Rock physics provides the link between reservoir properties and the seismic properties that can be observed with a geophysical survey. The reservoir parameters of importance are lithology, porosity, permeability, pore fluid types and saturations, temperature, reservoir effective stress, and pore fluid pressure. The related bulk properties that most impact seismic wave propagation are bulk density, and P- and S-wave velocities.

Bulk density is the easiest to understand and quantify. Density is the simple volumetric average of all mineral (solid) and pore fluid (solid, liquid, and gas) phases in the rocks. Density changes during reservoir production are primarily the result of replacing the initial set of fluids with another set.

Seismic velocity is always related to the ratio of elastic stiffness of the
fluid-bearing rocks to the bulk density of the rocks. The elastic
stiffness depends on the mineralogy, the stiffness of the pore space, and
the stiffness (incompressibility) *K*_{f} of the mixture of pore fluids in
the rock. This is most effectively quantified with the well-known
Gassmann's equation, which relates the bulk modulus of the saturated rock
*K*_{sat} to the dry rock bulk modulus *K*_{dry}, the mineral modulus
*K _{0}*, the fluid incompressibility, and the porosity :

(4) |

Important issues when doing fluid substitution:

- frequency: Gassmann's relation is most appropriate for very low frequencies as used in surface seismic. At higher frequencies as used in laboratory ultrasonic and sonic log measurements, fluid effects can give rise to velocity dispersion. This has to be taken into account when using velocity-porosity regressions obtained from such high frequency data. The amount of velocity dispersion depends on the nature of the pore space compressibility. It is enhanced in the presence of soft crack-like pore space, and decreases at high effective pressures when most of the crack-like porosity in closed.
- saturations and heterogeneity: the effective elastic stiffness of the rock depends not only on the saturation (among other things), but also on how the saturation is distributed within the pore space. A saturation distribution that is homogeneous and uniform at the pore scale within each grid block will give a different velocity than a heterogeneous saturation. The two situations require different mixing rules to estimate the effective seismic velocity. For the present exercise, the saturation was taken to be homogeneous within each grid block, and an effective fluid incompressibility (calculated as the Reuss or harmonic average of the individual fluid incompressibilities) was used in Gassmann's equation.

The fluid densities and incompressibilities used in the modeling were obtained from PetroTools Version 2.3, the seismic rock properties software by PetroSoft.

11/12/1997