含两项不混合/单项黏性流体孔隙介质分界面上反透射系数特征研究
|
摘要
弹性孔隙介质分界面上的反透射系数特征,在岩性划分、流体识别、储层边界判识等方面有重要的应用.本文研究上层为含两项不混合黏性流体孔隙介质、下层为含单项黏性流体孔隙介质分界面上的反透射理论.首先根据两种孔隙介质分界面上的能量守恒得到边界条件,再将波函数、位移、应力与应变关系代入边界条件,推导出完全连通孔隙情况下,第一类纵波入射到孔隙介质分界面上的反透射系数方程.通过建立砂岩孔隙介质模型,分别分析不同孔隙流体类型、不同含油饱和度及不同入射角情况下,各类波的反透射系数特征.研究表明,第二、三类纵波反透射系数数值比第一类纵波小多个数量级,且两者对入射角的变化不敏感,但对孔隙流体性质、含油饱和度的变化较敏感,而横波反透射系数特征恰好与此相反;第一类纵波反透射系数特征比较复杂,入射角、孔隙流体的性质及含油饱和度的变化都对其产生影响.不同孔隙流体弹性物性的差异、孔隙介质中含油饱和度的变化及不同入射角引起垂向和切向应力分量的变化都会影响各类波的反透射系数特征,分析这些特征可以为研究储层含油气性提供理论基础.
The characteristics of reflection and transmission coefficients at the interface of elastic porous media are of great importance in lithology division,fluid identification,reservoir boundary identification and other aspects.This paper studies the theory of reflection and transmission coefficients at the boundary of a porous medium saturated with two immiscible viscous fluids andaporous medium saturated with a single viscous fluid.According to the conservation of energy at the interface of two porous media,we first derive the boundary conditions,then substitute wave functions,displacements and stress-strain relationships into them,and further derive the equation of reflection and transmission coefficients in the case of connected pores and the first P-wave incidence.On a sandstone porous medium model,we analyze the characteristics of the reflection and transmission coefficients of various kinds of waves with different types of pore fluids,oil saturation and incident angles,respectively.The results show that the values of reflection and transmission coefficients of the second and third type of P-waves are several orders of magnitude smaller than those of the first type P-wave,and they are insensitive to the change of incident angles,but sensitive to the variation of pore fluid properties and oil saturation,while the characteristics of the S-wave′s coefficients are just the opposite.The reflection and transmission coefficients of the first type P-waves have complex characteristics,which are affected by the incident angles,the property of pore fluids and the change of oil saturation.The difference of elastic properties of different pore fluids,the change of oil saturation in porous media and the variation of vertical and tangential stress components caused by different incident angles can all affect the characteristics of reflection and transmission coefficients of various waves.The analysis of these characteristics can provide a theoretical basis for further study on features of oil and gas reservoirs.
The characteristics of reflection and transmission coefficients at the interface of elastic porous media are of great importance in lithology division,fluid identification,reservoir boundary identification and other aspects.This paper studies the theory of reflection and transmission coefficients at the boundary of a porous medium saturated with two immiscible viscous fluids andaporous medium saturated with a single viscous fluid.According to the conservation of energy at the interface of two porous media,we first derive the boundary conditions,then substitute wave functions,displacements and stress-strain relationships into them,and further derive the equation of reflection and transmission coefficients in the case of connected pores and the first P-wave incidence.On a sandstone porous medium model,we analyze the characteristics of the reflection and transmission coefficients of various kinds of waves with different types of pore fluids,oil saturation and incident angles,respectively.The results show that the values of reflection and transmission coefficients of the second and third type of P-waves are several orders of magnitude smaller than those of the first type P-wave,and they are insensitive to the change of incident angles,but sensitive to the variation of pore fluid properties and oil saturation,while the characteristics of the S-wave′s coefficients are just the opposite.The reflection and transmission coefficients of the first type P-waves have complex characteristics,which are affected by the incident angles,the property of pore fluids and the change of oil saturation.The difference of elastic properties of different pore fluids,the change of oil saturation in porous media and the variation of vertical and tangential stress components caused by different incident angles can all affect the characteristics of reflection and transmission coefficients of various waves.The analysis of these characteristics can provide a theoretical basis for further study on features of oil and gas reservoirs.
引文
Arora A,Tomar S K.2007.Elastic waves at porous/porous elastic half spaces saturated by two immiscible fluids.Journal of Porous Media,8:751-768.
Biot M A.1956.Theory of propagation of elastic waves in a fluidsaturated porous solid.I.Low-frequency range.The Journal of the Acoustical Society of America,28(2):168-178.
Biot M A.1962.Mechanics of deformation and acoustic propagation in porous media.Journal of Applied Physics,33(4):1482-1498.
Borcherdt R D.1982.Reflection-refraction of general P-and type-IS-waves in elastic and anelastic solids.Geophysical Journal International,70(3):621-638.
Geertsma J,Smit D C.1961.Some aspects of elastic wave propagation in fluid-saturated porous solids.Geophysics,26(2):169-181.
Kumar M,Saini R.2012.Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids.Applied Mathematics and Mechanics,33(6):797-816.
Kumar M,Saini R.2016.Reflection and refraction of waves at the boundary of a non-viscous porous solid saturated with single fluid and a porous solid saturated with two immiscible fluids.Latin American Journal of Solids and Structures,13(7):1299-1324.
Kumar M,Sharma M D.2013.Reflection and transmission of attenuated waves at the boundary between two dissimilar poroelastic solids saturated with two immiscible viscous fluids.Geophysical Prospecting,61(5):1035-1055.
Li S Y,Reuning L,Marquart G,et al.2017.Numerical model of halite precipitation in porous sedimentary rocks adjacent to salt diapirs.Journal of Geophysics and Engineering,14(5):1160-1166.
Lo W C,Sposito G,Majer E.2005.Wave propagation through elastic porous media containing two immiscible fluids.Water Resources Research,41(2):W02025,doi:10.1029/2004WR003162.
Lo W C,Sposito G,Majer E.2009a.Analytical decoupling of poroelasticity equations for acoustic-wave propagation and attenuation in a porous medium containing two immiscible fluids.Journal of Engineering Mathematics,64(2):219-235.
Lo W C,Sposito G,Majer E.2009b.Low-frequency dilatational wave propagation through unsaturated porous media containing two immiscible fluids.Transport in Porous Media,68(1):91-105.
Lovera O M.1987.Boundary conditions for a fluid-saturated porous solid.Geophysics,52(2):174-178.
Mu Y G.1996.Reservoir Geophysics.Beijing:Petroleum Industry Press.
Qin X L,Li X Y,Chen S Q,et al.2018.The modeling and analysis of frequency-dependent characteristics in fractured porous media.Journal of Geophysics and Engineering,15(5):1943-1952.
Ren H T,Goloshubin G,Hilterman F J.2009.Poroelastic analysis of amplitude-versus-frequency variations.Geophysics,74(6):N41-N48.
Rubino J G,Holliger K.2012.Seismic attenuation and velocity dispersion in heterogeneous partially saturated porous rocks.Geophysical Journal International,188(3):1088-1102.
Sharma M D.2008.Wave propagation across the boundary between two dissimilar poroelastic solids.Journal of Sound and Vibration,314(3-5):657-671.
Sharma M D,Gogna M L.1990.Propagation of elastic waves in a cylindrical bore in a liquid-saturated porous solid.Geophysical Journal International,103(1):47-54.
Sharma M D,Kumar M.2011.Reflection of attenuated waves at the surface of a porous solid saturated with two immiscible viscous fluids.Geophysical Journal International,184(1):371-384.
Silin D,Goloshubin G M.2010.An asymptotic model of seismic reflection from a permeable layer.Transport in Porous Media,83(1):233-256.
Tomar S K,Arora A.2006.Reflection and transmission of elastic waves at an elastic/porous solid saturated by two immiscible fluids.International Journal of Solids and Structure,43(7-8):1991-2013.
Tuncay K,Corapcioglu M Y.1996.Body waves in poroelastic media saturated by two immiscible fluids.Journal of Geophysical Research:Solid Earth,101(B11):25149-25159.
Tuncay K,Corapcioglu M Y.1997.Wave propagation in poroelastic media saturated by two fluids.Journal of Applied Mechanics,64(2):313-320.
Vashisth A K,Sharma M D,Gogna M L.1991.Reflection and transmission of elastic waves at a loosely bonded interface between an elastic solid and liquid-saturated porous solid.Geophysical Journal International,105(3):601-617.
Wang S X,Li X Y,Di B R,et al.2010.Reservoir fluid substitution effects on seismic profile interpretation:A physical modeling experiment.Geophysical Research Letters,37(10):L10306,doi:10.1029/2010GL043090.
Wang S X,Zhao J G,Li Z H,et al.2012.Differential acoustic resonance spectroscopy for the acoustic measurement of small and irregular samples in the low frequency range.Journal of Geophysical Research:Solid Earth,117(13):B06203,doi:10.1029/2011JB008808.
Yeh C L,Lo W C,Jan C D,et al.2010.Reflection and refraction of obliquely incident elastic waves upon the interface between two porous elastic half-spaces saturated by different fluid mixtures.Journal of Hydrology,395(1-2):91-102.
Yin X Y,Zong Z Y,Wu G C.2015.Research on seismic fluid identification driven by rock physics.Science China Earth Sciences,58(2):159-171.
Zhao L X,Han D H,Yao Q L,et al.2015.Seismic reflection dispersion due to wave-induced fluid flow in heterogeneous reservoir rocks.Geophysics,80(3):D221-D235.
Zong Z Y,Yin X Y,Li K.2016.Joint AVO inversion in the time and frequency domain with Bayesian interference.Applied Geophysics,13(4):631-640.
牟永光.1996.储层地球物理学.北京:石油工业出版社.
印兴耀,宗兆云,吴国忱.2015.岩石物理驱动下地震流体识别研究.中国科学:地球科学,45(1):8-21.
Biot M A.1956.Theory of propagation of elastic waves in a fluidsaturated porous solid.I.Low-frequency range.The Journal of the Acoustical Society of America,28(2):168-178.
Biot M A.1962.Mechanics of deformation and acoustic propagation in porous media.Journal of Applied Physics,33(4):1482-1498.
Borcherdt R D.1982.Reflection-refraction of general P-and type-IS-waves in elastic and anelastic solids.Geophysical Journal International,70(3):621-638.
Geertsma J,Smit D C.1961.Some aspects of elastic wave propagation in fluid-saturated porous solids.Geophysics,26(2):169-181.
Kumar M,Saini R.2012.Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids.Applied Mathematics and Mechanics,33(6):797-816.
Kumar M,Saini R.2016.Reflection and refraction of waves at the boundary of a non-viscous porous solid saturated with single fluid and a porous solid saturated with two immiscible fluids.Latin American Journal of Solids and Structures,13(7):1299-1324.
Kumar M,Sharma M D.2013.Reflection and transmission of attenuated waves at the boundary between two dissimilar poroelastic solids saturated with two immiscible viscous fluids.Geophysical Prospecting,61(5):1035-1055.
Li S Y,Reuning L,Marquart G,et al.2017.Numerical model of halite precipitation in porous sedimentary rocks adjacent to salt diapirs.Journal of Geophysics and Engineering,14(5):1160-1166.
Lo W C,Sposito G,Majer E.2005.Wave propagation through elastic porous media containing two immiscible fluids.Water Resources Research,41(2):W02025,doi:10.1029/2004WR003162.
Lo W C,Sposito G,Majer E.2009a.Analytical decoupling of poroelasticity equations for acoustic-wave propagation and attenuation in a porous medium containing two immiscible fluids.Journal of Engineering Mathematics,64(2):219-235.
Lo W C,Sposito G,Majer E.2009b.Low-frequency dilatational wave propagation through unsaturated porous media containing two immiscible fluids.Transport in Porous Media,68(1):91-105.
Lovera O M.1987.Boundary conditions for a fluid-saturated porous solid.Geophysics,52(2):174-178.
Mu Y G.1996.Reservoir Geophysics.Beijing:Petroleum Industry Press.
Qin X L,Li X Y,Chen S Q,et al.2018.The modeling and analysis of frequency-dependent characteristics in fractured porous media.Journal of Geophysics and Engineering,15(5):1943-1952.
Ren H T,Goloshubin G,Hilterman F J.2009.Poroelastic analysis of amplitude-versus-frequency variations.Geophysics,74(6):N41-N48.
Rubino J G,Holliger K.2012.Seismic attenuation and velocity dispersion in heterogeneous partially saturated porous rocks.Geophysical Journal International,188(3):1088-1102.
Sharma M D.2008.Wave propagation across the boundary between two dissimilar poroelastic solids.Journal of Sound and Vibration,314(3-5):657-671.
Sharma M D,Gogna M L.1990.Propagation of elastic waves in a cylindrical bore in a liquid-saturated porous solid.Geophysical Journal International,103(1):47-54.
Sharma M D,Kumar M.2011.Reflection of attenuated waves at the surface of a porous solid saturated with two immiscible viscous fluids.Geophysical Journal International,184(1):371-384.
Silin D,Goloshubin G M.2010.An asymptotic model of seismic reflection from a permeable layer.Transport in Porous Media,83(1):233-256.
Tomar S K,Arora A.2006.Reflection and transmission of elastic waves at an elastic/porous solid saturated by two immiscible fluids.International Journal of Solids and Structure,43(7-8):1991-2013.
Tuncay K,Corapcioglu M Y.1996.Body waves in poroelastic media saturated by two immiscible fluids.Journal of Geophysical Research:Solid Earth,101(B11):25149-25159.
Tuncay K,Corapcioglu M Y.1997.Wave propagation in poroelastic media saturated by two fluids.Journal of Applied Mechanics,64(2):313-320.
Vashisth A K,Sharma M D,Gogna M L.1991.Reflection and transmission of elastic waves at a loosely bonded interface between an elastic solid and liquid-saturated porous solid.Geophysical Journal International,105(3):601-617.
Wang S X,Li X Y,Di B R,et al.2010.Reservoir fluid substitution effects on seismic profile interpretation:A physical modeling experiment.Geophysical Research Letters,37(10):L10306,doi:10.1029/2010GL043090.
Wang S X,Zhao J G,Li Z H,et al.2012.Differential acoustic resonance spectroscopy for the acoustic measurement of small and irregular samples in the low frequency range.Journal of Geophysical Research:Solid Earth,117(13):B06203,doi:10.1029/2011JB008808.
Yeh C L,Lo W C,Jan C D,et al.2010.Reflection and refraction of obliquely incident elastic waves upon the interface between two porous elastic half-spaces saturated by different fluid mixtures.Journal of Hydrology,395(1-2):91-102.
Yin X Y,Zong Z Y,Wu G C.2015.Research on seismic fluid identification driven by rock physics.Science China Earth Sciences,58(2):159-171.
Zhao L X,Han D H,Yao Q L,et al.2015.Seismic reflection dispersion due to wave-induced fluid flow in heterogeneous reservoir rocks.Geophysics,80(3):D221-D235.
Zong Z Y,Yin X Y,Li K.2016.Joint AVO inversion in the time and frequency domain with Bayesian interference.Applied Geophysics,13(4):631-640.
牟永光.1996.储层地球物理学.北京:石油工业出版社.
印兴耀,宗兆云,吴国忱.2015.岩石物理驱动下地震流体识别研究.中国科学:地球科学,45(1):8-21.