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Journal of Porous Media
Impact-faktor: 1.49 5-jähriger Impact-Faktor: 1.159 SJR: 0.43 SNIP: 0.671 CiteScore™: 1.58

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

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v19.i6.50
pages 539-555

FINITE ANALYTIC METHOD FOR 2D FLUID FLOW IN POROUS MEDIA WITH PERMEABILITY IN TENSOR FORM

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

ABSTRAKT

The finite analytic method is developed to solve the two-dimensional fluid flow in heterogeneous porous media with permeability in tensor form. A local nodal analytic solution around the grid node joining the different permeability areas is derived. In general, the pressure follows the power-law distribution with gradient divergence as approaching the grid node, rather than having piecewise linear distribution. This nodal solution is employed to construct a finite analytic numerical scheme with a discretized boundary condition. It is interesting that the velocity on the boundary exhibits the power-law divergence behaviors in the case of permeability in tensor form because of the crossflow effects, which is different from that of the scalar permeability. Numerical examples show that, only with 2 × 2 or 3 × 3 subdivisions, our scheme can provide rather accurate solutions, and the convergence rate of the scheme is independent of the permeability heterogeneity, while a dramatic increase of the refinement ratio is needed when using the traditional method, especially for strong heterogeneous porous medium.