When modeling fluid flow in fractured reservoirs, it is common to represent the fractures as lower-dimensional inclusions embedded in the host medium. Existing discretizations of flow in porous media with thin inclusions assume that the principal directions of the inclusion permeability tensor are aligned with the inclusion orientation. While this modeling assumption works well with tensile fractures, it may fail in the context of faults, where the damage zone surrounding the main slip surface may introduce anisotropy that is not aligned with the main fault orientation. In this article, we introduce a generalized dimensional reduced model which preserves full-tensor permeability effects also in the out-of-plane direction of the inclusion. The governing equations of flow for the lower-dimensional objects are obtained through vertical averaging. We present a framework for discretization of the resulting mixed-dimensional problem, aimed at easy adaptation of existing simulation tools. We give numerical examples that show the failure of existing formulations when applied to anisotropic faulted porous media, and go on to show the convergence of our method in both two-dimensional and three-dimensional.

中文翻译：

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具有薄的全张量渗透性包裹体的多孔介质中流动的建模和离散化

在对裂缝性储层中的流体流动进行建模时，通常将裂缝表示为嵌入在宿主介质中的低维包裹体。现有的具有薄包裹体的多孔介质中流动的离散化假设包裹体渗透率张量的主方向​​与包裹体方向一致。虽然这种建模假设适用于拉伸裂缝，但它可能会在断层的情况下失效，其中主滑移面周围的损坏区域可能会引入与主断层方向不一致的各向异性。在本文中，我们介绍了一个广义降维模型，该模型在夹杂物的面外方向也保留了全张量渗透率效应。低维物体的流动控制方程是通过垂直平均得到的。我们提出了一个用于离散化由此产生的混合维度问题的框架，旨在轻松适应现有的模拟工具。我们给出了数值例子，说明了现有公式在应用于各向异性断层多孔介质时的失败，并继续展示了我们的方法在二维和三维上的收敛性。