A fractal analysis of permeability for fractured rocks

International Journal of Heat and Mass Transfer

Volumn 81, Issue , 2015, Pages 75-80

  Miao, Tongjun ^a,b   Yu, Boming ^a   Duan, Yonggang ^c   Fang, Quantang ^c  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b Xin Xiang Vocational and Technical College   (China)

^c SOUTHWEST PETROLEUM UNIVERSITY   (China)

Author keywords

Fractal; Fracture networks; Fractures; Permeability; Rock

Indexed keywords

FRACTURE; MECHANICAL PERMEABILITY; ROCKS;

FRACTAL ANALYSIS; FRACTURE NETWORK; FRACTURED ROCK;

FRACTALS;

EID: 84908433427     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2014.10.010     Document Type: Article

References (50)

1. T.D. van Golf-Racht, Fundamentals of Fractured Reservoir Engineering, Elsevier, 1982.
2. Y.S. Wu, C. Haukwa, G. Bodvarsson, A site-scale model for fluid and heat flow in the unsaturated zone of Yucca Mountain, Nevada, J. Contam. Hydrol. 38 (1999) 185-215.
3. K. Watanabe, H. Takahashi, Parametric study of the energy extraction from hot dry rock based on fractal fracture network model, Geothermics 24 (1995) 223-236.
4. D.T. Snow, A Parallel Plate Model of Fractured Permeable Media, University of California, Berkeley, 1965.
5. R. Kranzz, A. Frankel, T. Engelder, C. Scholz, The permeability of whole and jointed Barre granite, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 16 (1979) 225-234.
6. N. Koudina, R.G. Garcia, J.F. Thovert, P. Adler, Permeability of threedimensional fracture networks, Phys. Rev. E 57 (1998) 4466.
7. J.R. de Dreuzy, P. Davy, O. Bour, Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 2. Permeability of networks based on lognormal distribution of apertures, Water Resour. Res. 37 (2001) 2079-2095.
8. C. Klimczak, R.A. Schultz, R. Parashar, D.M. Reeves, Cubic law with aperture-length correlation: implications for network scale fluid flow, Hydrogeol. J. 18 (2010) 851-862.
9. T. Chelidze, Y. Guguen, Evidence of fractal fracture, Int. J. Rock Mech. Min. 27 (1990) 223-225.
10. J. Chang, Y. Yortsos, Pressure transient analysis of fractal reservoirs, SPE Form. Eval. 5 (1990) 31-38.
11. M. Sahimi, Flow phenomena in rocks: from continuum models to fractals, percolation, cellular automata, and simulated annealing, Rev. Mod. Phys. 65 (1993) 1393-1534.
12. K. Watanabe, H. Takahashi, Fractal geometry characterization of geothermal reservoir fracture networks, J. Geophys. Res: Solid Earth (1978-2012) 100 (1995) 521-528.
13. J.J. Andrade, E. Oliveira, A. Moreira, H. Herrmann, Fracturing the optimal paths, Phys. Rev. Lett. 103 (2009) 225503.
14. A. Jafari, T. Babadagli, Estimation of equivalent fracture network permeability using fractal and statistical network properties, J. Petrol. Sci. Eng. 92-93 (2012) 110-123.
15. P. Xu, B. Yu, M. Yun, M. Zou, Heat conduction in fractal tree-like branched networks, Int. J. Heat Mass Transfer 49 (2006) 3746-3751.
16. P. Xu, B. Yu, Y. Feng, Y. Liu, Analysis of permeability for the fractal-like tree network by parallel and series models, Physica A 369 (2006) 884-894.
17. S. Wang, B. Yu, A fractal model for the starting pressure gradient for Bingham fluids in porous media embedded with fractal-like tree networks, Int. J. Heat Mass Transfer 54 (2011) 4491-4494.
18. Q. Zheng, B. Yu, A fractal permeability model for gas flow through dual-porosity media, J. Appl. Phys. 111 (2012) 024316-0243167.
19. A. Torabi, S.S. Berg, Scaling of fault attributes: a review, Mar. Pet. Geol. 28 (2011) 1444-1460.
20. D. Kolyukhin, A. Torabi, Statistical analysis of the relationships between faults attributes, J. Geophys. Res: Solid Earth (1978-2012) 117 (2012) 15-20. B05406-1-14.
21. D. Kolyukhin, A. Torabi, Power-law testing for fault attributes distributions, Pure Appl. Geophys. 170 (2013) 2173-2183.
22. E. Bonnet, O. Bour, N.E. Odling, P. Davy, I. Main, P. Cowie, B. Berkowitz, Scaling of fracture systems in geological media, Rev. Geophys. 39 (2001) 347-383.
23. M. Sahimi, Flow and transport in porous media and fractured rock, Wiley.Com., 2012, p. 167.
24. J.H. Kruhl, Fractal-geometry techniques in the quantification of complex rock structures: a special view on scaling regimes, inhomogeneity and anisotropy, J. Struct. Geol. 46 (2013) 2-21.
25. B. Velde, J. Dubois, D. Moore, G. Touchard, Fractal patterns of fractures in granites, Earth Planet. Sci. Lett. 104 (1991) 25-35.
26. M. Vignes-Adler, A. Le Page, P.M. Adler, Fractal analysis of fracturing in two African regions, from satellite imagery to ground scale, Tectonophysics 196 (1991) 69-86.
27. C.A. Barton, M.D. Zoback, Self-similar distribution and properties of macroscopic fractures at depth in crystalline rock in the Cajon Pass Scientific Drill Hole, J. Geophys. Res: Solid Earth (1978-2012) 97 (1992) 5181-5200.
28. C. Hatton, I. Main, P. Meredith, Non-universal scaling of fracture length and opening displacement, Nature 367 (1994) 160-162.
29. R.A. Schultz, R. Soliva, H. Fossen, C.H. Okubo, D.M. Reeves, Dependence of displacement-length scaling relations for fractures and deformation bands on the volumetric changes across them, J. Struct. Geol. 30 (2008) 1405-1411.
30. B.B. Mandelbrot, The Fractal Geometry of Nature, Macmillan, 1983.
31. A. Majumdar, B. Bhushan, Role of fractal geometry in roughness characterization and contact mechanics of surfaces, J. Tribol. 112 (1990) 205-216.
32. I.G. Main, P.G. Meredith, P.R. Sammonds, C. Jones, Influence of fractal flaw distributions on rock deformation in the brittle field, Geol. Soc. 54 (1990) 81-96.
33. J. Feder, Fractals, Plenum Press, New York, 1988.
34. R. Nolen-Hoeksema, R.B. Gordon, Optical detection of crack patterns in the opening-mode fracture of marble, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 24 (1987) 135-144.
35. B.M. Yu, J.H. Li, Some fractal characters of porous media, Fractals 9 (2001) 365-372.
36. X. Zhang, D. Sanderson, Numerical study of critical behaviour of deformation and permeability of fractured rock masses, Mar. Pet. Geol. 15 (1998) 535-548.
37. A. Yazdi, H. Hamzehpour, M. Sahimi, Permeability, porosity, and percolation properties of two-dimensional disordered fracture networks, Phys. Rev. E 84 (2011) 046317.
38. P.M. Adler, J.-F. Thovert, Fractures and fracture networks, Springer, 1999.
39. M. Khamforoush, K. Shams, J.-F. Thovert, P. Adler, Permeability and percolation of anisotropic three-dimensional fracture networks, Phys. Rev. E 77 (2008) 056307.
40. B. Massart, M. Paillet, V. Henrion, J. Sausse, C. Dezayes, A. Genter, A. Bisset, Fracture characterization and stochastic modeling of the granitic basement in the HDR Soultz Project (France), in: Proceedings World Geothermal Congress 2010, 2010.
41. L. Landau, E. Lifshitz, Fluid Mechanics, Vol. 6. Course of Theoretical Physics, 1987.
42. K. Nazridoust, G. Ahmadi, D.H. Smith, A new friction factor correlation for laminar, single-phase flows through rock fractures, J. Hydrol. 329 (2006) 315-328.
43. J. Ge, Y. Liu, Y. Yao, The modern mechanics of fluids flow in oil reservoir, vol. 2, Petroleum Industry Press, 2003 (in Chinese).
44. R. Parsons, Permeability of idealized fractured rock, Old SPE J. 6 (1966) 126-136.
45. P.S. Huyakorn, B.H. Lester, C.R. Faust, Finite element techniques for modeling groundwater flow in fractured aquifers, Water Resour. Res. 19 (1983) 1019-1035.
46. J. Andersson, B. Dverstorp, Conditional simulations of fluid flow in threedimensional networks of discrete fractures, Water Resour. Res. 23 (1987) 1876-1886.
47. V. Lenti, C. Fidelibus, A BEM solution of steady-state flow problems in discrete fracture networks with minimization of core storage, Comput. Geosci.-UK. 29 (2003) 1183-1190.
48. H. Kazemi, Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution, SPE J. 9 (1969) 451-462.
49. A. Jafari, T. Babadagli, Effective fracture network permeability of geothermal reservoirs, Geothermics 40 (2011) 25-38.
50. A. Jafari, T. Babadagli, A sensitivity analysis for effective parameters on fracture network permeability, SPE Western Regional and Pacific Section AAPG Joint Meeting, 2008.