Evaluation of a coupled model for numerical simulation of a multiphase flow system in a porous medium and a surface fluid

• A numerical simulator coupling NS equations and Darcy equations was developed.
• Square-pillar experiments were conducted to estimate the ability of the simulator.
• The numerical simulator was able to reproduce the experimental results.
• Conditions across the boundary between materials were satisfied in the simulations.

Numerical simulations that couple flow in a surface fluid with that in a porous medium are useful for examining problems of pollution that involve interactions among atmosphere, water, and groundwater, including saltwater intrusion along coasts. Coupled numerical simulations of such problems must consider both vertical flow between the surface fluid and the porous medium and complicated boundary conditions at their interface. In this study, a numerical simulation method coupling Navier–Stokes equations for surface fluid flow and Darcy equations for flow in a porous medium was developed. Then, the basic ability of the coupled model to reproduce (1) the drawdown of a surface fluid observed in square-pillar experiments, using pillars filled with only fluid or with fluid and a porous medium and (2) the migration of saltwater (salt concentration 0.5%) in the porous medium using the pillar filled with fluid and a porous medium was evaluated. Simulations that assumed slippery walls reproduced well the results with drawdowns of 10–30 cm when the pillars were filled with packed sand, gas, and water. Moreover, in the simulation of saltwater infiltration by the method developed in this study, velocity was precisely reproduced because the experimental salt concentration in the porous medium after saltwater infiltration was similar to that obtained in the simulation. Furthermore, conditions across the boundary between the porous medium and the surface fluid were satisfied in these numerical simulations of square-pillar experiments in which vertical flow predominated. Similarly, the velocity obtained by the simulation for a system coupling flow in surface fluid with that in a porous medium when horizontal flow predominated satisfied the conditions across the boundary. Finally, it was confirmed that the present simulation method was able to simulate a practical-scale surface fluid and porous medium system. All of these numerical simulations, however, required a great deal of computational effort, because time was incremented in 0.05- to 0.10-s steps. Hereafter, the present simulation method needs to be improved so that the simulations can be conducted with less computational effort.