Two‐dimensional hydraulic fracturing simulations using the cohesive zone model (CZM) can be readily found in the literature; however, to our knowledge, verified 3D cohesive zone modeling is not available. We present the development of a 3D fully coupled hydro‐mechanical finite element method (FEM) model (with parallel computation framework) and its application to hydraulic fracturing. A special zero‐thickness interface element based on the CZM is developed for modeling fracture propagation and fluid flow. A local traction‐separation law with strain softening is used to capture tensile cracking. The model is verified by considering penny‐shaped hydraulic fracture and plain strain Kristianovich‑Geertsma‑de Klerk hydraulic fracture (in 3D) in the viscosity‐ and toughness‐dominated regimes. Good agreement between numerical results and analytical solutions has been achieved. The model is used to investigate the influence of rock and fluid properties on hydraulic fracturing. Lower stiffness tip cohesive elements tend to yield a larger elastic deformation around the fracture tips before the tensile strength is reached, generating a larger fracture length and lower fracture pressure compared with higher stiffness elements. It is found that the energy release rate has almost no influence on hydraulic fracturing in the viscosity‐dominated regime because the energy spent in creating new fractures is too small when compared with the total input energy. For the toughness‐dominated regime, the released energy during fracturing should be accurately captured; relatively large tensile strength should be used in order to match numerical results to the asymptotic analytical solutions. It requires smaller elements when compared with those used in the viscosity‐dominated regime.

中文翻译：

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使用耦合的水力-机械界面元素对3D平面水力裂缝传播进行有限元模拟

在文献中可以很容易地找到使用粘性区模型（CZM）的二维水力压裂模拟。但是，据我们所知，尚无经过验证的3D粘合区域建模。我们介绍了3D完全耦合的液压机械有限元方法（FEM）模型（具有并行计算框架）的开发及其在水力压裂中的应用。开发了一种基于CZM的特殊零厚度界面元素，用于模拟裂缝扩展和流体流动。使用具有应变软化作用的局部牵引分离定律来捕获拉伸裂纹。在粘性和韧性为主的情况下，通过考虑便士形的水力压裂和普通应变Kristianovich-Geertsma-de Klerk的水力压裂（以3D形式）进行了验证。数值结果与解析解之间已取得良好的一致性。该模型用于研究岩石和流体性质对水力压裂的影响。较低刚度的尖端内聚元件倾向于在达到抗拉强度之前在断裂尖端周围产生较大的弹性变形，与较高的刚度元件相比，产生较大的断裂长度和较低的断裂压力。已经发现，在以粘度为主的状态下，能量释放速率几乎对水力压裂没有影响，因为与总输入能量相比，用于产生新裂缝的能量消耗太小。对于以韧性为主的状态，应准确地捕获压裂过程中释放的能量；为了使数值结果与渐近解析解相匹配，应使用相对较大的拉伸强度。与粘度控制方案中使用的元素相比，它需要的元素更小。