Evaluation of SAFE-SEM Approach for Modeling Sonic Logging

The aim of this work is to analyze the performance of the semi-analytical finite element – spectral element method (SAFE-SEM) for computing dispersion curves of borehole modes for various formations. The modes of interest for sonic logging – Stoneley, flexural and quadrupole – are analyzed. The range of formations covers a range of slowness values and anisotropy (i.e., VTI, HTI, TTI). The dispersion curves are computed on meshes of different sizes and number of elements, and the calculations are carried out by both SAFE-SEM and traditional approaches. The results are compared to evaluate SAFE-SEM's performance. SAFE-SEM is capable of using curvilinear elements. As a result, the domain can be approximated with a smaller number of elements. The possibility to use tool model in the form of the fluid column (wireline tools) or the pipe (LWD tools) has been confirmed as well. The method can handle both fast and slow formations. The performance is good and does not depend on the formation type – isotropic, VTI, HTI, or TTI. The results are of similar quality to those of the traditional SAFE approach, which makes it possible to recommend SAFE-SEM for use in sonic logging data interpretation algorithms.