New theoretical model to calculate the apparent permeability of shale gas in the real state

Although many studies have been conducted to investigate the mechanisms of shale gas transport through a single nanopore, the mechanisms are not yet well understood. In this study, a theoretical model was developed to calculate the apparent permeability of shale gas in a real state through a single nanopore, and the apparent permeability of a bundle of nanopores was derived. Second, to improve the reliability of the newly developed model, two models for gas deviation factor and viscosity were selected based on 278 data points, and the models for surface diffusion coefficient were also discussed. Third, the validity of the developed model was investigated using two sets of experimental data from the literature. Finally, the effects of gas state, pore radius, temperature, adsorption parameters and pore radius distribution on apparent permeability were systematically analyzed. The results show that the developed model is capable of determining the apparent permeability of shale gas transport through a single nanopore and describing the migration process of shale gas. The Chen & Yang model, Dranchuk & Abou-Kassem model and Sutton model are selected to calculate the surface diffusion coefficient, gas deviation factor and viscosity, respectively. The effects of pore radius, temperature, and adsorption parameters are more remarkable at low pressures than at high pressures. In addition, the surface diffusion of shale gas in a single nanopore cannot be ignored, but it can be ignored in a shale core with large pores under reservoir conditions. Large pores in the shale core control the apparent permeability.