多孔介质中单相气体局部流动的均质化建模

李树光; 曲凯

doi:10.21656/1000-0887.440246

多孔介质中单相气体局部流动的均质化建模

doi: 10.21656/1000-0887.440246

李树光^,,
曲凯

大连海事大学理学院，辽宁大连 116026

基金项目:

辽宁省博士科研启动基金计划 2022-BS-093

详细信息

通讯作者:
李树光(1990—)，男，副教授，博士，硕士生导师(通讯作者. E-mail: shuguangli2008@126.com)

中图分类号: O3
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- 被引次数: 0
出版历程
- 收稿日期: 2023-08-17
- 修回日期: 2023-11-12
- 刊出日期: 2024-02-01

Homogenization Modeling of Single-Phase Gas Local Flow in Porous Media

LI Shuguang^,,
QU Kai

School of Science, Dalian Maritime University, Dalian, Liaoning 116026, P.R.China

摘要

摘要: 该文研究了渐近均质法在单相气体渗流理论中的应用，开发了气体在孔隙尺度下流动的数学模型和数值方法. 基于渐近均质法，建立了周期单元上描述周期性多孔结构孔隙尺度下单相气体流动的局部问题. 讨论了局部问题的特殊数学性质和物理意义. 利用一种基于对称性和反对称性扩展的简化方法，提出了求解局部问题的最小二乘有限元方法，克服了由于平均算子和周期性边界条件引起的数值困难. 局部问题的求解能够获得单孔内速度和压力的精确分布，并且在仅知道孔隙几何形状的情况下评估多孔介质的渗透性. 在局部问题的基础上，通过理论分析获得了微管中Poiseuille流动的解析解，验证了所提出的数学模型和数值算法. 最后，考虑了一种三维周期性多孔结构，获得了单孔中气体局部流动的数值结果和多孔介质的渗透系数.
- 渐近均质法 /
- 多孔介质 /
- 局部流动 /
- 渗透性 /
- 最小二乘有限元
Abstract: The application of asymptotic homogenization method was investigated based on the filtration theory for single-phase gas, and the mathematical model and numerical method for the gas flow at the pore scale were developed. With the asymptotic homogenization method, a local problem of periodic cells was established to describe the local flow process of a single-phase gas at the pore scale of the periodic porous medium. The special mathematical properties and physical significance of the local problem were discussed. With a simplified approach based on symmetric and antisymmetric extensions, a least squares finite element method for the local problem was proposed, to overcome the numerical difficulties due to averaging operators and periodic boundary conditions. The solution of the local problem was obtained with accurate local velocity and pressure distributions in a single pore, and with gas permeability evaluation of porous media only in knowledge of the pore geometry. Beyond the local problem, the analytical solution of the Poiseuille flow in microtubes was obtained through theoretical analysis, to verify the proposed mathematical model and the numerical algorithm. Finally, a 3D periodic porous structure was considered, and numerical results of local flow in a single pore and permeability coefficients in porous media were obtained.
- asymptotic homogenization method /
- porous medium /
- local flow /
- permeability /
- least squares finite element

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图 1 多孔介质的几何模型(显示为气体所占的孔隙)

Figure 1. Geometric modeling of the porous medium (showing the porosity occupied by gas)

下载: 全尺寸图片幻灯片

图 2 对称或反对称扩展中局部问题L⁽¹⁾的解的符号变化

Figure 2. Symbolic changes of solutions to local problem L⁽¹⁾ in symmetric or antisymmetric extensions

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图 3 圆柱形单通道结构的1/8周期单元

Figure 3. The 1/8 periodic cell of the cylindrical single channel structure

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图 4 单通道结构中Poiseuille流动的数值解及其与精确解比较

(a) Poiseuille流动的数值解(b) 与精确解的比较

Figure 4. The numerical solution of the Poiseuille flow in single channel structure, in comparison with the exact solution

(a) The numerical solution of the Poiseuille flow (b) Comparison of numerical and exact solutions

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图 5 局部问题L⁽¹⁾的数值结果

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 5. Numerical results of local problem L⁽¹⁾

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表 1 多孔介质孔隙率和渗透系数的计算结果

Table 1. Calculation results of the porosity and the permeability coefficient of porous media

	local problem L⁽¹⁾	local problem L⁽²⁾	local problem L⁽³⁾
permeability	0.000 232 222 744 711	0.000 231 967 234 967	0.000 232 933 436 047
porosity	0.204 745 216 893 771	0.204 745 216 893 771	0.204 745 216 893 771

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