An analytical model for spontaneous imbibition in fractal porous media including gravity

Spontaneous imbibition of wetting liquid into porous media is regarded as a crucially important driving mechanism for enhancing oil recovery from naturally fractured reservoir, especially with low permeability. Based on the fractal character of pores in porous media, a full analytical model for characterizing spontaneous imbibition of wetting liquid vertically into gas-saturated porous media has been derived including gravity over the entire imbibition process time frame. The weight of wetting liquid imbibed into porous media is a function of contact area, porosity, pore fractal dimension, tortuosity, maximum hydraulic pore diameter, liquid density, viscosity, surface tension and liquid–solid interactions. Factors influencing the imbibition process upon approaching equilibrium weight were also analyzed. The proposed analytical model is consistent with the previous models and the predictions are in good agreement with available experimental data published in the literature.