A three-dimensional, three-phase black oil simulator is used to model the flow regimes and flow geometries around sealing/non-sealing flow barriers in hydrocarbon reservoirs with homogeneous property distribution. A local grid refinement technique is utilized in these numerical simulation models to accurately capture the flow regimes and flow geometries. Previous work examined a local 'grid refinement algorithm that was applied to study flow around impermeable barriers, water coning problems, and waterflood front-tracking in horizontal wells. In this paper, we extend the application of the algorithm. to account for inclined faults. A system of faults in a large reservoir is considered in all of the cases studied. Sections of the reservoir are solved individually in the presence of geological discontinuities. The results from the static local grid refinement technique indicate a much higher level of accuracy over the results generated using a coarse grid approximation around faulted zones of the reservoir. This level of accuracy is characterized by comparing the results generated by a completely fine grid and/or by a conventional refinement protocol. The proposed model is capable of providing a better representation of faulted reservoir architectures using significantly less CPU time. The proposed model can also be used in pressure transient analysis of wells located near non-sealing fault structures.