Relative permeability for two-phase flow through corrugated tubes as model porous media

We report finite-element simulations of gas–liquid two-phase flows through a model porous medium made of corrugated tubes. By resolving the pore-scale fluid dynamics and interfacial morphology, we compute the relative permeability of the porous medium by averaging over a pore-size-distribution of a real porous medium. A constant pressure gradient is applied on both fluids to simulate a pressure-driven creeping flow, and a diffuse-interface model is used to compute the interfacial evolution and the contact line motion. We observe a number of flow regimes in the micro-pores, depending on the pore size, imposed pressure gradient, and other geometric and physical parameters. The flow rates vary nonlinearly with the pressure gradient, and the extended Darcy’s law does not hold in general. The interaction between the two phases, known as viscous coupling, is a prominent feature of the process. As a result, the relative permeability depends not only on saturation, but also on the capillary number, viscosity ratio, wettability of the solid wall, pore geometry, and the initial configuration. The effects of these factors are explored systematically and compared with previous studies.