Study on gas flow through nano pores of shale gas reservoirs

Unlike conventional gas reservoirs, gas flow in shale reservoirs is a complex and multiscale flow process which has special flow mechanisms. Shale gas reservoirs contain a large fraction of nano pores, which leads to an apparent permeability that is dependent on pore pressure, fluid type, and pore structure. Study of gas flow in nano pores is essential for accurate numerical simulation of shale gas reservoirs. However, no comprehensive study has been conducted pertaining to the gas flow in nano pores. In this paper, experiments for nitrogen flow through nano membranes (with pore throat size: 20 nm, 55 nm, and 100 nm) have been done and analyzed. Obvious discrepancy between apparent permeability and intrinsic permeability has been observed; and the relationship between this discrepancy and pore throat diameter (PTD) has been analyzed. Then, based on the advection-diffusion model, a new mathematical model has been constructed to characterize gas flow in nano pores. A new apparent permeability expression has been derived based on advection and Knudsen diffusion. A comprehensive coefficient for characterizing the flow process was proposed. Simulation results were verified against the experimental data for gas flow through nano membranes and published data. By changing the comprehensive coefficient, we found the best candidate for the case of argon with a membrane PTD of 235 nm. We verified the model using experimental data with different gases (oxygen, argon) and different PTDs (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, the Knudsen/Hagen-Poiseuille analytical solution, and existing models available in the literature. Results show that the model proposed in this study yielded a more reliable solution. Shale gas simulations, in which gas flowing in nano pores plays a critical role, can be made more accurate and reliable based on the results of this work.