Threshold capillary pressure in capillaries with curved sides

Modeling of fluid flow through permeable media is of great importance in assessing the performance of both hydrocarbon reservoirs and aquifers. In this process, network models based on cylindrical capillaries with circular cross sections are frequently used. This type of capillaries are not able to reproduce interesting physical phenomena observed in the experiments, for example, situations where there is flow by films with the wetting fluid occupying the crevices and wedges of the structure. We present an analysis of the behavior of the capillary pressure of a droplet of non-wetting fluid with an infinite length, inside objects of cylindrical symmetry with curved sides. The calculation is based on a method proposed by Mayer and Stowe and Princen (MS–P). Different capillary geometries are considered, and the behavior of the capillary pressure and transversal fluid saturation as a function of the shape factor is studied. The results found either analytically or numerically, allow to understand the relation between geometry and flow properties, and helps in the building of more realistic pore network models for flow studies at the pore scale.