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Volume 67 Number 4
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

The effective medium theory based on the Hertz–Mindlin contact law is the most popular theory to relate dynamic elastic moduli (or elastic velocities) and confining pressure in dry granular media. However, many experimental results proved that the effective medium theory predicts pressure trends lower than experimental ones and over‐predicts the shear modulus. To mitigate these mispredictions, several evolutions of the effective medium theory have been presented in the literature. Among these, the model named modified grain contact theory is an empirical approach in which three parametric curves are included in the effective medium theory model. Fitting the parameters of these curves permits to adjust the pressure trends of the Poisson ratio and the bulk modulus. In this paper, we present two variations of the modified grain contact theory model. First, we propose a minor modification in the fitting function for the porosity dependence of the calibration parameters that accounts for non‐linearity in the vicinity of the critical porosity. Second, we propose a major modification that reduces the three‐step modified grain contact theory model to a two‐step model, by skipping the calibration parameter–porosity fit in the model and directly modelling the calibration parameter–pressure relation. In addition to an increased simplicity (the fitting parameters are reduced from 10 to 6), avoiding the porosity fit permits us to apply the model to laboratory data that are not provided with accurate porosity measurements. For this second model, we also estimate the uncertainty of the fitting parameters and the elastic velocities. We tested this model on dry core measurements from literature and we verified that it returns elastic velocity trends as good as the original modified grain contact theory model with a reduced number of fitting parameters. Possible developments of the new model to add predictive power are also discussed.

© 2019 European Association of Geoscientists & Engineers © 2018 European Association of Geoscientists & Engineers
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2018-12-27
2024-04-19

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References

  1. AgnolinI. and RouxJ.N.2007a. Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks. Physical Review E ‐ Statistical, Nonlinear, and Soft Matter Physics76, 1–27.
     [Google Scholar]
  2. AgnolinI. and RouxJ.N.2007b. Internal states of model isotropic granular packings. II. Compression and pressure cycles. Physical Review E ‐ Statistical, Nonlinear, and Soft Matter Physics76.
     [Google Scholar]
  3. AgnolinI. and RouxJ.N.2007c. Internal states of model isotropic granular packings. III. Elastic properties. Physical Review E ‐ Statistical, Nonlinear, and Soft Matter Physics76, 1–22.
     [Google Scholar]
  4. AleardiM. and CiabarriF.2017. Assessment of different approaches to rock‐physics modeling: a case study from offshore Nile Delta. Geophysics82.
     [Google Scholar]
  5. AleardiM., CiabarriF., GarceaB., PeruzzoF. and MazzottiA.2016. Probabilistic Seismic‐petrophysical Inversion Applied for Reservoir Characterization in Offshore Nile Delta. 78th EAGE Conference & Exhibition, Vienna, Austria, June 2016.
  6. BachrachR.2006. Joint estimation of porosity and saturation using stochastic rock‐physics modeling. Geophysics71, 053–063.
     [Google Scholar]
  7. BachrachR. and AvsethP.2008. Rock physics modeling of unconsolidated sands: accounting for nonuniform contacts and heterogeneous stress fields in the effective media approximation with applications to hydrocarbon exploration. Geophysics73, E197.
     [Google Scholar]
  8. BachrachR., DvorkinJ. and NurA.M.2000. Seismic velocities and Poisson's ratio of shallow unconsolidated sands. Geophysics65, 559–564.
     [Google Scholar]
  9. BoschM., BertorelliG., ÁlvarezG., MorenoA. and ColmenaresR.2015. Reservoir uncertainty description via petrophysical inversion of seismic data. The Leading Edge34, 1018–1026.
     [Google Scholar]
  10. BranchM.A., ColemanT.F. and LiY.1999. A subspace, interior, and conjugate gradient method for large‐scale bound‐constrained minimization problems. SIAM Journal on Scientific Computing21(1), 1–23.
     [Google Scholar]
  11. DomenicoS.N. 1977. Elastic properties of unconsolidated porous sand reservoirs. Geophysics42, 1339–1368.
     [Google Scholar]
  12. DuffautK., LandrøM. and SollieR.2010. Using Mindlin theory to model friction‐dependent shear modulus in granular media. Geophysics75, E143–E152.
     [Google Scholar]
  13. DuttaT. 2009. Integrating Sequence Stratigraphy and Rock Physics to Interpret Seismic Amplitudes and Predict Reservoir Quality. Stanford University.
     [Google Scholar]
  14. DuttaT., MavkoG. and MukerjiT.2010. Improved granular medium model for unconsolidated sands using coordination number, porosity, and pressure relations. Geophysics75, E91.
     [Google Scholar]
  15. JenkinsJ., JohnsonD., La RagioneL. and MakseH.2005. Fluctuations and the effective moduli of an isotropic, random aggregate of identical, frictionless spheres. Journal of the Mechanics and Physics of Solids53, 197–225.
     [Google Scholar]
  16. JiaX. and MillsP.2001. Sound propagation in dense granular materials. In: Powders and Grains 2001 (ed. Y.Kishino ) pp. 105–112. Rotterdam, France: Balkema.
     [Google Scholar]
  17. KhidasY. and JiaX.2012. Probing the shear‐band formation in granular media with sound waves. Physical Review E ‐ Statistical, Nonlinear, and Soft Matter Physics85, 1–6.
     [Google Scholar]
  18. KuwanoR. and JardineR.J.2002. On the applicability of cross‐anisotropic elasticity to granular materials at very small strains. Géotechnique52, 727–749.
     [Google Scholar]
  19. La RagioneL. and JenkinsJ.T.2007. The initial response of an idealized granular material. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences463, 735–758.
     [Google Scholar]
  20. MagnanimoV., La RagioneL., JenkinsJ.T., WangP. and MakseH.A.2008. Characterizing the shear and bulk moduli of an idealized granular material. Europhysics Letter81, 34006p 1–34006p6.
     [Google Scholar]
  21. MagnanimoV., RagioneL.La., JenkinsJ.T., WangP. and MakseH.2008. Characterizing the shear and bulk moduli of an idealized granular material. Europhysics Letters81, 34006.
     [Google Scholar]
  22. MakseH.A., GlandN., JohnsonD.L. and SchwartzL.2004a. Granular packings: nonlinear elasticity, sound propagation, and collective relaxation dynamics. Physical Review E ‐ Statistical, Nonlinear, and Soft Matter Physics70, 1–19.
     [Google Scholar]
  23. MakseH.A., GlandN., JohnsonD.L. and SchwartzL.2004b. Granular packings: Nonlinear elasticity, sound propagation, and collective relaxation dynamics. Physical Review E ‐ Statistical, Nonlinear, and Soft Matter Physics70, 1–21.
     [Google Scholar]
  24. MakseH.A., GlandN., JohnsonD.L. and SchwartzL.M.1999. Why effective medium theory fails in granular materials. Physical Review Letters83, 5070–5073.
     [Google Scholar]
  25. MavkoG., MukerjiT. and DvorkinJ.2009. The Rock Physics Handbook. Stanford University.
     [Google Scholar]
  26. McCallK.R. and GuyerR.A.1994. Equation of state and wave propagation in hysteretic nonlinear elastic materials. Journal of Geophysical Research99, 887–897.
     [Google Scholar]
  27. MurphyW.F.1982. Effects of Microstructure and Pore Fluids on the Acoustic Properties of Granular Sedimentary Materials. Stanford University.
     [Google Scholar]
  28. PrasadM.2002. Acoustic measurements in unconsolidated sands at low effective pressure and overpressure detection. Geophysics67, 405.
     [Google Scholar]
  29. PrasadM. and MeissnerR.1992. Attenuation mechanisms in sands: laboratory versus theoretical (Biot) data. Geophysics57, 710–719.
     [Google Scholar]
  30. PrasadM., ZimmerM.A., BergeP.A. and BonnerP.2004. Laboratory measurements of velocity and attenuation in sediments. In: Near‐surface Geophysics (ed D.K.Butler), pp.491–502. Stanford University.
     [Google Scholar]
  31. PrideS.R.2005. Relationships between seismic and hydrological properties. Hydrogeophysics, 253–290.
     [Google Scholar]
  32. PrideS.R. and BerrymanJ.G.2009. Goddard rattler‐jamming mechanism for quantifying pressure dependence of elastic moduli of grain packs. Acta Mechanica205, 185–196.
     [Google Scholar]
  33. RimstadK., AvsethP. and OmreH.2012. Hierarchical Bayesian lithology/fluid prediction: a north sea case study. Geophysics77, B69–B85.
     [Google Scholar]
  34. SainR.2010. Numerical Simulation of Pore‐Scale Heterogeneity and its Effects on Elastic, Electrical, and Transport Properties. Stanford University.
     [Google Scholar]
  35. SajevaA., CapaccioliS., ScarpelliniD. and MazzottiA.2017. Predicting the pressure dependence of elastic velocities of dry granular assemblies using a modified GCT model. 79th EAGE Conference and Exhibition 2017, Extended Abstract.
  36. SaulM.J. and LumleyD.E.2013. A new velocity‐pressure‐compaction model for uncemented sediments. Geophysical Journal International193, 905–913.
     [Google Scholar]
  37. SaulM., LumleyD. and ShraggeJ.2013. Modeling the pressure sensitivity of uncemented sediments using a modified grain contact theory: incorporating grain relaxation and porosity effects. Geophysics78, D327–D338.
     [Google Scholar]
  38. YinH.1992. Acoustic Velocity and Attenuation of Rocks: Isotropy, Intrinsic Anisotropy and Stress Induced Anisotropy. Stanford University.
     [Google Scholar]
  39. ZimmerM.A.2003. Seismic Velocities in Unconsolidated Sands: Measurements of Pressure, Sorting, and Compaction Effects. Stanford University.
     [Google Scholar]
  40. ZimmerM.A., PrasadM., MavkoG. and NurA.2007. Seismic velocities of unconsolidated sands: Part 1 — Pressure trends from 0.1 to 20 MPa. Geophysics72, E1.
     [Google Scholar]
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A semi‐empirical approach to model pressure dependence of elastic moduli in granular media accounting for variations of coordination‐number and Poisson‐ratio
Geophysical Prospecting 67, 872 (2019); https://doi.org/10.1111/1365-2478.12709
/content/journals/10.1111/1365-2478.12709
/content/journals/10.1111/1365-2478.12709
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  • Article Type: Research Article
Keyword(s): Granular media; Rock Physics; Ultrasonic velocities

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