Two-Temperature Thermoporoelastic Modeling of Experimental Data for Wave Propagation in Glycerin-Saturated Tight Sandstones

Porous rocks in geothermal and ultradeep hydrocarbon reservoirs generally present large differences in temperature and thermal properties between the solid skeleton and pore fillings, leading to strong thermal coupling effects on the dissipation and attenuation of elastic waves, which remains unexplored theoretically. The theory of single-temperature thermoporoelasticity, as an extension of Biot poroelasticity by incorporating a single temperature (ST) and single-phase-lag (SPL)/dual-phase-lags (DPL) relaxation time of heat conduction, has been introduced in geophysics in recent years for wave propagation in non-isothermal porous rocks. However, the ST thermoporoelasticity assumes only an average temperature over the entire porous rock and becomes inadequate in describing the thermal relaxation of pore fillings and the thermal coupling due to heat transfer between the solid frame and pore fillings. We address this issue by proposing a two-temperature (TT) thermoporoelasticity with the DPL relaxation time of heat conduction, associated with analytical solutions and experimental verification. Plane wave analyses are performed for a comprehensive comparison of dispersion and attenuation between the TT-DPL, ST-DPL, and ST-SPL thermoporoelasticity models. The proposed TT-DPL model is used to interpret the laboratory measurements on a saturated sandstone with glycerin at different temperatures. It accounts for the effect of solid–fluid thermal expansion and shows larger thermal attenuation and velocity dispersion than the other two models. Ignoring the effect of solid–fluid thermal expansion when fitting the experimental data, however, leads to relatively high values of thermal conductivity and thermal relaxation time. The TT-DPL model provides a physically meaningful model for ultradeep hydrocarbon exploration, geothermal recovery, and other applications involving temperature variations between the solid frame and pore fillings.