Wave propagation in rock media with highly viscous fluids based on a fractional thermoporoelastic theory

Summary When highly viscous fluids are present in a rock medium, the viscous effect of such fluids cannot be neglected in the propagation of elastic waves. In this paper, a fractional thermoporoelastic theory is newly proposed, which is a further improvement of the two-temperature generalized thermoporoelastic theory. Firstly, by introducing the Kelvin-Voigt model into the stress-strain constitutive equation, the viscous effect of highly viscous fluids is considered. Then, fractional derivatives are introduced into the heat conduction equations of the solid and fluid phase to consider the anomalous heat conduction caused by the viscous effect in rock media. Plane wave analysis method is adopted to obtain the phase velocity and attenuation factor of four longitudinal waves (P1, P2, T1, T2). Numerical results show that the introduction of fluid viscosity leads to the appearance of new relaxation peaks in the P wave at high frequencies, and the introduction of fractional derivatives causes a decrease in the phase velocity and attenuation factor of T waves. The results provide a reference for further research on the wave propagation in rock media containing highly viscous fluids.