Reservoir Characterization. Группа авторов

2.15, the experimental and the estimated values of Young’s modulus are very close to one another and very comparable (%97).

2.5 Conclusions

      In this paper we evaluated the closeness of the estimated elastic wave velocities and elastic modulus of a rock sample via Gassmann - Greenberg - Castagna formula to those obtained from laboratory measurements at reservoir pressure.

       Estimating the physical parameters of rock samples from Gassmann - Greenberg - Castagna equations at high pressures is farther from the real situation. At high pressure, velocity values are more differentiated from each other and the estimated values are observed to be very far from the experimental (laboratory) values. Although it appears that at higher pressures cracks or fractures get closed, in substituting the fluid, especially brine for supercritical carbon dioxide and water, elasticity values have very high variations, and this very strongly influences the estimated compression wave velocities. And finally, this effect can be seen on the shear wave derived from compression wave. But since the shear wave velocity in the fluid and gas behave similarly, the effect was observed less on this wave.

       In the Gassmann assumptions it has been stated that pore fluid will not modify the elastic properties of the rocks. Thus, this theory predicts that shear modulus is not affected by the fluid saturation and will remain constant. In this study, the shear modulus didn’t remain constant during fluid saturation and during the transformation from gas-water saturation state to water saturation state; changes were detected to be around 2 percent. Because of this change in the shear modulus, it makes one hesitate to utilize the Gassmann theory to calculate the velocity. With the calculated and the experimental values of the shear modulus being variable, it can be concluded that Gassmann theory is not accurate for estimating the compressional wave velocity in a saturated state.

       The research found that the bulk modulus values obtained from the laboratory experiments show a very weak compatibility with the values calculated using Gassmann formulas. One of the probable reasons for this could be an influence of the transformation of the rock skeleton by brine (salt water). The overall conclusion from these studies is that, for samples saturated in brine at low pressures, good agreement exists between bulk modulus values calculated from Gassmann formula and experimental values obtained in the laboratory. While at high pressures when the rock is very strongly influenced by pressure, this agreement is nonexistent. This change was about 9% at low pressures and at high pressures, these differences reached up to 23%. Therefore, one should contemplate before utilizing Gassmann equation.

2.6 Acknowledgment

      Authors extended their appreciation to Petroleum Engineering Department, Curtin University of Technology, Australia that provided the authors the opportunity to utilize the laboratory core flooding system. Also, the authors thank and appreciate very much Prof. Vamegh Rasouli, Dr. Amin Nabipour, Dr. Mohammad Sarmadi and Dr. Mohsen Ghasemi for their help in conducting these experiments. Finally, the authors are very grateful and extend their deepest appreciation to the respected faculty of Petroleum Engineering and Geophysics departments, Curtin University of Technology that cooperated in the design, manufacturing and installation of the transducers.

References

      1. A. J. Engel and G. R. Bashford, A new method for shear wave speed estimation in shear wave elastography. IEEE T. Ultrason. Ferr. 62(12), 2016–2114 (2015).

      2. J. K. Jang, K. Kondo, T. Namita, M. Yamakava, and T. Shiina, Comparison of techniques for estimating shear-wave velocity in arterial wall using shear-wave elastography - FEM and phantom study, in IEEE International Ultrasonic Symposium, Taipei, Taiwan, p. 10, (2015).

      3. J. S. L. Heureux and M. Long, Correlations between shear wave velocity and geotechnical parameters in Norwegian clays, in 17th Nordic Geotechnical Meeting Challenges in Nordic Geotechnic, Reykjavik, Iceland, 299–308 (2016).

      4. B. Widarsono and P. M. Wong, Estimation of rock dynamic elastic property profiles through a combination of soft computing, acoustic velocity modeling, and laboratory dynamic test on core samples, SPE Asia Pacific Oil and Gas Conference, 68712 (2001).

      5. G. R. Pickett, Acoustic character logs and their application in formation evaluation. J. Petrol. Technol. 15, 650–667 (1963).

      6. P. Milholand, M. H. Manghnani, S. O. Schlanger, and G. H. Sutton, Geoacoustic modeling of deep-sea carbonate sediments. J. Acoust. Soc. Am. 68, 1351–1360 (1980).

      7. S. N. Domenico, Rock lithology and porosity determination from shear and compressional velocity. Geophysics 49, 1188–1195 (1984).

      8. L. Thomsen, Weak elastic anisotropy. Geophys 51, 1654–1966 (1986).

      9. D. Han, Empirical relationships among seismic velocity, effective pressure, porosity and clay content in sandstone. Geophysics 54, 82–89 (1989).

      10. M. Krief, J. Garat, J. Stellingwerf, and J. Venter, A petrophysical interpretation using the velocities of P and S waves (full wave from sonic). Log Anal, 31, 35–369 (1990).

11. J. P. Castagna, M. L. Batzle, and R. L. Eastwood, Relationship between compressional and shear wave velocities in silicate rocks. Geophysics 50, 571–581 (1985).

      12. M. L. Greenberg and J. P. Castagna, Shear wave velocity estimation in porous rocks: Theoretical formulation, prelimining verifcation and applications, Geophysics. Prospecting 40, 195–209 (1992).

      13. C. Tosaya and A. Nur, Effects of diagenesis and clays on compression velocities in rocks. Geophysics, Res. Lett. 9, 5–8 (1982).

      14. M. R. Rezaee, A. Kadkhodaie, and A. Barabadi, Prediction of shear wave velocity from petrophysical data utilizing intelligent systems: An example from a sandstone reservoir of Carnarvon Basin, Australia. J. Petrol. Sci. Eng. 55, 201–212 (2007).

      15. M. A. Dezfoolian, Body wave velocities estimation from wireline log data utilizing an artificial neural network for a carbonate reservoir, South Iran. J. Petrol. Sci. Technol. 31(1), 32–43 (2013).

      16. Sh. Malekia, A. Moradzadeha, R. Ghavami Riabia, R. Gholamib, and F. Sadeghzadehc, Prediction of shear wave velocity using empirical correlations and artificial intelligence methods. RIAG Journal of Astronomy and Geophysics 3(1), 70–81 (2014).

      17. F. G. Bell, Engineering Properties of Soil and Rocks, 4th ed., Back well science Ltd, United Kingdom (2000).

      18. F. Gassmann, On the elasticity of porous media: Viertelijahrsschrift der Naturforschenden Gesellschaft in Zurich. 96, 1–23 (1951).

      19. G.Mavko and T. Mukerji, Pore space compressibility and Gassmannn’s relation. Geophysics 60, 1743–1749 (1995).

      20. G. Mavko, T. Mukerji, and J. Dvorkin, Rock Phsycis Handbook: Tools for Seismic Analysis in Porous Media, Cambridge University Press, Cambridge (1998).

      21. M. R. J. Wyllie, A. R. Gregory, and L. W. Gardner, Elastic wave velocities in heterogeneous and porous media. Geophysics 21, 41–70 (1956).

      22. L. L. Raymer, E. R. Hunt, and J. S. Gardner, An improved sonic transit time-to-porosity transform, Paper P, in 21st Annual Logging Symposium Transactions, Lafayette, Lousiana (1980).

      23. D. Han, A. Nur, and D. Morgan, Effects of porosity and clay content on wave velocities in sandstones. Geophysics 51, 2093–2107 (1986).

      24. J. Raiga-clemenceau, J. P. Martin,