  Spontaneous imbibition has been receiving much attention due to its
significance in many subsurface and industrial applications. Unveiling
pore-scale wetting dynamics, and particularly its upscaling to the Darcy scale
are still unresolved. In this work, we conduct image-based pore-network
modeling of cocurrent spontaneous imbibition and the corresponding quasi-static
imbibition, in homogeneous sintered glass beads as well as heterogeneous
Estaillades. A wide range of viscosity ratios and wettability conditions are
taken into account. Based on our pore-scale results, we show the influence of
pore-scale heterogeneity on imbibition dynamics and nonwetting entrapment. We
elucidate different pore-filling mechanisms in imbibition, which helps us
understand wetting dynamics. Most importantly, we develop a non-equilibrium
model for relative permeability of the wetting phase, which adequately
incorporates wetting dynamics. This is crucial to the final goal of developing
a two-phase imbibition model with measurable material properties such as
capillary pressure and relative permeability. Finally, we propose some future
work on both numerical and experimental verifications of the developed
non-equilibrium permeability model.
