Flow in fractured media: A modified renormalization method

Water Resources Research

Volumn 34, Issue 2, 1998, Pages 177-191

  Gavrilenko, Pierre ^a   Guéguen, Yves ^a,b,c  

^a UNIVERSITÉ DE RENNES 1   (France)

^b LABORATOIRE DE GÉOLOGIE   (France)

^c ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

FLUID FLOW; FRACTURE; SCALING;

FRACTURE; PERMEABILITY; POROUS MEDIUM; SCALING;

FRACTURE; GROUP THEORY; SOLVENTS; STATISTICAL MECHANICS;

FRACTURE LENGTH; FRACTURE SYSTEMS; FRACTURED MEDIA; RENORMALIZATION; RENORMALIZATION GROUP THEORY; RENORMALIZATION METHODS; SCALE DEPENDENCE; THREE-DIMENSIONAL CALCULATIONS;

FLOW OF FLUIDS;

EID: 2642650363     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/97WR03042     Document Type: Article

References (30)

1. Ababou, R., and L. W. Gelhar, Self-similar randomness and spectral conditioning: Analysis of scale effects in surface hydrology, in Dynamics of Fluids in Hierarchical Porous Media, edited by J. H. Cushman, pp. 392-428, Academic, San Diego, Calif., 1990.
2. Allègre, C. J., J. L. Le Mouel, and A. Provost, Scaling rules in rocks fractures and possible implications for earthquake prediction, Nature, 297, 47-49, 1982.
3. Bernasconi, J., Real-space renormalization of bond disordered conductance lattices, Phys. Rev. B, 18, 2185-2191, 1978.
4. Brace, W. F., Permeability of crystalline and argillaceous rocks, Int. J. Rock Mech. Min. Sci., 17, 241-251, 1980.
5. Brace, W. F., Permeability of crystalline rocks: New in situ measurements, J. Geophys. Res., 89, 4327-4330, 1984.
6. Cladouhos, T. T., and R. Marrett, Are fault growth and linkage models consistent with power-law distributions of fault lengths?, J. Struct. Geol., 18, 281-293, 1996.
7. Clauser, C., Permeability of crystalline rocks, Eos Trans. AGU, 73(21), 233, 237-238, 1992.
8. Dagan, G., The significance of heterogeneity of evolving scales to transport in porous formations, Water Resour. Res., 30(12), 3327-3336, 1994.
9. Grindrod, P., and M. P. Impey, Fractal field simulations of tracer migration within the WIPP culebra dolomite, version 2, Rep. IM2856-1, Intera Inf. Technol., Denver, Colo., 1992.
10. Guéguen, Y., and J. K. Dienes, Transport properties of rock from statistics and percolation, Math. Geol., 21, 1-13, 1989.
11. Guéguen, Y., P. Gavrilenko, and M. Le Ravalec, Characteristic scales for rock permeability, Surv. Geophys., 17, 245-263, 1996.
12. Gutjahr, A. L., L. W. Gelhar, A. A. Bakr, and J. R. MacMillan, Stochastic analysis of spatial variability in subsurface flows, 2, Evaluation and application, Water Resour. Res., 14, 953-959, 1978.
13. Hadley, K., Comparison of calculated and observed crack densities and seismic velocities in westerly granite, J. Geophys. Res., 81, 3484-3494, 1976.
14. Hong, D. C., and H. E. Stanley, Cumulant renormalization group and its application to the incipient infinite cluster in percolation, J. Phys. A, 16, L525-L529, 1983.
15. Hsieh, P. A., A. M. Shapiro, D. J. Goode, and C. Tiedeman, Hydraulic conductivity of fractured crystalline rocks from meter to kilometer scale: Observation from the Mirror Lake site, New-Hampshire, paper presented at Chapman Conference on Hydrogeological Processes: Building and Testing Atomistic-to-Basin-Scale Models, AGU, Lincoln, Nebr., June 7-10, 1994.
16. King, P. R., The use of field theoretic methods for the study of flow in a heterogeneous porous medium, J. Phys. A Math Gen., 20, 3935-3947, 1987.
17. King, P. R., The use of renormalization for calculating effective permeability, Transp. Porous Media, 4, 37-58, 1989.
18. Madden, T. R., Random networks and mixing laws, Geophysics, 41, 1104-1125, 1976.
19. Madden, T. R., Microcrack connectivity in rocks: A renormalization group approach to the critical phenomena of conduction and failure in crystalline rocks, J. Geophys. Res., 88, 585-592, 1983.
20. Matheron, G., Eléments pour une Théorie des Milieux Poreux, Masson et Cie, Paris, 1967.
21. Neuman, S. P., Universal scaling of hydraulic conductivities and dispersivities in geologic media, Water Resour. Res., 26, 1749-1758, 1990.
22. Neuman, S. P., Generalized scaling of permeabilities: Validation and effect of support scale, Geophys. Res. Lett., 21, 349-352, 1994.
23. Neuman, S. P., On advective transport in fractal permeability and velocity fields, Water Resour. Res., 31, 1455-1460, 1995.
24. Reynolds, P. J., W. Klein, and H. E. Stanley, A real-space renormalization group for site and bond percolation, J. Phys. C Solid State Phys., 10, L167-L172, 1977.
25. Reynolds, P. J., H. E. Stanley, and W. Klein, Large cell Monte-Carlo renormalization group for percolation, Phys. Rev. B, 21, 1223-1244, 1980.
26. Smalley, R. F., Jr., D. L. Turcotte, and S. A. Solla, A renormalization group approach to the stick slip behavior of faults, J. Geophys. Res., 90, 1894-1900, 1985.
27. Stauffer, D., and A. Aharony, Introduction to Percolation Theory, 2nd ed., Taylor and Francis, Bristol, Pa., 1992.
28. Turcotte, D. L., Fractals and fragmentation, J. Geophys. Res., 91, 1921-1926, 1986.
29. Wilson, K. G., Renormalization group and critical phenomena, Phys. Rev. B, 4, 3174-3205, 1971.
30. Wilson, K. G., Les Phénomènes de Physique et les Echelles de Longueur, in L'ordre du Chaos, Bibliothèque pour la Sci., Belin, Paris, 1987.