Relative Permeability Model Taking the Roughness and Actual Fluid Distributions into Consideration for Water Flooding Reservoirs

Reservoir relative permeability is greatly important to the development of water flooding reservoirs. Currently, most researches on relative permeability have not taken the roughness of pore surface and actual fluid distributions into consideration. In this paper, a novel relative permeability model for water flooding reservoirs taking the roughness and actual fluid distributions into consideration has been proposed by using the fractal theory. The novel model contains some key parameters, all of which have clear physical meanings, such as the immobile liquid film thickness, relative roughness, tortuosity fractal dimension DT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ D_{\text{T}} $$\end{document} and pore fractal dimension Df\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ D_{\text{f}} $$\end{document}. The predicted results of the novel fractal relative permeability model are consistent with published experimental data. That verifies the correctness of the novel fractal relative permeability model. Finally, sensitive factor analysis of novel relative permeability model is conducted. We can find that the wetting fluid relative permeability decreases as the immobile wetting fluid film thickness or relative roughness increases. When the tortuosity fractal dimension or pore fractal dimension increases, the wetting relative permeability and non-wetting relative permeability will both decrease. An increase in maximum pore diameter or the decreasing of minimum pore diameter results in the reduction in fractal dimension of flow channel and discontinuous saturation. The increasing of maximum pore diameter results in an increase in the relative permeability of wetting fluid. The minimum pore diameter has tiny effect on the relative permeability.