Numerical simulation of ultrasonic waves in reservoir rocks with patchy saturation and fractal petrophysical properties

Computational Geosciences

Volumn 9, Issue 1, 2005, Pages 1-27

  Santos, J E ^a,b,c   Ravazzoli, C L ^a,b   Gauzellino, P M ^a   Carcione, J M ^d  

^a UNIVERSIDAD NACIONAL DE LA PLATA   (Argentina)

^b CONICET ^*  (Argentina)

^c PURDUE UNIVERSITY   (United States)

^d ISTITUTO NAZIONALE DI OCEANOGRAFIA E DI GEOFISICA SPERIMENTALE OGS   (Italy)

Author keywords

Finite elements; Fractals; Porous media; Reservoir geophysics

Indexed keywords

FINITE ELEMENT METHOD; FRACTAL ANALYSIS; HYDROCARBON RESERVOIR; NUMERICAL MODEL; POROSITY; SATURATION; ULTRASONICS;

EID: 25144515105     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10596-005-2848-9     Document Type: Article

References (48)

1. B. Arntsen and J.M. Carcione, Numerical simulation of the Biot slow wave in water-saturated Nivelsteiner sandstone, Geophys. 66 (2001) 890-896. 10.1190/1.1444978
2. J. Bear 1972 Dynamics of Fluids in Porous Media Dover, New York
3. J.G. Berryman 1982 Elastic waves in fluid saturated porous media Lecture Notes in Physics, Vol. 154 (Springer Berlin) 38-50
4. M.A. Biot, Theory of deformation of a porous viscoelastic anisotropic solid, J. Appl. Phys. 27 (1956) 459-467. 10.1063/1.1722402
5. M.A. Biot, Theory of propagation of elastic waves in a fluid-saturated porous solid I. Low frequency range, J. Acoust. Soc. Amer. 28 (1956) 168-171.
6. M.A. Biot, Theory of propagation of elastic waves in a fluid-saturated porous solid II. High frequency range, J. Acoust. Soc. Amer. 28 (1956) 179-191.
7. M.A. Biot, Mechanics of deformation and acoustic propagation in porous media, J. Appl. Phys. 33 (1962) 1482-1498. 10.1063/1.1728759
8. A. Brie, F. Pampuri, A. Marsala and O. Meazza, Shear sonic interpretation in gas-bearing sands, SPE Paper 30595 (1995) 701-710.
9. J.M. Carcione 2001 Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic and Porous Media Pergamon Press, Amsterdam
10. J.M. Carcione, F. Cavallini, J.E. Santos, C.L. Ravazzoli and P.M. Gauzellino, Wave propagation in partially saturated porous media: Simulation of a second slow wave, Wave Motion 39 (2004) 227-240. 10.1016/ j.wavemoti.2003.10.001
11. J.M. Carcione, H.B. Helle and N.H. Pham, White's model for wave propagation in partially saturated rocks: Comparison with poroelastic numerical experiments, Geophys. 68 (2003) 1389-1398. 10.1190/1.1598132
12. J. Douglas Jr. F. Furtado and F. Pereira 1995 The statistical behavior of instabilities in immiscible displacement subject to fractal geology A. Bourgeat C. Carasso S. Luckhaus A. Mikelic in: Mathematical Modelling of Flow through Porous Media (World Scientific Singapore) 115-137
13. J. Douglas, Jr., F. Furtado and F. Pereira, On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs, Comput. Geosci. 1 (1997) 155-190. 10.1023/A:1011565228179
14. J. Douglas, Jr., P.L. Paes Leme, J.E. Roberts and J. Wang, A parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods, Numer. Math. 65 (1993) 95-108. 10.1007/BF01385742
15. J. Douglas Jr. F. Pereira and J. Santos 1995 A domain decomposition approach to the simulation of waves in dispersive media ed. G. Cohen in: Proc. of the 3rd Internat. Conf. on Wave Propagation Phenomena SIAM Philadelphia, PA 673-682
16. J. Douglas, Jr., J.E. Santos and D. Sheen, Approximation of scalar waves in the space-frequency domain, Math. Models Methods Appl. Sci. 4 (1994) 509-531. 10.1142/S0218202594000297
17. J. Douglas, Jr., J.E. Santos and D. Sheen, Nonconforming Galerkin methods for the Helmholtz equation, Numer. Methods Partial Differential Equations 17 (2001) 475-494. 10.1002/num.1023
18. J. Douglas, Jr., J.E. Santos, D. Sheen and L. Bennethum, Frequency domain treatment of one-dimensional scalar waves, Math. Models Methods Appl. Sci. 3 (1993) 171-194. 10.1142/S0218202593000102
19. J. Douglas, Jr., J.E. Santos, D. Sheen and X. Ye, Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems, RAIRO Math. Modeling Numer. Anal. 33 (1999) 747-770. 10.1051/ m2an:1999161
20. N.C. Dutta and H. Odé, Seismic reflections from a gas-water contact, Geophys. 48 (1983) 148-162. 10.1190/1.1441454
21. J. Dvorkin, D. Moos, J. Packwood and A. Nur, Identifying patchy saturation from well logs, Geophys. 64 (1999) 1756-1759. 10.1190/ 1.1444681
22. J. Dvorkin and A. Nur, Acoustic signatures of patchy saturation, Internat. J. Solids Struct. 35 (1998) 4803-4810. 10.1016/ S0020-7683(98)00095-X
23. A. Frankel and R.W. Clayton, Finite difference simulation of seismic wave scattering: Implications for the propagation of short period seismic waves in the crust and models of crustal heterogeneity, J. Geophys. Res. 91 (1986) 6465-6489.
24. F. Gassmann, über die Elastizität poröser Medien, Vierteljahrsschrift der Naturforschenden Gessellschaft in Zurich 96 (1951) 1-23.
25. P.M. Gauzellino, J.E. Santos and D. Sheen, Frequency domain wave propagation modeling in exploration seismology, J. Comput. Acoustics 9 (2001) 941-955.
26. T. Ha, J.E. Santos and D. Sheen, Nonconforming finite element methods for the simulation of waves in viscoelastic solids, Comput. Methods Appl. Mech. Engrg. 191 (2002) 5647-5670. 10.1016/S0045-7825(02)00469-3
27. H.B. Helle, N.H. Pham and J.M. Carcione, Velocity and attenuation in partially saturated rocks - Poroelastic numerical experiments, Geophys. Prospecting 51 (2003) 551-566. 10.1046/j.1365-2478.2003.00393.x
28. J.L. Hensley, J. Douglas, Jr. and J.E. Santos, Dispersion of type II Biot waves in inhomogeneous media, in: Proc. of the 6th Internat. Conf. on Mathematical Methods in Engineering, Czechoslovakia (1991) pp. 67-83.
29. J.M. Hovem and G.D. Ingram, Viscous attenuation of sound in saturated sand, J. Acoust. Soc. Amer. 66 (1979) 1807-1812.
30. O. Kelder and D. Smeulders, Observation of the Biot slow wave in water-saturated Nivelsteiner sandstone, Geophys. 62 (1997) 1794-1796. 10.1190/1.1444279
31. R. Knight, J. Dvorkin and A. Nur, Acoustic signatures of partial saturation, Geophys. 63 (1998) 132-138. 10.1190/1.1444305
32. H.P. Liu, D.L. Anderson and H. Kanamori, Velocity dispersion due to anelasticity; implications for seismology and mantle composition, Geophys. J. Roy. Astr. Soc. 47 (1976) 41-58.
33. 3, Numer. Math. 35 (1980) 315-341. 10.1007/BF01396415
34. H. Pape, C. Clauser and J. Iffland, Permeability prediction based on fractal pore-space geometry, Geophys. 64 (1999) 1447-1460. 10.1190/ 1.1444649
35. D.W. Peaceman 1977 Fundamentals of Numerical Reservoir Simulation Elsevier Amsterdam
36. C.L. Ravazzoli, J.E. Santos and J.M. Carcione, Acoustic and mechanical response of reservoir rocks under variable saturation and effective pressure, J. Acoust. Soc. Amer. 113 (2003) 1801-1811. 10.1121/1.1554696
37. P.A. Raviart and J.M. Thomas 1975 Mixed finite element method for 2nd order elliptic problems in: Mathematical Aspects of the Finite Element Methods Lecture Notes in Mathematics 606 Springer New York
38. J.E. Santos, J.M. Corberó, C.L. Ravazzoli and J.L. Hensley, Reflection and transmission coefficients in fluid saturated porous media, J. Acoust. Soc. Amer. 91 (1992) 1911-1923.
39. J.E. Santos, J. Douglas, Jr. and J. Corberó, Static and dynamic behaviour of a porous solid saturated by a two-phase fluid, J. Acoust. Soc. Amer. 87 (1990) 1428-1438.
40. J.E. Santos, J. Douglas, Jr., J.M. Corberó and O.M. Lovera, A model for wave propagation in a porous medium saturated by a two-phase fluid, J. Acoust. Soc. Amer. 87 (1990) 1439-1448.
41. J.E. Santos, P.M. Gauzellino and C.L. Ravazzoli, Numerical simulation of waves in poroviscoelastic rocks saturated by immiscible fuids, in: Mecánica Computacional, Vol. 21, eds. S.R. Idelsohn, V.E. Sonzogni and A. Cardona (2002) pp. 652-669.
42. J.E. Santos, C.L. Ravazzoli, P.M. Gauzellino, J.M. Carcione and F. Cavallini, Simulation of waves in poro-viscoelastic rocks saturated by inmiscible fluids. Numerical evidence of a second slow wave, J. Comput. Acoustics 12 (2004) 1-21. 10.1142/S0218396X04002195
43. A.E. Scheidegger 1974 The Physics of Flow through Porous Media Univ. of Toronto Toronto
44. D. Sheen, Finite element methods for an acoustic well-logging problem associated with a porous medium saturated by a two-phase immiscible fluid, Numer. Methods Partial Differential Equations 9 (1993) 155-174. MR1203059
45. J.E. White, Computed seismic speeds and attenuation in rocks with partial gas saturation, Geophys. 40 (1975) 224-232. 10.1190/1.1440520
46. J. Yarus and R. Chambers, Stochastic modeling and geostatistics. Principles, methods and case studies, in: AAPG Computer Applications in Geology 64 (1995).
47. H. Yin, Acoustic velocity and attenuation of rocks: Isotropy, intrinsic anisotropy and stress-induced anisotropy, Ph.D. thesis, Stanford University (1993).
48. F.I. Zyserman, P.M. Gauzellino and J.E. Santos, Dispersion analysis of a non-conforming finite element method for the Helmholtz and elastodynamic equations, Internat. J. Numer. Methods Engrg. 58 (2003) 1381-1395. 10.1002/nme.822