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Journal of Porous Media
Facteur d'impact: 1.49 Facteur d'impact sur 5 ans: 1.159 SJR: 0.504 SNIP: 0.671 CiteScore™: 1.58

ISSN Imprimer: 1091-028X
ISSN En ligne: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v13.i2.50
pages 145-155

THE STABILITY OF EVAPORATING FRONTS IN POROUS MEDIA

O. A. Plumb
Department of Mechanical Engineering, University of Wyoming, Laramie, WY 82072
Alexander Y. Klimenko
School of Mechanical and Mining Engineering, The University of Queensland, Brisbane, QLD 4072, Australia

RÉSUMÉ

Evaporating fronts in porous media occur during drying processes, underground coal gasification, geothermal energy production from hot, dry rock, and around nuclear waste repositories. The stability of such fronts is pertinent to understanding the heat and mass transfer at the front. This article reports the results of linear stability analyses of evaporating fronts in infinite and semi-infinite domains. For the case of an infinite domain, subcooled or saturated liquid flows toward hot matrix rock above the saturation temperature, resulting in a moving evaporation front. For the semi-infinite domain, subcooled or saturated liquid flows toward a surface maintained at a temperature above the saturation temperature. For the infinite domain and an evaporating front normal to the gravitational vector, the front can be destabilized by gravity when a dense liquid overlies a less dense vapor. Whether the flow is vertical or horizontal, the front can be destabilized by mobility. It is demonstrated that evaporation, as characterized by the vapor phase Jakob number, has a destabilizing effect on mobility, however, this is countered by a stabilizing effect due to heat transfer at the interface. The stabilizing effect of heat transfer can dominate destabilizing effects of mobility and gravity at large wave numbers. For the semi-infinite domain, a stationary front can be shown to exist under certain conditions, and in this case, the stabilizing effect of heat transfer is always greater than the destabilizing effect of mobility for a fluid having the properties of water over a wide range of pressures.

RÉFÉRENCES

  1. Barbier, E., Geothermal energy technology and current status: An overview.

  2. Bejan, A., Heat Transfer.

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  4. Khadse, A. N., Qayyumi, M., Mahajani, S. M., and Agha-layam, P., Reactor model for underground coal gasification (UCG) channel.

  5. Miller, C. A., Stability of moving surfaces in fluid systems with heat and mass transport III. Stability of displacement fronts in porous media.

  6. Perkins, G. and Sahajwalla, V., A mathematical model for the chemical reaction of a semi-infinite block of coal in underground coal gasification.

  7. Plumb, O. A., Transport phenomena in porous media: Modeling the drying process.

  8. Saffman, P. G. and Taylor, G. I., The penetration of a fluid into a porous medium or Hele-shaw cell containing a more viscous liquid.

  9. Stewart, L. D. and Udell, K. S., The effect of gravity and multiphase flow on the stability of condensation fronts in porous media.

  10. Yang, J. and Edwards, R. N., Predicted groundwater circulation in fractured and unfractured anisotropic porous media driven by nuclear fuel waste heat generation.

  11. Yortsos, Y. C., Effect of lateral heat losses on the stability of thermal displacement fronts in porous media.


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