分形多孔介质渗透率与孔隙度理论关系模型

A new model for describing the relationship between the permeability and the porosity of fractal porous media

基于多孔介质微观孔隙结构的分形特征、毛管模型和Poiseuille方程建立了计算分形多孔介质宏观物性参数渗透率与孔隙度的理论模型,给出了二者之间新的理论关系式.分形多孔介质宏观物性参数及其关系式是多孔介质微观孔隙结构分维数、分形系数和微观结构参数的函数,不包含任何经验或实验常数.定量分析了多孔介质微观孔隙结构分维数、分形系数和微观结构参数对分形多孔介质宏观物性参数及其关联式的影响.理论计算结果与实验结果存在较好的一致性,表明理论模型是有效的.

The theoretical models for calculating the permeability and the porosity of fractal porous media are presented based on the fractal nature of the microstructure of the pores in the porous media,capillary model and Poiseuille formula,and a new model for describing the relationship between the permeability and the porosity is put forward.In the permeability,the porosity and their relationship formula are the functions of the fractal dimension,the fractal coefficient and microstructural parameters of pore microstructure.In the functions,any experimental and empirical constants are not contained.The influences of the fractal dimension,the fractal coefficient and the microstructural parameters on the permeability,porosity,and the relationship formula between them are quantitatively analyzed.There is excellent agreement between experimental data and calculated results,which verifies the validity of the models.