Seismic Reflection from an Interface Between an Elastic Solid and a Fractured Porous Medium with Partial Saturation
Tóm tắt
The theory of Tuncay and Corapcioglu (Transp Porous Media 23:237–258, 1996a) has been employed to investigate the possibility of plane wave propagation in a fractured porous medium containing two immiscible fluids. Solid phase of the porous medium is assumed to be linearly elastic, isotropic and the fractures are assumed to be distributed isotropically throughout the medium. It has been shown that there can exist four compressional waves and one rotational wave. The phase speeds of these waves are found to be affected by the presence of fractures, in general. Of the four compressional waves, one arises due to the presence of fractures in the medium and the remaining three are those encountered by Tuncay and Corapcioglu (J Appl Mech 64:313–319, 1997). Reflection and transmission phenomena at a plane interface between a uniform elastic half-space and a fractured porous half-space containing two immiscible fluids, are analyzed due to incidence of plane longitudinal/transverse wave from uniform elastic half-space. Variation of modulus of amplitude and energy ratios with the angle of incidence are computed numerically by taking the elastic half-space as granite and the fractured porous half-space as sandstone material containing non-viscous wetting and non-wetting fluid phases. The results obtained in case of porous half-space with fractures, are compared graphically with those in case of porous half-space without fractures. It is found that the presence of fractures in the porous half-space do affect the reflection/transmission of waves, which is responsible for raising the reflection and lowering the transmission coefficients.
Tài liệu tham khảo
Achenbach J.D.: Wave Propagation in Elastic Solids. North-Holland Publishing Co., Amsterdam (1973)
Arora A., Tomar S.K.: The effect of inertial coupling on seismic reflection amplitudes. Geophys. Prospect. 56(5), 643–654 (2008)
Bai M.: On equivalence of dual-porosity poroelastic parameters. J. Geophys. Res. 104, 10461–10466 (1999)
Bai M., Elsworth D., Roegiers J.-C.: Modeling of naturally fractured reservoirs using deformation dependent flow mechanism. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 30, 1185–1191 (1993a)
Bai M., Elsworth D., Roegiers J.-C.: Multiporosity/multipermeability approach to the simulation of naturally fractured reservoirs. Water Resour. Res. 29, 1621–1633 (1993b)
Barenblatt G.I.: On certain boundary value problems for the equations of seepage of a liquid in fissured rocks. J. Appl. Math. Mech. 27, 513–518 (1963)
Barenblatt, G.I., Zheltov, Yu.P.: Fundamental equations of filtration of homogeneous liquids in fissured rocks, Sov. Phys. Doklady 5, 522–525 (1960a) [English translation of: Doklady Akademii Nauk SSSR. 132, 545–548]
Barenblatt G.I., Zheltow I.P., Kochina T.N.: Basic concept in the theory of seepage of homogeneous liquids in fissured rocks. J. Appl. Math. Mech. 24, 1286–1303 (1960b)
Berryman J.G.: Confirmation of Biot’s theory. Appl. Phys. Lett. 37, 382–384 (1980)
Berryman J.G.: Elastic wave propagation in fluid saturated porous media. J. Acoust. Soc. Am. 69, 416–424 (1981)
Berryman J.G., Wang H.F.: The elastic coefficients of double porosity models for fluid transport in jointed rock. J. Geophys. Res. 100, 24611–24628 (1995)
Berryman J.G., Wang H.F.: Elastic wave propagation and attenuation in a double-porosity dual-permeability medium. Int. J. Rock Mech. Min. Sci. 37, 63–78 (2000)
Beskos D.E.: Dynamics of saturated rocks-I: equations of motion. J. Eng. Mech. ASCE 115, 983–995 (1989)
Beskos D.E., Aifantis E.C.: On the theory of consolidation with double porosity-II. Int. J. Eng. Sci. 24, 1697–1716 (1986)
Beskos D.E., Vgenopoulou I., Providakis C.P.: Dynamics of saturated rocks-II: body forces. J. Eng. Mech. ASCE 115, 996–1016 (1989a)
Beskos D.E., Providakis C.P., Woo H.S.: Dynamics of saturated rocks-III: Rayleigh waves. J. Eng. Mech., ASCE 115, 1017–1034 (1989b)
Biot M.A.: General solutions of the equations of elasticity and consolidation for a porous material. J. Appl. Mech. 23, 91–95 (1956a)
Biot M.A.: Theory of propagation of elastic waves in a fluid saturated porous solid. J. Acoust. Soc. Am. 28, 158–191 (1956b)
Biot M.A.: Mechanics of deformation and acoustic wave propagation in porous media. J. Appl. Phys. 33, 1482–1498 (1962)
Chin R.C.Y., Berryman J.G., Hedstrom G.W.: Generalized ray expansion for pulse-propagation and attenuation in fluid-saturated porous media. Wave Motion 7, 43–65 (1985)
Cho T.F., Plesha M.E., Haimson B.C.: Continuum modeling of jointed porous rock. Int. J. Numer. Anal. Methods Geomech. 15, 333–353 (1991)
Dai Z.-J., Kuang Z.-B., Zhao S-X.: Reflection and transmission of elastic waves at interface between an elastic solid and a double porosity medium. Int. J. Rock Mech. Min. Sci. 43, 961–971 (2006)
de la Cruz V., Hube J., Spanos T.J.T.: Reflection and transmission of seismic waves at the boundaries of porous media. Wave Motion 16, 323–338 (1992)
Deresiewicz H.: The effect of boundaries on wave propagation in a liquid-filled porous solid-I. Bull. Seism. Soc. Am. 50, 599–607 (1960)
Deresiewicz H., Levy A.: The effect of boundaries on wave propagation in a liquid-filled porous solid-II: Transmission through a stratified medium. Bull. Seism. Soc. Am. 57, 381–392 (1967)
Deresiewicz H., Rice J.T.: The effect of boundaries on wave propagation in a liquid-filled porous solid-III: Reflection of plane waves at a free plane boundary. Bull. Seism. Soc. Am. 52, 595–626 (1962)
Deresiewicz H., Rice J.T.: The effect of boundaries on wave propagation in a liquid-filled porous solid-V: Transmission across plane interface. Bull. Seism. Soc. Am. 54, 409–416 (1964)
Deresiewicz H., Skalak R.: On uniqueness in dynamic poroelasticity. Bull. Seism. Soc. Am. 53, 783–789 (1963)
Dutta N.C., Ode H.: Seismic reflection from a gas-water contact. Geophysics 48, 162–184 (1983)
Geertsma J.: The effect of fluid pressure decline on volumetric changes of porous rocks. Trans. AIME 210, 331–340 (1957)
Geertsma J., Smit D.C.: Some aspects of elastic wave propagation in a fluid saturated porous solids. Geophysics 26(2), 169–181 (1961)
Hajra S., Mukhopadhyay A.: Reflection and refraction of seismic waves incident obliquely at the boundary of a liquid-saturated porous solid. Bull. Seism. Soc. Am. 72, 1509–1533 (1982)
Kazemi H.: Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution. Soc. Petrol. Eng. J. 9, 451–462 (1969)
Khaled M.Y., Beskos D.E., Aifantis E.C.: On the theory of consolidation with double porosity-III: a finite-element formulation. Int. J. Numer. Anal. Methods Geomech. 8, 101–123 (1984)
Lewallen K.T., Wang H.F.: Consolidation of a double-porosity medium. Int. J. Solids Struct. 35, 4845–4867 (1998)
Lin C.-H., Lee V.W., Trifunac M.D.: The reflection of plane waves in a poroelastic half-space saturated with inviscid fluid. Soil Dyn. Earthq. Eng. 25(3), 205–223 (2005)
Lo, W.-C., Sposito, G., Majer, E.: Wave propagation through elastic porous media containing two immiscible fluids, Water Resour. Res. 41, W02025 (2005). doi:10.1029/2004WR003162
Nilson R.H., Lie K.H.: Double-porosity modelling of oscillatory gas motion and contaminant transport in a fractured porous medium. Int. J. Numer. Anal. Methods Geomech. 14, 565–585 (1990)
Plona T.J.: Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies. Appl. Phys. Lett. 36, 259–261 (1980)
Shapiro, A.M.: Transport equations for fractured porous media. In: Bear, J., Corapcioglu, M.Y. Advances in Transport Phenomena in Porous Media, pp. 406–471. Martinus Nijhoff, Dordrecht (1987)
Sharma M.D., Gogna M.L.: Reflection and refraction of plane harmonic waves at an interface between elastic solid and porous solid saturated by viscous liquid. Pure and Appl. Geo Phys. 138, 249–266 (1992)
Stoll R.D.: Reflection of acoustic waves at a water-sediment interface. J. Acoust. Soc. Am. 70, 149–156 (1981)
Tajuddin M., Hussaini S.J.: Reflection of plane waves at boundaries of a liquid filled poroelastic half-space. J. Appl. Geophys. 58(1), 59–86 (2005)
Tomar, S.K., Arora, A.: Reflection and transmission of elastic waves at an elastic/porous solid saturated by two immiscible fluids. Int. J. Solids Struct. 43, 1991–2013 (2006) [Erratum, ibid 44, 5796–5800 (2007)]
Tuncay K., Corapciaglu M.Y.: Effective stress principle for saturated fractured porous media. Water Resour. Res. 31, 3103–3106 (1995)
Tuncay K., Corapcioglu M.Y.: Wave propagation in fractured porous media. Transp. Porous Media 23, 237–258 (1996a)
Tuncay K., Corapcioglu M.Y.: Body waves in fractured porous media saturated by two immiscible newtonian fluids. Transp. Porous Media 23, 259–273 (1996b)
Tuncay K., Corapciaglu M.Y.: Wave propagation in poroelastic media saturated by two fluids. J. Appl. Mech. 64, 313–319 (1997)
Warren J.E., Root P.J.: The behavior of naturally fractured reservoirs. Soc. Pet. Eng. J. 3, 245–255 (1963)
Wilson R.K., Aifantis E.C.: On the theory of consolidation with double porosity. Int. J. Eng. Sci. 20, 1009–1035 (1982)
Wilson R.K., Aifantis E.C.: A double porosity model for acoustic wave propagation in fractured porous rock. Int. J. Eng. Sci. 22, 1209–1217 (1984)
Winkler K.W.: Dispersion analysis of velocity and attenuation in Berea sandstone. J. Geophys. Res. 90, 6793–6800 (1985)
Wu K.Y., Xue Q., Adler L.: Reflection and transmission of elastic waves from a fluid-saturated porous solid boundary. J. Acoust. Soc. Am. 87, 2349–2358 (1990)
Yew C.H., Jogi P.N.: Study of wave motion in fluid saturated porous rocks. J. Acoust. Soc. Am. 60, 2–8 (1976)