  We study the characteristics of fluid-fluid displacement in simple mixed-wet
porous micromodels numerically using a dynamic pore network model. The porous
micromodel consists of distinct water-wet and oil-wet regions, whose fractions
are systematically varied to yield a variety of displacement patterns over a
wide range of capillary numbers. We find that the impact of mixed-wettability
is most prominent at low capillary number, and it depends on the complex
interplay between wettability fraction and the intrinsic contact angle of the
water-wet regions. For example, the fractal dimension of the displacement
pattern is a monotonically increasing function of wettability fraction in flow
cells with strongly water-wet clusters, but it becomes non-monotonic with
respect to wettability fraction in flow cells with weakly water-wet clusters.
Additionally, mixed-wettability also manifests itself in the injection-pressure
signature, which exhibits fluctuations especially at low wettability fraction.
Specifically, preferential filling of water-wet regions leads to reduced
effective permeability and higher injection pressure, even at vanishingly small
capillary numbers. Finally, we demonstrate that scaling analyses based on a
weighted average description of the overall wetting state of the mixed-wet
system can effectively capture the variations in observed displacement pattern
morphology.
