Scanline method to determine the fractal nature of 2-D fracture networks

Mathematical Geology

Volumn 34, Issue 6, 2002, Pages 647-670

  Babadagli, Tayfun ^a  

^a SULTAN QABOOS UNIVERSITY   (Oman)

Author keywords

2 D fracture networks; Fractal; Fracture density; Fracture length; Fracture orientation; Scanning direction effect on fractal dimension

Indexed keywords

FRACTAL ANALYSIS; FRACTURE NETWORK;

EID: 17444365987     PISSN: 08828121     EISSN: 15738868     Source Type: Journal    
DOI: 10.1023/A:1019897008208     Document Type: Article

References (30)

1. Acuna, J. A., and Yortsos, Y. C., 1991, Numerical construction and flow simulation in networks of fractures using fractal geometry: SPE 22703, in Proc. Soc. Pet. Eng. 66th Annu. Tech. Conf. Exh., Dallas, TX, Oct. 6-9, 1991.
2. Acuna, J. A., and Yortsos, Y. C., 1995, Application of fractal geometry to the study of networks of fractures and their pressure transient: Wat. Resour. Res., v. 31, p. 527-540.
3. Barton, C. C., 1995, Fractal analysis of scaling and spatial clustering of fractures, in Barton, C. C., and La Pointe, P. R., eds., Fractals in the earth science: Plenum Press, New York, p. 141-178.
4. Barton, C. C., and Hsieh, P. A., 1989, Physical and hydrologic-flow properties of fractures, in Field Trip Guidebook T385: 28th Int. Geol. Cong., Washington, DC.
5. Barton, C. C., and Larsen, E., 1985, Fractal geometry of two-dimensional fracture networks at Yucca Mountain, southwestern Nevada, in Stephansson, O., ed., Proc. Int. Symp. Fundam. Rock Joints, Bjorkliden, Sweden, p. 77-84.
6. Boadu, F. K., and Long, L. T., 1994, The fractal character of fracture spacing and RQD: Int. J. Rock. Mech. Min. Sci. Geomech. Abstr., v. 31, p. 127-134.
7. Castaing, C., Genter, A., Chiles, J. P., Bourgine, B., and G. Ouillon, 1997, Scale effects in natural fracture networks: Int. J. Rock. Mech. Min. Sci. Geomech. Abstr. v. 34, p. 389.
8. Feder, J., 1988, Fractals: Plenum Press, New York, 283 p.
9. Gibson, R. L., and Toksoz, M. N., 1990, Permeability estimation from velocity anisotropy in fractured rock: J. Geophys. Res., v. 95, no. 15, p. 643-655.
10. Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Procaccia, I., and Shraiman, B. I., 1986, Fractal measures and their singularities: The characterization of strange sets: Phys. Rev. A, v. 33, no. 2, p. 1141-1151.
11. Hewett, T. A., 1994, Fractal methods for fracture characterization, in Yarus, J. M., and Chambers, R. L., eds., Stochastic modeling and geostatistics: American Association for Petroleum Geologists, Tulsa, OK, p. 249-260.
12. Hirata, T., 1989, Fractal dimension of fault systems in Japan: Fracture structure in rock fracture geometry at various scales: Pure Appl. Geophys., v. 131, p. 157-170.
13. Katz, A. J., and Thompson, A. H., 1985, Fractal sandstone pores: Implications for conductivity and pore formation: Phys. Rev. Lett., v. 54, p. 1325-1328.
14. Kranz, R. L., 1994, Fractal point patterns and fractal fracture traces, in Nelson, P. P., and Laubach, S. E., eds., Rock mechanics: Balkema, Rotterdam, The Netherlands, p. 793-800.
15. Krohn, C. E., 1988a, Sandstone fractal and Euclidean pore volume distributions: J. Geophys. Res., v. 93, p. 3286-3296.
16. Krohn, C. E., 1988b, Fractal measurements of sandstones, shales and carbonates: J. Geophys. Res., v. 93, p. 3297-3305.
17. Krohn, C. E., and Thompson, A. H., 1986, Fractal sandstone pores: Automated measurements using scanning-electron-microscope images: Phys. Rev. B, v. 33, p. 6366-6374.
18. La Pointe, P. R., 1988, A method to characterize fracture density and connectivity through fractal geometry: Int. J. Rock. Mech. Min. Sci. Geomech. Abstr., v. 25, p. 421-429.
19. Liu, H. H., and Molz, F. J., 1997, Multifractal analyses of hydraulic conductivity distributions: Wat. Resour. Res. v. 33, p. 2483-2488.
20. Muller, J., and McCauley, J. L., 1992, Implication of fractal geometry for fluid flow properties of sedimentary rocks: Transp. Porous Media, v. 8, p. 133-147.
21. Oda, M., 1986, An equivalent continuum model for coupled stress and fluid flow analyses in jointed rock masses: Wat. Resour. Res., v. 22, p. 1845-1856.
22. Priest, S. D., and Samaniego, A., 1984, A model for the analysis of discontinuity characteristics in two dimension in Fifth int. Cong. Rock Mech., A. A. Balkema, Rotterdam, The Netherlands, Vol. 2, p. F199-F207.
23. Sammis, C. G., An, L. J., and Ershaghi, I., 1991, Three dimensional characterization of the fracture network at the Geysers Geothermal Field: 17th Annu. Workshop Geotherm. Reservoir Eng., Stanford, CA, Jan. 29-31.
24. Sornette, A., Sornette, D., and Davy, P., 1990, Fractal fault patterns as a dual DLA problem, in Rossmanith, H.-P., ed., Mechanics of jointed and faulted rock: Balkema, Rotterdam, The Netherlands, p. 229-235.
25. Takayasu, H., 1990, Fractals in physical sciences: Manchester University Press, Manchester, 170 p.
26. Velde, B., Dubois, J., Touchard, G., and Badri, A., 1990, Fractal analysis of fractures in rocks: The Cantor's Dust method: Tectonophysics, v. 179, p. 345-352.
27. Wei, Z. Q., Egger, P., and Descoeudres, F., 1995, Permeability predictions for jointed rock masses: Int. J. Rock Mech. Min. Sci. Geomech. Abstr., v. 32, p. 251-261.
28. Xie, H., Wang, J., and Kwasniewski, M. A., 1999, Multifractal characterization of rock fracture surfaces: Int. J. Rock Mech. Min. Sci., Geomech. Abstr. v. 36. p. 19-27.
29. Yamamato, H., Kojima, K., and Tosaka, H., 1993, Fractal clustering of rock fractures and its modeling using cascade process, in Pinto da Cunha, A., ed., Scale effects in rock masses 93: Balkema, Rotterdam, The Netherlands, p. 81-86.
30. Zhang, X., Sanderson, D. J., Harkness, R. M., and Last, N. C., 1996, Evaluation of the 2-D permeability: Int. J. Rock Mech. Min. Sci. Geomech. Abstr., v. 33, p. 17-37.