应用CN-FDTD分析电磁波电阻率测井仪的电磁响应

Analyzing Response of Electromagnetic Wave Resistivity Tool by CN-FDTD

传统FDTD受到Courant稳定性条件限制,计算时间较长,而ADI-FDTD精度又比较低,Crank-Nicolson时域有限差分方法(CN-FDTD)在时间步长上的取值远大于CFL条件时仍旧能够保持良好的计算精度。采用无条件稳定的柱坐标系Crank-Nicolson时域有限差分方法(CN-FDTD)分析了轴对称地层环境中的随钻电磁波电阻率测井仪器的电磁响应。在CN-FDTD仿真中,采用稳定双共轭梯度法(Bi-CGSTAB)作为求解器用于求解每个时间步所产生的线性方程组。通过对随钻电磁波电阻率测井仪在多层地层下的电磁响应进行数值仿真,其数值仿真结果表明CN-FDTD的计算结果准确,计算速度比普通FDTD提高3倍。

Traditional FDTD simulation time-step sizes are limited by the smallest mesh size following the Courant stability condition. This makes the FDTD method need long computing time. However the ADI-FDTD method has larger truncation and dispersion errors than those of the traditional FDTD method The CN-FDTD method can overcome the stability condition and both the tnmcation and dispersion errors are similar to those of the traditional FDTD. An unconditionally stable finite-difference time-domain （FDTD） method in cylindrical coordinates was developed to analyze electromagnetic responses under axially symmetric logging while drilling （LWD） environments. The method is based on the application of the Crank-Nicolson scheme to the FDTD method in cylindrical coordinates. In order to solve the linear system generated by the CN-FDTD at each time step, the Bi-Conjugate Gradient Stabilized method （Bi-CGSTAB） was used. Numerical results demonstrate that the CN-FDTD method is very effective and a soeeduo factor of 3 can be achieved.