1887
Volume 50 Number 6
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

We obtain the wave velocities and quality factors of clay‐bearing sandstones as a function of pore pressure, frequency and partial saturation. The model is based on a Biot‐type three‐phase theory that considers the coexistence of two solids (sand grains and clay particles) and a fluid mixture. Additional attenuation is described with the constant‐ model and viscodynamic functions to model the high‐frequency behaviour. We apply a uniform gas/fluid mixing law that satisfies the Wood and Voigt averages at low and high frequencies, respectively. Pressure effects are accounted for by using an effective stress law. By fitting a permeability model of the Kozeny– Carman type to core data, the model is able to predict wave velocity and attenuation from seismic to ultrasonic frequencies, including the effects of partial saturation. Testing of the model with laboratory data shows good agreement between predictions and measurements.

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2002-11-18
2024-04-26
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References

  1. BearJ. and BachmatY.1990. Introduction to Modeling of Transport Phenomena in Porous Media.Kluwer Academic Publishers.
    [Google Scholar]
  2. BerrymanJ.G.1992. Effective stress for transport properties of inhomogeneous porous rock. Journal of Geophysical Research97, 17409 – 17424.
    [Google Scholar]
  3. BerrymanJ.G., ThigpenL. and ChinR.C.Y.1988. Bulk wave propagation for partially saturated porous solids. Journal of the Acoustical Society of America84, 360 – 373.
    [Google Scholar]
  4. BestA.I., McCannC. and SothcottJ.1994. The relationships between the velocities, attenuation and petrophysical properties of reservoir sedimentary rocks. Geophysical Prospecting42, 151 – 178.
    [Google Scholar]
  5. BiotM.A.1962. Mechanics of deformation and acoustic propagation in porous media.Journal of Applied Physics33, 1482 – 1498.
    [Google Scholar]
  6. BlandD.R.1960. The Theory of Linear Viscoelasticity. Pergamon Press, Inc.
    [Google Scholar]
  7. BourbiéT., CoussyO. and ZinsznerB.1987. Acoustics of Porous Media. Éditions Technip.
    [Google Scholar]
  8. BrieA., PampuriF., MarsalaA.F. and MeazzaO.1995. Shear sonic interpretation in gas‐bearing sands. SPE Annual Technical Conference #30595,701 – 710.
  9. CadoretT., MarionD. and ZinsznerB.1995. Influence of frequency and fluid distribution on elastic wave velocities in partially saturated limestones.Journal of Geophysical Research100, 9789 – 9803.
    [Google Scholar]
  10. CarcioneJ.M.1998. Viscoelastic effective rheologies for modelling wave propagation in porous media.Geophysical Prospecting46, 249 – 270.
    [Google Scholar]
  11. CarcioneJ.M.2001a. Energy balance and fundamental relations in dynamic anisotropic poro‐viscoelasticity.Proceedings of the Royal Society of London A457, 331 – 348.
    [Google Scholar]
  12. CarcioneJ.M.2001b. Wave fields in real media: wave propagation in anisotropic, anelastic and porous media.Handbook of Geophysical Exploration31. Pergamon Press, Inc.
    [Google Scholar]
  13. CarcioneJ.M., CavalliniF., MainardiF. and HanygaA.2001a. Time‐domain seismic modeling of constant‐Q wave propagation using fractional derivatives.PAGEOPH159, 1719 – 1736.
    [Google Scholar]
  14. CarcioneJ.M. and GangiA.2000a. Non‐equilibrium compaction and abnormal pore‐fluid pressures: effects on seismic attributes.Geophysical Prospecting48, 521 – 537.
    [Google Scholar]
  15. CarcioneJ.M. and GangiA.2000b. Gas generation and overpressure: effects on seismic attributes.Geophysics65, 1769 – 1779.
    [Google Scholar]
  16. CarcioneJ.M., GurevichB. and CavalliniF.2000. A generalized Biot–Gassmann model for the acoustic properties of clayey sandstones. Geophysical Prospecting48, 539 – 557.
    [Google Scholar]
  17. CarcioneJ.M., HelleH.B., PhamN.H. and ToverudT.2001b. Pore pressure estimation from seismic reflection data.Geophysics, in press.
    [Google Scholar]
  18. CoynerK.B.1984. Effects of stress, pore pressure, and pore fluids on bulk strain, velocity, and permeability of rocks. PhD thesis, MIT, Cambridge, MA.
    [Google Scholar]
  19. DullienF.A.L.1991. One and two phase flow in porous media and pore structure. In: Physics of Granular Media (eds D. Bideau and J. Dodds ), pp. 173 – 214.Science Publishers, Inc., New York.
    [Google Scholar]
  20. DvorkinJ., Nolen‐HoeksemaR. and NurA.1994. The squirt‐flow mechanism: macroscopic description.Geophysics59, 428 – 438.
    [Google Scholar]
  21. FedorovF.I.1968. Theory of Elastic Waves in Crystals.Plenum Press.
    [Google Scholar]
  22. GoldbergI. and GurevichB.1998. A semi‐empirical velocity‐porosity‐clay model for petrophysical interpretation of P‐ and S‐velocities.Geophysical Prospecting46, 271 – 285.
    [Google Scholar]
  23. HashinZ. and ShtrikmanS.1963. A variational approach to the elastic behaviour of multiphase materials.Journal of the Mechanics and Physics of Solids11, 127 – 140.
    [Google Scholar]
  24. HelleH.B., BhattA. and UrsinB.2001. Porosity and permeability from wireline logs using artificial neural networks: a North Sea case study.Geophysical Prospecting49, 431 – 444.
    [Google Scholar]
  25. HudsonJ.A.1988. Seismic wave propagation through materials containing partially saturated cracks.Geophysical Journal International92, 33 – 37.
    [Google Scholar]
  26. HudsonJ.A., LiuE. and CrampinS.1996. The mechanical properties of materials with interconnected cracks and pores.Geophysical Journal International124, 105 – 112.
    [Google Scholar]
  27. JohnsonD.L., KoplikJ. and DashenR.1987. Theory of dynamic permeability and tortuosity in fluid‐saturated porous media.Journal of Fluid Mechanics176, 379 – 402.
    [Google Scholar]
  28. KellerJ.D.1989. Acoustic wave propagation in composite fluid‐saturated media.Geophysics54, 1554 – 1563.
    [Google Scholar]
  29. KingM.S., MarsdenJ.R. and DennisJ.W.2000. Biot dispersion for P‐ and S‐wave velocities in partially and fully saturated sandstones.Geophysical Prospecting48, 1075 – 1089.
    [Google Scholar]
  30. KjartanssonE.1979. Constant‐Q wave propagation and attenuation.Journal of Geophysical Research84, 4737 – 4748.
    [Google Scholar]
  31. KlimentosT. and McCannC.1988. Why is the Biot slow compressional wave not observed in real rocks?Geophysics12, 1605 – 1609.
    [Google Scholar]
  32. KlimentosT. and McCannC.1990. Relationships among compressional wave attenuation, porosity, clay content, and permeability in sandstones.Geophysics55, 998 – 1014.
    [Google Scholar]
  33. KnightR. and DvorkinJ.1992. Seismic and electrical properties of sandstones at low saturations.Journal of Geophysical Research97, 17425 – 17432.
    [Google Scholar]
  34. KriefM., GaratJ., StellingwerffJ. and VentreJ.1990. A petrophysical interpretation using the velocities of P and S waves (full waveform sonic).The Log Analyst31, 355 – 369.
    [Google Scholar]
  35. MavkoG. and MukerjiT.1998. Bounds on low‐frequency seismic velocities in partially saturated rocks.Geophysics63, 918 – 924.
    [Google Scholar]
  36. MavkoG., MukerjiT. and DvorkinJ.1998. The Rock Physics Handbook: Tools for Seismic Analysis in Porous Media.Cambridge University Press.
    [Google Scholar]
  37. MavkoG. and NurA.1997. Effect of a percolation threshold in the Kozeny–Carman relation. Geophysics62, 1480 – 1482.
    [Google Scholar]
  38. MurphyW.F.1982. Effect of partial water saturation on attenuation of Massilon sandstone and Vycor porous glass.Journal of the Acoustical Society of America71, 1458 – 1468.
    [Google Scholar]
  39. PointerT., LiuE. and HudsonJ.A.2000. Seismic wave propagation in cracked porous media.Geophysical Journal International142, 199 – 231.
    [Google Scholar]
  40. Scott‐BlairG.W.1949. Survey of General and Applied Rheology. Pitman.
    [Google Scholar]
  41. StollR.D. and BryanG.M.1970. Wave attenuation in saturated sediments.Journal of the Acoustical Society of America47, 1440 – 1447.
    [Google Scholar]
  42. TejaA.S. and RiceP.1981a. Generalized corresponding states method for viscosities of liquid mixtures. Industrial and Engineering Chemistry: Fundamentals20, 77 – 81.
    [Google Scholar]
  43. TejaA.S. and RiceP.1981b. The measurement and prediction of the viscosities of some binary liquid mixtures containing n‐hexane.Chemical Engineering Science36, 7 – 10.
    [Google Scholar]
  44. Van GenuchtenM.T.1978. Calculating the unsaturated hydraulic conductivity with a closed form analytical model. Report 78‐WR‐08, Princeton University, NJ.
    [Google Scholar]
  45. WhiteJ.E.1975. Computed seismic speeds and attenuation in rocks with partial gas saturation. Geophysics40, 224 – 232.
    [Google Scholar]
  46. WorthingtonP.F.1991. Reservoir characterization at the mesoscopic scale. In: Reservoir Characterization II (eds L.W.Lake et al.), pp.123 – 165. Academic Press, Inc.
    [Google Scholar]
  47. YinC.S., BatzleM.L. and SmithB.J.1992. Effects of partial liquid/gas saturation on extensional wave attenuation in Berea sandstone.Geophysical Research Letters19, 1399 – 1402.
    [Google Scholar]
  48. ZimmermanR.W.1991. Compressibility of Sandstones. Elsevier Science Publishing Co.
    [Google Scholar]
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