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Modelling of the Dynamic Young’s Modulus of a Sedimentary Rock Subjected to Nonstationary Loading

Author

Listed:
  • Mikhail Guzev

    (Department of Oil and Gas Technologies, Perm National Research Polytechnic University, 614990 Perm, Russia
    Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, 690041 Vladivostok, Russia)

  • Evgenii Riabokon

    (Department of Oil and Gas Technologies, Perm National Research Polytechnic University, 614990 Perm, Russia)

  • Mikhail Turbakov

    (Department of Oil and Gas Technologies, Perm National Research Polytechnic University, 614990 Perm, Russia)

  • Evgenii Kozhevnikov

    (Department of Oil and Gas Technologies, Perm National Research Polytechnic University, 614990 Perm, Russia)

  • Vladimir Poplygin

    (Department of Oil and Gas Technologies, Perm National Research Polytechnic University, 614990 Perm, Russia)

Abstract

This paper presents a mathematical model that reflects the nature of the dynamic Young’s modulus of a dry sedimentary rock during nonstationary uniaxial loading. The model is based on an idealized model of a system suggested by Jaeger J.C. A rock sample is considered as a spring with stiffness, the bottom point of which is fixed, while the upper point carries a mass. A sample experiences dynamic load and the rock matrix response. Displacement of the mass from the equilibrium state sets the variation of the sample’s length. Displacement of all the sample’s points goes according to the same law regardless of the point location. The response of a rock to a disturbing nonstationary load is selected based on the combination of conditions of each experiment, such as the load frequency and amplitude and the mass, length, and diameter of a sample. The mathematical model is consistent with experimental data, according to which an increase in load frequency leads to an increase in the dynamic Young’s modulus for each value of the load. The accuracy of the models is evaluated. The relations underlying the model can be used as a basis to describe the Young’s modulus dispersion of sedimentary rocks under the influence of nonstationary loads.

Suggested Citation

  • Mikhail Guzev & Evgenii Riabokon & Mikhail Turbakov & Evgenii Kozhevnikov & Vladimir Poplygin, 2020. "Modelling of the Dynamic Young’s Modulus of a Sedimentary Rock Subjected to Nonstationary Loading," Energies, MDPI, vol. 13(23), pages 1-12, December.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:23:p:6461-:d:458130
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    Cited by:

    1. Evgenii Vasilevich Kozhevnikov & Mikhail Sergeevich Turbakov & Evgenii Pavlovich Riabokon & Vladimir Valerevich Poplygin, 2021. "Effect of Effective Pressure on the Permeability of Rocks Based on Well Testing Results," Energies, MDPI, vol. 14(8), pages 1-20, April.

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