Symmetry properties of macroscopic transport coefficients in porous media

Didier Lasseux (1) , F. Valdés-Parada

1 I2M - Institut de Mécanique et d'Ingénierie de Bordeaux

We report on symmetry properties of tensorial effective transport coefficients characteristic of many transport phenomena in porous systems at the macroscopic scale. The effective coefficients in the macroscopic models (derived by upscaling (volume averaging) the governing equations at the underlying scale) are obtained from the solution of closure problems that allow passing the information from the lower to the upper scale. The symmetry properties of the macroscopic coefficients are identified from a formal analysis of the closure problems and this is illustrated for several different physical mechanisms, namely, one-phase flow in homogeneous porous media involving inertial effects, slip flow in the creeping regime, momentum transport in a fracture relying on the Reynolds model including slip effects, single-phase flow in heterogeneous porous media embedding a porous matrix and a clear fluid region, two-phase momentum transport in homogeneous porous media, as well as dispersive heat and mass transport. The results from the analysis of these study cases are summarized as follows. For inertial single-phase flow, the apparent permeability tensor is irreducibly decomposed into its symmetric (viscous) and skew-symmetric (inertial) parts; for creeping slip-flow, the apparent permeability tensor is not symmetric; for one-phase slightly compressible gas flow in the slip regime within a fracture, the effective transmissivity tensor is symmetric, a result that remains valid in the absence of slip; for creeping one-phase flow in heterogeneous media, the permeability tensor is symmetric; for two-phase flow, we found the dominant permeability tensors to be symmetric, whereas the coupling tensors do not exhibit any special symmetry property; finally for dispersive heat transfer, the thermal conductivity tensors include a symmetric and a skew-symmetric part, the latter being a consequence of convective transport only. A similar result is achieved for mass dispersion. Beyond the physical mechanisms under consideration in the present work, the reported technique can be viewed as a general methodology applicable to any type of upscaled model obtained by volume averaging.

Domaines: Sciences de l'ingénieur [physics]; Milieux fluides et réactifs; Génie des procédés; Mécanique [physics.med-ph]; Mathématiques [math]; Physique [physics]; Sciences de l'environnement; Planète et Univers [physics]

Didier Lasseux, F. Valdés-Parada. Symmetry properties of macroscopic transport coefficients in porous media. Physics of Fluids, 2017, 29 (4), pp.043303. ⟨10.1063/1.4979907⟩. ⟨hal-03140913⟩