In this study, a novel triple pore network model (T-PNM) is introduced which is composed of a single pore network model (PNM) coupled to fractures and micro-porosities. We use two stages of the watershed segmentation algorithm to extract the required data from semi-real micro-tomography images of porous material and build a structural network composed of three conductive elements: meso-pores, micro-pores, and fractures. Gas and liquid flow are simulated on the extracted networks and the calculated permeabilities are compared with dual pore network models (D-PNM) as well as the analytical solutions. It is found that the processes which are more sensitive to the surface features of material, should be simulated using a T-PNM that considers the effect of micro-porosities on overall process of flow in tight pores. We found that, for gas flow in tight pores where the close contact of gas with the surface of solid walls makes Knudsen diffusion and gas slippage significant, T-PNM provides more accurate solution compared to D-PNM. Within the tested range of operational conditions, we recorded between 10 and 50% relative error in gas permeabilities of carbonate porous rocks if micro-porosities are dismissed in the presence of fractures.