垂直井眼中三维阵列感应测井资料自适应井眼校正

三维感应测井受井眼环境影响很大，如何消除这些不利影响是有效获取各向异性地层电导率真值并提高资料处理和解释质量的一项重要工作.本文以一维柱状各向异性地层模型为基础，通过最小平方反演技术从实际测量资料中快速反演井径、偏心距、泥浆电导率、地层水平电导率和各向异性系数等模型参数，设法减小井眼环境对测量结果的影响.首先，利用仪器偏心情况下不同旋转角电导率张量的关系方程，建立旋转角提取与校正方法，获取无旋转角三维感应测井数据.在此基础上，根据事先计算好的井眼校正库并结合多维非线性有限元逼近技术，建立快速计算三维感应测井响应以及Jacobi导数矩阵的插值公式，并利用自适应正则化迭代反演技术不断修改模型参数，实现理论合成资料与输入资料的最佳拟合.最后，通过反演出的模型参数计算三维感应测井资料所有分量的校正量，实现三维感应资料的井眼校正.理论模型和实际资料的处理结果均证实，在低阻井眼泥浆情况下，一维柱状模型中的反演方法仍然可以提取出较可靠的地层水平和垂直电导率，且井眼环境校正对于受井眼环境影响相对较小的测井曲线具有非常好的校正效果.

Adaptive borehole correction of three-dimensional array induction logging data in a vertical borehole

The three dimensional array induction logging tool (TDIT) has currently become an important technique for evaluation of anisotropic formations because it can provide the information about horizontal and vertical resistivity, dip, and azimuth of reservoirs simultaneously. However, due to the large effects of the borehole environment and bed thickness on the response of TDIT, it is usually very difficult to directly estimate the size of horizontal and vertical conductivities of formation from the different components of apparent conductivity tensors. Thus, these effects must be corrected to obtain reliable reservoir properties.
In this paper,we propose an adaptive borehole correction (ABHC) algorithm to reduce borehole effects on TDIT and efficiently extract the approximate horizontal and vertical conductivities from the TDIT logging data in a vertical well filled with conductive mud. In this technique, firstly the rotation angle of TDIT is extracted from the cross component of TDIT logging data and its influence on TDIT responses is removed through a rotation matrix. Then, an one-dimensional cylindrical model composed of borehole and anisotropic formation is applied to simplify the distribution of conduction in the real formation. So, we can use only five model parameters:borehole radius, mud conductivity, eccentric distance, formation horizontal conductivity and anisotropic coefficient to determine the response of TDIT. These five model parameters form a model vector. For any given model vector, an algorithm is established for forward modeling and Jacobi derivatives of its response with respective to all the model parameters by the borehole correction library of TDIT are calculated in advance with multi-dimensional nonlinear interpolation. Adaptive regularization iterative inversion is performed to reconstruct all model parameters from properly chosen main components of TDIT at each measurement position in order to assure a stabilization of inversion solution as well as realization of best fit of input data with modeling logs. After the inversion model vector is obtained, it is applied to compute the response in the cylindrical anisotropic model and in homogeneous anisotropic formation. The difference between the responses of the two different models is used as the borehole effect on TDIT and to correct raw TDIT data. Finally, tests on a theoretical model and real log data validate the effectiveness of the ABHC algorithm proposed in this work.