A Theoretical Study On Cement Bond Evaluation Method With Ultrasonic Oblique-Incident Finite Beam

Petroleum and natural gas are extracted through oil and gas well.To make sure the well has enough strength to keep from collapsing and to prevent reservoir fluid channeling,steel casing should be run and cemented in the well.The well after cemented is called “cased borehole”.The cementing conditions of the casing-cement interface and the cement-formation interface influence directly on the following operations downhole and the production life of well.Therefore,it is of great significance to evaluate the cement bond quality.The ultrasonic flexural wave detection is the novel cement bond evaluation technology.It uses an ultrasonic beam to excite flexural waves in the cased borehole.There is still much work to be done to study the propagation mechanism of wave groups in the reflected wave.In this paper,both the planar layered model and cylindrical layered model are used to study the reflection of an ultrasonic beam in a cased borehole.The main contents of this essay are as follows:1.A planar layered model of the reflection of an ultrasonic beam in a cased borehole is built to study the reflected wave in different cement conditions.When the frequency of the ultrasonic beam is high enough,the wavelength of the source will be much less than the borehole radius.The cylindrical layered model of the cased borehole can be approximated to a planar layered model under such condition.In the first part of this essay,the expression of the reflected wave in the planar layered model is derived.After that,the reflected waves for different cased borehole examples are synthesized.There are three wave groups in the reflected wave: the casing wave,the delayed casing wave and the inner-Stoneley wave.When the cementing is good,the amplitudes of the casing wave and the delayed casing wave are at a low-level while the attenuations at a high-level.When the cementing of the first interface(casing-cement interface)is bad,the amplitude of the casing wave increases and its attenuation decreases.When the cementing of the second interface(cement-formation interface)is bad,the amplitude of the delayed casing wave increases and its attenuation decreases.2.An inversion method is proposed to invert the shear velocity of the cement behind the casing by the travel time difference of wave groups in the reflected wave.Firstly,the dispersion curves of mode waves in the planar layered structure are calculated to study the propagation mechanism of wave groups in the reflected wave.The mode waves are also called flexural waves.After the discussion above,an inversion formula is put forward aimed to obtain the unknow propagation velocity in the medium behind the casing.There are five parameters in the inversion formula: the phase velocity of the flexural wave,the group velocity of the flexural wave,the travel-time difference between the casing wave and the delayed casing wave,and the thickness between the casing and the formation.Several cased borehole examples are calculated to testify the validity of this inversion formula.Numerical results show that the S-wave velocity of cement is inverted with an maximum error about 3%.3.A cylindrical layered model of the reflection of an ultrasonic beam in a cased borehole is built to study the reflected wave at different azimuthal angles.The planar layered model has ignored the influence of the circumferential angle.For this reason,the cylindrical layered model is built,and the refleceted waves are synthesized at different azimuthal angles.Numerical results show that the travel times of wave groups in the reflected wave at 0° are the same with those travel times in the planar layered model.The changs of amplitude with the cementing condition in these two models are the same,but the amplitude of the reflected wave in the cylindrical layered model is much less than that in the planar layered model.This work has verified the feasibility of the high-frequency approximation to qualitative research the ultrasonic flexural wave technology.Calculation results also indicate that on the circumference direction,the amplitudes and attenuations of the casing wave and the delayed casing wave are highest at the center of the acoustic beam.They decrease with the increasing of the azimuthal angle.Simulation on the circumferential angle is beyond the capability of the planar model.4.A novel approach is proposed to calculate the reflected wave of an eccentric source in the cased borehole.It decomposes the eccentric source into centric cylinder sources and uses the second kind Hankel function to approximate the reflected wave.This approach is verified by the reciprocal theorem.Calculation results show that the reflected wave received on the borehole axis from an eccentric point source is highly overlapped with the reflected wave received at the eccentric place from a point source located on the borehole axis.The eccentric distance of the point source has an unfavorable effect on the reflected wave calculation.The further the eccentric distance is,the more deviation the reflected wave has.Furthermore,the reflected waves received on the borehole axis from an eccentric beam are synthesize.When the beam scans from 0° to 180°,the amplitude of the reflected wave keeps decreasing until 90°,then increases afterwards.Since the curvature difference between the cylindrical wave and the casing,the amplitude of the reflected wave at 180° is higher than that at 0°.As long as an eccentric source can be expressed by the eccentric cylinder sources,its reflected wave on the borehole axis can be calculated.