Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-18T23:59:06.069Z Has data issue: false hasContentIssue false
  • English
  • Français

On the propagation of non-isothermal gravity currents in an inclined porous layer

Published online by Cambridge University Press:  23 September 2011

W. J. Rayward-Smith  and
Andrew W. Woods
W. J. Rayward-Smith
Affiliation:
BP Institute for Multiphase Flow, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
Andrew W. Woods*
Affiliation:
BP Institute for Multiphase Flow, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
*
†Email address for correspondence: andy@bpi.cam.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the buoyancy-driven flow in an inclined porous layer which results when fluid of different temperature and composition to that in the reservoir is injected from a horizontal line well. The thermal inertia of the porous matrix leads to a transition in the temperature of the injectate as it spreads from the well and heats up to reservoir temperature. Since the buoyancy and viscosity of the injectate change across this thermal transition, the alongslope characteristic speed of the current also changes. Density and viscosity typically decrease with temperature and, so, for injectate that is positively buoyant at reservoir temperature, the changes in density and viscosity with temperature have complementary effects on the characteristic speed. In contrast, for injectate that is negatively buoyant at reservoir temperature, the changes in viscosity and density with temperature have competing influences on the characteristic speed. The change in characteristic speed, combined with the change in buoyancy across the thermal transition, leads to a series of different flow morphologies with the thermally adjusted injectate either running ahead of or lagging behind the original injectate. By approximating the thermal transition as a discrete jump, we derive the leading-order structure of these currents for the different possible cases. We then build on this to develop a more detailed boundary layer description of the thermal transition based on the theory of thin gravity driven flows in porous media. Under certain injection conditions, we show that the thermal transition is gravitationally unstable and that this may lead to mixing across the thermal transition. We consider the implications of the models for several industrial processes including geothermal heat recovery, aquifer thermal storage and carbon dioxide sequestration.

JFM classification

Geophysical and Geological Flows: Ocean circulation Geophysical and Geological Flows: Ocean processes Geophysical and Geological Flows: Rotating flows Geophysical and Geological Flows: Shallow water flows Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 686 , 10 November 2011 , pp. 250 - 271
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Batzle, M. & Wang, Z. 1992 Seismic properties of pore fluids. Geophysics 57 (11), 1396–1408.CrossRefGoogle Scholar
2. Bear, J. 1972 Dynamics of Fluids in Porous Materials. American Elsevier.Google Scholar
3. Bickle, M., Chadwick, A., Huppert, H. E., Hallworth, M. & Lyle, S. 2007 Modelling carbon dioxide accumulation at Sleipner: implications for underground carbon storage. Earth Planet. Sci. Lett. 255, 164–176.CrossRefGoogle Scholar
4. Bolster, D., Neuweiler, I., Dentz, M. & Carrera, J. 2011 The impact of buoyancy on front spreading in heterogeneous porous media in two-phase immiscible flow. Water Resour. Res. 47, W02508.CrossRefGoogle Scholar
5. Elder, J. W. 1981 Geothermal Systems. Academic.Google Scholar
6. Hinch, E. J. & Bhatt, B. S. 1990 Stability of an acid front moving through porous rock. J. Fluid Mech. 212, 279–288.CrossRefGoogle Scholar
7. Huppert, H. E. & Woods, A. W. 1995 Gravity-driven flows in porous layers. J. Fluid Mech. 292, 55–69.CrossRefGoogle Scholar
8. Intergovernmental Panel on Climate Change. 2005 Special Report on Carbon Dioxide Capture and Storage. Cambridge University Press.Google Scholar
9. Jupp, T. E. & Woods, A. W. 2003 Thermally driven reaction fronts in porous media. J. Fluid Mech. 484, 329–346.CrossRefGoogle Scholar
10. Kangas, M. T. & Lund, P. D. 1994 Modelling and simulation of aquifer storage energy systems. Solar Energy 53 (3), 237–247.CrossRefGoogle Scholar
11. Lake, L. W. 1989 Enhanced Oil Recovery. Prentice-Hall.Google Scholar
12. Lu, M. & Connell, L. D. 2008 Non-isothermal flow of carbon dioxide in injection wells during geological storage. Intl J. Greenh. Gas Control 2, 248–258.CrossRefGoogle Scholar
13. Menand, T., Raw, A. & Woods, A. W. 2003 Thermal inertia and reversing buoyancy in flow in porous media. Geophys. Res. Lett. 30 (6), 1291.CrossRefGoogle Scholar
14. Nordbotten, J. M., Kavetski, D. & Celia, M. A. 2009 Model for CO2 leakage including multiple geological layers and multiple leaky wells. Environ. Sci. Technol. 43 (3), 743–749.CrossRefGoogle ScholarPubMed
15. Ortoleva, P., Merino, E., Moore, C. & Chadam, J. 1987 Geochemical self-organization. Part II. The reactive-infiltration instability. Am. J. Sci. 287, 1008–1040.CrossRefGoogle Scholar
16. Phillips, O. M. 1991 Flow and Reactions in Permeable Rocks. Cambridge University Press.Google Scholar
17. Pruess, K., Calore, C., Celati, R. & Wu, Y. S. 1987 An analytical solution for heat transfer at a boiling front moving through a porous medium. Intl J. Heat Mass Transfer 30 (12), 2595–2602.CrossRefGoogle Scholar
18. Raw, A. & Woods, A. W. 2003 On gravity-driven flow through a reacting porous rock. J. Fluid Mech. 474, 227–243.CrossRefGoogle Scholar
19. Rayward-Smith, W. J. & Woods, A. W. 2011 Some implications of cold CO2 injection into deep saline aquifers. Geophys. Res. Lett. 38, L06407.CrossRefGoogle Scholar
20. Verdon, J. & Woods, A. W. 2007 Gravity-driven reacting flows in a confined porous aquifer. J. Fluid Mech. 588, 29–41.CrossRefGoogle Scholar
21. Woods, A. W. 1999 Liquid and vapour flow in superheated rock. Annu. Rev. Fluid Mech. 31, 171–199.CrossRefGoogle Scholar