This paper presents a unified, embedded finite element formulation for simulating transient fluid flow in fractured porous media while accounting for transverse and longitudinal directions. The transverse flow arises due to pressure variations on both sides of fractures, as these typically exhibit lower permeability in the perpendicular direction. A simple coupling framework is introduced to connect independent sets of finite element meshes, one for the bulk porous media and the other for natural discontinuities. Importantly, the proposed coupling technique does not introduce additional degrees of freedom, and discontinuities can arbitrarily intersect the background elements of the continuum domain. Additionally, standard quadrature rules for integration can be used without modifications, thus avoiding additional remediation steps found with nodal enrichment strategies. These advantageous features make our method a robust technique capable of modelling transient fluid flow as an integral part of a coupled hydro-mechanical formulation. The performance is assessed using several numerical examples. These encompass various cases of fracture orientation relative to the background elements. The results demonstrate a good agreement with reference solutions. The effects of the coupling parameter, as well as the transverse and longitudinal permeabilities, in the temporal domain, are also investigated. The results demonstrated that the proposed method is capable of handling any values of transverse or longitudinal permeability compared to the surrounding porous domain. Moreover, the findings confirmed that, as a rule of thumb, a coupling parameter should be selected 10 times larger than the highest permeability used in the model.

中文翻译：

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使用新的嵌入式有限元方法对裂缝多孔介质进行瞬态压力建模


本文提出了一种统一的嵌入式有限元公式，用于模拟裂缝多孔介质中的瞬态流体流动，同时考虑横向和纵向。横向流动是由于裂缝两侧的压力变化而产生的，因为裂缝通常在垂直方向上表现出较低的渗透率。引入了一种简单的耦合框架来连接独立的有限元网格组，一组用于块体多孔介质，另一组用于自然不连续性。重要的是，所提出的耦合技术不会引入额外的自由度，并且不连续性可以任意与连续域的背景元素相交。此外，无需修改即可使用标准积分积分规则，从而避免了节点富集策略中发现的额外补救步骤。这些有利的特征使我们的方法成为一种强大的技术，能够将瞬态流体流动建模为耦合流体力学公式的组成部分。使用几个数值示例来评估性能。这些涵盖了相对于背景元素的断裂取向的各种情况。结果表明与参考解决方案非常吻合。还研究了耦合参数以及横向和纵向磁导率在时域中的影响。结果表明，与周围多孔域相比，所提出的方法能够处理任何横向或纵向渗透率值。此外，研究结果证实，根据经验，耦合参数应选择为模型中使用的最高渗透率的 10 倍。