Coupling schemes for modeling hydraulic fracture propagation using the XFEM

Computer Methods in Applied Mechanics and Engineering

Volumn 253, Issue , 2013, Pages 305-322

  Gordeliy, Elizaveta ^a   Peirce, Anthony ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Free boundary problems; Hydraulic fractures; XFEM

Indexed keywords

ASYMPTOTIC SOLUTIONS; BASIS FUNCTIONS; COUPLED ALGORITHMS; COUPLING SCHEME; CRACK PROBLEMS; DIRICHLET; DIRICHLET-TO-NEUMANN; ELASTIC CRACKS; ELASTIC MEDIUM; EXTENDED FINITE ELEMENT METHOD; FLUID FRONTS; FREE-BOUNDARY PROBLEMS; HYDRAULIC FRACTURE; HYDRAULIC FRACTURE PROPAGATION; LINEAR ELASTIC FRACTURE MECHANICS; POWER LAW INDEX; PRESSURE FIELD; REFERENCE SOLUTION; XFEM;

BRITTLE FRACTURE; COALESCENCE; CRACK PROPAGATION; CRACKS;

HYDRAULIC FRACTURING;

EID: 84868706538     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2012.08.017     Document Type: Article

References (53)

1. Jeffrey R., Mills K. Hydraulic fracturing applied to inducing longwall coal mine goaf falls. Pacific Rocks 2000 2000, 423-430. Balkema, Rotterdam.
2. van As A., Jeffrey R. Caving induced by hydraulic fracturing at Northparkes mines. Pacific Rocks 2000 2000, 353-360. Balkema, Rotterdam.
3. Valkó P., Economides M. Hydraulic Fracture Mechanics 1995, John Wiley & Sons, Chichester, UK.
4. Reservoir Stimulation 2000, John Wiley & Sons, Chichester, UK. third ed. M. Economides, K. Nolte (Eds.).
5. Frank U., Barkley N. Remediation of low permeability subsurface formations by fracturing enhancements of soil vapor extraction. J. Hazard. Mater. 2005, 40:191-201.
6. Murdoch L. Mechanical analysis of idealized shallow hydraulic fracture. J. Geotech. Geoenviron. 2002, 128(6):488-495.
7. A.R. Ingraffea, T.J. Boone, D.V. Swenson, Computer Simulation of Fracture Processes, 1991 (Chapter 12).
8. Shah K., Carter B., Ingraffea A. Hydraulic fracturing simulation in parallel computing environments. Int. J. Rock Mech. Min. Sci. 1997, 34(3/4):474.
9. Moës N., Dolbow J., Belytschko T. A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 1999, 46:131-150.
10. Stolarska M., Chopp D., Moes N., Belytschko T. Modeling crack growth by level sets and the extended finite element method. Int. J. Numer. Methods Eng. 2001, 51:943-960.
11. Sukumar N., Prevost J. Modeling quasi-static crack growth with the extended finite element method part i: computer implementation. Int. J. Solids Struct. 2002, 40:7513-7537.
12. A. Taleghani, Analysis of hydraulic fracture propagation in fractured reservoirs: an improved model for the interaction between induced and natural fractures, Ph.D. Thesis, The University of Texas at Austin, The University of Texas at Austin, May 2009.
13. Ren Q.-W., Dong Y.-W., Yu T.T. Numerical modeling of concrete hydraulic fracturing with extended finite element method. Sci. China Ser. E: Technol. Sci. 2009, 52:559-565.
14. Lecampion B. An extended finite element method for hydraulic fracture problems. Commun. Numer. Methods Eng. 2009, 25:121-133.
15. Desroches J., Detournay E., Lenoach B., Papanastasiou P., Pearson J., Thiercelin M., Cheng A.-D. The crack tip region in hydraulic fracturing. Proc. R. Soc. London, Ser. A 1994, 447:39-48.
16. Adachi J., Detournay E. Self-similar solution of a plane-strain fracture driven by a power-law fluid. Int. J. Numer. Anal. Methods Geomech. 2002, 26:579-604.
17. J. Adachi, E. Detournay, Plane-strain propagation of a fluid-driven fracture: finite toughness self-similar solution, Int. J. Solids Struct., in preparation.
18. Mitchell S.L., Kuske R., Peirce A.P. An asymptotic framework for the analysis of hydraulic fractures: the impermeable case. ASME J. Appl. Mech. 2007, 74(2):365-372.
19. Adachi J., Detournay E. Plane strain propagation of a hydraulic fracture in a permeable rock. Eng. Fract. Mech. 2008, 75(16):4666-4694.
20. Garagash D., Detournay E., Adachi J. Multiscale Tip Asymptotics in Hydraulic Fracture with Leak-off. J. Fluid Mech. 2011, 669:260-297.
21. Savitski A., Detournay E. Propagation of a fluid-driven penny-shaped fracture in an impermeable rock: asymptotic solutions. Int. J. Solids Struct. 2002, 39(26):6311-6337.
22. Bunger A., Detournay E. Asymptotic solution for a penny-shaped near-surface hydraulic fracture. Eng. Fract. Mech. 2005, 72(16):2468-2486.
23. Bunger A., Detournay E. Early time solution for a penny-shaped hydraulic fracture. ASCE J. Eng. Mech. 2007, 133(5):534-540.
24. Peirce A.P., Detournay E. An implicit level set method for modeling hydraulically driven fractures. Comput. Methods Appl. Mech. Eng. 2008, 197:2858-2885. 10.1016/j.cma.2008.01.013.
25. Mitchell S.L., Kuske R., Peirce A. An asymptotic framework for finite hydraulic fractures including leak-off. SIAM J. Appl. Math. 2007, 67(2):364-386.
26. E. Gordeliy, A.P. Peirce, D. Schötzau, Enrichment and convergence of the XFEM for hydraulic fracture problems, in preparation.
27. Carbonell R., Desroches J., Detournay E. A comparison between a semi-analytical and a numerical solution of a two-dimensional hydraulic fracture. Int. J. Solids Struct. 1999, 36(31-32):4869-4888.
28. Garagash D. Hydraulic fracture propagation in elastic rock with large toughness. Rock Around the Rim - Proc. 4th North American Rock Mechanics Symp. 2000, 221-228. Balkema, Rotterdam, pdf. J. Girard, M. Liebman, C. Breeds, T. Doe (Eds.).
29. Garagash D. Plane-strain propagation of a fluid-driven fracture during injection and shut-in: asymptotics of large toughness. Eng. Fract. Mech. 2006, 73(4):456-481. 10.1016/j.engfracmech.2005.07.012.
30. Rice J. Mathematical analysis in the mechanics of fracture. Fracture, an Advanced Treatise 1968, vol. II:191-311. Academic Press, New York, NY, (Chapter 3).
31. Detournay E. Propagation regimes of fluid-driven fractures in impermeable rocks. Int. J. Geomech. 2004, 4(1):1-11.
32. Peirce A.P. A Hermite cubic collocation scheme for plane strain hydraulic fractures. Comput. Methods Appl. Mech. Eng. 2010, 199(29-32):1949-1962. 10.1016/j.cma.2010.02.009.
33. Fries T.-P. A corrected XFEM approximation without problems in blending element. Int. J. Numer. Methods Eng. 2008, 75:503-532.
34. Ventura G., Gracie R., Belytschko T. Fast integration and weight function blending in the extended finite element method. Int. J. Numer. Methods Eng. 2009, 77:1-29.
35. Babuska I., Melenk J.M. The partition of unity method. Int. J. Numer. Methods Eng. 1997, 40:727-758.
36. Laborde P., Pommier J., Renard Y., Salaün M. High-order extended finite element method for cracked domains. Int. J. Numer. Methods Eng. 2005, 64:354-381.
37. Zilian A., Fries T.-P. A localized mixed-hybrid method for imposing interfacial constraints in the extended finite element method (XFEM). Int. J. Numer. Methods Eng. 2009, 79:733-752.
38. Marques J., Owen D. Infinite elements in quasi-static materially nonlinear problems. Comput. Struct. 1984, 18(4):739-751.
39. P. Bettess, Infinite Elements, Penshaw Press, 1992.
40. E. Gordeliy, E. Detournay, Numerical simulations of near-surface bowl-shaped hydraulic fractures, in preparation.
41. A. Bunger, E. Gordeliy, E. Detournay, Comparison between laboratory experiments and coupled simulations of saucer-shaped hydraulic fractures in homogeneous brittle-elastic solids, J. Mech. Phys. Solids, submitted for publication.
42. Gordeliy E., Detournay E. A fixed grid algorithm for simulating the propagation of a shallow hydraulic fracture with a fluid lag. Int. J. Numer. Anal. Methods Geomech. 2011, 35:602-629.
43. Erdogan F., Sih G.C. On the crack extension in plates under plate loading and transverse shear. J. Basic Eng. 1963, 85:519-527.
44. Zhang X., Detournay E., Jeffrey R. Propagation of a penny-shaped hydraulic fracture parallel to the free-surface on an elastic half-space. Int. J. Fract. 2002, 115:125-158.
45. E. Gordeliy, E. Detournay, Oribi: implicit fixed grid algorithm to simulate propagation of shallow hydraulic fractures, 2010. Available from: http://purl.umn.edu/57327.
46. R.S. Carbonell, Self-similar solution of a fluid-driven fracture, Ph.D. Thesis, University of Minnesota, Minneapolis, October 1996.
47. Belytschko T., Black T. Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Methods Eng. 1999, 45:601-620.
48. Moës N., Dolbow J., Belytschko T. A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 1999, 46:131-150.
49. Moës N., Gravouil A., Belytschko T. Non-planar 3d crack growth by the extended finite element and level sets - part i: mechanical model. Int. J. Numer. Methods Eng. 2002, 53:2549-2568.
50. Dolbow J.E., Gosz M. On the computation of mixed-mode stress intensity factors in functionally graded materials. Int. J. Solids Struct. 2002, 39:2557-2574.
51. Béchet E., Minnebo H., Moës N., Burgardt B. Improved implementation and robustness study of the X-FEM for stress analysis around cracks. Int. J. Numer. Methods Eng. 2005, 64:1033-1056.
52. Gosz M., Moran B. An interaction energy integral method for computation of mixed-mode stress intensity factors along non-planar crack fronts in three dimensions. Eng. Fract. Mech. 2002, 69:299-319.
53. Martin-Perez B., Pantazopoulou S.J., Thomas M.D.A. Numerical solution of mass transport equations in concrete structures. Comput. Struct. 2001, 79:1251-1264.