Towards pore network modelling of spontaneous imbibition: contact angle dependent invasion patterns and the occurrence of dynamic capillary barriers

Abstract

Imbibition is an important process encountered in many porous media applications. At the pore scale, pore network models (PNM) are computationally efficient and can model drainage accurately. However, using PNM to model imbibition still remains a challenge due to the complexities encountered in understanding pore-scale flow phenomena related to pore body filling (PBF) and snap-off along with the relative competition between these events. In this work, we use direct numerical simulations (DNS) to revisit the basic principles of PBF in a two-dimensional synthetic pore geometry. We notice that PBF during spontaneous imbibition is dependent on several parameters such as shape of the transition zone, contact angle and the fluid properties like density. The interactions between these parameters are investigated in a quantitative manner. We demonstrate the existence of a critical contact angle 𝜃c and a barrier contact angle 𝜃b. 𝜃c depends on the shape of the pore geometry, whereas 𝜃b depends on the pore geometry, contact angle and fluid properties. For a system comprising of light fluids, 𝜃b is only slightly larger than 𝜃c; whereas for a system occupied by dense fluids, 𝜃b is notably larger than 𝜃c. The contact angle of the wetting phase 𝜃 in relation to 𝜃c and 𝜃b decides if the wetting phase can imbibe a pore body. Imbibition always occurs if 𝜃 < 𝜃c. For 𝜃 > 𝜃c, we observe capillary barrier zones in which capillary forces accompany viscous forces to resist spontaneous imbibition. For this case, we observe smooth transition of the meniscus curvature while the meniscus enters and exits capillary barrier zones. For 𝜃c ≤ 𝜃 ≤ 𝜃b, inertia assists the wetting phase to overcome resisting forces and imbibe the pore space. For 𝜃 > 𝜃b, the resisting forces dominate over inertia so that the wetting phase cannot imbibe the pore space. For the synthetic pore geometries investigated, we provide analytical and semi-analytical expressions to determine 𝜃c and the position of capillary barrier zones respectively. The barrier contact angle 𝜃b is computed numerically for several inertial systems and for various shapes of the synthetic pore geometry. The results of this quantitative analysis can be utilised to improve the existing pore filling rules and predictive capabilities of PNM used for two-phase flows.