Biot-consistent framework for wave propagation with macroscopic fluid and thermal effects

Abstract

SUMMARY In principle, wave propagation in porous media can simultaneously trigger macroscopic fluid flow and thermal flow, which can be described by Biot's poroelasticity and Lord–Shulman thermoelasticity, respectively. The physical processes of those effects are significantly different, but phenomenologically, they can lead to identical wave attenuation and dispersion and are hard to be distinguished. By using Biot's virtual concept entropy flow, the Biot-consistent General Linear Solid (the GLS) framework and matrix notation, a rigorous and convenient tool is provided to reveal the similarities and disparities between poroelasticity and thermoelasticity. By using the same framework, a Biot-consistent thermo-poroelastic model is proposed to consider macroscopic effects of fluid and thermal flows simultaneously in an elegant way. These similarities allow us to directly translate many of the available results in poroelasticity to thermoelasticity and vice versa by a simple change of notation. The disparities indicate a fundamental difference in physical mechanisms. Plane-wave analysis shows that the primary P-wave modes of thermoelasticity and poroelasticity are all GSLS-equivalent (Generalized Standard Linear Solid) and can be identical if the model parameters are selected properly. However, the corresponding slow-wave modes have significantly different phase velocity dispersion although the attenuation spectra of which are identical. Such a surprising result can be explained by the GSLS non-equivalence of the slow-wave modes and the fundamentally different mechanisms. As expected, the thermo-poroelastic model predicts four wave modes, which are the fast- and slow-P, temperature (T wave) and S waves. Two attenuation peaks due to, respectively, the thermal- and fluid-flow effects are predicted for the fast-P wave. The slow-P wave mode due to fluid flow is influenced by the thermal effects, but the T wave seems unaffected by the fluid flow. The thermo-poroelastic model is then applied to laboratory observations at 200–106 Hz for the brine-saturated tight sandstone under 35 MPa effective pressure. The unified model provides a convenient framework for studying geothermal exploration, thermal-enhanced oil recovery and other applications involving temperature variations within the porous rock.