The modeling of fluid flow in heterogeneous, anisotropic and fractured porous media is relevant in many applications, including hydrocarbon and groundwater extraction, dispersion of contaminants, hydrogen or carbon dioxide (CO) storage. Thus, accurate and scalable simulation of fluid flow through these formations continues to be a great challenge. The presence of fractures that are explicitly modeled, ranging from flow barriers to highly conductive channels, significantly increases the complexity of the numerical simulation. The Embedded Discrete Fracture Model (EDFM) produces results that can be as accurate as those obtained using equidimensional Discrete Fracture Models (DFM) at a much lower computational cost for highly conductive fractures, but it is not adequate for impermeable barriers. In contrast, the pEDFM (projection-based Embedded Discrete Fracture Model) produces accurate results for both, channels and barriers by using additional matrix-fracture connectivities. In its current versions, it is restricted to cartesian and corner-point grid geometries and to the classical Two Point Flux Approximation (TPFA) scheme. In this work, for the first time, the pEDFM is extended to handle unstructured tetrahedral meshes (pEDFM-U). In addition, interface fluxes are approximated by using the Multipoint Flux Approximation method with a Diamond stencil (MPFA-D). This allows for simulation of highly heterogeneous and anisotropic geo-models. The developed method is robust and can deal with full permeability tensors on arbitrary tetrahedral meshes. The advective terms are discretized considering an implicit First Order Upwind (FOU) method. Our method is implemented within the DARSim (Delft Advanced Reservoir Simulation) open-source simulator framework. Through several test cases, the proposed method showed to be robust and capable to accurately capture the effects of both high and low permeability fractures for general tetrahedral meshes, under arbitrary heterogeneous and anisotropic permeability tensors for the rock matrix.

中文翻译：

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使用非结构化四面体网格上基于投影的嵌入式离散裂缝模型 (pEDFM-U) 模拟 3D 裂缝性油藏中的两相流

非均质、各向异性和裂隙多孔介质中的流体流动建模与许多应用相关，包括碳氢化合物和地下水提取、污染物分散、氢气或二氧化碳 (CO) 储存。因此，对流经这些地层的流体进行准确且可扩展的模拟仍然是一个巨大的挑战。明确建模的裂缝（从流动障碍到高传导通道）的存在显着增加了数值模拟的复杂性。对于高传导性裂缝，嵌入式离散裂缝模型 (EDFM) 生成的结果与使用等维离散裂缝模型 (DFM) 获得的结果一样准确，计算成本要低得多，但对于不透水屏障来说，它还不够。相比之下，pEDFM（基于投影的嵌入式离散断裂模型）通过使用额外的矩阵断裂连接，为通道和障碍生成准确的结果。在当前版本中，它仅限于笛卡尔和角点网格几何形状以及经典的两点通量近似（TPFA）方案。在这项工作中，pEDFM 首次扩展到处理非结构化四面体网格 (pEDFM-U)。此外，通过使用金刚石模板的多点通量近似方法 (MPFA-D) 来近似界面通量。这允许模拟高度异质和各向异性的地质模型。所开发的方法非常稳健，可以处理任意四面体网格上的全渗透率张量。考虑隐式一阶迎风 (FOU) 方法对平流项进行离散化。我们的方法是在 DARSim（代尔夫特高级油藏模拟）开源模拟器框架内实现的。通过多个测试案例，该方法表现出鲁棒性，能够在岩石基质的任意非均质和各向异性渗透率张量下准确捕获一般四面体网格的高渗透率和低渗透率裂缝的影响。