Permeabilities of unsaturated fractal porous media
, Jianhua Li
, Zhihua Li
, Mingqing Zou
Department of Physics and The State Key Laboratory of Plastic Forming and Die & Mold Tech.,
Huazhong University of Science and Technology, Wuhan 430074, PR China
Research Center of Biomedical Materials Engineering, Wuhan University of Technology, Wuhan 430070, China
Received 15 January 2003; received in revised form 29 June 2003
A fractal analysis of permeabilities for unsaturated fractal porous media is presented based on the fractal
natures of pores in the media. Both the fractal phase permeabilities and the fractal relative permeabilities
are derived and found to be a function of fractal dimension for tortuosity, pore area fractal dimension,
fractal dimensions for wetting and non-wetting phases, saturation and microstructural parameters. The
proposed fractal models for permeabilities, both the phase permeabilities and the relative permeabilities, do
not contain any empirical constant. To verify the validity of the present analysis, the predicted relative
permeability data are compared with those of the existing measurements, and excellent agreement between
the model predictions and existing experimental data is found.
Ó 2003 Elsevier Ltd. All rights reserved.
Keywords: Fractal; Permeability; Porous media; Multiphase ﬂow
The permeabilities for porous media, both saturated and unsaturated, have received much
attention (De Wiest, 1969; Bear, 1972; Bowles, 1984; Jumikis, 1984; Kaviany, 1995; Panﬁlov,
2000) due to practical applications including chemical engineering, soil science and engineering,
oil production, polymer composite molding and heat pipes etc. Since the microstructures of real
porous media are usually disordered and extremely complicated, this makes it very diﬃcult to
analytically ﬁnd the permeability of the media especially for unsaturated (or multiphase) porous
International Journal of Multiphase Flow 29 (2003) 1625–1642
Corresponding author. Tel.: +86-27-875-421-53; fax: +86-27-875-454-38.
E-mail address: firstname.lastname@example.org (B. Yu).
0301-9322/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved.