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Journal of Porous Media
IF: 1.752 5-Year IF: 1.487 SJR: 0.43 SNIP: 0.762 CiteScore™: 2.3

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

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v17.i8.80
pages 741-750

DERIVATION OF THE DARCY-SCALE FILTRATION EQUATION FOR POWER-LAW FLUIDS WITH THE VOLUME AVERAGING METHOD

Xiao-Hong Wang
Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China
Jiang-Tao Jia
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
Long-De Jin
Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China

ABSTRACT

The large-scale continuum models for transport of power-law fluids in porous media are derived from the pore-scale control equations using the volume averaging method. The averaging procedure leads to an equation of motion and a continuity equation expressed in terms of the volume-averaged pressure and velocity. The closure problem for the power-law fluid flow is assumed to be analogous to the Newtonian fluid flow. Then a tensorial form of Darcy-scale filtration equation is obtained and the power-law relation between the averaged velocity and the gradient of the averaged pressure are confirmed. Different from Newtonian fluids, the apparent permeability significantly depends upon the filtration velocity direction for higher-dimensional flow (d ≥ 2). Numerical test also validates this conclusion.


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