Abstract A fully coupled enriched-FEM (XFEM) model is proposed to investigate the interaction between hydraulic fractures and natural fractures in finite 2D porous media. The weak forms of both equilibrium and continuity equations are discretized in an enriched form in the space and by the Newmark scheme in the time domain. The Newton-Raphson method is adopted to solve these discretized equations. To account for the fluid flow in the porous matrix, 2D fluid leakage from the fractures to the matrix is considered by imposing internal flux boundary conditions on the fracture surfaces. A posteriori analysis is carried out to determine the equivalent leak off coefficient of the 1D Carter’s leak off law. The frictional contact of the fracture surface is modeled by the penalty method in the model. The junction ridge function is adopted to describe the weak discontinuities of the pressure field in the elements containing fracture intersection points. A crack initiation criterion based on the average tensile stress along the natural fracture is used to determine whether a hydraulic fracture can cross a natural fracture. The presented model is first validated against the analytical solutions of the KGD model and then several numerical examples are simulated to investigate the effects of the natural fracture properties, treatment parameters, matrix permeability, anisotropy stress and approaching angle on the interaction between hydraulic fractures and natural fractures. The numerical results suggest the acceptable accuracy and robustness of the presented model on modeling fracture interaction behaviors in the presence of fluid leakage into matrix.

中文翻译：

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基于富集有限元法的多孔介质中水力裂缝与天然裂缝相互作用的数值研究

摘要 提出了一种全耦合富集有限元（XFEM）模型来研究有限二维多孔介质中水力裂缝和天然裂缝之间的相互作用。平衡方程和连续方程的弱形式在空间中以丰富形式离散化，在时域中通过 Newmark 格式离散化。采用牛顿-拉夫森方法来求解这些离散方程。为了考虑多孔基质中的流体流动，通过在裂缝表面上施加内部通量边界条件来考虑从裂缝到基质的二维流体泄漏。进行后验分析以确定一维卡特泄漏定律的等效泄漏系数。断裂面的摩擦接触通过模型中的惩罚方法进行建模。采用交界脊函数来描述包含裂缝交点的单元中压力场的弱不连续性。基于沿天然裂缝的平均拉伸应力的裂纹萌生准则用于确定水力裂缝是否可以穿过天然裂缝。所提出的模型首先针对 KGD 模型的解析解进行验证，然后通过几个数值例子来研究天然裂缝性质、处理参数、基质渗透率、各向异性应力和接近角对水力裂缝与天然裂缝相互作用的影响。骨折。