【作者】 张振；

【导师】 孔凡敏；

【作者基本信息】 山东大学 ， 无线电物理， 2012， 硕士

【摘要】 随着世界石油工业的不断发展,随钻电磁波电阻率测井在油气勘探中得到广泛应用。时域有限差分方法是目前用于模拟随钻电磁波电阻率测井过程的重要数值方法,但任何一个方法都有其优点和缺点。传统的时域有限差分方法时间步长的选取受限于Courant-Friedrich-Levy(CFL)稳定性条件,即其时间步长的选取与空间步长相关,当对精细结构进行模拟时,传统的时域有限差分方法往往是十分耗时的。本文采用基于Crank-Nicolson差分格式的柱坐标系时域有限差分方法(CN-FDTD),克服了稳定性条件限制,结合CUDA平台,进一步加速Crank-Nicolson时域有限差分方法的计算速度。应用此高速平台分析研究了正弦源产生的电磁波在地层中传播的瞬态特性和随钻电磁波电阻率测井仪在各向同性地层中的电磁响应。首先,在分析随钻电磁波电阻率测井原理和钻井模型的基础上,推导出圆柱坐标系下的CN-FDTD递推公式,分析了CN-FDTD递推过程中激励源的设置和吸收边界问题。编程实现了基于通用图形处理器的CN-FDTD计算程序,为研究随钻电磁波电阻率测井的电磁响应搭建了高速计算平台。其次,本文通过研究正弦源产生的电磁波在不同电导率地层中的瞬态传播特性,观察到电磁波在电导率不为零的地层中传播时存在损耗,且距离越远,损耗越严重,因此,随钻电磁波电阻率测井应该研究电磁波在地层中的近场特性。通过观察不同频率的正弦波在地层中的传播情况,发现发射频率越高,电磁波受趋肤效应的影响越大,在地层中的衰减越快。最后,重点研究了CN-FDTD方法在随钻电磁波电阻率测井响应分析中的应用。通过比较CN-FDTD与FDTD方法在多层地层中的计算速度和内存占用比,可以看出,虽然CN-FDTD要占用更多的内存,但其计算结果与FDTD相当吻合,计算速度可以达到传统FDTD的6倍左右。研究分析了不同储集层厚度和不同侵入带深度对幅度比曲线和相位差曲线的影响。数值模拟表明,相位差曲线可分辨出更薄的地层,储集层厚度越薄,其电导率越容易受上下两层地层的影响。而且相位差曲线相对幅度比曲线,更容易受侵入带的影响,侵入深度很大时,曲线反映的主要是侵入带的电导率,而不是原状地层的电导率。以上工作和结论对CN-FDTD算法应用于随钻电磁波电阻率测井的模拟计算具有实际意义,对分析随钻电磁波电阻率测井仪的实际电磁响应提供了理论基础。更多还原

【Abstract】 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.更多还原