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Volumn 13, Issue 1, 2015, Pages 367-398

A phase-field method for propagating fluid-filled fractures coupled to a surrounding porous medium

Author keywords

Biot system; Finite elements; Fixed stress iterative coupling; Fracture propagation; Phase field

Indexed keywords

BENCHMARKING; FINITE ELEMENT METHOD; ITERATIVE METHODS; PHASE TRANSITIONS; POROUS MATERIALS;

EID: 84925146233     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/140967118     Document Type: Article
Times cited : (236)

References (47)
  • 2
    • 0007369404 scopus 로고
    • Consolidation settlement under a rectangular load distribution
    • M. A. BIOT, Consolidation settlement under a rectangular load distribution, J. Appl. Phys., 12 (1941), pp. 426-430.
    • (1941) J. Appl. Phys. , vol.12 , pp. 426-430
    • Biot, M.A.1
  • 3
    • 0345643551 scopus 로고
    • General theory of three-dimensional consolidation
    • M. A. BIOT, General theory of three-dimensional consolidation, J. Appl. Phys., 12 (1941), pp. 155-164.
    • (1941) J. Appl. Phys. , vol.12 , pp. 155-164
    • Biot, M.A.1
  • 4
    • 24944571072 scopus 로고
    • Theory of elasticity and consolidation for a porous anisotropic solid
    • M. A. BIOT, Theory of elasticity and consolidation for a porous anisotropic solid, J. Appl. Phys., 25 (1955), pp. 182-185.
    • (1955) J. Appl. Phys. , vol.25 , pp. 182-185
    • Biot, M.A.1
  • 6
    • 84874037791 scopus 로고    scopus 로고
    • A variational approach to the numerical simulation of hydraulic fracturing
    • Conference Paper 159154-MS
    • B. BOURDIN, C. CHUKWUDOZIE, AND K. YOSHIOKA, A variational approach to the numerical simulation of hydraulic fracturing, SPE Journal, Conference Paper 159154-MS, 2012.
    • (2012) SPE Journal
    • Bourdin, B.1    Chukwudozie, C.2    Yoshioka, K.3
  • 7
  • 9
    • 84877873156 scopus 로고    scopus 로고
    • An adaptive finite element approximation of a generalized Ambrosio-Tortorelli functional
    • 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.
    • (2013) Math. Models Methods Appl. Sci. , vol.23 , pp. 1663-1697
    • Burke, S.1    Ortner, C.2    Süli, E.3
  • 10
    • 84855197325 scopus 로고    scopus 로고
    • Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model
    • 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.
    • (2012) Eng. Fract. Mech. , vol.79 , pp. 312-328
    • Carrier, B.1    Granet, S.2
  • 11
    • 0029507393 scopus 로고
    • Coupled fluid flow and geomechanics in reservoir study I. Theory and governing equations
    • Conference Paper 30752
    • 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.
    • (1995) SPE Journal
    • Chen, H.-Y.1    Teufel, L.W.2    Lee, R.L.3
  • 15
    • 0031541111 scopus 로고    scopus 로고
    • An unsymmetric-pattern multifrontal method for sparse LU factorization
    • 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.
    • (1997) SIAM J. Matrix Anal. Appl. , vol.18 , pp. 140-158
    • Davis, T.A.1    Duff, I.S.2
  • 16
    • 58849129199 scopus 로고    scopus 로고
    • Hydraulic fracture predictions with a fully coupled geomechanical reservoir simulator
    • Conference Paper 116470-MS
    • R. H. DEAN AND J. H. SCHMIDT, Hydraulic fracture predictions with a fully coupled geomechanical reservoir simulator, SPE Journal, Conference Paper 116470-MS, 2008.
    • (2008) SPE Journal
    • Dean, R.H.1    Schmidt, J.H.2
  • 18
    • 84907314913 scopus 로고    scopus 로고
    • On the moving boundary conditions for a hydraulic fracture
    • E. DETOURNAY AND A. PEIRCE, On the moving boundary conditions for a hydraulic fracture, Internat. J. Engrg. Sci., 84 (2014), pp. 147-155.
    • (2014) Internat. J. Engrg. Sci. , vol.84 , pp. 147-155
    • Detournay, E.1    Peirce, A.2
  • 19
    • 0032139947 scopus 로고    scopus 로고
    • Revisiting brittle fracture as an energy minimization problem
    • G. A. FRANCFORT AND J.-J. MARIGO, Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, 46 (1998), pp. 1319-1342.
    • (1998) J. Mech. Phys. Solids , vol.46 , pp. 1319-1342
    • Francfort, G.A.1    Marigo, J.-J.2
  • 22
    • 84896574119 scopus 로고    scopus 로고
    • Modeling fluid injection in fractures with a reservoir simulator coupled to a boundary element method
    • 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.
    • (2014) Comput. Geosci. , vol.18 , pp. 613-624
    • Ganis, B.1    Mear, M.E.2    Sakhaee-Pour, A.3    Wheeler, M.F.4    Wick, T.5
  • 23
    • 0034155604 scopus 로고    scopus 로고
    • The tip region of a fluid-driven fracture in an elastic medium
    • 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.
    • (2000) ASME J. Appl. Mech. , vol.67 , pp. 183-192
    • Garagash, D.I.1    Detournay, E.2
  • 24
    • 0000357002 scopus 로고
    • The phenomena of rupture and flow in solids
    • A. A. GRIFFITH, The phenomena of rupture and flow in solids, Philos. Trans. R. Soc. Lond., 221 (1921), pp. 163-198.
    • (1921) Philos. Trans. R. Soc. Lond. , vol.221 , pp. 163-198
    • Griffith, A.A.1
  • 25
    • 84906099484 scopus 로고    scopus 로고
    • Simulation of non-planar three-dimensional hydraulic fracture propagation
    • 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.
    • (2014) Int. J. Numer. Anal. Meth. Geomech. , vol.38 , pp. 1397-1430
    • Gupta, P.1    Duarte, C.A.2
  • 26
    • 84870583301 scopus 로고    scopus 로고
    • Interaction between injection points during hydraulic fracturing
    • K. M. D. HALS AND I. BERRE, Interaction between injection points during hydraulic fracturing, Water Resour. Res., 48 (2012), doi: 10.1029/2012WR012265.
    • (2012) Water Resour. Res. , vol.48
    • Hals, K.M.D.1    Berre, I.2
  • 28
    • 77956102470 scopus 로고    scopus 로고
    • Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations
    • 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.
    • (2013) Internat. J. Numer. Methods Engrg. , vol.83 , pp. 1273-1311
    • Hofacker, M.1    Miehe, C.2    Welschinger, F.3
  • 29
    • 84872692898 scopus 로고    scopus 로고
    • A large deformation formulation for fluid flow in a progressively fracturing porous material
    • 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.
    • (2013) Comput. Methods Appl. Mech. Engrg. , vol.256 , pp. 29-37
    • Irzal, F.1    Remmers, J.J.C.2    Huyghe, J.M.3    De Borst, R.4
  • 30
    • 84892896941 scopus 로고    scopus 로고
    • A peridynamic formulation of pressure driven convective fluid transport in porous media
    • 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.
    • (2014) J. Comput. Phys. , vol.261 , pp. 209-229
    • Katiyar, A.1    Foster, J.T.2    Ouchi, H.3    Sharma, M.M.4
  • 33
    • 34548761354 scopus 로고    scopus 로고
    • An implicit algorithm for the propagation of hydraulic fracture with a fluid lag
    • 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.
    • (2007) Comput. Methods Appl. Mech. Engrg. , vol.196 , pp. 4863-4880
    • Lecampion, B.1    Detournay, E.2
  • 34
    • 84906942133 scopus 로고    scopus 로고
    • Numerical convergence study of iterative coupling for coupled flow and geomechanics
    • 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.
    • (2014) Comput. Geosci. , vol.18 , pp. 325-341
    • MikeliĆ, A.1    Wang, B.2    Wheeler, M.F.3
  • 35
    • 84876979141 scopus 로고    scopus 로고
    • Convergence of iterative coupling for coupled flow and geomechanics
    • A. MIKELIĆ AND M. F. WHEELER, Convergence of iterative coupling for coupled flow and geomechanics, Comput. Geosci., 17 (2013), pp. 455-461.
    • (2013) Comput. Geosci. , vol.17 , pp. 455-461
    • MikeliĆ, A.1    Wheeler, M.F.2
  • 39
    • 34247588057 scopus 로고    scopus 로고
    • An asymptotic framework for finite hydraulic fractures including leak-off
    • 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.
    • (2007) SIAM J. Appl. Math. , vol.67 , pp. 364-386
    • Mitchell, S.L.1    Kuske, R.2    Peirce, A.P.3
  • 40
    • 27744521353 scopus 로고    scopus 로고
    • On adaptive refinement techniques in multi-field problems including cohesive fracture
    • 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.
    • (2006) Comput. Methods Appl. Mech. Engrg. , vol.195 , pp. 444-461
    • Schrefler, B.A.1    Secchi, S.T.2    Simoni, L.3
  • 41
    • 0035454209 scopus 로고    scopus 로고
    • Advances in coupled geomechanical and reservoir modeling with applications to reservoir compaction
    • 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.
    • (2001) SPE J. , vol.6 , pp. 334-342
    • Settari, A.1    Walters, D.A.2
  • 42
    • 0004096099 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, UK
    • nd ed., Cambridge University Press, Cambridge, UK, 2011.
    • (2011) nd Ed.
    • Szeri, A.Z.1
  • 43
    • 79957521424 scopus 로고    scopus 로고
    • Finite element modeling of hydraulic fracturing on a reservoir scale in 2d
    • M. WANGEN, Finite element modeling of hydraulic fracturing on a reservoir scale in 2d, J. Petrol. Sci. Eng., 77 (2011), pp. 274-285.
    • (2011) J. Petrol. Sci. Eng. , vol.77 , pp. 274-285
    • Wangen, M.1
  • 44
    • 84880081381 scopus 로고    scopus 로고
    • Finite element modeling of hydraulic fracturing in 3D
    • M. WANGEN, Finite element modeling of hydraulic fracturing in 3D, Comput. Geosci., 17 (2013), pp. 647-659.
    • (2013) Comput. Geosci. , vol.17 , pp. 647-659
    • Wangen, M.1
  • 45
    • 84892887557 scopus 로고    scopus 로고
    • An augmented-Lagrangian method for the phase-field approach for pressurized fractures
    • 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.
    • (2014) Comput. Methods Appl. Mech. Engrg. , vol.271 , pp. 69-85
    • Wheeler, M.F.1    Wick, T.2    Wollner, W.3
  • 46
    • 84892624201 scopus 로고    scopus 로고
    • Solving monolithic fluid-structure interaction problems in arbitrary Lagrangian Eulerian coordinates with the deal.ii library
    • 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.
    • (2013) Arch. Numer. Software , vol.1 , pp. 1-19
    • Wick, T.1
  • 47
    • 84927660812 scopus 로고    scopus 로고
    • Pressurized fracture propagation using a phase-field approach coupled to a reservoir simulator
    • SPE 168597-MS
    • 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.
    • SPE Proc., 2013
    • Wick, T.1    Singh, G.2    Wheeler, M.F.3


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