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Permeability is usually considered to be related to porosity. However, rocks with the same porosity may have different permeabilities in some cases, because of the variations in pore and throat size and pore space connectivity. It is vitally important to understand the effect of throat size on the transport property. In this work, five sets of regular pore network models and six core-based models are employed to study the effect of throat size on permeability. Four kinds of random distributions, i.e., uniform, normal, Weibull, and log normal, are utilized to generate random pore size. Pore coordination number is set to be two and six for the verification of the effect of connectivity on permeability. Then, single-phase flow simulation is conducted based on the constructed pore network models. The simulation results show that permeability decreases significantly when only one of the nine throats reduces to half size in terms of diameter. The influence of pore coordination number on permeability is not obvious compared to that of small throat size. This study indicates that small throats play an extremely important role in determining permeability.

The microscopic pore shape and topology significantly affect fluid transport and occurrence in porous permeable rock. A quantitive characterization of the impact of pore morphology on permeability is currently lacking, which limits the efficient development of underground hydrocarbon resources. This work introduces the Euler number and shape factor to characterize the pore topology and shape of heterogeneous sandstone based on CT imaging. The pore morphology under different pore sizes and the correlation of the Euler number, shape factor, fractal dimension, and surface area are analyzed. Furthermore, a modified Kozeny–Carman equation is established to explain the influence of the Euler number and shape factor on permeability. The results show that with the increase of pore diameter, the Euler number decreases while the shape factor increases. In a connected pore system, the smaller Euler number corresponds to the complex pore network, which leads to the increase in the surface area, shape factor, and fractal dimension. At constant porosity, the shape factor is negatively correlated with permeability, and with increasing Euler number, the heterogeneity of the pore structure increases, resulting in an increase of flow resistance and a decrease of permeability. The results provide a new pore morphology characterization method for digital rock and help to understand the flow mechanism of hydrocarbons in complex pore networks.