Abstract
Velocities of seismic compressional and shear waves in porous rocks
under different saturation conditions are calculated theoretically
and compared with laboratory data. For theoretical formulations,
the rocks are represented by a solid matrix and pores of spherical
and oblate spheroidal shapes. The effect of confining pressure on
velocities is calculated by taking into account pore closing and
saturant compressibilities. The theoretical calculations show that
with all other parameters fixed, thin pores (small aspect ratios)
have much greater effects on elastic moduli and velocities than rounded
pores at the same concentration. The properties of the saturating
fluid (gas, oil, or water) have greater effects on the compressional
velocities than on shear velocities. The velocities of compressional
waves are higher when the rock is saturated with water than when
it is dry or gas-saturated. For shear waves the behavior is generally
opposite, with shear velocities higher in the dry or gas-saturated
case than in the water-saturated case. Compressional and shear velocities
measured as a function of pressure in laboratory samples of granite,
limestone, and sandstone, under dry and water-saturated states, are
fitted with theoretical curves and pore shape spectra which fit the
data are calculated. A spectrum of pore shapes ranging from spheres
to very fine cracks (aspect ratios 1 to 10-5) is required to fit
the data. Theoretical velocities calculated using these models fit
the measured velocities in water-saturated and frozen rocks, as well
as the compressional velocities in partially saturated rocks. With
the rock models derived on the basis of laboratory data, theoretical
seismic velocities are calculated for various pressures and temperatures
for reservoir rocks fully or partially saturated with gas, oil, or
brine. Compressional velocities are highest for brine saturation
and lowest for gas saturation. The difference decreases with increasing
pressure. The presence of a small amount (5 percent) of gas in brine
as an immiscible mixture reduces the compressional velocities significantly,
even below those of fully gas-saturated values at some pressures.
The reflection coefficients for compressional waves at a gas-brine
interface in a model of a sandstone are high at pressures corresponding
to shallow and moderate (less than about 8000 ft) depths. At greater
confining pressures, reflection coefficients become small, except
when the pore fluid pressure (gas pressure) is very high. Thus, large
reflections or "bright spots" from great depths may indicate overpressured
formations. The reflection coefficients from mixed gas-brine interfaces
are lower than those of pure gas interfaces. A combination of interval
velocities and reflection amplitudes may help identify the mixed
gas-brine reservoirs. Poisson's ratios for gas-saturated rocks are
lower than those for brine-saturated. This difference persists to
great depths.
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