泥质砂岩激发极化弛豫时间谱的正则化反演
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摘要
激发极化衰减谱是一系列单指数衰减的线性叠加,因此可以对衰减谱进行多指数反演,得到的弛豫时间谱可用于储层孔隙结构和渗透性评价,是一种非常有前途的技术。由于实际测井的信噪比相对较低,常规的奇异值分解方法难以获得合理的弛豫时间谱,为此,采用正则化约束,结合奇异值分解,对合成数据和实际测量的衰减谱进行反演,得到连续的弛豫时间谱;同时,讨论了弛豫时间谱的时间常数分布、正则化因子以及信噪比对反演结果的影响。研究结果表明:该方法适用于信噪比较低的实际测量结果的反演,弛豫时间常数的分布点数为32~64较为合适;随着正则化因子的增加,反演结果逐渐变得平滑,存在一个最优的正则化因子,用于获得最为合理的弛豫时间谱;在双对数图中,最优正则化因子随着信噪比的增加而线性降低,因此通过测量结果的信噪比,可以求取最优正则化因子,进而将该技术应用于实际。
The time-domain induced polarization( IP) decay curve is a linear superposition of IP signal from individual pores. It can be transformed to relaxation time spectrum related to the pore structure and can be used to estimate the permeability of the argillaceous sand. So the IP logging is a useful tool for reservoir characterizing. The singular value decomposition( SVD) method can be used to extract the relaxation time spectra from the decay data with high signal-to-noise ratio( SNR). This method is unstable and invalid for the practical downhole use because of the noisy decay data. In this study,a method of regularization was applied to extracting continuous IP relaxation time spectra from simulated and real decay data. Influence of the regularization factor,SNR and relaxation time arrangement on the spectra was also discussed. Firstly,for the simulated decay data with noise,the spectra become smoother with increasing regularization factor. There is an optimal value which can be used to get the most reasonable spectrum. The optimal factor decreases linearly with increasing SNR on a log-log scale. This relationship can be used to predict the optimal factor from a known SNR. Secondly,the influence of relaxation time arrangement on the spectra shows that the suitable relaxation distribution point ranges from 32 to 64. Finally,the developed algorithm and the prediction of the optimal factor are very suitable for the inversion of the spectra of the real data.
The time-domain induced polarization( IP) decay curve is a linear superposition of IP signal from individual pores. It can be transformed to relaxation time spectrum related to the pore structure and can be used to estimate the permeability of the argillaceous sand. So the IP logging is a useful tool for reservoir characterizing. The singular value decomposition( SVD) method can be used to extract the relaxation time spectra from the decay data with high signal-to-noise ratio( SNR). This method is unstable and invalid for the practical downhole use because of the noisy decay data. In this study,a method of regularization was applied to extracting continuous IP relaxation time spectra from simulated and real decay data. Influence of the regularization factor,SNR and relaxation time arrangement on the spectra was also discussed. Firstly,for the simulated decay data with noise,the spectra become smoother with increasing regularization factor. There is an optimal value which can be used to get the most reasonable spectrum. The optimal factor decreases linearly with increasing SNR on a log-log scale. This relationship can be used to predict the optimal factor from a known SNR. Secondly,the influence of relaxation time arrangement on the spectra shows that the suitable relaxation distribution point ranges from 32 to 64. Finally,the developed algorithm and the prediction of the optimal factor are very suitable for the inversion of the spectra of the real data.
引文
[1]刘崧.谱激电法[M].北京:中国地质大学出版社,1998.
[2]孟建国.浅谈激发极化法[J].吉林地质,2013,32(2):82-83,89.
[3]何继善.双频激电法[M].北京:高等教育出版社,2006.
[4]何继善,李大庆,汤井田.频谱激电非线性效应的理论模型[J].地球物理学,1995,38(5):662-669.
[5]何继善,李大庆,汤井田.双频道频谱激电非线性效应研究[J].地球物理学报,1995,38(5):670-675.
[6]何继善,熊彬,鲍力知,等.直接消除电磁耦合的斩波去耦方法[J].地球物理学,2006,49(6):1843-1850.
[7]何继善.频率域电法的新进展[J].地球物理学进展,2007,22(4):1250-1254.
[8]何继善.伪随机三频电法研究[J].中国有色金属学报,1994,4(1):1-7.
[9]何继善.电法勘探发展和展望[J].地球物理学报,1997,40(2):308-316.
[10]何继善.2n系列伪随机信号及应用[C]//中国地球物理学会年刊.北京:地震出版社,1998:199-199.
[11]何继善,柳建新.伪随机多频相位法及其应用简介[J].中国有色金属学报,2002(2):374-376.
[12]傅良魁.激发极化法[M].北京:地质出版社,1982.
[13]傅良魁.复电阻率异常及空间分布规律[J].地质与勘探,1981,17(2):46-53.
[14]傅良魁,张虎豹.频谱激电法若干理论研究[J].物探与化探,1985,9(6):410-420.
[15]傅良魁,李金铭,陈兆洪.埋藏极化体激电时间谱视参数的实验研究结果[J].地质与勘探,1985,21(12):38-43.
[16]傅良魁,刘若谷.时间域非线性激电效应的实验研究[J].桂林冶金地质学院学报,1989,9(1):81-91.
[17]罗延钟,张桂青.频率域激电法原理[M].北京:地质出版社,1988.
[18]罗延钟,方胜.极化椭球体上频谱激电法的异常性态[J].桂林冶金地质学院学报,1985,1(5):49-63.
[19]罗延钟,许妙立,吴之训.面极化球体上视复电阻率的频率特性和模拟相似性准则[J].桂林冶金地质学院学报,1986,6(2):145-155.
[20]罗延钟,姚建阳,何展翔,等.球形极化体上点源装置频谱激电异常的高级近似算法[J].物化探计算技术,1987,6(2):113-122.
[21]罗延钟,张胜业,熊彬.天然源激电法的可行性[J].地球物理学报,2003,46(1):125-130.
[22]杨进,孟海东,傅良魁.激电找水数据处理解释方法与系统[J].物探与化探,1998,22(3):204-210.
[23]杨进,刘兆平.天然场激发极化法在多金属矿区的野外试验效果[J].地学前缘,2008,15(4):217-221.
[24]杨进,谭捍东,傅良魁.被动源激发极化法的野外试验结果[J].现代地质,1998,12(3):437-441.
[25]刘崧.激电法直接探测油气藏的有效性及提高其应用效果的途径谱激电法,地质科技情报,1992,11(4):81-86.
[26]刘崧.计算视复电阻率的新的近似公式[J].地球物理学报,1988,31(6):687-694.
[27]刘崧,官善友,高鹏飞.求极化椭球体真Cole-Cole参数的联合谱激电反演[J].地球物理学报,1994,37(S1):542-551.
[28]刘崧,徐建华.用复电阻率法探测油气藏的研究[J].地球科学:中国地质大学学报,1997,22(6):627-632.
[29]王宏建.利用激发极化测井确定地层渗透率的研究进展[J].测井技术,2008,32(6):509-513.
[30]Barker R D.A note on the induced polarization of the Bunter sandstone[J].Geoexploration,1975,13:227-233.
[31]B?ner F D,Schopper J R,Weller A.Evaluation of transport and storage properties in the soil and groundwater zone from induced polarization measurements[J].Geophysical Prospecting,1996,44:583-602.
[32]Lesmes D P,Morgan F D.Dielectric spectroscopy of sedimentary rocks[J].Journal of Geophysical Research,2001:3329-13346.
[33]Marshall D J,Madden T R.Induced polarization,a study of its causes[J].Geophysics,1959,24:790-816.
[34]Worthington P F,Collar F A.Relevance of induced polarization to quantitative formation evaluation[J].Marine and Petroleum Geology,1984(1):14-26.
[35]Titov K,Komarov V,Tarasov V,et al.Theoretical and experimental study of time domain-induced polarization in water-saturated sands[J].Journal of Applied Geophysics,2002,50:417-433.
[36]王伟男,余钦范,姜亦忠.激发极化电位衰减谱的连续测井方法[J].石油地球物理勘探,2010,45(增刊1):214-216.
[37]Vinegar H J,Waxman M H.In-situ method for determining formation permeability[P].U S Patent:4743854,1988.
[38]Tong M S,Wang W N,Li L,et al.Estimation of permeability of shaly sand reservoir from induced polarization relaxation time spectra[J].Journal of Petroleum Science and Engineering,2004,45:1-10.
[39]Tong M,Li L,Wang W,et al.Determining capillary pressure curve,pore size distribution and permeability from induced polarization of shaly sand[J].Geophysics,2006,71(3):33-40.
[40]Vinegar H J,Waxman M H.In-situ method for determining pore size distribution,capillary pressure and permeability[P].U S Patent:4644283,1987.
[41]Prammer M G.NMR pore size distributions and permeability at the well site[J].SPE,1994:28368.
[42]Gallegos D P,Smith D M.A NMR technique for the analysis of pore structure:determination of continuous pore size distributions.Journal of Colloid and Interface Science,1988,122(1):143-153.
[2]孟建国.浅谈激发极化法[J].吉林地质,2013,32(2):82-83,89.
[3]何继善.双频激电法[M].北京:高等教育出版社,2006.
[4]何继善,李大庆,汤井田.频谱激电非线性效应的理论模型[J].地球物理学,1995,38(5):662-669.
[5]何继善,李大庆,汤井田.双频道频谱激电非线性效应研究[J].地球物理学报,1995,38(5):670-675.
[6]何继善,熊彬,鲍力知,等.直接消除电磁耦合的斩波去耦方法[J].地球物理学,2006,49(6):1843-1850.
[7]何继善.频率域电法的新进展[J].地球物理学进展,2007,22(4):1250-1254.
[8]何继善.伪随机三频电法研究[J].中国有色金属学报,1994,4(1):1-7.
[9]何继善.电法勘探发展和展望[J].地球物理学报,1997,40(2):308-316.
[10]何继善.2n系列伪随机信号及应用[C]//中国地球物理学会年刊.北京:地震出版社,1998:199-199.
[11]何继善,柳建新.伪随机多频相位法及其应用简介[J].中国有色金属学报,2002(2):374-376.
[12]傅良魁.激发极化法[M].北京:地质出版社,1982.
[13]傅良魁.复电阻率异常及空间分布规律[J].地质与勘探,1981,17(2):46-53.
[14]傅良魁,张虎豹.频谱激电法若干理论研究[J].物探与化探,1985,9(6):410-420.
[15]傅良魁,李金铭,陈兆洪.埋藏极化体激电时间谱视参数的实验研究结果[J].地质与勘探,1985,21(12):38-43.
[16]傅良魁,刘若谷.时间域非线性激电效应的实验研究[J].桂林冶金地质学院学报,1989,9(1):81-91.
[17]罗延钟,张桂青.频率域激电法原理[M].北京:地质出版社,1988.
[18]罗延钟,方胜.极化椭球体上频谱激电法的异常性态[J].桂林冶金地质学院学报,1985,1(5):49-63.
[19]罗延钟,许妙立,吴之训.面极化球体上视复电阻率的频率特性和模拟相似性准则[J].桂林冶金地质学院学报,1986,6(2):145-155.
[20]罗延钟,姚建阳,何展翔,等.球形极化体上点源装置频谱激电异常的高级近似算法[J].物化探计算技术,1987,6(2):113-122.
[21]罗延钟,张胜业,熊彬.天然源激电法的可行性[J].地球物理学报,2003,46(1):125-130.
[22]杨进,孟海东,傅良魁.激电找水数据处理解释方法与系统[J].物探与化探,1998,22(3):204-210.
[23]杨进,刘兆平.天然场激发极化法在多金属矿区的野外试验效果[J].地学前缘,2008,15(4):217-221.
[24]杨进,谭捍东,傅良魁.被动源激发极化法的野外试验结果[J].现代地质,1998,12(3):437-441.
[25]刘崧.激电法直接探测油气藏的有效性及提高其应用效果的途径谱激电法,地质科技情报,1992,11(4):81-86.
[26]刘崧.计算视复电阻率的新的近似公式[J].地球物理学报,1988,31(6):687-694.
[27]刘崧,官善友,高鹏飞.求极化椭球体真Cole-Cole参数的联合谱激电反演[J].地球物理学报,1994,37(S1):542-551.
[28]刘崧,徐建华.用复电阻率法探测油气藏的研究[J].地球科学:中国地质大学学报,1997,22(6):627-632.
[29]王宏建.利用激发极化测井确定地层渗透率的研究进展[J].测井技术,2008,32(6):509-513.
[30]Barker R D.A note on the induced polarization of the Bunter sandstone[J].Geoexploration,1975,13:227-233.
[31]B?ner F D,Schopper J R,Weller A.Evaluation of transport and storage properties in the soil and groundwater zone from induced polarization measurements[J].Geophysical Prospecting,1996,44:583-602.
[32]Lesmes D P,Morgan F D.Dielectric spectroscopy of sedimentary rocks[J].Journal of Geophysical Research,2001:3329-13346.
[33]Marshall D J,Madden T R.Induced polarization,a study of its causes[J].Geophysics,1959,24:790-816.
[34]Worthington P F,Collar F A.Relevance of induced polarization to quantitative formation evaluation[J].Marine and Petroleum Geology,1984(1):14-26.
[35]Titov K,Komarov V,Tarasov V,et al.Theoretical and experimental study of time domain-induced polarization in water-saturated sands[J].Journal of Applied Geophysics,2002,50:417-433.
[36]王伟男,余钦范,姜亦忠.激发极化电位衰减谱的连续测井方法[J].石油地球物理勘探,2010,45(增刊1):214-216.
[37]Vinegar H J,Waxman M H.In-situ method for determining formation permeability[P].U S Patent:4743854,1988.
[38]Tong M S,Wang W N,Li L,et al.Estimation of permeability of shaly sand reservoir from induced polarization relaxation time spectra[J].Journal of Petroleum Science and Engineering,2004,45:1-10.
[39]Tong M,Li L,Wang W,et al.Determining capillary pressure curve,pore size distribution and permeability from induced polarization of shaly sand[J].Geophysics,2006,71(3):33-40.
[40]Vinegar H J,Waxman M H.In-situ method for determining pore size distribution,capillary pressure and permeability[P].U S Patent:4644283,1987.
[41]Prammer M G.NMR pore size distributions and permeability at the well site[J].SPE,1994:28368.
[42]Gallegos D P,Smith D M.A NMR technique for the analysis of pore structure:determination of continuous pore size distributions.Journal of Colloid and Interface Science,1988,122(1):143-153.