Dynamic Pore-Scale Model of Drainage in Granular Porous Media: The Pore-Unit Assembly Method

Dynamics of drainage is analyzed for packings of spheres, using numerical experiments. For this purpose, a dynamic pore-scale model was developed to simulate water flow during drainage. The pore space inside a packing of spheres was extracted using regular triangulation, resulting in an assembly of grain-based tetrahedra. Then, pore units were constructed by identifying and merging tetrahedra that belong to the same pore, resulting in an assembly of pore units. Each pore unit was approximated by a volume-equivalent regular shape (e.g., cube and octahedron), for which a local capillary pressure-saturation relationship was obtained. To simulate unsaturated flow, a pore-scale version of IMPES (implicit pressure solver and explicit saturation update) was employed in order to calculate pressure and saturation distributions as a function of time for the assembly of pore units. To test the dynamic model, it was used on a packing of spheres to reproduce the corresponding measured quasi-static capillary pressure-saturation curve for a sand packing. Calculations were done for a packing of spheres with the same grain size distribution and porosity as the sand. We obtained good agreement, which confirmed the ability of the dynamic code to accurately describe drainage under low flow rates. Simulations of dynamic drainage revealed that drainage occurred in the form of finger-like infiltration of air into the pore space, caused by heterogeneities in the pore structure. During the finger-like infiltration, the pressure difference between air and water was found to be significantly higher than the capillary pressure. Furthermore, we tested the effects of the averaging, boundary conditions, domain size, and viscosity on the dynamic flow behavior. Finally, the dynamic coefficient was determined and compared to experimental data.