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White’s model for wave propagation in partially saturated rocks

White’s model for wave propagation in partially saturated rocks: Comparison with poroelastic numerical experiments




We use a poroelastic modelling algorithm to compute numerical experiment of wave propagation in White’s partial saturated model. The results are then compared to the theoretical predictions.


The model consists of a homogeneous sandstone saturated with brine and spherical gas pockets. White’s theory predicts a relaxation mechanism, due to pressure equilibration, causing attenuation and velocity dispersion of the wavefield.


We vary gas saturation either by increasing the radius of the gas pocket or by increasing the density of the gas bubbles. Despite that the modelling is two dimensional and interaction between the gas pockets is neglected in White’s model, the numerical results show the trends predicted by the theory.


In particular, we observe a similar increase in velocity at high frequencies (and low permeabilities). Furthermore, the behavior of the attenuation peaks versus water saturation and frequency is similar to that White’s model.


The modelling results show more dissipation and higher velocities than White’s model due to multiple scattering and local fluid-flow effect. Te conversion of fast P-wave energy into dissipating slow wave at the patches is the main mechanism of attenuation.


Differential motion between the rock skeleton and the fluids is highly enhanced by the presence of fluid/fluid interfaces and pressure gradients generated through them.

GEOPHYSICS, VOL. 68, NO. 4 (JULY-AUGUST 2003); P. 1389–1398,