A fast integral equation solver for 3D induction well logging in formations with large conductivity contrasts

Simulation of induction logging responses in formations with large conductivity contrasts is an important but challenging problem due to the singularity of a linear system caused by large contrasts. Also, three‐dimensional (3D) analysis of complex geophysical structures usually encounters high computational demands. In this paper, a pre‐corrected fast Fourier transform (pFFT)‐accelerated integral equation method is applied to overcome these difficulties. In the approach, the entire formation is included in the solution domain. The volume integral equation is set up in the region based on the fact that the total field is the summation of the excitation field and the secondary field. The emitted field by the transmitter coil (treated as a magnetic dipole) is regarded as the excitation of the system. Then the method of moments (MoM) is used to solve the integral equation. To reduce the high computational requirements of the MoM, the pFFT method is used to speed up the solution of the matrix equation and reduce the memory requirement as well. The resultant method is capable of computing induction logging problems involving large and complex formations. For problems with high conductivity contrasts, the solution of the matrix equation usually converges very slow or even fails to converge due to the large condition number of the coefficient matrix. To overcome this difficulty, an incomplete LU pre‐conditioner is used to significantly speed up the convergence of the matrix equation, thus further reducing the computation time. Numerical results show that the present method is efficient and flexible for 3D simulation of induction logging and is specifically superior for problems with high conductivity contrasts.     

张量感应测井视值解释方法的改进

三轴张量感应测井可探测地层电导率各向异性,Zhdanov et al.利用在横向各向同性均匀介质中测井响应的低频渐近式给出了由张量感应测井响应提取地层各向异性电导率和井孔倾角与方位角信息的解析公式,为张量感应测井资料解释奠定了基础.但是,他们给出的井孔倾角公式存在双值解的不确定性,其各向异性电导率解也不是最佳近似解.本文以更为简洁的推导和分析方法,给出了单值的井孔倾角解以及近似程度更好的各向异性电导率解,并通过数值模拟实例加以说明.本文的结果可为张量感应测井资料的视值解释提供更好的选择.     

Miniaturization of the flowing fluid electric conductivity logging technique

An understanding of the hydraulic properties of the aquifer and the depth distribution of salts is critical for evaluating the potential of ground water for conjunctive water use and for maintaining suitable ground water quality in agricultural regions where ground water is used extensively for irrigation and drinking water. The electrical conductivity profiles recorded in a well using the flowing fluid electric conductivity (FEC) logging method can be analyzed to estimate interval-specific hydraulic conductivity and estimates of the salinity concentration with depth. However, operating irrigation wells commonly allow limited access, and the traditional equipment used for FEC logging cannot fit through the small access pipe intersecting the well. A modified, miniaturized FEC logging technique was developed for use in wells with limited access. In addition, a new method for injecting water over the entire screened interval of the well reduces the time required to perform FEC logging.     

高频感应测井磁偶极子校正研究

高频感应测井是一种阵列型感应测井仪,采用单发双收线圈结构,测量感应电动势的相位差,仪器线圈是具有一定大小的螺线管.在传统资料处理中,一般将螺线管简化为成磁偶极子模型,但两者产生的电磁场空间分布是否存在差异需要进一步研究.本文首先利积分公式法(IFM)计算了螺线管高频感应电磁场分布,利用数值模式匹配法(NMM)计算了磁偶...     

用于固体矿床多分量感应测井响应模拟的矢量有限元法

本文开发了基于非结构化四面体网格的三维矢量有限元法,实现了固体矿床井眼中多分量感应测井响应的数值模拟,并分析了多分量感应测井仪器在复杂矿床模型中的响应特征.本文通过采用几何因子背景场,有效地避免了源的奇异性问题;同时,在井眼边界采用非均质网格并用Gauss-Legendre积分计算四面体单元的等效电导率.利用LU分解求解线性方程组,实现了一次网格划分多点的数值计算,提高了计算效率,从而实现快速连续的多分量感应测井模拟.非结构化的四面体网格确保了该方法可以模拟实际问题中所能遇到的复杂的矿体模型.基于水平三层分层和径向分层模型,验证了算法在各向同性和各向异性介质中的可靠性.我们还以三个不同的矿床模型为例,研究了多分量感应测井仪的不同分量的探测特性,结果表明,结合九个分量的信息,可以探测矿体的深度,也可以识别矿体的方位和走向,为精确地描述矿体的三维分布特征打下了基础.     

Solar-wind induction and lunar conductivity

A summary review of electromagnetic induction driven in the Moon by the interplanetary magnetic field is given. The point of view developed centers on inversion of Fourier transforms of the magnetic field in the free-stream solar wind (forcing function) and the response on the lunar surface measured by Lunar Surface Magnetometers. Conductivity profiles are shown to depend upon the central angle between the magnetometer given by local time and the incident wave-normal direction. The induction excites at least magnetic dipole and quadrupole “radiation”, but any scattered field is confined to the Moon's interior, save for propagation down the cavity where a TE-mode surface wave is generated. Confinement of the induced field on the sunward hemisphere and near the subsolar point is nearly complete, decreasing to the limbs, while in the diamagnetic cavity downstream of the Moon, partial confinement takes place. Both time and spatial multipoles of the induced field are present in the lunar interior complicating inversion into conductivity profiles. Profiles are reviewed and resolution limits are given and compared to those obtained from transient analysis. Finally a qualitative comparison to conductivity in the Earth is given.     

三分量感应测井仪及其对各向异性地层的识别

已发现的油藏中,各向异性油藏占总油藏的20%～30%,但常规电磁测井仪只能测量水平方向的电阻率,很容易低估和漏测产层.三分量感应测井仪通过布置三组相互正交的发射-接收线圈对可直接测量地层的水平电阻率和垂直电阻率,通过测量两个交叉分量还可得出地层的倾角和方位.避免了对产层的低估和漏测.本文介绍了各向异性地层的主要类型, 各向异性电阻率的计算公式,三分量感应测井仪的线圈系结构,多频聚焦方法以及包含围岩校正的反演方案.     

Establishment and application of logging saturation interpretation equation in vuggy reservoirs

Vuggy reservoirs are the most common, albeit important heterogeneous carbonate reservoirs in China. However, saturation calculations using logging data are not well developed, whereas Archie method is more common. In this study, electrical conduction in a vuggy reservoir is theoretically analyzed to establish a new saturation equation for vuggy reservoirs. We found that vugs have a greater effect on saturation than resistivity, which causes inflection in the rock-electricity curve. Using single-variable experiments, we evaluated the effects of vug size, vug number, and vug distribution on the rock-electricity relation. Based on the general saturation model, a saturation equation for vuggy reservoirs is derived, and the physical significance of the equation parameters is discussed based on the seepage-electricity similarity. The equation parameters depend on the pore structure, and vugs and matrix pore size distribution. Furthermore, a method for calculating the equation parameters is proposed, which uses nuclear magnetic resonance (NMR) data to calculate the capillary pressure curve. Field application of the proposed equation and parameter derivation method shows good match between calculated and experimental results, with an average absolute error of 5.8%.     

金属套管对多分量电磁感应测井信号的影响

研究金属套管对低频电磁场各分量透射信号和反射信号的影响规律对采用过套管电磁感应测井技术监测生产过程中的流体移动具有重要价值.采用柱状成层各向异性介质中的并矢Green函数模拟当发射源在套管内、接收器分别在套管内和套管外时多分量电磁感应的响应,并系统分析了金属套管对透射磁场和反射磁场各主分量的影响规律.计算结果表明,无论是透射场还是反射场,由于所采用的频率较低,金属套管对每个分量信号的影响可以与地层对该分量信号的影响分开.在低频段,磁性金属套管对磁场各分量仍存在稳定的反射,但不同分量被反射的程度不同,受套管磁屏蔽作用大的分量（如ρρ分量）被反射的程度高于受套管磁屏蔽作用小的分量（如zz分量）.随着频率的升高,反射磁场的强度逐渐增大并最终达到饱和,信号被全反射.磁性金属套管的存在导致透射磁场各分量出现不同程度的幅度衰减和相位延迟,受套管磁屏蔽作用大的分量的幅度衰减程度大.在固定套管参数和频率的情况下,磁性套管对透射磁场不同分量的影响程度虽然不同但是恒定,其所导致的各分量的幅度衰减和相位延迟与线圈系位置和地层电参数无关.在低频段,套管外透射场的各分量处于准静态,其幅度和相位均不随频率而改变,受套管磁屏蔽作用大的分量的幅度随套管磁导率和厚度的不同而存在明显变化.当频率超过某一临界值后,套管的影响逐渐从以静态屏蔽为主转到以趋肤效应为主,导致透射场幅度的衰减和相位的延迟,套管的厚度越大、套管的电导率和相对磁导率值越大,所对应的频率临界值越小.

     

Comparison between moving and stationary transmitter systems in induction logging

In a general treatment of the theory of induction logging, an exact integral representation has been obtained for the mutual impedance between a vertical dipole transmitter and a coaxial dipole receiver in a three layered earth. Based on this representation, a computer model has been devised using the traditional Slingram system of induction logging and the comparatively new Turam system, ignoring borehole effects. The model results indicate that due to its much larger response, the Turam system is in general preferable to the Slingram in mineral and groundwater investigations where formation conductivity much less than 1 S/m is generally encountered. However, if the surrounding media are conductive (more than 0.1 S/m), the Turam system suffers from large amplitude attenuation and phase rotation of the primary field caused by the conductive surrounding, and is less useful than the Slingram system which does not so suffer, unless the target bed is shallow. Because it is a more complex function of system parameters than the corresponding Slingram log, a Turam log can be conveniently interpreted only by the modern inverse method using a fast algorithm for the forward solution and a high speed digital computer.     

利用阵列感应测井进行储层渗透率评价

钻井过程中储层受到泥浆侵入影响的程度与储层岩性有着密切关系,其中储层渗透率对侵入深度有着较大影响,因此若可以获知泥浆侵入深度,则有望对储层渗透率进行评估.本文首先建立含泥饼增长的泥浆侵入数值模型,然后建立阵列感应测井数值模型,两者的联合正演模拟显示泥浆侵入对地层的影响可以反映在阵列感应测井响应上,利用阻尼最小二乘法对阵列感应测井响应进行反演可以得到侵入深度.对侵入深度和储层渗透率的关系进行分析发现：在渗透率为1~100 mD（1 mD=0.987×10-3μm2）数量级的储层中,渗透率的变化可以在侵入深度上得到反映.以储层和井数据进行二维数值模拟发现：利用阵列感应测井响应反演出来的侵入深度曲线反映了渗透率在地层上的变化趋势,采用解释图版的方法可以对储层各层段的渗透率进行粗略估算.     

高频感应测井仪器的响应特性及其应用研究

本文从高频感应测井仪器(VIKIZ)的线圈系结构及其工作原理出发,研究了仪器响应中井眼和偶极子模型的影响,获得了井眼校正方法和偶极子校正方法.同时提出了从高频测量信号中提取介电常数方法.研究表明,在盐水泥浆情况下,井眼因素对测井响应的影响不能忽略,要进行井眼校正.研究成果针对理想地层模型进行了验证,所开发处理软件已经成功用于处理实际测井资料中.     

用相位感应测井数据反演地层电阻率和介电常数

基于相位感应测井的两个接收线圈获取的总场相位差和幅度比曲线,在二维轴对称非均匀介质中同时反演地层电阻率和介电常数. 通过相位差和幅度比测井曲线提取地层纵向边界位置的初始值,利用测井响应方程和变分原理建立反演方程,然后采用共轭梯度(CG)法进行求解. 对多层地层的电阻率、介电常数和纵向边界位置进行整体反演,模拟计算结果表明了方法的可行性.     

井环境对阵列感应测井响应的影响分析

阵列感应测井资料经常出现与井眼环境有关的质量问题.采用三维矢量有限元法分别在椭圆形井眼、仪器偏心及斜井条件下的阵列感应测井原始响应进行了模拟,并对环境校正和合成聚焦后的数据进行了分析.结果表明,线圈距较短的原始测量信号更易受井眼椭圆度、仪器偏心、泥浆电阻率及与地层电阻率反差的影响;而合成聚焦后的浅探测曲线虽然经过了环境校正和合成聚焦等数据处理,但仍然受这些因素的影响,这反映出阵列感应测井的数据处理是不完善的或采用的校正模型是理想化的;在井斜影响方面,浅探测曲线受井斜角大小影响相对较小,深探测曲线在井斜角为60°以上时受其影响较大而必须进行进一步处理.     

振幅保真的单程波方程偏移理论

本报告综述了近年来发展起来的真振幅单程波方程偏移理论,对各种基于单程波方程的偏移振幅作出了系统的分析介绍.为了得到正确的偏移振幅,叠后偏移之前必须进行球面扩散校正.但是,作为叠后相位移偏移算法的推广,Dubrulle氏的共炮检距偏移除了零炮检距和平层两种特例外,它不能给出正确的偏移振幅.通过分析,我们发现传统的单程波单炮偏移不是保振幅算法.利用真振幅单程波方程分解和校正地表的初值条件,我们可以将常规偏移方法改造为真振幅算法并且证明在高频渐近的意义下,新方法的偏移振幅等价于Kirchhoff反演的结果.进一步研究发现可以利用单平方根算子和双平方根算子输出真振幅共反射角剖面.我们的分析指出,这时正确的成像条件为乘积pUp*D.与真振幅共炮偏移所需的商型成像条件pU/pD相比,共反射角偏移的计算稳定性大为改善并且在实际地震资料处理中有重要的应用.     

基于保真振幅单程波方程的叠前AVP成像方法

基于共聚焦点技术的叠前AVP（振幅随射线参数变化）分析与常规叠后反演方法相比优势明显,但传统通过褶积和互相关运算来实现的方法依赖于聚焦算子,而在复杂构造区走时计算困难且子波难以精确提取,从而导致了聚焦算子不准确,而且褶积和互相关运算会影响信噪比和分辨率,基于此,本文提出了基于保真振幅单程波延拓算法的叠前AVP成像方法.该方法利用保真振幅傅里叶有限差分延拓算法实现两步聚焦,分别生成共聚焦点道集和网格点道集,既充分利用了保真振幅延拓算法在振幅保持方面的优势,也可以发挥傅里叶有限差分方法对复杂构造区横向变速适应性强的优势,而且两步聚焦过程都不需要聚焦算子,从而解决了传统方法中走时计算和子波提取的问题.模型试算结果表明了方法的正确性和可行性,而针对实际地震资料的试处理结果与传统方法相比具有更高的信噪比和分辨率,表明了方法的有效性.该方法为复杂构造区油气检测提供了一种新的地球物理依据.     

Real time 2D inversion of induction logging data

Real time 2D inversion for an induction logging instrument may be achieved using a fast forward modeling and special inversion strategy. The fast forward modeling employs a low-frequency approximation of an induction response known as Doll's geometric factor. Modeling geometric factors is much faster than modeling the electromagnetic field in the frequency domain. To transform real data into the Doll's limit, multi-frequency skin-effect correction is applied. The correction technique involves an asymptotic theory of the integral equation for a 2D boundary value problem. The inversion is based on separating the parameter space into subspaces of lower dimension. Initially, adaptive overlapping windows split logging data into manageable portions. Each window consists of three subwindows: the predictor, corrector and upgrader. Further separation of parameters is introduced by Doll's approximation: the low-frequency response is linear with respect to formation conductivity. This allows us to split inversion for conductivity and geometric parameters. The next level of splitting inversion is achieved by independently determining parameters of the near borehole zone and remote formation areas. This is done by utilizing different subsets of sensors. The inversion does not require initial guess: layers are introduced dynamically, if necessary. The resolution is improved in sequential iterations by adding finer details to the previously obtained models. The final selection of parameters satisfies a variety of a priori constraints formulated as target resistivity distributions. The technique for imposing constraints is based on the analysis of data mapping into the model space. Interpretation of synthetic and real data confirms the viability of the method.     

张量感应测井资料处理中若干问题的研究

在横向各向同性（TI）介质中,张量感应测井响应与地层的水平和垂直电导率σh和σv、井眼斜角α、仪器方位角φ同时有关,其资料处理和解释相当复杂,一般采用先定出φ,然后在井眼坐标系中同时反演σh、σv和α的资料处理方式.我们发现将测井响应变换到井眼坐标系时实际上无法确定其交叉分量的符号而只能确定其绝对值,这个问题尚未引起重视.本文给出了无需确定φ就可由测井响应直接计算井眼坐标系磁感应张量的公式,此方法简单,所得结果不受φ提取精度的影响.在此基础上本文给出了利用井眼坐标系的磁感应张量的交叉分量曲线提取地层纵向边界和判别相邻地层电导率高低的一种特征识别方法.本文还给出了大斜度井中TI介质的电导率视值的一种简化近似公式.     

双轴各向异性介质多分量感应测井响应快速计算

为研究双轴各向异性介质多分量感应测井响应特征,本文基于三重傅里叶变换,推导任意方向偶极子源的谱域电磁场解析式;采用围线积分方法,自适应截断积分区间,结合谱域电磁场周期特性,实现三重傅里叶变换的精确快速积分;进而,针对双轴各向异性倾斜地层,模拟研究不同纵横向各向异性条件多分量感应测井响应特征.结果表明：利用谱域内电磁场在周向的周期特性简化解析式,可将计算速度提高4倍;自适应截断积分区间方法保证了计算精度,并极大地减少了积分节点数.对于倾斜双轴各向异性介质,倾角较大时,共面分量可反映地层横向各向异性,同轴分量可反映地层纵向各向异性;倾角较小时,同轴分量可反映地层横向各向异性,共面分量可反映地层纵向各向异性.

     

Electromagnetic induction of a three-dimensional conductivity inhomogeneity in the two-layered earth

Summary The calculation of the elements of Green's tensor function is presented for solving the problem of the electromagnetic induction by means of a vector integral equation. A two-layered Earth is considered as the medium, the surface layer including a three-dimensional conductivity inhomogeneity. Use is made of the boundary condition requiring the vertical component of the electric current to be zero at the Earth's surface which partly simplifies the theoretical computation. Long-period asymptotics of the individual complicated functions, occurring in Green's tensor function as well as in the tensor function required to calculate the components of the anomalous magnetic field at the surface of the halfspace, were effected. With the aid of these asymptotics one can obtain estimates of the functions occurring in the theoretical analysis of the problem.