Modeling the interaction between fluid-driven fracture and natural fault using an enriched-FEM technique

In this paper, the interaction between the fluid-driven fracture and frictional natural fault is modeled using an enriched-FEM technique based on the partition of unity method. The intersection between two discontinuities is modeled by introducing a junction enrichment function. In order to model the fluid effect within the fracture, the fluid pressure is assumed to be constant throughout the propagation process. The frictional contact behavior along the fault faces is modeled using an X-FEM penalty method within the context of the plasticity theory of friction. Finally, several numerical examples are solved to illustrate the accuracy and robustness of proposed computational algorithm as well as to investigate the mechanism of interaction between the fluid-driven fracture and the natural fault.

[1]  T. Belytschko,et al.  A method for multiple crack growth in brittle materials without remeshing , 2004 .

[2]  J. Cosgrove,et al.  Analysis of geological structures , 1989 .

[3]  Thomas J. Boone,et al.  A numerical procedure for simulation of hydraulically-driven fracture propagation in poroelastic media , 1990 .

[4]  M. C. Fehler,et al.  Hydraulic Fracturing of Jointed Formations , 1986 .

[5]  Agust Gudmundsson,et al.  Arrest and aperture variation of hydrofractures in layered reservoirs , 2004, Geological Society, London, Special Publications.

[6]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[7]  Amir R. Khoei,et al.  A Lagrangian-extended finite-element method in modeling large-plasticity deformations and contact problems , 2009 .

[8]  Ted Belytschko,et al.  Modelling crack growth by level sets in the extended finite element method , 2001 .

[9]  Ronaldo I. Borja,et al.  A contact algorithm for frictional crack propagation with the extended finite element method , 2008 .

[10]  T. Dahm Numerical simulations of the propagation path and the arrest of fluid‐filled fractures in the Earth , 2000 .

[11]  T. Belytschko,et al.  A method for growing multiple cracks without remeshing and its application to fatigue crack growth , 2004 .

[12]  Abbas Ali Daneshy,et al.  Hydraulic Fracture Propagation in the Presence of Planes of Weakness , 1974 .

[13]  Abbas Ali Daneshy,et al.  Hydraulic Fracture Propagation in Layered Formations , 1978 .

[14]  Amir R. Khoei,et al.  An augmented Lagrangian contact formulation for frictional discontinuities with the extended finite element method , 2015 .

[15]  Ahmad Ghassemi,et al.  Simulation of hydraulic fracture propagation near a natural fracture using virtual multidimensional internal bonds , 2011 .

[16]  Robert G. Jeffrey,et al.  A Comparison of Hydraulic Fracture Field Experiments, Including Mineback Geometry Data, with Numerical Fracture Model Simulations , 1995 .

[17]  T. L. Blanton,et al.  An Experimental Study of Interaction Between Hydraulically Induced and Pre-Existing Fractures , 1982 .

[18]  A. V. Akulich,et al.  Interaction between hydraulic and natural fractures , 2008 .

[19]  A. Khoei,et al.  An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model , 2013 .

[20]  D. Chopp,et al.  Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method , 2003 .

[21]  A. Khoei Extended Finite Element Method: Theory and Applications , 2015 .

[22]  Agust Gudmundsson,et al.  How hydrofractures become arrested , 2001 .

[23]  Amir R. Khoei,et al.  An enriched finite element algorithm for numerical computation of contact friction problems , 2007 .

[24]  Arcady Dyskin,et al.  Orthogonal crack approaching an interface , 2009 .

[25]  Jon E. Olson,et al.  Numerical Modeling of Multistranded-Hydraulic-Fracture Propagation: Accounting for the Interaction Between Induced and Natural Fractures , 2009 .

[26]  Julien Réthoré,et al.  A two‐scale approach for fluid flow in fractured porous media , 2006 .

[27]  F. W. Jessen,et al.  The Effects of Existing Fractures in Rocks on the Extension of Hydraulic Fractures , 1963 .

[28]  Bernhard A. Schrefler,et al.  On adaptive refinement techniques in multi-field problems including cohesive fracture , 2006 .

[29]  C. J. de Pater,et al.  Numerical implementation of displacement discontinuity method and its application in hydraulic fracturing , 2001 .

[30]  Amir R. Khoei,et al.  A mesh-independent finite element formulation for modeling crack growth in saturated porous media based on an enriched-FEM technique , 2014, International Journal of Fracture.

[31]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[32]  Yan Jin,et al.  Analysis of fracture propagation behavior and fracture geometry using a tri-axial fracturing system in naturally fractured reservoirs , 2008 .

[33]  M. E. Hanson,et al.  Theoretical and Experimental Research on Hydraulic Fracturing , 1980 .

[34]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[35]  Amir R. Khoei,et al.  A numerical contact algorithm in saturated porous media with the extended finite element method , 2014 .

[36]  Alfred Daniel Hill,et al.  The Effect of Natural Fractures on Hydraulic Fracture Propagation , 2005 .

[37]  Norman R. Warpinski,et al.  Influence of Geologic Discontinuities on Hydraulic Fracture Propagation (includes associated papers 17011 and 17074 ) , 1984 .

[38]  G. D. Anderson Effects of Friction on Hydraulic Fracture Growth Near Unbonded Interfaces in Rocks , 1981 .

[39]  T. Belytschko,et al.  Arbitrary branched and intersecting cracks with the eXtended Finite Element Method , 2000 .

[40]  Amir R. Khoei,et al.  An enriched FEM technique for modeling hydraulically driven cohesive fracture propagation in impermeable media with frictional natural faults: Numerical and experimental investigations , 2015 .

[41]  Robert G. Jeffrey,et al.  Deflection and propagation of fluid-driven fractures at frictional bedding interfaces: A numerical investigation , 2007 .

[42]  Jia Li,et al.  Debonding of the interface as 'crack arrestor' , 2000 .