×

zbMATH — the first resource for mathematics

A phase-field method for propagating fluid-filled fractures coupled to a surrounding porous medium. (English) Zbl 1317.74028

MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics
76S05 Flows in porous media; filtration; seepage
35Q86 PDEs in connection with geophysics
74A45 Theories of fracture and damage
Software:
deal.ii
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] W. Bangerth, T. Heister, G. Kanschat, et al., Differential Equations Analysis Library, 2012.
[2] M. A. Biot, Consolidation settlement under a rectangular load distribution, J. Appl. Phys., 12 (1941), pp. 426–430. · JFM 67.0837.02
[3] M. A. Biot, General theory of three-dimensional consolidation, J. Appl. Phys., 12 (1941), pp. 155–164. · JFM 67.0837.01
[4] M. A. Biot, Theory of elasticity and consolidation for a porous anisotropic solid, J. Appl. Phys., 25 (1955), pp. 182–185. · Zbl 0067.23603
[5] M. J. Borden, C. V. Verhoosel, M. A. Scott, T. J. R. Hughes, and C. M. Landis, A phase-field description of dynamic brittle fracture, Comput. Methods Appl. Mech. Engrg., 217 (2012), pp. 77–95. · Zbl 1253.74089
[6] B. Bourdin, C. Chukwudozie, and K. Yoshioka, A variational approach to the numerical simulation of hydraulic fracturing, SPE Journal, Conference Paper 159154-MS, 2012.
[7] B. Bourdin, G. A. Francfort, and J.-J. Marigo, Numerical experiments in revisited brittle fracture, J. Mech. Phys. Solids, 48 (2000), pp. 797–826. · Zbl 0995.74057
[8] B. Bourdin, G. A. Francfort, and J.-J. Marigo, The variational approach to fracture, J. Elasticity, 91 (2008), pp. 1–148. · Zbl 1176.74018
[9] S. Burke, C. Ortner, and E. Süli, An adaptive finite element approximation of a generalized Ambrosio-Tortorelli functional, Math. Models Methods Appl. Sci., 23 (2013), pp. 1663–1697. · Zbl 1266.74044
[10] B. Carrier and S. Granet, Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model, Eng. Fract. Mech., 79 (2012), pp. 312–328.
[11] H.-Y. Chen, L. W. Teufel, and R. L. Lee, Coupled fluid flow and geomechanics in reservoir study I. Theory and governing equations, SPE Journal, Conference Paper 30752, 1995.
[12] Z. Chen, G. Huan, and Y. Ma, Computational Methods for Multiphase Flows in Porous Media, SIAM, Philadelphia, 2006. · Zbl 1092.76001
[13] O. Coussy, Mechanics of Porous Continua, Wiley, New York, 1995. · Zbl 0838.73001
[14] O. Coussy, Poromechanics, Wiley, New York, 2004.
[15] T. A. Davis and I. S. Duff, An unsymmetric-pattern multifrontal method for sparse LU factorization, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 140–158. · Zbl 0884.65021
[16] R. H. Dean and J. H. Schmidt, Hydraulic fracture predictions with a fully coupled geomechanical reservoir simulator, SPE Journal, Conference Paper 116470-MS, 2008.
[17] J. Desroches, E. Detournay, B. Lenoach, P. Papanastasiou, J. R. A. Pearson, M. Thiercelin, and A. Cheng, The crack tip region in hydraulic fracturing, Proc. R. Soc. Lond., 447 (1994), pp. 39–48. · Zbl 0813.73051
[18] E. Detournay and A. Peirce, On the moving boundary conditions for a hydraulic fracture, Internat. J. Engrg. Sci., 84 (2014), pp. 147–155.
[19] G. A. Francfort and J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, 46 (1998), pp. 1319–1342. · Zbl 0966.74060
[20] X. Gai, A Coupled Geomechanics and Reservoir Flow Model on Parallel Computers, Ph.D. thesis, The University of Texas at Austin, Austin, TX, 2004.
[21] B. Ganis, V. Girault, M. Mear, G. Singh, and M. F. Wheeler, Modeling fractures in a poro-elastic medium, Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles, 69 (2014), pp. 515–528.
[22] B. Ganis, M. E. Mear, A. Sakhaee-Pour, M. F. Wheeler, and T. Wick, Modeling fluid injection in fractures with a reservoir simulator coupled to a boundary element method, Comput. Geosci., 18 (2014), pp. 613–624. · Zbl 1392.76078
[23] D. I. Garagash and E. Detournay, The tip region of a fluid-driven fracture in an elastic medium, ASME J. Appl. Mech., 67 (2000), pp. 183–192. · Zbl 1110.74448
[24] A. A. Griffith, The phenomena of rupture and flow in solids, Philos. Trans. R. Soc. Lond., 221 (1921), pp. 163–198.
[25] P. Gupta and C. A. Duarte, Simulation of non-planar three-dimensional hydraulic fracture propagation, Int. J. Numer. Anal. Meth. Geomech., 38 (2014), pp. 1397–1430.
[26] K. M. D. Hals and I. Berre, Interaction between injection points during hydraulic fracturing, Water Resour. Res., 48 (2012), doi: 10.1029/2012WR012265.
[27] T. Heister, M. F. Wheeler, and T. Wick, A Primal-Dual Active Set Method and Predictor-Corrector Mesh Adaptivity for Computing Fracture Propagation Using a Phase-Field Approach, Tech. Report, ICES-Preprint 14-27, The University of Texas, Austin, TX, 2014; available online from \burlhttps://www.ices.utexas.edu/research/reports/.
[28] M. Hofacker, C. Miehe, and F. Welschinger, Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations, Internat. J. Numer. Methods Engrg., 83 (2013), pp. 1273–1311. · Zbl 1202.74014
[29] F. Irzal, J. J. C. Remmers, J. M. Huyghe, and R. de Borst, A large deformation formulation for fluid flow in a progressively fracturing porous material, Comput. Methods Appl. Mech. Engrg., 256 (2013), pp. 29–37. · Zbl 1352.76113
[30] A. Katiyar, J. T. Foster, H. Ouchi, and M. M. Sharma, A peridynamic formulation of pressure driven convective fluid transport in porous media, J. Comput. Phys., 261 (2014), pp. 209–229. · Zbl 1349.76819
[31] Y. Kovalyshen, Fluid-Driven Fracture in Poroelastic Medium, Ph.D. thesis, University of Minnesota, Minneapolis, MN, 2010.
[32] O. A. Ladyzhenskaja, V. A. Solonnikov, and N. N. Uralceva, Linear and Quasi-linear Equations of Parabolic Type, Transl. Math. Monogr. 23, AMS, Providence, RI, 1968.
[33] B. Lecampion and E. Detournay, An implicit algorithm for the propagation of hydraulic fracture with a fluid lag, Comput. Methods Appl. Mech. Engrg., 196 (2007), pp. 4863–4880. · Zbl 1173.74383
[34] A. Mikelić, B. Wang, and M. F. Wheeler, Numerical convergence study of iterative coupling for coupled flow and geomechanics, Comput. Geosci., 18 (2014), pp. 325–341. · Zbl 1386.76115
[35] A. Mikelić and M. F. Wheeler, Convergence of iterative coupling for coupled flow and geomechanics, Comput. Geosci., 17 (2013), pp. 455–461. · Zbl 1392.35235
[36] A. Mikelić, M. F. Wheeler, and T. Wick, A Phase-Field Approach to the Fluid Filled Fracture Surrounded by a Poroelastic Medium, ICES-Preprint 13-15, The University of Texas, Austin, TX, 2013.
[37] A. Mikelić, M. F. Wheeler, and T. Wick, A Quasi-static Phase-Field Approach to the Fluid Filled Fracture, ICES-Preprint 13-22, The University of Texas, Austin, TX, 2013, submitted.
[38] A. Mikelić, M. F. Wheeler, and T. Wick, Phase-Field Modeling of Pressurized Fractures in a Poroelastic Medium, ICES-Preprint 14-18, The University of Texas, Austin, TX, 2014, submitted.
[39] S. L. Mitchell, R. Kuske, and A. P. Peirce, An asymptotic framework for finite hydraulic fractures including leak-off, SIAM J. Appl. Math., 67 (2007), pp. 364–386. · Zbl 1110.74047
[40] B. A. Schrefler, St. Secchi, and L. Simoni, On adaptive refinement techniques in multi-field problems including cohesive fracture, Comput. Methods Appl. Mech. Engrg., 195 (2006), pp. 444–461. · Zbl 1193.74158
[41] A. Settari and D. A. Walters, Advances in coupled geomechanical and reservoir modeling with applications to reservoir compaction, SPE J., 6 (2001), pp. 334–342.
[42] A. Z. Szeri, Fluid Film Lubrication, 2nd ed., Cambridge University Press, Cambridge, UK, 2011. · Zbl 1001.76001
[43] M. Wangen, Finite element modeling of hydraulic fracturing on a reservoir scale in 2d, J. Petrol. Sci. Eng., 77 (2011), pp. 274–285.
[44] M. Wangen, Finite element modeling of hydraulic fracturing in \(3\)D, Comput. Geosci., 17 (2013), pp. 647–659. · Zbl 1387.74116
[45] M. F. Wheeler, T. Wick, and W. Wollner, An augmented-Lagrangian method for the phase-field approach for pressurized fractures, Comput. Methods Appl. Mech. Engrg., 271 (2014), pp. 69–85. · Zbl 1296.65170
[46] T. Wick, Solving monolithic fluid-structure interaction problems in arbitrary Lagrangian Eulerian coordinates with the deal.ii library, Arch. Numer. Software, 1 (2013), pp. 1–19.
[47] T. Wick, G. Singh, and M. F. Wheeler, Pressurized fracture propagation using a phase-field approach coupled to a reservoir simulator, SPE 168597-MS, SPE Proc., 2013.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.