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Estimating mechanical properties with seismic
The relationship between seismic velocities and mechanical properties is a strong one. Moduli, such as bulk modulus (and its inverse, compressibility), rigidity (or shear modulus), and Young’s modulus, can be determined either from static (very slow) experiments or dynamic experiments, involving the passage of a seismic wave through the sample.
Use of seismic velocities
The relationship between seismic velocities and the dynamic bulk modulus (K), the dynamic shear modulus (G), and the density (ρ) are given by
....................(1)
and
....................(2)
Eqs. 1 and 2 are correct only for isotropic media and are strictly appropriate only for moduli measured at the same frequency and amplitude as the seismic wave. Investigators often ignore these distinctions and use the seismically determined moduli to approximate the static moduli sought by reservoir or completions engineers for compaction drive estimates or hydraulic-fracture design. When properly calibrated, the spatial or temporal variations in velocity-derived moduli can often be used to indicate changes in static moduli.[1]
The static or dynamic moduli are often related to other mechanical properties, such as strength, mostly because the features of the rock fabric that determine elastic moduli are also the features that determine strength. Thus, variations of moduli within a given rock type can often be correlated to variations in strength and other mechanical properties[2][3][4][5] (Fig. 1). (A simple analogy is worth describing: the integrity of railroad-carriage wheels can crudely be tested by a hammer strike; the intact wheel responds with a clear and distinct sound, while a cracked wheel sounds different and can be identified by this sound, providing a “seismic” evaluation of mechanical properties.) Again, with local calibration, these correlations can be quantitatively useful but otherwise should be considered to be qualitative and subjective estimates of relative differences.
![Modulus vs. strength diagram. The relationship of dynamic and static shear modulus to shear strength is shown for some selected weak sandstones (after Fjaer et al.127[4]).](/w/images/thumb/c/cc/Vol6_Page_038_Image_0001.png/281px-Vol6_Page_038_Image_0001.png)
Modulus vs. strength diagram. The relationship of dynamic and static shear modulus to shear strength is shown for some selected weak sandstones (after Fjaer et al.127[4]).
![Modulus vs. strength diagram. The relationship of dynamic and static shear modulus to shear strength is shown for some selected weak sandstones (after Fjaer et al.127[4]).](/File:Vol6_Page_038_Image_0001.png)
The monitoring of reservoir production in some instances includes monitoring of compaction,[6] partly for environmental or facility-design considerations (e.g., subsidence) or as a part of prudent reservoir management and efficient production strategies. Laboratory studies on core samples can be conducted to provide a relationship between pore pressure and porosity, bulk volume, compressibility (as a static measure), and seismic wave velocities (dynamically measured).[7] With such correlations, and accounting for the frequency/size scaling effects between ultrasonic laboratory measurements and low-frequency field seismic observations, the velocities observed in seismic time-lapse monitoring experiments can be interpreted in terms of pore compressibility and/or collapse.
Nomenclature
| G | = | dynamic shear modulus |
| K | = | dynamic bulk modulus |
| Vp | = | P-wave velocity |
| Vs | = | S-wave velocity |
| ρ | = | density |
References
- ↑ Yale, D.P. 1994. Static and Dynamic Rock Mechanical Properties in the Hugoton and Panoma Fields, Kansas. Presented at the SPE Mid-Continent Gas Symposium, Amarillo, Texas, 22-24 May 1994. SPE-27939-MS. http://dx.doi.org/10.2118/27939-MS.
- ↑ Edwards, D., Joranson, H., and Spurlin, J. 1988. Field Normalization of Formation Mechanical Properties for Use in Sand Control Management. Presented at the SPWLA 29th Annual Logging Symposium, San Antonio, Texas, 5-8 June. SPWLA-1988-Y.
- ↑ Holt, R.M., Ingsoy, P., and Mikkelson, M. 1989. Rock Mechanical Analysis of North Sea Reservoir Formations. SPE Form Eval 4 (1): 33-37. SPE-16796-PA. http://dx.doi.org/10.2118/16796-PA.
- ↑ 4.0 4.1 Fjar, E. et al. 1992. Petroleum Related Rock Mechanics. Developments in Petroleum Science, 338. Amsterdam, The Netherlands: Elsevier Publishing.
- ↑ Goodman, H.E., Perrin, V.P., and Gregory, D.H. 1998. The Integration of Rock Mechanics, Open Hole Logs and Seismic Geophysics for Petroleum Engineering Applications. Presented at the SPE/ISRM Rock Mechanics in Petroleum Engineering, Trondheim, Norway, 8-10 July 1998. SPE-47358-MS. http://dx.doi.org/10.2118/47358-MS.
- ↑ Kristiansen, T.G., Barkved, O., and Pattillo, P.D. 2000. Use of Passive Seismic Monitoring in Well and Casing Design in the Compacting and Subsiding Valhall Field, North Sea. Presented at the SPE European Petroleum Conference, Paris, France, 24–25 October. SPE-65134-MS. http://dx.doi.org/10.2118/65134-MS.
- ↑ Pedersen, S.H. and Rhett, D.W. 1998. A Parametric Study of Compressional and Shear Wave Velocities in Ekofisk Reservoir Chalk. Presented at the SPE/ISRM Rock Mechanics in Petroleum Engineering, Trondheim, Norway, 8-10 July 1998. SPE-47295-MS. http://dx.doi.org/10.2118/47295-MS.
Noteworthy papers in OnePetro
Bachrach, R. and Osypov, K. Integrating Seismic And Geomechanical Information: Principles And Applications. Presented at the 2008/1/1/.
Dewhurst, D.N., Siggins, A.F., Kuila, U. et al. Elastic, Geomechanical and Petrophysical Properties of Shales. Presented at the 2008/1/1/.
Dusseault, M. Petroleum Geomechanics: Excursions Into Coupled Behaviour. http://dx.doi.org/10.2118/99-12-DA.
Ghassemi, A., Jafarpour, B., and Tarrahi, M. Geomechanical Reservoir Characterization with Microseismic Data. Presented at the 2013/8/20/. http://dx.doi.org/10.2118/165683-MS.
Hatchell, P.J., van den Beukel, A., Molenaar, M.M. et al. Whole Earth 4D: Reservoir Monitoring Geomechanics. Presented at the 2003/1/1/.
Tarrahi, M., Hosseini, S.M., and Javadpour, F. Geomechanical Considerations in Seismicity Based Reservoir Characterization. Presented at the 2013/4/10/. http://dx.doi.org/10.2118/164551-MS.
External links
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See also
Seismic attributes for reservoir studies