Table 1 presents the velocity data of Wang and Nur (1991) on 14 pure
hydrocarbons, together with the known densities (Rossini et al, 1953;
Weast and Grasselli, 1989), and the adiabatic bulk moduli computed from these
values at 20
C. The estimated uncertainty in all the measured
velocities (pure hydrocarbon as well as hydrocarbon mixtures)
is stated to be 0.2 %. Including possible errors in the density
values, an error propagation analysis shows that the
error in computing the effective bulk modulus needed in Wood's formula from the
the measured velocities is about 0.5 %. It follows that the error in
the computed velocities for the mixtures using Wood's formula is about 0.3 %.
Table 2 compares the measured velocities of binary
alkene mixtures as a function of volume fraction to the computed
velocities using Wood's formula, the time average estimate, and the
volume average estimate. All three computed values lie within 0.6 % of
the measured values for all values of volume fraction. The volume average
estimate is generally closer to the measured values than either of the
other two estimates. However, when measurement errors in both the mixture
velocities and the two pure hydrocarbon velocities used to compute these
values are considered (0.3 + 0.2 = 0.5 %) together with the fact that
the nominally ``pure'' hydrocarbon samples may have only been 90-96 % pure
(Wang, 1988), the remaining differences are in fact too small
to allow us to distinguish the three formulas - except for the fact that
they are ordered, as I have shown. Note that the time average estimate
does appear to be a lower bound on the measured values in all cases.
The significance of this observation is unclear however, since the wavelengths
are long compared to the expected scale of the mixed fluid microstructure.
Table 3 compares the measured velocities of multicomponent hydrocarbon mixtures to the same three velocity estimates. All three estimates are again within 1 % of the measured values, but now the volume average estimate is not always the one closest to that observed. The more complex fluid mixtures seem to agree somewhat better with Wood's formula. In all but one case, Wyllie's time average velocity is again observed to be a lower bound on the measured velocities. However, the main conclusion appears to be that the three estimates are again virtually indistinguishable for this data set.