In this study, a fast and robust compositionally extended black-oil simulation approach is developed, which is capable of including the effect of large gas-oil capillary pressure for first and multi-contact miscible, and immiscible gas injection. The simulation approach is used to model primary depletion and gas flooding in a high-permeability reservoir using a five-spot flow pattern for different reservoir pressures. The comparison with fully-compositional model shows good agreement. For an initially undersaturated reservoir with both injection and production wells pressures above the original bubble-point pressure, gas evolves near the injection well and it later breaks through the production well as produced gas is injected. Additionally, the primary depletion and huff-n-puff gas injection in tight shale reservoirs by using the compositionally extended black-oil model indicates that the effect of large gas-oil capillary pressure on recovery becomes smaller as reservoir pressure is higher. Finally, a dynamic gas-oil relative permeability correlation that accounts for the compositional changes owing to the produced gas injection is introduced and applied, and its effect on oil recovery is examined.