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.