圆柱形压电换能器在井中激励的声场
|
摘要
声波测井是一种重要的测井方法,在油田勘探和开采、工程物探等许多领域有着广泛的应用。声源的特性对声波测井的结果有着很重要的影响。以往的文章主要考虑了传播媒质对接收的声波信号的影响,而很少考虑声源对接收的声波信号的影响,典型的做法是采用未知声源强度的点膨胀声源来模拟测井声场。考虑到测井采用柱状换能器发射声波的实际情况,本文研究在给定激励电压脉冲作用下柱状薄管换能器的辐射声场和井孔响应。
利用辐射阻抗的谐振条件,分析了圆柱压电换能器的暂态响应。在考虑周围介质耦合作用的情况下,根据留数定理,导出了圆柱形压电换能器的机电方程,建立了其等效电路,求解了时域、频域的传递函数,从而得到了在电信号激励下柱状换能器表面振动位移的时域和频域函数。
利用波数实轴积分法和快速傅立叶变换法,计算了柱源模型下弹性介质的井孔声场,绘出了声场的时域波形图,并且分析和讨论了不同介质中的波形的差异。与前人采用假设声源强度只能求出波场的相对幅度不同,本文求出了在给定激励电压下的测井声场幅度。
换能器辐射的声信号受到电压驱动信号和换能器自身特性的影响,在换能器物理特性的基础上,通过调整换能器的几何尺寸,改变周围耦合液体的参数,选择合适的电压脉冲信号,可使换能器在测井过程中辐射出满足特殊需要的声波信号。这对设计特定要求的换能器是很有意义的。
Acoustic well-logging is a widely used method in oil and gas exploration. The characteristics of acoustic wave source have an important influence on the acoustic well-logs. The former papers mainly research the influence of the media, the typical method adopts the point source of an unknown intensity to calculate the sound field in the borehole. Considering the practical circs, this paper research the radiated field of the cylindrical piezoelectric transducer and the borehole response.
This paper analyses the transient response of cylindrical piezoelectric transducer, develops its equivalent circuit and determines the relation between the applied electric signal and the radiated acoustic signal. By using the residue principle, the transient functions of the temporal and frequency domains for the transducer are determined analytically for any electrical driving signal.
The integral along the real wave-number axis and frequency axis are calculated .The waveform is plotted in the time domain. Several different waveforms are compared and discussed in different media. The sound field is different from the supposed point source, the exact intensity is got.
The radiating signals depend on both the type of the exciting voltage and the characteristics of the piezoelectric transducer, according to physical characteristics of the transducer choosing proper piezoelectric material, the suitable geometry of the transducer and the surrounding coupling fluid can improve the quality of the transmitted acoustic signal, and also make the transducer satisfy special purposes. The results are significant for designing the piezoelectric transducer.
利用辐射阻抗的谐振条件,分析了圆柱压电换能器的暂态响应。在考虑周围介质耦合作用的情况下,根据留数定理,导出了圆柱形压电换能器的机电方程,建立了其等效电路,求解了时域、频域的传递函数,从而得到了在电信号激励下柱状换能器表面振动位移的时域和频域函数。
利用波数实轴积分法和快速傅立叶变换法,计算了柱源模型下弹性介质的井孔声场,绘出了声场的时域波形图,并且分析和讨论了不同介质中的波形的差异。与前人采用假设声源强度只能求出波场的相对幅度不同,本文求出了在给定激励电压下的测井声场幅度。
换能器辐射的声信号受到电压驱动信号和换能器自身特性的影响,在换能器物理特性的基础上,通过调整换能器的几何尺寸,改变周围耦合液体的参数,选择合适的电压脉冲信号,可使换能器在测井过程中辐射出满足特殊需要的声波信号。这对设计特定要求的换能器是很有意义的。
Acoustic well-logging is a widely used method in oil and gas exploration. The characteristics of acoustic wave source have an important influence on the acoustic well-logs. The former papers mainly research the influence of the media, the typical method adopts the point source of an unknown intensity to calculate the sound field in the borehole. Considering the practical circs, this paper research the radiated field of the cylindrical piezoelectric transducer and the borehole response.
This paper analyses the transient response of cylindrical piezoelectric transducer, develops its equivalent circuit and determines the relation between the applied electric signal and the radiated acoustic signal. By using the residue principle, the transient functions of the temporal and frequency domains for the transducer are determined analytically for any electrical driving signal.
The integral along the real wave-number axis and frequency axis are calculated .The waveform is plotted in the time domain. Several different waveforms are compared and discussed in different media. The sound field is different from the supposed point source, the exact intensity is got.
The radiating signals depend on both the type of the exciting voltage and the characteristics of the piezoelectric transducer, according to physical characteristics of the transducer choosing proper piezoelectric material, the suitable geometry of the transducer and the surrounding coupling fluid can improve the quality of the transmitted acoustic signal, and also make the transducer satisfy special purposes. The results are significant for designing the piezoelectric transducer.
引文
1 M. A. Biot. Propagation of Elastic Waves in a Cylindrical Bore Containing a Fluid. J. Appl. Phy. 1952,(23):997~1005
2 M. A. Biot. Theory of Propagation of Elastic Waves in a Fluid-saturated Porous Solid. I Low-Frequency Range. J. Acoust. Soc. Am. 1956,(28):168~178
3 Aki K, Richard P. G.. Quantitative Seismology Theory and Methods. W. H. Freeman and Co. San Francisco.U.S. A. 1980:142~150
4 L Renlie, A. M Raaen. Sonic Wave Propagation in Fluid-filled Borehole Surrounded by a Formation with Stress Relief Induced Anisotropy. Geophysics. 1993,58:1257 ~1269
5 Kelly K C, Alforld R. M. Syntthetic Seismograms : a Finite Difference Approach. Geophysics. 1976,41(2):257~264
6 L Tsang and D Rader. Numerical Evaluation of the Transient Sonic Waveform Due to a Point Source in a Fluid-filled Borehole.Geophysics.1979,44:1706~1720
7 John P Castagna. Methods for Analysis of Sonic Logging. Dissertation for the Degree of PHD. 1982:3~16
8 Richard L, Gibson J r. Radiation from Seismic Sources in Cased and Cemented Borehole. Geophysics. 1994,59:518~533
9 D. A Berlincourt, D. R. Curran. Haffe. Piezoelectric and Piezomagnetic Materials and Their Function in Transducers. In: Physical Acoustics, Edited by W. P Mason, Academic, New York, 1964:223 ~224
10 Jean C .Piquette. Method for Transducer Suppression I: Thetory. J. Acoust .Soc. A m. 1992:1203 ~1213
11 Jean C Piquette. Method for Transducer Suppression II:Experiment. J.Acoust . Soc. A m. 1992:1214 ~1211
12 Jean C Piquette, Stepheen E Forsythe. Transducer Transient Suppression : Generalized Methods of Analysis. J .Acoust .Soc.A m. 1996 ,100:1577~1583
13 Jean C Piquette. Applications of the Method for Transducter Suppression to Various Transducer Types. J. Acoust. Soc. A m. 1994:646~651
14 A C Holly. A Method for the Generation of Broadband Acoustic Transmission. J . Acoust . Soc. A m. 1984,75:973~976
15 KostekS. Rand all C. J. Modelling of a Piezoelectric Transducer and Its Application to Full Waveform Acoustic Logging. J. Acoust. Soc.A.m.1994, 95:109~122
16 Edward W. Peterson. Acoustic Wave Propagation along a Fluid-filled Cylinder J.Appl.Phys.1994,45:3340~3350
17 J. E. White, R. E. Zechman. Computed Responses of an Acoustic Logging Tool. Geophysics. 1968,33:302~310
18 L. Tsang, J. A. Kong. Asymptotic Methods for the First Compressional Head Wave Arrival in a Filled Borehole. J. Acoust. Soc. Am.1979,63:647~654
19 A. L. Kurkjian. Numerical Computation of Individual Far-field Arrivals Excited by an Acoustic Source in a Borehole. Geophysics. 1985,50:852~866
20胡恒山,王克协.井孔周围轴对称声电耦合波.测井技术. 2000,241:3~13
21胡恒山,王克协,刘家琦.孔隙介质中快纵波的衰减特性和动力协调现象.计算物理. 2002,19(3):203~207
22胡恒山,马俊,王克协.井孔声场计算中的黎曼叶选择.吉林大学学报.1998,(2):115~124
23伍先运,王克协.利用声全波测井资料求取储层渗透率的方法与应用研究.地球物理学报. 1995,38(增刊):224~231
24董和风,王克协.弹性固体地层-流体井孔弹性波场的有限差分数值模拟.1995,38(增刊):205~215
25余仕成,伍先运,王克协.全波声测井理论研究中的声源模型及其影响.地球物理学报. 1995,38(增刊):232~241
26张海澜,王秀明,应崇福.弹性介质中充液井孔的漏模和井孔声场中的分波计算.地球物理学报.中国科学(A辑). 1995,(7):742~752
27马俊.井孔声波理论分析与复杂储层单、多极声源测井正反演研究.吉林大学博士学位论文. 1998:10~48
28 Hengshan Hu, Jiaqi Liu. Simulation of the Converted Electric Field. SEG Technical Program Expanded Abstracts. 2002: 348~351
29 Hengshan Hu, Jiaqi Liu. Attenuation and Seismoelectric Characteristics of Dynamically Compatible Porous Media SEG Technical Program Expanded Abstracts. 2002:1817~1820
30石昆法.震电效应原理和初步实验结果[I].地球物理学报. 2001,44(5):720~728
31 Mikhailov O V,Queen J, Toksoz M N. Using Borehole Electroseismic Measurements to Detect and Characterize Fractured Permeable Zones. Geophysics. 2000,65:1098~1112
32刘洪.震电效应研究在资源勘探中的应用前景I.地球物理学进展. 2002,17(2):211~217
33崔志文,王克协,曹正良.多孔介质BISQ模型中的慢纵波.物理学报. 2004,53(9):3083~3089
34 Han Q, Wang, Z. Time-domain simulation of SH-wave-induced electromagnetic field in heterogeneous porous media: a fast finite-element algorithm. Geophysics. 2001,66(2):488~461
35关威,胡恒山,储昭坦.声诱导电磁场的赫兹矢量表示与多极声电测井模拟.物理学报. 2006,55(1):267~274
36法林,林峰,陈文辉.石油勘探用薄圆环换能器的源函数推导和特性分析.地球物理学报. 1996,39(增刊):387~399
37法林,陈文辉,王克协,马瑞林.超声成像测井仪声波换能器的特性分析.石油仪器. 1997,11(2):26~30
38何祚镛,赵玉芳著.声学基础.国防工业出版社, 1981:218~220
39周士弘,王克协,马俊.利用井孔首波求取Vs和Qp值的广义线性反演方法的应用研究.1995,38(增刊):242~252
40阿肯巴赫.弹性固体中波的传播.洪镜如译.同济大学出版社, 1992:42~78
41 B. A.奥尔特.固体中的声场和波.孙承平译.科学出版社, 1982:258~264
42张福学.现代压电学.科学出版社, 2001:48~99
43林书玉.超声换能器的原理及设计.科学出版社, 2004:1~7
44栾桂冬,张金铎.压电换能器和换能器阵.北京出版社, 2004:113~126
45胡恒山,王克协.井孔周围轴对称声电耦合波:理论I.测井技术. 1999, 23(6):427~432
46胡恒山,王克协.声电效应测井模型实验研究I.测井技术. 2001, 25(2):89~95
47胡恒山.孔隙地层井壁上的声波首波及其诱导电磁场的原因.物理学报. 2003,52(8):1954~1959
2 M. A. Biot. Theory of Propagation of Elastic Waves in a Fluid-saturated Porous Solid. I Low-Frequency Range. J. Acoust. Soc. Am. 1956,(28):168~178
3 Aki K, Richard P. G.. Quantitative Seismology Theory and Methods. W. H. Freeman and Co. San Francisco.U.S. A. 1980:142~150
4 L Renlie, A. M Raaen. Sonic Wave Propagation in Fluid-filled Borehole Surrounded by a Formation with Stress Relief Induced Anisotropy. Geophysics. 1993,58:1257 ~1269
5 Kelly K C, Alforld R. M. Syntthetic Seismograms : a Finite Difference Approach. Geophysics. 1976,41(2):257~264
6 L Tsang and D Rader. Numerical Evaluation of the Transient Sonic Waveform Due to a Point Source in a Fluid-filled Borehole.Geophysics.1979,44:1706~1720
7 John P Castagna. Methods for Analysis of Sonic Logging. Dissertation for the Degree of PHD. 1982:3~16
8 Richard L, Gibson J r. Radiation from Seismic Sources in Cased and Cemented Borehole. Geophysics. 1994,59:518~533
9 D. A Berlincourt, D. R. Curran. Haffe. Piezoelectric and Piezomagnetic Materials and Their Function in Transducers. In: Physical Acoustics, Edited by W. P Mason, Academic, New York, 1964:223 ~224
10 Jean C .Piquette. Method for Transducer Suppression I: Thetory. J. Acoust .Soc. A m. 1992:1203 ~1213
11 Jean C Piquette. Method for Transducer Suppression II:Experiment. J.Acoust . Soc. A m. 1992:1214 ~1211
12 Jean C Piquette, Stepheen E Forsythe. Transducer Transient Suppression : Generalized Methods of Analysis. J .Acoust .Soc.A m. 1996 ,100:1577~1583
13 Jean C Piquette. Applications of the Method for Transducter Suppression to Various Transducer Types. J. Acoust. Soc. A m. 1994:646~651
14 A C Holly. A Method for the Generation of Broadband Acoustic Transmission. J . Acoust . Soc. A m. 1984,75:973~976
15 KostekS. Rand all C. J. Modelling of a Piezoelectric Transducer and Its Application to Full Waveform Acoustic Logging. J. Acoust. Soc.A.m.1994, 95:109~122
16 Edward W. Peterson. Acoustic Wave Propagation along a Fluid-filled Cylinder J.Appl.Phys.1994,45:3340~3350
17 J. E. White, R. E. Zechman. Computed Responses of an Acoustic Logging Tool. Geophysics. 1968,33:302~310
18 L. Tsang, J. A. Kong. Asymptotic Methods for the First Compressional Head Wave Arrival in a Filled Borehole. J. Acoust. Soc. Am.1979,63:647~654
19 A. L. Kurkjian. Numerical Computation of Individual Far-field Arrivals Excited by an Acoustic Source in a Borehole. Geophysics. 1985,50:852~866
20胡恒山,王克协.井孔周围轴对称声电耦合波.测井技术. 2000,241:3~13
21胡恒山,王克协,刘家琦.孔隙介质中快纵波的衰减特性和动力协调现象.计算物理. 2002,19(3):203~207
22胡恒山,马俊,王克协.井孔声场计算中的黎曼叶选择.吉林大学学报.1998,(2):115~124
23伍先运,王克协.利用声全波测井资料求取储层渗透率的方法与应用研究.地球物理学报. 1995,38(增刊):224~231
24董和风,王克协.弹性固体地层-流体井孔弹性波场的有限差分数值模拟.1995,38(增刊):205~215
25余仕成,伍先运,王克协.全波声测井理论研究中的声源模型及其影响.地球物理学报. 1995,38(增刊):232~241
26张海澜,王秀明,应崇福.弹性介质中充液井孔的漏模和井孔声场中的分波计算.地球物理学报.中国科学(A辑). 1995,(7):742~752
27马俊.井孔声波理论分析与复杂储层单、多极声源测井正反演研究.吉林大学博士学位论文. 1998:10~48
28 Hengshan Hu, Jiaqi Liu. Simulation of the Converted Electric Field. SEG Technical Program Expanded Abstracts. 2002: 348~351
29 Hengshan Hu, Jiaqi Liu. Attenuation and Seismoelectric Characteristics of Dynamically Compatible Porous Media SEG Technical Program Expanded Abstracts. 2002:1817~1820
30石昆法.震电效应原理和初步实验结果[I].地球物理学报. 2001,44(5):720~728
31 Mikhailov O V,Queen J, Toksoz M N. Using Borehole Electroseismic Measurements to Detect and Characterize Fractured Permeable Zones. Geophysics. 2000,65:1098~1112
32刘洪.震电效应研究在资源勘探中的应用前景I.地球物理学进展. 2002,17(2):211~217
33崔志文,王克协,曹正良.多孔介质BISQ模型中的慢纵波.物理学报. 2004,53(9):3083~3089
34 Han Q, Wang, Z. Time-domain simulation of SH-wave-induced electromagnetic field in heterogeneous porous media: a fast finite-element algorithm. Geophysics. 2001,66(2):488~461
35关威,胡恒山,储昭坦.声诱导电磁场的赫兹矢量表示与多极声电测井模拟.物理学报. 2006,55(1):267~274
36法林,林峰,陈文辉.石油勘探用薄圆环换能器的源函数推导和特性分析.地球物理学报. 1996,39(增刊):387~399
37法林,陈文辉,王克协,马瑞林.超声成像测井仪声波换能器的特性分析.石油仪器. 1997,11(2):26~30
38何祚镛,赵玉芳著.声学基础.国防工业出版社, 1981:218~220
39周士弘,王克协,马俊.利用井孔首波求取Vs和Qp值的广义线性反演方法的应用研究.1995,38(增刊):242~252
40阿肯巴赫.弹性固体中波的传播.洪镜如译.同济大学出版社, 1992:42~78
41 B. A.奥尔特.固体中的声场和波.孙承平译.科学出版社, 1982:258~264
42张福学.现代压电学.科学出版社, 2001:48~99
43林书玉.超声换能器的原理及设计.科学出版社, 2004:1~7
44栾桂冬,张金铎.压电换能器和换能器阵.北京出版社, 2004:113~126
45胡恒山,王克协.井孔周围轴对称声电耦合波:理论I.测井技术. 1999, 23(6):427~432
46胡恒山,王克协.声电效应测井模型实验研究I.测井技术. 2001, 25(2):89~95
47胡恒山.孔隙地层井壁上的声波首波及其诱导电磁场的原因.物理学报. 2003,52(8):1954~1959