HR: 09:50h
AN: H51K-06    [Abstracts]
TI: Dispersion in Porous and Fractured Media
AU: * Adler, P M
EM: adler@ipgp.jussieu.fr
AF: IPGP, 4, place Jussieu, Paris, 75252 France
AU: Thovert, J
EM: thovert@lcd.ensma.fr
AF: LCD, Rue Curie, Futuroscope, 86962 France
AB: This paper summarizes our contributions on dispersion in complex systems which are statistically homogeneous. Three major techniques can be used to analyse dispersion of a Brownian solute in a complex flow field, namely random walks, Taylor dispersion (or method of moments), and homogeneisation (or multiple scales). Random walks provide an easy introduction to the method of moments devised by Brenner which is presented and justified in a physical way. Some aspects are emphasized such as the constancy of the concentration field in the unit cell which provides a useful criterion to appreciate numerical precision. Then, the equivalence between the method of moments and homogeneization is addressed (1). The limiting case of diffusion is analyzed. First, the major results obtained in porous media in single phase are recalled. This is based on (2) which was the first comprehensive numerical study on this topic. Random walks are compared to Taylor dispersion. The long time behaviour and its Gaussian limit are also analyzed since some conditions on the measurements of the dispersion tensor can be derived. This analysis is extended to two phase flows (3) where only the random walk technique could be used. The asymptotic behaviour of the dispersion tensor for large P‚clet numbers can be represented by power laws. The exponents of these laws are shown to be relatively independent on the number of phases. Then, dispersion in fracture networks is addressed (4). The basic theory of Taylor dispersion is remarkably close to the one derived for porous media. Data derived from Taylor dispersion were also compared to results obtained with random walks. The networks can be described by the number of fractures per unit volume rho and the shape of the fractures of perimeter P and area S. A major result is that the data, when represented as functions of the dimensionless density rho' = rho A S /2, are independent of the shape of the fractures. Finally, the versatility of the random walk technique is illustrated by various examples of deposition/dissolution on various scales in one and two phase flows. References: (1) J.-L. Auriault, P.M. Adler, Taylor dispersion in porous media, Analysis by multiple scale expansions, Ad. Water Res. Res., 18, 217, 1995. (2) J. Salles, J.-F. Thovert, R. Delannay, L. Pr‚vors, J.L. Auriault, P.M. Adler : Taylor dispersion in porous media. Determination of the dispersion tensor. Physics Fluids A, 5, 2348, 1993. (3) S. B‚kri, P.M. Adler, Dispersion in multiphase flow through porous media, Int. J. Multiphase Flow, 28, 665, 2002. (4) O. Huseby, J.-F. Thovert, P.M. Adler, Dispersion in three-dimensional fracture networks, Physics of Fluids, 13, 594, 2001.
DE: 1805 Computational hydrology
DE: 1859 Rocks: physical properties
DE: 1875 Vadose zone
DE: 5139 Transport properties
SC: Hydrology [H]
MN: Fall Meeting 2005