“Finite difference forward modeling of induction tool in 3D geometry,” Petrophysics, Vol. 41, No. 6, pp. 503-511, 2000.
A computer code based on the finite difference method is developed to model multi-coil induction tools in complex 3-D formations such as layered reservoirs with various invasion profiles. The resulting linear system is solved by the Spectral Lanczos Decomposition Method in the frequency domain. The main characteristics of the code are presented, including the grid generation and the algorithm used to facilitate convergence in the Lanczos decomposition process. The code can simulate induction logging in highly dipping beds and in horizontal wells with various invasion patterns such as step, ramp, slope, or annulus profile. Also, non-circular boreholes and invasion profiles can be modeled. Several numerical examples are presented to illustrate the effects of those profiles on induction logs. The code has been tested against 1 -D and 2-D codes in various formations with satisfactory results. It has also been used to produce synthetic ILD and ILM logs in dipping beds with invasion zones. When compared with array induction logs, it is seen that the ILM responses are similar to 30-inch AIT logs and the ILD logs are similar to 60and 90-inch AIT logs. The code requires a minimum of 24 Mbytes of RAM and approximately 60 seconds of CPU time to compute responses of several receivers at one transmitter position on a 300 MHz personal computer.