Analytical Modeling and Comparative Analysis of Capillary Imbibition in Shale Pores of Various Geometries

Fluid imbibition from hydraulic fractures into shale formations is mainly affected by a combination of capillary forces and viscous resistance, both of which are closely related to the pore geometry. This study established five self-imbibition models with idealized pore structures and conducted a comparative analysis of these models. These models include circular, square, and equilateral triangular capillaries; a triangular star-shaped cross-section formed by three tangent spherical particles; and a traditional porous medium representation method. All these models are derived based on Newton’s second law, where capillary pressure is described by the Young-Laplace equation and viscous resistance is characterized by the Hagen-Poiret equation and Darcy’s law. All derived models predict that the fluid imbibition distance is proportional to the square root of time, in accordance with the classical Lucas-Washburn law. However, different pore structures exhibit significantly different characteristic imbibition rates. Compared to the single pore model, the conventional Darcy’s law-based model for porous media predicts significantly lower imbibition rates, which is consistent with the relatively slower uptake rates in actual shale nanoscale pore networks. These findings emphasize the important role played by pore geometry in fluid imbibition dynamics and further point to the need for optimizing pore structure to extend fluid imbibition duration in shale reservoirs in practical operations.