<
p id="
p-1">The effects of fluid substitution on P- and S-wave velocities in carbonates of com
plex texture are still not understood fully. The often-used Gassmann equation gives ambiguous results when com
pared with ultrasonic velocity data. We
present theoretical modeling of velocity and attenuation measurements obtained at a frequency of
pan class="inline-formula" id="inline-formula-1">![Formula](N35/embed/mml-math-1.gif)
pan> for six carbonate sam
ples com
posed of calcite and saturated with air, brine, and kerosene. Although
porosities (2%–14%) and
permeabilities
pan class="inline-formula" id="inline-formula-2">![Formula](N35/embed/mml-math-2.gif)
pan> are relatively low, velocity variations are large. Differences between the highest and lowest P- and S-wave velocities are about 18% and 27% for brine-saturated sam
ples at 60 and
pan class="inline-formula" id="inline-formula-3">![Formula](N35/embed/mml-math-3.gif)
pan> effective
pressure, res
pectively. S-wave velocities are measured for two orthogonal
polarizations; for four of six sam
ples, anisotro
py is revealed. The Gassmann model under
predicts fluid-substitution effects by
pan class="inline-formula" id="inline-formula-4">![Formula](N35/embed/mml-math-4.gif)
pan> for three sam
ples and by as much as 5% for the rest of the six sam
ples. Moreover, when dried, they also show decreasing attenuation with increasing confining
pressure. To model this behavior, we examine a
pore model made of two
pore systems: one constitutes the main and drainable
porosity, and the other is made of undrained cracklike
pores that can be associated with grain-to-grain contacts. In addition, these dried rock sam
ples are modeled to contain a fluid-filled-
pore system of grain-to-grain contacts,
potentially causing local fluid flow and attenuation. For the theoretical model, we use an inclusion model based on the T-matrix a
pproach, which also considers effects of
pore texture and geometry, and
pore fluid, global- and local-fluid flow. By using a dual-
pore system, we establish a realistic
physical model consistently describing the measured data.
p>