With urgent need of greenhouse gas sequestration and booming oil prices, underground oil/gas reservoirs seems the only value-added choice. A real portion of current CO2 injection projects in the world is in naturally fractured reservoirs. The matrix part of these reservoirs constitutes the major oil storage unit and this oil is targeted during CO2 injection. It is our intention to show that this media could also be used as permanent CO2 storage unit while recovering oil from it. These reservoirs, however, are complex in nature and the physics of the matrix-fracture interaction process during CO2 injection is still not known to a great extent To ease the complex nature of the problems, experiments were performed oil fractured sandstone cores (single fracture) saturated with n-decane and carbonate cores saturated with dead crude oil. CO2 was injected at constant rates into the fracture while maintaining the high pressure into the core and the system. Injection and production data were monitored and collected using continuous data logging system, After continuous injection, diffusion of CO2 was allowed to occur by Shutting down the system for a specific period of time and followed by a blowdown period to recover oil that diffused from matrix to fracture. At different pressure steps, produced liquid was analyzed using gas chromatography while the produced gas was measured using a flow meter. The CO2 storage capacity of the rock with change in the pressure and the amount of oil recovered during blow down period were analyzed. The results of the continuous injection experiments were used to obtain diffusion coefficients by matching the simulation results. Using dimensionless analysis and matrix-fracture diffusion groups, we obtained a critical number for optimal recovery/sequestration. The pressure decay behavior during the shutdown was analyzed in conjunction with the gas chromatograph analysis of produced oil sample collected during blowdown after the quasiequilibrium reached during pressure decay. This led to insights into the governing mechanism of extraction/condensation and miscibility for recovering lighter to heavier hydrocarbons during pressure depletion from fractured reservoirs.