An analytical model for shale gas permeability

• An analytical model for shale gas AP is derived for Knudsen numbers up to unity.
• Temperature and molecular weight have a significant effect on gas AP of shale samples.
• The Tangential Momentum Accommodation Coefficient has a minute effect on gas AP.
• Apparent permeability does not change linearly with adsorption surface coverage.
• R13 AP model matches well with Marcellus shale apparent permeability measurements.

Based on the kinetic theory of gases and using the regularized 13-moment method, the analytical R13 AP model is introduced for predicting gas apparent permeability of nanoporous shale samples. These samples are characterized by ultratight pores and may introduce significant rarefaction effects, especially under the laboratory conditions, which cannot be accounted for in the classical hydrodynamic equations. Due to the significance of the rarefaction effects, measured values of the gas apparent permeability depend on the operating parameters, such as pressure and temperature, and gas type in addition to pore size. The R13 AP model incorporates these parameters and can predict the apparent permeability for Knudsen numbers up to unity. This model is compared with the other models and experimental results. The results of the R13 AP model match the published experimental data of flow in nanochannels. It is shown that the gas molecular weight and temperature have a significant effect on apparent permeability of the nanochannels, and the Tangential Momentum Accommodation Coefficient (TMAC) has a minimal effect for its experimental range (0.8–1). The effect of adsorption on apparent permeability of nanochannels is studied by employing the experimental Langmuir isotherms of different shale samples. It is shown that the apparent permeability does not change linearly with surface coverage and, change of permeability with surface coverage becomes more pronounced as the surface coverage increases. R13 AP model results for apparent permeability of Carbon Dioxide and Nitrogen agree with the experimental measurements performed on a Marcellus shale sample. The absolute permeability values are calculated and compared with the ones estimated by the double slippage model for both gases. Unlike the double slippage model, the R13 AP model honors the values of apparent permeability at high pressure and estimates lower absolute permeability values. For Carbon Dioxide, the value is slightly lower due to the presence of an adsorbed layer.