纳微米级孔隙气体流动数学模型及应用

Mathematical model and application of gas flow in nano-micron pores

对纳微米级孔隙多孔介质内的气体流动进行了研究.利用克努森数划分流态,绘制了流态图版,阐明了不同区域的流动特征.基于Beskok--Karniadakis模型,对渗透率校正系数进行了改进,引入多项式修正系数,将Beskok--Karniadakis模型简化为二项式方程,并利用最小二乘法分段拟合得出多项式修正系数的取值.模型对比显示,简化后的模型具有较高的精确度.应用此模型推导出了纳微米级孔隙气体流量的计算公式.进行了室内微观渗流模拟实验,得到气体平面单向渗流规律,与由纳微米级孔隙气体流量公式计算所得渗流特征进行对比,结果显示本模型与实验数据拟合较好.采用本模型进行编程计算,对其影响因素进行分析,发现气体流量随压力平方差增加而增大,且增加趋势越来越快,并随多孔介质渗透率和克努森扩散系数的增加而增大.

This article focuses on gas flow regularity in nano-micron porous media. The flow state was judged by Knudsen number, and then the flow state chart was drawn. The flow characteristics were illustrated for different regions. The correction coefficient of per-meability was improved based on the Beskok-Karniadakis model. By introducing polynomial correction coefficients, the Beskok-Kar-niadakis model was simplified to a binomial equation, and the values of polynomial correction coefficients were obtained by the least squares method. Compared with the Beskok-Karniadakis model, the simplified model has high accuracy. The flow rate equation in nano-micron porous media was developed based on the simplified model. The gas unidirectional seepage law was derived from indoor micro seepage experiment. The flow rate equation in nano-micron porous media agrees with experimental data. Factors influencing the gas flow rate were numerically studied by programming on the base of this model. It is found that the gas flow rate increases more and more quickly with the pressure square difference, and increases with the permeability of porous media and the Knudsen diffusion coeffi-cient.