Study on the two-component gas apparent permeability model in shale nanopores considering Knudsen number correction

Abstract

At present, the technology of carbon dioxide flooding shale gas is a hot topic for scholars. The numerical simulation of shale gas driven by carbon dioxide is inseparable from the accurate understanding of gas percolation mechanism and the construction of two-component gas motion equation. During the flooding process, the gas apparent permeability and the Knudsen number both change with time and space. However, this has not been fully discussed in previous studies. In this paper, the percolation mechanisms of two-component gas are discussed. On this basis, the calculation formula of Knudsen number in porous media is modified, and the transport equation of two-component gas is established. According to the derivation of apparent permeability, the two-component gas apparent permeability model is deduced. Then, the correction effect of Knudsen number and the related properties of two-component apparent permeability are analyzed. The results show that: (1) the effect of Knudsen number correction is significant at low pressure. Under high pressure, that is, when the pressure is greater than 10 MPa, the effect can be ignored; (2) the effect of Knudsen number correction is mainly significant in the range of medium pores, which is generally 10 nm–60 nm. And the peak value range decreases with the increase of pressure; (3) for the relative component apparent permeability curve, it has the properties of both relative permeability and apparent permeability. Based on the data in this paper, for the pressure change, it can be concluded that the maximum change rate of methane is 47.79% and that of carbon dioxide is 51.36%. For the change of pore size, it can be concluded that the maximum change rate of methane is 223.45% and that of carbon dioxide is 106.19%. It can be shown that the relative permeability of carbon dioxide is sensitive to pressure and the relative permeability of methane is sensitive to pore size.