A Generalized Fractal-Based Approach For Stress-Dependent Permeability Of Porous Rocks

The pore geometry of porous rocks is fundamental for accurate description of stress dependence of effective permeability, which is an important parameter of mass transfer in porous rocks. An important physical assumption that porous rocks contain numerous elliptical or spherical pores has been shown to be successfully applied to many aspects of hydromechanical coupling properties of porous rocks. To investigate the detailed description of pore structures on the degree of effect on the coupled hydromechanical process, in this work, a generalized stress-dependent model for permeability of porous rocks has been proposed based on fractal geometry theory and mechanics of porous rock. The proposed model is expressed as a nonlinear function of pore structure parameters, such as aspect ratio (γσ), the fractal dimensions (DT,σ and DT,av) for tortuosity, the initial fractal dimension (Df,0), and initial porosity (ϕ0) as well as matrix elastic constants (E and ν) of porous rocks without any empirical parameter. The validity of the proposed models is verified by the good agreements between available experimental data and theoretical predictions of stress-dependent permeabilities of porous rocks. Detailed discussions of the essential effects of pore structures parameters and material elastic constants of porous rocks on the dimensionless stress-dependent permeabilities are performed. It is found that the stress parameters (E and γ0) have remarkable effects on the dimensionless stress-dependent permeabilities compared with other parameters (ϕ0 and ν). The proposed model may contribute to a better quantitative understanding of the coupled hydromechanical properties of porous rocks.