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 in a porous material. The macroscopic flow behavior can be determined based on the pore scale flow, at which emulsions cannot be treated as a single phase non Newtonian liquid, since the drop diameters are in the same order of magnitude of the pore throats. In the pore scale, emulsion flow needs to be studied as a two phase flow including capillary effects. In order to determine the effect of interfacial tension, viscosity ratio, drop size and capillary geometry in the pressure drop of the flow of a single oil drop immersed in water through a straight and constricted capillary, a Level Set type method including surface tension forces was incorporated to a fully coupled implicit Navier - Stokes solver using finite element method. The results clearly show that mobility control is achieved by two different mechanisms. One based on the simple substitution of a low viscosity by a high viscosity liquid and the other based on the capillary forces associated with the drop deformation as it flows through the constriction. The results can be used to construct a pore level model that will be incorporated in a capillary network model to study flow of emulsions through porous media.