Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-19T15:40:07.256Z Has data issue: false hasContentIssue false
  • English
  • Français

Natural convection and dispersion in a tilted fracture

Published online by Cambridge University Press:  26 April 2006

Andrew W. Woods  and
Stefan J. Linz
Andrew W. Woods
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics. University of Cambridge, Silver Street, Cambridge CB3 9EW. UK
Stefan J. Linz
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

In many geophysical situations, fluid is contained in long narrow fractures embedded within an impermeable medium of different thermal conductivity: and there may be a uniform vertical temperature gradient imposed upon the system. We show that whenever the slot is tiled to the vertical, convection develops in the fluid, even if the background temperature increases with height. We then investigate the transport of passive material governed by this flow. The dispersion coefficient of a passive contaminant transported by this flow DT = f[R sin2ϕ] k2 cot2 ϕ/D, where k and D are the thermal and compositional diffusivities, ϕ is the angle of tilt and R is a Rayleigh number for the slot.

Using typical values for the physical properties of a water-filled fracture, we show that the Earth's geothermal gradient produces a convective flow in a fracture through the mechanism above; this has an associated dispersion coefficient DT ∼ 102-103D in fractures about a centimetre wide. We show that this shear dispersion could transport radioactive material, of half-life 104 years, tens of metres along the fracture within one half-life; without this dispersion, the material would only diffuse a few metres along the fracture within one half-life.

If there is a background salinity gradient along the slot in addition to the thermal gradient, analogous steady flow solutions exist; if the flow is stable, the salinity may either enhance or reduce the steady flow and associated dispersion of passive tracer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 241 , August 1992 , pp. 59 - 74
Copyright
© 1992 Cambridge University Press

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

Bjorlykke K. 1989 Sedimentology and Petroleum Geology. Springer.
Chen C. F. 1974 Double-diffusive convection in an inclined slot. J. Fluid Mech. 72, 721.Google Scholar
Davis S. H., Rosenblat S., Wood, J. R. & Hewitt T. A. 1985 Convective fluid flow and diagenetic patterns in domed sheets. Am. J. Sci. 285, 207.Google Scholar
Linz, S. J. & Woods A. W. 1992 Natural convection, Taylor dispersion and diagenesis in a porous tilted layer. Phys. Rev. (submitted).Google Scholar
Phillips O. M. 1970 On flows induced by diffusion in a stably stratified fluid. Deep-Sea Res. 17, 435.Google Scholar
Phillips O. M. 1991 Flow and Reactions in Permeable Rocks, pp. 1–285. Cambridge University Press
Taylor G. I. 1953 Dispersion of soluble matter in soluble matter in solvent flowing slowly through a tube Proc. R. Soc. Lond. A 219, 186.Google Scholar
Woods A. W. 1991 Boundary-driven mixing. J. Fluid Mech. 226, 625.Google Scholar
Wunsch C. 1970 On oceanic boundary mixing. Deep-Sea Res. 17, 293.Google Scholar