Skip to main content
Log in

Dispersion Phenomena in Thermal Diffusion and Modelling of Thermogravitational Experiments in Porous Media

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

In a TIPM paper published in 1992, the authors presented a simple model of thermogravitational diffusion in packed columns (TPC). Though qualitatively in agreement with the experimental results, this model exhibited a systematic discrepancy with respect to the magnitude of the permeability of maximum separation in the TPC experiments. Here, the results of a re-examination of the classical phenomenology of irreversible thermodynamics in porous media, applied to TPC, are described. Through the interpretation of additional TPC experiments, we show that the effective thermal diffusion coefficient in TPC includes a dependency upon the fluid velocity. This dependency is consistent with a nonlinear extension of irreversible thermodynamics, and the model so amended accounts for a correct re-interpretation of the experiments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Adler, P.: 1992, Porous Media: Geometry and Transport, Butterworths-Heinemann.

  • Bear J.: 1972, Dynamics of Fluids in Porous Media, American-Elsevier New York.

    Google Scholar 

  • Bénet J. C., et Jouanna, P.: 1983, Non équilibre thermodynamique dans les milieux poreux non saturés avec changement de phase, Int. J. Heat Mass Transfer 26(11), 1585-1595.

    Google Scholar 

  • Costesèque, P.: 1982, Sur la migration sélective des isotopes et des éléments par thermodiffusion dans les solutions. Applications de l'effet thermogravitationnel en milieu poreux; observations expérimentales et conséquences géochimiques, Thése Doct. Etat, Université Paul Sabatier, Toulouse.

    Google Scholar 

  • De Groot, S. R. and Mazur, P.: 1962, Non-equilibrium Thermodynamics, North-Holland, Amsterdam.

    Google Scholar 

  • Ecenarro, O., Madariaga, J. A., Navarro, J., Santamaria, C. M., Carrion, J. A. and Saviron, J. M.: 1989, Non steady-state density effects in liquid thermal diffusion columns, J. Phys.: Condens. Matter 1, 9741.

    Google Scholar 

  • El Maâtaoui, M.: 1983, Etude sur la permabilité monophasique des lits poreux meubles, Mémoire de D.E.A., Laboratoire de Minéralogie et Cristallographie, Université Paul Sabatier, Toulouse, France.

    Google Scholar 

  • El Maâtaoui, M.: 1986, Conséquences de la thermodiffusion en milieu poreux sur l'hydrolyse des solutions de chlorures ferriques et sur les migrations d'hydrocarbures dans les mélanges de n-alcanes et dans un pétrole brut; implications géochimiques, Thèse Doct. 3me Cycle, Université Paul Sabatier, 1986.

  • Fargue D. et Jamet Ph.: 1994, Les équations opérationnelles du transport en milieu poreux déduites de la thermodynamique des systèmes ouverts, Entropie 184–185, 17-22.

    Google Scholar 

  • Fer, F.: 1971, Thermodynamique macroscopique: systèmes ouverts, Gordon and Breach.

  • Furry, W. H., Jones, R. C. and Onsager, L.: 1939, On the theory of isotope separation by thermal diffusion, Phys. Rev. 55, 1083-1095.

    Google Scholar 

  • Hafskjold, B., Ikeshoji, T. and Kjelstrup Ratkje, S.: 1993, On the molecular mechanism of thermal diffusion in liquids, Molec. Phys. 80, 1389-1412.

    Google Scholar 

  • Hassanizadeh, S. M.: 1989, Derivation of basic equations of mass transport in porous media, 2. Generalized Darcy's and Fick's laws, Adv. Water Res. 24, 321-330.

    Google Scholar 

  • Jamet, Ph.: 1991, Sur certains aspects du couplage en milieu poreux entre les champs de température et de concentration, Mémoires des Sciences de la Terre, Ecole des Mines de Paris, No. 14.

    Google Scholar 

  • Jamet, Ph. et al.: 1992, The thermogravitational effect in porous media: a modelling approach, Transport in Porous Media 9 223-240.

    Google Scholar 

  • Jamet, Ph., Costesque, P. and Fargue, D.: 1996, Determination of the effective transport coefficients for the separation of binary mixtures of organic compounds into packed thermal diffusion columns, Chem. Engng. Sci. 51(19), 4463-4475.

    Google Scholar 

  • Koch, D. L. and Brady, J. F.: 1985, Dispersion in fixed beds, J. Fluid Mech. 154, 399-428.

    Google Scholar 

  • Legros, J. C., Goemaere, P. and Platten, J. K.: 1985, Soret coefficient and the two-component Bernard convection in the benzene-methanol system, Phys Rev. 32(3), 1903-1905.

    Google Scholar 

  • Lorenz, M. and Emery, A. H.: 1959, The packed thermal diffusion column, Chem. Engng. Sci. 11, 16-23.

    Google Scholar 

  • Marcoux, M., Platten, J. K. et Chavepeyer, G.: 1996, Diffusion thermogravitationnelle entre deux cylindres coaxiaux: effet de la courbure, forthcoming issue of Entropie.

  • Pfannkuch, O.: 1963, Contribution à l'étude des déplacements de fluides miscibles dans un milieu poreux, Rev. Inst. Fr. Pétrol. 2(18), 215-270.

    Google Scholar 

  • Sanchez V.: 1975, La diffusion thermique et son application au fractionnement des mélanges binaires, Thése Doc. Etat, Université Paul Sabatier.

  • Scheidegger, A. E.: 1961, General theory of dispersion in porous media, J. Geophys. Res. 66, 3273-3278.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fargue, D., Jamet, P. & Costesèque, P. Dispersion Phenomena in Thermal Diffusion and Modelling of Thermogravitational Experiments in Porous Media. Transport in Porous Media 30, 323–344 (1998). https://doi.org/10.1023/A:1006599028786

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1006599028786

Navigation