Apparent gas permeability behaviour in the near critical region for real gases

Abstract

Gas apparent permeability is an important parameter for gas flow in the reservoir rocks. It is higher than the absolute permeability measured using liquid. The Klinkenberg equation corrects the liquid permeability to the apparent gas permeability allowing for the pressure dependent effects of interactions between gas molecules and pore walls. However, in this paper it is shown that Klinkenberg equation does not apply for gas flow in the near critical region for real gases. This has important implications for a number of reservoir management applications including carbon geosequestration and gas condensate reservoirs. In this paper, a series of permeability measurements with respect to pressure and temperature are presented on sandstone core samples using carbon dioxide (CO2), ethane (C2H6) and helium (He). The experimental results show that the apparent permeability is enhanced in the near-critical region. CO2 apparent permeability at 311 K (critical temperature of 304.25 K) increases about 2.24 times from 7.18 MPa to 8.6 MPa (critical pressure of 7.37 MPa) on the Sandstone Sample M1 and 1.83 times on the Sandstone Sample M2 for the same pressure change. C2H6 apparent permeability at 311 K (critical temperature of 305.35 K) increases 1.83 times from 4.6 MPa to 5.4 MPa (critical pressure of 4.9 MPa) on the Sandstone Sample M1 and 1.59 times on the Sandstone Sample M2 for the same pressure change. These results suggest that the permeability enhancement is stronger for the lower permeability sample. Moreover, the experimental results show that enhancement decreases as temperature increases. Modelling work shows that applying Klinkenberg equation is invalid for describing the apparent gas permeability in near critical region, even with attempts to use different equations to calculate the mean free path required in the Klinkenberg equation. A dual mechanism model, which simultaneously considers convection flow and molecular diffusion, is modified allowing the gas diffusivity to be a function of gas density and it can well describe the gas apparent permeability in the near critical region. It is suggested that the flow is in the viscous flow regime or weak slip flow regime for the near critical gas on the sandstone samples studied in this work, and the enhancement of permeability in the near critical region is attributed to the higher density (concentration) gradient with respect to pressure.