Analysis Of Response Of LWD’s Electromagnetic Wave Propagation Tool With The CN-FDTD Method

As the worldwide petroleum industry has significantly progressed, resistivity LWD has become the key technique of complex oil reservoir development and been used widely. The finite-difference time-domain (FDTD) method is one of the most important methods which have been used to understand electromagnetic responses under different logging environment. However, the FDTD method still has its disadvantages. The selection of the time steps’size in traditional finite-difference time-domain(FDTD) method is restricted to the Courant-Friedrichs-Levy stability condition. The time step has relationship with the space step. So it will take long time to simulate fine structures using traditional FDTD. In this paper, the three-dimensional Crank-Nicolson difference scheme FDTD in cylindrical coordinate system based on Computer Unified Device Architecture(CUDA) is introduced. The response of electromagnetic logging and transient characteristic of electromagnetic wave propagation in isotropic formation was researched using the CN-FDTD being out of the CFL conditions of stability.First of all, based on the analysis of the theory of LWD and the LWD model, the basic theory formulas of three-dimensional cylindrical coordinate system CN-FDTD method in isotropic formation are developed. The settings of the excitation source and the absorbing boundary are introduced. At the same time, the code is designed based on the General Purpose Graphics Processing Units(GPGPU).Secondly, the CN-FDTD is applied to analyze the transient characteristic of the electromagnetic wave generated by the sinusoidal source. We observed that the electromagnetic waves in the conductivity isotropic formation are not zero transmission loss. The farther the distance, the more serious loss. So the near-field characteristics of electromagnetic waves in the formation should be studied of LWD. Further more, the transient characteristics of the electromagnetic wave at different transmitting frequency is analyzed. The results show that the higher frequency, the attenuation of the wave is faster and the skin effect is more serious.Finally, the CN-FDTD method is used to calculate the response of LWD in the various formations. In the multilayer formation simulation, the CN-FDTD method can achieve a speed-up ratio of6over the traditional FDTD method. In addition, the relative errors of these two simulations are found to be very small. It is readily found that CN-FDTD will consume more memory because it has to solve a matrix. The influencing regularity of LWD are simulated in layered isotropic formation considering different thickness and different invasion depth. The results show that the phase difference can distinguish thinner layer. The reservoir thickness is thinner, its conductivity is more close to the conductivity of the upper and lower layer. The phase difference is more susceptible to the effects of the invaded zone. When the invaded zone depth is large, the cure represents the invaded zone conductivity, rather than the virgin layer conductivity.All above results will provide practical significance for the simulation of LWD by CN-FDTD and the theoretical foundation for the response analysis of resistivity LWD.