Reservoir quality in some carbonate reservoirs of the Zagros basin depends primarily upon how diagenetic processes have modified the rock microstructure, leading to significant heterogeneity and anisotropy. The aim of this thesis is to investigate the factors governing fluid flow through the carbonate rocks of the Kometan Formation; a low permeability carbonate reservoir rock in Kurdistan and North Iraq. It considers the factors affecting the distribution of porosity, permeability and reservoir quality using regional stratigraphy, outcrop sections, well logs and core material from 15 wells, as well as a large suite of laboratory petrophysical measurements. The Kometan formation has been classified into three lithological units, two microfacies and three petrofacies. Petrofacies P1 (porosity 0.005±0.005 - 0.10±0.005, permeability 65±0.008 nD - 0.051±0.008 mD) is a dense, compacted, cemented wackstone/packstone with intercrystalline pores and stylolites that is characterized by intercrystalline pores (0.09±0.007 µm to 1±0.007 µm) connected by small pore throats <0.1±0.001 µm, and is only prospective in areas containing open fractures which improve its permeability (to 9.75±0.008 mD). Petrofacies P2 (porosity 0.12±0.005 to 0.25±0.005; permeability 0.065±0.008 to 0.60±0.008 mD) is a prospective carbonate mudstone that has undergone dissolution and dolomitisation with intercrystalline pores (1.0±0.05 µm to 10.0±0.05 µm) distributed unimodally and connected by pore throats larger than 0.10±0.013 µm. Petrofacies P3 (porosity 0.20±0.005 to 0.29±0.005; permeability 0.09±0.008 to 0.7±0.008 mD) is a prospective dissolved wackstone/packstone with moldic pores 10±2.5 µm to 200±2.5 µm in size, which improve the porosity but are connected by small pore throats, restricting the overall permeability. A secondary aim was to assess the available models for estimating permeability of tight carbonates. Over 12 models were tested, most of which did not provide good estimates. The Winland and Pittman models provided the best estimates, while the Kamath and Swanson methods should be avoided for tight carbonate rocks.