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GSIS: an efficient and accurate numerical method to obtain the apparent gas permeability of porous media
Computers & Fluids ( IF 2.5 ) Pub Date : 2020-06-01 , DOI: 10.1016/j.compfluid.2020.104576
Wei Su , Minh Tuan Ho , Yonghao Zhang , Lei Wu

Abstract The apparent gas permeability (AGP) of a porous medium is an important parameter to predict production of unconventional gas. The Klinkenberg correlation, which states that the ratio of the AGP to the intrinsic permeability is approximately a linear function of reciprocal mean gas pressure, is one of the most popular estimations to quantify AGP. However, due to the difficulty in defining the characteristic flow length in complex porous media where the rarefied gas flow is multiscale, the slope in the Klinkenberg correlation varies significantly for different geometries such that a universal expression seems impossible. In this paper, by solving the gas kinetic equation using the general synthetic iterative scheme (GSIS), we compute the AGP in porous media that are represented by Sierpinski fractals and pore body/throat systems. With the abilities of fast convergence to steady-state solution and asymptotic preserving of Navier-Stokes limit, it is shown that GSIS is a promising tool to simulate low-speed rarefied gas flow through complex multiscale geometries. A new definition of the characteristic flow length is proposed as a function of porosity, tortuosity and intrinsic permeability of porous media, which enables to find a unique slope in the Klinkenberg correlation for all the considered geometries. This research also shows that the lattice Boltzmann method using simple wall scaling for the effective shear viscosity is not able to predict the AGP of porous media.

中文翻译:

GSIS:一种获得多孔介质表观气体渗透率的有效而准确的数值方法

摘要 多孔介质的表观气体渗透率(AGP)是预测非常规天然气产量的重要参数。Klinkenberg 相关性表明 AGP 与固有渗透率的比率近似是平均气压倒数的线性函数,是量化 AGP 的最流行的估计之一。然而,由于在稀薄气体流动是多尺度的复杂多孔介质中定义特征流动长度很困难,克林伯格相关性的斜率对于不同的几何形状变化很大,因此通用表达式似乎是不可能的。在本文中,通过使用通用合成迭代方案 (GSIS) 求解气体动力学方程,我们计算了由谢尔宾斯基分形和孔体/喉道系统表示的多孔介质中的 AGP。凭借快速收敛到稳态解的能力和 Navier-Stokes 极限的渐近保持能力,GSIS 是一种很有前途的工具,可以通过复杂的多尺度几何来模拟低速稀薄气流。特征流动长度的新定义被提出作为多孔介质的孔隙度、曲折度和固有渗透率的函数,这使得能够在所有考虑的几何形状的 Klinkenberg 相关性中找到独特的斜率。该研究还表明,使用简单壁标度计算有效剪切粘度的格子 Boltzmann 方法无法预测多孔介质的 AGP。结果表明,GSIS 是一种很有前途的工具,可以通过复杂的多尺度几何形状模拟低速稀薄气体流动。特征流动长度的新定义被提出作为多孔介质的孔隙度、曲折度和固有渗透率的函数,这使得能够在所有考虑的几何形状的 Klinkenberg 相关性中找到独特的斜率。该研究还表明,使用简单壁标度计算有效剪切粘度的格子 Boltzmann 方法无法预测多孔介质的 AGP。结果表明,GSIS 是一种很有前途的工具,可以通过复杂的多尺度几何形状模拟低速稀薄气体流动。特征流动长度的新定义被提出作为多孔介质的孔隙度、曲折度和固有渗透率的函数,这使得能够在所有考虑的几何形状的 Klinkenberg 相关性中找到独特的斜率。该研究还表明,使用简单壁标度计算有效剪切粘度的格子 Boltzmann 方法无法预测多孔介质的 AGP。
更新日期:2020-06-01
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