用矢量有限元方法模拟随钻测井仪在倾斜各向异性地层中的电磁响应

The electromagnetic modeling of logging-while-drilling tool in tilted anisotropic formations using vector finite element method

用矢量有限元法模拟和分析了电各向异性倾斜沉积岩层的随钻测井电磁响应,为很好地模拟钻铤、井眼和激励线圈等,采用了基于圆柱坐标下的六面体剖分;同时采用了高阶叠层矢量基函数来描述每个剖分单元内的场,有利于减少剖分单元数和未知量.三维有限元程序采用数值模式匹配(当处于简单地层时)以及时域有限差分法计算的结果进行了验证,显示吻合非常好.最后仿真了不同各向异性系数和不同倾角的各向异性地层的随钻电阻率测井响应,有助于对各向异性及地层倾角的校正,以及对储层作出正确评价.

In this study, the vector finite element method is used to simulate and analyze the logging-while-drilling electromagnetic response of tilted sedimentary formation with electric anisotropy. In order to best model steel mandrel, borehole and the transmitter, the hexahedral mesh based on cylindrical coordinate is applied here. Meanwhile, the basis function of higher order vector basis function is used to describe the field of each mesh unit, so the number of mesh units and the number of unknowns is reduced. The 3-D finite element program is validated by comparing the results calculated from numerical mode matching （NMM） in simple formations and from finite difference time-domain （FDTD）, which show good agreement. It is then used to simulate the resistivity responses of LWD tools in anisotropic formations with different anisotropic coefficients and different dipping angles, which is helpful to the correction of the influence imposed by anisotropic and tilted formations and helpful to obtain a correct hydrocarbon evaluation.