Towards pore-network modelling of imbibition: Dynamic barriers and contact angle dependent invasion patterns

Imbibition is an ubiquitous 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), snap-off events along with the relative competition between them. 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 interdependent on several parameters such as the shape of the pore and fluid properties (contact angle, density of the fluids). The interaction between these interdependent parameters is investigated in a quantitative manner. We demonstrate the existence of a critical contact angle that determines the occurrence of a capillary barrier zone in which the capillary forces act against imbibition. Farther and larger the contact angle of the wetting phase compared to the critical contact angle results in a wider capillary barrier zone. It is important to acknowledge the occurrence of the capillary barriers as they can potentially prevent filling of the pore space and play a vital role in choosing the invasion path. For the synthetic pore geometries considered, we provide analytical and semi-analytical expressions to determine the critical contact angle and the position of the capillary barrier zone respectively. During spontaneous imbibition, only inertial forces can dynamically help the interface overcome the capillary barrier zone where interfacial reconfigurations are observed. The inertial contact angle is the contact angle of the wetting phase that can overcome the capillary barrier zone using inertial forces. The inertial contact angle is computed numerically for several inertial systems and for various shapes of the synthetic pore geometry. The results of this quantitative analysis can be utilized to improve the existing pore filling rules and better the predictive capabilities of PNM related to two phase flow dynamics.