A GENERAL FORMULA FOR CAPILLARY SUCTION-PRESSURE IN POROUS MEDIA

Imbibition or injection of a liquid into a porous medium is often modeled as a fully saturated flow behind a clearly defined liquid front. In such a quasi-steady moving-boundary problem, the capillary pressure is needed as a pressure boundary condition on the liquid front to pull the front along during such an imbibition/injection process. A simple, general formula has been developed for the capillary suction pressure in porous media, which relates the capillary pressure to the microstructure of various porous media. The energy-balance principle is applied during the wicking process to develop this expression for the capillary pressure in a general porous medium. The proposed formula can be applied to both the homogeneous as well as inhomogeneous porous media. To validate the suggested theory, six different cases of the capillary pressure from the literature are considered. It is shown that the new formula leads to an identical expression for the capillary pressure for each of the studied cases. The proposed equation can also be used to estimate the capillary pressure from the micrographs of a porous medium.