各向同性多孔介质中Kozeny-Carman常数的分形分析  

Fractal analysis of Kozeny-Carman constant in the homogenous porous media

作　　者：徐鹏[1] 邱淑霞[1] 姜舟婷[1] 江影[1] 

机构地区：[1]中国计量学院理学院,浙江杭州310018

出　　处：《重庆大学学报（自然科学版）》2011年第4期78-82,共5页Journal of Chongqing University

基　　金：国家自然科学基金资助项目(10947153)

摘　　要：Kozeny-Carman(KC)方程是多孔介质渗流领域最著名的半经验公式,长期以来,KC方程及其推广形式被广泛用于估算多孔介质的渗透率。但是,方程中的KC常数是一个没有确切物理意义的经验常数,且被证明并非一个常数值。天然多孔介质中的孔隙分布往往表现出自相似的分形标度律。因此,根据多孔介质的分形特征利用微观几何模型计算了各向同性多孔介质的有效渗透率,并进一步推导了KC常数的解析表达式。结果表明,KC常数是由多孔介质的微结构决定的,是孔隙率和分形维数的函数,且随着孔隙率的增加而增大。The semi-empirical Kozeny-Carman（KC） equation,the most well-known permeability-porosity relation,is widely used in the field of seepage flow in porous media.However,the physical mechanisms behind the empirical KC constant are not clear,and the KC constant has not been proved to be a constant.The fractal scaling laws of pores have been extensively found in porous media.Therefore,the effective permeability of homogenous porous media is presented and the analytical expression of KC constant is derived based on the fractal characteristics of porous media and the microcosmic geometrical model.The results indicate that the fractal analytical expression of KC constant depends on the micro-structure of porous media.As a function of porosity and fractal dimensions,KC constant increases with the increase of porosity.

关 键 词：多孔介质 Kozeny-Carman方程 分形 有效渗透率 

分 类 号：O359[理学—流体力学]