Interface tracking of an oil ganglion inside a cascade of pore bodies and pore throats: A quasistatic investigation

Abstract

The study of the permeation of oil droplets through a network of pore bodies and pore throats is complicated because of the need to track both the advancing and the receding interfaces and the possible branching of the oil ganglion. For the sake of simplicity and to gain understanding of the features associated with the motion of a droplet in a network, in this work, we eliminate the possibility of branching. In other words, we consider the case in which the oil droplet moves through a cascade of pore bodies and pore throats. In this case only two interfaces need to be tracked; namely the receding and the advancing interfaces. While it was possible to derive analytical expressions to determine the critical entry pressures when the oil droplet is still at the surface of the cascade, it remains challenging to find such analytical expressions when the oil droplet completely enters it. In this case both the advancing and the receding interfaces play a role. When the oil droplet completely enters the cascade, it becomes an oil ganglion, the movement of which is determined by the entry pressure. The entry pressure depends on the curvatures of both the leading and receding interfaces. This implies that the entry pressure is changing along the cascade. The largest values of the entry pressure, however, are those obtained when the leading interface is in a pore throat and the receding interface is in a pore body. In this work, we estimate the entry pressure in two situations; namely, when the leading interface is at the entrance of a pore throat and, likewise, when it is at the end. One can then infer how the entry pressure changes along the pore throat length. To determine the curvature of the receding interface, we use the fact that, for incompressible fluids (which is our case), the volume of the oil ganglion is conserved and that the interfaces assume the static contact angle at the contact with the wall. A nonlinear algebraic equation is developed, the solution of which provides the radius of curvature of the receding interface. Interesting results are obtained including the entry pressure values at different locations, the distribution of the oil ganglion along the cascade, and the radius of curvatures of the leading and the receding interfaces.