Study of gas slippage factor in anisotropic porous media using the lattice Boltzmann method
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ORIGINAL PAPER
Study of gas slippage factor in anisotropic porous media using the lattice Boltzmann method Tao Li 1 & Yong Hu 2 & Qian Li 1 & Xian Peng 1 & Min Li 3 Received: 19 December 2019 / Accepted: 7 August 2020 # Springer Nature Switzerland AG 2020
Abstract In unconventional reservoir rocks, pore anisotropy and gas high Knudsen number (Kn) effect are prominent, while gas slippage factor is a crucial parameter to evaluate their apparent permeability. To analyze the correlation of gas slippage factor with pore anisotropy of porous media and Kn, two-dimensional bundle models and anisotropic porous media with same characteristic length were skillfully constructed in this work. A multi-relaxation-time Lattice Boltzmann model combining diffusive reflection boundary condition and Bosanquet-type viscosity model was applied to simulate gas high-Kn flow (Kn = 0.05–0.53) in them. The results showed that Kn and pore-scale anisotropy jointly determine gas slippage factor of anisotropic porous media, which has nothing to do with porosity, specific surface area, and intrinsic permeability in nature. Pore-scale anisotropy leads to the distinct nonlinear changes of gas slippage factor with Kn. When pore-scale anisotropy factor is between 5.37 and 14.58, gas slippage factor of porous media is positively correlated with Kn. But as pore-scale anisotropy factor is in a range from 1.0 to 5.37, gas slippage factor decreases with an increase of Kn. In addition, gas slippage factor of porous media increases with an increase of pore-scale anisotropy as Kn is in a range of 0.18 to 0.53. This work further improves the understanding of gas slippage factor and gas high-Kn effect in anisotropic porous media. Keywords Anisotropic porous media . Apparent permeability . Gas slippage factor . Pore-scale anisotropy . Knudsen number
1 Introduction Micro/nano-pores widely exist in unconventional reservoir rocks, including tight sandstones and shale [1, 2]. The gas slippage occurs on the surface when pore sizes are comparable with the mean free path of gas molecules (λ), which would lead to the prominent gas high-Kn (Kn is defined as the ratio of λ and characteristic length of pore (Heq) [3]) effect [2, 4] and their apparent (gas) permeability (kapp) notably greater than * Tao Li [email protected] * Qian Li [email protected] 1
Exploration and Development Research Institute, PetroChina Southwest Oil & Gasfield Company, Chengdu 610041, China
2
PetroChina Southwest Oil & Gasfield Company, Chengdu 610051, China
3
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China
intrinsic permeability (k0) [5, 6]. The k0 reflects the ability of porous media to allow fluid to pass through, while kapp refers to the ability of porous media to allow gas to pass through considering gas slippage. Based on bundle model composed by parallel microchannels, Klinkenberg [7] first proposed a permeability model considering gas slippage as Eq. (1), where b is gas slippage factor and pm
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