A model for predicting gas-water relative permeability of rock media based on fractal dimension characteristics

The relative permeability is an essential mechanical parameter characterizing the two-phase flow of rock media, and how to obtain the relative permeability quickly and effectively has become a critical issue to be solved in the current studies. A fractal analytical model for predicting the relative permeability of two-phase flow is developed using the fractal method to equate the rock pores as the capillaries with varying sizes and establish the equilibrium equation for gas-water phase flow based on the momentum balance. Then, the influences of the pore structure of the rock media on the permeability characteristics of the two-phase flow are studied based on the pore size scale and the tortuosity characteristics of the flow path. The relative permeability curves obtained by the model are in good agreement with the relevant experimental data, which verifies the reasonableness of the model. The results show that the model has better accuracy than other relative permeability models. The permeability characteristics of the rock media are related to fluid properties and pore structure. The smaller the fractal dimension D_f and the tortuous fractal dimension D_T, the larger the permeability of two-phase flow. In addition, increasing the value of D_T decreases the relative permeability of the water phase and increases the relative permeability of the gas phase. The model does not use any empirical constants to calculate the relative permeability, which avoids tedious data processing and can be effectively used in engineering fields such as shale gas extraction.