Flow of a drop through a constricted microcapillary

Abstract

Oil–water emulsion can be used as a mobility control agent in enhanced oil recovery methods in order to achieve a more efficient sweep of the reservoir. The application of such technique requires full understanding of how emulsions flow through porous media. The macroscopic behavior is directly determined by the pore-scale flow, at which emulsions cannot be treated as a single phase non-Newtonian liquid, since the drop diameter can be of the same order of magnitude of the pore throats. Experiments and theoretical analyses of flow of oil–water emulsions through straight and constricted capillaries, which can be considered as models for the geometry of a pore throat connecting two adjacent pore bodies, have shown that for emulsion flow, the pressure drop at a fixed flow rate is raised by two different mechanisms: a viscous effect related to the substitution of a lower viscosity (water) liquid by a higher viscosity liquid (oil) and a capillary effect related to the deformation of the oil–water interface as it passes through the capillary throat.In order to determine the pressure drop – flow rate relation of emulsion flow as a function of drop diameter, capillary geometry, viscosity of both phases and flow rate, we study the flow of a single drop suspended in a continuous immiscible phase flowing through a constricted microcapillary. The transient free boundary capillary flow problem is solved by coupling a modified level-set method to a fully-implicit finite element method.The effect of the dispersed phase on the flow is characterized by a mobility reduction factor, defined as the ratio of the pressure drop of the continuous phase alone to the peak pressure difference of the drop flow, at the same flow rate. The predictions show that the mobility reduction factor falls as the capillary number decreases and drop size rises; pore scale mobility control by emulsion injection is more effective at low enough capillary number and large drops.