A comprehensive model for oil-water relative permeabilities in low-permeability reservoirs by fractal theory

Oil-water relative permeability curve is an important parameter for analyzing the characters of oil and water seepages in low-permeability reservoirs. The fluid flow in low-permeability reservoirs exhibits distinct nonlinear seepage characteristics with starting pressure gradient. However, the existing theoretical model of oil-water relative permeability only considered few nonlinear seepage characteristics such as capillary pressure and fluid properties. Studying the influences of reservoir pore structures, capillary pressure, driving pressure and boundary layer effect on the morphology of relative permeability curves is of great significance for understanding the seepage properties of low-permeability reservoirs. Based on the fractal theory for porous media, an analytically comprehensive model for the relative permeabilities of oil and water in a low-permeability reservoir is established in this work. The analytical model for oil-water relative permeabilities obtained in this paper is found to be a function of water saturation, fractal dimension for pores, fractal dimension for tortuosity of capillaries, driving pressure gradient and capillary pressure between oil and water phases as well as boundary layer thickness. The present results show that the relative permeabilities of oil and water decrease with the increase of the fractal dimension for tortuosity, whereas the relative permeabilities of oil and water increase with the increase of pore fractal dimension. The nonlinear properties of low-permeability reservoirs have the prominent significances on the relative permeability of the oil phase. With the increase of the seepage resistance coefficient, the relative permeability of oil phase decreases. The proposed theoretical model has been verified by experimental data on oil-water relative permeability and compared with other conventional oil-water relative permeability models. The present results verify the reliability of the oil-water relative permeability model established in this paper.