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Theoretical Prediction of Effective Thermodiffusion Coefficient In Porous Media

Hossein Davarzani1, Manuel Marcoux1, and Michel Quintard2. (1) Institut de Mécaniqe des Fluides de Toulouse, Allee Soula, Toulouse, 31400, France, (2) Institut de Mécanique des Fluides, allee C. Soula, Toulouse, 31400, France

Thermodiffusion or Soret effect has been taken into account in many porous media applications, in particular in petroleum engineering and geophysics. Traditionally, the classical dispersion equation is completed with an additional effective thermodiffusion term. The question of the relationship of the effective thermodiffusion coefficient to micro-scale parameters (mixture thermodiffusion coefficient, pore-scale geometry, thermal conductivity ratio, Péclet numbers, ...) is still an open question. In this paper, new results are presented using the classical framework of the theory of volume averaging. The macro-scale equations are derived based on a decomposition of the temperature and concentration in terms of averaged values and deviations. A closure problem mapping the deviations to the gradients of the average values allows to write macro-scale equations and to derive the effective parameters from the pore-scale physical characteristics. The closure problems are solved numerically for a simple pore-scale geometry. The results show, among other things, that the effective Soret coefficient does not depend on the thermal conductivity ratio for a Péclet number equal to zero. For non-zero Péclet numbers, the effective Soret coefficient shows a diffusive regime followed by a “dispersive regime”, i.e., some dependence with the Péclet number. Finally, and as a validation, the initial pore-scale problem is solved numerically over an array of cylinders, and the resulting averaged temperature and concentration fields are compared favourably to macro-scale theoretical predictions.