A large percentage of oil and gas reservoirs in the most productive regions such as the Middle East, South America, and Southeast Asia are naturally fractured reservoirs (NFR). The major difference between conventional reservoirs and naturally fractured reservoirs is the discontinuity in media in fractured reservoir due to tectonic activities. These discontinuities cause remarkable difficulties in describing the petrophysical structures and the flow of fluids in the fractured reservoirs. Predicting fluid flow behavior in naturally fractured reservoirs is a challenging area in petroleum engineering. Two classes of models used to describe flow and transport phenomena in fracture reservoirs are discrete and continuum (i.e. dual porosity) models. The discrete model is appealing from a modeling point of view, but the huge computational demand and burden of porting the fractures into the computational grid are its shortcomings. The affect of natural fractures on the permeability anisotropy can be determined by considering distribution and orientation of fractures. Representative fracture permeability, which is a crucial step in the reservoir simulation study, must be calculated based on fracture characteristics. The diagonal representation of permeability, which is customarily used in a dual porosity model, is valid only for the cases where fractures are parallel to one of the principal axes. This assumption cannot adequately describe flow characteristics where there is variation in fracture spacing, length, and orientation. To overcome this shortcoming, the principle of the full permeability tensor in the discrete fracture network can be incorporated into the dual porosity model. Hence, the dual porosity model can retain the real fracture system characteristics. This study was designed to develop a novel approach to integrate dual porosity model and full permeability tensor representation in fractures. A fully implicit, parallel, compositional chemical dual porosity simulator for modeling naturally fractured reservoirs has been developed. The model is capable of simulating large-scale chemical flooding processes. Accurate representation of the fluid exchange between the matrix and fracture and precise representation of the fracture system as an equivalent porous media are the key parameters in utilizing of dual porosity models. The matrix blocks are discretized into both rectangular rings and vertical layers to offer a better resolution of transient flow. The developed model was successfully verified against a chemical flooding simulator called UTCHEM. Results show excellent agreements for a variety of flooding processes. The developed dual porosity model has further been improved by implementing a full permeability tensor representation of fractures. The full permeability feature in the fracture system of a dual porosity model adequately captures the system directionality and heterogeneity. At the same time, the powerful dual porosity concept is inherited. The implementation has been verified by studying water and chemical flooding in cylindrical and spherical reservoirs. It has also been verified against ECLIPSE and FracMan commercial simulators. This study leads to a conclusion that the full permeability tensor representation is essential to accurately simulate fluid flow in heterogeneous and anisotropic fracture systems. / text