  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.
