随钻方位电磁波电阻率测井关键技术研究
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摘要
在油气资源勘探开发中,利用导电特性测量电阻率是开展地层含油、含气、含水或油水同层定性评价的依据,同时也是定量评价储层含油气饱和度的重要参数之一。随钻测井具有实时、高效等特点,可以有效降低钻井液入侵对测量地层电阻率的影响,对准确评价储层含油情况具有重要意义。为提高采收率和降低成本,水平井、大斜度井和分支井日益增多,而在这些井中,由于井眼周围的电性参数不再是轴对称分布,与垂直井相比,测井响应发生了较大的变化,基于大斜度井和水平井中电测井响应正反演数值模拟研究是当前研究的热点。同时,在石油钻井中,迫切需要一种能开展实时地质导向及复杂油气层钻进的随钻测井系统,对未钻地层进行预测,使井眼轨迹保持在期望的储层内。近年来,在传统随钻电阻率测量技术的基础上,国外测井巨头斯伦贝谢、哈里伯顿、贝克休斯等开展了随钻方位电磁波电阻率测井技术研究,已研制出相应的仪器并开始投入商业使用,但国内对其研究尚处在起步阶段,如何发展和拥有具有自主知识产权的未钻地层预测随钻方位电磁波电阻率测井系统,是国内迫切需要解决的关键科技问题,因此开展随钻方位电磁波电阻率测井技术研究对提升国内随钻测井技术水平以及打破国外技术封锁和垄断都具有重要意义。
在此背景下,基于未来对仪器研制的考虑,本文围绕随钻方位电磁波电阻率测井关键技术,以电磁场理论、电测井方法原理和电子信息技术为理论基础,从测井响应正演数值模拟和测井响应弱信号检测角度进行先导研究。对于测井响应正演模拟问题,在对电磁场时域有限差分计算方法和随钻电磁波测井原理分析研究的基础上,采用三维ADI-FDTD方法,在圆柱坐标系中基于Yee氏非均匀交错网格对Maxwell时域方程进行差分离散,通过地层空间坐标系与仪器空间坐标系的变换,从而可在以仪器轴为z轴的坐标系中表示各向异性倾斜地层空间的电导率张量矩阵,利用面积加权平均求取共形网格中介质有效电导率,基于UPML(单轴各向异性介质完全匹配层)吸收边界条件,实现仪器在各向异性倾斜地层中测井响应正演模拟；对于测井弱信号检测问题,在对随钻测井噪声分析的基础上,利用非线性理论和电子信息技术开展随钻电磁测井弱信号检测方法研究,采用一维非线性振子建立基于Duffing振子的弱信号检测模型,在对Duffing振子动力学特征分析的基础上揭示Duffing振子用于弱信号检测的机理,利用时间尺度变换方法,将Duffing振子应用于随钻方位电磁波电阻率幅度衰减比和相位差的测量中,通过电路模拟设计和仿真调试,实现了基于Duffing振子的随钻电磁波测井响应信号的检测。通过正演技术模拟研究,掌握仪器在地层中的测井响应特征,既为测井资料的处理解释提供理论依据,也为仪器的研制提供设计方法指导；通过测井弱信号的检测技术方法研究,降低可检测信号的信噪比,提高仪器的径向探测深度,增加未钻地层预测的距离,为仪器的研制提供测井响应信号采集技术支持。
本论文主要研究了电磁场三维时域有限差分计算方法、随钻方位电磁波电阻率仪器测井响应数值模拟算法、随钻方位电磁波电阻率测井响应特征正演模拟、Duffing振子的动力学行为与噪声影响、系统相态的判别算法和基于Duffing振子的随钻电磁波测井弱信号的检测与实现等内容,其主要研究工作和成果如下：
1.电磁场三维时域有限差分计算方法
电磁场三维时域有限差分计算方法研究以时域Maxwell方程组为理论基础,基于Yee氏网格在直角坐标系下对Maxwell旋度方程进行差分离散,从差分计算的角度,分别论述差分方程的迭代、数值稳定性与数值色散、吸收边界条件、网格剖分、共形网格介质参数的确定、激励源的设置以及时谐场振幅和相位的提取等相关问题。在此基础上,针对常规FDTD方法的空间离散步长和时间步长需满足Courant条件的问题,研究了ADI-FDTD方法和ADI-FDTD方法的UPML边界条件：针对矩形网格剖分带来“阶梯”误差问题以及基于随钻测井中井眼的实际形状,研究了圆柱形非均匀Yee网格,基于迭代方程中轴线方向上电场出现奇异的问题,研究了在轴线附近采用Maxwell方程的积分形式进行特殊处理的方法。通过对电磁场三维时域有限差分计算方法的研究,推导给出了直角坐标系和圆柱坐标系下时域推进迭代方程；结合隐式差分特点,将UPML吸收边界条件推广到ADI-FDTD方法中,推导给出了三维ADI-FDTD方法中实现UPML吸收边界条件的计算公式。
2.随钻方位电磁波电阻率仪器测井响应数值模拟算法
在圆柱坐标系下,以时域Maxwell旋度方程为基础,利用Yee氏交错网格对各向异性地层时域Maxwell旋度方程进行差分离散,从而得到每个交错节点上电磁场的时域递推方程；基于倾斜地层,通过旋转矩阵,先将地层空间直角坐标系变换成仪器空间直角坐标系,再将仪器空间直角坐标系变换成仪器空间圆柱坐标系,通过2次坐标旋转变换,求出圆柱坐标空间中各向异性倾斜地层电导率矩阵张量；基于随钻测井中仪器偏心导致在井眼和地层的交界面处出现部分填充网格,其与圆柱坐标网格不共形问题,采用面积加权平均准静态近似技术计算其等效电导率张量,从而提高模拟的精度；基于计算机内存有限导致FDTD的计算必须在有限区域开展的问题,利用UPML吸收边界条件降低外边界反射,实现有限网格空间的截断,提高模拟的效率；基于简单的均匀地层模型和数值模式匹配算法(NMM),对本文提出的算法进行验证,结果表明算法正确。通过对随钻方位电磁波电阻率仪器测井响应数值模拟算法的研究,建立了一套基于坐标系变换和面积加权近似表示共形网格有效介质电导率矩阵张量的表示方法,此方法可推广适用于其他随钻电法测井仪器在各向异性倾斜地层中测井响应模拟研究。
3.随钻方位电磁波电阻率测井响应特征正演模拟
在电磁场三维时域有限差分计算方法和随钻方位电磁波电阻率仪器测井响应数值模拟算法的基础上,开展随钻方位电磁波电阻率测井仪器在复杂条件下测井响应特征研究。通过对不同地层模型的测井响应数值模拟,表明：1)在各向异性地层中,测量视电阻率是水平电导率和垂直电导率的综合反映；2)随着倾角的增大,地层的视厚度也增宽,当倾斜角度较大时,相位差和幅度比曲线在地层的边界处出现牛角效应,而且倾斜角度越大,牛角效应越明显；3)当泥浆的电导率和周围地层的电导率相差较小时,仪器偏心对测井响应的影响较小,但当泥浆的电导率和周围地层的电导率相差较大时,仪器偏心对测井响应的影响明显,且随着偏心距的增大,幅度衰减比也增大；4)在倾斜角度相同时,随着仪器偏心距的增大,在地层边界处牛角效应越明显；5)对于线圈系面垂直于钻铤的随钻电磁波电阻率仪器,以大的倾斜角度穿越地层边界时,测井响应曲线在上下边界处均出现角峰,且角峰的形状相似宽度也窄,利用此角峰可以指示地层边界的存在；对于线圈系面倾斜于钻铤的随钻电磁波电阻率仪器,以大的倾斜角度穿越地层边界时,测井响应曲线在地层边界处出现的角峰不对称,且角峰宽而深,利用此角峰不仅可以指示地层边界的存在,而且还可以提前指示未钻地层是高阻地层还是低阻地层,可用于实时的地质导向,使钻头保持在高阻含油层中钻进。通过对测井响应特征正演模拟研究,比较深入的认识了随钻方位电磁波电阻率测井仪器在复杂条什下的测井响应特征,为将来反演计算、仪器的自主研制和测井资料的解释提供了理论依据。
4.Duffing振子的动力学行为与噪声影响
研究了Duffing振子动力学行为与噪声影响。基于一维非线性振子的模型建立Duffing振子的一般检测模型,在此基础上研究周期策动力和噪声对Duffing振子运动的影响规律,通过理论推导和仿真分析,表明：1)随着周期策动力的增加,Duffing振子的相轨迹会依次按照同宿轨道状态、分岔状态、混沌状态、外轨道大周期运动状态演变,非线性动力特性十分明显；2)Duffing振子对于任意分布的平稳随机噪声都具有良好的免疫性能,对初值具有敏感性,输入信号的幅度越小,系统对信号越敏感,系统的抗噪性能越好,信噪比越低；3)噪声对Duffing振子运动状态的影响与噪声的强度有关,噪声的存在和强弱会影响系统检测的性能。通过Duffing振子动力学行为与噪声影响的研究,为基于Duffing振子的弱信号检测提供了依据,揭示了基于Duffing振子的弱信号检测系统有最低的检测门限。
5.系统相态自动判别算法
研究了系统相态判别方法。在常规系统相态判别方法研究的基础上,从工程实现的角度,针对测量仪器识别系统相态问题,研究系统相态自动判别算法,提出了功率谱能量因子和相图图像区域穿越两种相态自动判别方法。在功率谱计算的基础上,以主频谱分量为中心,基于一段频率窗内的谱分量,用功率谱能量因子来定量描述运动系统的能量特征。在相图中设置一个区域,将相图划分为区域外和区域内两个部分,进而判断相轨迹曲线是否穿越到区域内以及穿越过的次数,通过计算穿越次数判别系统的相态。两种方法计算量小,实时性好,可以移植到硬件中实现,模拟仿真表明方法有效。通过对系统相态自动判别算法的研究,为Duffing振子实际应用于弱信号的检测提供了有效的判别手段。
6.基于Duffing振子的随钻方位电磁波电阻率测井信号检测电路设计
研究了随钻方位电磁波电阻率测井弱信号Duffing检测硬件电路。在对基于Duffing振子进行弱信号检测的基础上分析了待测信号与策动力信号之间存在相位差和频率差时对测量结果的影响,通过时间尺度变换方法,将Duffing振子扩展到频率为2MHz的信号检测,在此基础上研究基于Duffing振子测量随钻方位电磁波电阻率仪器响应中幅度衰减比和相位差的基本原理,设计了检测系统的硬件电路整体框图,并用具体的硬件电路实现了Duffing振子模型,通过模拟输入热噪声,电路仿真表明设计的Duffing电路可对频率为2MHz的信号进行检测,电路对参数非常敏感,同时对噪声有一定的免疫力,随着检测临界阈值精度的提高,信噪比降低。通过此内容的研究,利用具体的电路实现Duffing振子模型,为基于Duffing电路的随钻电磁弱信号检测提供了技术支持。
本论文全文共分5章。第一章为绪论,阐述了研究的目的与意义、研究的现状以及研究内容、研究方法和创新点：第二章为电磁场的时域有限差分计算方法,论述了直角坐标系和圆柱坐标系中三维电磁波时域有限差分计算问题,为随钻方位电磁波电阻率测井响应模拟提供支持：第三章为随钻方位电磁波电阻率测井响应数值模拟,论述了其测井的基本原理和正演模拟算法,模拟不同模型的测井响应并开展未钻地层预测研究；第四章为随钻测井弱信号检测方法与设计,论述了基于Duffing振子的测井弱信号检测方法技术和Duffing电路的设计：第五章为总结与建议,对全文进行总结以及提出今后研究的建议。
In the exploration and development of oil and gas resources, the resistivity based on conductive characteristics of the reservoir is the basis of the qualitative evaluation whether the formation is oil-bearing strata, oil or water-bearing layer, and it is also one of the important parameters of the reservoir hydrocarbon saturation. LWD has characteristic of real-time and efficient, it can effectively reduce the impact of the drilling fluid invasion to the formation, and it is significance to accurate evaluation of reservoir oil-bearing. In order to enhance oil recovery and reduce costs, horizontal wells, deviate wells and multilateral wells are used, and the number of these wells is increasing. Comparing with vertical wells, the logging response has changed because the electrical parameters surrounding the borehole are the nonaxisymmetrical distribution, research on electric logging of modeling and inversion numerical simulation based on horizontal wells and deviate wells is hot. Meanwhile, in oil drilling, it is urgent need a LWD system that can carry out real-time geosteering and it is suit to the complex oil&gas layer, predict the undrilled formation to maintain the borehole within the desired geological. In recent years, based on the techniques of traditional resistivity LWD, Schlumberger, Halliburton, Baker Hughes have researched on the azimuth resistivity measurement, the corresponding instrument has been developed and been put into commercial use, but this research is still in infancy in China, it is important to solve the key scientific and technological issues about how to develop the azimuth electromagnetic wave resistivity LWD, therefore, it has great significance for us to research it in raising domestic LWD technical level as well as to break the blockade and monopoly of foreign technology.
In this context, considering on development of instrument for the future, we focuses on the key technologies of azimuth electromagnetic wave resistivity LWD in this dissertation, study on the forward numerical simulation of logging response and weak signal detection with the theoretical basis of electromagnetic theory, electrical logging method and electronic information technology. To the forward simulation problem, based on the principle analysis of calculation method and electromagnetic wave LWD, we employ ADI-FDTD directly with Yee's non-uniform staggered grid in three-dimensional cylindrical coordinates, transfer coordinate system between strata space and instrument space, which the conductivity tensor of the anisotropic and dipping formation can be expressed in coordinates of instrument, use area weighted average to compute the effective conductivity of partially-filled grid cells at interfaces and use UPML absorbing boundary conditions to truncate the computational domain. To the weak signal detection of logging problem, based on the analysis of noise from LWD, we use nonlinear theory and electronic information technology to research weak signal detection method of electromagnetic LWD, make a Duffing model to detect weak signal based on one-dimensional nonlinear oscillator, reveal the mechanism of Duffing oscillator which is used in weak signal detection based on the analysis of the dynamics characteristics, design circuit and use Duffing circuit to measure the amplitude attenuation ratio and phase difference of electromagnetic LWD with method of time-scale transformation. We master the logging response characteristics of the instrument by forward modeling, it is not only provides a theoretical basis for the logging data processing and interpretation but also provides a guidance of design methodology for the development of instrument. By researching of logging weak signal detection, we can down the detected SNR, improve the radial depth of instrument and enhance the predicted distance of the undrilled formation, it provides the technical support of signal acquisition for the development of the instrument.
In this dissertation, those work was researched such as the calculation method of electromagnetic field with FDTD in three-dimensional, numerical simulation algorithm, forward simulation of electromagnetic wave resistivity LWD, dynamic behavior of Duffing oscillator and effect of noise, discriminate algorithm on phase state of system, electromagnetic wave logging weak signal detection and realization based on Duffing oscillator, its main research work and achievements are as follows:
1. FDTD calculation method of electromagnetic field in three-dimensional
Research on FDTD calculation method of electromagnetic field is based on the theory of time-domain Maxwell equations and Yee's grid. From the calculation of differential, iteration of differential equations, numerical stability and numerical dispersion, absorbing boundary conditions, spatial discretization, effective parameters of conformal grid, the excitation of source, and the extraction of time-harmonic field for amplitude and phase is discoursed, respectively. On this basis, for the problem of Courant criterion leads to oversampling in time, the alternating direction implicit (ADI)-FDTD method and UPML boundary conditions of ADI-FDTD are studied, for the problem of staircasing error from rectangular grid and based on the actual shape of borehole, the non-uniform cylindrical Yee grid is studied, for the singular electric field problem of iterative equation in the axial direction, special processing method of the integral form of the Maxwell equations is used near the axial. Based on the research of FDTD calculation method, the time-domain iterative equation is derived in Cartesian and cylindrical coordinate system, combining characteristics of implicit differential, UPML absorbing boundary conditions is extended to the ADI-FDTD method, and the formula of UPML absorbing boundary conditions in3D ADI-FDTD method is derived.
2. Numerical simulation algorithm of azimuth electromagnetic wave resistivity LWD
We use Yee's staggered grid to differential discretize the time domain Maxwell's curl equations of the anisotropic formation in cylindrical coordinates, thus time domain recursive equation of each staggered node is obtained. To the deviate wells, we use rotation matrix to transform stratum space Cartesian coordinate into instrument space Cartesian coordinate, then transform it into cylindrical coordinate system, thus conductivity matrix tensor of anisotropy formation in cylindrical coordinate can be expressed. To the partially filled grid, the eccentered interface indicated between the borehole and the formation is non-conformal to the cylindrical grid, we employ an area-weighted average of quasi-static approximation to compute effective conductivities and approximate them as uniformly filled cells, so as to improve the accuracy of the simulation. To the problem of limited memory of computer, we use UPML absorbing boundary conditions to reduce the reflection of the outer boundary and truncate the computational domain, so as to improve the efficiency of the simulation. In order to validate the proposed algorithm, we compare the proposed algorithm with NMM based on model of simple homogeneous formation, and results show that the algorithm is correct. By studying the numerical simulation algorithm of azimuth electromagnetic wave resistivity LWD, we set up an algorithm to express the conductivity tensor in dipping and anisotropic earth formations with rotation matrix and area-weighted average, this algorithm can be extended to numerical simulation of other electrical LWD.
3. Forward modeling on response characteristics of logging
Based on the research of the calculation methods and numerical simulation algorithms, we study the response characteristics of azimuth electromagnetic resistivity LWD in complicated conditions. By simulating for different model, results are shown as follows.1) In anisotropic formation, the measured apparent resistivity is a comprehensive reflection of the horizontal conductivity and vertical conductivity.2) The apparent thickness is widened with the inclination increases, and the horn effect can be seen in the phase difference response and amplitude ratio response for larger dipping angles, as the dipping angle is increased, the horn effect is more obvious.3) In general, the effect of eccentricity on the tool response is smaller when the conductivity contrast between the mud and the surrounding formation is low. Nevertheless, when the conductivity contrast between the mud and the surrounding formation is high, the effect of eccentricity on the tool response is larger, what's more, with the eccentricity increases, and the amplitude attenuation ratio is also increased.4) At the same dipping angle, with the eccentric distance increases, horns effect of the boundary is more obvious.5) For the electromagnetic LWD tool that surface of coil is perpendicular to the mandrel, when tool penetrating through an the boundary with large dipping angle, in the logging response curve, horns are appeared on both upper and lower boundaries, moreover, the shape of horn is similar and width of horn is narrow, according to the shape of horn, it can indicate the presence of formation boundaries. However, for the titled coil electromagnetic LWD tool, when tool penetrating through the boundary with large dipping angle, horn of logging response curve is asymmetric, what's more, the shape of horn is wide and deep, this horn is not only used to indicate the presence of formation boundaries, but also indicate the resistivity of the undrilled formation is high or low in advance, this allows for a proactive adjustment of the dipping angle and azimuth direction of the drill, hence, geosteering capabilities. By studying characteristics of logging response in forward modeling, we are familiar with the response of azimuth electromagnetic resistivity LWD in complex conditions, it provides a theoretical basis for the inversion calculation, development of instrument independently and interpretation of logging data for the future.
4. Dynamic behavior of Duffing oscillator and impact of noise
In this dissertation, dynamic behavior of Duffing oscillator and impact of noise are researched. We establish a detection model of Duffing oscillator based on one-dimensional nonlinear oscillator model, study the influence of movement state by the cycle perturbation and noise, theoretical analysis and numerical simulation show that:1) With the cycle perturbation increases, the phase trajectory of Duffing oscillator will be followed in accordance with the state of the homoclinic orbit, bifurcation state, chaotic state, the state of large-scale period, and the nonlinear dynamic characteristics is very obvious.2) Duffing oscillator is immune to any distribution of random noise and is sensitive to initial value of signal, the smaller amplitude of the input signal, the more sensitive to the signal for the system, the better anti-noise performance of the system, and the lower SNR.3) The impact of noise to the movement state of Duffing oscillator is relative to the intensity of noise, the presence and strength of noise effect the performance of detection system. By researching the dynamic behavior of Duffing oscillator and impact of noise, providing the support to weak signal detection based on Duffing oscillator, and revealing the weak signal detection system based on Duffing oscillator has the lowest detection threshold.
5. Discriminate algorithm on phase state of system automatically
In this dissertation, discriminate algorithm on phase state of system is researched. Based on the conventional discrimination method, we study the automatic discrimination method from the view of engineering, and present two automatic discrimination methods which are energy factor of the power spectrum and crossing zone of the phase diagram. On the basis of the power spectrum calculation, we use some spectral components within the frequency window to quantitatively describe the energy factor that express the energy characteristics of the motion system, and main spectral components is the center of window. By setting a zone, the phase diagram is divided into two regions, one is inside, the other is outside, and the state of system is determined by the count of crossing. The presented methods have characteristics of low calculation amount, real-time, and it is easy to be ported to hardware, results show the methods are effective. The research provides effective means to discriminate state of system for the Duffing oscillator applied to the detection of weak signals actually.
6. Design of detection circuit for azimuth electromagnetic resistivity LWD based on Duffing oscillator
We design a detection circuit based on Duffing oscillator. On the basis of weak signal detection with Duffing oscillator, we analyses the impact of measurement by phase difference and frequency difference between the signal and cycle perturbation. With the method of time scale transformation, Duffing oscillator is extended to detect the signal which frequency is2MHz. And the measurement principle of amplitude ratio and phase difference based on Duffing oscillator is studied, we design the overall block diagram of detection system, moreover, we use specific hardware circuit to realize the Duffing oscillator model. By inputting the thermal noise and simulating, results show that the designed Duffing circuit can detect signal with frequency of2MHz, circuit is very sensitive to parameters, meanwhile, circuit is very immunity to noise, with the accuracy of the critical threshold improves, the detectable SNR decreases. This research provides technical support to detect electromagnetic weak signal LWD based on Duffing circuit.
This dissertation consists of five chapters, it's organized as follows. In Chapter I, we describe the purpose and significance of research, status of relative technology, as well as research task, research methods and innovation. In Chapter II, we describe the method of FDTD, discuss the problem of calculation in Cartesian and cylindrical coordinates, it is supported to simulate the logging response for azimuth electromagnetic resistivity LWD. In Chapter III, we describe the principles of azimuth electromagnetic resistivity LWD, discuss the algorithms of forward modeling, and simulate the logging response for different model. In Chapter IV, we discuss the method of logging weak signal detection and Duffing circuit design. In Chapter V, we briefly summarize the work of dissertation, and present the proposal for future research.
在此背景下,基于未来对仪器研制的考虑,本文围绕随钻方位电磁波电阻率测井关键技术,以电磁场理论、电测井方法原理和电子信息技术为理论基础,从测井响应正演数值模拟和测井响应弱信号检测角度进行先导研究。对于测井响应正演模拟问题,在对电磁场时域有限差分计算方法和随钻电磁波测井原理分析研究的基础上,采用三维ADI-FDTD方法,在圆柱坐标系中基于Yee氏非均匀交错网格对Maxwell时域方程进行差分离散,通过地层空间坐标系与仪器空间坐标系的变换,从而可在以仪器轴为z轴的坐标系中表示各向异性倾斜地层空间的电导率张量矩阵,利用面积加权平均求取共形网格中介质有效电导率,基于UPML(单轴各向异性介质完全匹配层)吸收边界条件,实现仪器在各向异性倾斜地层中测井响应正演模拟；对于测井弱信号检测问题,在对随钻测井噪声分析的基础上,利用非线性理论和电子信息技术开展随钻电磁测井弱信号检测方法研究,采用一维非线性振子建立基于Duffing振子的弱信号检测模型,在对Duffing振子动力学特征分析的基础上揭示Duffing振子用于弱信号检测的机理,利用时间尺度变换方法,将Duffing振子应用于随钻方位电磁波电阻率幅度衰减比和相位差的测量中,通过电路模拟设计和仿真调试,实现了基于Duffing振子的随钻电磁波测井响应信号的检测。通过正演技术模拟研究,掌握仪器在地层中的测井响应特征,既为测井资料的处理解释提供理论依据,也为仪器的研制提供设计方法指导；通过测井弱信号的检测技术方法研究,降低可检测信号的信噪比,提高仪器的径向探测深度,增加未钻地层预测的距离,为仪器的研制提供测井响应信号采集技术支持。
本论文主要研究了电磁场三维时域有限差分计算方法、随钻方位电磁波电阻率仪器测井响应数值模拟算法、随钻方位电磁波电阻率测井响应特征正演模拟、Duffing振子的动力学行为与噪声影响、系统相态的判别算法和基于Duffing振子的随钻电磁波测井弱信号的检测与实现等内容,其主要研究工作和成果如下：
1.电磁场三维时域有限差分计算方法
电磁场三维时域有限差分计算方法研究以时域Maxwell方程组为理论基础,基于Yee氏网格在直角坐标系下对Maxwell旋度方程进行差分离散,从差分计算的角度,分别论述差分方程的迭代、数值稳定性与数值色散、吸收边界条件、网格剖分、共形网格介质参数的确定、激励源的设置以及时谐场振幅和相位的提取等相关问题。在此基础上,针对常规FDTD方法的空间离散步长和时间步长需满足Courant条件的问题,研究了ADI-FDTD方法和ADI-FDTD方法的UPML边界条件：针对矩形网格剖分带来“阶梯”误差问题以及基于随钻测井中井眼的实际形状,研究了圆柱形非均匀Yee网格,基于迭代方程中轴线方向上电场出现奇异的问题,研究了在轴线附近采用Maxwell方程的积分形式进行特殊处理的方法。通过对电磁场三维时域有限差分计算方法的研究,推导给出了直角坐标系和圆柱坐标系下时域推进迭代方程；结合隐式差分特点,将UPML吸收边界条件推广到ADI-FDTD方法中,推导给出了三维ADI-FDTD方法中实现UPML吸收边界条件的计算公式。
2.随钻方位电磁波电阻率仪器测井响应数值模拟算法
在圆柱坐标系下,以时域Maxwell旋度方程为基础,利用Yee氏交错网格对各向异性地层时域Maxwell旋度方程进行差分离散,从而得到每个交错节点上电磁场的时域递推方程；基于倾斜地层,通过旋转矩阵,先将地层空间直角坐标系变换成仪器空间直角坐标系,再将仪器空间直角坐标系变换成仪器空间圆柱坐标系,通过2次坐标旋转变换,求出圆柱坐标空间中各向异性倾斜地层电导率矩阵张量；基于随钻测井中仪器偏心导致在井眼和地层的交界面处出现部分填充网格,其与圆柱坐标网格不共形问题,采用面积加权平均准静态近似技术计算其等效电导率张量,从而提高模拟的精度；基于计算机内存有限导致FDTD的计算必须在有限区域开展的问题,利用UPML吸收边界条件降低外边界反射,实现有限网格空间的截断,提高模拟的效率；基于简单的均匀地层模型和数值模式匹配算法(NMM),对本文提出的算法进行验证,结果表明算法正确。通过对随钻方位电磁波电阻率仪器测井响应数值模拟算法的研究,建立了一套基于坐标系变换和面积加权近似表示共形网格有效介质电导率矩阵张量的表示方法,此方法可推广适用于其他随钻电法测井仪器在各向异性倾斜地层中测井响应模拟研究。
3.随钻方位电磁波电阻率测井响应特征正演模拟
在电磁场三维时域有限差分计算方法和随钻方位电磁波电阻率仪器测井响应数值模拟算法的基础上,开展随钻方位电磁波电阻率测井仪器在复杂条件下测井响应特征研究。通过对不同地层模型的测井响应数值模拟,表明：1)在各向异性地层中,测量视电阻率是水平电导率和垂直电导率的综合反映；2)随着倾角的增大,地层的视厚度也增宽,当倾斜角度较大时,相位差和幅度比曲线在地层的边界处出现牛角效应,而且倾斜角度越大,牛角效应越明显；3)当泥浆的电导率和周围地层的电导率相差较小时,仪器偏心对测井响应的影响较小,但当泥浆的电导率和周围地层的电导率相差较大时,仪器偏心对测井响应的影响明显,且随着偏心距的增大,幅度衰减比也增大；4)在倾斜角度相同时,随着仪器偏心距的增大,在地层边界处牛角效应越明显；5)对于线圈系面垂直于钻铤的随钻电磁波电阻率仪器,以大的倾斜角度穿越地层边界时,测井响应曲线在上下边界处均出现角峰,且角峰的形状相似宽度也窄,利用此角峰可以指示地层边界的存在；对于线圈系面倾斜于钻铤的随钻电磁波电阻率仪器,以大的倾斜角度穿越地层边界时,测井响应曲线在地层边界处出现的角峰不对称,且角峰宽而深,利用此角峰不仅可以指示地层边界的存在,而且还可以提前指示未钻地层是高阻地层还是低阻地层,可用于实时的地质导向,使钻头保持在高阻含油层中钻进。通过对测井响应特征正演模拟研究,比较深入的认识了随钻方位电磁波电阻率测井仪器在复杂条什下的测井响应特征,为将来反演计算、仪器的自主研制和测井资料的解释提供了理论依据。
4.Duffing振子的动力学行为与噪声影响
研究了Duffing振子动力学行为与噪声影响。基于一维非线性振子的模型建立Duffing振子的一般检测模型,在此基础上研究周期策动力和噪声对Duffing振子运动的影响规律,通过理论推导和仿真分析,表明：1)随着周期策动力的增加,Duffing振子的相轨迹会依次按照同宿轨道状态、分岔状态、混沌状态、外轨道大周期运动状态演变,非线性动力特性十分明显；2)Duffing振子对于任意分布的平稳随机噪声都具有良好的免疫性能,对初值具有敏感性,输入信号的幅度越小,系统对信号越敏感,系统的抗噪性能越好,信噪比越低；3)噪声对Duffing振子运动状态的影响与噪声的强度有关,噪声的存在和强弱会影响系统检测的性能。通过Duffing振子动力学行为与噪声影响的研究,为基于Duffing振子的弱信号检测提供了依据,揭示了基于Duffing振子的弱信号检测系统有最低的检测门限。
5.系统相态自动判别算法
研究了系统相态判别方法。在常规系统相态判别方法研究的基础上,从工程实现的角度,针对测量仪器识别系统相态问题,研究系统相态自动判别算法,提出了功率谱能量因子和相图图像区域穿越两种相态自动判别方法。在功率谱计算的基础上,以主频谱分量为中心,基于一段频率窗内的谱分量,用功率谱能量因子来定量描述运动系统的能量特征。在相图中设置一个区域,将相图划分为区域外和区域内两个部分,进而判断相轨迹曲线是否穿越到区域内以及穿越过的次数,通过计算穿越次数判别系统的相态。两种方法计算量小,实时性好,可以移植到硬件中实现,模拟仿真表明方法有效。通过对系统相态自动判别算法的研究,为Duffing振子实际应用于弱信号的检测提供了有效的判别手段。
6.基于Duffing振子的随钻方位电磁波电阻率测井信号检测电路设计
研究了随钻方位电磁波电阻率测井弱信号Duffing检测硬件电路。在对基于Duffing振子进行弱信号检测的基础上分析了待测信号与策动力信号之间存在相位差和频率差时对测量结果的影响,通过时间尺度变换方法,将Duffing振子扩展到频率为2MHz的信号检测,在此基础上研究基于Duffing振子测量随钻方位电磁波电阻率仪器响应中幅度衰减比和相位差的基本原理,设计了检测系统的硬件电路整体框图,并用具体的硬件电路实现了Duffing振子模型,通过模拟输入热噪声,电路仿真表明设计的Duffing电路可对频率为2MHz的信号进行检测,电路对参数非常敏感,同时对噪声有一定的免疫力,随着检测临界阈值精度的提高,信噪比降低。通过此内容的研究,利用具体的电路实现Duffing振子模型,为基于Duffing电路的随钻电磁弱信号检测提供了技术支持。
本论文全文共分5章。第一章为绪论,阐述了研究的目的与意义、研究的现状以及研究内容、研究方法和创新点：第二章为电磁场的时域有限差分计算方法,论述了直角坐标系和圆柱坐标系中三维电磁波时域有限差分计算问题,为随钻方位电磁波电阻率测井响应模拟提供支持：第三章为随钻方位电磁波电阻率测井响应数值模拟,论述了其测井的基本原理和正演模拟算法,模拟不同模型的测井响应并开展未钻地层预测研究；第四章为随钻测井弱信号检测方法与设计,论述了基于Duffing振子的测井弱信号检测方法技术和Duffing电路的设计：第五章为总结与建议,对全文进行总结以及提出今后研究的建议。
In the exploration and development of oil and gas resources, the resistivity based on conductive characteristics of the reservoir is the basis of the qualitative evaluation whether the formation is oil-bearing strata, oil or water-bearing layer, and it is also one of the important parameters of the reservoir hydrocarbon saturation. LWD has characteristic of real-time and efficient, it can effectively reduce the impact of the drilling fluid invasion to the formation, and it is significance to accurate evaluation of reservoir oil-bearing. In order to enhance oil recovery and reduce costs, horizontal wells, deviate wells and multilateral wells are used, and the number of these wells is increasing. Comparing with vertical wells, the logging response has changed because the electrical parameters surrounding the borehole are the nonaxisymmetrical distribution, research on electric logging of modeling and inversion numerical simulation based on horizontal wells and deviate wells is hot. Meanwhile, in oil drilling, it is urgent need a LWD system that can carry out real-time geosteering and it is suit to the complex oil&gas layer, predict the undrilled formation to maintain the borehole within the desired geological. In recent years, based on the techniques of traditional resistivity LWD, Schlumberger, Halliburton, Baker Hughes have researched on the azimuth resistivity measurement, the corresponding instrument has been developed and been put into commercial use, but this research is still in infancy in China, it is important to solve the key scientific and technological issues about how to develop the azimuth electromagnetic wave resistivity LWD, therefore, it has great significance for us to research it in raising domestic LWD technical level as well as to break the blockade and monopoly of foreign technology.
In this context, considering on development of instrument for the future, we focuses on the key technologies of azimuth electromagnetic wave resistivity LWD in this dissertation, study on the forward numerical simulation of logging response and weak signal detection with the theoretical basis of electromagnetic theory, electrical logging method and electronic information technology. To the forward simulation problem, based on the principle analysis of calculation method and electromagnetic wave LWD, we employ ADI-FDTD directly with Yee's non-uniform staggered grid in three-dimensional cylindrical coordinates, transfer coordinate system between strata space and instrument space, which the conductivity tensor of the anisotropic and dipping formation can be expressed in coordinates of instrument, use area weighted average to compute the effective conductivity of partially-filled grid cells at interfaces and use UPML absorbing boundary conditions to truncate the computational domain. To the weak signal detection of logging problem, based on the analysis of noise from LWD, we use nonlinear theory and electronic information technology to research weak signal detection method of electromagnetic LWD, make a Duffing model to detect weak signal based on one-dimensional nonlinear oscillator, reveal the mechanism of Duffing oscillator which is used in weak signal detection based on the analysis of the dynamics characteristics, design circuit and use Duffing circuit to measure the amplitude attenuation ratio and phase difference of electromagnetic LWD with method of time-scale transformation. We master the logging response characteristics of the instrument by forward modeling, it is not only provides a theoretical basis for the logging data processing and interpretation but also provides a guidance of design methodology for the development of instrument. By researching of logging weak signal detection, we can down the detected SNR, improve the radial depth of instrument and enhance the predicted distance of the undrilled formation, it provides the technical support of signal acquisition for the development of the instrument.
In this dissertation, those work was researched such as the calculation method of electromagnetic field with FDTD in three-dimensional, numerical simulation algorithm, forward simulation of electromagnetic wave resistivity LWD, dynamic behavior of Duffing oscillator and effect of noise, discriminate algorithm on phase state of system, electromagnetic wave logging weak signal detection and realization based on Duffing oscillator, its main research work and achievements are as follows:
1. FDTD calculation method of electromagnetic field in three-dimensional
Research on FDTD calculation method of electromagnetic field is based on the theory of time-domain Maxwell equations and Yee's grid. From the calculation of differential, iteration of differential equations, numerical stability and numerical dispersion, absorbing boundary conditions, spatial discretization, effective parameters of conformal grid, the excitation of source, and the extraction of time-harmonic field for amplitude and phase is discoursed, respectively. On this basis, for the problem of Courant criterion leads to oversampling in time, the alternating direction implicit (ADI)-FDTD method and UPML boundary conditions of ADI-FDTD are studied, for the problem of staircasing error from rectangular grid and based on the actual shape of borehole, the non-uniform cylindrical Yee grid is studied, for the singular electric field problem of iterative equation in the axial direction, special processing method of the integral form of the Maxwell equations is used near the axial. Based on the research of FDTD calculation method, the time-domain iterative equation is derived in Cartesian and cylindrical coordinate system, combining characteristics of implicit differential, UPML absorbing boundary conditions is extended to the ADI-FDTD method, and the formula of UPML absorbing boundary conditions in3D ADI-FDTD method is derived.
2. Numerical simulation algorithm of azimuth electromagnetic wave resistivity LWD
We use Yee's staggered grid to differential discretize the time domain Maxwell's curl equations of the anisotropic formation in cylindrical coordinates, thus time domain recursive equation of each staggered node is obtained. To the deviate wells, we use rotation matrix to transform stratum space Cartesian coordinate into instrument space Cartesian coordinate, then transform it into cylindrical coordinate system, thus conductivity matrix tensor of anisotropy formation in cylindrical coordinate can be expressed. To the partially filled grid, the eccentered interface indicated between the borehole and the formation is non-conformal to the cylindrical grid, we employ an area-weighted average of quasi-static approximation to compute effective conductivities and approximate them as uniformly filled cells, so as to improve the accuracy of the simulation. To the problem of limited memory of computer, we use UPML absorbing boundary conditions to reduce the reflection of the outer boundary and truncate the computational domain, so as to improve the efficiency of the simulation. In order to validate the proposed algorithm, we compare the proposed algorithm with NMM based on model of simple homogeneous formation, and results show that the algorithm is correct. By studying the numerical simulation algorithm of azimuth electromagnetic wave resistivity LWD, we set up an algorithm to express the conductivity tensor in dipping and anisotropic earth formations with rotation matrix and area-weighted average, this algorithm can be extended to numerical simulation of other electrical LWD.
3. Forward modeling on response characteristics of logging
Based on the research of the calculation methods and numerical simulation algorithms, we study the response characteristics of azimuth electromagnetic resistivity LWD in complicated conditions. By simulating for different model, results are shown as follows.1) In anisotropic formation, the measured apparent resistivity is a comprehensive reflection of the horizontal conductivity and vertical conductivity.2) The apparent thickness is widened with the inclination increases, and the horn effect can be seen in the phase difference response and amplitude ratio response for larger dipping angles, as the dipping angle is increased, the horn effect is more obvious.3) In general, the effect of eccentricity on the tool response is smaller when the conductivity contrast between the mud and the surrounding formation is low. Nevertheless, when the conductivity contrast between the mud and the surrounding formation is high, the effect of eccentricity on the tool response is larger, what's more, with the eccentricity increases, and the amplitude attenuation ratio is also increased.4) At the same dipping angle, with the eccentric distance increases, horns effect of the boundary is more obvious.5) For the electromagnetic LWD tool that surface of coil is perpendicular to the mandrel, when tool penetrating through an the boundary with large dipping angle, in the logging response curve, horns are appeared on both upper and lower boundaries, moreover, the shape of horn is similar and width of horn is narrow, according to the shape of horn, it can indicate the presence of formation boundaries. However, for the titled coil electromagnetic LWD tool, when tool penetrating through the boundary with large dipping angle, horn of logging response curve is asymmetric, what's more, the shape of horn is wide and deep, this horn is not only used to indicate the presence of formation boundaries, but also indicate the resistivity of the undrilled formation is high or low in advance, this allows for a proactive adjustment of the dipping angle and azimuth direction of the drill, hence, geosteering capabilities. By studying characteristics of logging response in forward modeling, we are familiar with the response of azimuth electromagnetic resistivity LWD in complex conditions, it provides a theoretical basis for the inversion calculation, development of instrument independently and interpretation of logging data for the future.
4. Dynamic behavior of Duffing oscillator and impact of noise
In this dissertation, dynamic behavior of Duffing oscillator and impact of noise are researched. We establish a detection model of Duffing oscillator based on one-dimensional nonlinear oscillator model, study the influence of movement state by the cycle perturbation and noise, theoretical analysis and numerical simulation show that:1) With the cycle perturbation increases, the phase trajectory of Duffing oscillator will be followed in accordance with the state of the homoclinic orbit, bifurcation state, chaotic state, the state of large-scale period, and the nonlinear dynamic characteristics is very obvious.2) Duffing oscillator is immune to any distribution of random noise and is sensitive to initial value of signal, the smaller amplitude of the input signal, the more sensitive to the signal for the system, the better anti-noise performance of the system, and the lower SNR.3) The impact of noise to the movement state of Duffing oscillator is relative to the intensity of noise, the presence and strength of noise effect the performance of detection system. By researching the dynamic behavior of Duffing oscillator and impact of noise, providing the support to weak signal detection based on Duffing oscillator, and revealing the weak signal detection system based on Duffing oscillator has the lowest detection threshold.
5. Discriminate algorithm on phase state of system automatically
In this dissertation, discriminate algorithm on phase state of system is researched. Based on the conventional discrimination method, we study the automatic discrimination method from the view of engineering, and present two automatic discrimination methods which are energy factor of the power spectrum and crossing zone of the phase diagram. On the basis of the power spectrum calculation, we use some spectral components within the frequency window to quantitatively describe the energy factor that express the energy characteristics of the motion system, and main spectral components is the center of window. By setting a zone, the phase diagram is divided into two regions, one is inside, the other is outside, and the state of system is determined by the count of crossing. The presented methods have characteristics of low calculation amount, real-time, and it is easy to be ported to hardware, results show the methods are effective. The research provides effective means to discriminate state of system for the Duffing oscillator applied to the detection of weak signals actually.
6. Design of detection circuit for azimuth electromagnetic resistivity LWD based on Duffing oscillator
We design a detection circuit based on Duffing oscillator. On the basis of weak signal detection with Duffing oscillator, we analyses the impact of measurement by phase difference and frequency difference between the signal and cycle perturbation. With the method of time scale transformation, Duffing oscillator is extended to detect the signal which frequency is2MHz. And the measurement principle of amplitude ratio and phase difference based on Duffing oscillator is studied, we design the overall block diagram of detection system, moreover, we use specific hardware circuit to realize the Duffing oscillator model. By inputting the thermal noise and simulating, results show that the designed Duffing circuit can detect signal with frequency of2MHz, circuit is very sensitive to parameters, meanwhile, circuit is very immunity to noise, with the accuracy of the critical threshold improves, the detectable SNR decreases. This research provides technical support to detect electromagnetic weak signal LWD based on Duffing circuit.
This dissertation consists of five chapters, it's organized as follows. In Chapter I, we describe the purpose and significance of research, status of relative technology, as well as research task, research methods and innovation. In Chapter II, we describe the method of FDTD, discuss the problem of calculation in Cartesian and cylindrical coordinates, it is supported to simulate the logging response for azimuth electromagnetic resistivity LWD. In Chapter III, we describe the principles of azimuth electromagnetic resistivity LWD, discuss the algorithms of forward modeling, and simulate the logging response for different model. In Chapter IV, we discuss the method of logging weak signal detection and Duffing circuit design. In Chapter V, we briefly summarize the work of dissertation, and present the proposal for future research.
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