Immiscible two-phase Darcy flow model accounting for vanishing and discontinuous capillary pressures: application to the flow in fractured porous media
Tóm tắt
Từ khóa
Tài liệu tham khảo
Ahmed, R., Edwards, M., Lamine, S., Huisman, B.: Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model. J. Comput. Phys. 284, 462–489 (2015)
Alboin, C., Jaffre, J., Roberts, J., Serres, C.: Modeling fractures as interfaces for flow and transport in porous media. Fluid Flow Transp. Porous Media 295, 13–24 (2002)
Angot, P., Boyer, F., Hubert, F.: Asymptotic and numerical modelling of flows in fractured porous media. Math. Model. Numer. Anal. 43, 239–275 (2009)
Brenner, K., Groza, M., Guichard, C., Lebeau, G., Masson, R.: Gradient discretization of hybrid dimensional Darcy flows in fractured porous media. Numer. Math. 134(3), 569–609 (2016). doi: 10.1007/s00211-015-0782-x
Brenner, K., Groza, M., Guichard, C., Masson, R.: Vertex approximate gradient scheme for hybrid dimensional two-phase Darcy flows in fractured porous media. Math. Model. Numer. Anal. 49, 303–330 (2015)
Brenner, K., Hennicker, J., Masson, R., Samier, P.: Gradient discretization of hybrid-dimensional Darcy flow in fractured porous media with discontinuous pressures at matrix-fracture interfaces. IMA J. Numer. Anal. (2016). doi: 10.1093/imanum/drw044
Brenner, K., Hennicker, J., Masson, R., Samier, P.: Hybrid dimensional modelling and discretization of two phase Darcy flow through DFN in porous media. In: ECMOR XV- 15th European Conference on the Mathematics of Oil Recovery, 29 August–1 September 2016. Amsterdam (2016)
Cancès, C., Pierre, M.: An existence result for multidimensional immiscible two-phase flows with discontinuous capillary pressure field. SIAM. J. Math. Anal. 44, 966–992 (2012)
Ding, D., Langouet, H., Jeannin, L.: Simulation of fracturing induced formation damage and gas production from fractured wells in tight gas reservoirs. SPE 153255, 246–258 (2012). doi: 10.2118/153255-PA
Eymard, R., Guichard, C., Herbin, R.: Small-stencil 3D schemes for diffusive flows in porous media. Math. Model. Numer. Anal. 46, 265–290 (2010)
Eymard, R., Guichard, C., Herbin, R., Masson, R.: Gradient schemes for two-phase flow in heterogeneous porous media and Richards equation. ZAMM - J. Appl. Math. Mech. 94, 560–585 (2014)
Flauraud, E., Nataf, F., Faille, I., Masson, R.: Domain decomposition for an asymptotic geological fault modeling. C. R. Acad. Bulg. Sci. Méc. 331, 849–855 (2003)
Hoteit, J., Firoozabadi, A.: An efficient numerical model for incompressible two-phase flow in fracture media. Adv. Water Resour. 31, 891–905 (2008)
Karimi-Fard, M., Durlofsky, L.J., Aziz, K.: An efficient discrete-fracture model applicable for general-purpose reservoir simulators. SPE J. 9(2), 227–236 (2004)
Martin, V., Jaffré, J., Roberts, J.: Modeling fractures and barriers as interfaces for flow in porous media. SIAM J. Sci. Comput. 26, 1667–1691 (2005)
Monteagudu, J., Firoozabadi, A.: Control-volume model for simulation of water injection in fractured media: incorporating matrix heterogeneity and reservoir wettability effects. SPE J. 12, 355– 366 (2007)
Reichenberger, V., Jakobs, H., Bastian, P., Helmig, R.: A mixed-dimensional finite volume method for multiphase flow in fractured porous media. Adv. Water Resour. 29, 1020– 1036 (2006)
Sandve, T., Berre, I., Nordbotten, J.: An efficient multi-point flux approximation method for discrete fracture-matrix simulations. J. Comput. Phys. 231, 3784–3800 (2012)
Si, H.: TetGen, TetGen, a delaunay-based quality tetrahedral mesh generator. ACM Trans. Math. Softw. 41(2), Article 11 (2015). doi: 10.1145/2629697