基于Biot-Squirt方程的波场模拟
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摘要
Biot流动和喷射流动是含流体多孔隙介质中流体流动的两种重要力学机制 ,对地震波和声波的传播均产生重要影响 .Dvorkin和Nur提出了同时包含Biot流动和喷射流动力学机制的统一的BISQ(Biot Squirt)模型 ,基于这一模型 ,尽管有关弹性波在多孔隙介质中的衰减和频散问题已被广泛研究 ,然而 ,基于BISQ波传播方程的波场数值模拟至今仍未见报道 .本文从同时包含两种力学机制的孔隙弹性波方程出发 ,利用FCT有限差分法对含流体孔隙各向同性介质中的地震波和声波进行了数值模拟 ,并与基于Biot流动的Biot理论之模拟结果进行比较 .数值模拟结果表明 :同时包含Biot流动和喷射流动影响的地震波和声波速度比仅包含Biot流动作用的地震波和声波速度慢 ,慢P波的衰减比根据Biot理论模拟的慢P波衰减更强 .
The Biot-flow and squirt-flow mechanisms are two important mechanisms of fluid flow in porous media with fluids. The effects of the two mechanisms on propagation of seismic and acoustic waves are very important. Dvorkin and Nur presented an unified BISQ (Biot-Squirt) model, where the Biot and squirt-flow mechanisms are treated simultaneously. Although the attenuation and dispersion of the poroelastic waves have been widely investigated based on the model, so far as we know, no result about wave-field modeling based on the BISQ equation has been reported. In this paper, the wave-field simulation based on the BISQ equation in the isotropic medium is performed by using the FCT finite difference method, and the wave-field snapshots are compared with the results obtained from Biot's theory only including the Biot mechanism. Model results show that the seismic and acoustic propagations affected simultaneously by the Biot and squirt-flow mechanism are slower than those affected only by the Biot mechanism, and the slow P-wave attenuation based on the BISQ model is stronger than that based on the Biot model.
The Biot-flow and squirt-flow mechanisms are two important mechanisms of fluid flow in porous media with fluids. The effects of the two mechanisms on propagation of seismic and acoustic waves are very important. Dvorkin and Nur presented an unified BISQ (Biot-Squirt) model, where the Biot and squirt-flow mechanisms are treated simultaneously. Although the attenuation and dispersion of the poroelastic waves have been widely investigated based on the model, so far as we know, no result about wave-field modeling based on the BISQ equation has been reported. In this paper, the wave-field simulation based on the BISQ equation in the isotropic medium is performed by using the FCT finite difference method, and the wave-field snapshots are compared with the results obtained from Biot's theory only including the Biot mechanism. Model results show that the seismic and acoustic propagations affected simultaneously by the Biot and squirt-flow mechanism are slower than those affected only by the Biot mechanism, and the slow P-wave attenuation based on the BISQ model is stronger than that based on the Biot model.
引文
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[13] YANGDingHui,ZHANGZhongJie.EffectsoftheBiotandthesquirtflowcouplinginteractiononanisotropicelasticwaves.ChineseScienceBulletion,2000,45:2130—2138.
[14] DvorkinJ,NolenHoeksemaR ,NurA .Thesquirtflowmechanism:Macroscopicdescription.Geophysics,1994,59:428—438.
[15] DvorkinJ,MavkoG ,NurA .Squirtflowinfullysaturatedrocks.Geophysics,1995,60:97—107.
[16] DialloMS ,AppelE .Acousticwavepropagationinsaturatedporousmedia:reformationoftheBiot squirtflowtheory.J.Appl.Geophys.,2000,44:313—325.
[17] YangDH ,ZhangZJ.PoroelasticwaveequationincludingtheBiot squirtmechanismandthesolid fluidcouplinganisotropy.WaveMotion,2002,35:223—245.
[18] 杨顶辉,滕吉文.各向异性介质中三分量地震波记录的FCT有限差分模拟.石油地球物理勘探,1997,32:181—190.YANGDingHui,TENGJiWen.FCTfinitedifferencemodelingofthree componentseismicrecordsinanisotropicmedia.OilGeophysicalProspecting,1997,32:181—190.
[19] YangDH ,LiuE ,ZhangZJ,etal.Finite differencemodellingintwo dimensionalanisotropicmediausingaflux correctedtransporttechnique.Geophys.J.Int.,2002,148:320—328.
[2] WinklerKW .DispersionanalysisofvelocityandattenuationinBereasandstone.J.Geophys.Res.,1985,90:6793—6800.
[3] WinklerKW .Estimatesofvelocitiesdispersionbetweenseismicandultrasonicfrequencies.Geophysics,1986,51:183—189.
[4] WangZ ,NurA .Dispersionanalysisofacousticvelocitiesinrocks.J.Acoust.Soc.Am.,1990,87:2384—2395.
[5] MavkoG ,NurA .Waveattenuationinpartiallysaturatedrocks.Geophysics,1979,44(2):161—178.
[6] MiksisMJ.Effectofcontactlinemovementonthedispersionofwaveinpartiallysaturatedrocks.J.Geophys.Res.,1988,93(B6):6624—6634.
[7] PalmerID ,TravioliaML .Attenuationbysquirtflowinundersaturatedgassands.Geophysics,1980,45:1780—1792.
[8] DvorkinJ,NurA .Dynamicporoelasticity:AunifiedmodelwiththesquirtandtheBiotmechanisms.Geophysics,1993,58:524—533.
[9] ParraJO .ThetransverselyisotropicporoelasticwaveequationincludingtheBiotandthesquirtmechanisms:Theoryandapplication.Geophysics,1997,62:309—318.
[10] ParaJO .Poroelasticmodeltorelateseismicwaveattenuationanddispersiontopermeabilityanisotropy.Geophysics,2000,65:201—210.
[11] 杨顶辉.孔隙各向异性介质中基于BISQ模型的弹性波传播理论及有限元方法[博士后研究报告].北京:石油大学,1998.YANGDingHui.TheoryofpropagationofelasticwavesbasedontheBISQmodelandfiniteelementmethodinporousanisotropicmedia[PostdoctoralResearchReport].Beijing:PetroleumUniversity,1998.
[12] 杨顶辉,陈小宏,牟永光.双相介质中基于固流耦合各向异性的应力波方程.中国学术期刊文摘(科技快报),2000,6:75—77.YANGDingHui,CHENXiaoHong,MOUYongGuang.Astresswaveequationbasedontheanisotropyofsolid fluidcouplingdensityintwo phasemedia.ChineseScienceAbstracts(ScienceandTechnologyLetters),2000,6:75—77.
[13] YANGDingHui,ZHANGZhongJie.EffectsoftheBiotandthesquirtflowcouplinginteractiononanisotropicelasticwaves.ChineseScienceBulletion,2000,45:2130—2138.
[14] DvorkinJ,NolenHoeksemaR ,NurA .Thesquirtflowmechanism:Macroscopicdescription.Geophysics,1994,59:428—438.
[15] DvorkinJ,MavkoG ,NurA .Squirtflowinfullysaturatedrocks.Geophysics,1995,60:97—107.
[16] DialloMS ,AppelE .Acousticwavepropagationinsaturatedporousmedia:reformationoftheBiot squirtflowtheory.J.Appl.Geophys.,2000,44:313—325.
[17] YangDH ,ZhangZJ.PoroelasticwaveequationincludingtheBiot squirtmechanismandthesolid fluidcouplinganisotropy.WaveMotion,2002,35:223—245.
[18] 杨顶辉,滕吉文.各向异性介质中三分量地震波记录的FCT有限差分模拟.石油地球物理勘探,1997,32:181—190.YANGDingHui,TENGJiWen.FCTfinitedifferencemodelingofthree componentseismicrecordsinanisotropicmedia.OilGeophysicalProspecting,1997,32:181—190.
[19] YangDH ,LiuE ,ZhangZJ,etal.Finite differencemodellingintwo dimensionalanisotropicmediausingaflux correctedtransporttechnique.Geophys.J.Int.,2002,148:320—328.
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