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Chin. Phys. B, 2014, Vol. 23(4): 044701    DOI: 10.1088/1674-1056/23/4/044701
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

A fractal approach to low velocity non-Darcy flow in a low permeability porous medium

Cai Jian-Chao
Institute of Geophysics and Geomatics, Key Laboratory of Tectonics and Petroleum Resources of Ministryof Education, China University of Geosciences, Wuhan 430074, China
Abstract  In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach. The analytical expressions for flow rate and velocity of non-Newtonian fluid flow in the low permeability porous medium are derived, and the threshold pressure gradient (TPG) is also obtained. It is notable that the TPG (J) and permeability (K) of the porous medium analytically exhibit the scaling behavior J K-DT/(1 + DT), where DT is the fractal dimension for tortuous capillaries. The fractal characteristics of tortuosity for capillaries should be considered in analysis of non-Darcy flow in a low permeability porous medium. The model predictions of TPG show good agreement with those obtained by the available expression and experimental data. The proposed model may be conducible to a better understanding of the mechanism for nonlinear flow in the low permeability porous medium.
Keywords:  fractal      porous media      non-Darcy flow      threshold pressure gradient      scaling law  
Received:  11 June 2013      Revised:  05 September 2013      Accepted manuscript online: 
PACS:  47.50.-d (Non-Newtonian fluid flows)  
  05.45.Df (Fractals)  
  47.15.-x (Laminar flows)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 41102080), the Fundamental Research Funds for the Central Universities, China (Grant Nos. CUG130404 and CUG130103), the Fund from the Key Laboratory of Tectonics and Petroleum Resources of Ministry of Education, China University of Geosciences (Wuhan), China (Grant No. TPR-2013-18).
Corresponding Authors:  Cai Jian-Chao     E-mail:  caijc@cug.edu.cn
About author:  47.50.-d; 05.45.Df; 47.15.-x

Cite this article: 

Cai Jian-Chao A fractal approach to low velocity non-Darcy flow in a low permeability porous medium 2014 Chin. Phys. B 23 044701

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