In this work, we derive an effective mean free path (MFP) model for the confined gases in nanopores of shale gas reservoirs by taking into account the effects of the geometrical termination and the surface-gas interaction of the boundary. Among which, the effect of the surface-gas interaction is represented by a probability distribution function for the free flight directions of the gas molecules depending on the surface-gas potential strength ratio (εwf/εff). The validity of the model is verified by comparing the obtained MFP distribution with molecular dynamics (MD) simulation data in previous literatures. Results show that the effective MFP decreases with the increasing Knudsen number (Kn) as well as the increasing surface-gas potential strength ratio, and it is more sensitive to Kn; moreover, the reduction extent is more obvious in the center of the channel than that near channel wall region at both conditions.
With the improvement of manufacturing technology in recent years, the application of micro/nano scale devices is more and more extensive (Cao, et al., 2009; Giordano, et al., 2001; Arlemark1, et al., 2010), which has attracted considerable attention and interests of many experts and scholars. Compared with macro-scale apparatus, the micro/nano scale one has a much larger surface-to-volume ratio, which even shows a huge difference with several orders of magnitude according to Cao et al. (2009). In shale gas reservoirs, most of the pores are also nanoscale and the specific surface area is generally large (some even up to 103.7 m2/g), which are significantly different from that of conventional oil and gas reservoirs (Wu and Chen, 2016). The surface-related factors have a great impact on the flow of confined gas, and among these factors, the surface force or the surface-gas interaction strength plays an important role in the momentum and energy transport, and it cannot be neglected (Barisik and Beskok, 2012).