Generalized Thermo-poroelasticity Equations and Wave Simulation

We establish a generalization of the thermoelasticity wave equation to the porous case, including the Lord–Shulman (LS) and Green–Lindsay (GL) theories that involve a set of relaxation times ( τ i , i = 1 , … , 4 ). The dynamical equations predict four propagation modes, namely, a fast P wave, a Biot slow wave, a thermal wave, and a shear wave. The plane-wave analysis shows that the GL theory predicts a higher attenuation of the fast P wave, and consequently a higher velocity dispersion than the LS theory if τ 1 = τ 2 > τ 3 , whereas both models predict the same anelasticity for τ 1 = τ 2 = τ 3 . We also propose a generalization of the LS theory by applying two different Maxwell–Vernotte–Cattaneo relaxation times related to the temperature increment ( τ 3 ) and solid/fluid strain components ( τ 4 ), respectively. The generalization predicts positive quality factors when τ 4 ≥ τ 3 , and increasing τ 4 further enhances the attenuation. The wavefields are computed with a direct meshing algorithm using the Fourier pseudospectral method to calculate the spatial derivatives and a first-order explicit Crank–Nicolson time-stepping method. The propagation illustrated with snapshots and waveforms at low and high frequencies is in agreement with the dispersion analysis. The study can be useful for a comprehensive understanding of wave propagation in high-temperature high-pressure fields.