Schuler-Cotton Valley sandstone

 

scvvsq_all2
Figure 2 Square of the velocity data for the Schuler-Cotton Valley sandstone measured by Murphy (1982) at about 200 kHz. The dashed lines are the DEM results for compressional and shear when it is assumed that the saturation is homogeneous in each pore. The solid lines are the results for patchy saturation. In this case, all the data for compressional waves fall closer to the patchy saturation line than to the curve for homogeneous saturation. The data for shear waves seem to be much less sensitive to the assumed crack aspect ratio than were the compressional wave data. The results seem to suggest that the cracks that dominate compressional wave propagation are not the same as the ones dominating shear wave propagation for this sample.

The data presented here on Schuler-Cotton Valley sandstone are from Murphy (1982). Walls (1982) also studied permeability variations of other samples from the same formation, but both of his samples had higher porosity than the one studied by Murphy ($\phi = 0.033$). Murphy's compressional wave measurements were made at about 200 kHz and the shear measurements at about 150 kHz. The fitting parameters chosen for this sample were K_m = 41.8 GPa, $\mu_m = 36.7$ GPa, and $\alpha = 0.015$. Otherwise the analysis was identical to that for Sierra White granite. Results are shown in Figure 3. These curves are similar to those for the granite since the compressional wave data show a very clear trend along the patchy saturation line. The shear wave data were harder to fit for this case, since the change in shear wave speed does not mimic that of the compressional wave as one might expect. For the Sierra White granite, a single value of $\alpha$ was sufficient to bring both P- and S-wave speeds into good agreement with the theoretical curves. Here, this was not possible, as the variation in compressional wave speed is substantially greater than that for the shear wave speed. A possible conclusion from this observed behavior is that the cracks that dominate compressional wave speed changes are not the same as those for the shear wave speed changes in this rock. But if this is true, it is not clear how to go about modeling such an effect.