General capillary pressure and relative permeability expressions for through-plane fluid transport in thin fibrous sheets

The rate of fluid transport in partially saturated porous media depends on the media's instantaneous (function of saturation) relative permeability, k_r(S), and capillary pressure, P_c(S). Obtaining functional relationships for relative permeability and capillary pressure is only possible via experimentation or expensive microscale simulations, and needs to be repeated for different media having different fiber diameters, thicknesses, or porosities. In this concern, we conducted series of 3-D microscale simulations to investigate the effect of the above parameters on the relative permeability and capillary pressure of fibrous porous sheets. The results of our parameter study are utilized to develop general expressions for k_r(S) and P_c(S). Our general expressions are based on the existing empirical correlations of two-phase flow in granular media, and can easily be included in macroscale fluid transport equations to predict the rate of fluid release from partially saturated fibrous sheets in a time and cost-effective manner.