An a priori error analysis of a Lord–Shulman poro-thermoelastic problem with microtemperatures

Baldonedo, Jacobo; Bazarra, Noelia; Quintanilla, R.

doi:10.1007/s00707-020-02738-z

Cited by 7 publications

(4 citation statements)

References 44 publications

(61 reference statements)

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“…LS thermoelasticity has been elongated to model the behaviour of porous media, known as thermo-poroelasticity. This approach predicts the traditional Biot slow wave associated with fluid flow, as demonstrated by several studies (Noda, 1990; Sharma, 2008; Carcione et al , 2019a, 2019b; Baldonedo et al , 2020). The velocity of the classical P wave in homogeneous media is greater than that of the uncoupled case (isothermal case), but the S wave remains unaffected by temperature.…”

Section: Introductionmentioning

confidence: 73%

Inhomogeneous waves propagation in double-porosity thermoelastic media

Kumar

Bhagwan

Kaswan

et al. 2023

HFF

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Purpose The purpose of this study is to investigate the reflection of plane waves in a double-porosity (DP) thermoelastic medium. Design/methodology/approach To derive the theoretical formulas for elastic wave propagation velocities through the potential decomposition of wave-governing equations. The boundary conditions have been designed to incorporate the unique characteristics of the surface pores, whether they are open or sealed. This approach provides a more accurate and realistic mathematical interpretation of the situation that would be encountered in the field. The reflection coefficients are obtained through a linear system of equations, which is solved using the Gauss elimination method. Findings The solutions obtained from the governing equations reveal the presence of five inhomogeneous plane waves, consisting of four coupled longitudinal waves and a single transverse wave. The energy ratios of reflected waves are determined for both open and sealed pores on the stress-free, the thermally insulated surface of DP thermoelastic medium. In addition, the energy ratios are compared for the cases of a DP medium and a DP thermoelastic medium. Originality/value A numerical example is considered to investigate the effect of fluid type in inclusions, temperature and inhomogeneity on phase velocities and attenuation coefficients as a function of frequency. Finally, a sensitivity analysis is performed graphically to observe the effect of the various parameters on propagation characteristics, such as propagation/attenuation directions, phase shifts and energy ratios as a function of incident direction in double-porosity thermoelasticity medium.

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Section: Introductionmentioning

confidence: 73%

Inhomogeneous waves propagation in double-porosity thermoelastic media

Kumar

Bhagwan

Kaswan

et al. 2023

HFF

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“…The LS theory has been extended to the porous case (i.e., the so-called thermo-poroelasticity) by incorporating Biot poroelasticity to couple elastic deformations with temperature (Noda, 1990;Nield and Bejan, 2006;Sharma, 2008;Carcione et al, 2019;Baldonedo et al, 2020). The theory predicts the presence of both Biot and thermal slow P waves besides the classical P and S waves.…”

Section: Introductionmentioning

confidence: 99%

Thermoporoelastic AVO modeling of Olkaria geothermal reservoirs

Cheng¹,

Fu²,

Hou³

et al. 2023

Preprint

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<p>Seismic AVO has a significant potential for fluid identification in time-lapse monitoring of the cyclic recovery of geothermal reservoirs. With this goal, we develop an AVO method based on the reflection and transmission (R/T) of elastic waves at an interface between two fluid-saturated thermo-poroelastic media. The method is applied to the Olkaria geothermal reservoirs in Kenya. This system is characteristic of a natural cyclic recovery, where cyclic meteoric water undergoes complex phase transition and thermo-hydro-mechanical coupling process. Conceptual models are built based on petrophysical and thermophysical properties of trachyte thermal reservoirs in the eastern field, with an attempt to model the shallow steam and deep boiling water zones. A plane-wave analysis illustrates the effects of thermal conductivity, specific heat, and porosity on velocity dispersion and attenuation of the fast-P, Biot slow-P, and thermal slow-P waves. AVO modeling by P-wave incidence is conducted to investigate the effects of temperature, porosity, specific heat, and fluid type on the R/T coefficients. For trachyte reservoirs with a temperature less than 400°C, limited changes in the thermophysical properties (e.g., thermal conductivity and specific heat) have negligible effects on wave propagation, whereas significant effects are due to temperature, porosity, and fluid type. Particularly, comparisons of cyclic recovery using water, supercritical CO2, and gas (dry case) as the heat transfer fluid, demonstrate that the crossplot of fluid factors and intercept gradient (PG) can be used as a precursor to hydrofracturing-induced permeability, fluid leakage or short circuits.</p>

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“…Boldonedo et al. [20] examined the numerical analysis of Lord–Shulman problem with porosity and microtemperatures. Marin et al.…”

Section: Introductionmentioning

confidence: 99%

Wave analysis in porous thermoelastic plate with microtemperature

Rani,

Kumar,

Partap

2023

Z Angew Math Mech

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In the current study, wave analysis in porous thermoelastic plates with microtemperature subject to insulated or isothermal boundaries is the main focus. The governing equations, after expressing for the two‐dimensional case, are converted into nondimensional quantities. For further simplification, potential functions have been used. The normal mode analysis technique is applied to solve the problem. This technique is an influential methodology that furnishes suitable solutions with no presumed limitations. For stress‐free insulated, or isothermal boundaries, the frequency equations for symmetric and skew‐symmetric modes of wave propagation are derived. The attributes of waves (phase velocity, attenuation coefficient, specific loss, and penetration depth) are computed numerically and presented graphically to show the impacts of porosity and microtemperature. Particular cases of porous thermoelastic plates and thermoelastic plates with microtemperatures are presented. The present problem provides a theoretical foundation for the design and development of new composite materials and surface acoustic devices.

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An a priori error analysis of a Lord–Shulman poro-thermoelastic problem with microtemperatures

Cited by 7 publications

References 44 publications

Inhomogeneous waves propagation in double-porosity thermoelastic media

Inhomogeneous waves propagation in double-porosity thermoelastic media

Thermoporoelastic AVO modeling of Olkaria geothermal reservoirs

Wave analysis in porous thermoelastic plate with microtemperature

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