Wave Propagation In A Fluid-filled Borehole Surrounded By An Anisotropic Elastic Solid

Sonic logging is an important method of exploration of oil and gas resources.With the continuous innovation of acoustic logging technology,it also promotes the theoretical research on wellbore acoustics.Due to the anisotropic characteristics of the strata,the sound field in the anisotropic formation is getting more and more attention.In this paper,the expression of the displacement potential function of the multipole source field in the isotropic formation is deduced from the basic equation of elastic dynamics,and the definition of SH wave and SV wave in cylindrical coordinate system is explained.The mathematical model of the multipole source and the generalized sound pressure receiver on the well axis is established.The monopole source,the dipole source and the quadrupole source excitation of the two typical strata(hard and soft strata)are programmed.The information of each wave group in the multipole source field is extracted by STC method.It is found that the velocity of the flexural wave excited by the dipole source and the screw wave excited by the quadrupole source is close to the shear wave velocity of the formation at 4 kHz.And then the wave propagation in a full-filled borehole surrounded by transverse isotropy formation is studied.Firstly,the physical meaning of each elastic coefficient in the constitutive equation of TI medium is studied.Then,the multipole source field in the wellbore of TI formation is deduced.Finally,the full wave signal of the multi-pole source field received in the well axis of the TI dielectric layer is calculated by programming.Based on the analytical results,the inversion of the shear anisotropy is inverted.In the fast formation,the shear modulus 66 c is retrieved by the Stoneley wave,and shear modulus 44 c is retrieved by the transverse wave.In the slow formation,the shear modulus 66 c is retrieved by the Stoneley wave,and shear modulus 44 c is retrieved by the flexual wave.In the process of inverting the shear modulus 66 c of TI media,the approximate relationship between the velocity of the Stoneley wave and the horizontal shear modulus of the TI formation is given when the center frequency of the source is 6 kHz.Finally,the finite element software COMSOL Multiphysics is used to simulate the monopole source field in the isotropic formayion and TI dielectric formation.The simulation results of the finite element are compared with those calculated from the analysis of the borehole acoustic field analysis.