Homogeneous Volume-of-Fluid (VOF) Model for Simulating the Imbibition in Porous Media Saturated by Gas

Biphasic flow in porous media is of great interest in several areas, such as petroleum and oil recovery, food impregnation, hydrology, and soil science. In this work, the penetration of an external liquid-into a porous medium saturated with air, caused by the macroscopic pressure difference, was studied (impregnation). For that, a porous medium saturated with air was considered and immersed in a container with a wetting liquid. In this situation, a forced imbibition of the porous space occurs, until the equilibrium between internal and external pressure is reached, after internal gas compression. A mathematical model for this impregnation process was developed for a two-dimensional (2D) homogeneous porous medium using the volume-of-fluid (VOF) method. The medium impregnation rate calculated with the model developed in the present study was compared to the values obtained from reference analytic solutions, i.e., the equations of Lucas-Washburn and Darcy's law. An excellent agreement was found between simulation results and the reference mathematical solutions, which indicates that the dynamics of liquid invasion can be predicted if the global pressure gradient is known. The model allows for following the interface advance for classical and non-classical geometries, using a fixed mesh, without the need of its reconstruction at each interface displacement. This procedure is timesaving and inputs robustness to the computational model.