本文将应用2.5维数值模式匹配算法研究建立柱状横向同性地层中偏心条件下磁流源并矢Green函数的高效算法,并利用该算法高效计算多分量阵列感应井眼校正库.首先,通过Fourier展开技术将偏心条件下磁流源并矢Green函数的数值模拟转化为一系列的轴对称问题;然后利用模式匹配算法求解轴对称问题,得到柱状介质中偏心条件下磁流源并矢Green函数的半解析解;最后,结合中国石油集团测井有限公司开发的三维感应测井仪器(TDIT)的结构参数,推导出复合线圈系视电导率张量的计算公式.在此基础上,根据井场实际地层资料归纳出理论地层模型相应参数的变化范围,高效高精度建立一套直接应用于工业生产的多分量阵列感应井眼校正库,并利用井眼校正库详细地分析考察各模型参数对TDIT响应的影响.%The array multicomponent induction logging (AMCIL) has been successfully applied in the last decade for evaluation of various types of anisotropic formations,such as thin laminated sand/shale beds,by means of the determined resistivity anisotropy (horizontal and vertical resistivity),dip,and azimuth.So far,due to the 2D or 3D data processing technique on AMCIL data is weak with low efficiency,the 1D inversion remains the main way to interpret the AMCIL data.However,one of the largest hurdles is the borehole effect on the logging data.So,the borehole correction database about the AMCIL data must be built to eliminate borehole environment influence on the AMCIL data.In this work,we develop an efficient and high-precision modeling algorithm of electromagnetic dyadic Green of magnetic current source in cylindrically inhomogeneous TI media at the condition of tool eccentricity by a 2.5D numerical matching mode method(NMM),and establish a borehole correction database for array multicomponent induction logging (AMCIL) by the fast algorithm.Firstly,the computation of the AMCIL responses at the condition of tool eccentricity is transformed into three axially symmetrical problems about the EM fields by means of Fourier series expanding.Then the NMM is used to fast solve the axially symmetrical problems,and obtain the semi-analytic solutions of the EM fields excited by the triaxial transmitters in the cylindrically inhomogeneous TI media.Finally,combining with the structural parameters of three-dimensional induction tool (TDIT) developed by the China Petroleum Logging Limited Corporation,we obtain the computational formula of apparent conductivity tensors of composite coil arrays.On this basis,according to the formation data at the actual well site,the variation range of the relevant formation parameters can be inferred so as to establish an efficient and applicable borehole correction database for TDIT.The stability and precision of the NMM algorithm are validated.The response characteristics of the TDIT in the borehole correction database on the model parameters are investigated in detail.The results show that when the tool is eccentric along x axis,the apparent conductivity σa,xx is greatly influenced by the borehole radius,and a little by the eccentricity.The conductivity σa.yy is greatly influenced both by the borehole radius and eccentricity.The influence of eccentricity on conductivity σa,zz becomes larger along with the increasing borehole radius.The conductivities response of a shorter spaced array is more influenced by the borehole radius and the eccentricity.Each array response appears monotonous tendency with formation model parameters,which indicates using the borehole correction database to correct the multicomponent logging data of TDIT is feasible.
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