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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