Two-phase regularized phase-field density gradient Navier–Stokes based flow model: Tuning for microfluidic and digital core applications

Here we present a regularized phase-field Navier–Stokes two-phase flow model with density gradient theory for interface treatment. The usage of regularization allows us for faster computations — for some particular simulation cases the time step could be increased x9 times. The computations are stable and spurious layers are suppressed with the help of nonlinear surface energy model. To verify the model we test rigorously against major classic problems: (1) droplet on a flat wall with given contact angle, (2) analytical solution for capillary rise, (3) hydrodynamical focusing within a micro-channel, (4) displacement in a pore doublet. As the application example, we simulate two-phase flow displacement within an X-ray microtomography scan of oil-bearing rock and demonstrate computation of relative permeabilities. We believe that developed model will be useful in numerous research applications: porous media design with desired physical properties, digital core technology applications to obtain flow properties of rocks and enhance hydrocarbon recovery, hydrological applications to study unsaturated flow in soils. Finally, we discuss potential improvements of the model as related to computational efficiency.