Prediction of capillary pressure-saturation relationship for primary drainage in a 3D fibrous porous medium using volume-of-fluid method

The unsaturated flow through fibrous porous media at the macroscale is typically described using the Richards equation which requires constitutive relations for capillary pressure and relative permeability as a function of liquid saturation. In literature, these constitutive relations are typically estimated using reduced-order modeling approaches such as pore-network (PN) models, full-morphology (FM) method etc. In this paper, we determine quasi-static capillary pressure-saturation relationship (Pc-S) for primary drainage in a 3D isotropic fibrous medium by performing direct numerical simulations (at microscale) with the volume-of-fluid (VOF) method, which takes into account the detailed description of the pore structure and interface dynamics. As a first step, the accuracy of the VOF method was verified by simulating a test case of quasi-static drainage between two cylinders. Next, a grid-convergence study was performed to determine the optimal grid resolution required for the 3D simulations of quasi-static drainage. Using this grid, the Pc-S relationship for primary drainage in an isotropic fibrous structure was calculated from the direct simulations, and the results were compared with the Pc-S estimated using full-morphology method, which is a quasi-static reduced-order geometric approach. In the VOF method, no modeling assumptions are made on the geometry of the pore structure and the liquid propagation, and thus, the results from direct simulations can be used to gain insights into the limitations of the reduced-order models.