Investigation of the critical entry pressure values associated with the permeation of an oil droplet through a cascade of pore throats and pore bodies: A quasistatic analysis

Abstract

In this work the problem of permeation of an oil droplet through a cascade of pore bodies and pore openings is investigated. When the oil droplet becomes totally within the pore cascade, it is called an oil ganglion. The cascade is considered composed of spherical pore bodies and cylindrical pore throats. The capillary entry pressure in relation to the applied pressure difference determines whether the oil ganglion will move or get trapped. Several cases are considered including the case when the leading part of the oil droplet is inside the cascade and the receding part is at the surface, the case when both the interfaces are within pore throats, the case when the two interfaces are within pore bodies, and the case when one interface is in a pore throat and the other is in the pore body. An algebraic equation has been developed to determine the entry pressure when part of the droplet is still at the surface of the cascade. This formula reduces to that found in literature when the whole droplet pins at the surface. This provides confidence in the developed relationship and the modeling approach. The entry pressure associated with all these cases is determined. Several examples have been considered to show how the critical entry pressure may vary throughout the cascade. It is found that, the influence of the receding part of the droplet at the surface of the membrane is not significant on the entry pressure formula. In other words, one can use the critical pressure formula associated with the leading interface to determine the breakthrough through the different parts of the cascade.