Two-scale expansion with drift approach to the Taylor dispersion for reactive transport through porous media

Grégoire Allaire (1, 2) , Robert Brizzi (1) , Andro Mikelic (3) , Andrey Piatnitski (4)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 DeFI - Shape reconstruction and identification
3 ICJ - Institut Camille Jordan
4 LPI RAS - P. N. Lebedev Physical Institute of the Russian Academy of Sciences [Moscow]

In this work we study reactive flows through porous media. We suppose dominant Peclet's number, dominant Damköhler's number and general linear reactions at the pore boundaries. Our goal is to obtain the dispersion tensor and the upscaled model. We introduce the multiple scale expansions with drift for the problem and use this technique to upscale the reactive flow equations. Our result is illustrated with numerical simulations for the dispersion tensor.

Domaines: Analyse numérique [cs.NA]; Equations aux dérivées partielles [math.AP]

Grégoire Allaire, Robert Brizzi, Andro Mikelic, Andrey Piatnitski. Two-scale expansion with drift approach to the Taylor dispersion for reactive transport through porous media. Chemical Engineering Science, 2010, 65, pp.2292-2300. ⟨hal-00784057⟩