Abstract A large proportion of world's oil reserves resides in naturally fractured reservoirs. Implementing IOR and EOR processes in these reservoirs is a high risk/high reward activity. For instance, on one side water/gas may rapidly break-through along fracture corridors and then jeopardize the IOR/EOR scheme results. On the other side, fracture networks may effectively promote gas-oil gravity drainage or spontaneous imbibition. Accurate and efficient simulation of fractured media is a recognised challenge for reservoir simulators. Various approaches, with different balance between efficiency and accuracy, have been proposed in literature. Up to now the most diffused methods to deal with fractures, have been the adoption of a Dual Porosity/Dual Permeability (DPDK) formulation in a logically structured grid, or the use of unstructured grids. In this work EOR processes in a fractured reservoir were modeled using the Embedded Discrete Fracture Model (Li and Lee, 2008). EDFM represents a practical and efficient compromise between DPDK and unstructured gridding, combining a corner point geometry grid for matrix and an unstructured network for fractures. EDFM was implemented using commercial simulators. The target of the work was sour gas reinjection in a carbonate reservoir characterised by a matrix dominated platform and a fractured rim, with some transition between these two environments. The input of the study was a discrete fracture network, developed using seismic curvature lineaments, and a geological model for the matrix. EDFM and DPDK models were first compared. Then, the new approach was used to investigate fracture impact as a risk for premature gas break-through. The results indicated that the containment of the injection inside the platform, possibly far away from the rim, is an effective way to control the EOR process.