Abstract
The thermogravitational effect may induce large concentration contrasts, particularly in porous media. This phenomenon arises from a coupling of the Soret effect and convection currents in a temperature field. The present study of this phenomenon is motivated by the safety assessment of nuclear waste repositories, which are sources of thermal energy. Here, we present a modelling approach of laboratory experiments carried out at the University of Toulouse. The results of this model, though more adequate than the analytical solution to account for the influence of permeability, remain far from the experimental ones. In conclusion, it appears that the research must now focus on both a comprehensive phenomenology of the transport processes and experiments with new dimensional constraints.
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Abbreviations
- C :
-
concentration of the solute
- c :
-
mass fraction of the solute
- D :
-
molecular diffusion coefficient
- D′:
-
coefficient of thermodiffusion
- F 1 :
-
external forces on the solute
- F 2 :
-
external forces on the solvent
- g :
-
gravity
- J q :
-
heat flux
- J l :
-
solute mass flux
- J x :
-
horizontal mass flux of the solute
- k :
-
intrinsic permeability
- k L :
-
longitudinal permeability
- k T :
-
transverse permeability
- T 0 :
-
reference temperature
- U :
-
Darcy velocity
- Β :
-
thermal expansion coefficient of the mixture
- λ :
-
thermal conductivity
- ε :
-
porosity of the medium
- η :
-
dynamic viscosity of the mixture
- η 0T :
-
dynamic viscosity of pure water atT
- η 1T :
-
dynamic viscosity of 1 atT
- η 2T :
-
dynamic viscosity of 2 atT
- Μ 1 :
-
chemical potential of the solute
- Μ 2 :
-
chemical potential of the solvent
- ρ :
-
specific mass of the fluid
- ρ 0 :
-
specific mass of pure water atT 0
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Jamet, P., Fargue, D., Costesèque, P. et al. The thermogravitational effect in porous media: A modelling approach. Transp Porous Med 9, 223–240 (1992). https://doi.org/10.1007/BF00611968
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DOI: https://doi.org/10.1007/BF00611968