Laboratory and sonic log measurements show that velocities usually decrease
with porosity, though the velocity-porosity relations are not always
unique. P and S velocities are also often well correlated.
Velocity-porosity and *V*_{P}-*V*_{S} regressions have been presented in the
literature for different lithologies by various authors. We used similar
regressions to define a reference *V*_{P}, *V*_{S}, and density. For the sand
facies we choose a regression of the form with a coefficient of variation around the regression of about
2.4%. The *V*_{P}-*V*_{S} regression was *V*_{S} (*km*/*s*) = 0.775 *V*_{P} - 0.67,
with about 2% coefficient of variation. These are representative of
typical water saturated sands from North Sea fields. The regressions
(along with the spreads around the regressions) were used to generate the
reference *V*_{P} and *V*_{S} data. We did not include the effect of pressure
variations on the and *V*_{P}-*V*_{S} regressions, though the effect
of pressure on the fluid properties was taken into account. The reference
velocities were transformed, applying Gassmann's equations, to the
reservoir conditions using the pressure, saturations, and Gas-Oil ratio
obtained from the flow simulator. This was done at each time step of
interest in the reservoir production history. The fluid
incompressibilities and densities as a function of pressure and Gas-Oil
ratio were calculated from published laboratory relations incorporated in
PetroTools Version 2.3. For the shale
facies, which was assigned a zero porosity and negligible permeability, we
assigned fixed *V*_{P}, *V*_{S}, and density of 2.5 km/s, 1.3 km/s, and 2.27
gm/cc respectively. Anisotropy of seismic velocities was neglected in this
initial model.

11/12/1997