Biot介质中井外声源激发井孔声场的理论研究与数值模拟
摘要
从理论上研究不同类型声源产生的地震波与井孔的相互作用,是典型的地震波散射问题,它对解释垂直地震剖面法和井间地震的测量资料有直接的意义。
本文依照Biot理论,针对孔隙地层中井外爆炸点源、井外点力源及两口井的井内居中爆炸点源三种地震模型进行了理论研究和数值模拟。考虑接收器所在的井均为裸眼井情况,对三种模型的井孔内外的声场进行了详细的理论推导并给出了计算公式,并针对不同源距、不同声源主频和不同地层参数对井内声场进行了全波模拟和特性分析,其中重点研究了井外点力源模型,首先考察了井外的直达波,发现这时的直达波有快纵波、慢纵波和SV波,但起主导作用的是快纵波和SV波;然后在不同条件下考察井内的全波特征,并对孔隙度、渗透率及方位角等影响全波波形的因素进行了考察和比较,进行了分析和描述;最后进行了频率—波数分析,从而对井内的各极波场的相速度大小和频散现象有更直观的了解。本文在研究两口井的井间地震模型时,只考虑了井间一次散射的情况,通过波场模拟发现井间地震模型的声波场特征与井外点力源模型的声波场特征极其相似。
本文针对不同的地震模型进行理论研究和模拟,有利于掌握井间地震中波场的传播规律和特性,对实际波场的识别与分离也具有一定的指导意义。
Acoustic logging is a variety of specific acoustic technology logging collectively. The theoretical foundation is the elastic Wave’s excitation and propagation in the columnar layered medium. Theoretically studies the rule of acoustic excitation, propagation and reception in the borehole. The acoustic logging theory’s main content researches the interaction of the elastic wave and the borehole entrance from different angle, so we should not only consider the different type of acoustic source, but also consider the type of stratum medium and the borehole system’s geometry structure and so on in theoretical research. This work is also the main subject in the theoretical studies of acoustic logging.
For many years , acoustic logging get a rapid development. Conventional acoustic logging put acoustic sources and detectors in the same borehole, but acoustic logging is not very good on stratum far from the hole. Although seismic on the ground can detect large range, but it has not high precision on stratum. Cross well is one of methods that can remedy the lack of acoustic logging and seismic. It put up a bridge between acoustic logging and seismic. Measuring the stratum across the borehole and reservoir specificity can remedy the lack of cross detectability in the borehole. It also can settle many questions such as the unbalance of gathering the information type and the information abundance between the borehole and the cross well.
So we should establish physics model base on the fact circs on cross well seismic. Resolving and computing acoustic field radiation, propagation and effect between boreholes from strict wave-equation and further studies on the rule of sound wave in cross well seismic are necessary. We should research the dielectric feature out the borehole and the effect stratum interface to the full wave field and the partial wave field in the borehole. This work can make the mode perfect and help us comprehend the actual measuring method and the results.
My subject launches based on such goal.In this paper I discuss apart three models in the Biot solid these excited by an external explosive point source of cross well, the model of external single point force source, the model of explosive point source located at axis in two wells through theoretical analysis and numerical simulation. Actually all these models belong to the model of cross well seismic.
In the model that excited by an external explosive point source of cross well, the theoretical expressions were solved in and out borehole about all of frequency. The direct field only have longitudinal wave. According to the theoretical expressions, I found that the acoustic field in borehole excited by an external explosive point source is quite to the summation of acoustic field excited by infinite orders multipole sources located at the axis of borehole. This article puts up the numerical simulation and frequency wave-number analysis of full wave to acoustic sound field in the borehole which selects different center frequency, different radial spacing and different stratum. The stimulation shows that we must take into account more order of multipole term with increasing of center frequency, different stratum, receive distance offset the axis of borehole and degree of eccentricity. At the same time, Results of numerical analysis showed that the amplitude of Stoneley excited by the borehole will increase when reduce the center frequency in the same distance and stratum. The rule is uniform as acoustic logging. The amplitude of Stoneley wave excited in the borehole and other waves will be reduced even disappeared with the increasing of the distance. It will only left the longitudinal wave because the effect between the spherical wave excited by an external explosive point source of cross well and the borehole become lower with the increasing of the distance. The amplitude of Stoneley wave is larger in hard stratum than in soft stratum in the same distance and center frequency.
The model of external explosive point source of cross well can only measure the speed of longitudinal wave. It can’t reflect all the stratum information accurately. This paper has simulated the model of external single point force source about this lack. The direct field is not only has longitudinal wave but also has SV wave in this model of external single point force source. It can receive longitudinal wave, transverse wave and all kinds of mode waves. We solve the theoretical expressions in and out borehole about all of frequency. The acoustic field in borehole excited by an external explosive point source is quite to the summation of acoustic field excited by infinite orders multipole sources located at the axis of borehole. Results of numerical analysis showed that the effect by different center frequency, different stratum and receive distance offset the axis of borehole in model of external single point force source is very resemble to the model of external explosive point source. It can receive longitudinal wave, transverse wave and all kinds of mode waves. We can acquire details about configuration. We can receive critical refractive longitudinal wave and receive critical refractive longitudinal wave in soft and hard stratum. The amplitude of transition critical longitudinal wave main associated with center frequency of sound source, stratum parameter, incident transversal wave’s strength. At the same time, I also considered the influence to full wave about some pore parameter and the position angle. The results show that porosity and the rate of permeation widely impact Stoneley wave and dipole flexural wave. In numerical simulation of frequency-wave number, it obviously shows that the comparation of phase velocity about the model wave’s of unipolar field, dipole field and four-pole field and dispersive situation. Through numerical simulation and analysis, we should comprehend the feature of seismic wave field in the pore stratum borehole. It is advantageous to realize and separate the seismic field in the borehole and receive the seismic field spread along well direction. That can help us obtain the details of reservoir and the stratum structure.
At last, we studied the model of explosive point source located at axis in two wells in theory. Its direct field has longitudinal wave and SV wave. At the same time, Critical refractive longitudinal wave , Critical refractive longitudinal wave and all kinds of mode waves are received in the other well. Acoustic field has become comparatively infirmness once transmission and scattering. So we only calculate one time scattering. We solve the theoretical expressions in and out borehole about all of frequency. Acoustic field had been simulated and analyzed. Numerical value showed that the result of full wave is alike to external single point force. But because the distance between two wells is several-ten meters to several-hundred meters, A lot of seismic waves are excitated. It make me obtain abundant information of acoustic field. It is avail to identify and analyze different waves in full wave field.
In this paper, I discuss the different models of cross well seismic in the Biot solid, Its theoretical study and numerical simulation to full wave field’s identifying and separation, to explaintion of cross well seismic’s data has much reference. It also make us have more comprehender and understanding in cross well seismic’s field.
本文依照Biot理论,针对孔隙地层中井外爆炸点源、井外点力源及两口井的井内居中爆炸点源三种地震模型进行了理论研究和数值模拟。考虑接收器所在的井均为裸眼井情况,对三种模型的井孔内外的声场进行了详细的理论推导并给出了计算公式,并针对不同源距、不同声源主频和不同地层参数对井内声场进行了全波模拟和特性分析,其中重点研究了井外点力源模型,首先考察了井外的直达波,发现这时的直达波有快纵波、慢纵波和SV波,但起主导作用的是快纵波和SV波;然后在不同条件下考察井内的全波特征,并对孔隙度、渗透率及方位角等影响全波波形的因素进行了考察和比较,进行了分析和描述;最后进行了频率—波数分析,从而对井内的各极波场的相速度大小和频散现象有更直观的了解。本文在研究两口井的井间地震模型时,只考虑了井间一次散射的情况,通过波场模拟发现井间地震模型的声波场特征与井外点力源模型的声波场特征极其相似。
本文针对不同的地震模型进行理论研究和模拟,有利于掌握井间地震中波场的传播规律和特性,对实际波场的识别与分离也具有一定的指导意义。
Acoustic logging is a variety of specific acoustic technology logging collectively. The theoretical foundation is the elastic Wave’s excitation and propagation in the columnar layered medium. Theoretically studies the rule of acoustic excitation, propagation and reception in the borehole. The acoustic logging theory’s main content researches the interaction of the elastic wave and the borehole entrance from different angle, so we should not only consider the different type of acoustic source, but also consider the type of stratum medium and the borehole system’s geometry structure and so on in theoretical research. This work is also the main subject in the theoretical studies of acoustic logging.
For many years , acoustic logging get a rapid development. Conventional acoustic logging put acoustic sources and detectors in the same borehole, but acoustic logging is not very good on stratum far from the hole. Although seismic on the ground can detect large range, but it has not high precision on stratum. Cross well is one of methods that can remedy the lack of acoustic logging and seismic. It put up a bridge between acoustic logging and seismic. Measuring the stratum across the borehole and reservoir specificity can remedy the lack of cross detectability in the borehole. It also can settle many questions such as the unbalance of gathering the information type and the information abundance between the borehole and the cross well.
So we should establish physics model base on the fact circs on cross well seismic. Resolving and computing acoustic field radiation, propagation and effect between boreholes from strict wave-equation and further studies on the rule of sound wave in cross well seismic are necessary. We should research the dielectric feature out the borehole and the effect stratum interface to the full wave field and the partial wave field in the borehole. This work can make the mode perfect and help us comprehend the actual measuring method and the results.
My subject launches based on such goal.In this paper I discuss apart three models in the Biot solid these excited by an external explosive point source of cross well, the model of external single point force source, the model of explosive point source located at axis in two wells through theoretical analysis and numerical simulation. Actually all these models belong to the model of cross well seismic.
In the model that excited by an external explosive point source of cross well, the theoretical expressions were solved in and out borehole about all of frequency. The direct field only have longitudinal wave. According to the theoretical expressions, I found that the acoustic field in borehole excited by an external explosive point source is quite to the summation of acoustic field excited by infinite orders multipole sources located at the axis of borehole. This article puts up the numerical simulation and frequency wave-number analysis of full wave to acoustic sound field in the borehole which selects different center frequency, different radial spacing and different stratum. The stimulation shows that we must take into account more order of multipole term with increasing of center frequency, different stratum, receive distance offset the axis of borehole and degree of eccentricity. At the same time, Results of numerical analysis showed that the amplitude of Stoneley excited by the borehole will increase when reduce the center frequency in the same distance and stratum. The rule is uniform as acoustic logging. The amplitude of Stoneley wave excited in the borehole and other waves will be reduced even disappeared with the increasing of the distance. It will only left the longitudinal wave because the effect between the spherical wave excited by an external explosive point source of cross well and the borehole become lower with the increasing of the distance. The amplitude of Stoneley wave is larger in hard stratum than in soft stratum in the same distance and center frequency.
The model of external explosive point source of cross well can only measure the speed of longitudinal wave. It can’t reflect all the stratum information accurately. This paper has simulated the model of external single point force source about this lack. The direct field is not only has longitudinal wave but also has SV wave in this model of external single point force source. It can receive longitudinal wave, transverse wave and all kinds of mode waves. We solve the theoretical expressions in and out borehole about all of frequency. The acoustic field in borehole excited by an external explosive point source is quite to the summation of acoustic field excited by infinite orders multipole sources located at the axis of borehole. Results of numerical analysis showed that the effect by different center frequency, different stratum and receive distance offset the axis of borehole in model of external single point force source is very resemble to the model of external explosive point source. It can receive longitudinal wave, transverse wave and all kinds of mode waves. We can acquire details about configuration. We can receive critical refractive longitudinal wave and receive critical refractive longitudinal wave in soft and hard stratum. The amplitude of transition critical longitudinal wave main associated with center frequency of sound source, stratum parameter, incident transversal wave’s strength. At the same time, I also considered the influence to full wave about some pore parameter and the position angle. The results show that porosity and the rate of permeation widely impact Stoneley wave and dipole flexural wave. In numerical simulation of frequency-wave number, it obviously shows that the comparation of phase velocity about the model wave’s of unipolar field, dipole field and four-pole field and dispersive situation. Through numerical simulation and analysis, we should comprehend the feature of seismic wave field in the pore stratum borehole. It is advantageous to realize and separate the seismic field in the borehole and receive the seismic field spread along well direction. That can help us obtain the details of reservoir and the stratum structure.
At last, we studied the model of explosive point source located at axis in two wells in theory. Its direct field has longitudinal wave and SV wave. At the same time, Critical refractive longitudinal wave , Critical refractive longitudinal wave and all kinds of mode waves are received in the other well. Acoustic field has become comparatively infirmness once transmission and scattering. So we only calculate one time scattering. We solve the theoretical expressions in and out borehole about all of frequency. Acoustic field had been simulated and analyzed. Numerical value showed that the result of full wave is alike to external single point force. But because the distance between two wells is several-ten meters to several-hundred meters, A lot of seismic waves are excitated. It make me obtain abundant information of acoustic field. It is avail to identify and analyze different waves in full wave field.
In this paper, I discuss the different models of cross well seismic in the Biot solid, Its theoretical study and numerical simulation to full wave field’s identifying and separation, to explaintion of cross well seismic’s data has much reference. It also make us have more comprehender and understanding in cross well seismic’s field.
引文
1.J.E.White 著,陈俊生 译,1987,《地下声波-地震波的应用》,石油工业出版社。
2.鲍亦应,毛昭宙著,刘殿魁,苏先樾译,1993,《弹性波的衍射与动应力集中》,科学出版社.
3.周来江,井外声源激发井孔声波场及井间地震的理论研究与数值模拟,吉林大学硕士学位论文, 2006.
4.吕伟国,用孔隙柱管模拟测井声系的数值分析与交叉偶极声测井资料反演的应用研究,吉林大学硕士学位论文,2004.
5.Biot , M. A., Propagation of elastic waves in a cylindrical bore containing a fluid, J. Appl. Phys.,23,997-1005,1952.
6.White, J. E. and Zechman, R. E. Computed responses of an acoustic logging tool, Geophysics,33,302-310,1968
7.Petersion, E.W., Acoustic wave propagation along a fluid-filled cylinder, J. Appl. Phys.,45,3340-3350,1974.
8.Roever,W. L., Rosenbaum, J. H., and Vining, T. F., Acoustic waves from an impulsive source in a fluid-filled borehole, J. Acoust. Soc. Am., 55, 1144-1157, 1974.
9.Rosenbaum, J.H., Synthetic microseismograms: logging in porous formation: Geophysics,39,14-32,1974.
10.Biot , M. A., Theory of Propagation of elastic waves in a fluid-filled saturated porous solid in Low frequency range, J. Acoust.Soc. Am., Vol., 28,168-178., 1956.
11.Tsang, L., and Kong, J. A., Asymptotic methods for the first compressional wave arrival in a fluid-filled borehole, J. Acoust..Soc.Am., 65,647-654,1979
12.王克协,董庆德等,柱状双层准弹性介质中声辐射场的理论分析—声波测井理论研究(Ⅰ),吉林大学自然科学学报,2,47-56,1979.
13.Biot. M. A., Theory of Propagation of elastic waves in a fluid-filled saturated porous solid, J. Acoust.Soc. Am., 28,a168-178. b179-191, 1956.
14.Biot. M. A., Mechanics of deformation and acoustic propagation in porous media. J. Appl. Phys., 33, 1482-1483,1962.
15.Pride S R, Tromeur E and Berryman J G., Biot slow-wave effects in stratified rock, Geophysics, 67,271-281,2002.
16.Pride S R. and Garambois , The role of slow waves in electroseismic wave phenomena., J.Acoust.Soc.Am.,111(2),697-706,2002.
17.Rosenbaum,J.H.,Synthetic microseismograms: logging in porous formation: Geophysics,39,14-32,1974.
18.王克协,董庆德,渗透性地层油井中声场的理论分析与计算,石油学报,7,59-68,1986.
19.White, J. E., 1967.The hula log :A proposed acoustic tool . SPWLA,8th LOG,Symposium。
20.Roever, W.,Rosenbaum, J.,and Vining, T.,1974,Acoustic waves from an impulsive source in a fluid-filled borehole , J.Acoust.Soc.Am.,55,1144-1157.
21.Tongtaow. C., 1982. Wave propagation along a cylindrical borehole in a transversely isotropic medium: Ph. D. dissertation, Colorado School of Mines.
22.Kurkjian, A. L., and Chang, S. K., 1983. Geometric decay of the headwaves excited by a point force in a fluid-filled borehole: Presented at the 53rd Ann. Internat. Mtg. And Expos., Soc. Explor. Geophys., Las Vegas.
23.Winbow, G., and Rice, J. A., 1984.Theoretical performance of multipole sonic logging tools: Presented at the 54th Ann. Internat. Mtg. and Expos., Soc. Explor. Geophys., Atlanta.
24.张金钟, 郑传汉, 1988。裸眼井中弹性波传播的非对称模式的数值研究。地球物理学报, 31: 464-469.
25.张碧星,王克协,董庆德,1995,双相介质井孔多级源声测井理论及分波与全波计算,地球物理学报,38(增刊 1),178-192.
26.崔志文,多孔介质声学模型与多极源声电效应测井和多极随钻声测井的理论与数值研究,吉林大学博士学位论文, 2004.
27.丛令梅,BISQ 横向各向同性地层流体井孔中多极源声波场的理论求解与数值模拟,吉林大学硕士学位论文, 2005.
28. 董世振,杜春,2002,井中地震勘探仪器的现状与发展,物探装备,12(4)227-234.
29.[苏]E.I.加尔比林著,朱光明,肖慈珣,余惠宁等译,《垂直地震剖面》,石油工业出版社,1983.
30.董世泰,井间地震应用技术,中国石油勘探开发研究院,博士学位论文,2004.
31.吴律,《层析基础及其在井间地震中的应用》,石油出版社,1997.
32.郭建,2004,VSP 技术应用现状及发展趋势,勘探地球物理进展,勘探地球物理进展,27(1):3-8
33.周建宇,井间地震研究与应用,中国科学院研究生院博士学位论文, 2002.
34.刘合,王玉普,隋军,薛家峰,刘兵编写,《国外井间地震技术》,石油工业出版社,1998.
35.K.Dautenhahn Wyatt,1981.Synthetic vertical seismic profile. 、Geophysics, 46(6):880-891.
36. Philippe Jean and Michel Bouchon,1991,Cross-borehole simulation of wave propagation, Geophysics ,56(7),1103-1113
37.A. M. Ionov and G. A. Maximov,1999.Excitation of a tube wave in a borehole by an external seismic source. Acoust. Phys,45:311–316.
38.吕秀梅,偏心点源激发声信号的数值仿真及利用交叉偶极声测井资料提取地层各向异性信息的方法与应用研究,吉林大学硕士学位论文,2002.
39.王克协,J.E. White,伍先运,1996,Biot介质中P波与井孔的耦合,地球物理学报,39(1):103-112.
40.沈建国,张海澜,2000.井内偏心声源激发的三维声场的数值研究,地球物理学报,43(2):279-286。
41.闫慧欣, Biot 介质中倾斜入射平面 P 波与井孔耦合的理论研究和数值模拟,吉林大学硕士学位论文, 2007.
2.鲍亦应,毛昭宙著,刘殿魁,苏先樾译,1993,《弹性波的衍射与动应力集中》,科学出版社.
3.周来江,井外声源激发井孔声波场及井间地震的理论研究与数值模拟,吉林大学硕士学位论文, 2006.
4.吕伟国,用孔隙柱管模拟测井声系的数值分析与交叉偶极声测井资料反演的应用研究,吉林大学硕士学位论文,2004.
5.Biot , M. A., Propagation of elastic waves in a cylindrical bore containing a fluid, J. Appl. Phys.,23,997-1005,1952.
6.White, J. E. and Zechman, R. E. Computed responses of an acoustic logging tool, Geophysics,33,302-310,1968
7.Petersion, E.W., Acoustic wave propagation along a fluid-filled cylinder, J. Appl. Phys.,45,3340-3350,1974.
8.Roever,W. L., Rosenbaum, J. H., and Vining, T. F., Acoustic waves from an impulsive source in a fluid-filled borehole, J. Acoust. Soc. Am., 55, 1144-1157, 1974.
9.Rosenbaum, J.H., Synthetic microseismograms: logging in porous formation: Geophysics,39,14-32,1974.
10.Biot , M. A., Theory of Propagation of elastic waves in a fluid-filled saturated porous solid in Low frequency range, J. Acoust.Soc. Am., Vol., 28,168-178., 1956.
11.Tsang, L., and Kong, J. A., Asymptotic methods for the first compressional wave arrival in a fluid-filled borehole, J. Acoust..Soc.Am., 65,647-654,1979
12.王克协,董庆德等,柱状双层准弹性介质中声辐射场的理论分析—声波测井理论研究(Ⅰ),吉林大学自然科学学报,2,47-56,1979.
13.Biot. M. A., Theory of Propagation of elastic waves in a fluid-filled saturated porous solid, J. Acoust.Soc. Am., 28,a168-178. b179-191, 1956.
14.Biot. M. A., Mechanics of deformation and acoustic propagation in porous media. J. Appl. Phys., 33, 1482-1483,1962.
15.Pride S R, Tromeur E and Berryman J G., Biot slow-wave effects in stratified rock, Geophysics, 67,271-281,2002.
16.Pride S R. and Garambois , The role of slow waves in electroseismic wave phenomena., J.Acoust.Soc.Am.,111(2),697-706,2002.
17.Rosenbaum,J.H.,Synthetic microseismograms: logging in porous formation: Geophysics,39,14-32,1974.
18.王克协,董庆德,渗透性地层油井中声场的理论分析与计算,石油学报,7,59-68,1986.
19.White, J. E., 1967.The hula log :A proposed acoustic tool . SPWLA,8th LOG,Symposium。
20.Roever, W.,Rosenbaum, J.,and Vining, T.,1974,Acoustic waves from an impulsive source in a fluid-filled borehole , J.Acoust.Soc.Am.,55,1144-1157.
21.Tongtaow. C., 1982. Wave propagation along a cylindrical borehole in a transversely isotropic medium: Ph. D. dissertation, Colorado School of Mines.
22.Kurkjian, A. L., and Chang, S. K., 1983. Geometric decay of the headwaves excited by a point force in a fluid-filled borehole: Presented at the 53rd Ann. Internat. Mtg. And Expos., Soc. Explor. Geophys., Las Vegas.
23.Winbow, G., and Rice, J. A., 1984.Theoretical performance of multipole sonic logging tools: Presented at the 54th Ann. Internat. Mtg. and Expos., Soc. Explor. Geophys., Atlanta.
24.张金钟, 郑传汉, 1988。裸眼井中弹性波传播的非对称模式的数值研究。地球物理学报, 31: 464-469.
25.张碧星,王克协,董庆德,1995,双相介质井孔多级源声测井理论及分波与全波计算,地球物理学报,38(增刊 1),178-192.
26.崔志文,多孔介质声学模型与多极源声电效应测井和多极随钻声测井的理论与数值研究,吉林大学博士学位论文, 2004.
27.丛令梅,BISQ 横向各向同性地层流体井孔中多极源声波场的理论求解与数值模拟,吉林大学硕士学位论文, 2005.
28. 董世振,杜春,2002,井中地震勘探仪器的现状与发展,物探装备,12(4)227-234.
29.[苏]E.I.加尔比林著,朱光明,肖慈珣,余惠宁等译,《垂直地震剖面》,石油工业出版社,1983.
30.董世泰,井间地震应用技术,中国石油勘探开发研究院,博士学位论文,2004.
31.吴律,《层析基础及其在井间地震中的应用》,石油出版社,1997.
32.郭建,2004,VSP 技术应用现状及发展趋势,勘探地球物理进展,勘探地球物理进展,27(1):3-8
33.周建宇,井间地震研究与应用,中国科学院研究生院博士学位论文, 2002.
34.刘合,王玉普,隋军,薛家峰,刘兵编写,《国外井间地震技术》,石油工业出版社,1998.
35.K.Dautenhahn Wyatt,1981.Synthetic vertical seismic profile. 、Geophysics, 46(6):880-891.
36. Philippe Jean and Michel Bouchon,1991,Cross-borehole simulation of wave propagation, Geophysics ,56(7),1103-1113
37.A. M. Ionov and G. A. Maximov,1999.Excitation of a tube wave in a borehole by an external seismic source. Acoust. Phys,45:311–316.
38.吕秀梅,偏心点源激发声信号的数值仿真及利用交叉偶极声测井资料提取地层各向异性信息的方法与应用研究,吉林大学硕士学位论文,2002.
39.王克协,J.E. White,伍先运,1996,Biot介质中P波与井孔的耦合,地球物理学报,39(1):103-112.
40.沈建国,张海澜,2000.井内偏心声源激发的三维声场的数值研究,地球物理学报,43(2):279-286。
41.闫慧欣, Biot 介质中倾斜入射平面 P 波与井孔耦合的理论研究和数值模拟,吉林大学硕士学位论文, 2007.