2013 YOU-IJMPC-A fractal approach to spontaneous imbibition height in natural porous media.pdf
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2013 YOU-IJMPC-A fractal approach to spontaneous imbibition height in natural porous media
A FRACTAL APPROACH TO SPONTANEOUS IMBIBITION
HEIGHT IN NATURAL POROUS MEDIA
LIJUN YOU*, JIANCHAO CAI?,? and YILI KANG*
*State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation
Southwest Petroleum University
Chengdu 610500, P. R. China
?Key Laboratory of Tectonics and Petroleum Resources of Ministry of Education
Institute of Geophysics and Geomatics
China University of Geosciences
Wuhan 430074, P. R. China
?caijc@cug.edu.cn
LIANG LUO
Laboratory of Advanced Energy Systems
Guangzhou Institute of Energy Conversion
Chinese Academy of Sciences
Guangzhou 510640, P. R. China
Received 23 February 2013
Accepted 28 May 2013
Published 9 July 2013
Spontaneous imbibition of wetting liquids in porous media is of great importance in many ˉelds.
In this paper, an analytical model for characterizing spontaneous imbibition height versus time
in natural porous media was derived using fractal approach. The average imbibition height in
porous media is in terms of porosity, fractal dimensions, maximum pore size and viscosity,
surface tension and liquidsolid interactions. The developed model is consistent with previous
results and is tested against available experimental data showing fair agreements.
Keywords: Spontaneous imbibition; fractal; porous media; BCLW equation.
PACS Number(s): 47.56.+r, 47.55.nb, 05.45.Df.
1. Introduction
Since the pioneering studies Bell and Cameron in 1906,1 Lucas in 19182 and
Washburn in 19213 (refer to BCLW equation), spontaneous capillary imbibition in
porous media has received great attention from theoretical perspectives to engi-
neering applied science such as oil recovery, soil physics, groundwater engineering,
?Corresponding author.
International Journal of Modern Physics C
Vol. 24, No. 9 (2013) 1350063 (10 pages)
#.c World Scientiˉc Publishing Company
DOI: 10.1142/S0129183113500630
1350063-1
as well as areas of packing of particulates, ˉbrous and building materials.421
The BCLW equation describes a liquid rising in a cylindrical capill
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