Infiltration of oil into porous sediments F.M. Allan a , M.T. Kamel b, * , T.A. Mughrabi c , M.H. Hamdan b a Department of Mathematics and Computer Science, United Arab Emirates University, P.O. Box 15551, Al-Ain, United Arab Emirates b Department of Mathematical Sciences, University of New Brunswick, P.O. Box 5050, Saint John, NB, Canada E2L 4L5 c Department of Mathematics, Al-Quds University, Abu Deis, Jerusalem, West Bank, via, Israel Abstract The continuum flow of a dilute system through a porous sediment is considered. The fluid system is composed of a car- rier fluid-phase and an oil-phase. Model equations governing the time-dependent flow of the incompressible two-phase fluid are developed based on volume averaging. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Porous media; Two-phase flow; Volume averaging 1. Introduction Petroleum products represent a dangerous potential source of groundwater pollution and sediment contam- ination due to the toxicity of a number of the oil components, such as benzene, toluene, ethylene and xylene (BTEX). These can reach the water table through various pathways, including highway run-off, direct oil spills resulting from road accidents, wave-washing of oil spilled in coastal waters, and the improper disposal of hydrocarbon products through urban sewer systems. Due to the costly clean-up processes of oil-contaminated sediments it is imperative to predict the outreach of oil components, their motion in the sediment, the physical (and chemical) behaviour of the redistributed oil and how the oil components reach the water table. A large volume of research work, both theoretical and experimental, has been carried out in this field in recent years and has been centered around single and multiphase flow through porous media (cf. [3,6,7,10] and references therein), and the dynamics of (1) oil emulsions and suspended sediments (cf. [1,2] and references therein); (2) waxy crude oils (cf. [4] and references therein); (3) non-Newtonian fluid flow through porous media (cf. [8] and references therein); (4) viscoelastic fluid flow through porous media (cf. [9] and references therein). 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.09.096 * Corresponding author. E-mail address: kamel@unbsj.ca (M.T. Kamel). Applied Mathematics and Computation 177 (2006) 659–664 www.elsevier.com/locate/amc