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Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity.

Chen L, Zhang L, Kang Q, Viswanathan HS, Yao J, Tao W - Sci Rep (2015)

Bottom Line: Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability.The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature.Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.

View Article: PubMed Central - PubMed

Affiliation: 1] Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, China [2] Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA.

ABSTRACT
Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.

No MeSH data available.


Correction factor between apparent permeability and intrinsic permeability predicted by LB simulations and empirical correlations for transport in a cylinder.
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f4: Correction factor between apparent permeability and intrinsic permeability predicted by LB simulations and empirical correlations for transport in a cylinder.

Mentions: The apparent permeability can also be determined based on the Dusty gas model (DGM)2425. According to this model, the total flux of gas in a pore can be considered as a combined result of viscous flow and Knudsen diffusion2425where J (kg m−2 s−1) is the mass flux per unit area, µ (Pa.s) is viscosity, ρ (kg m−3) is density and (Pa m−1) is pressure gradient. Jd is the viscous flow flux term and Jk is the Knudsen diffusion flux term where z is the gas compressibility factor, accounting for the effect of non-ideal gas. Therefore, the total flow flux can be expressed as Shale gas is a mixture of several components, but the methane dominates with mole fraction of about 90%5. Therefore, in this study shale gas is considered to be composed of pure methane, and binary gas diffusion is neglected. Based on Eq. (10), the apparent permeability can be determined Fig. 4 shows the correction factor in a cylinder predicted by Klinkenberg's correlation (Eq. (4)), Beskok and Karniadakis – Civan's correlation (Eqs. (5–6)) as well as DGM (Eq. (11)). For gas transport in a cylinder, the intrinsic permeability is With the mean free path λ given by15the correction factor based on the DGM is as follows As shown in Fig. 4, when Kn is quite low (Kn<0.01), i.e., in the range of Darcy flow regime, the above equations predict quite similar values as the term with Kn can be neglected. However, as Kn increases, the discrepancy between Klinkenberg's correlation and other correlations becomes larger. The Beskok and Karniadakis-Civan's correlation is more accurate than Klinkenberg's correlation, especially at high Kn regime35. Values predicted by Eq. (11) agree well with Beskok and Karniadakis-Civan's correlation.


Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity.

Chen L, Zhang L, Kang Q, Viswanathan HS, Yao J, Tao W - Sci Rep (2015)

Correction factor between apparent permeability and intrinsic permeability predicted by LB simulations and empirical correlations for transport in a cylinder.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4308705&req=5

f4: Correction factor between apparent permeability and intrinsic permeability predicted by LB simulations and empirical correlations for transport in a cylinder.
Mentions: The apparent permeability can also be determined based on the Dusty gas model (DGM)2425. According to this model, the total flux of gas in a pore can be considered as a combined result of viscous flow and Knudsen diffusion2425where J (kg m−2 s−1) is the mass flux per unit area, µ (Pa.s) is viscosity, ρ (kg m−3) is density and (Pa m−1) is pressure gradient. Jd is the viscous flow flux term and Jk is the Knudsen diffusion flux term where z is the gas compressibility factor, accounting for the effect of non-ideal gas. Therefore, the total flow flux can be expressed as Shale gas is a mixture of several components, but the methane dominates with mole fraction of about 90%5. Therefore, in this study shale gas is considered to be composed of pure methane, and binary gas diffusion is neglected. Based on Eq. (10), the apparent permeability can be determined Fig. 4 shows the correction factor in a cylinder predicted by Klinkenberg's correlation (Eq. (4)), Beskok and Karniadakis – Civan's correlation (Eqs. (5–6)) as well as DGM (Eq. (11)). For gas transport in a cylinder, the intrinsic permeability is With the mean free path λ given by15the correction factor based on the DGM is as follows As shown in Fig. 4, when Kn is quite low (Kn<0.01), i.e., in the range of Darcy flow regime, the above equations predict quite similar values as the term with Kn can be neglected. However, as Kn increases, the discrepancy between Klinkenberg's correlation and other correlations becomes larger. The Beskok and Karniadakis-Civan's correlation is more accurate than Klinkenberg's correlation, especially at high Kn regime35. Values predicted by Eq. (11) agree well with Beskok and Karniadakis-Civan's correlation.

Bottom Line: Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability.The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature.Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.

View Article: PubMed Central - PubMed

Affiliation: 1] Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, China [2] Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA.

ABSTRACT
Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.

No MeSH data available.