多孔介质中单相气体局部流动的均质化建模

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

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.

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.