Acoustoelastic effects on mode waves in a fluid-filled pressurized borehole in triaxially stressed formations

Based on the nonlinear theory of acoustoelasticity, considering the triaxial terrestrial stress, the fluid static pressure in the borehole and the fluid nonlinear effect jointly, the dispersion curves of the monopole Stoneley wave and dipole flexural wave propagating along the borehole axis in a homogeneous isotropic formation are investigated by using the perturbation method. The relation of the sensitivity coefficient and the velocity-stress coefficient to frequency are also analyzed. The results show that variations of the phase velocity dispersion curve are mainly affected by three sensitivity coefficients related to third-order elastic constant. The borehole stress concentration causes a split of the flexural waves and an intersection of the dispersion curves of the flexural waves polarized in directions parallel and normal to the uniaxial horizontal stress direction. The stress-induced formation anisotropy is only dependent on the horizontal deviatoric terrestrial stress and independent of the horizontal mean terrestrial stress, the superimposed stress and the fluid static pressure. The horizontal terrestrial stress ratio ranging from 0 to 1 reduces the stress-induced formation anisotropy. This makes the intersection of flexural wave dispersion curves not distinguishable. The effect of the fluid nonlinearity on the dispersion curve of the mode wave is small and can be ignored.