Pore-scale visualization and characterization of viscous dissipation in porous media

The effects of mutual transfer of momentum between two immiscible flowing fluids in porous media are not well understood nor predictable yet. From considerations at the pore-scale, it should be possible to determine whether and to what extent interfacial viscous coupling effects are significant.

We visualize the velocity distributions inside immobile globules of wetting phase (water) while a non-wetting phase (oil) is injected. We investigate viscous coupling effects and their relationship with the viscosity ratio and the capillary number.

Four regimes of viscous dissipation are identified: (i) a regime for which the fluid-fluid interface acts as a solid wall; (ii) a regime where the wetting phase is dragged in the direction of the imposed flow; (iii) and (iv) two regimes for which the trapped globule of water shows a recirculating motion due to the shear stress at the oil/water interface. We demonstrate the significant role of the lubricating effect and of the topology of the pore space on the magnitude of viscous dissipation. Importantly, for a viscosity ratio close to one and low capillary number, we demonstrate that viscous coupling effects should be incorporated into the existing Darcy's law formulation for two-phase flow in porous media.