A “near wellbore modeling” software will, when executed by a processor of a computer, model a localized area of a reservoir field which surrounds and is located near a specific wellbore in the reservoir field by performing the following functions: (1) receive input data representative of a reservoir field containing a plurality of wellbores, (2) establish a boundary around one specific wellbore in the reservoir field which will be individually modeled and simulated, (3) impose an “fine scale” unstructured grid inside the boundary consisting of a plurality of tetrahedrally shaped grid cells and further impose a fine scale structured grid about the perforated sections of the specific wellbore, (4) determine a plurality of fluxes / pressure values at the boundary, the fluxes / pressure values representing characteristics of the reservoir field located outside the boundary, (5) establish one or more properties for each tetrahedral cell of the unstructured grid and each cylindrical grid cell of the structured grid, (6) run a simulation, using the fluxes / pressure values at the boundary to mimic the reservoir field outside the boundary and using the fine scale grid inside the boundary, to thereby determine a plurality of simulation results corresponding, respectively, to the plurality of grid cells located inside the boundary, the plurality of simulation results being representative of a set of characteristics of the reservoir field located inside the boundary, (7) display the plurality of simulation results which characterize the reservoir field located inside the boundary, and (8) reintegrate by coarsening the grid inside the boundary, imposing a structured grid outside the boundary, and re-running a simulation of the entire reservoir field.