Skip to main content
SpringerLink
Log in

Direct and inverse problems of gas emission and the sorptive deformation of coal beds

  • Published:
Journal of Applied and Industrial Mathematics Aims and scope Submit manuscript

Abstract

Using the equations of state for fractured-porous media that describe the sorptioninduced deformation of coal, we develop a geomechanical model for radial gas influx to a borehole drilled in a coal bed with the concurrent evolution of stress field in the borehole environment. A numerical-and-analytical method is proposed for solving the corresponding system of equations for poroelastic media. A relation is found between the volume of slack withdrawn in the borehole (when opening up the gas-bearing seams), the sorption-and-storage capacities of coal, the permeability k, and the horizontal component σ h of the natural stress field. We demonstrate the solvability of the inverse boundary-coefficient problem of determining k and σ h on the basis of pressure in the closed borehole. We substantiate an express-method for estimating the permeability by the measurements of pressure in the borehole operating in the “pressure drop” mode.

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. Yu. N. Malyshev and A. T. Airuni, Complex Degassing of Coal Mines (Izd. AGN, Moscow, 1999) [in Russian].

    Google Scholar 

  2. L. A. Puchkov, S. V. Slastunov, and K. S. Kolikov, Methane Recovery from Coal Seams (Moskov. Gos. Gorn. Univ., Moscow, 2002) [in Russian].

    Google Scholar 

  3. J. Enever, D. Casey, and M. Bocking, “The Role of In-Situ Stress in Coalbed Methane Exploration,” in Coalbed Methane: Scientific, Environmental, and Economic Evaluation, Ed. by M. Mastalerz, M. Glikson, and S. D. Golding (Dordrecht, Kluwer Acad. Publ., 1999), pp. 297–303.

    Google Scholar 

  4. J. Seidle, Foundations of Coalbed Methane Reservoir Engineering (PennWell Books, Tulsa, 2011).

    Google Scholar 

  5. H. H. Liu, J. Rutqvist, and J. G. Berryman, “On the Relationship between Stress and Elastic Strain for Porous and Fractured Rock,” Internat. J. RockMech. Min. Sci. 46 (2), 289–296 (2009).

    Article  Google Scholar 

  6. J. Rutqvist, Y.-S. Wu, C.-F. Tsang, and G. Bodvarsson, “A Modeling Approach for Analysis of Coupled Multiphase Fluid Flow, Heat Transfer, and Deformation in Fractured Porous Rock,” Internat. J. RockMech. Min. Sci. 39, 429–442 (2002).

    Article  Google Scholar 

  7. G. I. Barenblatt, Yu. P. Zheltov, and I. N. Kochina, “On Main Concepts of Theory of Filtration in Fractured Media,” Prikl. Mat. Mekh. 24 (5), 58–73 (1960).

    Google Scholar 

  8. L. D. Connell, “Coupled Flow and Geomechanical Processes during Gas Production from Coal Seams,” Internat. J. Coal Geology 79 (1–2), 18–28 (2009).

    Article  MathSciNet  Google Scholar 

  9. J. Q. Shi and S. Durucan, “A Bidisperse Pore DiffusionModel forMethane Displacement Desorption in Coal by CO2 Injection,” Fuel 82, 1219–1229 (2003).

    Article  Google Scholar 

  10. L. Brochard, M. Vandamme, and R. J.-M. Pellenq, “Poromechanics of Microporous Medium,” J. Mech. Phys. Solids 60, 606–612 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  11. D. N. Espinoza, M. Vandamme, P. Dangla, J.-M. Pereira, S. Vidal-Gilbert, “A Transverse Isotropic Model for Microporous Solids Application to Coal Matrix Adsorption and Swelling,” J. Geophys. Res. Solid Earth 118, 6113–6123 (2013).

    Article  Google Scholar 

  12. D. N. Espinoza, M. Vandamme, J.-M. Pereira, et al. “Measurement and Modeling of Adsorptive-Poromechanical Properties of Bituminous Coal Cores Exposed to COme2: Adsorption, Swelling Strains, Swelling Stresses, and Impact on Fracture Permeability,” Internat. J. Coal Geology 134–135, 80–95 (2014).

    Article  Google Scholar 

  13. O. Coussy, Mechanics and Physics of Porous Solids (JohnWiley & Sons, New York, 2010).

    Book  Google Scholar 

  14. S. A. Khristianovich and Yu. F. Kovalenko, “On Measurement of Gas Pressure in Coal Seams,” Fiz.-Tekhn. Problemy Razrabotki Poleznykh Iskopaemykh No. 3, 3–24 (1988).

    Google Scholar 

  15. S. A. Khristianovich, “On Fundamentals of Filtration Theory,” Fiz.-Tekhn. Problemy Razrabotki Poleznykh Iskopaemykh No. 1, 3–17 (1991).

    Google Scholar 

  16. A. A. Samarskii, Introduction to the Theory of Difference Schemes (Nauka, Moscow, 1971) [in Russian].

    Google Scholar 

  17. L. Tavernini, Continuous-Time Modeling and Simulation (Gordon and Breach, Amsterdam, 1996).

    MATH  Google Scholar 

  18. V. Novatskii, Elasticity Theory (Government Scientific Publ. House, Warsaw, 1970; Mir, Moscow, 1975).

    Google Scholar 

  19. RD 05–350–00. Instructions for the Safe Conducting of Work on Seams Dangerous for Sudden Releases of Coal (Rock) and Gas. Appendix 2: Prevention of Gas-Dynamic Phenomena in CoalMines (Gosgortekhnadzor, 2004) [in Russian].

  20. Directory (Cadastre) of Physical Properties of Rocks, Ed. by N. V. Mel’nikov, M. M. Protod’yakonov, and V. V. Rzhevskii (Nedra, Moscow, 1975) [in Russian].

  21. L. A. Nazarova, L. A. Nazarov, G. Ya. Polevshchikov, and R. I. Romin, “Inverse Problem Solution for Estimating Gas Content and Gas Diffusion Coefficient of Coal,” Fiz.-Tekhn. Problemy Razrabotki Poleznykh Iskopaemykh No. 5, 15–23 (2012) [J. of Mining Science 48 (5), 781 (2012)].

    Google Scholar 

  22. V. G. Romanov, Inverse Problems of Mathematical Physics (Nauka, Moscow, 1984; VNU Science Press, Utrecht, 1987).

    Google Scholar 

  23. O. M. Alifanov, E. A. Artyukhin, and S. V. Rumyantsev, ExtremeMethods for Solving Ill-Posed Problems (Nauka, Moscow, 1988) [in Russian].

    MATH  Google Scholar 

  24. L. A. Nazarova, L. A. Nazarov, A. L. Karchevsky, and M. Vandamme, “Estimating Diffusion-Capacity Parameters of a Coal Bed Using the Gas Pressure Measured in a Hole and the Solution of an Inverse Problem,” Sibirsk. Zh. Industr. Mat. 17 (1), 78–85 (2014) [J. Appl. Indust. Math. 8 (2), 267-273 (2014)].

    MATH  Google Scholar 

  25. A. A. Duchkov and A. L. Karchevsky, “Estimation of Terrestrial Heat Flux from TemperatureMeasurements in BottomSediments,” Sibirsk. Zh. Industr. Mat. 16 (3), 61–85 (2013) [J. Appl. Indust. Math. 7 (4), 480-502 (2013)].

    Google Scholar 

  26. A. L. Karchevsky, “Numerical Solution of anOne-Dimensional Inverse Problem for the System of Elasticity,” Dokl. Akad. Nauk 375 (2), 235–238 (2000).

    Google Scholar 

  27. A. L. Karchevsky, “NumericalReconstruction ofMediumParameters ofMember of ThinAnisotropic Layers,” J. Inverse Ill-Posed Probl. 12 (5), 519–634 (2004).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chinakal Institute of Mining, Krasnyi pr. 54, Novosibirsk, 630091, Russia

    L. A. Nazarova & L. A. Nazarov

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    L. A. Nazarova & L. A. Nazarov

  3. Universite Paris-Est, Laboratoire Navier (UMR 8205), CNRS, ENPC, IFSTTAR, F-77455, Marne-la-Vallee, France

    M. Vandamme & J.-M. Pereira

Authors
  1. L. A. Nazarova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. A. Nazarov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Vandamme
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J.-M. Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. A. Nazarova.

Additional information

Original Russian Text © L.A. Nazarova, L.A. Nazarov, M. Vandamme, J.-M. Pereira, 2017, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2017, Vol. XX, No. 2, pp. 41–49.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nazarova, L.A., Nazarov, L.A., Vandamme, M. et al. Direct and inverse problems of gas emission and the sorptive deformation of coal beds. J. Appl. Ind. Math. 11, 236–243 (2017). https://doi.org/10.1134/S1990478917020090

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1990478917020090

Keywords

Search

Navigation