Abstract In this article, 3-D simulations of hydraulic fracture propagation with the Generalized Finite Element Method (GFEM) are compared with several experiments. The GFEM in this work uses mesh adaptivity and a quadratic basis to control discretization error while avoiding the mapping of 3-D solutions between propagation steps. Linear Elastic Fracture Mechanics is adopted and geometrical singular enrichments are used around the fracture front for robust and accurate stress intensity factors extraction. The time step that leads to satisfaction of the propagation criterion is computed automatically using a simple and yet computationally efficient algorithm. The laboratory experiments used in this article include planar and nonplanar fracture geometries as well as propagation in toughness- and viscosity-dominated regimes. The time evolution of fracture radius and opening, and wellbore fluid pressure are compared with experimental data. They show that the GFEM captures well the relevant physics of the hydraulic fracturing process. A modification is proposed to one of the experimental setups to explore and demonstrate the 3-D capabilities and robustness of the method.

中文翻译：

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三维水力压裂扩展的广义有限元方法：与实验的比较

摘要 在本文中，将使用广义有限元方法 (GFEM) 的水力压裂扩展 3-D 模拟与多个实验进行了比较。这项工作中的 GFEM 使用网格自适应和二次基来控制离散化误差，同时避免在传播步骤之间映射 3-D 解决方案。采用线弹性断裂力学，并在裂缝前沿周围使用几何奇异富集，以实现稳健而准确的应力强度因子提取。使用简单但计算效率高的算法自动计算导致满足传播标准的时间步长。本文中使用的实验室实验包括平面和非平面断裂几何形状以及在韧性和粘度占主导地位的情况下的传播。将裂缝半径和开度以及井筒流体压力的时间演化与实验数据进行了比较。他们表明 GFEM 很好地捕捉了水力压裂过程的相关物理。建议对其中一个实验设置进行修改，以探索和演示该方法的 3-D 功能和稳健性。