Acoustic wave propagation in oil wells: A comparison between semi-analytical and finite element modeling approaches

Acoustic logging is one of the most used techniques for inspecting the integrity of oil wells. Traditional acoustic techniques have some limitations to analyze the condition of the cement layer of wells, such as the need for removing the production tubing, which is costly and time-consuming. This increased the interest in alternative solutions that allow the assessment of cement quality in multi-string wells. Acoustic-guided waves can be employed to inspect the cement condition in a multi-string scenario, which have recently shown to be promising, mainly regarding inspection through the production tubing. This article compares semi-analytical finite elements method and finite element method to model wave propagation in multilayered cylindrical media, mimicking an oil well under the presence of defects, in order to assess the integrity of oil wells either in the multi or single string well scenarios. In addition, a thorough investigation, through the application of the two-dimensional Fourier transform, was carried out to identify which guided wave mode is most affected by the presence and the severity of common downhole defects in the cement casing. Results show that, the semi-analytical finite element method can be used to identify guided wave modes that are more sensitive to defects in the cement layer and those that do not propagate. In general, the comparisons in the frequency domain for single or dual-string cases had good agreement, showing that the most considerable variation of the wavemodes occurs at slownesses below $700\mu s$/m in the frequency range from 5 to 25 kHz. The semi-analytical method had a lower computational cost and faster mode acquisition speed than the finite element method. The semi-analytical method in single-string case was up to approximately 6.5 fold faster than the finite element method and, in the most complex case, it was 1.8 fold faster than the finite element method; whereas the semi-analytical method in dual-string case, the quickest case was approximately 3.5 fold faster than the finite element method and, the most complex case was 1.2 fold faster than the finite element method. Therefore, it was proven that the use of the semi-analytical finite element method is a viable alternative for the analysis of the integrity of oil wells.