本文针对中国石油集团测井有限公司(CPL)三维阵列感应测井仪器(Three Dimensional Induction Tool,TDIT)的真实结构与参数,利用2.5维数值模式匹配技术研究建立水平层状非均质TI地层中仪器偏心情况下三维感应测井响应的高效数值模拟算法.首先,利用2.5维数值模式匹配技术给出水平层状非均质TI模型中偏心磁流源并矢Green函数的半解析解.在此基础上,结合三维阵列感应测井仪器参数以及测量过程中出现的仪器偏心与旋转等实际情况,通过叠加原理推导出该仪器响应的有效计算公式.最后,通过数值模拟结果分析考察仪器偏心、仪器自旋角等参数对测井响应的影响以及变化特征,为多分量感应资料处理与解释提供理论基础.%Three-dimensional induction logging tool (TDIT) or multicomponent induction logging has been become one of the most important techniques in electrical logging methods because it is currently the unique way to obtain the formation information on horizontal and vertical conductivities simultaneously.CNPC Logging Limited Company (CPL) recently developed a three-dimensional array induction tool,which is composed of a tri-axial transmitter and eight groups of receiver coils.The four receivers close to the transmitter are conventional induction coils with offsets of 6,9,12 and 15 in (1 in=2.54 cm),while the remaining four sets of coils are built as tri-axial receivers with spacing of 21,27,39 and 72 in,respectively.The tool operates at three different frequencies by sequentially exciting each of the coils (x,y,and z directions) in the tri-axial transmitter.The four conventional induction coils measure the signals excited at two highest frequencies only and each of other tri-axial receivers do two tensor signals at two lowest frequencies.At every logging depth,the tool can provide 96 different apparent conductivity curves with different vertical resolutions and investigation depths.Theoretically,we can extract the formation information such as horizontal and vertical conductivity,bed thickness,and dip angle of the bed from the TDIT data which allow us to effectively evaluate anisotropic reservoirs.However,the results of both the numerical simulation and actual well-site logging data show that although the logging data truly include the previous useful formation information,the tool response is also sensitive to the borehole environment parameters such as borehole radius,mud conductivity,tool eccentricity and spin angle.In order to establish some effective approaches for reconstruction of the useful formation parameters,it is very important to carefully and deeply investigate the comprehensive influence of the borehole environment and formation parameters on the TDIT response.In this paper,we firstly apply the 2.5D numerical matching mode (NMM) method to establish the semi-analytic solution of electromagnetic dyadic Green of a magnetic current source at an arbitrary position in a horizontal layered inhomogeneous TI medium.Then,based on the superposition principle,we give the formulas to compute the TDIT response at the condition of tool eccentricity with different spin angles in the formation according to the real coils structure of the TDIT.On this base,the numerical results will validate the stability and precision of the NMM algorithm.Finally,we investigate the response characteristics of the TDIT in the horizontally layered inhomogeneous medium by comparison of the numerical results obtained at two different spin angles of 0 and 30 degrees.The results show that the spin angle has great influence on the TDIT response.When the tool is eccentric and spin angle equals to zero,only main components (xx,yy and zz) and second main components (xz and zr) in each tensor conductivity are nonzero while other components (ry and yr) become zero at every measurement point.However,when the spin angle is 30 degree,all conductivity components become nonzero.Because the spin angel of the tool is often difficult to control and randomly varied during logging,both the eccentricity and spin of the tool will complicate measurement results.Therefore,in order to obtain the reliable formation information from TDIT data,it is required to develop some new technique to reduce the influence.
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