A NOVEL FRACTAL MODEL FOR THE INVASION DEPTH OF FLUID THROUGH THE TORTUOUS CAPILLARY BUNDLE WITH ROUGHENED SURFACES IN POROUS MEDIA

Abstract

In this paper, a novel fractal model for the invasion depth of fluid through the tortuous capillary bundle with roughened surfaces in porous media is proposed. The capillary pressure effect is considered in the proposed model. The proposed model is expressed as a function of structure parameters of porous media, including the relative roughness, the fractal dimension for pore size distribution, the contact angle, the density, the gravitational acceleration, the tortuosity and porosity. The invasion depth can be quantitatively characterized by the proposed model. By using the fractal theory, the effect of relative roughness on the invasion depth is discussed. It is observed that the invasion depth decreases with increasing the relative roughness of the tortuous capillary bundle with roughened surfaces. In addition, it is found that the invasion depth increases with the increase of the invasion time. The proposed model predictions are in good agreement with the available experimental data. Each parameter in our model has clear a distinct physical meaning, which may contribute to comprehend the better understanding of seepage mechanisms.