Abstract In this study, a fully coupled model is presented for simulating the propagation of multiple hydraulic fractures in anisotropic formation. Rock anisotropy is captured by using anisotropic constitutive relation to describe solid deformation and using modified maximum circumferential stress to determine fracture propagation. Besides, fluid flow in the wellbore is established to partition injection into each fracture for consideration of stress shadowing effect. The extended finite element method is used in the discretization of stress equation, and Newton’ iteration is proposed to solve the fully coupled problems. The numerical method is verified against other solutions for one fracture and two fractures propagation problems in the literature. The effect of rock anisotropy on hydraulic fractures is analyzed in the following aspects: material angle, ratio of Young's modulus and fracture toughness. If material angle is not aligned with fractures initiating direction, fractures would deflect towards the direction of material angle. Ratio of Young's modulus could enhance this effect, but it is in the opposite for ratio of fracture toughness. Results indicate that the simultaneous propagation of multiple hydraulic fractures in anisotropic formation is determined by two competing factors: stress shadowing and rock anisotropy.

中文翻译：

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各向异性地层多裂缝扩展数值模拟

摘要 在这项研究中，提出了一个全耦合模型，用于模拟各向异性地层中多个水力压裂的扩展。岩石各向异性是通过使用各向异性本构关系来描述固体变形并使用修正的最大周向应力来确定裂缝扩展来捕获的。此外，为了考虑应力遮蔽效应，在井筒内建立流体流动以将注入分配到每个裂缝中。应力方程的离散化采用扩展有限元法，提出牛顿迭代法求解全耦合问题。该数值方法针对文献中的一个裂缝和两个裂缝扩展问题的其他解决方案进行了验证。从以下几个方面分析岩石各向异性对水力裂缝的影响：材料角度、杨氏模量与断裂韧性之比。如果材料角与裂缝起始方向不一致，则裂缝会向材料角方向偏转。杨氏模量比可以增强这种效果，但断裂韧度比则相反。结果表明，各向异性地层中多个水力裂缝的同时扩展由两个相互竞争的因素决定：应力阴影和岩石各向异性。