This paper presents an extension of Discrete Fracture Matrix (DFM) models to compositional two-phase Darcy flow accounting for phase transitions and Fickian diffusion. The hybrid-dimensional model is based on nonlinear transmission conditions at matrix fracture (mf) interfaces designed to be consistent with the physical processes. They account in particular for the saturation jump induced by the different rock types, for the Fickian diffusion in the fracture width, as well as for the thermodynamical equilibrium formulated by complementary constraints. The model is validated by numerical comparison with a reference equi-dimensional model using a TPFA approximation in space and a fully implicit Euler time integration. It is also compared with the usual approach based on an harmonic averaging of the transmissivities at mf interfaces combined with a two-point upwinding of the mobilities jumping over the mf interfaces. Our approach is shown to provide basically the same accuracy than the equi-dimensional model as opposed to the classical harmonic averaging approach which is shown to exhibit physical inconsistency. It is then applied to simulate the desaturation by suction at the interface between a fractured Callovo-Oxfordian argilite storage rock and a ventilation tunnel with data set provided by Andra.

本文介绍了离散断裂矩阵 (DFM) 模型的扩展，以解释相变和 Fickian 扩散的成分两相达西流。混合维模型基于设计为与物理过程一致的基体断裂 (mf) 界面处的非线性传输条件。它们特别说明了由不同岩石类型引起的饱和度跳跃、裂缝宽度中的 Fickian 扩散以及由互补约束制定的热力学平衡。该模型通过与参考等维模型的数值比较进行验证，该模型使用空间中的 TPFA 近似和完全隐式欧拉时间积分。它还与基于 mf 界面处透射率的谐波平均以及跳过 mf 界面的迁移率的两点上风相结合的通常方法进行了比较。与经典的谐波平均方法相比，我们的方法显示出与等维模型基本相同的精度，而经典谐波平均方法显示出物理上的不一致。然后使用 Andra 提供的数据集，将其应用于模拟卡洛沃-牛津泥质岩存储岩和通风隧道之间界面处的吸力去饱和。与显示物理不一致的经典谐波平均方法相反，我们的方法显示出与等维模型基本相同的精度。然后将其应用到由安德拉提供的数据集，在破裂的卡洛夫-牛津辉石闪石储层岩石与通风隧道之间的界面处通过吸力模拟脱饱和。与显示物理不一致的经典谐波平均方法相反，我们的方法显示出与等维模型基本相同的精度。然后使用 Andra 提供的数据集，将其应用于模拟卡洛沃-牛津泥质岩存储岩和通风隧道之间界面处的吸力去饱和。