Pore-scale numerical modeling of coupled fluid flow and medium geometrical deformations in an unconsolidated porous medium

The interplay of fluid flow and medium grains' deformation/movement in unconsolidated porous media was numerically studied. The numerical simulations were done through coupling Cahn-Hilliard phase field and Navier-Stokes equations for fluid flow as well as stress-strain and Arbitrary Lagrangian/Eulerian mesh alteration equations for geomechanical effects, by the finite-element method. Single/two-phase flow through a real patterned micro-scale medium with/without grains' deformation and movements/rotation were studied. In single-phase models, the fluid velocity distribution was quite similar for the cases with rigid grains and that with only deformed grains. However, in an unconsolidated medium, the velocity magnitude and distribution were modified. The medium porosity had a linear trend with pressure, and was independent of the grains' movement/rotation. The models with deformed grains showed good agreement with Kozeny-Carman equation in permeability variation versus pressure. In the two-phase flow models, the velocity/displacement profiles, relative permeability end-points and capillary pressure were quantitatively compared in rigid and unconsolidated media versus medium wettability. The effect of the grains' deformation on the fluid distributions was negligible at low capillary numbers, especially in water-wet and neutral wetting conditions. However, the grains' movement/rotation considerably modified the flow regime at different grains' contact angles. At higher capillary numbers, the grains' deformation effect was more pronounced.