Optimal displacement of immiscible two-phase fluids in a pore doublet

Abstract

Multiphase fluid flow in a pore doublet is a fundamental problem and is important for understanding the transport mechanisms of multiphase flows in porous media. During the displacement of immiscible two-phase fluids in a pore doublet, the transport process is influenced not only by the capillary and viscous forces, but also the channel geometry. In this paper, a mathematical model is presented of the two-phase fluid displacement in a pore doublet considering the effects of capillary force, viscous force, and the geometric structure. This leads to a new and more general analytical solution for the pore doublet system, and it is found that the displacement process is dominated by the capillary number, viscosity, and radius ratios. Also, the optimal displacement is defined, which refers to the wetting fluids in the two daughter channels breaking through the branches simultaneously (i.e., both having the same breakthrough time). Also, the critical capillary number corresponding to the optimal displacement is obtained, which is related to the radius ratio of the two daughter channels and the viscosity ratio of the two immiscible fluids. Finally, analytical results are presented for the displacement in the pore doublet, which can be used to explain and understand the preferential flows in porous media, such as for improving oil recovery from porous media; these are usually observed in oil recovery, groundwater pollution, and the geological sequestration of carbon dioxide.