The double-displacement process (DDP) in dipping reservoirs has resulted in large oil recoveries with low operating costs. The large recoveries in the field result from high sweep efficiency and very low residual oil saturation, where very low saturation is obtained by oil flow through thin spreading films. Oil spreads to saturations near zero owing to competing interfacial tensions at contact points between three phases (oil, water, and gas). Experimental studies with micromodels and pore scale imaging support oil flow through films, where the rate of recovery and film drainage are controlled by parameters such as fluid compositions and topology of the water and gas interface within a give pore morphology. The interface topology is largely controlled by phase saturation, gas phase connectivity, pore structure and fluid wettability. Current relative permeability models, however, do not model spreading reliably as they do not include a mechanistic model for dynamics of film spreading on relative permeability. We use the relative permeability equation of state (kr-EOS) to mechanistically model dynamics of film spreading and its effect on relative permeability. The reconnection of oil phase by spreading is modeled with a compositional evolution function for Euler characteristic. The IFTs and spreading coefficients are calculated based on phase compositions. Then, the physically based kr-EOS is implemented in our in-house fully compositional reservoir simulator. The simulation results are compared to published core flood and field data. We also performed a sensitivity analysis to determine the effects of gas and oil composition, miscibility, and reservoir heterogeneity on recovery rates and timing. These results show that saturation profiles from simulation are similar to those observed from CT-scanning of core floods, demonstrating good accuracy from the new mechanistic relative permeability model.