基于先验信息约束的核磁共振数据反演新方法
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摘要
针对核磁共振(NMR)测井T2谱短弛豫组分反演不精确的问题,提出一种基于先验信息约束的NMR反演新方法(ILT+)。首先利用积分变换方法直接从核磁共振原始回波数据中提取先验信息,具体为利用指数双曲正弦变换方法(ESHT)计算T_2谱锥形区域面积,利用梅林变换方法(MT)计算T_2的ω次幂的均值(〈T_2~ω〉);然后将提取的先验信息作为约束条件构造新的目标函数并反演求解。数值模拟和实际井资料处理结果表明:同时施加两种先验信息作为约束条件的ILT+方法综合了单独施加时的ILT+方法的优点,提高了T_2谱短弛豫组分的反演精度。新方法对于小孔占优的致密砂岩、页岩等非常规储层的NMR回波数据反演具有广阔的应用前景。
A new inversion method of nuclear magnetic resonance(NMR) logging constrained by priori information(ILT+) was presented for the inaccuracy of NMR inversion at short relaxation times. The priori information was computed directly from NMR echo trains using integral transforms. Specially the T_2 tapered areas were computed using exponential hyperbolic sine transform(ESHT) and the mean value of the ω-th moment of T_2 was computed using Mellin transform(MT). The numerical simulation and well data processing showed that the new method simultaneously constrained by two priori information synthesized the advantages of the new method constrained by single priori information, and improved the inversion accuracy of T_2 spectrum at short relaxation times. This new method has broad application prospects for NMR data inversion in unconventional reservoirs such as tight sandstone and shale which usually contain more small pores.
A new inversion method of nuclear magnetic resonance(NMR) logging constrained by priori information(ILT+) was presented for the inaccuracy of NMR inversion at short relaxation times. The priori information was computed directly from NMR echo trains using integral transforms. Specially the T_2 tapered areas were computed using exponential hyperbolic sine transform(ESHT) and the mean value of the ω-th moment of T_2 was computed using Mellin transform(MT). The numerical simulation and well data processing showed that the new method simultaneously constrained by two priori information synthesized the advantages of the new method constrained by single priori information, and improved the inversion accuracy of T_2 spectrum at short relaxation times. This new method has broad application prospects for NMR data inversion in unconventional reservoirs such as tight sandstone and shale which usually contain more small pores.
引文
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[2] 谢然红,肖立志,刘家军,等.核磁共振多回波串联合反演方法[J].地球物理学报,2009,52(11):2913-2919.XIE Ranhong,XIAO Lizhi,LIU Jiajun,et al.A method for multiple echo trains jointing inversion of NMR relaxation measurements [J].Chinese Journal of Geophysics,2009,52(11):2913-2919.
[3] 闫伟超,孙建孟,崔利凯,等.一种估算砂岩核磁T2谱新方法[J].中国石油大学学报(自然科学版),2017,41(1):60-68.YAN Weichao,SUN Jianmeng,CUI Likai,et al.A new method of estimating NMR T2 spectrum of sandstone [J].Journal of China University of Petroleum (Edition of Natural Science),2017,41(1):60-68.
[4] 廖广志,肖立志,谢然红,等.孔隙介质核磁共振弛豫测量多指数反演影响因素研究[J].地球物理学报,2007,50(3):932-938.LIAO Guangzhi,XIAO Lizhi,XIE Ranhong,et al.Influence factors of multi-exponential inversion of NMR relaxation measurement in porous media[J].Chinese Journal of Geophysics,2007,50(3):932-938.
[5] 李志愿,崔云江,关叶钦,等.基于孔径分布和T2谱的低孔渗储层渗透率确定方法[J].中国石油大学学报(自然科学版),2018,42(4):34-40.LI Zhiyuan,CUI Yunjiang,GUAN Yeqin,et al.Permeability confirmation method of low porosity and permeability reservoirs based on pore distribution and T2 spectrum[J].Journal of China University of Petroleum (Edition of Natural Science),2018,42(4):34-40.
[6] 陈华,潘克家,谭永基.核磁共振弛豫信号多指数反演新方法[J].测井技术,2009,33(1):37-41.CHEN Hua,PAN Kejia,TAN Yongji.A new method for multi-exponential inversion of NMR relaxation signal[J].Well Logging Technology,2009,33(1):37-41.
[7] 谭茂金,石耀霖,谢关宝.基于遗传算法的核磁共振T2分布反演[J].测井技术,2007,31(5):413-416.TAN Maojin,SHI Yaolin,XIE Guanbao.NMR T2 distribution inversion based on genetic algorithm[J].Well Logging Technology,2007,31(5):413-416.
[8] ZOU Y,XIE R,DING Y,et al.Inversion of nuclear magnetic resonance echo data based on maximum entropy[J].Geophysics,2016,81(1):D1-D8.
[9] PRAMMER M G.NMR pore size distributions and permeability at the well site[R].SPE 28368,1994.
[10] 姜瑞忠,姚彦平,苗盛,等.核磁共振T2谱奇异值分解反演改进算法[J].石油学报,2005,26(6):57-59.JIANG Ruizhong,YAO Yanping,MIAO Sheng,et al.Improved algorithm for singular value decomposition inversion of T2 spectrum in nuclear magnetic resonance[J].Acta Petrolei Sinica,2005,26(6):57-59.
[11] BUTLER J P,REEDS J A,DAWSON S V.Estimating solutions of first kind integral equations with nonnegative constraints and optimal smoothing[J].SIAM Journal on Numerical Analysis,1981,18(3):381-397.
[12] BORGIA G C,BROWN R J S,FANTAZZINI P.Uniform-penalty inversion of multiexponential decay data[J].Journal of Magnetic Resonance,1998,132(1):65-77.
[13] BORGIA G C,BROWN R J S,FANTAZZINI P.Uniform-penalty inversion of multiexponential decay data.II.data spacing,T(2) data,systemic data errors,and diagnostics.[J].Journal of Magnetic Resonance,2000,147(2):273-285.
[14] VENKATARAMANAN L,GRUBER F K,HABASHY T M,et al.Mellin transform of CPMG data[J].Journal of Magnetic Resonance,2010,206(1):20-31.
[15] VENKATARAMANAN L,HABASHY T M,FREED D E,et al.Continuous moment estimation of CPMG data using Mellin transform[J].Journal of Magnetic Resonance,2012,216:43-52.
[16] GRUBER F K,VENKATARAMANAN L,HABASHY T M,et al.Estimation of petrophysical and fluid properties using integral transforms in nuclear magnetic resonance[J].Journal of Magnetic Resonance,2013,228:104-115.
[17] GRUBER F K,VENKATARAMANAN L,HABASHY T M,et al.A more accurate estimate of T2 distribution from direct analysis of NMR measurements [J].Journal of Magnetic Resonance,2013,228(1):95-103.
[18] EPSTEIN C L,SCHOTLAND J.The bad truth about Laplace's transform[J].SIAM Review,2008,50(3):504-520.
[19] KLEINBERG R L,BOYD A.Tapered cutoffs for magnetic resonance bound water volume[R].SPE 38737,1997.
[20] SEZGINER A.Determining bound and unbound fluid volumes using nuclear magnetic resonance pulse sequences:5363041[P].1994-11-08.