Gassmann saturated velocities

We used Gassmann's relation to predict the saturated Massillon velocities from the dry rock lab measurements. The Gassmann predicted values are: = 2811 m/s and = 1644 m/s. The saturated shear velocity compares well with the measured value = 1744 $\pm$ 201 m/s, however, the = 3380 $\pm$ 78 m/s value does not. It is significant that each of our four independent dry rock lab measurements gave a Gassmann saturated prediction on the order of 20% less than the corresponding lab measurement of saturated, as seen in Figure . A possible explanation for this discrepancy may be that a significant amount of the 22.1% porosity is made up of clay content, which was not included in the Gassmann calculation. Clay would tend to expand in the pore space after saturation, and would thus stiffen the actual rock sample compared to Gassmann's theoretical rock model, resulting in a higher lab measurement of . Another possible explanation is that since the lab measurements were made at much higher frequencies (50 kHz) than Gassmann assumes (zero frequency), velocity dispersion as a function of frequency may be significant. High frequencies allow less time for fluid to flow in the pore space, resulting in a stiffer rock matrix and higher lab measurement of than would be predicted by the low frequency Gassmann model.

Castagna et al. (1991) noted that their Gassmann predictions of saturated velocities were inaccurate when the dry shear modulus was significantly different from the dry bulk modulus, which is the case for our Massillon sandstone sample in which $\mu_d$ = 6.1 GPa and K_d = 9.2 GPa. In particular, they tabulate values for a Gulf Coast sandstone in their Table 1, which has a similar and to our Massillon sample, and in which the Gassmann saturated value is significantly lower than the lab measurement. In our case, the grossly underestimated saturated value could be very misleading to a reservoir geophysicist trying to quantify predicted properties of oil or water-saturated reservoir sandstone given dry core samples from a nearby borehole.