Finite-difference simulation of borehole EM measurements in 3D anisotropic media using coupled scalar-vector potentials
Finite-difference simulation of borehole EM measurements in 3D anisotropic media using coupled scalar-vector potentials
复制标题
DOI：
10.1190/1.2245467
复制
发表时间：
2006-08
期刊：
影响因子：
3.3
通讯作者：
Junsheng Hou;R. Mallan;C. Torres‐Verdín
中科院分区：
文献类型：
--
作者：
Junsheng Hou;R. Mallan;C. Torres‐Verdín
本文描述了一种新的交错网格有限差分算法的实现和成功验证，该算法用于频域电磁钻孔测量的数值模拟。该算法适用于basedonacoupledscalar-vectorpotentialformulationforarbitrary三维非均匀各向异性电介质。我们在Yee交错网格和标准网格上用中心有限差分逼近耦合标量矢量势的二阶偏微分方程组。适当边界条件的Thediscretizationofthepartialdifferentialequationsandthe实施产生了一个复杂的线性方程组，我们使用带预条件的双共轭梯度法迭代求解。Theaccuracyandefficiencyofthealgorithmisassessedwith在均质、一维各向异性、二维各向异性和三维各向异性地层中采集的多分量井眼电磁感应测量实例。模拟实例考虑了有或没有井眼和泥浆侵入区域的直井和斜井。利用1D、2D和3D基准代码获得的标量-矢量耦合potentialformulationfavorablycompareinaccuracywithresults在DC到兆赫的频率范围内获得的模拟结果对于electricalconductivity.Ournumericalexercisesindicatethat的大对比度，耦合的标量-矢量势方程提供了在存在大电导率对比、倾斜势垒、电各向异性介质和几何复杂的电导模型的情况下从DC到兆赫的generalandconsistentalgorithmicformulationtosimulateborehole电磁测量。
This paper describes the implementation and successful validation of a new staggered-grid, finite-difference algorithm for the numerical simulation of frequency-domain electromagnetic borehole measurements. The algorithm is basedonacoupledscalar-vectorpotentialformulationforarbitrary 3D inhomogeneous electrically anisotropic media. We approximate the second-order partial differential equations for the coupled scalar-vector potentials with central finite differences on both Yee’s staggered and standard grids. Thediscretizationofthepartialdifferentialequationsandthe enforcement of the appropriate boundary conditions yields a complex linear system of equations that we solve iteratively using the biconjugate gradient method with preconditioning. Theaccuracyandefficiencyofthealgorithmisassessedwith examples of multicomponent-borehole electromagnetic-induction measurements acquired in homogeneous, 1D anisotropic,2Disotropic,and3Danisotropicrockformations.The simulation examples consider vertical and deviated wells with and without borehole and mud-filtrate invasion regions. Simulation results obtained with the scalar-vector coupled potentialformulationfavorablycompareinaccuracywithresults obtained with 1D, 2D, and 3D benchmarking codes in the dc to megahertz frequency range for large contrasts of electricalconductivity.Ournumericalexercisesindicatethat the coupled scalar-vector potential equations provide a generalandconsistentalgorithmicformulationtosimulateborehole electromagnetic measurements from dc to megahertz in the presence of large conductivity contrasts, dipping wells, electrically anisotropic media, and geometrically complex modelsofelectricalconductivity.