Efficient prediction of gas permeability by hybrid DSBGK-LBM simulations

Abstract

Gas permeability changes with the pore pressure, or Knudsen number (Kn) in general, due to the Klinkenberg slippage effect. Most of the traditional simulation methods based on the Navier-Stokes equation with slip boundary condition are valid only at small Kn while the generally valid DSMC method is very time-consuming at low speed due to stochastic noise. On the other hand, the DSBGK method based on a simplified Boltzmann equation is also accurate at arbitrary Kn and has been successfully applied to compute the gas permeability of real digital rock over a wide range of Kn by pore-scale simulations of low-speed gas flows. However, its computational cost increases as Kn decreases due to cell refinement required at low Kn. We present a hybrid-simulation scheme to significantly save the computational cost, in which the ordinary lattice Boltzmann method is used to compute the intrinsic permeability at Kn equal to zero and the DSBGK method will be applied only at a single large Kn condition to get another permeability data point without cell refinement, then the two permeabilities can be used to calibrate the Klinkenberg correlation model as a data fitting formula. The calibrated Klinkenberg correlation model is validated by comparing with the accurate DSBGK data at different Kn in both artificial and real rock geometries. The current study shows that the proposed hybrid-simulation scheme is accurate and applicable for real applications.