A finite element approach to the simulation of hydraulic fractures with lag

We presented a finite-element-based algorithm to simulate plane-strain, straight hydraulic fractures in an impermeable elastic medium. The algorithm acCOllllts for the nonlinear coupling between the fluid pressure and the crack opening and separately tracks the evolution of the crack tip and the fluid front. It therefore allows the existence of a fluid lag. The fluid front is advanced explicitly in time, but an implicit strategy is needed for the crack tip to guarantee the satisfaction of Griffith's criterion at each time step. We enforced the coupling between the fluid and the rock by simultaneously solving for the pressure field in the fluid and the crack opening at each time step. We provided verification of our algorithm by performing sample simulations and comparing them with two known similarity solutions.

[1]  Emmanuel M Detournay,et al.  Plane strain propagation of a hydraulic fracture in a permeable rock , 2008 .

[2]  Anthony Peirce,et al.  An efficient multi‐layer planar 3D fracture growth algorithm using a fixed mesh approach , 2002 .

[3]  M. Popescu.  Boundary element methods in solid mechanics , 1985 .

[4]  Rodney J. Clifton,et al.  Containment of massive hydraulic fractures , 1978 .

[5]  Jose Adachi,et al.  Computer simulation of hydraulic fractures , 2007 .

[6]  Ahmed S. Abou-Sayed,et al.  A Variational Approach To The Prediction Of The Three-Dimensional Geometry Of Hydraulic Fractures , 1981 .

[7]  R. D. Barree,et al.  A practical numerical simulator for three-dimensional fracture propagation in heterogeneous media , 1983 .

[8]  Emmanuel M Detournay,et al.  The Tip Region of a Fluid-Driven Fracture in an Elastic Medium , 2000 .

[9]  Yu.N. Gordeyev,et al.  Growth of a crack produced by hydraulic fracture in a poroelastic medium , 1993 .

[10]  Graham F. Carey,et al.  Derivative calculation from finite element solutions , 1982 .

[11]  Emmanuel M Detournay,et al.  The crack tip region in hydraulic fracturing , 1994, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[12]  B. Lecampion.  An extended finite element method for hydraulic fracture problems , 2009 .

[13]  A. Khristianovic Zheltov,et al.  3. Formation of Vertical Fractures by Means of Highly Viscous Liquid , 1955 .

[14]  T. K. Perkins,et al.  Widths of Hydraulic Fractures , 1961 .

[15]  Emmanuel M Detournay,et al.  Self‐similar solution of a plane‐strain fracture driven by a power‐law fluid , 2002 .

[16]  Rodney J. Clifton,et al.  Adaptive Optimal Mesh Generator For Hydraulic Fracturing Modeling , 1992 .

[17]  M. Dowell,et al.  The “Pegasus” method for computing the root of an equation , 1972 .

[18]  Emmanuel M Detournay,et al.  Plane-Strain Propagation of a Fluid-Driven Fracture: Small Toughness Solution , 2005 .

[19]  T. Fries.  A corrected XFEM approximation without problems in blending elements , 2008 .

[20]  Emmanuel M Detournay,et al.  Propagation Regimes of Fluid-Driven Fractures in Impermeable Rocks , 2004 .

[21]  Anthony R. Ingraffea,et al.  Simulation of hydraulic fracture propagation in poroelastic rock with application to stress measurement techniques , 1991 .

[22]  R. P. Nordgren,et al.  Propagation of a Vertical Hydraulic Fracture , 1972 .

[23]  T. Belytschko,et al.  Non‐planar 3D crack growth by the extended finite element and level sets—Part I: Mechanical model , 2002 .

[24]  Dmitry I. Garagash,et al.  Propagation of a plane-strain hydraulic fracture with a fluid lag: Early-time solution , 2006 .

[25]  M. Dowell,et al.  A modified regula falsi method for computing the root of an equation , 1971 .

[26]  B. Moran,et al.  An interaction energy integral method for computation of mixed-mode stress intensity factors along non-planar crack fronts in three dimensions , 2002 .

[27]  N. Moës,et al.  Improved implementation and robustness study of the X‐FEM for stress analysis around cracks , 2005 .

[28]  J. Geertsma,et al.  A Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures , 1969 .

[29]  Adrian J. Lew,et al.  An optimally convergent discontinuous Galerkin‐based extended finite element method for fracture mechanics , 2010 .

[30]  Luciano Simoni,et al.  Cohesive fracture mechanics for a multi‐phase porous medium , 2003 .

[31]  M. Biot.  General Theory of Three‐Dimensional Consolidation , 1941 .

[32]  A. D. Taleghani.  Analysis of hydraulic fracture propagation in fractured reservoirs: An improved model for the interaction between induced and natural fractures , 2009 .

[33]  Jon E. Olson,et al.  Analysis of Multistranded Hydraulic Fracture Propagation: An Improved Model for the Interaction Between Induced and Natural Fractures , 2009 .

[34]  A. R. Ingraffea,et al.  Simulating Fully 3 D Hydraulic Fracturing , 2003 .

[35]  P. W. Sharp,et al.  Self-similar solutions for elastohydrodynamic cavity flow , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[36]  Emmanuel M Detournay,et al.  An implicit algorithm for the propagation of a hydraulic fracture with a fluid lag , 2007 .

[37]  Dan Givoli,et al.  A finite element method for large domains , 1989 .

[38]  Allan M. Rubin,et al.  Propagation of Magma-Filled Cracks , 1995 .

[39]  Dmitry I. Garagash,et al.  Plane-strain propagation of a fluid-driven fracture during injection and shut-in: Asymptotics of large toughness , 2006 .