SH Wave In Cylindrical Multilayered Biot Porous Media

Shear Horizontal Wave(SH wave)is a kind of shear wave polarization,it is often found in shear wave and multi-wave seismic survey.Compared with P wave and SV wave,SH wave is reflected on the surface parallel to the polarization direction,it will not be converted into other types of waves,and there will be few clutter echoes,so SH wave can carry easily identified formation information,the advantages of SH wave is not found in other types of waves,so the people have paying more attention on the theories and methods of SH wave in geophysical exploration and ultrasonic non-destructive testing.Since the inner media of well is a fluid medium,it is difficult to excite the SH wave in the wellbore.Therefore,there are few reports on the use of SH waves to achieve direct shear wave logging.However,with the continuous improvement and development of technology,the excitation and reception of SH waves in the well become possible.Therefore,it is practical significance to study the characteristics of SH wave field under the cylindrical structure of wellbore.Since the actual formation is usually a porous formation,in this thesis,the Biot theoretical model is used to simulate the porous formation outside the well.A theoretical model is established and analyzed for the propagation of SH waves in the multi-cylindrical Biot two-phase porous media.The research results will provide a theoretical basis for the detection of cylindrical porous media using SH wave.Firstly,this paper establishes three-layer and two-layer cylindrical Biot two-phase porous media models,and derives the Love wave field in the wave field theoretically.The SH wave potential function is introduced and the boundary conditions of the SH wave propagation under this model are used,the dispersion equation is obtained,and the dispersion and excitation intensity of the Love wave under this model are calculated,and the full waveforms of the acoustic field are simulated.The influences of the main acoustic parameters of the pore formation,such as porosity and permeability,on the full-wave waveform in the time domain and the Love wave attenuation are analyzed.The results show that,compared with two-layer cylindrical Biot two-phase porous media model,the dispersion curve after the first and second orders are weaker under the three-layer cylindrical Biot two-phase porous medium model.The excitation intensity decreases first and then increases rapidly and then decreases.With the increase of porosity,the amplitude of the time-domain full wave is significantly reduced.With different permeability,the attenuation of the first-order Love wave varies greatly with frequency.The model of that the porous medium outside the well is infinite also simulated,the result shows it is different with that of the three-layer cylindrical Biot two-phase porous media model.There is not Love wave in the acoustic field,and only a SH wave propagating along the axial direction at the velocity of the formation shear wave can be recorded by the receivers on the well wall.Secondly,the propagation characteristics of SH wave in the single-layer fluid-saturated porous cylindrical shell model and the double-layer fluid-saturated porous cylindrical shell model are studied respectively.Solving the dispersion equation of the single-layer fluid-saturated cylindrical shell model,the guided SH wave of the acoustic field under this model includes both antisymmetric mode and symmetric mode,i.e.,the base order is an almost non-dispersive mode and other orders are the dispersive modes.The base order has no cut-off frequency and propagates at the shear wave velocity of the porous cylindrical shell.The excitation intensity of the SH guided wave is calculated and the results show that each order SH guided wave has a peak of excitation intensity,and the excitation intensity of the base order SH guided wave is relatively small,which also indicates that in the application we need to select suitable excitation frequency according to the dispersion characteristics and excitation intensity frequency response characteristics of each order.The approximate formula for the phase velocity and cut-off frequency of the SH guided wave is obtained,and the value given by the approximation formula is compared with the calculated value,the results show that at high frequencies it can give a good approximation.The effects of porosity on SH guided wave attenuation and time domain full wave are investigated,the results show that,with the increase of porosity,the attenuation of SH guided wave increases and the amplitude of full wave in time domain decreases.The SH guided wave dispersion curve and excitation intensity are calculated under the two-layer fluid-saturated porous cylindrical shell model.The dispersion and excitation intensity characteristics of the SH guided wave are obtained,the difference with the single-layer fluid-saturated porous cylindrical shell model is that,there is no base order of symmetric propagation mode without cut-off frequency.With the addition,the time-domain full waveform under this model is simulated and the results show that the acoustic field time-domain waveform is more complicated than the acoustic field time-domain waveform in the cylindrical three-layer Biot two-phase porous media model.From the model structure we can recognize the single-layer porous cylindrical shell corresponds to the cylindrical three-layer Biot two-phase porous media model when the interface between the first layer and the second layer of the porous media layer is non-bonded.The double-layer porous cylindrical shell corresponds to the cylindrical three-layer Biot two-phase porous media model when the interface between the second layer and the outermost layer of the porous media layer is non-bonded.When the cylindrical three-layer Biot two-phase porous medium model is adopted,the differences of wave field characteristics can be used to judge the condition of interface bonding or non-bonding.In this paper,the study of the SH wave field in the cylindrical porous media outside the well not only enriches the theoretical study of SH wave,but also provides a theoretical foundation for the acoustic wave detection of SH wave applied to cylindrical porous media.