三维频率域随钻电磁波测井数值模拟

在现有的普通计算机的内存和运算速度的条件下，三维频率域电磁波测井数值模拟非常困难，为了研究随钻仪器在复杂测井环境中的响应规律，从Maxwell电磁响应方程出发，针对大斜度井井眼和侵入剖面的几何特点，采用新的网格划分方法，并应用基于交错网格的有限差分得到了三维频率域电磁响应差分计算格式，采用改进的ICCG（不完全乔尔斯基共轭梯度）方法，对一维变带宽存储的大型复稀疏矩阵进行了求解，得到了随钻电磁波测井响应.计算结果表明：一维变带宽存储方法很好地解决了大型稀疏矩阵的存储问题；改进的ICCG方法得到的结果真实可靠并大大提高了求解效率；随钻电阻率曲线随着井斜角度增大会出现“极化角”，低阻侵入会使“极化角”弱化；相位电阻率曲线受围岩影响较小，受侵入影响较大.

Three-dimensional numerical simulation of electromagnetic logging-while-drilling tool response in frequency domain

The numerical simulation of three-dimensional electromagnetic logging responses in frequency domain is a great challenge in the current condition of computer memory and operation speed. In order to study the response of electromagnetic logging-while-drilling (LWD) tools in complex situations, the difference equations to calculate the electromagnetic response were derived from Maxwell's equations by using the staged-grid finite difference method. A new mesh generation method was adopted according to the geometric characteristics of deviated well models with borehole and invasion. The large scale complex equations were stored by one-dimensional variant-banded way and were solved by the method of improved incomplete Choleskey conjugate gradient and the response of electromagnetic LWD tool was obtained. The results show that the storage problem of large scale complex matrix was well solved by the one-dimensional variable-bandwidth store method. The improved ICCG method was efficient and accurate. The polarization angels appear in the resistivity curve with the increase of deviation angle and the polarization angles will be weakened with the low-invasion. The phase resistivity is influenced less by shoulder and larger by invasion.