Comptes Rendus
no. 2
Impact of local diffusion on macroscopic dispersion in three-dimensional porous media
Arthur Dartois1 ; Anthony Beaudoin1  ; Serge Huberson1
1 Institut Pprime, SP2MI – Téléport 2, boulevard Marie-et-Pierre-Curie, BP 30179, 86962 Futuroscope Chasseneuil cedex, France
Comptes Rendus. Mécanique, Volume 346 (2018) no. 2, pp. 89-97.

While macroscopic longitudinal and transverse dispersion in three-dimensional porous media has been simulated previously mostly under purely advective conditions, the impact of diffusion on macroscopic dispersion in 3D remains an open question. Furthermore, both in 2D and 3D, recurring difficulties have been encountered due to computer limitation or analytical approximation. In this work, we use the Lagrangian velocity covariance function and the temporal derivative of second-order moments to study the influence of diffusion on dispersion in highly heterogeneous 2D and 3D porous media. The first approach characterizes the correlation between the values of Eulerian velocity components sampled by particles undergoing diffusion at two times. The second approach allows the estimation of dispersion coefficients and the analysis of their behaviours as functions of diffusion. These two approaches allowed us to reach new results. The influence of diffusion on dispersion seems to be globally similar between highly heterogeneous 2D and 3D porous media. Diffusion induces a decrease in the dispersion in the direction parallel to the flow direction and an increase in the dispersion in the direction perpendicular to the flow direction. However, the amplification of these two effects with the permeability variance is clearly different between 2D and 3D. For the direction parallel to the flow direction, the amplification is more important in 3D than in 2D. It is reversed in the direction perpendicular to the flow direction.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2017.12.012
Mots clés : Dispersion, Diffusion, Covariance function, Lagrangian velocity, Tracker method, Monte Carlo approach
Arthur Dartois 1 ; Anthony Beaudoin 1 ; Serge Huberson 1

1 Institut Pprime, SP2MI – Téléport 2, boulevard Marie-et-Pierre-Curie, BP 30179, 86962 Futuroscope Chasseneuil cedex, France 
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Arthur Dartois; Anthony Beaudoin; Serge Huberson. Impact of local diffusion on macroscopic dispersion in three-dimensional porous media. Comptes Rendus. Mécanique, Volume 346 (2018) no. 2, pp. 89-97. doi : 10.1016/j.crme.2017.12.012. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.12.012/

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