Enhanced oil recovery methods based on emulsion injection in porous media are based on the higher pressure drop in the emulsion flow when it is compared to the flow of the continuous phase at the same flow rate. This phenomenon depends on both viscous and capillary effects at the pore scale as the drops flow through the pore throats. In this work, we present a broad numerical study on the flow of planar emulsion drops through a constricted microcapillary channel that represents a pore throat connecting two adjacent pore bodies in a typical porous media. The emulsion concentration in the constriction region was controlled by a process of continuous injection of drops upstream the narrow channel. Both velocity and traction fields at the channel boundaries and drop surface are computed with the Boundary Element Method, and the position of the free surfaces in the flow is evolved by solving a kinematic equation in a Lagrangian representation. We investigate the effects of drop size, drop-to-basis fluid viscosity ratio and capillary number on the pressure loss by using a mobility reduction factor. The flow rate - pressure drop relation is studied by analyzing the mobility reduction factor as a function of the capillary number. It was found that a more efficient pore scale mobility control by emulsion injection can be achieved for high-viscosity drops that have the same size or are larger than the constriction at very low capillary number. (C) 2018 Elsevier Ltd. All rights reserved.