Experimental and numerical study of the validity of Hele–Shaw cell as analogue model for variable-density flow in homogeneous porous media C. Oltean * , F. Golfier, M.A. Bue `s Nancy Universite ´ – Laboratoire Environnement, Ge ´ome ´canique et Ouvrages, E ´ cole Nationale Supe ´rieure de Ge ´ologie, Rue du Doyen Marcel Roubault – BP 40 F – 54501 Vandœuvre-le `s-Nancy, France Received 26 October 2006; received in revised form 26 June 2007; accepted 27 June 2007 Available online 5 July 2007 Abstract Several laboratory experiments were conducted to identify the validity domain under which a Hele–Shaw cell may serve as a suitable analogue for variable-density flow in homogeneous porous media. These experiments are concerned with the injection into a Hele–Shaw cell of a salt solute at different concentrations and flow rates. The experimental data analysis highlighted two types of mixing zone shape: with and without ‘fingers’. A semi-empirical criterion based on the ratio between gravitational and injected velocities was used to forecast the change from one shape to another. The experimental data were then analysed using numerical solutions of the classical Hele–Shaw equations by taking into account an anisotropic dispersion tensor whose components depend on fluid density gradients. The good agree- ment between experimental and numerical results clearly shows that the validity of the concentration-dependent dispersion tensor strongly depends on the local Pe ´clet number variation. For Pe ´clet numbers lower 50, the Hele–Shaw cell can be considered as an anal- ogous model of a homogeneous and isotropic 2D porous medium. It can be successfully used to study, at the laboratory scale, the grav- itational instability effects induced by flow and transport phenomena into a porous medium. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Hele–Shaw cell; Variable-density flow; Porous medium; Homogenization; Experimental data; Stability criterion; Numerical simulations 1. Introduction In case of accidental or natural groundwater contamina- tion, flow and transport forecasts are required to provide information for water resources management. The exten- sion to which these forecasts are efficient very much depends on flow and transport processes. For non-reactive miscible contaminants, physical properties such as density and/or dynamic viscosity of the fluid can vary with concen- tration. In order to better understand the influence of the density variation on the plume propagation, a large num- ber of laboratory experiments have investigated miscible fluid displacements. Globally, these experiments carried out in vertical column (1D) or in flow containers (2 or 3D) have concentrated on the spatial extension of the mix- ing zone and/or on plume stability [2,4,10,12,17,21,22, 25,26,28,30–32,35]. In these laboratory studies, the concen- tration distribution inside the mixing zone was generally measured by electric conductivity [2,4,10,12,17,26,32], by flow visualization [25,28,31,35] or by dual-energy gamma radiation techniques [22]. Although these methods are very useful, they do contain some disadvantages. The first involves the depression of several pairs of electrodes in the porous media which can disturb flow and transport. Moreover, it involves only a point measurement. The sec- ond is generally used for qualitative analysis. Although it could be improved by using a technique based on the 0309-1708/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.advwatres.2007.06.007 * Corresponding author. Tel.: +33 383596316; fax: +33 383596300. E-mail addresses: Constantin.Oltean@ensg.inpl-nancy.fr (C. Oltean), Fabrice.Golfier@ensg.inpl-nancy.fr (F. Golfier), Michel.Bues@ensg.inpl- nancy.fr (M.A. Bue `s). www.elsevier.com/locate/advwatres Available online at www.sciencedirect.com Advances in Water Resources 31 (2008) 82–95