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NER is actively performing experiments designed to better understand the deformation and velocities of deep water Gulf of Mexico sands during simulated reservoir depletions. In preparation for these studies, we have performed a number of exploratory experiments using Berea Sandstone as an analog sandstone. The results of some of these experiments are provided here in order to promote discussion among petrophysicists and reservoir engineers concerning rock physics issues facing the oil and gas industry.

There are many interesting aspects of these data sets. We welcome a discussion of these and related results. Please feel free to download the data and analyze it in your own way. We always welcome any comments or new findings.

EFFECTIVE STRESS LAWS FOR RESERVOIR DEPLETION

We have recently published a result of an experiment in Shafer et al. (2008). The data discussed in the early sections of that paper are provided below in a few simple spreadsheets. The data set includes stress versus strain and ultrasonic velocity for a complex loading sequence designed to probe the effects of pore pressure for both hydrostatic and uniaxial strain loading paths. Both axial and radial ultrasonic velocities were measured, providing information about stress induced velocity anisotropy.

To answer questions raised by this experiment, we performed a similar experiment on a sister sample of Berea Sandstone. This sample was tested 100% brine saturated rather than the mixed oil and brine used in the previous experiment. Only axial velocities were measured, but otherwise the test was identical to the first test. This additional test was motivated by the desire to determine the influence of fluid properties on the effective stress law for velocities. We find that for the 100% brine case the observed effective stress law for velocities is notably different, as postulated in Shafer et al. (2008),. For the hydrostatic loading portion of the experiments, αVp changes from 0.82 with oil+brine to 0.95 with 100% brine as determined in the second experiment. Similarly αVs increases from 0.95 with oil+brine to a value slightly greater than 1 when saturated with 100% brine. An alpha of 0.78 for bulk volume is the same for the two tests, indicating that pore fluid has no effect (as simple theory would predict).

Overall, velocities are somewhat slower (~4 to 8%) and the pressure dependence is greater for sample 2 with brine in comparison to sample 1 with oil and brine. This may well be a result of the different pore fluid more-so than a difference between the two samples. It would be consistent with the argument that the presence of oil leads to a viscosity stiffening mechanism that increases both the P and S velocities. The lower α's for P and S velocity in the case of oil+brine would suggest that the viscosity effect is dependent on pore pressure.

The viscosity effect is likely to be an ultrasonic phenomenon (or at least an effect that is exaggerated at ultrasonic frequencies). Thus the alpha's for P and S velocity measured in the case of sample 1 are not values that one should use at lower frequencies (and or for different fluids as our second test indicates). The two tests indicate that the laboratory results should not be used without consideration of the viscosity stiffening mechanism. More work is needed to see if the α's for velocities in the case of sample 2 with brine are consistent with low frequency Biot-Gassmann theory.

• Shafer et al. 2008 Data Links
• 100% Brine Test

Reference:
Shafer, John L., Boitnott, Greg N., and Ewy, Russel T., Effective Stress Laws For Petrophysical Rock Properties, SPWLA 49th Annual Logging Symposium, May 25-28, 2008.

Related References:
Hofmann, R., Xu, X., Batzle, M., Prasad, M., Furre, A-K. and Pillitteri, A., Effective pressure or what is the effect of pressure?, The Leading Edge 24, 1256 (2005), DOI:10.1190/1.2149644

OTHER LINKS OF INTEREST:
Another interesting data set on Berea Sandstone originally discussed by Boitnott (1997) and later analyzed in Boudjema et al. (2003), contains stress vs. strain and velocity data over a wider range of loading paths. This data set contains some interesting findings on the relationship between velocities, elastic constants, and loading path. Links to available published papers are provided below. Please come back, as we plan to post spreadsheet versions of this data set at a later date.

References:
Boudjema, M., Santos, I. B., McCall, K. R., Guyer, R. A., and Boitnott, G. N., Linear and nonlinear modulus surfaces in stress space, from stress-strain measurements on Berea sandstone, Nonlinear Processes in Geophysics, (2003) 10: 589–597

Boitnott, G. N.: Experimental characterization of the nonlinear rheology of rock, Int. J. Rock Mech. & Min. Sci., 34, 379–388, 1997.

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