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ArticleNo Access

SEEPAGE PROPERTIES OF ROCK FRACTURES WITH POWER LAW LENGTH DISTRIBUTIONS

    https://doi.org/10.1142/S0218348X19500579Cited by:16 (Source: Crossref)
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    Abstract

    Fractures with power law length distributions abound in nature such as carbonate oil and gas reservoirs, sandstone, hot dry rocks, etc. The fluid transport properties and morphology characterization of fracture networks have fascinated numerous researchers to investigate for several decades. In this work, the analytical models for fracture density and permeability are extended from fractal fracture network to general fracture network with power law length distributions. It is found that the fracture density is related to the power law exponents (α,n) and the area porosity ϕ of fracture network. Then, a permeability model for the fracture length distribution with general power law exponent α and the power law exponent n for fracture length versus aperture is proposed based on the well-known cubic law in individual fracture. The analytical expression for permeability of fractured networks is found to be a function of power law exponents (α,n), area porosity ϕ of fracture network, and the micro-structural parameters (maximum fracture length lmax, fracture azimuth 𝜃1 and fracture dip angle 𝜃2). The present model may shed light on the mechanism of seepage in fracture networks with power law length distributions.

    References

    • 1. M. Sahimi , Flow and Transport in Porous Media and Fractured Rock (Wiley-VCH, Weinheim, Germany, 2011), p. 159. Crossref, Google Scholar
    • 2. A. Torabi and S. S. Berg , Scaling of fault attributes: A review, Mar. Pet. Geol. 28(8) (2011) 1444–1460. Crossref, ISI, Google Scholar
    • 3. J. R. De Dreuzy, P. Davy and O. Bour , Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 1. Effective connectivity, Water Resour. Res. 37(8) (2001) 2065–2078. Crossref, ISI, Google Scholar
    • 4. J. R. De Dreuzy, P. Davy and 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(8) (2001) 2079–2095. Crossref, ISI, Google Scholar
    • 5. J. R. De Dreuzy, P. Davy and O. Bour , Hydraulic properties of two-dimensional random fracture networks following power law distributions of length and aperture, Water Resour. Res. 38(12) (2002) 12-1–12-9. Crossref, ISI, Google Scholar
    • 6. I. Bogdanov, V. Mourzenko, J. F. Thovert and P. M. Adler , Effective permeability of fractured porous media with power law distribution of fractures sizes, Phys. Rev. E 76(3 Pt2) (2007) 036309. Crossref, ISI, Google Scholar
    • 7. E. Bonnet, O. Bour, N. E. Odling, P. Davy, I. Main, P. Cowie and B. Berkowitz , Scaling of fracture systems in geological media, Rev. Geophys. 39(3) (2001) 347. Crossref, ISI, Google Scholar
    • 8. R. Liu, L. Yu, Y. Jiang, Y. C. Wang and B. Li , Recent developments on relationships between the equivalent permeability and fractal dimension of two-dimensional rock fracture networks, J. Nat. Gas Sci. Eng. 45 (2017) 771–785. Crossref, ISI, Google Scholar
    • 9. G. Pickering, J. M. Bull and D. J. Sanderson , Sampling power law distributions, Tectonophysics 248(1–2) (1995) 1–20. Crossref, ISI, Google Scholar
    • 10. A. Jafari and T. Babadagli , Estimation of equivalent fracture network permeability using fractal and statistical network properties, J. Nat. Gas Sci. Eng. 92–93(4) (2012) 110–123. Google Scholar
    • 11. T. Miao, A. Chen, Y. Xu and S. Cheng , A permeability model for water–gas phase flow in fractal fracture networks, Fractals 26(6) (2018) 1850087. Link, ISI, Google Scholar
    • 12. T. Miao, S. Cheng, A. Chen and B. Yu , Analysis of axial thermal conductivity of dual-porosity fractal porous media with random fractures, Int. J. Heat Mass Transf. 102 (2016) 884–890. Crossref, ISI, Google Scholar
    • 13. R. Liu, B. Li, Y. Jing, H. Jing and L. Yu , On the relationship between equivalent permeability and fractal dimension of dual-porosity media, Fractals 26(5) (2018) 1850072. Link, ISI, Google Scholar
    • 14. T. Miao, B. Yu, Y. Duan and Q. Fang , A fractal analysis of permeability for fractured rocks, Int. J. Heat Mass Transf. 81(81) (2015) 75–80. Crossref, ISI, Google Scholar
    • 15. R. Liu, Y. Jiang, B. Li and X. Wang , A fractal model for characterizing fluid flow in fractured rock masses based on randomly distributed rock fracture networks, Comput. Geotech. 65 (2015) 45–55. Crossref, ISI, Google Scholar
    • 16. J. Watterson, J. J. Walsh, P. A. Gillespie and S. Easton , Scaling systematics of fault sizes on a large range fault map, J. Struct. Geol. 18(2–3) (1996) 199–214. Crossref, ISI, Google Scholar
    • 17. N. E. Odling, P. Gillespie and B. Bourgine , Variations in fracture system geometry and their implications for fluid flow in fractures hydrocarbon reservoirs, Petrol. Geosci. 5(4) (1999) 373–384. Crossref, ISI, Google Scholar
    • 18. T. Miao, S. Yang, Z. Long and B. Yu , Fractal analysis of permeability of dual-porosity media embedded with random fractures, Int. J. Heat Mass Transf. 88 (2015) 814–821. Crossref, ISI, Google Scholar
    • 19. A. J. Katz and A. H. Thompson , Fractal sandstone pores: Implications for conductivity and pore formation, Phys. Rev. Lett. 54(12) (1995) 1325–1328. Crossref, ISI, Google Scholar
    • 20. B. Yu , Analysis of flow in fractal porous media, Appl. Mech. Rev. 61 (2008) 050801. Crossref, ISI, Google Scholar
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