利用声偶极测井资料求取各向异性储层衰减与渗透率研究
|
摘要
本文着重进行实测(交叉)偶极声测井资料衰减的提取和各向异性渗透率反演的应用研究。
根据各向同性和横向各向同性双相介质的理论公式,编制了计算实测声测井资料各向同性、各向异性衰减的提取和渗透率反演的MATLAB程序,利用信号频域加权相似法,提取并作出实测资料的全波波形、频散、频谱曲线,分析其图像,采用开窗方法提取弯曲波,再采用不同道幅度比作出衰减曲线,提取弯曲波的衰减作为实测数值,最后利用最小二乘法,反演渗透率。
由于实际地层情况比较复杂,我们首先把地层先看成是各向同性地层,确定各向同性地层弹性模量,反演计算了某口井的一段渗透率,并与已有斯通利波渗透率的结果相对比;其次根据各向异性弹性模量确定的操作路线,地层可能为各向异性(TIV)地层,因此确定了各向异性(TIV)地层的弹性模量,反演了软,硬地层的纵、横向渗透率。最后,从交叉偶极阵列声测井数据提取的图像分析中,发现XX,YY方向的频散曲线有一定的分裂,我们尝试性的用各向同性近似的方法来研究TIH介质,分别反演XX、YY方向的渗透率,并反演了一段深度的渗透率值。
本文从三种地层角度逐渐深入分析,对于各向同性地层弯曲波渗透率的反演,与斯通滤波渗透率相对比,发现在有一小段深度点趋势相同,孔隙度大的,渗透率大,但数值上相差10到100倍;对于各向异性(TIV)介质,横向渗透率比纵向渗透率反演的情况要好,软地层纵向渗透率反演具有可行性,而硬地层纵向渗透率反演并没有反演出结果,还有待于进一步研究;各向异性(TIH)介质,从作出的结果看XX—YY发生横(弯曲)波分裂的同时,衰减也发生分裂,这说明水平面内各向异性。
Permeability is one of the most important parameter that estimates the reserves of formation. There are a lot of works to gained the permeability in long time. Biot established the two-phase medium elastic theory in 1956, indicate the parameters like permeability and porosity effects the acoustic character of hole medium. Rosenbaum use this theory on the side of acoustic well logging, found that permeability is closely related to Stoneley-wave. Kexie Wang had reviewed the permeability’s and porosity’s effect on the field of well acoustic in cylindrical model, established definitely that the attenuation of Stoneley-wave is the most sensitive to permeability. Jun Ma used the flexural wave to calculate the permeability of formation first, gained satisfactory result. In this paper, we use the dipole acoustic well logging data to calculate the permeability in the isotropy model and transverse isotropy model.
Firstly, prove theory expressions the field of acoustic which is excitated by dipole source in isotropy and transverse isotropy hole model, and simulate in numerical value, draw the full wave picture which is excitated by dipole source. Analyse the mode wave in each model, research the guide wave which is toward the apices residua in apex wave number plane. Calculate the exact analytic formula from the dispersion formula of the guide wave, and make the program of it.
Secondly, research the flexural wave’s dispersion, attenuation and the range ratio of two wave in fast and slow formation of the two models, found that in isotropy model, the dispersion of flexural wave is sensitive to different porosities, but not to different permeabilities; in contrary that its attenuation is sensitive to different permeabilities but not to different porosities, so we believe that we can use the attenuation to calculate the permeability of formation. In transverse isotropy model, the dispersion of flexural wave is sensitive different porosities, but the distinction become little when in high frequency field, it is sensitive to neither horizontal nor vertical permeability. In fast formation, the attenuation is very sensitive to different horizontal permeabilities, but it does nothing to vertical permeability, even its change by different porosities is more obviously. In slow formation, the condition is better than fast formation, the attenuation is more sensitive to both horizontal permeability and vertical permeability. So we conjecture that it is feasible to use the attenuation of flexural wave to calculate the permeability of transverse isotropy formation, especially in slow formation. In fast formation, the horizontal permeability can be calculated also.
Third, in the isotropic formation model, the use of flexural wave inversion of permeability and Stoneley wave permeability known relative to a short stratigraphic penetration curve,Images observed from the results of inversion or less the same trend, but the gap between the larger values, we have the results are generally in less than 100mD, The information given by the Stoneley wave permeability 6000mD some even as high as above, in the numerical accuracy but also need to be further verify the error. In the anisotropy (TIH) formation model, the extraction with the same well depth point XX, YY direction of the field data, we try to approximate isotropy of the methods used to study the TIH medium inversion, respectively, XX, YY direction penetration. Inversion of the XX, YY different direction of penetration, within reasonable limits basic. Flexural wave in the soft strata permeability inversion XX, YY vary in both directions, and for the hard formation may be the reasons for data quality, good results can not extract the field data.
Finally, using the measured isotropic dipole acoustic logging data, the extraction of anisotropic attenuation and the use of their inversion of stratigraphic penetration rate, To obtain more satisfactory results.we use the flexural wave which intercept from full wave as the sampling function and the flexural wave which is calculated by residua of pole formula as the theory model function, calculate the permeability by nonlinear ordinary least squares estimation. Confirmed the reliability of the inversion. From the inversion results, in the transversely isotropic medium, the result of soft strata than in the hard strata, have been relatively satisfied with the results.
根据各向同性和横向各向同性双相介质的理论公式,编制了计算实测声测井资料各向同性、各向异性衰减的提取和渗透率反演的MATLAB程序,利用信号频域加权相似法,提取并作出实测资料的全波波形、频散、频谱曲线,分析其图像,采用开窗方法提取弯曲波,再采用不同道幅度比作出衰减曲线,提取弯曲波的衰减作为实测数值,最后利用最小二乘法,反演渗透率。
由于实际地层情况比较复杂,我们首先把地层先看成是各向同性地层,确定各向同性地层弹性模量,反演计算了某口井的一段渗透率,并与已有斯通利波渗透率的结果相对比;其次根据各向异性弹性模量确定的操作路线,地层可能为各向异性(TIV)地层,因此确定了各向异性(TIV)地层的弹性模量,反演了软,硬地层的纵、横向渗透率。最后,从交叉偶极阵列声测井数据提取的图像分析中,发现XX,YY方向的频散曲线有一定的分裂,我们尝试性的用各向同性近似的方法来研究TIH介质,分别反演XX、YY方向的渗透率,并反演了一段深度的渗透率值。
本文从三种地层角度逐渐深入分析,对于各向同性地层弯曲波渗透率的反演,与斯通滤波渗透率相对比,发现在有一小段深度点趋势相同,孔隙度大的,渗透率大,但数值上相差10到100倍;对于各向异性(TIV)介质,横向渗透率比纵向渗透率反演的情况要好,软地层纵向渗透率反演具有可行性,而硬地层纵向渗透率反演并没有反演出结果,还有待于进一步研究;各向异性(TIH)介质,从作出的结果看XX—YY发生横(弯曲)波分裂的同时,衰减也发生分裂,这说明水平面内各向异性。
Permeability is one of the most important parameter that estimates the reserves of formation. There are a lot of works to gained the permeability in long time. Biot established the two-phase medium elastic theory in 1956, indicate the parameters like permeability and porosity effects the acoustic character of hole medium. Rosenbaum use this theory on the side of acoustic well logging, found that permeability is closely related to Stoneley-wave. Kexie Wang had reviewed the permeability’s and porosity’s effect on the field of well acoustic in cylindrical model, established definitely that the attenuation of Stoneley-wave is the most sensitive to permeability. Jun Ma used the flexural wave to calculate the permeability of formation first, gained satisfactory result. In this paper, we use the dipole acoustic well logging data to calculate the permeability in the isotropy model and transverse isotropy model.
Firstly, prove theory expressions the field of acoustic which is excitated by dipole source in isotropy and transverse isotropy hole model, and simulate in numerical value, draw the full wave picture which is excitated by dipole source. Analyse the mode wave in each model, research the guide wave which is toward the apices residua in apex wave number plane. Calculate the exact analytic formula from the dispersion formula of the guide wave, and make the program of it.
Secondly, research the flexural wave’s dispersion, attenuation and the range ratio of two wave in fast and slow formation of the two models, found that in isotropy model, the dispersion of flexural wave is sensitive to different porosities, but not to different permeabilities; in contrary that its attenuation is sensitive to different permeabilities but not to different porosities, so we believe that we can use the attenuation to calculate the permeability of formation. In transverse isotropy model, the dispersion of flexural wave is sensitive different porosities, but the distinction become little when in high frequency field, it is sensitive to neither horizontal nor vertical permeability. In fast formation, the attenuation is very sensitive to different horizontal permeabilities, but it does nothing to vertical permeability, even its change by different porosities is more obviously. In slow formation, the condition is better than fast formation, the attenuation is more sensitive to both horizontal permeability and vertical permeability. So we conjecture that it is feasible to use the attenuation of flexural wave to calculate the permeability of transverse isotropy formation, especially in slow formation. In fast formation, the horizontal permeability can be calculated also.
Third, in the isotropic formation model, the use of flexural wave inversion of permeability and Stoneley wave permeability known relative to a short stratigraphic penetration curve,Images observed from the results of inversion or less the same trend, but the gap between the larger values, we have the results are generally in less than 100mD, The information given by the Stoneley wave permeability 6000mD some even as high as above, in the numerical accuracy but also need to be further verify the error. In the anisotropy (TIH) formation model, the extraction with the same well depth point XX, YY direction of the field data, we try to approximate isotropy of the methods used to study the TIH medium inversion, respectively, XX, YY direction penetration. Inversion of the XX, YY different direction of penetration, within reasonable limits basic. Flexural wave in the soft strata permeability inversion XX, YY vary in both directions, and for the hard formation may be the reasons for data quality, good results can not extract the field data.
Finally, using the measured isotropic dipole acoustic logging data, the extraction of anisotropic attenuation and the use of their inversion of stratigraphic penetration rate, To obtain more satisfactory results.we use the flexural wave which intercept from full wave as the sampling function and the flexural wave which is calculated by residua of pole formula as the theory model function, calculate the permeability by nonlinear ordinary least squares estimation. Confirmed the reliability of the inversion. From the inversion results, in the transversely isotropic medium, the result of soft strata than in the hard strata, have been relatively satisfied with the results.
引文
[1]Biot , M. A., Propagation of elastic waves in a cylindrical bore containing a fluid, J. Appl. Phys.,23,997-1005,1952.
[2]M.A.Biot,Theory of elasticity and consolidation for a porous anisotropic solid,Journal of applied physics,Vol.26,No.2,1955
[3]Petersion, E.W., Acoustic wave propagation along a fluid-filled cylinder, J. Appl. Phys.,45,3340-3350,1974.
[4]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.
[5] Rosenbaum, J.H., Synthetic microseismograms: logging in porous formation: Geophysics,39,14-32,1974.
[6]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.
[7]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
[8]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.
[9]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.
[10]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.
[11] Biot. M. A., Mechanics of deformation and acoustic propagation in porous media. J. Appl. Phys., 33, 1482-1483,1962.
[12]Pride S R, Tromeur E and Berryman J G., Biot slow-wave effects in stratified rock, Geophysics, 67,271-281,2002.
[13] Pride S R. and Garambois , The role of slow waves in electroseismic wave phenomena.J.Acoust.Soc.Am.,111(2),697-706,2002.
[14]D.P.Schmitt,.M.Bouchon and G.Bonnet., Full-wave synthetic acoustic lons in radially semiinfinite saturated porous media,Geophysics,53,807-823,1988
[15] D.P.Schmitt, Acoustic multipole logging in transversely isotropic poroelastic formation, J.Acoust.Soc.Am,86,2397-2421,1989
[16]Bixing Zhang, Hefeng Dong and Kexie Wang, Multipole sources in a fluid-filled borehole surrounded by a transverly isotropic elastic solid, J.Acoust.Soc.Am.,1994
[17]Zhu,X. and McMechan, G.A., Numerical simulation of seismic responses of poroelastic reservoirs using Biot theory,Geophysics,56,328-339,1991
[18]巴音贺希格无限Biot双相介质中水平流体层声波场的理论分析和数值计算,吉林大学硕士学位论文,2002
[19]Winkler,K.W.,Liu,H.L. and Johnson, D.L., Permeability and borehole Stoneley waves: Comparison between experiment and theory, Geophysics,54,66-67,1989.
[20]Norris,A.N.,1998,Stoneley wave attenuation and dispersion in permeable formations,Geophysics,53,519-527,1988.
[21]Tang,X.M., cheng,C.H.,Toks?z,M.N.,Dynamic permeability and borehole Stoneley waves:A simplified Boit-Rosenbaum model. J.Acoust.Soc.Am.,90(3),1632-1646,1991.
[22]Tang,X.M., and Cheng,C.H., Fast inversion of formation permeability from Stoneley wave logs using a simplified Biot-Rosenbaum model, Geophysics,61(3),639-645,1996.
[23]伍先运,王克协,郭立等,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,38(增刊),224-231,1995.
[24] Liu.H., and Johson.D.L., Effects of an elastic membrane on tube waves in permeable formations. J.Acoust.Soc.Am., 101:3322-3329,1997.
[25] Tichelaar. B.W, Liu.H. and Johnson.D.L., Modeling of borehole stoneley waves in the presence of skin effects. J.Acoust.Soc.Am.,105(2):601-609,1999。
[26] White, J.E., 1967,The hula log-a proposed acoustical tool, paper I, in 8th Annual Well Logging Symposium Transactions: SPLWLA, pI1-I25. [in Seismic Wave Propagation:Collected Works of J.E.White, Edited by J.E.White,2000]
[27]Zemanck, J.,gona,F.A.,Wolliams,D.M. and Caldwell, R.L., Continuous Acoustic shear wave logging, SPWLA.,25th Log. Symposium,1984.
[28]Winbow,G.A., A theoretical study of acoustic S-wave and P-wave velocity logging with conventional and dipole sources in soft formation,Geophysics,53,1334-1442,1988.
[29]Chen,S.T., Shear-wave logging with quadrupole Sources , Geophysics,54,590-597,1989.
[30]Kurkjian, A.L, Chang, S.K., Acoustic multipole sources in fluid-filled boreholes. Geophysics, 51(1): 148-163,1986.
[31]王克协,马俊等,利用偶极声测井中弯曲波反演渗透率的方法研究,地球物理年会,1997.
[32]马俊,1998,井孔声波理论分析与复杂储层单、多极声测井正反演研究,吉林大学博士论文
[33]Kexie Wang, et.al., Determinationn of permeability from flexural waves in dipole acoustic logging waves, SEG99, Annual Meeting, Abstract, 1999.
[34]Kimball,C.V., Shear Slowness measurement by dispersive processing of the borehole flexural mode, Geophysics,63,No.2,337-346,1998.
[35] Biot. M. A and Willis, D.G, 1957, The elastic coefficients of the theory of consolidation: J.Appl.Mech.24: 594-601.
[36]张碧星1994各向异性介质地层流体井孔中多极源声测井理论和数值研究吉林大学博士学位论文
[37] White, J.E. and Tongtaow, C., Cylindrical waves in transverlyisotropic media, J. Acoust.Soc.Am, 1981,1147-1155.
[38] Chan,A.K. and Tsang L., propagation of acoustic wave in a fluid-filled borehole surrounded by a concentrically layered transversely isotropic formation, J.Acoust.Soc.Am., 1983,74,1606-1616.
[39] Biot,M.A., Theory of elasticity and consolidation for a porous anistrpic solid, J.Appl.Phys., 1955,26,182-185.
[40]张碧星,王克协,董庆德,横向各向同性双相介质地层井孔多极源声测井理论与数值模拟,中国地球物理研讨会论文集,1993.
[41]Sayers,C.M., Stress-dependent seismic anisotropy of shakes., Geophysics, 1999,59,233-244.
[42]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:中国石油大学,1998。
[43]丛令梅2004 BISQ横向各向同性地层流体井孔中多极源激发声波场的理论求解和数值分析吉林大学硕士学位论文
[44]谢馥励2006利用偶极弯曲波求取孔隙VTI介质各向异性渗透率的正、反演研究吉林大学硕士学位论文
[2]M.A.Biot,Theory of elasticity and consolidation for a porous anisotropic solid,Journal of applied physics,Vol.26,No.2,1955
[3]Petersion, E.W., Acoustic wave propagation along a fluid-filled cylinder, J. Appl. Phys.,45,3340-3350,1974.
[4]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.
[5] Rosenbaum, J.H., Synthetic microseismograms: logging in porous formation: Geophysics,39,14-32,1974.
[6]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.
[7]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
[8]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.
[9]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.
[10]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.
[11] Biot. M. A., Mechanics of deformation and acoustic propagation in porous media. J. Appl. Phys., 33, 1482-1483,1962.
[12]Pride S R, Tromeur E and Berryman J G., Biot slow-wave effects in stratified rock, Geophysics, 67,271-281,2002.
[13] Pride S R. and Garambois , The role of slow waves in electroseismic wave phenomena.J.Acoust.Soc.Am.,111(2),697-706,2002.
[14]D.P.Schmitt,.M.Bouchon and G.Bonnet., Full-wave synthetic acoustic lons in radially semiinfinite saturated porous media,Geophysics,53,807-823,1988
[15] D.P.Schmitt, Acoustic multipole logging in transversely isotropic poroelastic formation, J.Acoust.Soc.Am,86,2397-2421,1989
[16]Bixing Zhang, Hefeng Dong and Kexie Wang, Multipole sources in a fluid-filled borehole surrounded by a transverly isotropic elastic solid, J.Acoust.Soc.Am.,1994
[17]Zhu,X. and McMechan, G.A., Numerical simulation of seismic responses of poroelastic reservoirs using Biot theory,Geophysics,56,328-339,1991
[18]巴音贺希格无限Biot双相介质中水平流体层声波场的理论分析和数值计算,吉林大学硕士学位论文,2002
[19]Winkler,K.W.,Liu,H.L. and Johnson, D.L., Permeability and borehole Stoneley waves: Comparison between experiment and theory, Geophysics,54,66-67,1989.
[20]Norris,A.N.,1998,Stoneley wave attenuation and dispersion in permeable formations,Geophysics,53,519-527,1988.
[21]Tang,X.M., cheng,C.H.,Toks?z,M.N.,Dynamic permeability and borehole Stoneley waves:A simplified Boit-Rosenbaum model. J.Acoust.Soc.Am.,90(3),1632-1646,1991.
[22]Tang,X.M., and Cheng,C.H., Fast inversion of formation permeability from Stoneley wave logs using a simplified Biot-Rosenbaum model, Geophysics,61(3),639-645,1996.
[23]伍先运,王克协,郭立等,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,38(增刊),224-231,1995.
[24] Liu.H., and Johson.D.L., Effects of an elastic membrane on tube waves in permeable formations. J.Acoust.Soc.Am., 101:3322-3329,1997.
[25] Tichelaar. B.W, Liu.H. and Johnson.D.L., Modeling of borehole stoneley waves in the presence of skin effects. J.Acoust.Soc.Am.,105(2):601-609,1999。
[26] White, J.E., 1967,The hula log-a proposed acoustical tool, paper I, in 8th Annual Well Logging Symposium Transactions: SPLWLA, pI1-I25. [in Seismic Wave Propagation:Collected Works of J.E.White, Edited by J.E.White,2000]
[27]Zemanck, J.,gona,F.A.,Wolliams,D.M. and Caldwell, R.L., Continuous Acoustic shear wave logging, SPWLA.,25th Log. Symposium,1984.
[28]Winbow,G.A., A theoretical study of acoustic S-wave and P-wave velocity logging with conventional and dipole sources in soft formation,Geophysics,53,1334-1442,1988.
[29]Chen,S.T., Shear-wave logging with quadrupole Sources , Geophysics,54,590-597,1989.
[30]Kurkjian, A.L, Chang, S.K., Acoustic multipole sources in fluid-filled boreholes. Geophysics, 51(1): 148-163,1986.
[31]王克协,马俊等,利用偶极声测井中弯曲波反演渗透率的方法研究,地球物理年会,1997.
[32]马俊,1998,井孔声波理论分析与复杂储层单、多极声测井正反演研究,吉林大学博士论文
[33]Kexie Wang, et.al., Determinationn of permeability from flexural waves in dipole acoustic logging waves, SEG99, Annual Meeting, Abstract, 1999.
[34]Kimball,C.V., Shear Slowness measurement by dispersive processing of the borehole flexural mode, Geophysics,63,No.2,337-346,1998.
[35] Biot. M. A and Willis, D.G, 1957, The elastic coefficients of the theory of consolidation: J.Appl.Mech.24: 594-601.
[36]张碧星1994各向异性介质地层流体井孔中多极源声测井理论和数值研究吉林大学博士学位论文
[37] White, J.E. and Tongtaow, C., Cylindrical waves in transverlyisotropic media, J. Acoust.Soc.Am, 1981,1147-1155.
[38] Chan,A.K. and Tsang L., propagation of acoustic wave in a fluid-filled borehole surrounded by a concentrically layered transversely isotropic formation, J.Acoust.Soc.Am., 1983,74,1606-1616.
[39] Biot,M.A., Theory of elasticity and consolidation for a porous anistrpic solid, J.Appl.Phys., 1955,26,182-185.
[40]张碧星,王克协,董庆德,横向各向同性双相介质地层井孔多极源声测井理论与数值模拟,中国地球物理研讨会论文集,1993.
[41]Sayers,C.M., Stress-dependent seismic anisotropy of shakes., Geophysics, 1999,59,233-244.
[42]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:中国石油大学,1998。
[43]丛令梅2004 BISQ横向各向同性地层流体井孔中多极源激发声波场的理论求解和数值分析吉林大学硕士学位论文
[44]谢馥励2006利用偶极弯曲波求取孔隙VTI介质各向异性渗透率的正、反演研究吉林大学硕士学位论文