A FRACTAL MODEL FOR WATER FLOW THROUGH UNSATURATED POROUS ROCKS

Abstract

In this work, considering the effect of porosity, pore size, saturation of water and tortuosity fractal dimension, an analytical model for the capillary pressure and water relative permeability is derived in unsaturated porous rocks. Besides, the formulas of calculating the capillary pressure and water relative permeability are given by taking into account the fractal distribution of pore size and tortuosity of capillaries. It can be seen that the capillary pressure for water phase decreases with the increase of saturation in unsaturated porous rocks. It is found that the capillary pressure for water phase decreases as the tortuosity fractal dimension decreases. It is further seen that the capillary pressure for water phase increases with the decrease of porosity, and at low porosity, the capillary pressure increases sharply with the decrease of porosity. Besides, it can be observed that the water relative permeability increases with the increase of saturation in unsaturated porous rocks. This predicted the capillary pressure and water relative permeability of unsaturated porous rocks based on the proposed models which are in good agreement with the experimental data and model predictions reported in the literature. The proposed model improved the understanding of the physical mechanisms of water flow through unsaturated porous rocks.