The effect of a surfactant on wettability alteration and emulsion inversion is studied using Dissipative Particle Dynamics (DPD) modeling. The DPD model contains 1200 oil molecules, 4800 water molecules, 400 oil soluble (indigenous to the oil) surfactants with a head-tail configuration and 400 water soluble molecules to mimic a surface active chemical/ion in the water. Results show that surfactant migrates to the fluid-fluid interface in general, where its potential energy is minimal. However, thermal kinetic energy can lead to a "tunneling" through the interface and into the other phase with a small probability. The same effect lead to migration of the oil soluble surfactant from the oil phase onto the water wet surface, and caused wetting alternation from a water-wet to a surfactant coated effectively oil-wetting surface. The water soluble surface active molecule suppressed this effect when added. Additional emulsion inversion studies confirmed the "Bancroft rule": oil-in-water emulsions were induced by water soluble surfactant, and water-in-oil emulsions were induced for oil soluble surfactant. The explored cases were characterized by high interfacial curvature. For cases in which the surfactant is just as soluble in water as in oil, the interface had a minimal curvature; i.e., a flat interface or a more geometrically complex gyroid interface with a minimal average curvature. Results demonstrate that DPD represents a suitable numerical laboratory to investigate the macroscopic behavior (topology and morphology) of an oil/water/surface system as function of the molecular parameters such as solubility.