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Corner film flow governed by dimensionality and wettability profoundly impacts displacement patterns, yet its effect on relative permeability remains unclear. We use a multiple-relaxation-time color-gradient lattice Boltzmann model with geometric wetting boundaries to examine, under identical pore structures, how capillary number, wettability, and viscosity ratio modulate the influence of wetting films on relative permeabilities. We find that in 3D (three-dimensional) capillary bridges link corner films into secondary pathways that increase wetting connectivity and strengthen interfacial viscous coupling. Increasing capillary number raises the relative permeabilities of both phases in 2D (two-dimensional) and 3D. At high capillary number or high wetting saturation, bulk flow dominates and the difference in wetting permeability shrinks, whereas the non-wetting permeability remains higher in 3D than in 2D due to stronger viscous coupling. Decreasing the contact angle enhances viscous coupling and weakens non-wetting–solid interactions, thereby increasing the non-wetting relative permeability and widening the 3D over 2D gap. The wetting-phase response to wettability depends on the presence of films and saturation. Increasing the viscosity ratio markedly elevates the non-wetting relative permeability, with the larger interfacial area in 3D further amplifying viscous coupling. The wetting-phase relative permeability decreases with viscosity ratio, yet at very high viscosity ratios the initial phase configuration becomes influential. This study clarifies the dimensional mechanisms governing relative permeability, especially the controlling role of wetting films, which is critical for judging when multiphase-flow physics can be simplified.
Zhu et al. (Mon,) studied this question.