A Fractal Model for the Stress-Dependent Permeability and Relative Permeability in Tight Sandstones

Stress-dependent permeability and relative permeability in porous media are important in petroleum-engineering fields. It has been shown that stress-dependent permeability and relative permeability play important roles in determination of flow characteristics for tight-sandstone porous media. In this work, novel predictive models for stress-dependent permeability and relative permeability in microporous media with lower permeability are developed on the basis of fractal theory. The predictions of irreducible water saturation, normalized porosity, normalized permeability, and the ratio K-rw/K-rg by the proposed model show a variation trend similar to that of the available experimental data. On the basis of the proposed normalized porosity and normalized permeability model, it is found that the normalized porosity and permeability decrease with effective stress, thus predicted results are in good agreement with former experiments. The proposed normalized porosity and normalized permeability are expressed as a function of the effective stress, rock elastic modulus, microstructural parameters, and initial irreducible water saturation. The theoretical study of relative permeability under stress demonstrates that wetting-phase relative permeability is related to the effective stress, microstructural parameters, and initial irreducible water saturation.