1887
Volume 72, Issue 5
  • E-ISSN: 1365-2478

Abstract

Abstract

The strong sensitivity of velocity to stress observed in many sandstones originates from the response of stress‐sensitive discontinuities such as grain contacts and microcracks to a change in effective stress. If the change in stress is anisotropic, then the change in elastic wave velocities will also be anisotropic. Characterization of stress‐induced elastic anisotropy in sandstones may enable estimation of the in situ three dimensional stress tensor with important application in solving problems occurring during drilling, such as borehole instability, and during production, such as sanding and reservoir compaction. Other applications include designing hydraulic fracture stimulations and quantifying production‐induced stresses which may lead to rock failure. Current methods for estimating stress anisotropy from acoustic anisotropy rely on third‐order elasticity, which ignores rock microstructure and gives elastic moduli that vary linearly with strain. Elastic stiffnesses in sandstones vary non‐linearly with stress. Using P‐ and S‐wave velocities measured on Gulf of Mexico sandstones, this non‐linearity is found to be consistent with a micromechanical model in which the discontinuities are represented by stress‐dependent normal and shear compliances. Stress‐induced anisotropy increases with increasing stress anisotropy at small stress but then decreases at larger stresses as the discontinuities close and their compliance decreases. When the ratio of normal‐to‐shear compliance of the discontinuities is unity, the stress‐induced anisotropy is elliptical, but for values different from unity, the stress‐induced anisotropy becomes anelliptic. Although vertical stress can be obtained by integrating the formation's bulk density from the surface to the depth of interest, and minimum horizontal stress can be estimated using leak‐off tests or hydraulic fracture data, maximum horizontal stress is more difficult to estimate. Maximum horizontal stress is overpredicted based on third‐order elasticity using measured shear moduli, with estimates of pore pressure, vertical stress and minimum horizontal stress as input. The non‐linear response of grain contacts and microcracks to stress must be considered to improve such estimates.

© 2024 European Association of Geoscientists & Engineers. © 2024 European Association of Geoscientists & Engineers.
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2024-05-21
2026-01-25

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References

  1. Alkhalifah, T. & Tsvankin, I. (1995) Velocity analysis for transversely isotropic media. Geophysics, 60, 1550–1566.
     [Google Scholar]
  2. Ampomah, W., Will, R., McMillan, M., Bratton, T., Huang, L., El‐Kaseeh, G. et al. (2021) Improving subsurface stress characterization for carbon dioxide storage projects. Proceedings of the 15th Greenhouse Gas Control Technologies Conference, pp. 15–18. Available at SSRN: https://doi.org/10.2139/ssrn.3816723
  3. Angelier, J. (1979) Determination of the mean principal directions of stresses for a given fault population. Tectonophysics, 56(3–4), T17–T26.
     [Google Scholar]
  4. Asaka, M. (2022) Anisotropic 4D seismic response inferred from ultrasonic laboratory measurements: a direct comparison with the isotropic response. Geophysical Prospecting, 71(1), 17–28.
     [Google Scholar]
  5. Bathija, A.P., Batzle, M.L. & Prasad, M. (2009) An experimental study of the dilation factor. Geophysics, 74(4), E181–E191.
     [Google Scholar]
  6. Bauer, A., Bhuiyan, M.H., Fjær, E., Holt, R.M., Lozovyi, S., Pohl, M. et al. (2016) Frequency‐dependent wave velocities in sediments and sedimentary rocks: laboratory measurements and evidences. The Leading Edge, 35(6), 490–494.
     [Google Scholar]
  7. Carcione, J.M. & Tinivella, U. (2001) The seismic response to over‐pressure: a modelling study based on laboratory, well and seismic data. Geophysical Prospecting, 49, 523–539.
     [Google Scholar]
  8. Collet, O., Gurevich, B., Madadi, M. & Pervukhina, M. (2014) Modeling elastic anisotropy resulting from the application of triaxial stress. Geophysics, 79(5), C135–C145.
     [Google Scholar]
  9. Eberhart‐Phillips, D., Han, D.‐H. & Zoback, M.D. (1989) Empirical relationships among seismic velocity, effective pressure, porosity and clay content in sandstone. Geophysics, 54, 82–89.
     [Google Scholar]
  10. Freund, D. (1992) Ultrasonic compressional and shear velocities in dry clastic rocks as a function of porosity, clay content, and confining pressure. Geophysical Journal International, 108, 125–135.
     [Google Scholar]
  11. Gassmann, F. (1951) Über die Elastizität poröser Medien. Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich, 96, 1–23.
     [Google Scholar]
  12. Gurevich, B., Pervukhina, M. & Makarynska, D. (2011) An analytic model for the stress‐induced anisotropy of dry rocks. Geophysics, 76(3), WA125–WA133.
     [Google Scholar]
  13. Han, D.H. (1986) Effects of porosity and clay content on acoustic properties of sandstones and unconsolidated sediments. Doctoral dissertation, Stanford: Stanford University.
  14. Han, D.H., Nur, A. & Morgan, D. (1986) Effects of porosity and clay content on wave velocities in sandstones. Geophysics, 51(11), 2093–2107.
     [Google Scholar]
  15. Hertz, H. (1882) Über die Berührung fester elastischer Körper. Journal für die reine und angewandte Mathematik, 1882, 156–171.
     [Google Scholar]
  16. Hettema, M.H.H., Schutjens, P.M.T.M., Verboom, B.J.M. & Gussinklo, H.J. (2000) Production‐induced compaction of a sandstone reservoir: the strong influence of field stress. SPE Reservoir Evaluation and Engineering3, 342–347.
     [Google Scholar]
  17. Holt, R.M. & Fjaer, E. (1987) Acoustic behaviour of sedimentary rocks during failure. In North Sea Oil and Gas Reservoirs, London: Graham and Trotman, pp. 311–316.
     [Google Scholar]
  18. Hughes, D.S. & Kelly, J.L. (1953) Second‐order elastic deformation of solids. Physical Review, 92(5), 1145.
     [Google Scholar]
  19. Johnson, D.L., Schwartz, L.M., Elata, D., Berryman, J.G., Hornby, B. & Norris, A.N. (1998) Linear and nonlinear elasticity of granular media: stress‐induced anisotropy of a random sphere pack. Journal of Applied Mechanics, 65(2), 380–388.
     [Google Scholar]
  20. Jones, S.M. (1995) Velocities and quality factors of sedimentary rocks at low and high effective pressures. Geophysical Journal International, 123, 774–780.
     [Google Scholar]
  21. Kachanov, M. (1992) Effective elastic properties of cracked solids: critical review of some basic concepts. Applied Mechanics Reviews, 45, 304–335.
     [Google Scholar]
  22. Khaksar, A., Griffiths, C.M. & McCann, C. (1999) Compressional and shear‐wave velocities as a function of confining stress in dry sandstone. Geophysical Prospecting, 47, 487–508.
     [Google Scholar]
  23. Khazanehdari, J. & McCann, C. (2005) Acoustic and petrophysical relationships in low‐shale sandstone reservoir rocks. Geophysical Prospecting, 53(4), 447–461.
     [Google Scholar]
  24. Kirstetter, O. & MacBeth, C. (2001) Compliance‐based interpretation of dry frame pressure sensitivity in shallow marine sandstone. In: 71st Annual International Meeting, SEG, Expanded Abstracts. Houston, TX, SEG. pp. 2132–2135.
  25. Lebedev, V.I. (1976) Quadratures on a sphere. USSR Computational Mathematics and Mathematical Physics, 16, 10–24.
     [Google Scholar]
  26. MacBethC. (2004) A classification for the pressure‐sensitive properties of a sandstone rock frame. Geophysics, 69, 497–510.
     [Google Scholar]
  27. Madadi, M., Pervukhina, M. & Gurevich, B. (2013) Modelling elastic anisotropy of dry rocks as a function of applied stress. Geophysical Prospecting, 61, (2‐Rock Physics for Reservoir Exploration, Characterisation and Monitoring), 391–403.
     [Google Scholar]
  28. Makse, H.A., Gland, N., Johnson, D.L. & Schwartz, L. (2004) Granular packings: nonlinear elasticity, sound propagation, and collective relaxation dynamics. Physical Review E, 70(6), 061302.
     [Google Scholar]
  29. Mavko, G. & Jizba, D. (1991). Estimating grain‐scale fluid effects on velocity dispersion in rocks. Geophysics, 56(12), 1940–1949.
     [Google Scholar]
  30. MavkoG., MukerjiT. & GodfreyN.1995. Predicting stress‐induced velocity anisotropy of rocks. Geophysics, 60, 1081–1087.
     [Google Scholar]
  31. Miller, D.E. & Spencer, C. (1994) An exact inversion for anisotropic moduli from phase slowness data. Journal of Geophysical Research: Solid Earth, 99 (B11), 21651–21657.
     [Google Scholar]
  32. Mindlin, R.D. (1949) Compliance of elastic bodies in contact. Journal of Applied Mechanics, 16, 259–268.
     [Google Scholar]
  33. Mindlin, R.D. & Deresiewicz, H. (1953) Elastic spheres in contact under varying oblique forces. ASME Journal of Applied Mechanics, 75, 327–344.
     [Google Scholar]
  34. Nye, J.F. (1985) Physical properties of crystals. Oxford, UK: Oxford University Press.
     [Google Scholar]
  35. Pervukhina, M., Gurevich, B., Golodoniuc, P. & Dewhurst, D.N. (2011) Parameterization of elastic stress sensitivity in shales. Geophysics, 76(3), WA147–WA155.
     [Google Scholar]
  36. Prasad, M. & Manghnani, M.H. (1997) Effects of pore and differential pressure on compressional wave velocity and quality factor in Berea and Michigan sandstones. Geophysics, 62(4), 1163–1176.
     [Google Scholar]
  37. Rudnicki, J.W. (1999) Alteration of regional stress by reservoirs and other inhomogeneities: stabilizing or destabilizing?Proceedings of the Ninth International Congress on Rock Mechanics. pp. 1629–1637. ISRM‐9CONGRESS‐1999‐303 at https://onepetro.org/isrmcongress/proceedings-abstract/CONGRESS99/All-CONGRESS99/ISRM-9CONGRESS-1999-303/168935
  38. Ruistuen, H., Teufel, L.W. & Rhett, D. (1999) Influence of reservoir stress path on deformation and permeability of weakly cemented sandstone reservoirs. SPE Reservoir Evaluation and Engineering, 2, 266–272.
     [Google Scholar]
  39. Sammonds, P.R., Ayling, M.R., Meredith, P.G., Murrell, S.A. F. & Jones, C. (1989) A laboratory investigation of acoustic emission and elastic wave velocity changes during rock failure under triaxial stresses. In: Maury, V. & Fourmaintraux, D. (Eds.) Rock at great depth, Amsterdam: A.A. Balkema, pp. 233–240.
     [Google Scholar]
  40. Sayers, C.M. (2007a) Asymmetry in the time‐lapse seismic response to injection and depletion. Geophysical Prospecting, 55, 699–705.
     [Google Scholar]
  41. Sayers, C.M. (2007b) Effects of borehole stress concentration on elastic wave velocities in sandstones. International Journal of Rock Mechanics and Mining Sciences, 44(7), 1045–1052.
     [Google Scholar]
  42. Sayers, C.M. (2010) Geophysics under stress: geomechanical applications of seismic and borehole acoustic waves. Houston/Utrecht, the Netherlands: Society of Exploration Geophysicists/European Association of Geoscientists and Engineers.
     [Google Scholar]
  43. Sayers, C.M. (2023) The effect of clay and contacts between sand grains on the elastic properties of sandstones. Geophysical Prospecting, 71(3), 456–470.
     [Google Scholar]
  44. Sayers, C.M. & Han, D.H. (2002) The effect of pore fluid on the stress‐dependent elastic wave velocities in sandstones [Expanded abstracts]. 72nd Annual International Meeting. Houston, TX, SEG, pp. 1842–1845.
  45. Sayers, C.M. & Kachanov, M. (1995) Microcrack‐induced elastic wave anisotropy of brittle rocks. Journal of Geophysical Research, 100, 4149–4156.
     [Google Scholar]
  46. Sayers, C.M. & Schutjens, P.M. (2007) An introduction to reservoir geomechanics. The Leading Edge, 26(5), 597–601.
     [Google Scholar]
  47. Sayers, C.M., van Munster, J.G. & King, M.S. (1990) Stress‐induced ultrasonic anisotropy in Berea sandstone. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 27, 429–436.
     [Google Scholar]
  48. Schlömer, N., Papior, N., Arnold, D., Blechta, J. & Zetter, R. (2022) quadpy: Numerical integration (quadrature, cubature) in Python. https://github.com/sigma‐py/quadpy [Accessed April 24, 2023].
  49. Schoenberg, M. (2002) Time‐dependent anisotropy induced by pore pressure variation in fractured rock. Journal of Seismic Exploration, 11, 83–105.
     [Google Scholar]
  50. Schutjens, P.M.T.M., Hanssen, T.H., Hettema, M.H.H., Merour, J., de Bree, P., Coremans, J.W.A. et al. (2004) Compaction‐induced porosity/permeability reduction in sandstone reservoirs: data and model for elasticity‐dominated deformation: SPE Reservoir Evaluation and Engineering, 7, 202–216.
     [Google Scholar]
  51. Scott, T.E., Ma, Q. & Roegiers, J.C. (1993) Acoustic velocity changes during shear enhanced compaction of sandstone. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 30, 763–769.
     [Google Scholar]
  52. Shapiro, S.A. (2003) Elastic piezosensitivity of porous and fractured rocks. Geophysics, 68, 482–486.
     [Google Scholar]
  53. Sinha, B.K., Vissapragada, B., Renlie, L. & Skomedal, E. (2006) Horizontal stress magnitude estimation using the three shear moduli—a Norwegian sea case study. Paper presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, September 2006 (SPE‐103079‐MS).
  54. Sinha, B.K., Vissapragada, B., Wendt, A.S., Kongslien, M., Eser, H., Skomedal, E. et al. (2007) Estimation of formation stresses using radial variation of three shear moduli—a Case Study from a high‐pressure and high‐temperature reservoir in a Norwegian Continental Shelf. Paper presented at the SPE Annual Technical Conference and Exhibition, Anaheim, California, U.S.A., November 2007 (SPE‐109842‐MS).
  55. Sinha, B.K., Wang, J., Kisra, S., Li, J., Pistre, V., Bratton, T. et al. (2008) Estimation of formation stresses using borehole sonic data. Paper presented at SPWLA 49th Annual Logging Symposium, Austin, Texas, May 2008 (SPWLA‐2008‐F).
  56. Thomsen, L. (1986) Weak elastic anisotropy. Geophysics, 51, 1954–1966.
     [Google Scholar]
  57. Thurston, R.N. & Brugger, K. (1964) Third‐order elastic constants and the velocity of small amplitude elastic waves in homogeneously stressed media. Physical Review, 133, A1604.
     [Google Scholar]
  58. Toupin, R.A. & Bernstein, B. (1961) Sound waves in deformed perfectly elastic materials. Acoustoelastic effect. The Journal of the Acoustical Society of America, 33(2), 216–225.
     [Google Scholar]
  59. Tsvankin, I. (1997) Anisotropic parameters and P‐wave velocity for orthorhombic media. Geophysics, 62, 1292–1309.
     [Google Scholar]
  60. Vlastos, S., Liu, E., Main, I.G., Schoenberg, M., Narteau, C., Li, X.Y. et al. (2006) Dual simulations of fluid flow and seismic wave propagation in a fractured network: effects of pore pressure on seismic signature. Geophysical Journal International, 166(2), 825–838.
     [Google Scholar]
  61. Voigt, W. (1928) Lehrbuch der Kristallphysik. Leipzig: B. G. Teuhner.
     [Google Scholar]
  62. Wallace, D.C. (1970) Thermoelastic theory of stressed crystals and higher‐order elastic constants. In: Solid state physics, vol. 25. Cambridge: Academic Press, pp. 301–404.
     [Google Scholar]
  63. Winkler, K.W. & Liu, X. (1996) Measurements of third‐order elastic constants in rocks. The Journal of the Acoustical Society of America, 100(3), 1392–1398.
     [Google Scholar]
  64. Zimmerman, R.W., Somerton, W.H. & King, M.S. (1986) Compressibility of porous rocks. Journal of Geophysical Research, 91, 12765–12777.
     [Google Scholar]
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Stress‐induced anisotropy in Gulf of Mexico sandstones and the prediction of in situ stress
Geophysical Prospecting 72, 1852 (2024); https://doi.org/10.1111/1365-2478.13497
/content/journals/10.1111/1365-2478.13497
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  • Article Type: Research Article
Keyword(s): anisotropy; elastics; reservoir geophysics; rock physics; seismics

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