Biofilms in porous media: development of macroscopic transport equations via volume averaging with closure for local mass equilibrium conditions

Fabrice Golfier (1) , Brian D. Wood (2) , Laurent Orgogozo (1) , Michel Quintard (3) , Michel Bues (1)

1 LAEGO - Laboratoire Environnement Géomécanique et Ouvrages
2 School of Chemical, Biological, and Environmental Engineering
3 IMFT - Institut de mécanique des fluides de Toulouse

In this work, we upscale a pore-scale description of mass transport in a porous medium containing biofilm to develop the relevant Darcy-scale equations. We begin with the pore-scale descriptions of mass transport, interphase mass transfer, and biologically-mediated reactions; these processes are then upscaled using the method of volume averaging to obtain the macroscale mass balance equations. We focus on the case of local mass equilibrium conditions where the averaged concentrations in the fluid and biological phases can be assumed to be proportional and for which a one-equation macroscopic model may be developed. We predict the effective dispersion tensor by a closure scheme that is solved for the cases of both simple and complex unit cells. The domain of validity of the approach is clearly identified, both theoretically and numerically, and unitless groupings indicating the domain of validity are reported.

Mots clés: Biofilm; Dispersion; Local mass equilibrium; Averaging; Homogenization

Domaines: Ecologie, Environnement

Fabrice Golfier, Brian D. Wood, Laurent Orgogozo, Michel Quintard, Michel Bues. Biofilms in porous media: development of macroscopic transport equations via volume averaging with closure for local mass equilibrium conditions. Advances in Water Resources, 2009, 32, pp.463-485. ⟨10.1016/j.advwatres.2008.11.012⟩. ⟨hal-03561295⟩