Effect of size-dependent mixed-wettability on pore-scale immiscible displacement dynamics: A numerical study

Immiscible displacement in porous media is governed by pore-scale interfacial dynamics and strongly modulated by wettability heterogeneity. Pore-scale observations indicate that wettability can depend on pore size, yet the consequences for invasion patterns remain unclear. Here we perform direct numerical simulations of immiscible displacement under four wettability conditions, focusing on two size-dependent mixed-wet distributions: (i) a binary distribution with an abrupt weakly hydrophilic–strongly hydrophobic transition and (ii) a continuum distribution with a smooth wettability gradient. In both mixed-wet cases, larger pores are assigned more hydrophobic contact angles; uniformly weakly hydrophilic and uniformly strongly hydrophobic conditions serve as references. At Ca=2.0×10⁻⁵ and viscosity ratio M=0.02, the continuum distribution develops the narrowest preferential pathways and the highest residual saturation, whereas the binary distribution yields more compact invasion and lower residual saturation. Mechanistic analysis of representative pore-filling events shows that the binary distribution promotes contact-line pinning at sharp wettability transitions, suppressing post-Haines-jump relaxation and limiting fingering, while the continuum distribution retains partial mobility that sustains preferential invasion. Breakthrough residual saturation decreases with decreasing Ca in the binary case but is nearly independent of Ca in the continuum case, and decreases with increasing M in all cases. Reversing the pore-size wettability trend suppresses fingering most clearly at intermediate times and yields lower residual saturation in the binary case than in the corresponding continuum case. These results show that the functional form of pore-size-dependent wettability strongly controls invasion pathways and residual trapping. Predictive models of subsurface immiscible displacement should therefore represent pore-scale wettability correlations, rather than only their average strength or overall trend.