Mathematical model of liquid spontaneous imbibition into gas-saturated porous media with dynamic contact angle and gravity

Abstract

Liquid imbibition with dynamic contact angle is a ubiquitous phenomenon of fluid flow in porous media, but its analytical solution is challenging to derive. In this work, the analytical solution of liquid imbibition in an inclined capillary tube with velocity-dependent contact angle and gravity is first derived. The time required for the liquid-gas interface to reach a certain distance by spontaneous imbibition with static contact angle and dynamic contact angle are provided. Assuming that the porous medium consists of a bundle of tortuous capillary tubes with fractal distribution of pore size, a mathematical model of liquid imbibition in core-scale porous media with dynamic contact angle and gravity is developed. The studies show that the dynamic contact angle can significantly reduce the imbibition velocity at the initial stage of imbibition, especially in large pores, which forms a nonlinear correlation between imbibition velocity and imbibition time in a log-log plot.