| 饶翔,何旭鹏,赵辉,刘怡娜.基于模拟有限差分法的两相渗流流线模拟新方法[J].计算力学学报,2025,42(1):26~36 |
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| 基于模拟有限差分法的两相渗流流线模拟新方法 |
| A mimetic finite difference based novel streamline simulation method for two-phase porous flow |
| 投稿时间：2023-06-11 修订日期：2023-08-27 |
| DOI：10.7511/jslx20230611001 |
| 中文关键词: 模拟有限差分 流线模拟 间断伽辽金 油水两相渗流 |
| 英文关键词:mimetic finite difference method streamline-based simulation discontinuous Galerkin method oil-water two-phase porous flow |
| 基金项目:国家自然科学基金(52104017)资助项目. |
| 作者 | 单位 | E-mail | | 饶翔 | 油气钻采工程湖北省重点实验室(长江大学), 武汉 430199, 中国
阿卜杜拉国王科技大学 物理科学与工程部Ali I. Al-Naimi石油工程研究中心, 吉达 23955-6900, 沙特阿拉伯
沙特阿美国家石油公司 EXPEC高级研究中心, 达曼 0096613, 沙特阿拉伯 | raoxiang0103@163.com | | 何旭鹏 | 阿卜杜拉国王科技大学 物理科学与工程部Ali I. Al-Naimi石油工程研究中心, 吉达 23955-6900, 沙特阿拉伯
沙特阿美国家石油公司 EXPEC高级研究中心, 达曼 0096613, 沙特阿拉伯 | | | 赵辉 | 油气钻采工程湖北省重点实验室(长江大学), 武汉 430199, 中国 | | | 刘怡娜 | 油气钻采工程湖北省重点实验室(长江大学), 武汉 430199, 中国 | |
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| 中文摘要: |
| 首次提出了基于模拟有限差分法的流线模拟新方法,该方法利用适用于全张量渗透率及非结构网格的模拟有限差分法获取高精度的压力及渗流速度分布,采用简易的流线追踪方法在二维三角网格或三维四面体网格情况下快速获取流线分布并计算流线上的飞行时间分布,使用基于简化龙格库塔格式的间断伽辽金法在各一维流线上获取低数值耗散的含水饱和度分布。理论上来说,相较于传统各类流线模拟方法,该方法能够同时适用于复杂油藏几何和各向异性储层,相较于仅计算网格平均饱和度的有限体积、模拟有限差分等方法,能够显著降低饱和度计算的数值耗散,相较于计算网格顶点饱和度的间断伽辽金法等高阶方法,该方法能避免强稳定性条件对时间步的限制而提高计算效率,且能进一步降低数值耗散。数值算例也表明该方法能够在各向异性渗透率、非结构网格、复杂几何情况下具有计算精度和计算效率的双重优势,且能够提供直观的流动诊断结果。 |
| 英文摘要: |
| In this paper,a new streamline simulation method based on mimetic finite difference method (denoted as MFD-SL) is proposed for the first time.This method uses mimetic finite difference method applicable for full tensor permeability and unstructured meshes to obtain high-accuracy pressure and flow velocity distributions and a simple streamline tracking method to quickly obtain the streamline distribution in a two-dimensional triangular or a three-dimensional tetrahedral mesh and calculate the flight time distribution on the streamlines.The discontinuous Galerkin method based on the simplified Runge-Kutta scheme is used to obtain the water saturation distribution of low numerical dissipation on each one-dimensional streamline.Theoretically,compared with traditional streamline simulation methods,this method can be applied to both complex-shaped reservoirs and anisotropic reservoirs.Compared with finite volume and mimetic finite difference methods,which only calculates the grid-average saturation,this method can significantly reduce the numerical dissipation of saturation calculation.Compared with high-order methods such as the discontinuous Galerkin method,which calculates the vertex saturation of the grid,this method can avoid the time step restriction of the strong stability condition,improve the computational efficiency,and further reduce the numerical dissipation.Numerical examples in this paper also show that the proposed method has the advantages of both accuracy and efficiency in the case of anisotropic permeability,unstructured meshing and complex geometry,and can provide intuitive flow diagnosis results. |
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