Investigation of the Filling of a Spherical Pore Body with a Nonwetting Fluid: A Modeling Approach and Computational Fluid Dynamics analysis

Understanding the dynamics of the filling process of a pore body with a nonwetting fluid is important in the context of dynamic pore network models and others. It can justify many of the assumptions behind the different rules that describe how the network behaves during imbibition and drainage processes. It also provides insight into the different regimes pertinent to this system. The filling process starts with the contact line pinning at the pore entrance. Three regimes can be identified during the filling process that is related to how the contact line advances. In the first two regimes, the contact line pins at the pore entrance while the emerging droplet develops, and in the third one, the contact line departs the entrance of the pore and advances along the pore surface. During the first regime, which is brief, the curvature of the meniscus increases, and likewise, the corresponding capillary pressure, while in the other two regimes, the curvature decreases and so does the capillary pressure. Such behavior results in the rate at which the nonwetting fluid invades the pore to change. It initially decreases, then increases as the meniscus advances. The radius of curvature of the meniscus, eventually, increases to infinity for which the interface assumes a flat configuration. A one-dimensional modeling approach is developed that accounts for all these regimes. The model also considers the two immiscible fluids over a wide spectrum of contrast in viscosity. Information about the mean velocity of the invading fluid, the location of the contact line, the radius of curvature of the meniscus, the volume of the emerging droplet, and several others are among the details that the model provides. A computational fluid dynamics (CFD) simulation has also been considered to confirm the proposed fates of the interface and to provide a framework for comparisons. The results of the validation process show, generally, a very good match between the model and the CFD analysis.