Advanced computation of steady-state fluid flow in Discrete Fracture-Matrix models: FEM–BEM and VEM–VEM fracture-block coupling

Springer Science and Business Media LLC - Tập 9 Số 2 - Trang 377-399 - 2018
Stefano Berrone1, Andrea Borio1, Corrado Fidelibus2, Sandra Pieraccini3, Stefano Scialò1, Fabio Vicini1
1Dipartimento di Scienze Matematiche, Politecnico di Torino, Turin, Italy
2Dipartimento di Ingegneria dell’Innovazione, Università del Salento, Lecce, Italy
3Dipartimento di Ingegneria Meccanica e Aerospaziale, Politecnico di Torino, Turin, Italy

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Aavatsmark, I.: An introduction to multipoint flux approximations for quadrilateral grids. Comput. Geosci. 6(3), 405–432 (2002). https://doi.org/10.1023/A:1021291114475

Ahmad, B., Alsaedi, A., Brezzi, F., Marini, L.D., Russo, A.: Equivalent projectors for virtual element methods. Comput. Math. Appl. 66, 376–391 (2013)

Ahmed, R., Edwards, M., Lamine, S., Huisman, B., Pal, M.: Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model. J. Comput. Phys. 284, 462–489 (2015). https://doi.org/10.1016/j.jcp.2014.12.047

Al-Hinai, O., Srinivasan, S., Wheeler, M.F.: Domain decomposition for flow in porous media with fractures. In: SPE Reservoir Simulation Symposium 23–25 February 2013, Houston, Texas, USA, Society of Petroleum Engineers (2015). https://doi.org/10.2118/173319-MS

Alboin, C., Jaffré, J., Roberts, J., Serres, C.: Domain decomposition for flow in porous media with fractures. In: Lai, C.H., Bjorstad, P.E., Cross, M., Widlund, O.B. (eds.) Proceedings of the 11th International Conference on Domain Decomposition Methods in Greenwich, pp. 371–379 (1999)

Aldejain, A.: Implementation of dual porosity model in a chemical flooding simulator. Ph.D. thesis, The University of Texas at Austin, Texas (1999)

Angot, P., Boyer, F., Hubert, F.: Asymptotic and numerical modelling of flows in fractured porous media. ESAIM: M2AN 43(2), 239–275 (2009). https://doi.org/10.1051/m2an/2008052

Antonietti, P., Formaggia, L., Scotti, A., Verani, M., Verzott, N.: Mimetic finite difference approximation of flows in fractured porous media. ESAIM: M2AN 50(3), 809–832 (2016). https://doi.org/10.1051/m2an/2015087

Bai, M., Ma, Q., Roegiers, J.: A nonlinear dual-porosity model. Appl. Math. Model. 18(11), 602–610 (1994). https://doi.org/10.1016/0307-904X(94)90318-2

Beirão da Veiga, L., Brezzi, F., Cangiani, A., Manzini, G., Marini, L.D., Russo, A.: Basic principles of virtual element methods. Math. Models Methods Appl. Sci. 23(01), 199–214 (2013a). https://doi.org/10.1142/S0218202512500492

Beirão da Veiga, L., Brezzi, F., Marini, L.D.: Virtual elements for linear elasticity problems. SIAM J. Numer. Anal. 51(2), 794–812 (2013b). https://doi.org/10.1137/120874746

Beirão Da Veiga, L., Brezzi, F., Marini, L.D., Russo, A.: The hitchhiker’s guide to the virtual element method. Math Models Methods Appl Sci 24(8), 1541–1573 (2014)

Beirão da Veiga, L., Lipnikov, K., Manzini, G.: The Mimetic Finite Difference Method for Elliptic Problems, Modeling, Simulation and Applications, vol 11. Springer, Berlin (2014).

Beirão da Veiga, L., Brezzi, F., Marini, L.D., Russo, A.: Virtual element methods for general second order elliptic problems on polygonal meshes. Math. Models Methods Appl. Sci. 26(04), 729–750 (2015). https://doi.org/10.1142/S0218202516500160

Benedetto, M., Berrone, S., Pieraccini, S., Scialò, S.: The virtual element method for discrete fracture network simulations. Comput. Methods Appl. Mech. Eng. 280, 135–156 (2014). https://doi.org/10.1016/j.cma.2014.07.016

Benedetto, M., Berrone, S., Borio, A., Pieraccini, S., Scialò, S.: A hybrid mortar virtual element method for discrete fracture network simulations. J. Comput. Phys. 306, 148–166 (2016a). https://doi.org/10.1016/j.jcp.2015.11.034

Benedetto, M., Berrone, S., Scialò, S.: A globally conforming method for solving flow in discrete fracture networks using the virtual element method. Finite Elem. Anal. Des. 109, 23–36 (2016b). https://doi.org/10.1016/j.finel.2015.10.003

Benedetto, M.F., Berrone, S., Borio, A.: The Virtual Element Method for underground flow simulations in fractured media. Advances in Discretization Methods, SEMA SIMAI Springer Series, vol. 12, pp. 167–186. Springer International Publishing, Basel (2016c)

Berrone, S., Borio, A.: Orthogonal polynomials in badly shaped polygonal elements for the Virtual Element Method. Finite Elements Anal. Des. 129, 14–31 (2017a). https://doi.org/10.1016/j.finel.2017.01.006

Berrone, S., Borio, A.: A residual a posteriori error estimate for the virtual element method. Math. Models Methods Appl. Sci. 27(08), 1423–1458 (2017b). https://doi.org/10.1142/S0218202517500233

Berrone, S., Pieraccini, S., Scialò, S.: On simulations of discrete fracture network flows with an optimization-based extended finite element method. SIAM J. Sci. Comput. 35(2), A908–A935 (2013a). https://doi.org/10.1137/120882883

Berrone, S., Pieraccini, S., Scialò, S.: A PDE-constrained optimization formulation for discrete fracture network flows. SIAM J. Sci. Comput. 35(2), B487–B510 (2013b). https://doi.org/10.1137/120865884

Berrone, S., Fidelibus, C., Pieraccini, S., Scialò, S.: Simulation of the steady-state flow in discrete fracture networks with non-conforming meshes and extended finite elements. Rock Mech. Rock Eng. 47(6), 2171–2182 (2014a). https://doi.org/10.1007/s00603-013-0513-5

Berrone, S., Pieraccini, S., Scialò, S.: An optimization approach for large scale simulations of discrete fracture network flows. J. Comput. Phys. 256, 838–853 (2014b). https://doi.org/10.1016/j.jcp.2013.09.028

Berrone, S., Pieraccini, S., Scialò, S., Vicini, F.: A parallel solver for large scale DFN flow simulations. SIAM J. Sci. Comput. 37(3), C285–C306 (2015). https://doi.org/10.1137/140984014

Berrone, S., Borio, A., Scialò, S.: A posteriori error estimate for a PDE-constrained optimization formulation for the flow in DFNs. SIAM J. Numer. Anal. 54(1), 242–261 (2016a). https://doi.org/10.1137/15M1014760

Berrone, S., Pieraccini, S., Scialò, S.: Towards effective flow simulations in realistic discrete fracture networks. J. Comput. Phys. 310, 181–201 (2016b). https://doi.org/10.1016/j.jcp.2016.01.009

Berrone, S., Pieraccini, S., Scialò, S.: Flow simulations in porous media with immersed intersecting fractures. J. Comput. Phys. 345, 768–791 (2017). https://doi.org/10.1016/j.jcp.2017.05.049

Brebbia, C., Telles, J., Wrobel, L.: Boundary Element Techniques, Theory and Apllications in Engineering. Springer, Berlin (1984)

Brenner, K., Groza, M., Guichard, C., Lebeau, G., Masson, R.: Gradient discretization of hybrid dimensional darcy flows in fractured porous media. Numerische Mathematik 134(3), 569–609 (2016a). https://doi.org/10.1007/s00211-015-0782-x

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. (2016b). https://doi.org/10.1093/imanum/drw044

Brezzi, F., Falk, R.S., Marini, L.D.: Basic principles of mixed virtual element methods. ESAIM Math. Model. Numer. Anal. 48(4), 1227–1240 (2014). https://doi.org/10.1051/m2an/2013138

Chave, F., Di Pietro, D., Formaggia, L.: A hybrid high-order method for darcy flows in fractured porous media. SIAM J. Sci. Comput. 40(2), A1063–A1094 (2018). https://doi.org/10.1137/17M1119500

D’Angelo, C., Scotti, A.: A mixed finite element method for darcy flow in fractured porous media with non-matching grids. ESAIM: M2AN 46(2), 465–489 (2012). https://doi.org/10.1051/m2an/2011148

Faille, I., Fumagalli, A., Jaffré, J., Roberts, J.E.: Model reduction and discretization using hybrid finite volumes for flow in porous media containing faults. Comput. Geosci. 20(2), 317–339 (2016). https://doi.org/10.1007/s10596-016-9558-3

Fidelibus, C., Barla, G., Cravero, M.: A mixed solution for two-dimensional unsteady flow in fractured porous media. Int. J. Numer. Anal. Methods Geomech. 21(9), 619–633 (1997)

Flemisch, B., Berre, I., Boon, W., Fumagalli, A., Schwenck, N., Scotti, A., Stefansson, I., Tatomir, A.: Benchmarks for single-phase flow in fractured porous media. Adv. Water Resour. 111, 239–258 (2018). https://doi.org/10.1016/j.advwatres.2017.10.036

Formaggia, L., Scotti, A., Sottocasa, F.: Analysis of a Mimetic Finite Difference approximation of flows in fractured media. Technical Report 49/2016, MOX, Mathematical Department, Politecnico di Milano (2016)

Fries, T.P., Belytschko, T.: The extended/generalized finite element method: an overview of the method and its applications. Int. J. Numer. Methods Eng. 84(3), 253–304 (2010). https://doi.org/10.1002/nme.2914

Frih, N., Martin, V., Roberts, J.E., Saâda, A.: Modeling fractures as interfaces with nonmatching grids. Comput. Geosci. 16(4), 1043–1060 (2012). https://doi.org/10.1007/s10596-012-9302-6

Fumagalli, A., Keilegavlen, E.: Dual virtual element method for discrete fractures networks. SIAM J. Sci. Comput. 40, B228–B258 (2018). https://doi.org/10.1137/16M1098231

Fumagalli, A., Scotti, A.: A numerical method for two-phase flow in fractured porous media with non-matching grids. Adv. Water Resour. 62, 454–464 (2013). https://doi.org/10.1016/j.advwatres.2013.04.001

Fumagalli, A., Keilegavlen, E., Scialò, S. (2018) Conforming, non-conforming and non-matching discretization couplings in discrete fracture network simulations. arXiv:1803.01732

Hajibeygi, H., Karvounis, D., Jenny, P.: A hierarchical fracture model for the iterative multiscale finite volume method. J. Comput. Phys. 230(24), 8729–8743 (2011). https://doi.org/10.1016/j.jcp.2011.08.021

Huyakorn, P., Pinder, G.: The Computational Methods in Subsurface Flow. Academic Press, Cambridge (1983). doi: 10.1016/B978-0-12-363480-1.50001-4.

Hyman, J.D., Karra, S., Makedonska, N., Gable, C.W., Painter, S.L., Viswanathan, H.S.: dfnworks: a discrete fracture network framework for modeling subsurface flow and transport. Comput. Geosci. 84, 10–19 (2015). https://doi.org/10.1016/j.cageo.2015.08.001

Kazemi, H., Gilman, J.: Multiphase flow in fractured petroleum reservoirs. In: Bear, J., Tsang, C., de Marsily, G. (eds.) Flow and Contaminant Transport in Fractured Rock, pp. 267–323. AcademicPress, San Diego (1993)

Makedonska, N., Painter, S.L., Bui, Q.M., Gable, C.W., Karra, S.: Particle tracking approach for transport in three-dimensional discrete fracture networks. Comput. Geosci. 19(5), 1123–1137 (2015). https://doi.org/10.1007/s10596-015-9525-4

Martin, V., Jaffré, J., Roberts, J.E.: Modeling fractures and barriers as interfaces for flow in porous media. SIAM J. Sci. Comput. 26(5), 1667–1691 (2005). https://doi.org/10.1137/S1064827503429363

Reichenberger, V., Jakobs, H., Bastian, P., Helmig, R.: A mixed-dimensional finite volume method for two-phase flow in fractured porous media. Adv. Water Resour. 29(7), 1020–1036 (2006). https://doi.org/10.1016/j.advwatres.2005.09.001

Sandve, T., Berre, I., Nordbotten, J.: An efficient multi-point flux approximation method for discrete fracture-matrix simulations. J. Comput. Phys. 231(9), 3784–3800 (2012). https://doi.org/10.1016/j.jcp.2012.01.023

Shapiro, A.M., Andersson, J.: Steady state fluid response in fractured rock: a boundary element solution for a coupled, discrete fracture continuum model. Water Resour. Res. 19(4), 959–969 (1983). https://doi.org/10.1029/WR019i004p00959

Warren, M.A., Root, P.J.: The behavior of naturally fractured reservoirs. Soc. Petrol. Eng. J. 3(3), 245–279 (1963)