1887
Volume 68, Issue 6
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

An inclusion model, based on the Kuster–Toksöz effective medium theory along with Gassmann theory, is tested to forward model velocities for fluid‐saturated rocks. A simulated annealing algorithm, along with the inclusion model, effectively inverts measured compressional velocity () to achieve an effective pore aspect ratio at each depth in a depth variant manner, continuously along with depth. Early Cretaceous syn‐rift clastic sediments at two different depth intervals from two wells [well A (2160–2274 m) and well B (5222–5303 m)], in the Krishna–Godavari basin, India, are used for this study. Shear velocity () estimated using modelled pore aspect ratio offers a high correlation coefficient (>0.95 for both the wells) with measured data. The modelled pore aspect ratio distribution suggests the decrease in pore aspect ratio for the deeper interval, mainly due to increased effective vertical stress. The pore aspect ratio analysis in relation to total porosity and volume of clay reveals that the clay volume has insignificant influence in shaping the pore geometry in the studied intervals. An approach based on multiple linear regression method effectively predicts velocity as a linear function of total porosity, the volume of clay and the modelled pore‐space aspect ratio of the rock. We achieved a significant match between measured and predicted velocities. The correlation coefficients between measured and modelled velocities are considerably high (approximately 0.85 and 0.8, for and , respectively). This process indicates the possible influence of pore geometry along with total porosity and volume of clay on velocity.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12955
2020-05-13
2024-04-24
Loading full text...

Full text loading...

References

  1. Arya, A.K., Bhanumurty, N. and Kumar, A. (2011) Prospectivity of rift fill sequence in Krishna–Godavari basin. Geohorizon Journal, 24, 8. https://www.spgindia.org/geohorizon/geo_june2011/aka_geohrz.pdf
    [Google Scholar]
  2. Athy, L.F. (1930) Density, porosity and compaction of sedimentary rocks. Bulletin of the American Association of Petroleum Geologists (AAPG Bulletin), 14, 1–24.
    [Google Scholar]
  3. Batzle, M. and Wang, Z. (1992) Seismic properties of pore fluids. Geophysics, 57(11), 1396–1408. https://doi.org/10.1190/1.1443207.
    [Google Scholar]
  4. Bai, Y.J., Yue, C.Q., Liang, Y.Q., Song, Z.X., Ling, S., Zhang, Y. and Wu, W. (2013) Variable aspect ratio method in the Xu‐White model for Shear‐wave velocity estimation. Journal of Geophysics and Engineering, 10, 035008. https://doi.org/10.1088/1742-2132/10/3/035008.
    [Google Scholar]
  5. Berryman, J.G. (1980) Long‐wavelength propagation in composite elastic media. The Journal of the Acoustical Society of America, 68, 1809–1831. https://doi.org/10.1121/1.385172
    [Google Scholar]
  6. Bertsimas, D. and Tsitsiklis, J. (1993) Simulated annealing. Statistical Science, 8(1), 10–15.
    [Google Scholar]
  7. Castagna, J.P., Batzle, M.L. and Eastwood, R.L. (1985) Relationship between compressional‐wave shear‐wave velocities in clastic silicate rocks. Geophysics, 50, 571–581. https://doi.org/10.1190/1.1441933
    [Google Scholar]
  8. Cheng, C.H. and Toksöz, MN. (1979) Inversion of seismic velocities for the pore aspect ratio spectrum of a rock. Journal of Geophysical Research, 84(B13), 7533–7543. https://doi.org/10.1029/JB084iB13p07533
    [Google Scholar]
  9. Deer, W.A, Howie, R.A. and Zussman, J. (1966) An Introduction to the Rock Forming Minerals. Harlow, Essex: Longman.
    [Google Scholar]
  10. Dvorkin, Jack P. (2008) Yet another Vs equation. Geophysics, 73(2), E35–E39. https://doi.org/10.1190/1.2820604.
    [Google Scholar]
  11. Dvorkin, J., Mavko, G. and Nur, A. (1999) Overpressure detection from compressional and shear wave data. Geophysical Research Letters, 26(22), 3417–3420.
    [Google Scholar]
  12. Eshelby, J.D. (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of theRoyal Society A, 241(1226), 376–396. https://doi.org/10.1098/rspa.1957.0133.
    [Google Scholar]
  13. Gardner, G.H.F., Gardner, L.W. and Gregory, A.R. (1974) Formation velocity and density‐the diagnostic basics for stratigraphic traps. Geophysics, 39(6), 770–780. https://doi.org/10.1190/1.1440465
    [Google Scholar]
  14. Gassmann, F. (1951) Über die Elastizität poröser Medien. Vierteljahrsschrift der Naturforschenden Gesellschaft in Zurich, 96, 1–23.
    [Google Scholar]
  15. Guo, Z. and Li, X.Y. (2015) Rock physics model‐based prediction of shear velocity in the Barnett shale formation. Journal of Geophysics and Engineering, 12, 527–534. https://iopscience.iop.org/article/10.1088/1742-2132/12/3/527.
    [Google Scholar]
  16. Haiyang, W., Sun, S.Z., Haijun, Y., Hongliang, G., Youjun, X. and Hongru, H. (2011) The influence of pore structure on P‐ &S‐wave velocities in complex carbonate reservoirs with secondary storage space. Petroleum Science, 8(4), 394–405. https://doi.org/10.1007/s12182-011-0157-6
    [Google Scholar]
  17. Han, D., Nur, A., and Morgan, D. (1986) Effects of porosity and clay content on wave velocities in sandstones. Geophysics, 51(11), 2093–2107. https://doi.org/10.1190/1.1442062.
    [Google Scholar]
  18. Hill, R. (1952) The elastic behavior of a crystalline aggregate. Proceedings of Physical Society A, 65(5), 349–354. https://doi.org/10.1088/0370-1298/65/5/307.
    [Google Scholar]
  19. Juhasz, I. (1986) Assessment of the distribution of shale, porosity and hydrocarbon saturation in shaly sands. In: Proceedings of the 10th European Formation Evaluation Symposium, Aberdeen.
  20. Kirkpatrick, S., Gelatt, C.D. and Vecchi, M.P. (1983) Optimization by simulated annealing. Science, 220, 671–679. https://doi.org/10.1126/science.220.4598.671.
    [Google Scholar]
  21. Klimentos, T. (1991) The effect of porosity‐permeability‐clay content on the velocity of compressional waves. Geophysics, 56(12), 1930–1939. https://doi.org/10.1190/1.1443004.
    [Google Scholar]
  22. Kuster, G.T. and Toksöz, M.N. (1974) Velocity and attenuation of seismic waves in two phase media: Part: I. Theoretical formulation. Geophysics, 39(5), 587–606. https://doi.org/10.1190/1.1440451.
    [Google Scholar]
  23. Manmohan, M., Rao, M.R.R., Kamaraju, A.V.V.S. and Yalamarty, S.S. (2003) Origin and occurrence of lower cretaceous high gamma‐high resistivity (Raghavapuram) Shale ‐a key stratigraphic sequence for hydrocarbon exploration in Krishna–Godavari basin, A.P. Journal of Geological Society of India, 62(3), 271–289.
    [Google Scholar]
  24. Mavko, G., Mukerji, T. and Dvorkin, J. (2009) The Rock Physics Handbook (2nd edition). New York: Cambridge University Press.
  25. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and Teller, E. (1953) Equation of state calculation by fast computing machines. Journal of Chemical Physics, 21, 1087–1092.
    [Google Scholar]
  26. Minear, M.J. (1982) Clay models and acoustic velocities: Presented at the 57th Annual Meeting of the American Institute of Mining and Metallurgical Engineers, New Orleans.
  27. Norris, A.N. (1985) A differential scheme for the effective moduli of composites. Mechanics of Materials, 4, 1–16. https://doi.org/10.1016/0167-6636(85)90002-X.
    [Google Scholar]
  28. Nur, A. and Simmons, G. (1969) The effect of saturation on velocity in low porosity rock. Earth Planetary Science Letters, 7, 183–193.
    [Google Scholar]
  29. O'Connell, R.J. and Budiansky, B. (1974) Seismic velocities in dry and saturated cracked solids. Journal of Geophysical Research, 79, 4626–4627. https://doi.org/10.1029/JB079i035p05412.
    [Google Scholar]
  30. Ramm, M. and BjØrlykke, K. (1994) Porosity/depth trends in reservoir sandstones: assessing the quantitative effects of varying pore‐pressure, temperature history and mineralogy, Norwegian Shelf data. Clay Minerals, 29, 475–490.
    [Google Scholar]
  31. Rao, G.N. (2001) Sedimentation, stratigraphy, and petroleum potential of Krishna–Godavari basin, East Coast of India. AAPG Bulletin, 85(9), 1623‐1643. DOI: https://doi.org/10.1306/8626CCDF-173B-11D7-8645000102C1865D.
    [Google Scholar]
  32. Raymer, L.L., Hunt, E.R. and Gardner, J.S. (1980) An improved sonic transit time‐to‐porosity transform: SPWLA 21 Annual. Logging Symposium, 8–11 July, 1–12.
    [Google Scholar]
  33. Sampath, A. and Dobriyal, J.P. (2015) Understanding a low permeable, HPHT, Syn‐rift reservoir in K.G. Basin offshore through integrated G&G study, SPG, 11th biennial International Conference and Exposition, Jaipur.
  34. Sams, M. and Focht, T. (2013) An effective inclusion‐based rock physics model for a sand‐shale sequence. First Break, 31(3), 61–71. https://doi.org/10.3997/1365-2397.2013007.
    [Google Scholar]
  35. Sams, M., Focht, T.J. and Sidik, N.A.C. (2012) Xu and White revisited: EAGE Conference and Exhibition, Copenhagen.
  36. Sams, M.S. and Andrea, M. (2001) The effect of clay distribution on the elastic properties of sandstones. Geophysical Prospecting, 49(1), 128–150. https://doi.org/10.1046/j.1365-2478.2001.00230.x.
    [Google Scholar]
  37. Smith, T.M., Sayers, C.M. and Sondergeld, C.H. (2009) Rock properties in low‐porosity/low‐permeability sandstones. The Leading Edge, 28(1), 48–59. https://doi.org/10.1190/1.3064146.
    [Google Scholar]
  38. Sun, Y.F. and Goldberg, D. (1997) Estimation of aspect‐ratio changes with pressure from seismic velocities. Geological Society of London, 122(1), 131–139. https://doi.org/10.1144/GSL.SP.1997.122.01.10.
    [Google Scholar]
  39. Thomas, E.C. and Steiber, S.J. (1975) The distribution of shale in sandstones and its effects on porosity. In: Trans. SPWLA 16th Annual Logging Symp., 4–7 June.
  40. Tosaya, C. and Nur, A. (1982) Effects of diagenesis and clays on compressional velocities in rocks. Geophysical Research Letters, 9(1), 5–8. https://doi.org/10.1029/GL009i001p00005.
    [Google Scholar]
  41. Tyagi, A.K., Guha, R., Voleti, D. and Saxena, K. (2009) Challenges in the reservoir characterization of a laminated sand shale sequence. In: Proceedings of the Second SPWLA‐India Regional Symposium, 19–20 November, Mumbai, India.
  42. Wang, P., Wu, G., Dai, R. and Zhang, W. (2014) A new rock physics model for tight reservoirs, SEG technical program expanded abstract, Denver.
  43. Wyllie, M.R.J., Gregory, A.R. and Gardner, L.W. (1956) Elastic wave velocities in heterogeneous and porous media. Geophysics, 21(1), 41–70. https://doi.org/10.1190/1.1438217.
    [Google Scholar]
  44. Wu, T.T. (1966) The effect of inclusion shape on the elastic moduli of a two‐phase material. International Journal of Solids and Structures, 2, 1–8.
    [Google Scholar]
  45. Xu, S. and White, W.R. (1995) A new velocity model for clay‐sand mixtures. Geophysical Prospecting, 43(1), 91–118. https://doi.org/10.1111/j.1365-2478.1995.tb00126.x.
    [Google Scholar]
  46. Yan, J., Li, X.Y. and Liu, E. (2002) Effects of pore aspect ratios on velocity prediction from well‐log data. Geophysical Prospecting, 50(4), 289–300. https://doi.org/10.1046/j.1365-2478.2002.00313.x.
    [Google Scholar]
  47. Yan, J., Lubbe, R. and Pillar, N. (2008) Modified velocity model for seismic study via AVO. Journal of Seismic Exploration, 17, 371–390
    [Google Scholar]
  48. Zhang, J.J. and Bentley, L.R. (2013) Pore geometry and elastic moduli in sandstones. CREWS Research Report, 15.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12955
Loading
/content/journals/10.1111/1365-2478.12955
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Elastic properties; Pore aspect ratio; Simulated annealing; Velocity; Wave

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error