倾斜各向异性地层随钻电磁波测井响应模拟
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摘要
为实现实时随钻地质导向和储层精细评价,深入认识倾斜各向异性地层随钻电磁波测井响应特征,基于赫兹矢量位函数,将任意方向的磁偶极子源分解为水平方向和垂直方向分别求解。低角度时采用高斯积分,高角度时利用Hankel变换对Bessel函数进行积分,实现了倾斜层状各向异性地层随钻电磁波测井响应的模拟,将结果与EM1D的模拟结果进行比较验证算法的正确性。通过对不同模型条件随钻电磁波响应的模拟,研究地层各向异性系数、发射频率、井斜角等参数对随钻电磁波测井响应的影响。井斜角较小时视电阻率主要反映水平电阻率随井斜角增大而增大;视电阻率逐渐由水平电阻率向垂直电阻率过渡。当地层各向异性系数与井斜角较大时,测量信号将远大于水平电阻率甚至超过垂直电阻率;井斜角越大,发射频率越高,随钻电磁波视电阻率受地层各向异性影响越大,且相位差电阻率较幅度比电阻率更加敏感。
In order to realize real-time geosteering and accurate formation evaluation while drilling and to deeply research the characteristics of electromagnetic logging response while drilling in anisotropic dipping formation,a free oriented magnetic dipole is divided into horizontal and vertical sub-sources which are solved respectively on the basis of Hertz potential function.Gauss integral and Hankel transform integral are adopted in low angle and high angle respectively to compute the generalized integral with Bessel function,thereby realizing simulation of electromagnetic logging response while drilling in anisotropic dipping formation.Compared with the simulation results of EM1D,the algorithm is reliable.The effects of anisotropy ratio,frequency and deviation angle on electromagnetic logging response while drilling are then studied through simulation of the responses under different formation models.The results show that when the deviation angle is low,the apparent resistivity is nearly at the horizontal resistivity,as the deviation angle becomes larger,the apparent resistivity increases from the horizontal resistivity to the vertical resistivity,when both anisotropy ratio and deviation angle are relatively large,the apparent resistivity is far greater than the horizontal resistivity and even greater than the vertical resistivity.With higher deviation angle and frequency,the electromagnetic response is more affected by formation anisotropy and the phase difference resistivity is more sensitive than the attenuation resistivity.
In order to realize real-time geosteering and accurate formation evaluation while drilling and to deeply research the characteristics of electromagnetic logging response while drilling in anisotropic dipping formation,a free oriented magnetic dipole is divided into horizontal and vertical sub-sources which are solved respectively on the basis of Hertz potential function.Gauss integral and Hankel transform integral are adopted in low angle and high angle respectively to compute the generalized integral with Bessel function,thereby realizing simulation of electromagnetic logging response while drilling in anisotropic dipping formation.Compared with the simulation results of EM1D,the algorithm is reliable.The effects of anisotropy ratio,frequency and deviation angle on electromagnetic logging response while drilling are then studied through simulation of the responses under different formation models.The results show that when the deviation angle is low,the apparent resistivity is nearly at the horizontal resistivity,as the deviation angle becomes larger,the apparent resistivity increases from the horizontal resistivity to the vertical resistivity,when both anisotropy ratio and deviation angle are relatively large,the apparent resistivity is far greater than the horizontal resistivity and even greater than the vertical resistivity.With higher deviation angle and frequency,the electromagnetic response is more affected by formation anisotropy and the phase difference resistivity is more sensitive than the attenuation resistivity.
引文
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[2]Davydycheva S.3D Modeling of New-generation(1999-2010)Resistivity Logging Tools,Society of Explora-tion[J].Geophysicists,2010,29(7):780-789.
[3]Bittar M,Rodney P.The Effect of Rock Anisotropy on MWD Electromagnetic Wave Resistivity Sensors[J].The Log Analyst,1996,37(1):20-30.
[4]Abubakar A,Habashy T M,Druskin V,et al.A3DParametric Inversion Algorithm for Triaxial Induction Data[J].Geophysics,2006,71(1):G1-G9.
[5]沈金松.用有限差分法计算各向异性介质中多分量感应测井的响应[J].地球物理学进展,2004,19(1):101-107.
[6]王昌学,周灿灿,储昭坦,等.电性各向异性地层频率域电磁响应模拟[J].地球物理学报,2006,49(6):1874-1883.
[7]Li J,Bhardwaj A,et al.Computation of Triaxial In-duction Logging Tools in Layered Anisotropic Dipping Formations[C]∥IEEE,2008,46(4):1149-1163.
[8]徐建华.层状媒质中的电磁场与电磁波[M].北京:石油工业出版社,1997:172-183.
[9]其木苏荣,孙丙西.水平层状介质中任意方向磁偶极子的电磁场分布[J].内蒙古民族大学学报:自然科学版,2004,19(3):248-256.
[10]莫平华.一阶贝塞尔函数广义积分的数值计算[J].数学理论与应用,2007,27(1):66-67.
[11]张辉,李桐林,董瑞霞,等.利用高斯求积和连分式展开计算电磁张量格林函数积分[J].地球物理学进展,2005,20(3):667-670.
[12]Walter L A.Computer Program Numerical Integration of Related Hankel Transforms of Oders0and1by Adaptive Digital Filtering[J].Geophysics,1979,44(7):1287-1305.
[13]Nam M J,Pardo D,Torres-Verdín C.Simulation of Triaxial Induction Measurements in Dipping,Invaded,and Anisotropic Formations Using a Fourier Series Ex-pansion in a Nonorthogonal System of Coordinates and a Self-Adaptive Hp Finite-element Method[J].Geo-physics,2010,75(3):F83-F95.
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