Gas injection into a naturally fractured oil reservoir keeps the reservoir pressure and increments the initial recovery from the reservoir. The main aim of this work was to develop a numerical model to calculate the mass transfer (molecular diffusion and convection) between a gas injected in the fracture and residual fluid (gas and oil) in a matrix block. The dual continuum model is applied to describe flow behaviour and fluid recovery in porous media. Finally, the model is validated by comparing the outcomes with the results of two experimental works available in the literature. The mathematical model results are in agreement with the laboratory data including recovery of each component, saturation profile, and the pressure gradient between matrix and fracture. Modeling results show that after 25 days of N2 injection, the lighter and heavier components (C1 and C5) are recovered about 51% and 39%, respectively. These amounts for CO2 injection are 49% and 27%. It is found that the convection mechanism has a great effect on preventing the pressure drop of the reservoir during injection operations. In the nitrogen injection, without considering the convection, after 30 days, the matrix pressure reaches 1320 Psi from 1479 Psi but after 30 days, considering the convection, the pressure reaches 1473 Psi from 1479 Psi.