Field data suggest that hydraulic fractures under in situ conditions are three-dimensional and non-planar in shale gas reservoirs. In this study, a fully coupled deformation, fracture growth, and fluid flow model is developed to simulate this complex phenomenon with a focus on the reduction of the total computational effort. An extended finite element method with high-order tip enrichment functions is used to simulate the rock deformation while the finite element method for the laminar flow in fractures. The explicit fracture representation is adopted to describe the non-planar 3D fractures. Schemes for identifying the fluid elements, selecting the enriched nodes, and subdividing the enriched elements are presented. The Newton-Raphson scheme is used to solve the coupled equilibrium and fluid flow equations in an element-by-element fashion. Within each Newton-Raphson iteration step, only enriched degrees of freedom are involved in the solution process by using the reduction technique to further reduce the computational effort. A displacement extrapolation method considering high-order terms is proposed to extract stress intensity factors from the displacement field. Several examples are performed to demonstrate the applicability and effectiveness of the proposed approach. The effectiveness of MPI parallel implementation of the proposed method is also investigated.

现场数据表明，在页岩气储层中，原位条件下的水力压裂是三维的且非平面的。在这项研究中，开发了一个完全耦合的变形，裂缝扩展和流体流动模型来模拟此复杂现象，重点是减少总计算量。具有高阶尖端富集功能的扩展有限元方法用于模拟岩石变形，而裂缝中层流的有限元方法则用于模拟岩石变形。采用显式裂缝表示来描述非平面3D裂缝。提出了识别流体元素，选择富集节点和细分富集元素的方案。牛顿-拉夫森（Newton-Raphson）方案用于逐个元素地求解耦合的平衡和流体流动方程。在每个Newton-Raphson迭代步骤中，通过使用归约技术进一步减少计算量，仅丰富的自由度参与了求解过程。提出了一种考虑高阶项的位移外推法，从位移场中提取应力强度因子。进行了几个例子来证明所提出方法的适用性和有效性。还研究了MPI并行实现该方法的有效性。进行了几个例子来证明所提出方法的适用性和有效性。还研究了MPI并行实现该方法的有效性。进行了几个例子来证明所提出方法的适用性和有效性。还研究了MPI并行实现该方法的有效性。