Understanding vertical heat transfer and through flow in porous media such as geothermal reservoirs is of great interest. In a geothermal system, a denser layer of liquid water may overlie a less dense layer of water vapour. Vertical and horizontal thermal diffusion stabilises such configurations, but the buoyancy contrast can cause instability. In this study, the mechanisms contributing to the stability and instability of such systems are analysed using a separate-phase model with a sharp interface be- tween liquid and vapour. The governing equations representing incompressibility, Darcy’s law and energy conservation for each phase are linearised about suitable base states and the stability of these states is investigated. We have considered two different thermal boundary conditions, both with and without a vertical through- flow. In the first case, the boundaries above and below the layer of interest are assumed to be isothermal. We found that due to the competition between thermal and hydrostatic effects, the liquid–vapour interface may have multiple positions. A two-dimensional linear stability analysis of these basic states shows that the Rayleigh–Taylor mechanism is the dominant contributor to instability, but that there are circumstances under which the basic state may be stable, especially when the front is close to one of the boundaries. In the second case, a constant heat flux is imposed at the liquid boundary and a fixed temperature at the vapour boundary. We have shown that competition between the effects of cooling and the viscosity difference between the fluid phases causes multiple liquid-vapour front positions, whether or not gravity is considered. The stability analysis has shown that along with the Rayleigh-Taylor (buoyancy- driven) mechanism, a Saffman-Taylor viscous fingering mechanism can also play an important rule in the transition to instability.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:570459 |
| Date | January 2011 |
| Creators | Khan, Zafar Hayat |
| Publisher | University of Strathclyde |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=16850 |
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