In this work, a Lattice Boltzmann model for multi-component fluids augmented with repulsive near-contact interactions is employed to simulate the dynamics of flowing emulsions within idealized pores. The model is firstly tested on experimental data of droplets’ self-assembly in diverging-converging micro-channels from literature and then used to investigate the trapping/mobilization of the dispersed phase of an emulsion in an idealized series of pores, as influenced by both the Capillary number and the solid walls wettability. Both parameters may vary as the result of an injection of surfactants, a procedure commonly adopted in soil remediation and Enhanced Oil Recovery applications. The analysis shows that the proposed model is able to reproduce correctly the experimental data and gives interesting insights on the trapping/mobilization phenomenon resulting from a modification of the flow conditions caused by the injection of surfactants.