含横向喷射流的部分饱和介质的纵波衰减和频散特性研究
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摘要
当纵波在部分饱和多孔介质中传播时,孔隙内的流体会同时产生宏观、微观和中观流动,这3种尺度的流体流动共同作用,使纵波在较宽的频带范围内产生衰减和速度频散现象。目前同时考虑3种尺度流体流动的研究不多。为了研究流体的多尺度流动对纵波传播的影响,在层状双孔模型的基础上,引入了横向喷射流,建立了含横向喷射流的层状部分饱和模型。通过求解模型介质内的平均流体压力,推导了含横向喷射流的层状部分饱和模型的波动方程。利用平面波分析,得到了快纵波和两类慢纵波的相速度和品质因子,研究了3种尺度流体流动同时存在时的纵波衰减和速度频散特性,同时分析了岩石参数对纵波衰减和速度频散的影响。结果表明,在3种尺度流体流动的共同作用下,快纵波在低频和高频范围内都出现了衰减和速度频散现象,且由于喷射流的影响,快纵波在高频范围内出现了强衰减和高频散。快纵波相速度对模型的含气饱和度较为敏感,且随着模型孔隙度的减小,低频范围内的频散曲线和衰减峰向低频方向移动;随着喷射长度的增加,高频范围内的频散曲线和衰减峰向低频方向移动。
When P-waves propagate in partially-saturated porous media,the fluid in the pores produce macroscopic,microscopic,and mesoscopic flow simultaneously.Different scales of fluid flow together to cause the attenuation and velocity dispersion of the P wave over a wide frequency band.There were few cases to consider all these three kinds of fluid flow mechanisms.To study the influence of the multi-scale fluid flow on the P wave propagation,we introduced the transverse squirt flow and established a layered partially-saturated model,based on the layered double-porosity model.By determining the average fluid pressure in the media,the wave equations of the layered partially-saturated model with transverse squirt flow were derived.According to the plane wave analysis,the phase velocities and quality factors of the fast P-wave and two types of slow P-waves were obtained.Then we studied the characteristics of P wave attenuation and velocity dispersion under the simultaneous existence of the three scales of fluid flow,and analyzed the effect of rock property parameters on P wave attenuation and velocity dispersion.The results demonstrated that under the combined effect of the three scales of fluid flow,the attenuation and velocity dispersion of fast P-waves occur in both low-frequency and high-frequency ranges.Moreover,due to the influence of the squirt flow,the fast P wave encounters strong attenuation and high velocity dispersion over the high frequency range.The fast P-wave phase velocity was sensitive to the gas saturation of the model.The dispersive curve and attenuation peak in the low frequency range moved toward low frequencies with the decrease of the porosity of the model,while the dispersive curve and attenuation peak in the high frequency range moved toward low frequencies with the increase of the squirt-flow length.
When P-waves propagate in partially-saturated porous media,the fluid in the pores produce macroscopic,microscopic,and mesoscopic flow simultaneously.Different scales of fluid flow together to cause the attenuation and velocity dispersion of the P wave over a wide frequency band.There were few cases to consider all these three kinds of fluid flow mechanisms.To study the influence of the multi-scale fluid flow on the P wave propagation,we introduced the transverse squirt flow and established a layered partially-saturated model,based on the layered double-porosity model.By determining the average fluid pressure in the media,the wave equations of the layered partially-saturated model with transverse squirt flow were derived.According to the plane wave analysis,the phase velocities and quality factors of the fast P-wave and two types of slow P-waves were obtained.Then we studied the characteristics of P wave attenuation and velocity dispersion under the simultaneous existence of the three scales of fluid flow,and analyzed the effect of rock property parameters on P wave attenuation and velocity dispersion.The results demonstrated that under the combined effect of the three scales of fluid flow,the attenuation and velocity dispersion of fast P-waves occur in both low-frequency and high-frequency ranges.Moreover,due to the influence of the squirt flow,the fast P wave encounters strong attenuation and high velocity dispersion over the high frequency range.The fast P-wave phase velocity was sensitive to the gas saturation of the model.The dispersive curve and attenuation peak in the low frequency range moved toward low frequencies with the decrease of the porosity of the model,while the dispersive curve and attenuation peak in the high frequency range moved toward low frequencies with the increase of the squirt-flow length.
引文
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[21]杨盈盈,关继腾,庄显丽.基于孔隙介质BISQ模型的震电慢纵波传播特性[J].工程地球物理学报,2016,13(1):27-34YANG Y Y,GUAN J T,ZHUANG X L.The seismo-electric slow waves propagation characteristics based on BISQ poroelastic model[J].Chinese Journal of Engineering Geophysics,2016,13(1):27-34
[22]凌云,杜向东,曹思远.基于Zener线性体的黏弹孔隙介质衰减频散特征分析[J].地球物理学进展,2017,32(1):205-209LING Y,DU X D,CAO S Y.Attenuation and dispersion characteristics analysis in visco-poroelastic medium based on Zener linear solid[J].Progress in Geophysics,2017,32(1):205-209
[23]BA J,CARCIONE J M,NIE J X.Biot-Rayleigh theory of wave propagation in double-porosity media[J].Journal of Geophysical Research Atmospheres,2011,116(B06202):1-12
[24]BA J,ZHANG L,SUN W T.Velocity field of wave-induced local fluid flow in double-porosity media[J].Science China(Physics,Mechanics&Astronomy),2014,57(6):1020-1030
[25]BA J,ZHAO J,CARCIONE J M.Compressional wave dispersion due to rock matrix stiffening by clay squirt flow[J].Geophysical Research Letters,2016,43(12):6186-6195
[26]SONG Y J,HU H S,RUDNICKI J W.Shear properties of heterogeneous fluid-filled porous media with spherical inclusions[J].International Journal of Solid and Structures,2016,83(5):154-168
[27]BA J,XU W H,FU L Y.Rock anelasticity due to patchy saturation and fabric heterogeneity:a double double-porosity model of wave propagation[J].Journal of Geophysical Research:Solid Earth,2017,122(3):1949-1976
[28]ZHAO Z Y,YIN X Y,ZONG Z Y,et al.Wave attenuation and velocity dispersion in layered double-porosity media[J].Expanded Abstracts of 87th Annual Internat SEG Mtg,2017:3596-3600
[29]ZHENG P,DING B Y,SUN X T.Elastic wave attenuation and dispersion induced by mesoscopic flow in double-porosity rocks[J].International Journal of Rock Mechanics&Mining Sciences,2017,91(1):104-111
[30]DAI Z J,KUANG Z B,ZHAO S X.Reflection and transmission of elastic waves from the interface of a fluid-saturated porous solid and a double porosity solid[J].Transport in Porous Media,2006,65(2):237-264
[31]ZHAO L X,HAN D H,YAO Q L,et al.Seismic reflection dispersion due to wave-induced fluid flow in heterogeneous reservoir rocks[J].Geophysics,2015,80(3):D221-D235
[32]PRIDE S R,BERRYMAN J G,HARRIS J M.Seismic attenuation due to wave-induced flow[J].Journal of Geophysical Research Atmospheres,2004,109(B1):59-70
[33]贺鹏飞,夏唐代,刘志军,等.双重孔隙介质中P1波在自由边界上的反射[J].岩土力学,2016,37(6):1753-1761HE P F,XIA T D,LIU Z J,et al.Reflection of P1wave from free surfaces of double-porosity media[J].Rock and Soil Mechanics,2016,37(6):1753-1761
[2]BIOT M A.Theory of propagation of elastic waves in fluid-saturated porous solid:I.low-frequency range[J].Journal of the Acoustical Society of America,1956,28(2):168-178
[3]BIOT M A.Theory of propagation of elastic waves in fluid-saturated porous solid:II.higher frequency range[J].Journal of the Acoustical Society of America,1956,28(2):179-191
[4]BIOT M A.Mechanics of deformation and acoustic propagation in porous media[J].Journal of Applied Physics,1962,33(4):1482-1498
[5]DVORKIN J,NOLEN-HOEKSEMA R,NUR A.The squirt-flow mechanisms:macroscopic description[J].Geophysics,1994,59(3):428-438
[6]MAVKO G M,NUR A.Wave attenuation in partially saturated rocks[J].Geophysics,1979,44(2):161-178
[7]WHITE J E.Computed seismic speeds and attenuation in rocks with partial gas saturation[J].Geophysics,1975,40(2):224-232
[8]WHITE J E,MIHAILOVA N G,LYAKHOVITSKIYF M.Low-frequency seismic waves in fluid-saturated layered rocks[J].Physics of the Solid Earth,1975,11(S1):654-659
[9]DUTTA N C,ODEH.Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation(White model)-part I:Biot theory[J].Geophysics,1979,44(11):1777-1788
[10]DUTTA N C,ODEH.Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation(White model)-part II:results[J].Geophysics,1979,44(11):1789-1805
[11]杜伟,邓继新,曲寿利,等.含裂隙孔隙介质中纵波传播特征研究[J].石油物探,2013,52(4):339-346DU W,DENG J X,QU S L,et al.A study of the propagation properties of P-wave in a porous media with aligned cracks[J].Geophysical Prospecting for Petroleum,2013,52(4):339-346
[12]SUN W T,BA J,CARCIONE J M.Theory of wave propagation in partially saturated double-porosity rocks:a triple-layer patchy model[J].Geophysical Journal International,2016,205(1):22-37
[13]CHEN X H,ZHONG W L,HE Z H.Frequency-dependent attenuation of compressional wave and seismic effects in porous reservoirs saturated with multi-phase fluids[J].Journal of Petroleum Science and Engineering,2016,147(11):371-380
[14]未晛.随机斑块饱和孔隙介质模型研究[J].石油物探,2017,56(3):319-327WEI X.Study on the continuous random porosity model of patchy saturation[J].Geophysical Prospecting for Petroleum,2017,56(3):319-327
[15]DVORKIN J,NUR A.Dynamic poroelasticity:a unified model with the squirt and the Biot mechanisms[J].Geophysics,1993,58(4):524-533
[16]DIALLO M S,APPEL E.Acoustic wave propagation in saturated porous media:reformulation of the Biot/Squirt flow theory[J].Journal of Applied Geophysics,2000,44(4):313-325
[17]杨顶辉,陈小宏.含流体多孔介质的BISQ模型[J].石油地球物理勘探,2001,36(2):146-159YANG D H,CHEN X H.BISQ model for fluid-filled porous medium[J].Oil Geophysical Prospecting,2001,36(2):146-159
[18]杜艺可,张会星,孙万元.双相Biot模型的纵波相速度与衰减特性及其与BISQ模型的对比[J].工程地球物理学报,2011,8(4):452-458DU Y K,ZHANG H X,SUN W Y.A comparison of velocity and attenuation of P-waves on Biot and BISQmodel[J].Chinese Journal of Engineering Geophysics,2011,8(4):452-458
[19]YANG L,YANG D H,NIE J X.Wave dispersion and attenuation in viscoelastic isotropic media containing multiphase flow and its application[J].Science China(Physics,Mechanics&Astronomy),2014,57(6):1068-1077
[20]LIU J W,YONG W A.Stability analysis of the Biot/squirt models for wave propagation in saturated porous media[J].Physics,2015,204(1):853-861
[21]杨盈盈,关继腾,庄显丽.基于孔隙介质BISQ模型的震电慢纵波传播特性[J].工程地球物理学报,2016,13(1):27-34YANG Y Y,GUAN J T,ZHUANG X L.The seismo-electric slow waves propagation characteristics based on BISQ poroelastic model[J].Chinese Journal of Engineering Geophysics,2016,13(1):27-34
[22]凌云,杜向东,曹思远.基于Zener线性体的黏弹孔隙介质衰减频散特征分析[J].地球物理学进展,2017,32(1):205-209LING Y,DU X D,CAO S Y.Attenuation and dispersion characteristics analysis in visco-poroelastic medium based on Zener linear solid[J].Progress in Geophysics,2017,32(1):205-209
[23]BA J,CARCIONE J M,NIE J X.Biot-Rayleigh theory of wave propagation in double-porosity media[J].Journal of Geophysical Research Atmospheres,2011,116(B06202):1-12
[24]BA J,ZHANG L,SUN W T.Velocity field of wave-induced local fluid flow in double-porosity media[J].Science China(Physics,Mechanics&Astronomy),2014,57(6):1020-1030
[25]BA J,ZHAO J,CARCIONE J M.Compressional wave dispersion due to rock matrix stiffening by clay squirt flow[J].Geophysical Research Letters,2016,43(12):6186-6195
[26]SONG Y J,HU H S,RUDNICKI J W.Shear properties of heterogeneous fluid-filled porous media with spherical inclusions[J].International Journal of Solid and Structures,2016,83(5):154-168
[27]BA J,XU W H,FU L Y.Rock anelasticity due to patchy saturation and fabric heterogeneity:a double double-porosity model of wave propagation[J].Journal of Geophysical Research:Solid Earth,2017,122(3):1949-1976
[28]ZHAO Z Y,YIN X Y,ZONG Z Y,et al.Wave attenuation and velocity dispersion in layered double-porosity media[J].Expanded Abstracts of 87th Annual Internat SEG Mtg,2017:3596-3600
[29]ZHENG P,DING B Y,SUN X T.Elastic wave attenuation and dispersion induced by mesoscopic flow in double-porosity rocks[J].International Journal of Rock Mechanics&Mining Sciences,2017,91(1):104-111
[30]DAI Z J,KUANG Z B,ZHAO S X.Reflection and transmission of elastic waves from the interface of a fluid-saturated porous solid and a double porosity solid[J].Transport in Porous Media,2006,65(2):237-264
[31]ZHAO L X,HAN D H,YAO Q L,et al.Seismic reflection dispersion due to wave-induced fluid flow in heterogeneous reservoir rocks[J].Geophysics,2015,80(3):D221-D235
[32]PRIDE S R,BERRYMAN J G,HARRIS J M.Seismic attenuation due to wave-induced flow[J].Journal of Geophysical Research Atmospheres,2004,109(B1):59-70
[33]贺鹏飞,夏唐代,刘志军,等.双重孔隙介质中P1波在自由边界上的反射[J].岩土力学,2016,37(6):1753-1761HE P F,XIA T D,LIU Z J,et al.Reflection of P1wave from free surfaces of double-porosity media[J].Rock and Soil Mechanics,2016,37(6):1753-1761