The Study Of Multipole Acoustic Field In The Horizontal Well With Horizontal Stress

The underground stress field is one of the most important problems in exploration of oil and gas reservoirs.Acoustic logging provides a nondestructive technique for detecting formation stress.Generally,horizontal well is applicable to thin oil and gas reservoirs or fractured reservoirs.The horizontal stress often exists in practical underground reservoir.However,there is still a lack of understanding that acoustic field in horizontal well with horizontal stress.In this paper,under these circumstances,the basic characteristics of multipole acoustic field are studied.It is of great significance to quantitatively evaluate the regional stress distribution of oil and gas reservoirs.It is also of practical significance to provide information about the distribution of the stress,where around the well fracturing of tight sandstone reservoir.Based on the acoustoelastic theory,starting from equations of motion describing the intermediate state,approximately equivalent elastic moduli of the stress-induced anisotropic medium are derived.That is approximately equivalent five elastic moduli of transversely isotropic medium.When the horizontal uniaxial stress applied to isotropic formation,it produces stress-induced transverse isotropic medium,the axis of symmetry is parallel to the axis of horizontal well.This situation can be solved analytically.The acoustic field potential function are introduced in the cylindrical coordinate system along the well axis,the theoretical solution of the wave equation satisfying the multipole acoustic field inside and outside the wellbore are solved.The expressions of acoustic field potential function are obtained.It is applied to the borehole boundary conditions for solving the generalized reflection coefficient of well potential function,so as to confirm the expression of acoustic multipole source in borehole.By means of complex analysis,and calculating the sound pressure field poles and residues in borehole,the dispersion and excitation curves of the borehole mode waves are calculated.The typical parameters are investigated and analyzed.Numerical results show that the velocity and arrival time of pseudo-Rayleigh,flexural and screw waves increase and decrease with increasing horizontal uniaxial stress,respectively.However,in some formations,the velocity and arrival time of Stoneley wave at low frequency decrease and increase with increasing horizontal uniaxial stress.The velocity,arrival time and amplitude of wave changes with horizontal uniaxial stress increasing in horizontal well.These phenomenons prove that the characteristics of borehole wave field carry the information of the horizontal stress.The research results in this paper can provide theoretical reference for horizontal well logging interpretation with horizontal stress and using sonic wave to judge horizontal stress.