Homogenization Modeling of Single-Phase Gas Local Flow in Porous Media

LI Shuguang; QU Kai

doi:10.21656/1000-0887.440246

Volume 45 Issue 2

Feb. 2024

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Article Navigation > Applied Mathematics and Mechanics > 2024 > 45(2): 175-183

LI Shuguang, QU Kai. Homogenization Modeling of Single-Phase Gas Local Flow in Porous Media[J]. Applied Mathematics and Mechanics, 2024, 45(2): 175-183. doi: 10.21656/1000-0887.440246

Citation:

LI Shuguang, QU Kai. Homogenization Modeling of Single-Phase Gas Local Flow in Porous Media[J]. Applied Mathematics and Mechanics, 2024, 45(2): 175-183. doi: 10.21656/1000-0887.440246

Citation:

LI Shuguang, QU Kai. Homogenization Modeling of Single-Phase Gas Local Flow in Porous Media[J]. Applied Mathematics and Mechanics, 2024, 45(2): 175-183. doi: 10.21656/1000-0887.440246

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Homogenization Modeling of Single-Phase Gas Local Flow in Porous Media

doi: 10.21656/1000-0887.440246

LI Shuguang^,,
QU Kai

School of Science, Dalian Maritime University, Dalian, Liaoning 116026, P.R.China

Received Date: 2023-08-17
Rev Recd Date: 2023-11-12
Publish Date: 2024-02-01

Abstract

Abstract

The application of asymptotic homogenization method was investigated based on the filtration theory for single-phase gas, and the mathematical model and numerical method for the gas flow at the pore scale were developed. With the asymptotic homogenization method, a local problem of periodic cells was established to describe the local flow process of a single-phase gas at the pore scale of the periodic porous medium. The special mathematical properties and physical significance of the local problem were discussed. With a simplified approach based on symmetric and antisymmetric extensions, a least squares finite element method for the local problem was proposed, to overcome the numerical difficulties due to averaging operators and periodic boundary conditions. The solution of the local problem was obtained with accurate local velocity and pressure distributions in a single pore, and with gas permeability evaluation of porous media only in knowledge of the pore geometry. Beyond the local problem, the analytical solution of the Poiseuille flow in microtubes was obtained through theoretical analysis, to verify the proposed mathematical model and the numerical algorithm. Finally, a 3D periodic porous structure was considered, and numerical results of local flow in a single pore and permeability coefficients in porous media were obtained.
- asymptotic homogenization method,
- porous medium,
- local flow,
- permeability,
- least squares finite element

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References(18)

References

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