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Thermoplastic constitutive modeling of shale based on temperature-dependent Drucker-Prager plasticity

Journal Article


Abstract


  • High temperatures (120~238 ��C) from deep burial of shale affects strongly the eventual extractions of shale gas. Different from rocks at normal temperatures, the mechanical properties of shale change significantly at high-temperature of deep reservoirs, where its thermoplastic behavior needs further investigation. In this study, we propose a thermoplastic constitutive model for shale, incorporating temperature-dependent Drucker-Prager hardening rule, thermal loading/unloading criteria, and completely coupled stress-strain-temperature relation. The thermoplastic properties in the proposed model are obtained by further processing of published thermo-mechanical test data done on Tournemire shale by Masri et al. with the following key findings: (1) The hydrostatic-pressure-dependent (HPD) and stress-deviator-dependent (SDD) initial/critical yield parameters are found to be quadratically and linearly dependent on temperatures. (2) In the range of 20~250 ��C, the HPD and SDD hardening parameters vary linearly and quadratically with internal variables ��1 and ��2, respectively. All three coefficients in the correlative equations between hardening parameters and internal variables depend linearly on temperatures. (3) The temperature sensitivity modulus, as a function of hydrostatic pressure, hardening parameters, and initial temperature, is used for characterizing the contraction or expansion of the yield surface with temperatures. This proposed model was validated with thermo-mechanical measurements of Tournemire shale, fitting well with experiment data (correlation coefficient: 93%). During the plastic loading, temperature-sensitive modulus was found to be positively corresponding to the expansion of the yield surface with temperatures, and the SDD loading/unloading discriminant coefficient is positive. The proposed model may be applicable to other rock materials.

Publication Date


  • 2020

Citation


  • Xing, Y., Zhang, G., & Li, S. (2020). Thermoplastic constitutive modeling of shale based on temperature-dependent Drucker-Prager plasticity. International Journal of Rock Mechanics and Mining Sciences, 130. doi:10.1016/j.ijrmms.2020.104305

Scopus Eid


  • 2-s2.0-85082685771

Volume


  • 130

Issue


Place Of Publication


Abstract


  • High temperatures (120~238 ��C) from deep burial of shale affects strongly the eventual extractions of shale gas. Different from rocks at normal temperatures, the mechanical properties of shale change significantly at high-temperature of deep reservoirs, where its thermoplastic behavior needs further investigation. In this study, we propose a thermoplastic constitutive model for shale, incorporating temperature-dependent Drucker-Prager hardening rule, thermal loading/unloading criteria, and completely coupled stress-strain-temperature relation. The thermoplastic properties in the proposed model are obtained by further processing of published thermo-mechanical test data done on Tournemire shale by Masri et al. with the following key findings: (1) The hydrostatic-pressure-dependent (HPD) and stress-deviator-dependent (SDD) initial/critical yield parameters are found to be quadratically and linearly dependent on temperatures. (2) In the range of 20~250 ��C, the HPD and SDD hardening parameters vary linearly and quadratically with internal variables ��1 and ��2, respectively. All three coefficients in the correlative equations between hardening parameters and internal variables depend linearly on temperatures. (3) The temperature sensitivity modulus, as a function of hydrostatic pressure, hardening parameters, and initial temperature, is used for characterizing the contraction or expansion of the yield surface with temperatures. This proposed model was validated with thermo-mechanical measurements of Tournemire shale, fitting well with experiment data (correlation coefficient: 93%). During the plastic loading, temperature-sensitive modulus was found to be positively corresponding to the expansion of the yield surface with temperatures, and the SDD loading/unloading discriminant coefficient is positive. The proposed model may be applicable to other rock materials.

Publication Date


  • 2020

Citation


  • Xing, Y., Zhang, G., & Li, S. (2020). Thermoplastic constitutive modeling of shale based on temperature-dependent Drucker-Prager plasticity. International Journal of Rock Mechanics and Mining Sciences, 130. doi:10.1016/j.ijrmms.2020.104305

Scopus Eid


  • 2-s2.0-85082685771

Volume


  • 130

Issue


Place Of Publication