Wave propagation through elastic porous media containing two immiscible fluids

Water Resources Research

Volumn 41, Issue 2, 2005, Pages 1-20

  Lo, Wei Cheng ^a,b,c   Sposito, Garrison ^a,b   Majer, Ernest ^b  

^a Berkeley   (United States)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

^c NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

AQUIFERS; ATTENUATION; COMPUTER SIMULATION; PARTIAL DIFFERENTIAL EQUATIONS; POROUS MATERIALS; SATURATION (MATERIALS COMPOSITION); SOLUBILITY; VISCOSITY; WAVE PROPAGATION;

ELASTIC POROUS MEDIA; IMMISCIBLE FLUIDS; INERTIAL COUPLING; POROELASTIC BEHAVIOR;

GROUNDWATER;

IMMISCIBLE FLUIDS; POROELASTICITY; POROUS MEDIUM; WAVE PROPAGATION;

ACOUSTIC WAVE; IMMISCIBLE FLUID; POROELASTICITY; POROUS MEDIUM; WAVE PROPAGATION;

EID: 15444368124     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2004WR003162     Document Type: Article

References (63)

1. Bear, J. (1988), Dynamics of Fluids in Porous Media, Dover, Mineola, N. Y.
2. Beresnev, I. A., and P. A. Johnson (1994), Elastic-wave stimulation of oil production: A review of methods and results, Geophysics, 59(6), 1000-1017.
3. Berryman, J. G. (1980), Confirmation of Biot's theory, Appl. Phys. Lett., 37(4), 382-384.
4. Berryman, J. G. (1983), Effective conductivity by fluid analogy for a porous insulator filled with a conductor, Phys. Rev. B, 27(12), 7789-7792.
5. Berryman, J. G., L. Thigpen, and R. C. Y. Chin (1988), Bulk elastic wave propagation in partially saturated porous solids, J. Acoust. Soc. Am., 84(1), 360-373.
6. Biot, M. A. (1956a), Theory of propagation of elastic waves in a fluid-saturated porous solid, I. Low-frequency range, J. Acoust. Soc. Am., 28(2), 168-178.
7. Biot, M. A. (1956b), Theory of propagation of elastic waves in a fluid-saturated porous solid, II. Higher frequency range, J. Acoust. Soc. Am., 28(2), 179-191.
8. Biot, M. A. (1962), Mechanics of deformation and acoustic propagation in porous media, J. Appl. Phys., 33(4), 1482-1498.
9. Biot, M. A., and D. G. Willis (1957), The elastic coefficients of the theory of consolidation, J. Appl. Mech., 24, 594-601.
10. Brooks, R. H., and A. T. Corey (1964), Hydraulic properties of porous media, Hydrol. Pap. 3, Civ. Eng. Dep., Colo. State Univ., Fort Collins.
11. Brutsaert, W. (1964), The propagation of elastic waves in unconsolidated unsaturated granular mediums, J. Geophys. Res., 69(2), 243-257.
12. Burdine, N. T. (1953), Relative permeability calculations from pore size distribution data, Trans. Am. Inst. Min. Metall. Pet. Eng., 198, 71-77.
13. Chen, J., J. W. Hopmans, and M. E. Grismer (1999), Parameter estimation of two-fluid capillary pressure-saturation and permeability functions, Adv. Water Resour., 22(5), 479-493.
14. Cosenza, P., M. Ghoreychi, G. de Marsily, G. Vasseur, and S. Violette (2002), Theoretical prediction of poroelastic properties of argillaceous rocks from in situ specific storage coefficient, Water Resour. Res., 35(10), 1207, doi:10.1029/2001WR001201.
15. Coussy, O., L. Dormieux, and E. Detournay (1998), From mixture theory to Biot's approach for porous media, Int. J. Solids Struct., 35(34/35), 4619-4635.
16. Das, B. M. (1997), Advanced Soil Mechanics, Taylor and Francis, Philadelphia, Pa.
17. de la Cruz, V., P. N. Sahay, and T. J. T. Spanos (1993), Thermodynamics of porous media, Proc. R. Soc. London, Ser. A, 443, 247-255.
18. de Marsily, G. (1986), Quantitative Hydrogeology: Groundwater Hydrology for Engineers, Elsevier, New York.
19. Drew, D. A., and R. T. Lahey (1979), Application of general constitutive principles to the derivation of multidimensional two-phase flow equations, Int. J. Multiphase Flow, 5(4), 243-264.
20. Drew, D., L. Cheng, and R. T. Lahey (1979), The analysis of virtual mass effects in two-phase flow, Int. J. Multiphase Flow, 5(4), 233-242.
21. Dullien, F. L. A. (1992), Porous Media: Fluid Transport and Pore Structure, Elsevier, New York.
22. Ehrlich, R. (1993), Viscous coupling in two-phase flow in porous media and its effect on relative permeabilities, Transp. Porous Media, 11, 201-218.
23. Fetter, C. W. (1999), Contaminant Hydrogeology, Prentice-Hall, Upper Saddle River, N. J.
24. Gambolati, G., P. Teatini, D. Baú, and M. Ferronato (2000), Importance of poroelastic coupling in dynamically active aquifers of the Po River basin, Italy, Water Resour. Res., 36(9), 2443-2459.
25. Garg, S. K., and A. H. Nayfeh (1986), Compressional wave propagation in liquid and/or gas saturated elastic porous media, J. Appl. Phys., 60(9), 3045-3055.
26. Geller, J. T., and L. R. Myer (1995), Ultrasonic imaging of organic liquid contaminants in unconsolidated porous media, J. Contam. Hydrol., 19(2), 85-104.
27. Graff, K. F. (1975), Wave Motion in Elastic Solids, Dover, Mineola, N. Y.
28. Gray, W. G. (1983), General conservation equations for multi-phase systems: 4. Constitutive theory including phase change, Adv. Water Resour., 6, 130-140.
29. Gray, W. G. (1999), Thermodynamics and constitutive theory for multi-phase porous-media flow considering internal geometric constraints, Adv. Water Resour., 22(5), 521-547.
30. Hillel, D. (1980), Fundamentals of Soil Physics, Elsevier, New York.
31. Johnson, D. L. (1986), Recent developments in the acoustic properties of porous media, in Proceedings of the International School of Physics "Enrico Fermi" Course XCIII, Frontiers in Physical Acoustics, edited by D. Sette, pp. 255-290, Elsevier, New York.
32. Johnson, D. L., T. J. Plona, C. Scala, F. Pasierb, and H. Kojima (1982), Tortuosity and acoustic slow waves, Phys. Rev. Lett., 49(25), 840-844.
33. Jury, W. A., W. R. Gardner, and W. H. Gardner (1991), Soil Physics, John Wiley, Hoboken, N. J.
34. Kouznetsov, O. L., E. M. Simkin, G. V. Chilingar, and S. A. Katz (1998), Improved oil recovery by application of vibro-energy to waterflooded sandstones, J. Pet. Sci. Eng., 19(3-4), 191-200.
35. Lake, L. W. (1989), Enhanced Oil Recovery, Prentice-Hall, Upper Saddle River, N. J.
36. Lamb, H. (1945), Hydrodynamics, Dover, Mineola, N. Y.
37. Levy, M. (2001), Elastic properties of solids: Theory, elements and compounds, novel materials, technological materials, alloys, and building materials, in Handbook of Elastic Properties of Solids, Liquids, and Gases, vol. II, pp. 27-29, Elsevier, New York.
38. Lewis, R. W., and B. A. Schrefler (1998), The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media, John Wiley, Hoboken, N. J.
39. Li, X., L. Zhong, and L. J. Pyrak-Nolte (2001), Physics of partially saturated porous media: Residual saturation and seismic-wave propagation, Annu. Rev. Earth Planet. Sci., 29, 419-460.
40. Lin, Y.-B., Y.-C. Tan, T.-C. J. Yeh, C.-W. Liu, and C.-H. Chen (2004), A viscoelastic model for groundwater level changes in the Cho-Shui River alluvial fan after the Chi-Chi earthquake in Taiwan, Water Resour. Res., 40, W04213, doi:10.1029/2003WR002412.
41. Lo, W.-C., G. Sposito, and E. Majer (2002), Immiscible two-phase fluid flows in deformable porous media, Adv. Water Resour., 25(8-12), 1105-1117.
42. Love, A. E. H. (1934), A Treatise on the Mathematical Theory of Elasticity, Cambridge Univ. Press, New York.
43. Mavko, R., and A. Nur (1975), Melt squirt in asthenosphere, J. Geophys. Res., 80(11), 1444-1448.
44. Mualem, Y. (1976), A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res., 12(3), 513-522.
45. Plona, T. J. (1980), Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies, Appl. Phys. Lett., 36(4), 259-261.
46. Pride, S. R., and J. G. Berryman (1998), Connecting theory of experiment in poroelasticity, J. Mech. Phys. Solids, 46(4), 719-747.
47. Pride, S. R., A. F. Gangi, and F. D. Morgan (1992), Deriving the equations of motion for porous isotropic media, J. Acoust. Soc. Am., 92(6), 3278-3290.
48. Roberts, P. M., A. Sharma, V. Uddameri, M. Monagle, D. E. Dale, and L. K. Steck (2001), Enhanced DNAPL transport in a sand core during dynamic stress stimulation, Environ. Eng. Sci., 18(2), 67-79.
49. Rossi, C., and J. R. Nimmo (1994), Modeling of soil water retention from saturation to oven dryness, Water Resour. Res., 30(3), 701-708.
50. Santos, J. E., J. M. Corbero, and J. Douglas (1990a), Static and dynamic behavior of a porous solid saturated by a two-phase fluid, J. Acoust. Soc. Am., 87(4), 1428-1438.
51. Santos, J. E., J. Douglas, J. Corbero, and O. M. Lovera (1990b), A model for wave propagation in a porous medium saturated by a two-phase fluid, J. Acoust. Soc. Am., 87(4), 1439-1448.
52. Santos, J. E., C. L. Ravazzoli, P. M. Gauzellino, J. M. Carcione, and F. Cavallini (2004), Simulation of waves in poro-viscoelastic rocks saturated by immiscible fluids. Numerical evidence of a second slow wave, J. Comput. Acoust., 12(1), 1-21.
53. Schrefler, B. A., and X. Y. Zhan (1991), A fully coupled model for water-flow and air-flow in deformable porous-media, Water Resour. Res., 29(1), 155-167.
54. Seifert, P. K., J. T. Geller, and L. R. Johnson (1998), Effect of P-wave scattering on velocity and attenuation in unconsolidated sand saturated with immiscible liquids, Geophysics, 63(1), 161-170.
55. Stoll, R. D. (1974), Acoustic waves in saturated sediments, Physics of Sound in Marine Sediments, edited by L. Hampton, pp. 19-39, Springer, New York.
56. Truesdell, C. (1984), Rational Thermodynamics, Springer, New York.
57. Tuncay, K., and M. Y. Corapcioglu (1996), Body waves in poroelastic media saturated by two immiscible fluids, J. Geophys. Res., 111(B11), 25,149-25,159.
58. Tuncay, K., and M. Y. Corapcioglu (1997), Wave propagation in poroelastic media saturated by two fluids, J. Appl. Mech., 64(2), 313-320.
59. van Genuchten, M. T. (1980), A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44(5), 892-898.
60. Wang, H. F. (2000), Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology, Princeton Univ. Press, Princeton, N. J.
61. Wei, C., and K. K. Muraleetharan (2002), A continuum theory of porous media saturated by multiple immiscible fluids: I. Linear poroelasticity, Int. J. Eng. Sci., 40, 1807-1833.
62. Whitaker, S. (1973), Transport equations for multiphase system, Chem. Eng. Sci., 28(1), 139-147.
63. Yuster, S. T. (1951), Theoretical considerations of multiphase flow in idealized capillary systems, Proc. World Pet. Congr., 3, 436-445.