Optimal Wetting Angles in Lattice Boltzmann Simulations of Viscous Fingering

We conduct pore-scale simulations of two-phase flow using the 2D Rothman–Keller colour gradient lattice Boltzmann method to study the effect of wettability on saturation at breakthrough (sweep) when the injected fluid first passes through the right boundary of the model. We performed a suite of 189 simulations in which a “red” fluid is injected at the left side of a 2D porous model that is initially saturated with a “blue” fluid spanning viscosity ratios $$M = \nu _\mathrm{r}/\nu _\mathrm{b} \in [0.001,100]$$ and wetting angles $$\theta _\mathrm{w} \in [ 0^\circ ,180^\circ ]$$ . As expected, at low-viscosity ratios $$M=\nu _\mathrm{r}/\nu _\mathrm{b} \ll 1$$ we observe viscous fingering in which narrow tendrils of the red fluid span the model, and for high-viscosity ratios $$M \gg 1$$ , we observe stable displacement. The viscous finger morphology is affected by the wetting angle with a tendency for more rounded fingers when the injected fluid is wetting. However, rather than the expected result of increased saturation with increasing wettability, we observe a complex saturation landscape at breakthrough as a function of viscosity ratio and wetting angle that contains hills and valleys with specific wetting angles at given viscosity ratios that maximize sweep. This unexpected result that sweep does not necessarily increase with wettability has major implications to enhanced oil recovery and suggests that the dynamics of multiphase flow in porous media has a complex relationship with the geometry of the medium and the hydrodynamical parameters.