A reduced fracture model for two-phase flow with different rock types

Adimurthi, 2004, Godunov-type methods for conservation laws with a flux function discontinuous in space, SIAM J. Numer. Anal., 42, 179, 10.1137/S003614290139562X Agouzal, 1995, Connection between finite volumes and mixed finite element methods for a diffusion problem with nonconstant coefficients, with application to convection–diffusion, East-West J. Numer. Anal., 3, 237 Alboin, 1999, Domain decomposition for flow in porous media with fractures, 371 Alboin, 2002, Modeling fractures as interfaces for flow and transport in porous media, vol. 295, 13 Alboin, 2000, Domain decomposition for some transmission problems in flow in porous media, 22 Amir, 2006, Décomposition de domaine pour un milieu poreux fracturé: un modèle en 3d avec fractures qui s’ intersectent, Arima, 5, 11 Andreianov, 2014, A phase-by-phase upstream scheme that converges to the vanishing capillarity solution for countercurrent two-phase flow in two-rock media, Comput. Geosci., 18, 211, 10.1007/s10596-014-9403-5 Angot, 2009, Asymptotic and numerical modelling of flows in fractured porous media, ESAIM: Math. Model. Numer. Anal., 43, 239, 10.1051/m2an/2008052 Aziz, 1979 Baca, 1984, Modelling fluid flow in fractured-porous rock masses by finite element techniques, Internat. J. Numer. Methods Fluids, 4, 337, 10.1002/fld.1650040404 Bastian, 2000, Numerical simulation of multiphase flow in fractured porous media, 50 Bogdanov, 2003, Two-phase flow through fractured porous media, Phys. Rev. E, 68, 1, 10.1103/PhysRevE.68.026703 Borouchaki, 2000, Parametric surface meshing using a combined advancing-front–generalized-Delaunay approach, Internat. J. Numer. Methods Engrg., 49, 233, 10.1002/1097-0207(20000910/20)49:1/2<233::AID-NME931>3.0.CO;2-G Bourgeat, 1995, A result of existence for a model of two-phase flow in a porous medium made of different rock types, Appl. Anal., 56, 381, 10.1080/00036819508840332 Brenier, 1991, Upstream differencing for multiphase flow in reservoir simulation, SIAM J. Numer. Anal., 28, 685, 10.1137/0728036 Brenner, 2015, Vertex approximate gradient scheme for hybrid dimensional two-phase Darcy flows in fractured porous media, ESAIM: Math. Model. Numer. Anal., 49, 303, 10.1051/m2an/2014034 Chavent, 1976, A new formulation of diphasic incompressible flows in porous media, 258 Chavent, 1986 Droniou, 2010, A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume methods, Math. Models Methods Appl. Sci., 20, 265, 10.1142/S0218202510004222 Faille, 2016, Model reduction and discretization using hybrid finite volumes for flow in porous media containing faults, Comput. Geosci., 1 Formaggia, 2014, A reduced model for Darcy’s problem in networks of fractures, ESAIM: Math. Model. Numer. Anal., 48, 1089, 10.1051/m2an/2013132 Frey, 2008 Frih, 2012, Modeling fractures as interfaces with nonmatching grids, Comput. Geosci., 16, 1043, 10.1007/s10596-012-9302-6 Fumagalli, 2013, A numerical method for two-phase flow in fractured porous media with non-matching grids, Adv. Water Resour., 62, 454, 10.1016/j.advwatres.2013.04.001 Glowinski, 1988, Domain decomposition and mixed finite element methods for elliptic problems, 144 Haegland, 2009, Comparison of cell- and vertex-centered discretization methods for flow in a two-dimensional discrete-fracture-matrix system, Adv. Water Resour., 32, 1740, 10.1016/j.advwatres.2009.09.006 Hoang, 2013, Space–time domain decomposition methods for diffusion problems in mixed formulations, SIAM J. Numer. Anal., 51, 3532, 10.1137/130914401 T.T.P. Hoang, C. Japhet, M. Kern, J.E. Roberts, Space–time domain decomposition methods for advection-diffusion problems in mixed formulations, Math. Comput. Simulation (submitted). Hoang, 2016, Space–time domain decomposition methods for reduced fracture models in mixed formulation, SIAM J. Numer. Anal., 54, 288, 10.1137/15M1009651 Hoteit, 2008, An efficient numerical model for incompressible two-phase flow in fractured media, Adv. Water Resour., 31, 891, 10.1016/j.advwatres.2008.02.004 Hoteit, 2008, Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures, Adv. Water. Resour., 31, 56, 10.1016/j.advwatres.2007.06.006 Jaffré, 2011, A discrete fracture model for two-phase flow with matrix-fracture interaction, Procedia Comput. Sci., 4, 967, 10.1016/j.procs.2011.04.102 Karimi-Fard, 2003, Numerical simulation of water injection in 2D fractured media using discrete-fracture model, SPE Reserv. Eval. Eng., 4, 117, 10.2118/83633-PA Kelley, 1995 Kim, 2000, Finite element, discrete-fracture model for multiphase flow in porous media, AIChE J., 46, 1120, 10.1002/aic.690460604 K.A. Lie, An Introduction to Reservoir Simulation Using MATLAB: User guide for the Matlab Reservoir Simulation Toolbox (MRST), SINTEF ICT, Norway, 2014. Martin, 2005, Modeling fractures and barriers as interfaces for flow in porous media, SIAM J. Sci. Comput., 26, 1667, 10.1137/S1064827503429363 Mishra, 2010, On the upstream mobility scheme for two-phase flow in porous media, Comput. Geosci., 14, 105, 10.1007/s10596-009-9135-0 Mondteagudu, 2007, Control-volume model for simulation of water injection in fractured media: incorporating matrix heterogeneity and reservoir wettability effects, SPE J., 12, 355, 10.2118/98108-PA Morales, 2010, The narrow fracture approximation by channeled flow, J. Math. Anal. Appl., 365, 320, 10.1016/j.jmaa.2009.10.042 Nédélec, 1980, Mixed finite elements in R3, Numer. Math., 35, 315, 10.1007/BF01396415 Pop, 2016, VJM, 1 Reichenberger, 2006, A mixed-dimensional finite volume method for two-phase flow in fractured porous media, Adv. Water Resour., 29, 1020, 10.1016/j.advwatres.2005.09.001 Roberts, 1991, Mixed and hybrid methods, 523, 10.1016/S1570-8659(05)80041-9 Tunc, 2012, A model for conductive faults with non-matching grids, Comput. Geosci., 16, 277, 10.1007/s10596-011-9267-x Van Duijn, 1995, The effect of capillary forces on immiscible two-phase flow in heterogeneous porous media, Transp. Porous Media, 21, 71, 10.1007/BF00615335 Vohralík, 2013, Mixed finite element methods: implementation with one unknown per element, local flux expressions, positivity, polygonal meshes, and relations to other methods, Math. Models Methods Appl. Sci., 23, 803, 10.1142/S0218202512500613 Younès, 2004, From mixed finite elements to finite volumes for elliptic PDEs in two and three dimensions, Internat. J. Numer. Methods Engrg., 59, 365, 10.1002/nme.874