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

Abstract

We use a poroelastic modeling algorithm to compute numerical experiments of wave propagation in White's partial saturation 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 gas bubbles. Despite that the modeling 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 of White's model. The modeling results show more dissipation and higher velocities than White's model due to multiple scattering and local fluid-flow effects. The conversion of fast P-wave energy into dissipating slow waves 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.

Experimental observation of water saturation effects on shear wave splitting in synthetic rock with fractures aligned at oblique angles

“…The presence of partial gas saturation is known to cause dispersion believed to be as a result of wave induced fluid flow (e.g., mesoscopic and microscopic "squirt" flow) (see Müller et al, 2010). White's model considers only one dispersion mechanism (mesoscopic flow) and this could lead to an underprediction of the amount of dispersion as a result of partial saturation (e.g., Carcione et al, 2003). An additional mechanism not considered by White's model, but believed to be responsible for the additional dispersion (at partial gas and full water saturation) observed at high frequencies, is squirt or local fluid flow (see Mavko and Nur, 1979, Winkler, 1985, Dvorkin et al, 1994, Carcione et al, 2003.…”

“…White's model considers only one dispersion mechanism (mesoscopic flow) and this could lead to an underprediction of the amount of dispersion as a result of partial saturation (e.g., Carcione et al, 2003). An additional mechanism not considered by White's model, but believed to be responsible for the additional dispersion (at partial gas and full water saturation) observed at high frequencies, is squirt or local fluid flow (see Mavko and Nur, 1979, Winkler, 1985, Dvorkin et al, 1994, Carcione et al, 2003. The presence of fractures is also known to cause dispersion in saturated rocks through the squirt flow mechanism (see Chapman, 2003, Gurevich et al, 2009.…”

Compressional seismic waves in permeable media: an asymptotic representation

“…Основные причины это-го кроются в слабом сейсмическом эффекте флюидной проводимости в случае толстослоистых, слоисто-одно-родных представлений о пористой среде. Сейсмиче-ский эффект становится заметным при включении в рассмотрение проницаемых неоднородностей [Carcione et al, 2003], например, тонкослоистых пропластков ме-нее метра. Однако реализация модели Био в производ-ственном масштабе с использованием мелких неодно-родностей осложнена.…”

A low-frequency asymptotic model of seismic reflection from a high-permeability layer

“…We assume that the deformations are small and the elastic properties of the skeleton are adequately described by the Hooke's law for a homogeneous isotropic elastic medium [38], whereas the fluid flow is governed by the dynamic Darcy's law [1]. We demonstrate that this modification of the Darcy's law is equivalent to a linearization of the law introduced in [11,13,34] for a periodic oscillatory flow. It turns out that the relaxation time in the dynamic Darcy's law is associated with the coupling factor in Biot's model.…”

“…A comprehensive overview of the Biot's theory is presented in [40]. Further extensions accounting for local heterogeneities including double-porosity or layered media have been developed in [3,10,11,29,31,41,42]. The reflection and transmission coefficients predicted by the Biot's theory for a wave crossing a planar interface have been calculated in [17,28].…”