Ascertaining the pore connection criterion has always been a challenge for geoscientists. In the framework of this research, an attempt was made to study the pore connectivity in a heterogeneous carbonate rock by combining several techniques. Pore types and rock facies were investigated for 321 thin sections. The abundance of connected porosities, cementation type and intensity which significantly control the matrix pore connectivity were specified on thin sections and finally a connectivity log was extracted that showed an accurate result on poro-perm cross-plots. Most of the porosity volumes were related to interparticle, vuggy and moldic porosities which are microscale. The velocity deviation log, estimated in four wells, indicates the presence of micro-porosity, which is consistent with the results of thin-sections. Zero velocity deviation is usually associated with the predominant presence of micro-pores. Different permeability values in identical lithological facies, as well as micro-fracture markers, prompted us to conduct more extensive research on fractures. FMI analysis proved that the studied reservoir is intensively fractured. The recorded high permeability in a sample with low matrix connectivity is specifically a fracture indication. Fracture apertures vary from microscale (<50 μm) to 12.5 mm and calculated fracture density is raised up to 2 fractures per meter. Determined fractured intervals are very consistent with mud-loss information, for instance, a complete loss has been reported in the fault zone identified in well B. The detected fractures somewhat follow the main Zagros fault trend (NW-SE). Eventually, calculated connectivity was predicted in other wells using Artificial Neural Network (ANN) and a 3D model was constructed with respect to seismic attributes which gives a precise perspective of pore connection distribution throughout the studied field.