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| Titel |
Using Homogenization Theory to Study Convection in Thermohaline Systems |
| VerfasserIn |
J. L. Musuuza, F. A. Radu, S. Attinger |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250067579
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| Zusammenfassung |
| We study a density-driven system in which the density gradients arise from salinity and
temperature differences. Since the solute and heat diffuse at different rates, such
systems are also called double-diffusive and arise in many practical applications like
carbon dioxide sequestration, geothermal energy exploitation and the storage of
nuclear and normal waste in geological formations. A typical sedimentary-basin
set-up is adopted where both salinity and temperature increase with depth. In such
systems, the buoyancy forces caused by salinity and temperature gradients give rise
to counter-acting convection cells. The homogenization theory ideas originally
developed in Held et al. (2005) are applied to the solute and heat transport equations
and the two resulting cell problems solved coupled. A dimensionless number is
derived from the solutions to the cell problems in terms of the physical variables
temperature, viscosity and density contrasts; gravity-driven velocity, domain size and
formation hydro-geological properties. The sign of the number changes to negative
when the thermal-convection predominates over solutal-convection. The derived
dimensionless number is tested against numerical simulations performed with the
software package d3 f on sufficiently refined grids that deliver stable numerical
solutions without upwind techniques (Frolkovic and De Schepper, 2001). We also
investigate the possibility of groundwater intrusion into a geological formation by
applying a horizontal drift at the top of the domain. The evolution of fingers in haline
density-driven systems was studied e.g. in Musuuza et al. (2009) and such a velocity
aligned orthogonal to the direction of finger propagation was found to retard finger
growth.
Frolkovic, P. and De Schepper, H. (2001), ’Numerical modelling of convection
dominated transport coupled with density-driven flow in porous media’, Ad. Wat.
Resour. 24, 63-72.
Held, R, S. Attinger and Kinzelbach, W. (2005), ’Homogenization and effective
parameters for the Henry problem in heterogeneous formations’, Wat. Resour.
Res. 41.
Musuuza, J. L., Radu, F. A., and Attinger, S. (2009), ’An extended stability
criterion for density-driven flows in homogeneous porous media’, Ad. Wat.
Resour. 32(6), 796-808. |
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