Skip to main content
SpringerLink
Log in

Thermodynamic compatible model of microfractured porous media and Stoneley waves

  • Published:
Journal of Engineering Thermophysics Aims and scope

Abstract

Nonstationary theory of two-velocity continuum describing the propagation of acoustic waves inmicrofractured porousmedia is based on general physical principles: the first law of thermodynamics, the conservation laws, the kinematic relationships in the metric tensor and the Galilean principle of relativity. As a physical application, the theory of the Stoneley wave in microfractured porous media is developed. The simulation results are compared with the results of physical measurement of the Stoneley wave parameters in the boreholes. It is shown that an additional fluid transport through fractures makes it possible to satisfactorily correlate the experimental and theoretical data. In general, the developed theory is a nonlinear physical model of fluid dynamics in fractured porous media.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dorovsky, V., Nefedkin, Yu., Fedorov, A., and Podberezhnyy, M., A Logging Method for Estimating Permeability, Velocity of Second Compressional Wave, and Electroacoustic Constant in Electrolyte-Saturated Porous Formations, Russ. Geol. Geophys., 2010, vol. 51, pp. 1247–1322.

    Google Scholar 

  2. Landau, L.D. and Lifshitz, E.M., Course of Theoretical Physics, Fluid Mechanics, Pergamon Press, 1987.

    Google Scholar 

  3. Dorovsky, V.N., Continual Theory of Filtration, Sov. Geol. Geophys., 1989, vol. 30, no. 7, pp. 39–45.

    Google Scholar 

  4. Dvorkin, J. and Nur, A., Dynamic Poroelasticity: A UnifiedModel with the Squirt and the BiotMechanisms, Geophys., 1993, vol. 58, pp. 524–533.

    Article  Google Scholar 

  5. Parra, J.O., The Transversely Isotropic Poroelastic Wave Equation Including the Biot and the Squirt Mechanisms: Theory and Application, Geophys., 1997, vol. 62, pp. 309–318.

    Article  Google Scholar 

  6. Diallo, M.S. and Appel, E., Acoustic Wave Propagation in Saturated Porous Media: Reformulation of the Biot/Squirt Flow Theory, J. Appl. Geophys., 2000, vol. 44, pp. 313–325.

    Article  ADS  Google Scholar 

  7. Chen, Y.F., Yang, D.H., and Zhang, H.Z., Biot/Squirt Model in Viscoelastic Porous Media, Chin. Phys. Lett., 2002, vol. 19, pp. 445–448.

    Article  ADS  Google Scholar 

  8. Yang, D. and Zhang, Z., Poroelastic Wave Equation Including the Biot/Squirt Mechanism and the Solid/Fluid Coupling Anisotropy, Wave Motion, 2002, vol. 35, pp. 223–245.

    Article  MATH  Google Scholar 

  9. Adelinet, M., Fortin, J., and Gueguen, Y., Dispersion of ElasticModuli in a Porous-Cracked Rock: Theoretical Predictions for Squirt-Flow, Tectonophys., 2011, vol. 503, nos. 1/2, pp. 173–181.

    Article  Google Scholar 

  10. Tang, X.M., A Unified Theory for ElasticWave Propagation through PorousMedia Containing Cracks—An Extension of Biot’s PoroelasticWave Theory, Science China Earth Sci., 2011, vol. 54, no. 9, pp. 1441–1452.

    Article  Google Scholar 

  11. Tang, X.-M., Chen, X.-L., and Xu, X.-K., A Cracked Porous Medium Elastic Wave Theory and Its Application to Interpreting Acoustic Data from Tight Formations, Geophys., 2012, vol. 77, no. 6, pp. D245–D252.

    Article  Google Scholar 

  12. Mavko, G. and Nur, A., Melt Squirt in the Asthenosphere, J. Geophys. Res., 1975, vol. 80, pp. 1444–1448.

    Article  ADS  Google Scholar 

  13. Mavko, G. and Nur, A., Wave Attenuation in Partially Saturated Rocks, Geophys., 1979, vol. 44, pp. 161–178.

    Article  Google Scholar 

  14. Thomsen, L., Biot-Consistent Elastic Moduli of Porous Rocks: Low-Frequency Limit, Geophys., 1985, vol. 50, pp. 2797–2807.

    Article  Google Scholar 

  15. Tuncay, K. and Corapcioglu, M.Y., Wave Propagation in Fractured Porous Media, Transport in Porous Media, 1996, vol. 23, no. 3, pp. 237–258.

    Google Scholar 

  16. Pride, S.R. and Berryman, J.G., Linear Dynamics of Double Porosity Dual-Permeability Materials, I, II, Phys. Rev. E, 2003, vol. 68, ID 036603, 036604.

    Article  ADS  MathSciNet  Google Scholar 

  17. Cui, Z.W. and Wang, K.X., Influence of the Squirt Flow on Reflection and Refraction of Elastic Waves at a Fluid/Fluid–Saturated Poroelastic Solid Interface, Int. J. Eng. Sci., 2003, vol. 41, pp. 2179–2191.

    Article  Google Scholar 

  18. Cui, Z.W., Liu, J.-X., and Wang, K.X., Influence of Squirt Flow on Guided Waves in a Borehole, J. Jilin Univ., 2005, vol. 43, no. 6, pp. 803–808.

    Google Scholar 

  19. Wu, X. and Yin, H., Method for Determining Reservoir Permeability Form Borehole Stoneley Wave Attenuation Using Biot’s Poroelastic Theory, USPatent, 7830744 B2, 2010.

    Google Scholar 

  20. Dorovsky, V., Dubinsky, V., Fedorov, A., Podberezhnyy, M., Nefedkin, Yu., and Perepechko, Yu., Method and Apparatus for Estimating Formation Permeability and Electroacoustic Constant of an Electrolyte-Saturated Multi-Layered Rock Taking into Account Osmosis, Patent Appl. Publ., US 2010/0254218 A1, 2010.

    Google Scholar 

  21. Winkler, K.W., Liu, H.L., and Johnson, D.J., Permeability and Borehole Stoneley Waves: Comparison between Experiment and Theory, Geophys., 1989, vol. 54, pp. 66–75.

    Article  Google Scholar 

  22. Dorovsky, V., Perepechko, Yu., and Fedorov, A., The Stoneley Waves in the Biot–Johnson Theory and Continual Filtration Theory, Russ. Geol. Geophys., 2012, vol. 53, pp. 621–630.

    Article  Google Scholar 

  23. Dorovsky, V., Perepechko, Yu., and Fedorov, A., Stoneley Wave Electroacoustic Ratio, Electric Field in Presence of Radial Borehole Waves, and Related Method of Measuring Permeability and Electroacoustic Constant, Russ. Geol. Geophys., 2013, vol. 54, pp. 621–630.

    Google Scholar 

  24. Zoback, M.D., Reservoir Geomechanics, Stanford University, 2010.

    MATH  Google Scholar 

  25. Godunov, S.K. and Romenskii, E.I., Elements of ContinuumMechanics and Conservation Laws, Kluwer, 2003.

    Book  MATH  Google Scholar 

  26. Dorovsky, V.N. and Perepechko, Yu.V., Phenomenological Description of Two-Velocity Media with Relaxing Shear Stresses, J. Appl. Mech. Tech. Phys., 1992, vol. 33, no. 3, pp. 403–409.

    Article  ADS  Google Scholar 

  27. Dorovsky, V.N., Mathematical Models of Two-Velocity Media, Math. Comput. Model., 1995, vol. 21, no. 7, pp. 17–28.

    Article  MathSciNet  MATH  Google Scholar 

  28. Dorovsky, V.N. and Perepechko, Yu.V., Mathematical Models of Two-Velocity Media, Part II: Math. Comput. Model., 1996, vol. 24, no. 10, pp. 69–80.

    MathSciNet  MATH  Google Scholar 

  29. Blohin, A.M. and Dorovsky, V.N., Mathematical Modeling in the Theory of Multivelocity Continuum, Nova Sci. Publ., 1995.

    Google Scholar 

  30. Dorovsky, S., An Approach to Automated Development of HydrodynamicModels, Progr. Syst., 2011, vol. 4, pp. 123–129.

    Google Scholar 

  31. Tisza, L., Sur la supraconductibilitéThermique de l’hélium IIliquide et la Statistique de Bose–Einstein, Comptes Rendus Ac. Sci. (Paris), 1938, vol. 207, pp. 1035–1037.

    Google Scholar 

  32. Tisza, L., La viscositéde l’hélium II liquide et la Statistique de Bose–Einstein, Comptes Rendus Ac. Sci. (Paris), 1938, vol. 207, pp. 1186–1189.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Novosibirsk Technology Centre, Baker Hughes Incorporated, Novosibirsk, Russia

    V. Dorovsky & Yu. Perepechko

  2. Sobolev Institute of Geology and Mineralogy, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

    Yu. Perepechko

  3. Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

    Yu. Perepechko

  4. Sobolev Institute ofMathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

    E. Romenski

  5. Novosibirsk State University, Novosibirsk, Russia

    M. Podberezhnyy

Authors
  1. V. Dorovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. Perepechko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Romenski
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Podberezhnyy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. Perepechko.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dorovsky, V., Perepechko, Y., Romenski, E. et al. Thermodynamic compatible model of microfractured porous media and Stoneley waves. J. Engin. Thermophys. 25, 182–196 (2016). https://doi.org/10.1134/S1810232816020041

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1810232816020041

Keywords

Search

Navigation