1887
Volume 30, Issue 1
  • ISSN: 1354-0793
  • E-ISSN:

Abstract

Although pore geometry plays an important role in carbonate rock physics modelling, few studies have been carried out on its analytic relationship with other pore space properties such as pore space stiffness. We propose an analytical workflow based on the differential effective medium (DEM) to estimate the elastic properties of carbonate rocks. The validity of our results is then cross-checked with the Xu and Payne model on a real carbonate dataset. This workflow establishes a direct and quantitative link between the pore geometry of carbonate rock and its other pore space properties such as the Biot coefficient and pore space stiffness. This relationship can, furthermore, be utilized in defining rock physics templates (RPTs) to investigate the role of pore geometry on the rock elastic properties. Furthermore, we extended the Biot–Gassmann–Krief (BGK) model through our proposed workflow by establishing a theoretical framework to relate the main components of the BGK model to the pore geometry usually estimated in the laboratory or empirically. This can help to investigate the impact of fluid substitution on each of these main components. Our investigation suggests that the higher the Biot and Gassmann coefficients, the more sensitive the rock is to fluid substitution. Moreover, this analytical workflow has been employed to examine the role of selecting different rotational spheroids (i.e. oblate and prolate) on the modelled velocities. Our results show that the modelled velocities depend on this selection in such a way that prolate pores are less sensitive to the variations in their pore aspect ratio compared with oblate pores.

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2023-12-14
2024-04-24
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References

  1. Anselmetti, F.S. and Eberli, G.P.1997. Sonic velocity in carbonate sediments and rocks. In: Palaz, I. and Marfurt, K.J. (eds) Carbonate Seismology. Geophysical Developments, 6. Society of Exploration Geophysicists, Tulsa, OK, 53–74, https://doi.org/10.1190/1.9781560802099.ch4
    [Google Scholar]
  2. Anselmetti, F.S. and Eberli, G.P.1999. The velocity-deviation log: A tool to predict pore type and permeability trends in carbonate drill holes from sonic and porosity or density logs. AAPG Bulletin, 83, 450–466, https://doi.org/10.1306/00AA9BCE-1730-11D7-8645000102C1865D
    [Google Scholar]
  3. Assefa, S., McCann, C. and Sothcott, J.2003. Velocities of compressional and shear waves in limestones. Geophysical Prospecting, 51, 1–13, https://doi.org/10.1046/j.1365-2478.2003.00349.x
    [Google Scholar]
  4. Avseth, P., Mukerji, T. and Mavko, G.2005. Quantitative Seismic Interpretation: Applying Rock Physics Tools to Reduce Interpretation Risk. Cambridge University Press, Cambridge, UK.
    [Google Scholar]
  5. Babasafari, A.A., Bashir, Y., Ghosh, D.P., Salim, A.M.A., Janjuhah, H.T., Kazemeini, S.H. and Kordi, M.2020. A new approach to petroelastic modeling of carbonate rocks using an extended pore-space stiffness method, with application to a carbonate reservoir in Central Luconia, Sarawak, Malaysia. The Leading Edge, 39, 592a1–592a10, https://doi.org/10.1190/tle39080592a1.1
    [Google Scholar]
  6. Baechle, G.T., Weger, R., Eberli, G.P. and Colpaert, A.2006. Pore size and pore type effects on velocity–implication for carbonate rock physic models. Abstract of a paper presented at theCIPR ‘Sound of Geology’ Workshop, 26–28 April 2006, Bergen, Norway.
    [Google Scholar]
  7. Batzle, M. and Wang, Z.1992. Seismic properties of pore fluids. Geophysics, 57, 1396–1408, https://doi.org/10.1190/1.1443207
    [Google Scholar]
  8. Berryman, J.G.1980. Long-wavelength propagation in composite elastic media II. Ellipsoidal inclusions. Journal of the Acoustical Society of America, 68, 1820–1831, https://doi.org/10.1121/1.385172
    [Google Scholar]
  9. Berryman, J.G.1995. Mixture theories for rock properties. In: Ahrens, T.J. (ed.) Rock Physics & Phase Relations: A Handbook of Physical Constants. AGU Reference Shelf Series, 3. American Geophysical Union, Washington, DC, 205–228.
    [Google Scholar]
  10. Eberli, G.P., Baechle, G.T., Anselmetti, F.S. and Incze, M.L.2003. Factors controlling elastic properties in carbonate sediments and rocks. The Leading Edge, 22, 654–660, https://doi.org/10.1190/1.1599691
    [Google Scholar]
  11. Fabricius, I.L.2003. How burial diagenesis of chalk sediments controls sonic velocity and porosity. AAPG Bulletin, 87, 1755–1778, https://doi.org/10.1306/06230301113
    [Google Scholar]
  12. Fabricius, I.L.2014. Burial stress and elastic strain of carbonate rocks. Geophysical Prospecting, 62, 1327–1336, https://doi.org/10.1111/1365-2478.12184
    [Google Scholar]
  13. Fabricius, I.L., Olsen, C. and Prasad, M.2005. Log interpretation of marly chalk, the Lower Cretaceous Valdemar Field, Danish North Sea: application of iso-frame and pseudo water film concepts. The Leading Edge, 24, 496–505, https://doi.org/10.1190/1.1926807
    [Google Scholar]
  14. Falahat, R. and Farrokhnia, F.2020. Rock physics modelling of the carbonate reservoirs: A log-based algorithm to determine the pore aspect ratio. Journal of Applied Geophysics, 173, 103930, https://doi.org/10.1016/j.jappgeo.2019.103930
    [Google Scholar]
  15. Fang, Y., Shi, Y., Sheng, Y. and Zhang, Z.2018. Modeling of Biot's coefficient for a clay-bearing sandstone reservoir. Arabian Journal of Geosciences, 11, 1–17, https://doi.org/10.1007/s12517-018-3663-7
    [Google Scholar]
  16. Fournier, F., Pellerin, M. et al.2018. The equivalent pore aspect ratio as a tool for pore type prediction in carbonate reservoirs. AAPG Bulletin, 102, 1343–1377, https://doi.org/10.1306/10181717058
    [Google Scholar]
  17. Gassmann, F.1951. Elastic waves through a packing of spheres. Geophysics, 16, 673–685, https://doi.org/10.1190/1.1437718
    [Google Scholar]
  18. Hall, J. and Alvarez, E.2010. Overcoming the limitations of rock physics modelling in porous rock with complex mineralogy. Paper SPWLA-2010-69661 presented at theSPWLA 51st Annual Logging Symposium, 19–23 June 2010, Perth, Australia.
    [Google Scholar]
  19. Hashin, Z. and Shtrikman, S.1963. A variational approach to the theory of the elastic behaviour of multiphase materials. Journal of the Mechanics and Physics of Solids, 11, 127–140, https://doi.org/10.1016/0022-5096(63)90060-7
    [Google Scholar]
  20. Khadem, B., Saberi, M.R., Eslahati, M. and Arbab, B.2020. Integration of rock physics and seismic inversion for rock typing and flow unit analysis: a case study. Geophysical Prospecting, 68, 1613–1632, https://doi.org/10.1111/1365-2478.12952
    [Google Scholar]
  21. Khadem, B., Saberi, M.R. and Avseth, P.2021. Rock physics of sand–shale mixtures: classifications, theoretical formulations and study on real dataset. Marine and Petroleum Geology, 134, 105366, https://doi.org/10.1016/j.marpetgeo.2021.105366
    [Google Scholar]
  22. Krief, M., Garat, J., Stellingwerff, J. and Ventre, J.1990. A petrophysical interpretation using the velocities of P and S waves (full-waveform sonic). The Log Analyst, 31(6), SPWLA-1990-v31n6a2
    [Google Scholar]
  23. Kumar, M. and Han, D.H.2005. Pore shape effect on elastic properties of carbonate rocks. Paper SEG-2005-1477 presented at the2005 SEG Annual Meeting, 6–11 November 2005, Houston, Texas, USA.
    [Google Scholar]
  24. Li, H. and Zhang, J.2010. Modulus ratio of dry rock based on differential effective-medium theory. Geophysics, 75, N43–N50, https://doi.org/10.1190/1.3360312
    [Google Scholar]
  25. Li, H. and Zhang, J.2011. Elastic moduli of dry rocks containing spheroidal pores based on differential effective medium theory. Journal of Applied Geophysics, 75, 671–678, https://doi.org/10.1016/j.jappgeo.2011.09.012
    [Google Scholar]
  26. Li, H. and Zhang, J.2012. Analytical approximations of bulk and shear moduli for dry rock based on the differential effective medium theory. Geophysical Prospecting, 60, 281–292, https://doi.org/10.1111/j.1365-2478.2011.00980.x
    [Google Scholar]
  27. Mavko, G. and Mukerji, T.1995. Seismic pore space compressibility and Gassmann's relation. Geophysics, 60, 1743–1749, https://doi.org/10.1190/1.1443907
    [Google Scholar]
  28. Mavko, G., Mukerji, T. and Dvorkin, J.2020. The Rock Physics Handbook. University Printing House, Cambridge, UK, https://doi.org/10.1017/9781108333016[
    [Google Scholar]
  29. Mirkamali, M.S., Javaherian, A., Hassani, H., Saberi, M.R. and Hosseini, S.A.2020. Quantitative pore-type characterization from well logs based on the seismic petrophysics in a carbonate reservoir. Geophysical Prospecting, 68, 2195–2216, https://doi.org/10.1111/1365-2478.12989
    [Google Scholar]
  30. Müller, T.M. and Sahay, P.N.2016. Biot coefficient is distinct from effective pressure coefficient. Geophysics, 81, L27–L33, https://doi.org/10.1190/geo2015-0625.1
    [Google Scholar]
  31. Odegaard, E. and Avseth, P.A.2004. Well log and seismic data analysis using rock physics templates. First Break, 22, 37–43, https://dx.doi.org/10.3997/1365-2397.2004017
    [Google Scholar]
  32. Olsen, C., Hedegaard, K., Fabricius, I.L. and Prasad, M.2008. Prediction of Biot's coefficient from rock-physical modeling of North Sea chalk. Geophysics, 73, E89–E96, https://doi.org/10.1190/1.2838158
    [Google Scholar]
  33. Russell, B.2013. A Gassmann-consistent rock physics template. CSEG Recorder, 38, 22–30.
    [Google Scholar]
  34. Russell, B.H. and Smith, T.2007. The relationship between dry rock bulk modulus and porosity – an empirical study. CREWES Research Report, 19, 1–14.
    [Google Scholar]
  35. Saberi, M.R.2017. A closer look at rock physics models and their assisted interpretation in seismic exploration. Iranian Journal of Geophysics, 10, 71–84.
    [Google Scholar]
  36. Saberi, M.R.2020. Geology-guided pore space quantification for carbonate rocks. First Break, 38, 49–55, https://doi.org/10.3997/1365-2397.fb2020018
    [Google Scholar]
  37. Saxena, V., Krief, M. and Adam, L.2018. Handbook of Borehole Acoustics and Rock Physics for Reservoir Characterization. Elsevier, Amsterdam.
    [Google Scholar]
  38. Sharifi, J., Mirzakhanian, M., Saberi, M.R., Moradi, M. and Sharifi, M.2018. Quantification of pore type system in carbonate rocks for rock physics modelling. In: 80th EAGE Conference and Exhibition 2018. European Association of Geoscientists & Engineers (EAGE), Houten, The Netherlands, https://doi.org/10.3997/2214-4609.201800674
    [Google Scholar]
  39. Sun, S.Z., Wang, H., Liu, Z., Li, Y., Zhou, X. and Wang, Z.2012. The theory and application of DEM-Gassmann rock physics model for complex carbonate reservoirs. The Leading Edge, 31, 152–158, https://doi.org/10.1190/1.3686912
    [Google Scholar]
  40. Tucker, M.E. (ed.) 2001. Sedimentary Petrology: An Introduction to the Origin of Sedimentary Rocks. John Wiley & Sons, Chichester, UK.
    [Google Scholar]
  41. Verwer, K., Braaksma, H. and Kenter, J.A.2008. Acoustic properties of carbonates: effects of rock texture and implications for fluid substitution. Geophysics, 73, B51–B65, https://doi.org/10.1190/1.2831935
    [Google Scholar]
  42. Voigt, W.1890. Bestimmung der Elasticitätsconstanten des brasilianischen Turmalines. Annalen der Physik, 277, 712–724, https://doi.org/10.1002/andp.18902771205
    [Google Scholar]
  43. Wang, Z.2001. Fundamentals of seismic rock physics. Geophysics, 66, 398–412, https://doi.org/10.1190/1.1444931
    [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, https://doi.org/10.1016/0020-7683(66)90002-3
    [Google Scholar]
  45. Wyllie, M.R.J., Gregory, A.R. and Gardner, L.W.1956. Elastic wave velocities in heterogeneous and porous media. Geophysics, 21, 41–70, https://doi.org/10.1190/1.1438217
    [Google Scholar]
  46. Xia, L.W., Cao, J., Wang, M., Mi, J.L. and Wang, T.T.2019. A review of carbonates as hydrocarbon source rocks: basic geochemistry and oil–gas generation. Petroleum Science, 16, 713–728, https://doi.org/10.1007/s12182-019-0343-5
    [Google Scholar]
  47. Xu, S. and Payne, M.A.2009. Modeling elastic properties in carbonate rocks. The Leading Edge, 28, 66–74, https://doi.org/10.1190/1.3064148
    [Google Scholar]
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