Prediction of spontaneous imbibition in fractal porous media based on modified porosity correlation

Spontaneous imbibition plays a significant role in different technical applications, and several analytical models have been proposed for predicting the fluid imbibition mass into porous media based on the fractal theory. Herein, these previous models are reconsidered in view of the obvious difference between the effective porosity and the areal porosity of porous media. Firstly, an implicit equation for fractal tortuosity is proposed and a modified correlation for the areal porosity is presented; then, a semi-analytical prediction model for fluid imbibition mass with gravity pressure is derived; finally, comparisons of predictions among several previous models with the present model are carried out. The modeling results show consistency with the experimental data published in the literature.