: Gas injection in naturally fractured reservoirs for improving oil recovery is applicable for a long time. Gas injection maintains the reservoir pressure, and increases oil recovery by gravity drainage and to a lesser extent by mass transfer between the flowing gas in the fracture and the porous matrix or by evaporating middle or heavy components. Because injected gas isn’t in equilibrium with reservoir oil at first, contact between phases causes mass transfer and change properties of two phases. When gas injected into an unsaturated reservoir, gas entered into the matrix and fracture system. At first, the oil of fracture displaced and then oil of matrix contact with gas. Gas components, diffuse into the fracture and vice versa. This action, swell oil and displace oil from matrix to out of that. Effect of gas dissolvation in oil recovery is related to gas-oil system properties, mas transfer rate by diffusion, effective diffusion length and matrix- fracture contact surface. Although gravity drainage has been studied extensively, there has been limited research on mass-transfer mechanisms between the gas flowing in the fracture and fluids in the porous matrix. This dissertation presents a mathematical model which describes the mass transfer between a gas flowing in a fracture and a horizontal matrix block. The model accounts for diffusion and convection mechanisms in both gas and liquid phases in the porous matrix. The injected gas diffuses into the porous matrix through gas and liquid phases causing the vaporization of oil in the porous matrix which is traorted by convection and diffusion to the gas flowing in the fracture. Then numerical model is discretized with IMPESC (Implicit Pressure Explicit Saturation Composition) method. The mathematical model was validated by comparing calculations to two sets of experimental data reported in the literature (Morel et. al. and Le Romancer et. al.), one involving nitrogen flow in the fracture and the second with carbon dioxide flow. The matrix was a chalk. The resident fluid in the porous matrix was a mixture of methane and pentane. In the nitrogen injection experiments, liquid and vapor phases were initially present, while in the carbon dioxide experiment the matrix was saturated with a liquid phase. Calculated results match the experimental data, including recovery of each component, saturation profile, and pressure gradient between matrix and fracture. Finally, after solving the equation revealed that recovery of light component is more than heavy component. In addition, convection doesn’t have very important role in recovery of each component while diffusion is dominant mechanism in recovery of components. With passing the time, maximum saturation percentage decreased and more gas come out from porous matrix and with precession of nitrogen in length of core, because of porous media in core, gas moves towards end of core. Also the simulation shows that convection has very important role in preventing pressure drop during injection. The simulation revealed the presence of countercurrent flow inside the block. Diffusion was the main mass-transfer mechanism between matrix and fracture during nitrogen injection. In the carbon dioxide experiment, diffusion and convection were both important. Key words: Fractured reservoir, Matrix, Fracture, Core, Diffusion, Convection, Gravity drainage