A coupled fractal model for predicting the relative permeability of rocks considering both irreducible fluid saturation and stress effects

The relative permeability of rocks is an essential parameter for evaluating two-phase flow characteristics and plays an important role in engineering fields such as resource exploitation. To this end, a mathematical model for predicting relative permeability was first developed based on an equivalent capillary model and fractal theory. The proposed model considers the irreducible fluid saturation under stress and quantifies the influence of the pore structure characteristics on the relative permeability. This model was then compared with relevant experimental data and existing theoretical expressions to verify its validity. Finally, the factors affecting the two-phase seepage characteristics were discussed. The results show that the irreducible fluid saturation is intimately connected to the fractal dimensions, pore size, fluid viscosity, pressure drop gradient, and elastic modulus. Fluid properties and pore structure characteristics are the main factors affecting relative permeability. The wetting phase relative permeability is more sensitive to pore structure and irreducible fluids. Increased effective stress increases irreducible fluid saturation, reduces two-phase flow capacity, and significantly decreases the relative permeability of wetting phase fluids. Increased elastic modulus and Poisson's ratio decrease the irreducible fluid content under stress and increase the permeability.