Investigation on permeability of shale matrix using the lattice Boltzmann method

• A lattice Boltzmann model for gas flow in shale matrix is presented.
• The DBB boundary scheme for non-ideal gas is proposed to deal with curved walls.
• The effects of surface diffusion, gas slippage and non-ideal gas are considered.
• Characteristics of the permeability of shale matrix are analyzed in detail.
• The application scope of the Klinkenberg correlation is obtained.

Permeability is an important parameter for the measurement of fluid transport capacity in a porous medium. Therefore it is necessary to be able to predict permeability in shale-gas reservoirs. However, predicting permeability of shale matrix is challenging because of the effects of surface diffusion and gas slippage in nanoscale pores. This paper presents a lattice Boltzmann model for gas flow in shale matrix under shale-gas reservoir conditions. The model can take into account the effects of surface diffusion, gas slippage, and a non-ideal gas. The present model, in which the diffuse-bounce-back boundary scheme is proposed to deal with the curved walls in the shale matrix, is an extension of that by Ren et al. [Transp. Porous Med. 106(2), 285-301 (2015)]. Simulations are conducted to study the intrinsic permeability and apparent permeability of shale matrix. It is found that for shale matrix with a small average pore size, the intrinsic permeability is noticeably lower than the apparent permeability. When the average pore size is less than 10 nm, the Klinkenberg correlation is unable to describe the relationship between the apparent permeability and intrinsic permeability. However, when the average pore size is larger than 50 nm, the Klinkenberg correlation can describe the relationship quite accurately. In particular, it is demonstrated that the classic Klinkenberg correlation is not applicable to shale-gas reservoirs but is suitable for low-permeability gas reservoirs and coalbed methane reservoirs.