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Journal of Porous Media
IF: 1.49 5-Year IF: 1.159 SJR: 0.504 SNIP: 0.671 CiteScore™: 1.58

ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.2018021170
pages 977-992

A LOCAL EXPANSION METHOD FOR SOLVING THE MACROSCOPIC MOMENTUM EQUATION OF THE SINGLE PHASE FLOW IN HIGHLY PERMEABLE POROUS MEDIA

Jun-wen Liu
Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China
Zhi-Fan Liu
Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China
Zhi-Feng Liu
Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China
Xiao-Hong Wang
Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China
An-Feng Shi
Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China

ABSTRACT

The macroscopic momentum equation is derived from the pore-scale Navier–Stokes equations using the volume averaging method. The macroscopic pressure gradient can be expressed as a power series of the averaged velocity with a group of tensorial coefficients. Each tensorial coefficient is intrinsic and can be calculated by solving its corresponding closure problem. Thus the specific form of the cubic filtration law for isotropic porous structure in weak inertia regime can be determined from the power series equation. In order to avoid the complex calculations of the tensorial coefficients for the high order terms, a local expansion method is proposed where only a series of auxiliary Stokes problems are successively solved. In the procedure of the derivation of the filtration law for fluid flows in porous media considering the inertial effects, the proposed method can avoid the complex calculations of solving the full Navier–Stokes equations and therefore reduce computation cost tremendously. Several numerical tests are performed and the numerical results are consistent with the calculations published in previous literature.


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