【摘要】 提出了采用四面体矢量棱边元素方法模拟三维复杂环境中的感应测井响应,解决了节点有限元法中电场切向分量不连续的矛盾.在柱坐标系下进行网格剖分,有效地模拟感应测井装置在水平成层非轴对称介质中的响应.采用稳定双共轭梯度迭代法对离散得到的大型复系数方程组进行求解.将代数多重网格作为预处理算子,改善了迭代的收敛性.用该算法计算和分析感应仪器在斜井以及水平井中的响应特性,综合考虑井斜、井眼以及侵入带等因素的影响.数值结果表明了该算法的有效性.更多还原

【Abstract】 The tetrahedral elements based vector finite element method(VFEM) is used to compute electro-magnetic fields in 3-D inhomogeneous media with arbitrary distribution of conductivity.Because of the cylindrical symmetry of the well logging system,a cylindrical grid is used for the simulation.The iterative stabilized biconjugate-gradient(BICGSTAB) technique combined with a Algebraic Multigrid(AMG).Preconditioning algorithm was used to solve the large scale complex linear system discrete by the finite element method.The algorithm is then applied to simulate the resistivity responses of deviated and horizontal wells in inhomogeneous formation.Both the borehole and the invaded zone are considered in the simulation procedure.Numerical results show the efficiency of the developed method in 3-D induction well logging problems.更多还原