用等效介质理论模拟裂缝溶洞型孔隙对速度和弹性模量的影响
摘要
针对缝洞型储层流体性质识别的困难,采用Kuster-Toksz(K-T)模型、Berryman自恰模型(SCM)和差分等效介质(DEM)三类近似模型,用不同纵横比的孔隙模拟了缝洞型储层的地震波速度和弹性参数响应,定量分析了溶蚀孔洞和裂缝二类次生孔隙对地下储层弹性性质的影响。明确了孔隙几何结构对岩石弹性参数的影响趋势和幅度大小,为利用地震信息评价孔隙结构提供了理论基础。根据物理模型的裂缝介质参数,分别采用K-T模型、SCM自恰模型和DEM差分等效介质模型,计算了裂缝介质的纵横波速度,考察了三个模型对缝洞型储层弹性响应计算的适用性,得到了有意义的认识。
Facing to the encountered difficulty of the identification of hydrocarbon reservoir in formation with fractures and vuggs,the seismic responses of velocity and elastic modules have been simulated for the reservoir formation with vuggs and fractures based on the effective media approximation methods of three models of Kuster-Toksz(K-T) model,the self consistent model(SCM) and the differential effective model(DEM) by using different porosity aspects.We also have quantitatively analyzed the effects of the vuggs and fractures on the elastic responses of the vugged and fractured formation.Through the numerical simulation,we have recognized the trend and the magnitude of the effects of the different porosity type and the porosity geometric structure on the elastic responses of the reservoir formation.It lays a solid foundation for the deduction of the effects of the porosity type and the porosity geometric structure from the seismic responses.In order to obtain an insight into the application conditions of the K-T model,the SCM model and the DEM model,we have estimated the P and S velocity of the physical modeling media of different fracture parameters by using the above three effective models,and compared them with experimental results acquired with large physical seismic instrument,and meaningful results have been achieved.
Facing to the encountered difficulty of the identification of hydrocarbon reservoir in formation with fractures and vuggs,the seismic responses of velocity and elastic modules have been simulated for the reservoir formation with vuggs and fractures based on the effective media approximation methods of three models of Kuster-Toksz(K-T) model,the self consistent model(SCM) and the differential effective model(DEM) by using different porosity aspects.We also have quantitatively analyzed the effects of the vuggs and fractures on the elastic responses of the vugged and fractured formation.Through the numerical simulation,we have recognized the trend and the magnitude of the effects of the different porosity type and the porosity geometric structure on the elastic responses of the reservoir formation.It lays a solid foundation for the deduction of the effects of the porosity type and the porosity geometric structure from the seismic responses.In order to obtain an insight into the application conditions of the K-T model,the SCM model and the DEM model,we have estimated the P and S velocity of the physical modeling media of different fracture parameters by using the above three effective models,and compared them with experimental results acquired with large physical seismic instrument,and meaningful results have been achieved.
引文
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[14]HUDSON J A.A higher order approximation to the wave propagation constants for a cracked solid[J].Geophys.J.R.Astr.Sot,1986,87:265.
[15]KACHANOV M.Effective elastic properties of cracked solids:Critical review of some basic concepts[J].Appl.Mech.Rev,1992,45(1):304.
[16]魏建新,狄帮让,王椿镛,各向异性介质中扭转波分裂的实验观测[J].地球物理学进展,2006,21(2):535.
[17]魏建新,狄帮让.裂隙张开度对地震波特性影响的模型研究[J].中国科学D辑,2008,39(增1):211.
[18]JIANXIN W.A physical model study of different crack densities[J].Geophys Eng,2004,1(1):70.
[19]TOKSSZ M N,CHENG C M,TIMUR A.Velocities of seismic waves in porous rocks[J].Geophysics,1976,41(3):621.
[20]WU TAI TE.The effect of inclusion shape on the elastic moduli of a two phase material[J].Int.J.Solids Structures,1996,2(1):1.
[21]ESHELBY J D.The determination of the elastic field of an ellipsoidal inclusion,and related problems[C].Proc.R.Sot.Lond.,1957,A241:376.
[22]O′CONNELL R J,BUDIANSKY B.Seismic velocities in dry and saturated cracked solids[J].Geophys.Res.,1974,(79):5412.
[23]O′CONNELL R J,BUDIANSKY B.Viscoelastic properties of fluid-saturated cracked solids[J].Geophys.Res,1977(82):5719.
[24]BERRYMAN J G.Origin of Gassmann′s equations[J].Geophysics,1999,64(6):1627.
[25]BERGE P A,BERRYMAN J G,BONNER B P.Influence of microstructure on rock elastic properties[J].Geophys.Res.Letters,1993(20):2619.
[26]WILLIS J R.A polarization approach to the scattering of elastic waves.Part II:Multiple scattering from inclusions[J].Mech.Phys.Solids,1980,28(1):307.
[2]ANTHONY L,ENDRES,ROSEMARY KNIGHT.The effects of pore-scale fluid distribution on the physical properties of partially saturated tight sandstones[J].Appl.Phys,1991,69(2):1092.
[3]PATRICIA A B,BERRYMAN J G,BONNER B P.Influence of microstructure on rock elastic properties[J].Geophysical Research Letters,1993,20(23):2619.
[4]KUSTER G,TOKSZ N.Velocity and attenuation of seismic waves in two-phase media,I,Theoretical formulations[J].Geophysics,1974,39(3):587.
[5]BERRYMAN J G.Long-wavelength propagation in composite elastic media II.Ellipsoidal inclusions[J].Acoust.Soc.Am.1980,68(6):1820.
[6]BERRYMAN J G.Long-Wavelength Propagation in Composite Elastic Media,Part I:Spherical Inclusions[J].Acoust.Sot.Am.1980,68(6):1809.
[7]KORRINGA J,BROWN R J S,THOMPSON D D.Self-Consistent Imbedding and the Ellipsoidal Model for Porous Rocks[J].Journal of Geophysical Research,1979,84(B10):5591.
[8]NORRIS A N.A differential scheme for the effective moduli of composites[J].Mech.Mater,1985,4(1):1.
[9]AVELLANEDA M.Iterated homogenization,differential effective medium theory and applications[J].Commun.Pure Appl.Math,1987,40(2):527.
[10]SMYSHLYAVE V P,WILLIS J R,SABINA F J.Self-consistent analysis of waves in a matrix-inclusion composite-A matrix containing cracks[J].Mech.Phys.Solids,1993,41(3):1809.
[11]HUDSON J A.Overall properties of a cracked solid[C].Math.Proc.Camb.Phil.Sot.,1980,88:371.
[12]HUDSON J A.Wave speeds and attenuation of elastic waves in material containing cracks[J].Geophys.R.Astr.Sot,1981(64):133.
[13]HUDSON J A.Overall elastic properties of isotropic materials with arbitrary distribution of circular cracks[J].Geophys.J.Int,1990,102(1):465.
[14]HUDSON J A.A higher order approximation to the wave propagation constants for a cracked solid[J].Geophys.J.R.Astr.Sot,1986,87:265.
[15]KACHANOV M.Effective elastic properties of cracked solids:Critical review of some basic concepts[J].Appl.Mech.Rev,1992,45(1):304.
[16]魏建新,狄帮让,王椿镛,各向异性介质中扭转波分裂的实验观测[J].地球物理学进展,2006,21(2):535.
[17]魏建新,狄帮让.裂隙张开度对地震波特性影响的模型研究[J].中国科学D辑,2008,39(增1):211.
[18]JIANXIN W.A physical model study of different crack densities[J].Geophys Eng,2004,1(1):70.
[19]TOKSSZ M N,CHENG C M,TIMUR A.Velocities of seismic waves in porous rocks[J].Geophysics,1976,41(3):621.
[20]WU TAI TE.The effect of inclusion shape on the elastic moduli of a two phase material[J].Int.J.Solids Structures,1996,2(1):1.
[21]ESHELBY J D.The determination of the elastic field of an ellipsoidal inclusion,and related problems[C].Proc.R.Sot.Lond.,1957,A241:376.
[22]O′CONNELL R J,BUDIANSKY B.Seismic velocities in dry and saturated cracked solids[J].Geophys.Res.,1974,(79):5412.
[23]O′CONNELL R J,BUDIANSKY B.Viscoelastic properties of fluid-saturated cracked solids[J].Geophys.Res,1977(82):5719.
[24]BERRYMAN J G.Origin of Gassmann′s equations[J].Geophysics,1999,64(6):1627.
[25]BERGE P A,BERRYMAN J G,BONNER B P.Influence of microstructure on rock elastic properties[J].Geophys.Res.Letters,1993(20):2619.
[26]WILLIS J R.A polarization approach to the scattering of elastic waves.Part II:Multiple scattering from inclusions[J].Mech.Phys.Solids,1980,28(1):307.
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