Study On The Response Of Borehole Acoustic Waves In Fractured-Vuggy And Porous Formations

Based on the elastic wave equation and Biot's porous medium theory,the finite difference(FD)numerical simulation is used to study the propagation mechanism of borehole acoustic wave excited by monopole in fractured,cave and porous formations.At the same time,this paper proposes a method to extract the Choi-Williams distribution of P-wave,S-wave and Stoneley wave from the actual acoustic data by using EMD and fractional Fourier Transform.This method can effectively reduce the time-frequency coupling between mode waves to obtain the independent timefrequency characteristics of each component wave.The study of borehole acoustic wave from the perspective of numerical simulation and measured data can provide some new ideas and basis for the logging acoustic wave interpretation of fractured,cave and porous formation.In fractured formation,the new horizontal fracture models are established,which include semi-filled fracture and fracture with variable width.Based on elastic wave equation,the relationship between horizontal fracture and borehole Stoneley wave is explored by discontinuous variable grid finite difference(FD)method.It is found that the fully-filled fracture is equivalent to a very thin lithologic interface,and the reflected wave is related to the wave impedance difference.The influence of filling degree of semi filled fracture on Stoneley wave is much greater than that of filling material.For fracture with varying width,the two models with the width from large to small and from small to large are designed.It is found that when the opening width is greater than the inner diameter,the influence of the inner diameter on the attenuation and reflection of Stoneley wave can not be ignored.This conclusion is contrary to the model that the opening width is less than the inner diameter.In the cave formation,the model of cave near the well is established,and the interaction between the cave and the full wavetrain of acoustic logging excited by highfrequency source is studied.Firstly,the FD equations of axisymmetric elastic wave in cylindrical coordinate system is used to calculate the borehole wave field excited by high-frequency monopole in cave formation.It is found that the radius and distance of the cave near the borehole have a great influence on the wave field of the well.The influence of cave on P-wave is mainly reflected in the time of the first peak and the amplitudes of the first shear wave and Stoneley wave are attenuated.At the same time,scattered waves appear.The cave near the well actually belongs to a highly heterogeneous three-dimensional geological structure.The axisymmetric model is used as an approximate simulation of the three-dimensional model to obtain qualitative results.Therefore,in this paper,the elastic wave equation in the 3D rectangular coordinate system is used to calculate the full wavetrain of acoustic logging in the cave model near the well.It is found that the law of caves on each component of acoustic waves under the three-dimensional model is completely consistent with the axisymmetric model except that the response is weakened.The results of numerical simulation are used to explain the measured acoustic data,and it is found that they are in good agreement.In porous formation,new mud invasion models,mud cake model and inclined porous formation model are established to study the relationship between them and Stoneley wave attenuation coefficient and reflection coefficient.When the elastic formation and porous formation are layered,the reflected Stoneley wave is formed and accompanied by energy attenuation after encountering the dense-pore interface in the propagation of Stoneley wave.Sometimes mud invasion occurs in porous formation.Especially when there is no mud cake,a great difference in the reflection coefficient of Stoneley wave appears between mud invading gas and water layers.When there is mud cake,the amplitude of Stoneley wave in the borehole will increase,and the reflected Stoneley wave can only reflect the properties of mud cake.The attenuation of Stoneley wave in tilted porous formation is stronger than that in horizontal porous formation but the reflection coefficient.In inclined porous formation,The Stoneley wave attenuation coefficient has a good linear relationship with the source distance.For the processing of measured data,in this paper,the time-frequency extraction method combining EMD and fractional Fourier transform is adopted to extract the separate Choi-Williams distribution of P-wave,S-wave and Stoneley wave from complex acoustic signals,which has the advantages of simple principle and intuitive output.Taking the time-frequency characteristics of array acoustic curves of fractured formations with different angles as an example,the reasons for the changes of P-wave,S-wave and Stoneley wave in frequency,first arrival and energy are analyzed theoretically.This method can separately compare the differences of P-wave,S-wave and Stoneley wave in different formations,which suitable for application in fracture,lithology and fluid identification.