Velocities of seismic waves in porous rocks

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 (super -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.