The best way to analyze the sensitivity of dual porosity (DP) or dual permeability (DK) systems is his interaction with small and large scale petrophysical features using a fine grid, since in a coarser scale, small scale heterogeneities are always integrate in an upscaled background matrix. Two significant petrophysical features in carbonate reservoirs were applied over a background matrix, defined by, low permeability but with separate vugs (SV) randomly distributed with high porosity and permeability: (1) tectonic fractures (nearly vertical) and (2) touching vugs (nearly horizontal), were defined as large scale fractures, with high permeability and low porosity. These features are combined and tested in two cases. In the first case, the flow is controlled by touching vugs and tectonic fractures. In the second case, the flow is controlled only by touching vugs. The two cases were tested with and without SV in the background matrix. In both cases, oil recovery factor (ORF) is higher in presence of SV. ORF in DK system is also higher than in DP system. In Case 1A, the ORF for the DP system is nearly equal to the case 1B, showing that the flow rate between matrix blocks is highly important in the presence of SV, leading to the necessity of a DK system application. Without SV, ORF is nearly equal for DP and DK systems thus disregarding the necessity of a DK system, given the higher flow simulation time. The front of injected water in second case is nearly horizontal and homogeneous in fracture component resulting in a higher flow rate between SV to fracture network. The heterogeneous front of injected water in first case reduces the significance presence of SV. This work gives a valuable sensitivity of DP/DK systems in the study of small and large scale heterogeneities.