【作者】 张烨；

【导师】 汪宏年；

【作者基本信息】 吉林大学 ， 理论物理， 2012， 博士

【摘要】 随着人类对油气资源需要的不断增加以及勘探技术的不断发展，砂-泥岩薄交互储层、页岩气等非常规油气资源的勘探和开发已成为当前非常重要的研究课题。这种非常规储层的典型特点是电参数的各向异性，为了同时测量地层各向异性电导率以便对非常规油气进行有效评价，需要一种新型的多分量感应测井技术。与常规的感应测井不同，多分量感应测井仪器采用三分量正交发射线圈和接收线圈系，同时测量出完整的磁场强度张量，因此，可以提取出地层纵横向电导率、地层倾角和方位角等参数。然而，由于共面线圈系电磁场的非轴对称性以及对井眼泥浆和侵入带电导率、水平界面深度等变化的敏感性，复杂地层条件下多分量感应测井响应的有效数值模拟与软件研制仍然面临诸多挑战。本文针对各向异性储层中多分量感应测井响应数值模拟过程中，三维数值效率低且在大反差电导率地层中难以取得满意数值结果等问题，建立了一套基于电场矢势-标势的3D有限体积算法，从Maxwell方程的矢势-标势分解、有限体积法离散、非对称矩阵的压缩存储、不完全LU分解预处理以及稳定双共轭梯度法(BICGSTAB)快速求解大型复代数方程等方面展开了全面深入研究，并研制开发出相应的计算软件。通过对垂直井模型和倾斜井模型中多分量感应测井响应的大量数值计算，系统考察了井眼泥浆电导率、层厚、各向异性系数、侵入深度、地层倾角、仪器偏心效应、裂缝、源距以及工作频率等变化对多分量感应测井响应的影响，此外，利用交叉分量合成技术深入探讨了快速提取层界面深度、地层倾角以及各向异性系数等处理方法，取得非常有意义的结果，为多分量感应测井仪器参数的优化设计、资料处理等提供理论基础和有效的方法手段。为克服低频发射或高阻地层导致的低感应数问题，有效提高三维电磁数值模拟算法效率与应用范围,首先利用电场标势与矢势将Maxwell方程转化为满足库仑规范条件的耦合势Helmholtz方程,以Yee氏交错网格中不同位置上的节点为中心建立四种控制体积单元,通过对控制体积单元中矢势、标势以及电导率的体积积分平均实现耦合势方程和磁偶极子旋度的离散,得到一个关于各个离散节点上电场标势与矢势的大型稀疏代数方程。此外,针对多分量感应仪器结构以及地层模型特点,规定了非均匀网格的剖分规则以及数值计算区域的范围,给出了离散电磁场和多分量感应测井响应的计算表达式。针对离散化过程得到的大型稀疏矩阵中非零元素的分布特点,利用行格式压缩方法(CSR)对离散方程系数矩阵进行压缩存储,节省计算机的存储空间、减少无用的计算量。为有效降低系数矩阵的条件数提高Krylov子空间法的迭代速度,采用不完全LU分解预处理技术对系数矩阵进行优化,并结合稳定双共轭梯度法(BICGSTAB)有效地提高了大型离散方程的求解效率与精度。并利用数值结果对频率变化对迭代收敛速度的影响进行了考察,结果证明基于电场标势与矢势3D有限体积算法,由于释放了▽×▽算子的零空间,使得在较低频率下仍然能够保持较快的收敛速度和满意的数值结果。为了对基于电场标势与矢势3D有限体积算法以及开放出的相应软件的有效性进行检验,分别用一维、二维垂直井模型中解析方法(ANA)和数值模式匹配方法(NMM)的数值结果与3D有限体积算法的结果进行了充分对比分析。在此基础上,进一步利用3D数值模拟软件系统研究考察了地层厚度、各向异性系数、线圈源距、井眼泥浆电阻率、泥浆侵入半径、以及仪器工作频率等因素对多分量感应测井响应的影响。此外,为有效模拟倾斜井眼中多分量感应的响应,借助于旋转矩阵实现了地层电阻率由地层坐标系向仪器坐标系的变换,系统考察倾斜井眼中多分量测井响应的三个主分量以及两个非零的交叉分量的响应特征,并对仪器偏心效应的成因以及井眼垂直裂缝对测井响应的影响等进行了深入研究。最后,利用数值结果对井眼倾斜多分量感应测井中两个非零的交叉分量的组合(σ(？)-σ(?))和(σ(?)+σ(?))的探测能力进行了检验,结果证明组合曲线(σ(?)-σ(?))能够提高对地层边界探测能力,并且可根据(σ(?)-σ(?))的正负判断层边界两侧电导率的高低,而组合曲线(σ(?)+σ(?))能够提高对各向异性地层的判断能力，且通过数值结果进一步系统考察了仪器倾角、线圈系源距、井眼泥浆电阻率对组合曲线的影响，并试探性的研究了含方位角变化的多分量感应测井响应特征。更多还原

【Abstract】 With the increasing needs of oil and gas resource and the development ofexploration technology, exploration and development of unconventional oil and gasresource such as the laminated sand and shale reservoir, shale gas has become animportant research topic. The typical feature of the unconventional reservior iselectrical anisotropy. In order to simultaneously measure the anisotropicconductivity of the formations for effective evaluation of unconventional oil and gas,we need a new type of multicomponent induction logging (MCIL) technique.Different from the conventional induction logging, MCIL’s tool has a triaxial coilstransmitter and a triaxil coils receivers in order to measure the full tensor ofmagnetic field. Therefore, the parameters of the horizontal and vertical conductivityof formation, dipping angle of formation, azimuth angle of MCIL’s tool could beextracted by means of magnetic field tensor. However, because of the asymmetry ofelectromagnetic fields inducted by coplanar coils and sensitivity of change ofborehole and invasion conductivity horizontal interface depth, many challengessuch as the numerical simulation and software development of MCIL’ response incomplex anisotropic fornation modle should be faced. In the paper, we establish afinite volume method based on coupled vector-scalar potentials in order to solve thelow efficiency problem and difficulty of large conductivity contrast in3D numerical simulation of MCIL’s response. We comprehensively study the contents ofMaxwell’s vector-scalar potentials decomposition, finite volume discrete, compressstorage of ansymetric matrix, ILU(0), BICGSTAB. We also develop thecorresponding software. By a large number computation of MCIL’S response invertical an dipping borehole model, we systematically investigate the effect onMCIL’s response such as mud resistivity, thickness, anisotropy coefficient, invasionradius, borehole dipping angle, eccentricity, vertical fracture and so on. In addition,we apply the composite technique of cross components to study the method toextract the boundary locaton, borehole dipping anlge and anisotropic coefficient andobtain many useful numerical results. These results provide the theoretical basis andeffective methods to optimize MCIL’s tool and data processing.In recent years, the research on induction logging response in anisotropicformations has become more and more active. However，as a result of thecomplexity of electromagnetic responses in anisotropy formation, there is still a lackof fast simulation algorithm so far. And then，we establish a3dimensional finitevolume algorithm (FVM) based on vector and scalar potentials to simulate theresponse of multi-component induction logging(MCIL) tool. And the correspondingcomputation codes are developed on the basis of FVM. Applying these codes, we doa large number of numerical calculations on MCIL’s response in vertical anddipping borehole models. We can obtain many useful numerical results that providethe theoretical basis on MCIL’s data analysis and tool’s improvements.In order to overcome the low induction numbers problems (LINs), extend theapplication range of the3D EM modeling and enhance algorithm efficiency in thelow frequency domain and high resistivity formation, we first reformulateMaxwell’s equation into Helmholtz equations in terms of coupled scalar-vectorpotentials with Coulomb gauge. According to the different location of node in theYee’s non-uniform staggered grids, we set up four kinds of control volume cells.With volume integral averaging of vector potential, scalar potential and conductivitytensor on the control volume, we discrete the Helmholtz equations and the rotationof magnetic dipole sources successfully. The discrete form of the rotations of magnetic dipole sources can be approximately considered as discrete electricaldipole sources. The expression of discrete electromagnetic fields and MCIL’sresponse are also given in this paper. According to characteristic of MCIL’sinstrument structure and formation model, we define the rules of dividingnon-uniform grid and the size of numerical calculation area.The choice of appropriate computation method is the crucial for solvingdiscrete equation efficiently. Through the analysis of distribution of non-zero matrixelements in discrete equation’s coefficient matrix, we can conclude that thecoefficient matrix is a large, sparse and complex matrix. In order to save thecomputer storage space and reduce the useless computation, we apply thecompressed sparse row (CSR) method to save the coefficient matrix of discretesystem. The condition number of coefficient matrix must be reduced in order toaccelerate the iterative convergence speed of Krylov subspace method. And then,the incomplete LU-decomposition preconditioner is applied to optimize thecoefficient matrix, and combine with the Bi-conjugate gradient stabilization(BICGSTAB) method to solve the discrete system efficiently. In the paper, we alsoinvestigate the effect of frequency change on iterative speed; the numerical resultsshow that FVM based on coupled potentials deflate the null space of curl-curloperator so that it can maintain fast iterative speed in low frequency.In the Chapter4, we investigate characteristics of MCIL response in1D and2Dvertical borehole model. FVM is validated by means of Comparing numerical resultwith the analytical method and numerical mode matching method. Wesystematically investigate the effect of the anisotropic coefficient, spacing of coils,borehole mud resistivity, invasion radius, tool’s frequency on MCIL’s response. Inaddition, we also analyze the physical cause of eccentricity and investigate theeffect of the vertical fracture.In the Chapter5, we achieve to transform the conductivity tensor from themedia coordinate system to the instrument coordinate system by means of rotationmatrices. The FVM based on coupled potentials are applied to calculate andinvestigate the response characteristics of MCIL in dipping well model. Numerical results of finite element method software are used to verify the validity of FVM in the complex3D Formation model. Because of the appearance of dipping borehole, there exist two non-zero cross components (σAXZ,σ) in MCIL’s responses. Composite curves (σAXZ-σAZX) of cross component improve the detection capability of boundary in the formation. According the positive and negative of (σAXZ-σAZX), we can determine the difference of conductivity in the both sides of layer boundaries. Composite curves (σAXZ+σAZX)can be used to determine anisotropy in the formation. We also systematically studied the effect of the dipping angle, spacing of coils, borehole mud resistivity, on (σAXZ-σAZX) and (σAXZ-σAZX).In the end, the characteristics of MCIL’s response with azimuth change are tentatively studied.更多还原