The effect of Maxwellian fluid on wave propagation in porous media

TL;DR

This paper models how Maxwellian fluids affect wave propagation in porous media, revealing significant impacts on wave velocities and fluid-solid coupling, with implications for oil and gas exploration.

Contribution

It introduces an analytical framework for wave dispersion and attenuation in poroelastic media saturated with fractional derivative Maxwellian fluids, highlighting the fluid's influence on wave behavior.

Findings

Viscous-elastic fluid effects significantly alter wave velocities.

Fluid-solid coupling transitions from dissipative to elastic regimes.

Predicted velocities match laboratory observations of viscoelastic fluids.

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.