基于hp-FEM的随钻电磁波测井仪器响应正演分析

为研究复杂井周条件下随钻电磁波测井的响应规律,优化仪器参数,开展了基于hp-FEM算法的随钻电磁波测井仪器响应正演研究.根据时谐电磁场理论建立数学模型,考虑边界条件建立了变分方程,采用hp-FEM算法对仪器在二维旋转对称性地层模型中的响应进行模拟.数值模拟结果表明,均匀地层hp-FEM数值解与解析解相对误差仅0.046 3%,验证了正演程序的精确性.在其他参数不变的条件下,发射线圈频率越大,相位差曲线变化幅度越大,且极化角所处位置越靠近真实模型的分界面;仪器的源距越小,极化角越明显,纵向分辨能力越强.相对于低阻层,仪器进入高阻层时,相位差曲线上出现的极化角较大.研究结果表明,提高频率和缩短源距可以更加精确地反映地层界面位置,为地质导向决策提供测井资料支持. 

Forward Modeling of Responses of an ELWD Tool Based on hp-FEM

In order to identify the responses of the electromagnetic logging while drilling (ELWD) tool under complex near-wellbore conditions and to optimize the tool parameters, the forward modeling of such responses was carried out based on hp-FEM. A mathematical model was established based on the theory of time harmonic electromagnetic field, and a variation equation built considering boundary conditions, the response of the instrument in a two-dimensional rotational symmetric formation model was simulated by using the hp-FEM algorithm. The result of the numerical simulation shows that the relative error between numerical solutions and analytic solutions is only 0.046 3% in the homogeneous formation model, and the accuracy of the forward modeling program can be verified. When other parameters are kept constant, the higher the emission frequency of coil, the larger the change of the phase difference curve, and the closer the location of polarization angle to the interface of true model;when the source spacing of the instrument is smaller, the polarization angle is more evident, and the vertical resolution is higher. As the tool goes into a high-resistivity zone, the polarization angle in the phase difference curve is larger than that in the low-resistivity zone. The research results show that the tool parameters can be optimized by increasing the frequency and shortening the source spacing, so as to reflect the formation interface accurately, and to provide the support for geosteering decisions with logging data.