Work conjugate principle-constrained volume averaging technique for multiphase porous media  

作　　者：ZHANG ZhiHong XU ZhaoGang XU ChengShun DU XiuLi 

机构地区：[1]Key Lab of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing 100124, China

出　　处：《Science China(Technological Sciences)》2017年第12期1966-1974,共9页中国科学（技术科学英文版）

基　　金：supported by the National Basic Research Program of China(Grant No.2014CB744702);the National Natural Science Foundation of China(Grant No.51678012)

摘　　要：Volume averaging is a standard method for the development of macroscopic balance equations for modelling the thermodynamic behaviors of multiphase porous media. However, work conjugate principle which is a common practice in continuum mechanics is not emphasized by the volume averaging technique resulting in the macroscopic balance equations are not capable of comprehensively describing the kinematic behaviors of multiphase porous media due to the loss of essential macroscopic variables. This study derives the macroscopic mass and momentum balance equations for the pore fluid of a fluid-solid porous medium by use of the volume averaging technique. We show(1) if the procedure of the volume averaging is implemented in its traditional manner, only the average flux of the pore fluid described by its mass average velocity is captured;(2) if the work conjugate principle is employed to define a work-conjugate velocity for the pore fluid at the macroscale, both the average flux(described by the mass average velocity) and the dispersive flux(described by the deviation of the mass average velocity from the work-conjugate one) are reproduced. This theoretical analysis demonstrates that the work conjugate principle is an essential thermodynamic constraint to improve the volume averaging technique, in the sense that the macroscopic balance equations are required to be capable of comprehensively describing the macroscopic kinematic behaviors of multiphase porous media.Volume averaging is a standard method for the development of macroscopic balance equations for modelling the thermodynamic behaviors of multiphase porous media. However, work conjugate principle which is a common practice in continuum mechanics is not emphasized by the volume averaging technique resulting in the macroscopic balance equations are not capable of comprehensively describing the kinematic behaviors of multiphase porous media due to the loss of essential macroscopic variables. This study derives the macroscopic mass and momentum balance equations for the pore fluid of a fluid-solid porous medium by use of the volume averaging technique. We show（1） if the procedure of the volume averaging is implemented in its traditional manner, only the average flux of the pore fluid described by its mass average velocity is captured;（2） if the work conjugate principle is employed to define a work-conjugate velocity for the pore fluid at the macroscale, both the average flux（described by the mass average velocity） and the dispersive flux（described by the deviation of the mass average velocity from the work-conjugate one） are reproduced. This theoretical analysis demonstrates that the work conjugate principle is an essential thermodynamic constraint to improve the volume averaging technique, in the sense that the macroscopic balance equations are required to be capable of comprehensively describing the macroscopic kinematic behaviors of multiphase porous media.

关 键 词：volume averaging technique work conjugate principle work-conjugate velocity dispersive flux multiphase porous media 

分 类 号：TK12[动力工程及工程热物理—工程热物理]