Generalized Thermo-poroelasticity Equations and Wave Simulation

Acoustothermoelasticity for Joint Effects of Stress and Thermal Fields on Wave Dispersion and Attenuation

“…Figures 4 and 5 show that P wave and T wave both have a relaxation peak in an unstressed thermoelastic rock, related to the thermal loss mechanism, while the second S wave is not affected by thermal effects. Previous studies conclude that S wave is uncoupled with T wave inducing no energy dissipation caused by thermal effect in homogeneous media (Green & Lindsay, 1972; Hetnarski & Ignaczak, 1999; Lord & Shulman, 1967; Wang et al., 2021), which is consistent with the predicted physical behavior of S wave in unstressed isotropic thermoelastic media (in homogeneous media). However, applied stress makes an isotropic thermoelastic medium become inhomogeneous, thus, an interesting phenomenon not observed in the conventional models is predicted, that is, fast S wave has a small relaxation peak induced by thermal loss in a pre‐stressed thermoelastic medium, as shown in Figure 5b.…”

“…Different stress magnitudes and states (e.g., uniaxial, biaxial and triaxial stresses) have different effects on rock physical properties (e.g., elastic moduli and anisotropy) (Chen et al., 2021; Johnson & Rasolofosaon, 1996). The thermoelastic parameters, especially, bulk specific heat c , are relevant to the wave dispersion and attenuation (Carcione et al., 2019; Wang et al., 2021). Therefore, the physical behaviors of dispersion and attenuation corresponding to different stresses and bulk specific heats are investigated in this section.…”

“…(2019) and Wang et al. (2021), these given thermoelastic parameters can approximately represent a typical rock.…”

“…The theory of thermoelasticity is a fusion between heat conduction theory and classic linear elasticity theory (Chandrasekharaiah, 1986; Wang et al., 2021). It builds a coupling between thermal field and deformation filed to describe the wave propagation in thermoelastic media.…”

“…Another dataset is the laboratory measurements ofPrioul et al (2004) on a Colton sandstone under triaxial stress circle at ultrasonic frequency. The second-order and third-order elastic parameters of saturated and dry Berea sandstones and Colton sandstone are given in Table2, and the corresponding thermoelastic parameters of three sandstones are set as the parameters same to Rock A, that is, β = 6 × 10 5 kg/(m s 2 °K), θ 0 = 300°K, k = 1.5 × 10 7 m kg/(s 3 K), α = 3 × 10 −3 s, and α 0 = 1.5 × 10 −3 s. Based onCarcione et al (2019) andWang et al (2021), these given thermoelastic parameters can approximately represent a typical rock.…”