Most carbonate reservoirs in Middle East are characterized as porous fractured reservoirs. Estimation of relative permeability of these highly heterogeneous reservoirs is challenging due to the existence of discontinuity in the fluid flow fractured porous media. Although relative permeability is an essential data for simulation of flow in fractured media, few attempts have so far been made to estimate the relative permeability curves. Most notable are the studies by Akin (J Pet Sci Eng 30(1)1–14, 2001), Al-sumaiti and Kazemi (2012), and Fahad (2013). This paper presents an integrated approach to history matching the oil drainage tests, which were carried out by unsteady state, on glass bed models with a single fracture at different orientations and to estimate the relative permeability curve. The integrated approach includes an inversion algorithm coupled with forward numerical modeling of fluid flow. The history matching of the displacement test data was obtained by using the Levenberg–Marquardt algorithm to minimize the error between the simulated and experimental data. In this algorithm, Corey-type power law is used to create relative permeability curves during the optimization procedures. The forward modeling is a 3D multiphase fluid simulator for flow through discrete fractures. Numerical results of fluid flow profiles and the optimized relative permeability curves for single fracture with different orientations and experimental validation with oil drainage tests are presented. The results of the optimized relative permeability data for single fracture are in a good agreement with the data derived by the correlation of Fahad (2013). These results prove that the presented approach can be used to upscale the relative permeability curve from laboratory scale to reservoir grid scale. The work on the upscaling of the estimated relative permeability curve of fractured porous media is under preparation and will be published soon.

中文翻译：

---

压裂多孔介质相对渗透率估算的综合方法：实验室和数值模拟研究

中东大多数碳酸盐岩储层的特征是多孔裂缝性储层。由于在流体破裂的多孔介质中存在不连续性，因此估算这些高度非均质储层的相对渗透率具有挑战性。尽管相对渗透率是模拟裂缝介质流动的基本数据，但迄今为止，几乎没有任何尝试来估算相对渗透率曲线。最值得注意的是Akin（J Pet Sci Eng 30（1）1–14，2001），Al-sumaiti和Kazemi（2012）和Fahad（2013）的研究。本文提出了一种综合方法，用于对在非定向状态下具有单一裂缝，不同方向的玻璃床模型进行非稳定状态下的排油测试，并估算相对渗透率曲线。集成方法包括反演算法以及流体流动的正向数值建模。位移测试数据的历史匹配是通过使用Levenberg-Marquardt算法获得的，以使模拟数据与实验数据之间的误差最小。在该算法中，使用Corey型幂定律在优化过程中创建相对磁导率曲线。正向建模是用于流经离散裂缝的3D多相流体模拟器。给出了不同方向的单一裂缝流体流动剖面的数值结果和优化的相对渗透率曲线，并通过排油试验进行了实验验证。单个裂缝的最佳相对渗透率数据的优化结果与Fahad（2013）的相关性得出的数据非常吻合。这些结果证明，该方法可用于将相对渗透率曲线从实验室规模放大到储层网格规模。裂缝多孔介质的估计相对渗透率曲线的按比例放大的工作正在准备中，将很快发表。