第36卷第6期 北京科技大学学报 Vol.36 No.6 2014年6月 Journal of University of Science and Technology Beijing Jun.2014 纳微米级孔隙气体流动数学模型及应用 朱维耀，马千，邓佳四，马东旭，宋智勇，岳明 北京科技大学土木与环境工程学院，北京100083 ☒通信作者，E-mail:dengjia_123@126.com 摘要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. 关键词多孔介质：纳微米级孔隙：气体流动：渗透率：数学模型：流动模型 分类号TE37 Mathematical model and application of gas flow in nano-micron pores ZHU Wei-yao,MA Qian,DENG Jia,MA Dongu,SONG Zhi-yong,YUE Ming School of Civil and Environmental Engineering,University of Science and Technology Beijing,Beijing 100083,China Corresponding author,E-mail:dengjia_123@126.com 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 per- meability was improved based on the Beskok-Kamiadakis 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. KEY WORDS porous media:nano-micron pores:gas flow;permeability:mathematical models:flow models 多孔介质内流体流动问题的研究己成为很制.因此，深入了解流体在多孔介质内的流动特 多应用科学和工程技术领域的基础，诸如土壤力 性有着重大的实际意义、通常，模拟流体流动时 学、地下水水文学、石油工程、水的净化、工业过采用连续假设或者分子假设，连续假设适用于很 滤、陶瓷工程、粉末治金和防毒（气体）面罩的研 多的流动状态.但是，随着系统长度尺度的减少， 收稿日期：201303-29 基金项目：国家重点基础研究发展计划资助项目(2013CB228002):提高油气采收率教有部重点实验室开放课题资助项目(NEPU-E0R-2012- 003) DOI:10.13374/j.issn1001-053x.2014.06.001:http:/journals.ustb.edu.cn第 36 卷 第 6 期 2014 年 6 月 北京科技大学学报 Journal of University of Science and Technology Beijing Vol． 36 No． 6 Jun． 2014 纳微米级孔隙气体流动数学模型及应用 朱维耀，马 千，邓 佳，马东旭，宋智勇，岳 明 北京科技大学土木与环境工程学院，北京 100083  通信作者，E-mail: dengjia_123@ 126． com 摘 要 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． 关键词 多孔介质; 纳微米级孔隙; 气体流动; 渗透率; 数学模型; 流动模型 分类号 TE37 Mathematical model and application of gas flow in nano-micron pores ZHU Wei-yao，MA Qian，DENG Jia ，MA Dong-xu，SONG Zhi-yong，YUE Ming School of Civil and Environmental Engineering，University of Science and Technology Beijing，Beijing 100083，China  Corresponding author，E-mail: dengjia_123@ 126． com 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 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． KEY WOＲDS porous media; nano-micron pores; gas flow; permeability; mathematical models; flow models 收稿日期: 2013--03--29 基金项目: 国家重点基础研究发展计划资助项目( 2013CB228002) ; 提高油气采收率教育部重点实验室开放课题资助项目( NEPU--EOＲ--2012-- 003) DOI: 10． 13374 /j． issn1001--053x． 2014． 06． 001; http: / /journals． ustb． edu． cn 多孔介质内流体流动问题的研究已成为很 多应用科学和工程技术领域的基础，诸如土壤力 学、地下水 水 文 学、石 油 工 程、水 的 净 化、工 业 过 滤、陶瓷工程、粉末冶金和防毒( 气体) 面罩的研 制． 因此，深入了解流体在多孔介质内的流动特 性有着重大的实际意义． 通常，模拟流体流动时 采用连续假设或者分子假设，连续假设适用于很 多的流动状态． 但是，随着系统长度尺度的减少