  The displacement of multiphase fluid flow in a pore doublet is a fundamental
problem, and is also of importance in understanding of the transport mechanisms
of multiphase flows in the porous media. During the displacement of immiscible
two-phase fluids in the pore doublet, the transport process is not only
influenced by the capillary and viscous forces, but also affected by the
channel geometry. In this paper, we first present a mathematical model to
describe the two-phase fluid displacement in the pore doublet where the effects
of capillary force, viscous force and the geometric structure are included.
Then we derive an analytical solution of the model for the first time, and find
that the displacement process is dominated by the capillary number, the
viscosity ratio and the radius ratio. Furthermore, we define the optimal
displacement that the wetting fluids in two daughter channels break through the
branches simultaneously (both of them have the same breakthrough time), and
also obtain the critical capillary number corresponding to the optimal
displacement, which is related to the radius ratio of two daughter channels and
viscosity ratio of two immiscible fluids. Finally, it is worthy noting that the
present analytical results on the displacement in the pore doublet can be used
to explain and understand the phenomenon of preferential imbibition or
preferential flow in porous media.
