Producing gas from shale gas reservoirs has played an increasingly important role in the volatile energy industry over recent years in North America for considerable volume of natural gas stored in the reservoirs. Unlike conventional gas reservoirs, the gas flow in shale reservoirs is a complex multi-scale flow process and has special flow mechanisms. Most importantly, the shale gas reservoir contains a large portion of nano pores. The study of flow in nano pores is essential for accurate shale gas numerical simulation. However, there is still not a comprehensive study in understanding how gas flows in nano pores.

In this paper, based on the advection-diffusion model, we constructed a new mathematical model to characterize gas flow in nano pores. We derived a new apparent permeability expression based on advection and Knudsen diffusion. Acomprehensive coefficient in characterizing the flow process was proposed. Simulation results were verified against the experimental data for gas flow through nano membranes. By changing the comprehensive coefficient, we found the best candidate for the case of Argon with membrane pore diameter 235 nm. We verified the model using different gases (Oxygen, Argon) and different pore diameters (235 nm, 220 nm). The comparison shows that the new model matches the experimental data very closely. Additionally, we compared our results with experimental data, Knudsen/Hagen-Poiseuille analytical solution, and existing researcher’s work. The results show that this study yielded a more reliable solution. For shale gas simulation where gas flowing in nano pores plays a critical role, the results from this work will made the simulation more accurate and reliable.

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