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 Krw/Krg 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.

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Multiphase flow in porous media is very important in various scientific and engineering fields. It has been shown that relative permeability plays an important role in determination of flow characteristics for multiphase flow. The accurate prediction of multiphase flow in porous media is hence highly important. In this work, a novel predictive model for relative permeability in porous media is developed based on the fractal theory. The predictions of two-phase relative permeability by the current mathematical models have been validated by comparing with available experimental data. The predictions by the proposed model show the same variation trend with the available experimental data and are in good agreement with the existing experiments. Every parameter in the proposed model has clear physical meaning. The proposed relative permeability is expressed as a function of the immobile liquid film thickness, pore structural parameters (pore fractal dimension D f and tortuosity fractal dimension D T ) and fluid viscosity ratio. The effects of these parameters on relative permeability of porous media are discussed in detail.

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