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Buoyant flow of $\text{CO}_{2}$ through and around a semi-permeable layer of finite extent

Published online by Cambridge University Press:  15 November 2016

Tri Dat Ngo ,
Emmanuel Mouche  and
Pascal Audigane
Tri Dat Ngo*
Affiliation:
Laboratoire des Sciences du Climat et de l’Environnement, UMR 8212 CEA-CNRS-UVSQ, C.E. de Saclay, F-91191 Gif-sur-Yvette CEDEX, France
Emmanuel Mouche
Affiliation:
Laboratoire des Sciences du Climat et de l’Environnement, UMR 8212 CEA-CNRS-UVSQ, C.E. de Saclay, F-91191 Gif-sur-Yvette CEDEX, France
Pascal Audigane
Affiliation:
Bureau des Recherches Géologiques et Minières, 3 Avenue Claude Guillemin – BP6009 – 45060 Orléans CEDEX 1, France
*
†Email address for correspondence: tridatxf@gmail.com
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Abstract

The buoyancy- and capillary-driven counter-current flow of $\text{CO}_{2}$ and brine through and around a semi-permeable layer is studied both numerically and theoretically. The continuities of the capillary pressure and the total flux at the interface between the permeable matrix and layer control the $\text{CO}_{2}$ saturation discontinuity at the interface and the balance between the buoyant and capillary diffusion fluxes on each side of the interface. This interface process is first studied in a one-dimensional (1-D) vertical column geometry using the concept of extended capillary pressure and a graphical representation of the continuity conditions in the ($S_{L}$, $S_{U}$) plane, where $S_{L}$ and $S_{U}$ are the lower and upper saturation traces at the interface, respectively. In two dimensions, we heuristically extend the two-phase gravity current model to the case where the current is bounded by a semi-permeable layer. Consequently, the current is not saturated with $\text{CO}_{2}$, and its saturation and shape are derived from the flux and capillary pressure continuity conditions at the interface. This simplified model, which depends on $\text{CO}_{2}$ saturation only, is compared to fine grid simulations in the capillary-free and gravity-dominant cases. A good agreement is obtained in the second case; the current geometrical characteristics are accurately described. In the capillary-free case, we demonstrate that the local total velocity, which is, on average, zero because the flow is counter-current, must be considered in the total flux at the interface to obtain the same level of agreement.

JFM classification

Geophysical and Geological Flows: Gravity currents Multiphase and Particle-laden Flows: Multiphase flow Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 809 , 25 December 2016 , pp. 553 - 584
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Copyright
© 2016 Cambridge University Press 

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