Wave propagation in double-porosity thermoelastic media

The Lord-Shulman thermoporoelasticity theory couples the Biot and hyperbolic heat equations to describe wave propagation, modeling explicitly the effects of heat and fluid flows. We have extended the theory to the case of double porosity by taking into account the local heat flow (LHF) and local fluid flow (LFF) due to wave propagation. The plane-wave analysis finds the presence of the classical P and S waves and three slow P waves, namely, the slow (Biot) P-1, the slow (Biot) P-2, and a thermal slow P wave (or T wave). The frequency-dependent attenuation curves find that these slow waves manifest as Zener-like relaxation peaks, which are loosely related to the LFF, Biot, and LHF loss mechanisms. The viscosity and thermoelasticity properties can lead to the diffusive behavior of the three slow P modes. However, the S wave is considered to be independent of fluid and temperature influence. We examine the effect of thermophysical properties (e.g., thermal conductivity and relaxation time) on the wave velocity and attenuation of different modes. It is confirmed that the T wave is prone to be observed in media with high thermal conductivities and high homogeneity at high frequencies. Our double-porosity thermoelastic model reasonably explains laboratory measurements and well-log data from ultradeep fractured carbonates at high temperatures.