Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-16T17:18:20.116Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow and transport in single rock fractures

Published online by Cambridge University Press:  26 April 2006

K. Muralidhar
K. Muralidhar
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, India
Get access Rights & Permissions [Opens in a new window]

Abstract

The present work is a numerical study of fluid flow and energy transport in single rock fractures. Each fracture is modelled as a parallel channel with a distribution of contact areas where the fracture aperture is zero. The pressure drop required to sustain a given rate of flow is calculated by solving the Stokes equations along with the incompressibility constraint. The permeability of the fracture is then determined as the ratio of mean flow and pressure drop. With flow distribution known, the advection–diffusion equation is solved for a thermal mixing problem. All differential equations have been solved by the finite-element technique.

Results show that the fracture permeability is affected by the presence of contact areas and the magnitude of h, the mean fracture aperture. The limiting case of zero aperture is realized at h/L [les ] 0.016, where L is the characteristic dimension of the fracture. The other limiting case of a two-dimensional fracture is seen for h/L [ges ] 1. The thermal dispersion profiles at steady state are unaffected by the size of aperture h and the presence of contact areas for Péclet numbers Pe less than 50 and a contact fraction of up to 20%. However, the transient dispersion problem is seen to be influenced by the contact areas for Pe > 10.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 215 , June 1990 , pp. 481 - 502
Copyright
© 1990 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

Baker, A. J. 1983 Finite Element Computational Fluid Mechanics. McGraw-Hill.
Bear, J. 1972 Dynamics of Fluids in Porous Media. Elsevier.
Brown, S. R. 1987 Fluid flow through rock joints: the effect of surface roughness. J. Geophys. Res. 92, 1337–1347.Google Scholar
Chapman, N. A. & McKinley, I. G. 1987 The Geologic Disposal of Nuclear Waste. John Wiley.
Coulaud, O., Morel, P. & Caltagirone, J. P. 1988 Numerical modelling of non-linear effects in laminar flow through a porous medium. J. Fluid Mech. 190, 393–408.Google Scholar
Dagan, G. 1987 Theory of solute transport by groundwater. Ann. Rev. Fluid Mech. 19, 183–216.Google Scholar
Duff, I. S. 1980 MA28 — A set of Fortran subroutines for sparse unsymmetric linear equations. AERE, Harwell.
Kays, W. M. & Crawford, M. E. 1980 Convective Heat and Mass Transfer. McGraw-Hill.
Montazer, P. & Wilson, W. E. 1984 Conceptual hydrologic model of flow in the unsaturated zone, Yucca Mountain, Nevada. Water Resources Investigations Rep. 84-4345. US Geological Survey.
Napolitano, M. & Orlandi, P. 1985 Laminar flow in a complex geometry: a comparison. Intl J. Num. Methods Fluids 5, 667–683.Google Scholar
Patankar, S. V. 1980 Numerical Heat Transfer. Hemisphere.
Peyret, R. & Taylor, T. D. 1983 Computational Methods of Fluid Flow. Springer.
Pyrak-Nolte, L. J., Myer, L., Cook, N. G. W. & Witherspoon, P. A. 1987 Hydraulic and mechanical properties of natural fractures in low permeability rock. Presented at the 6th Inl Congr. on Rock Mechanics, Montreal, Canada.
Schlichting, H. 1979 Boundary-Layer Theory. McGraw-Hill.
Snow, D. T. 1968 Rock fracture spacings, openings and porosities. J. Soil Mech. Found. Div. Proc. ASCE 94, 73–91.Google Scholar
Tsang, Y. W. 1984 The effect of tortuosity on fluid flow through a single fracture. Water Resources Res. 20, 1209–1215.Google Scholar
Walsh, J. B. & Brace, W. F. 1984 The effect of pressure on porosity and transport properties of rocks. J. Geophys. Res. 89, 9425–9431.Google Scholar
Wang, J. S. Y. & Narasimhan, T. N. 1985 Hydrologic mechanisms governing fluid flow in partially saturated, fractured porous tuff at Yucca Mountain. Prepared for Sandia Laboratories, Sandia Contract 47-7550. Also, Water Resources Res. 21, 1861–1874.Google Scholar