Extension of the SAFE-PML method for modal analysis of 3D multiphysics waveguides in infinite porous media

• Extension of SAFE-PML to simulate infinite 3D porous media; • Analysis of wave modes and dispersion in fluid-filled wells within 3D porous solids; • Dispersion and mode behavior studied under different physical conditions and parameters; • Application to sonic logging and multiphysics scenarios; • Symmetry breaking and coupling of propagating modes induced by an eccentric logging tool; Fast and accurate numeric simulation of wave propagation in sonic well logging is of extreme practical interest. We present the extension of the Semi-Analytical Finite Element (SAFE) method combined with Perfectly Matched Layers (PML) to model wave propagation in fluid-filled boreholes surrounded by infinite porous formations. The borehole system is treated as a multilayered and multiphysics 3D waveguide. Biot’s poroelastic theory is incorporated using the ( u s , w ) formulation to accurately capture fluid–porous solid interactions. The SAFE-PML approach enables the simulation of both trapped and leaky modes under open and closed porous boundary conditions. Validation is performed using analytical solutions, demonstrating excellent agreement. A sonic logging tool is also explicitly included in the model, allowing the analysis of its eccentricity on the dispersion characteristics. In particular, we show how the tool eccentricity breaks the radial symmetry of the trapped modes (like the Stoneley), lowering their phase velocity and breaking higher-order modes degeneracy. Our numerical results demonstrate the method’s ability to capture key effects relevant to borehole acoustics, especially those associated with symmetry breaking, which can be challenging to treat analytically. It also demonstrates that the SAFE-PML method can serve as an efficient and accurate modeling framework for realistic borehole acoustic scenarios involving poroelastic formations.