VEM, Numer. Math. 133, 2, 303–332. ISSN 0945-3245. https://doi.org/10.1007/s00211-015-0746-1. [Google Scholar]
  • da Veiga L.B., Brezzi F., Marini L.D., Russo A. (2016) Mixed virtual element methods for general second order elliptic problems on polygonal meshes, ESAIM: M2AN 50, 3, 727–747. https://doi.org/10.1051/m2an/2015067. [Google Scholar]
  • Brezzi F., Falk R.S., Marini D.L. (2014) Basic principles of mixed virtual element methods, ESAIM: M2AN 48, 1227–1240. https://doi.org/10.1051/m2an/2013138. [CrossRef] [EDP Sciences] [Google Scholar]
  • Frih N., Martin V., Roberts J.E., Saâda A. (2012) Modeling fractures as interfaces with nonmatching grids, Comput. Geosci. 16, 4, 1043–1060. ISSN 1420-0597. https://doi.org/10.1007/s10596-012-9302-6. [Google Scholar]
  • Nordbotten J.M., Boon W., Fumagalli A., Keilegavlen E. (2018) Unified approach to discretization of flow in fractured porous media, Comput. Geosci. ISSN 1573-1499. https://doi.org/10.1007/s10596-018-9778-9. [Google Scholar]
  • Berrone S., Pieraccini S., Scialò S. (2013) On simulations of discrete fracture network flows with an optimization-based extended finite element method, SIAM J. Sci. Comput. 35, 2, 908–935. https://doi.org/10.1137/120882883. [Google Scholar]
  • D’Angelo C., Scotti A. (2012) A mixed finite element method for Darcy flow in fractured porous media with nonmatching grids, Math. Model. Numer. Anal. 46, 2, 465–489. https://doi.org/10.1051/m2an/2011148. [CrossRef] [EDP Sciences] [Google Scholar]
  • Del Pra M., Fumagalli A., Scotti A. (2017) Well posedness of fully coupled fracture/bulk Darcy flow with XFEM, SIAM J. Numer. Anal. 55, 2, 785–811. https://doi.org/10.1137/15M1022574. [Google Scholar]
  • Fumagalli A., Scotti A. (2013) A numerical method for two-phase flow in fractured porous media with non-matching grids, Adv. Water Res. 62, Part C(0), 454–464. ISSN 0309-1708. https://doi.org/10.1016/j.advwatres.2013.04.001. URL https://www.sciencedirect.com/science/article/pii/S0309170813000523. Computational Methods in Geologic CO2 Sequestration. [CrossRef] [Google Scholar]
  • Fumagalli A., Scotti A. (April 2014) An efficient XFEM approximation of Darcy flows in arbitrarily fractured porous media, Oil Gas Sci. Technol. - Rev. IFP Energies nouvelles 69, 4, 555–564. https://doi.org/10.2516/ogst/2013192. URL https://ogst.ifpenergiesnouvelles.fr/articles/ogst/abs/2014/04/ogst130007/ogst130007.html. [CrossRef] [Google Scholar]
  • Tene M., Al Kobaisi M.S., Hajibeygi H. (2016) Multiscale projection-based embedded discrete fracture modeling approach (f-ams-pedfm), ECMOR XIV-15th European Conference on the Mathematics of Oil Recovery, August 29–1 September 2016, Beurs van Berlage, EAGE. https://doi.org/10.3997/2214-4609.201601890. [Google Scholar]
  • Fumagalli A., Zonca S., Formaggia L. (July 2017) Advances in computation of local problems for flow-based upscaling in fractured reservoirs, Math. Comput. Simul. 137, 299–324. https://doi.org/10.1016/j.matcom.2017.01.007. URL https://www.sciencedirect.com/science/article/pii/S0378475417300320. [Google Scholar]
  • Li L., Lee S.H. (2008) Efficient field-scale simulation of black oil in a naturally fractured reservoir through discrete fracture networks and homogenized media, SPE Reserv. Eval. Eng. 11, 750–758. https://doi.org/10.2118/103901-PA. [CrossRef] [Google Scholar]
  • Berrone S., Pieraccini S., Scialò S. (2013) A PDE-constrained optimization formulation for discrete fracture network flows, SIAM J. Sci. Comput., 35, 2, B487–B510. https://doi.org/10.1137/120865884. [Google Scholar]
  • Formaggia L., Fumagalli A., Scotti A., Ruffo P. (2014) A reduced model for Darcy’s problem in networks of fractures, ESAIM: Math. Model. Numer. Anal. 48, 1089–1116. https://doi.org/10.1051/m2an/2013132. URL https://www.esaim-m2an.org/articles/m2an/abs/2014/04/m2an130132/m2an130132.html. [CrossRef] [EDP Sciences] [Google Scholar]
  • Boon W.M., Nordbotten J.M., Vatne J.E. (2017) Mixeddimensional elliptic partial differential equations. Technical report, arXiv:1710.00556 [math.AP]. [Google Scholar]
  • Fumagalli A., Scotti A. (2013) A reduced model for flow and transport in fractured porous media with nonmatching grids, in: Cangiani A., Davidchack R.L., Georgoulis E., Gorban A.N., Levesley J., Tretyakov M.V. (eds), Numerical mathematics and advanced applications 2011, Berlin, Heidelberg, Springer, pp. 499–507. ISBN 978-3-642-33133-6. https://doi.org/10.1007/978-3-642-33134-3_53. [CrossRef] [Google Scholar]
  • Grisvard P. (1985) Elliptic problems in non-smooth domains, Vol. 24, Monographs and studies in mathematics, Pitman. [Google Scholar]
  • Geuzaine C., Remacle J.-F. (2009) Gmsh: A 3-d finite element mesh generator with built-in pre- and post-processing facilities, Int. J. Numer. Methods Eng. 79, 11, 1309–1331. ISSN 1097-0207. https://doi.org/10.1002/nme.2579. [Google Scholar]
  • Fumagalli A. (Dec. 2018) Dual virtual element method in presence of an inclusion, Appl. Math. Lett. 86, 22–29. https://doi.org/10.1016/j.aml.2018.06.004. URL https://www.sciencedirect.com/science/article/pii/S0893965918301812. [Google Scholar]
  • Flemisch B., Berre I., Boon W., Fumagalli A., Schwenck N., Scotti A., Stefansson I., Tatomir A. (January 2018) Benchmarks for single-phase flow in fractured porous media, Adv. Water Res. 111, 239–258. https://doi.org/10.1016/j.advwatres.2017.10.036. URL https://www.sciencedirect.com/science/article/pii/S0309170817300143. [CrossRef] [Google Scholar]
  • Keilegavlen E., Fumagalli A., Berge R., Stefansson I., Berre I. (2017) Porepy: An open source simulation tool for flow and transport in deformable fractured rocks. Technical report, arXiv:1712.00460 [cs.CE]. URL https://arxiv.org/abs/1712.00460. [Google Scholar]
  • Flemisch B., Rainer H. (2008) Numerical investigation of a mimetic finite difference method, in: Finite volumes for complex applications V – Problems and perspectives, Wiley–VCH, Germany, pp. 815–824. [Google Scholar]
  • Geiger S., Dentz M., Neuweiler I. (2011) A novel multi-rate dual-porosity model for improved simulation of fractured and multiporosity reservoirs, SPE Reservoir Characterisation and Simulation Conference and Exhibition, 9–11 October, Abu Dhabi. [Google Scholar]
  • Sausse J., Dezayes C., Dorbath L., Genter A., Place J. (2010) 3d model of fracture zones at soultzsous-for Sts based on geological data, image logs, induced microseismicity and vertical seismic profiles, C. R. Geosci. 342, 7, 531–545. ISSN 1631-0713. doi: http://doi.org/10.1016/j.crte.2010.01.011. URL http://www.sciencedirect.com/science/article/pii/S1631071310000489. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.