横向同性地层中井间电磁响应的三维频域耦合势正演模拟研究

Study on the 3D frequency domain coupled potential forward modeling of crosswell electromagnetic response in transversely isotropic formation

本文针对电导率横向同性地层中三轴发射-接收线圈系的井间电磁响应,开展三维正演算法及模拟研究.首先将发射线圈简化为三轴正交磁偶极子源.为克服低频电磁产生的数值迭代收敛缓慢问题,利用低感应数预处理方法将频域Maxwell方程组转化为基于矢势与标势的Helmholtz方程.采用非等间距的Yee氏交错网格、电导率的体积加权平均技术以及积分形式的有限差分格式实现对控制方程的离散化.借助于不完全LU分解预处理的稳定双共轭梯度法计算井间电磁响应的数值解,并通过与有限元软件COMSOL的数值结果对比验证本文模型与算法的有效性.数值计算结果表明:在横向同性地层的垂直井模型中,测井响应横向分量xx和yy能反映出地层电导率各向异性信息,但横向探测能力较差.轴向分量zz虽只反映地层水平电阻率信息,但具有较好的横向探测能力,且对地层中异常体非常敏感,而交叉分量xz、zx则具备较强的层边界识别能力.

In this paper,a three-dimensional forward algorithm and simulation for the crosswell electromagnetic responses of the triaxial coils system in the transversely isotropic（TI）formation are presented.The transmit coils are simplified to the triaxial perpendicular magnetic dipole source firstly.To solve the problem of low convergence caused by low electromagnetic frequency,low induction number（LIN）preconditioner is applied to transform Maxwell equations to the Helmholtz equations.Conductivity volume weighted average,non-uniform Yee′s grid and integral finite difference scheme are used to discrete the governing equations.Incomplete LU factorization preconditioning technique and bi-conjugate gradient stabilized method are applied to obtain thenumerical solution of cross-well electromagnetic responses,and the numerical results given by the finite element software Comsol verify the validity of the proposed model and algorithm.The numerical results show that the lateral components xxand yycan reflect the formation anisotropy information in the vertical well model of TI formation,but its lateral detection ability is poor.Although the axial component zzonly reflects the horizontal resistivity information,it has a good ability of lateral detection and is very sensitive to the anomalies in the formation.The cross components xz,zxhave a strong ability to identify the boundary layer.