The effect of Maxwellian fluid on wave propagation in porous media

Abstract: This study investigates the effect of a Maxwellian fluid on the propagation of waves in poroelastic media. Based on a fractional derivative stress-strain relation, a viscous dissipation function is obtained to measure the viscoelastic fluid-solid coupling effect. With the viscous dissipation function, elastic waves propagation is formulated in poroelastic media saturated by a fractional derivative Maxwellian fluid, and the analytical expression of the P- and S-wave dispersion/attenuation is presented. Numerical examples show that the fractional derivative Maxwell strain-stress relation has a significant influence on wave velocities and causes the fluid-solid coupling transition from a dissipative regime to an elastic regime. In addition, the predicted fluid velocities are consistent with the laboratory observations of viscoelastic fluids under an oscillating pressure gradient. The results indicate that a viscous-elastic fluid effect may account for the velocity oscillation observed in laboratory. The method elucidates dynamical differences for viscous and viscoelastic fluid in porous medium, which may be of great importance to unconventional oil/gas exploration industry as well as theoretical researches.