Many naturally fractured reservoirs around the world have depleted significantly and improved oil recovery (IOR) processes are necessary for further development. Hence, the modeling of fractured reservoirs has received increased attention recently. Accurate modeling and simulation of naturally fractured reservoirs is still challenging owing to permeability anisotropies and contrasts. Non-physical abstractions inherent in conventional dual porosity and dual permeability models make them inadequate for solving different fluid-flow problems in fractured reservoirs. Also, recent technologies of discrete fracture modeling suffer from large simulation run times and the industry has not found applications for them yet, even though they give more accurate representations of fractured reservoirs than dual continuum models. We developed a novel discrete fracture model for an in-house compositional reservoir simulator that borrows the dual-medium concept from conventional dual continuum models and also incorporates the effect of each fracture explicitly. In contrast to dual continuum models, fractures have arbitrary orientations and can be angled or vertical, honoring the complexity of a typical fractured reservoir. Likewise, the new discrete fracture model does not need mesh refinement around fractures and offers computationally-efficient simulations compared to other discrete fracture models. Examples of water-flooding and gas injection are presented in this paper to demonstrate the accuracy, robustness, and applicability of the developed model for studying IOR processes in naturally fractured reservoirs. Simulations show that favorable rock wettability along with capillary pressure contrasts between matrix and fractures causes noticeable incremental oil recovery in water floods. Likewise, simulations of gas injection demonstrate that high-permeability fractures not only expedite gas breakthrough, but also increase segregation of gas towards the top of the reservoir, leading to very low sweep efficiency. Furthermore, oil recovery from naturally fractured reservoirs is found to be sensitive to the fracture inclination angle.