A simple model for deviations from the cubic law for a fracture undergoing dilation or closure

Pure and Applied Geophysics

Volumn 160, Issue 5-6, 2003, Pages 1009-1022

  Sisavath, Sourith ^a   Al Yaarubi, Azzan ^a   Pain, Chris C ^a   Zimmerman, Robert W ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Cubic law; Fractures; Hydraulic conductivity; Navier Stokes; Permeability

Indexed keywords

FRACTURE MECHANICS; NAVIER-STOKES EQUATIONS; PERMEABILITY; ROCK MECHANICS;

CREEP; FRACTURE FLOW; FRACTURE MECHANICS; HYDRAULIC CONDUCTIVITY; NAVIER-STOKES EQUATIONS; PERMEABILITY;

EID: 0037401236     PISSN: 00334553     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00012558     Document Type: Article

References (29)

1. BEAR, J., Dynamics of Fluids in Porous Media (Elsevier, New York, 1972).
2. BERNABE, Y. and OLSON, J. F. (2000), The Hydraulic Conductance of a Capillary with a Sinusoidally Varying Cross-section, Geophys. Res. Lett. 27, 245-248.
3. BROWN, S. R. (1987), Fluid Flow through Rock Joints: The Effect of Surface Roughness. J. Geophys. Res. B 92, 1337-1347.
4. BROWN, S. R., STOCKMAN, H. W., and REEVES, S. J. (1995), Applicability of the Reynolds Equation for Modelling Fluid Flow between Rough Surfaces, Geophys. Res. Lett. 22, 2537-2540.
5. COOK, N. G. W. (1992), Natural Joints in Rock: Mechanical, Hydraulic and Seismic Behaviour and Properties under Normal Stress, Int. J. Rock Mech. 29, 198-223.
6. DURHAM, W. B. and BONNER, B. P. (1994), Self-propping and Fluid-flow in Slightly Offset Joints at High Effective Pressures, J. Geophys. Res. 99, 9391-9399.
7. HASEGAWA, E. and IZUCHI, H. (1983), On Steady Flow through a Channel Consisting of an Uneven Wall and a Plane Wall - Part 1. Case of No Relative Motion in Two Walls, JSME Bull. 26, 514-520.
8. KITANIDIS, P. K. and DYKAAR, B. B. (1997), Stokes Flow in a Slowly Varying Two-Dimensional Periodic Pore, Transp. Porous Media 26, 89-98.
9. MEHEUST, Y. and SCHMITTBUHL, J. (2000), Flow Enhancement of a Rough Fracture, Geophys. Res. Lett. 27, 2989-2992.
10. MEHEUST, Y. and SCHMITTBUHL, J. (2001), Geometrical Heterogeneities and Permeability Anisotropy of Rough Fractures, J. Geophys. Res. 106, 2089-2102.
11. MOURZENKO, V. V., THOVERT, J.-F., and ADLER, P. M. (1995), Permeability of a Single Fracture-Validity of the Reynolds Equation, J. Phys II 5, 465-482.
12. NICHOLL, M. J., RAJARAM, H., GLASS, R. J., and DETWILER, R. (1999), Saturated Flow in A Single Fracture: Evaluation of the Reynolds Equation in Measured Aperture Fields. Wat. Resour. Res. 35, 3361-3373.
13. NOLTE, D. D., PYRAK-NOLTE, L. J., and COOK, N. G. W. (1989), The Fractal Geometry of Flow Paths in Natural Fractures in Rock and the Approach to Percolation, Pure Appl. Geophys. 131, 111-138.
14. ORON, A. P. and BERKOWITZ, B. (1998), Flow in Rock Fractures: The Local Cubic Law Assumption Re-examined, Wat. Resour. Res. 34, 2811-2824.
15. PAIN, C. C., Brief Description and Capabilities of the General Purpose CFD Code: Fluidity (Internal Report, Imperial College, London, 2000).
16. POZRIKIDIS, C., Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge U. P., Cambridge, 1992).
17. PYRAK-NOLTE, L. J., MYER, L. R., COOK, N. G. W., and WITHERSPOON, P. A., Hydraulic and mechanical properties of natural fractures in low permeability Rock. In Proc. Sixth Int. Congr. Rock Mech. (eds. Herget G. and Vongpaisal S.) (Balkema, Rotterdam 1987) pp. 225-231.
18. RAVEN, K. G., NOVAKOWSKI, K. S., and LAPCEVIC, P. A. (1987), Interpretation of Field Tracer Tests of a Single Fracture using a Transient Solute Storage Model, Wat. Resour. Res. 24, 2019-2032.
19. SCHLICHTING, H., Boundary-Layer Theory (McGraw-Hill, New York, 1968).
20. SILLIMAN, S. E. (1989), An Interpretation of the Difference between Aperture Estimates Derived from Hydraulic and Tracer Tests in a Single Fracture, Wat. Resour. Res. 25, 2275-2283.
21. SKJETNE, E., HANSEN, A., and GUDMUNDSSON, J. S. (1999), High-Velocity Flow in a Rough Fracture, J. Fluid Mech. 383, 1-28.
22. TSANG, Y. W. and WITHERSPOON, P. A. (1981), Hydromechanical Behaviour of a Deformable Rock Fracture Subject to Normal Stress, Wat. Resour. Res. 86, 9287-9298.
23. VAN DYKE, M. (1987), Slow Variations in Continuum Mechanics. Adv. Appl. Mech. 25, 1-43.
24. VANDEMBROUCQ, D. and ROUX, S. (1997), Conformal Mapping on Rough Boundaries 1: Applications to Harmonic Problems, Phys. Rev. E 55, 6171-6185.
25. WALSH, J. B., BROWN, S. R., and DURHAM, W. B. (1997), Effective Medium Theory with Spatial Correlation for Flow in a Fracture, J. Geophys. Res. 102, 22,587-22,594.
26. WITHERSPOON, P. A., WANG, J. S. Y., IWAI, K., and GALE, J. E. (1980), Validity of Cubic Law for Fluid Flow in a Deformable Rock Fracture, Wat. Resour. Res. 16, 1016-1024.
27. YEO, I. W., DE FREITAS, M. H., and ZIMMERMAN, R. W. (1998), Effect of Shear Displacement on the Aperture and Permeability of a Rock Fracture, Int. J. Rock Mech. 35, 1051-1070.
28. ZIMMERMAN, R. W. and BODVARSSON, G. S. (1996), Hydraulic Conductivity of Rock Fractures, Transp. Porous Media 23, 1-30.
29. ZIMMERMAN, R. W., KUMAR, S., and BODVARSSON, G. S. (1991), Lubrication Theory Analysis of Rough-Walled Fractures, Int. J. Rock. Mech. 28, 325-331.