Lack of accurate estimation of reservoir permeability has been one of the most challenging problems for enhanced hydrocarbon recovery. Pore-structure variation in carbonate rocks caused by diagenesis controls reservoir permeability heterogeneity. In this paper, we propose a rock-physics-based method of quantitative characterization of pore structure and permeability heterogeneity using core and sonic logs. Mercury injection capillary pressure (MICP) and Leverett J-function curves can be first used to classify the pore systems and permeability variation in the reservoirs. Shear frame flexibility factor (γµ) derived from sonic logs is further used to quantify the pore type and permeability variation in the reservoir zones. In the studied Puguang gas field, different pore systems in five reservoir zones are identified: moldic, sucrosic macrointercrystalline, mixed moldic and intercrystalline, meso-intercrystalline, and micro-intercrystalline pores respectively in the upward shallowing sequence of the Early Triassic reservoir. Permeability varies significantly between the five zones. Results show that at a fixed porosity, moldic pores show higher velocity, resistivity, yet much lower permeability than intercrystalline pores. When γµ < 4, the reservoir zone is dominated by moldic pores; when 4 < γµ < 8, meso- to macro-intercrystalline pores are dominant; and when γµ > 8, micro-intercrystalline pores are prevalent. Two different permeability-porosity trends controlled by distinctive pore types are also distinguishable by γµ. Reservoirs dominated by isolated moldic pores, at a given porosity, has much lower permeability than the ones dominated by connected intercrystalline pores. The results on pore-type discrimination and permeability estimation have been successfully used to understand the production problems in the Puguang reservoir.