A stable spreading film between water and gas can extract a significant amount of bypassed non-aqueous phase liquid (NAPL) through immiscible three-phase gas/water injection cycles. In this study, the pore-scale displacement mechanisms by which NAPL is mobilized are incorporated into a three-dimensional pore morphology-based model under water-wet and capillary equilibrium conditions. The approach is pixel-based and the sequence of invasions is determined by the fluids’ connectivity and the threshold capillary pressure of the advancing interfaces. In addition to the determination of three-phase spatial saturation profiles, residuals, and capillary pressure curves, dynamic finite element simulations are utilized to predict the effective permeabilities of the rock microtomographic images as reasonable representations of the geological formations under study. All the influential features during immiscible fluid flow in pore-level domains including wetting and spreading films, saturation hysteresis, capillary trapping, connectivity, and interface development strategies are taken into account. The capabilities of the model are demonstrated by the successful prediction of saturation functions for Berea sandstone and the accurate reconstruction of three-phase fluid occupancies through a micromodel.