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納微米級孔隙氣體流動數學模型及應用

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

  • 摘要: 對納微米級孔隙多孔介質內的氣體流動進行了研究.利用克努森數劃分流態,繪制了流態圖版,闡明了不同區域的流動特征.基于Beskok-Karniadakis模型,對滲透率校正系數進行了改進,引入多項式修正系數,將Beskok-Karniadakis模型簡化為二項式方程,并利用最小二乘法分段擬合得出多項式修正系數的取值.模型對比顯示,簡化后的模型具有較高的精確度.應用此模型推導出了納微米級孔隙氣體流量的計算公式.進行了室內微觀滲流模擬實驗,得到氣體平面單向滲流規律,與由納微米級孔隙氣體流量公式計算所得滲流特征進行對比,結果顯示本模型與實驗數據擬合較好.采用本模型進行編程計算,對其影響因素進行分析,發現氣體流量隨壓力平方差增加而增大,且增加趨勢越來越快,并隨多孔介質滲透率和克努森擴散系數的增加而增大.

     

    Abstract: 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 permeability was improved based on the Beskok-Karniadakis model. By introducing polynomial correction coefficients, the Beskok-Karniadakis 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 coefficient.

     

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