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Theoretical and experimental determination of effective diffusion and thermodiffusion coefficients in porous media

Davarzani, Hossein. Theoretical and experimental determination of effective diffusion and thermodiffusion coefficients in porous media. PhD, Institut National Polytechnique de Toulouse, 2010

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Official URL: http://ethesis.inp-toulouse.fr/archive/00001075/

Abstract

A multicomponent system, under nonisothermal condition, shows mass transfer with cross effects described by the thermodynamics of irreversible processes. The flow dynamics and convective patterns in mixtures are more complex than those of one-component fluids due to interplay between advection and mixing, solute diffusion, and thermal diffusion (or Soret effect). This can modify species concentrations of fluids crossing through a porous medium and leads to local accumulations. There are many important processes in nature and industry where thermal diffusion plays a crucial role. Thermal diffusion has various technical applications, such as isotope separation in liquid and gaseous mixtures, identification and separation of crude oil components, coating of metallic parts, etc. In porous media, the direct resolution of the convection-diffusion equations are practically impossible due to the complexity of the geometry; therefore the equations describing average concentrations, temperatures and velocities must be developed. They might be obtained using an up-scaling method, in which the complicated local situation (transport of energy by convection and diffusion at pore scale) is described at the macroscopic scale. At this level, heat and mass transfers can be characterized by effective tensors. The aim of this thesis is to study and understand the influence that can have a temperature gradient on the flow of a mixture. The main objective is to determine the effective coefficients modelling the heat and mass transfer in porous media, in particular the effective coefficient of thermodiffusion. To achieve this objective, we have used the volume averaging method to obtain the modelling equations that describes diffusion and thermodiffusion processes in a homogeneous porous medium. These results allow characterising the modifications induced by the thermodiffusion on mass transfer and the influence of the porous matrix properties on the thermodiffusion process. The obtained results show that the values of these coefficients in porous media are completely different from the one of the fluid mixture, and should be measured in realistic conditions, or evaluated with the theoretical technique developed in this study. Particularly, for low Péclet number (diffusive regime) the ratios of effective diffusion and thermodiffusion to their molecular coefficients are almost constant and equal to the inverse of the tortuosity coefficient of the porous matrix, while the effective thermal conductivity is varying by changing the solid conductivity. In the opposite, for high Péclet numbers (convective regime), the above mentioned ratios increase following a power law trend, and the effective thermodiffusion coefficient decreases. In this case, changing the solid thermal conductivity also changes the value of the effective thermodiffusion and thermal conductivity coefficients. Theoretical results showed also that, for pure diffusion, even if the effective thermal conductivity depends on the particle-particle contact, the effective thermal diffusion coefficient is always constant and independent of the connectivity of the solid phase. In order to validate the theory developed by the up-scaling technique, we have compared the results obtained from the homogenised model with a direct numerical simulation at the microscopic scale. These two problems have been solved using COMSOL Multiphysics, a commercial finite elements code. The results of comparison for different parameters show an excellent agreement between theoretical and numerical models. In all cases, the structure of the porous medium and the dynamics of the fluid have to be taken into account for the characterization of the mass transfer due to thermodiffusion. This is of great importance in the concentration evaluation in the porous medium, like in oil reservoirs, problems of pollution storages and soil pollution transport. Then to consolidate these theoretical results, new experimental results have been obtained with a two-bulb apparatus are presented. The diffusion and thermal diffusion of a helium-nitrogen and helium-carbon dioxide systems through cylindrical samples filled with spheres of different diameters and thermal properties have been measured at the atmospheric pressure. The porosity of each medium has been determined by construction of a 3D image of the sample made with an X-ray tomograph device. Concentrations are determined by a continuous analysing the gas mixture composition in the bulbs with a katharometer device. A transient-state method for coupled evaluation of thermal diffusion and Fick coefficients in two bulbs system has been proposed. The determination of diffusion and thermal diffusion coefficients is done by comparing the temporal experimental results with an analytical solution modelling the mass transfer between two bulbs. The results are in good agreement with theoretical results and emphasize the porosity of the medium influence on both diffusion and thermal diffusion process. The results also showed that the effective thermal diffusion coefficients are independent from thermal conductivity ratio and particle-particle touching.

Item Type:PhD Thesis
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Institution: Université de Toulouse > Institut National Polytechnique de Toulouse - INPT
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Research Director:
Quintard, Michel
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