随机多孔介质的蒙特卡罗重构与渗流特性模拟

doi:10.19596/j.cnki.1001-246x.8315

摘要/Abstract

摘要：

根据多孔介质微观结构的分形尺度标度特征，采用蒙特卡罗方法分别重构随机多孔介质的微观颗粒和孔隙结构，并基于分形毛管束模型研究多尺度多孔介质的气体渗流特性，建立多孔介质微观结构和宏观渗流特性的定量关系。结果表明：分形蒙特卡罗重构的多孔介质微细结构接近真实介质结构，气体渗流特性的计算结果与格子玻尔兹曼模拟数据较为吻合; 多孔介质气体渗透率随着克努森数的增加而增大，孔隙分形维数对于气体渗流的微尺度效应具有显著影响，而迂曲度分形维数对于表观渗透率和固有渗透率的比值影响可以忽略。提出的分形蒙特卡罗方法具有收敛速度快且计算误差与维数无关的优点，有利于深入理解多尺度多孔介质的渗流机理。

关键词: 多孔介质, 蒙特卡罗, 分形, 重构, 渗流

Abstract:

According to the fractal scaling law of microstructures, the particle and pore structures of random porous media were reconstructed with Monte Carlo method. The seepage property of multiscale porous media was studied with a fractal capillary bundle model. A quantitative relation between macroscopic seepage properties and microscopic structures was addressed. It shows that microstructures of porous media reconstructed by the fractal Monte Carlo method are close to that of real media. Calculated results for gas flow through porous media agree well with those by lattice Boltzmann method. It is shown that gas permeability increases with the increment of Knudsen number. The pore fractal dimension takes important effect on the microscale effect of gas flow through porous media, while the influence of tortuosity fractal dimension on the ratio of apparent gas permeability to intrinsic permeability is marginal. The method shows advantages that the convergence speed is fast and the calculation error is independent of dimension. It is helpful in understanding seepage mechanisms of multiscale porous media.

Key words: porous media, Monte Carlo, fractal, reconstruction, seepage

中图分类号:

O359

王敏, 申玉清, 陈震宇, 徐鹏. 随机多孔介质的蒙特卡罗重构与渗流特性模拟[J]. 计算物理, 2021, 38(5): 623-630.

Min WANG, Yuqing SHEN, Zhenyu CHEN, Peng XU. Reconstruction and Seepage Simulation of Random Porous Media with Monte Carlo Method[J]. Chinese Journal of Computational Physics, 2021, 38(5): 623-630.

图/表 6

图1 多孔介质颗粒相二维和三维重构 (ε=0.1，黑色和白色分别表示颗粒和孔隙。)

Fig.1 Two- and three-dimensional reconstruction of solid phase in porous media (ε=0.1, black and white color represent solid and pore phases, respectively.)

图2 多孔介质孔隙相二维和三维重构 (ϕ=0.1，白色和黑色分别表示孔隙和固体。)

Fig.2 Two- and three-dimensional reconstruction of pore phase in porous media (ϕ=0.1, black and white color represent solid and pore phases, respectively.)

图3 分形蒙特卡罗方法和格子玻尔兹曼方法计算的渗透率

Fig.3 Permeability by fractal Monte Carlo method and lattice Boltzmann method

图4 表观渗透率和固有渗透率比值与克努森数的关系

Fig.4 Relations between the ratio of apparent gas permeability to intrinsic permeability and Knudsen number

图5 孔隙分形维数对于表观渗透率和固有渗透率比值的影响(a) ϕ=0.20, Dt=1.10; (b) λmin, p/λmax, p=0.01, Dt=1.10; (c) ϕ=0.20, Dt=1.10, Kn=1

Fig.5 Effect of pore fractal dimension on the ratio of apparent gas permeability to intrinsic permeability (a) ϕ=0.20, Dt=1.10; (b) λmin, p/λmax, p=0.01, Dt=1.10; (c) ϕ=0.20, Dt=1.10, Kn=1

图6 迂曲度分形维数对表观渗透率和固有渗透率比值的影响

Fig.6 Effect of tortuosity fractal dimension on the ratio of apparent gas permeability to intrinsic permeability

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