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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 predicted by numerical simulations and empirical correlations under different pressure.
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f5: Correction factor predicted by numerical simulations and empirical correlations under different pressure.

Mentions: Fig. 5 shows the correction factor predicted by the LB simulations and empirical correlations under different pressures, and Fig. 6 displays correction factor under different Kn. For the wide pressure range investigated, fc is always greater than 1 as shown in Fig. 5, indicating Knudsen diffusion always plays a role on the shale gas transport mechanisms in the reconstructed shales. This is also confirmed in Fig. 6, where all data fall within the slip flow regime, transition flow regime and Knudsen diffusion regime, with no Darcy flow regime observed as Kn is always greater than 0.03. As the pressure decreases or the Kn increases, the Knudsen diffusion becomes increasingly dominant. For pressure lower than 100 psi, the correction factor can be as high as 10, implying that Knudsen diffusion dominates and the viscous flow can be ignored. Most of the values of correction factor are located in the transition and slip flow regimes. The simulation results are in better agreement with Beskok and Karniadakis-Civan's correlation, in consistence with that in Fig. 4. The values from our simulations are a little higher than that of Beskok and Karniadakis-Civan's correlation. By investigating the experimental data of tight gas sandstones from seven major tight gas basins in the United States, Ziarani and Aguilera35 also found Beskok and Karniadakis-Civan's correlation performed the best, especially for extremely tight porous media, and Klinkenberg's correlation underestimates the correction factor. Note that the Beskok and Karniadakis-Civan's correlation as well as Eq. (1) are derived based on the diffusion process in a cylinder1430. However, pores in the shales are complex and can hardly be described by a collection of cylinders. Using Eq. (1) will overestimate the Knudsen diffusivity in porous media. Therefore, in future simulations, complex structures of the pores as well as the nature of the redirecting collision between walls and gas molecules should be considered to improve Eq. (1)3738.


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 predicted by numerical simulations and empirical correlations under different pressure.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f5: Correction factor predicted by numerical simulations and empirical correlations under different pressure.
Mentions: Fig. 5 shows the correction factor predicted by the LB simulations and empirical correlations under different pressures, and Fig. 6 displays correction factor under different Kn. For the wide pressure range investigated, fc is always greater than 1 as shown in Fig. 5, indicating Knudsen diffusion always plays a role on the shale gas transport mechanisms in the reconstructed shales. This is also confirmed in Fig. 6, where all data fall within the slip flow regime, transition flow regime and Knudsen diffusion regime, with no Darcy flow regime observed as Kn is always greater than 0.03. As the pressure decreases or the Kn increases, the Knudsen diffusion becomes increasingly dominant. For pressure lower than 100 psi, the correction factor can be as high as 10, implying that Knudsen diffusion dominates and the viscous flow can be ignored. Most of the values of correction factor are located in the transition and slip flow regimes. The simulation results are in better agreement with Beskok and Karniadakis-Civan's correlation, in consistence with that in Fig. 4. The values from our simulations are a little higher than that of Beskok and Karniadakis-Civan's correlation. By investigating the experimental data of tight gas sandstones from seven major tight gas basins in the United States, Ziarani and Aguilera35 also found Beskok and Karniadakis-Civan's correlation performed the best, especially for extremely tight porous media, and Klinkenberg's correlation underestimates the correction factor. Note that the Beskok and Karniadakis-Civan's correlation as well as Eq. (1) are derived based on the diffusion process in a cylinder1430. However, pores in the shales are complex and can hardly be described by a collection of cylinders. Using Eq. (1) will overestimate the Knudsen diffusivity in porous media. Therefore, in future simulations, complex structures of the pores as well as the nature of the redirecting collision between walls and gas molecules should be considered to improve Eq. (1)3738.

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.