In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using uncoupled methods. In recent years, significant research has focused on discretization strategies for these coupled systems, particularly in the presence of complicated fracture network geometries. In this work, we explore a finite-volume discretization for the multiphase flow equations coupled with a finite-element scheme for the mechanical equations. Fractures are treated as lower dimensional surfaces embedded in a background grid. Interactions are captured using the Embedded Discrete Fracture Model (EDFM) and the Embedded Finite Element Method (EFEM) for the flow and the mechanics, respectively. This non-conforming approach significantly alleviates meshing challenges. EDFM considers fractures as lower dimension finiten volumes which exchange fluxes with the rock matrix cells. The EFEM method provides, instead, a local enrichment of the finite-element space inside each matrix cell cut by a fracture element. Both the use of piecewise constant and piecewise linear enrichments are investigated. They are also compared to an Extended Finite Element (XFEM) approach. One key advantage of EFEM is the element-based nature of the enrichment, which reduces the geometric complexity of the implementation and leads to linear systems with advantageous properties. Synthetic numerical tests are presented to study the convergence and accuracy of the proposed method. It is also applied to a realistic scenario, involving a heterogeneous reservoir with a complex fracture distribution, to demonstrate its relevance for field applications.

中文翻译：

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嵌入离散裂缝的多孔介质中的耦合多相流和地质力学模拟

在裂缝性自然地层中，控制流体流动和地质力学的方程是强耦合的。流体动力学特性取决于机械配置，因此使用非耦合方法难以准确解析它们。近年来，重要的研究集中在这些耦合系统的离散化策略上，特别是在存在复杂裂缝网络几何形状的情况下。在这项工作中，我们探索了多相流动方程的有限体积离散化以及机械方程的有限元方案。裂缝被视为嵌入背景网格中的低维表面。使用嵌入式离散断裂模型 (EDFM) 和嵌入式有限元方法 (EFEM) 分别针对流动和力学捕获相互作用。这种不一致的方法显着减轻了网格划分的挑战。EDFM 将裂缝视为与岩石基质单元交换通量的低维有限体积。相反，EFEM 方法提供了由断裂元素切割的每个矩阵单元内有限元空间的局部富集。研究了分段常数和分段线性富集的使用。它们还与扩展有限元 (XFEM) 方法进行了比较。EFEM 的一个关键优势是富集的基于元素的性质，这降低了实现的几何复杂性并导致线性系统具有有利的特性。提出了综合数值试验来研究所提出方法的收敛性和准确性。它也适用于现实场景，