A fractal model for predicting irreducible fluid saturation of two-phase flows in rock media under stress

The irreducible fluid saturation is a significant parameter for predicting the relative permeability in two-phase flows and plays an important role in engineering fields such as oil and gas reservoir development. To this end, the rock is equated as an aggregate of solid clusters based on the fractal theory and capillary model, and different fractal dimensions are introduced to characterize the scale distribution of solid clusters and the tortuosity of flow paths, respectively. Then, a model for predicting the irreducible fluid saturation under stress is proposed and validated using the experimental data. Finally, the stress sensitivity of irreducible fluid saturation and the influence mechanism of each parameter in the model are analyzed. The results show that the irreducible fluid saturation is closely related to the fluid viscosity, pore structure parameters, pressure drop gradient and elastic modulus. The effective stress increases the irreducible fluid saturation. The fractal dimensions can represent the thickness of the fluid film formed by the irreducible fluid and the actual flow length, which quantifies the influences of the pore structure characteristics on the irreducible fluid saturation.