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Displacement field potentials for deformation in elastic Media: Theory and application to pressure-loaded boreholes

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  • Weijermars, Ruud
  • Ettehad, Mahmood

Abstract

This study demonstrates how analytical solutions for displacement field potentials of deformation in elastic media can be obtained from known vector field solutions for analog fluid flow problems. The theoretical basis is outlined and a geomechanical application is elaborated. In particular, closed-form solutions for deformation gradients in elastic media are found by transforming velocity field potentials of fluid flow problems, using similarity principles. Once an appropriate displacement gradient potential is identified, solutions for the principal displacements, elastic strains, stress magnitudes and stress trajectories can be computed. An application is included using the displacement gradient due to the internal pressure-loading of single and multiple wellbores. The analytical results give perfect matches with results obtained with an independent discrete element modeling method.

Suggested Citation

  • Weijermars, Ruud & Ettehad, Mahmood, 2019. "Displacement field potentials for deformation in elastic Media: Theory and application to pressure-loaded boreholes," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 276-295.
    • Handle: RePEc:eee:apmaco:v:340:y:2019:i:c:p:276-295
    DOI: 10.1016/j.amc.2018.08.029
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    References listed on IDEAS

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    1. Jiwei Song & Ye Yuan & Sui Gu & Xianyu Yang & Ye Yue & Jihua Cai & Guosheng Jiang, 2017. "2D Numerical Simulation of Improving Wellbore Stability in Shale Using Nanoparticles Based Drilling Fluid," Energies, MDPI, vol. 10(5), pages 1-23, May.
    2. Hartmann, Niklas & Vöhringer, O. & Kruck, C. & Eltrop, L., 2012. "Simulation and analysis of different adiabatic Compressed Air Energy Storage plant configurations," Applied Energy, Elsevier, vol. 93(C), pages 541-548.
    3. Wang, Tongtao & Yan, Xiangzhen & Yang, Henglin & Yang, Xiujuan & Jiang, Tingting & Zhao, Shuai, 2013. "A new shape design method of salt cavern used as underground gas storage," Applied Energy, Elsevier, vol. 104(C), pages 50-61.
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    Cited by:

    1. Tri Pham & Ruud Weijermars, 2020. "Hydraulic Fracture Propagation in a Poro-Elastic Medium with Time-Dependent Injection Schedule Using the Time-Stepped Linear Superposition Method (TLSM)," Energies, MDPI, vol. 13(24), pages 1-22, December.
    2. Weijermars, Ruud & Pham, Tri & Ettehad, Mahmood, 2020. "Linear superposition method (LSM) for solving stress tensor fields and displacement vector fields: Application to multiple pressure-loaded circular holes in an elastic plate with far-field stress," Applied Mathematics and Computation, Elsevier, vol. 381(C).

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