In naturally fractured reservoirs, improving the matrix fracture interactions is critical to the success of the applied improved oil recovery method. Therefore, a study of the mechanisms that control the mass exchanges between fracture and matrix can help to optimize recovery. This paper concerns an experimental and simulation study to investigate the performance of the gas oil gravity drainage process in naturally fractured reservoirs. In this study, five gas injection experiments were conducted at different miscibility (i.e., immiscible and fully miscible) conditions using CO2, N-2, and a synthetic flue gas composed of 20% (v/v) CO2 and 80% (v/v) N-2. The impact of switching from an immiscible (i.e., nitrogen or flue gas) gas to a non-equilibrium and fully miscible CO, injection is investigated. The effect of miscibility on the block block interaction is also examined using a stacked core with an impermeable barrier. The results reveal that injection of non-equilibrium gas with higher solubility in the oil phase results in a zone of decreased oil viscosity, which leads to an improved gravity mediated recovery. The results also show that the ultimate oil recovery increases considerably once miscibility is achieved. A numerical model is implemented to perform compositional simulations of multiphase, multicomponent gas injections at different miscibility conditions. Agreement of the developed model with the experimental results indicates that gravity drainage, capillary holdup, and mixing are the main controlling mechanisms.