Gas injection in naturally fractured reservoirs maintains the reservoir pressure, and increases oil recovery primarily by gravity drainage and to a lesser extent by mass transfer between the flowing gas in the fracture and the porous matrix. 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 paper presents a mathematical model which describes the mass transfer in one dimension 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 transported by convection and diffusion to the gas flowing in the fracture. Compositions of equilibrium phases are computed using the Peng‑Robinson EOS. The mathematical model was validated by comparing calculations to two sets of experimental data reported in the literature (reference), 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 diffusion 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. The simulation reveals 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.