Cement bond quality evaluation based on acoustic variable density logging

PETROLEUM EXPLORATION AND DEVELOPMENT Volume 43, Issue 3, June 2016 Online English edition of the Chinese language journal Cite this article as: PETROL. EXPLOR. DEVELOP., 2016, 43(3): 514–521.

RESEARCH PAPER

Cement bond quality evaluation based on acoustic variable density logging TANG Jun1, 2, *, ZHANG Chengguang1, 2, ZHANG Bixing3, SHI Fangfang3 1. Key Laboratory of Exploration Technologies for Oil and Gas Resources, Ministry of Education, Yangtze University, Wuhan 430100, China; 2. School of Geophysics and Oil resources, Yangtze University, Wuhan 430100, China; 3. Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China

Abstract: A new method of cement bond quality evaluation was proposed by combining numerical simulation and calibrated cased hole acoustic logging data. The effects of the cement channel angle and the quality of the second bond interface (the interface of cement with formation) on acoustic variable density logging data were analyzed. Based on the analysis result, a new cement bond evaluation standard was presented after revising the traditional CBL/VDL method. The axisymmetric acoustic field was simulated by real axis integral method, while the non-axisymmetric acoustic field was simulated by 2.5-D finite differential method. After comparing with the calibrated cased hole acoustic logging data, the research has the below results: the numerical simulation result matches with the calibrated well logging data very well and the new method is reliable; the amplitude of the first acoustic arrival in the case hole decreases as the angle of cement channel decreases, and the denser the cement is, the faster the amplitude of cased hole acoustic waveform decays; the lower limit of cement channel angle is around 45 degrees which can be detected by acoustic logging; the formation acoustic waveform is not easy to be detected in time domain, however it is easy to be detected in frequency domain, especially in limestone formation, the first arrival only can be detected when the annulus width of the second bond interface is small. According to the research result of the numerical simulation of cased hole acoustic field and acoustic variable density logging data, new evaluation criteria of cement bound quality were presented. Key words: cement bond quality; acoustic variable density logging; acoustic field in cased well; cement channel angel; interface bond index

Introduction To ensure production safety of oil and gas wells and extend service life of casing, the space between the casing and formation is usually filled by cement, to bind the casing and formation closely. As oil and gas wells are generally more than 1 000 m deep, quick and effective evaluation of cement quality in cased wells is particularly important. Acoustic logging is the main method nowadays used in evaluating the cement quality in oil and gas industry. The evaluation includes bond interface I (the bond interface of casing and cement) and bond interface II (the bond interface of cement and formation). Previous researches have already proved that bond interface I can be evaluated from the casing arrival waveform, while bond interface II can be evaluated from the formation arrival waveform[12]. Borehole acoustic field study is the foundation of cement quality evaluation with acoustic logging. A lot of researches and studies on this topic have been conducted at home and abroad[311], most of them were theory research based on wave

equation. But in the real cased wells, the anisotropy of formation and borehole fluid, and the acoustic logging tool itself will definitely affect the borehole acoustic field. Although some researchers have already studied the effect of logging tool, casing type, fracture, formation dip on the cased well acoustic field with numerical simulation[1217], limited by experimental conditions, the physical models in the researches normally were only a few meters long, much shorter than the real cased wells in oilfields. That is to say the previous researches had their limitations. In addition, there are a lot of different kinds of acoustic logging tools in the market, though CBL/VDL is the cheapest and quickest acquisition tool widely used in the oilfield to evaluate the cement quality, there aren't much report about its application in evaluating cement channeling and bond interface cement quality. According to the actual size of oil and gas wells, the non-axisymmetric acoustic field has been numerically simulated with 2.5-D finite differential method and then compared with the casing waveform acquired by acoustic variable den-

Received date: 26 Mar. 2015; Revised date: 25 Feb. 2016. * Corresponding author. E-mail: [email protected] Foundation item: Supported by the National Natural Science Foundation of China (41274141). Copyright © 2016, Research Institute of Petroleum Exploration and Development, PetroChina. Published by Elsevier BV. All rights reserved.

TANG Jun et al. / Petroleum Exploration and Development, 2016, 43(3): 514–521

sity logging tool in the calibration wells to evaluate the reliability of the numerical simulation method and analyze the effect of cement channeling angle on the acoustic variable density logging; and the axisymmetric acoustic field has been calculated with real axis integral method to analyze the effect of the annulus width of bond interface II on the casing arrival waveform and formation arrival waveform; based on the analysis of the effect of cement density and cement channeling angle on the CBL/VDL logging quality, a new improved cement bond quality evaluation method with CBL/VDL data has been advanced in this study.

1. Research methods of acoustic field in cased well Real acoustic logging data and the numerical simulated data in standard calibration wells were used to study acoustic field in cased well. On one hand, the real logging data taken from calibrated wells can validate the reliability and accuracy of the new simulation method, on the other hand, the numerical simulation can compensate the limited number of calibration wells and lower research cost. 1.1.

General introduction of the calibration wells

The calibration wells were constructed by Xin Jiang Logging Service Company to calibrate downhole logging tools. There are eight calibration wells named as Well 1–8. The cement density in these calibration wells is from 1.20 to 2.25 g/cm3 and the formation lithology includes shale, sandstone,

Fig. 1.

limestone and granite. Well 3 and Well 4 were used to model the situation of sector cement channeling. Both of them have a casing diameter of 139.70 mm, casing thickness of 7.72 mm, cement sheath thickness of 38 mm, formation inner diameter of 216 mm and outer diameter of 1216 mm. Five different situations from the well bottom to the top, eccentric casing and different cement channel angles of bond interface I of 22.5°, 45°, 90°, 180° and 360°, (Fig. 1) were simulated. The cement density of Well 3 is 1.89 g/cm3, while Well 4 is 1.20 g/cm3. As Fig. 1 shows, the amplitude of the casing arrival becomes smaller with the decrease of the cement channeling angle. The same variation trend of the cement channeling angle and the amplitude of the casing arrival waveform shows that acoustic logging data can be used to evaluate cement channeling angle. 1.2.

Numerical simulation of acoustic field in cased well

Poor cementation between casing and formation can be separated into two different types, non-cementation of annulus and partial cementation of annulus. Non-cementation means there is no cement between casing and formation. Partial cementation means there is cement in part of the annulus between casing and formation. The former would result in axisymmetric acoustic field, while the latter non-axisymmetric acoustic field. 1.2.1.

Axisymmetric acoustic field

The axisymmetric acoustic field was numerically simulated

The model of No.3 calibration well and waveform from CBL/VDL.

 515 

TANG Jun et al. / Petroleum Exploration and Development, 2016, 43(3): 514–521

Tyy

Vy  V Vy   x   K z  iVz    2  Gyy t y y  x   V Vy  Tzz  x   K z  iVz    t y  x  2 K z  iVz   Gzz

by real axis integral method in this study. Casing, cement and formation are symmetrical along the well axis. This kind of symmetric acoustic field can be treated as multi-layer media cylindrical open acoustic field which has the analytical solution and the borehole acoustic field can be described as below:   p  r , d , t     X   e  it  A1I0  kr r  e  ikd d  dk     

1.2.2.

(1)

 V Vy    x   t x   y

Fig. 2 is the model of non-axisymmetric casing well which can represent the absent of cement between casing and formation at an interval, so coming a sector space between casing and formation, that is the so-called cement channeling. In this study, 2.5-D finite differential method was used to simulate the non-axisymmetric acoustic field to save the computer capacity and improve the computing speed. In the research of borehole acoustic field, borehole and formation parameters only vary in x-y plane and keep constant in z plane representing the borehole axis. This assumption can simplify the 3-D differential equation to 2-D finite differential equation after Fourier Transform in z plane which corresponds to the different z component kz; and then the 3-D result can be obtained after inverse Fourier Transform. For an inhomogeneous isotropic medium in Cartesian coordinate system, the density can be defined as ρ(x,y,z) and Lame Constant can be defined as λ(x,y,z) and μ(x,y,z). This is a second order hyperbolic partial differential equation. The solution can be separated into first order partial differential equation about velocity and stress, then doing Fourier Transform along z axis to the equations, we can get:

 

Vx Txx Txy    K z  iTxz  t x y Vy t



Txy x



Tyy y

 K z  iTyz 

Vz   iTxz    iTyz     K z Tzz t x y

 V Vy  Txx V  x   K z  iVz    2 x  Gxx t y x  x 

  iTxz  t

  iTyz  t

   iVz       K zVx   x  

(9)

  iVz        K zV y   y  

(10)

For the monopole acoustic source, the 2-D borehole acoustic fields come from the 2-D finite differential calculation in x-y plane according to different kz. After inverse Fourier Transform, we can get the 3-D acoustic field in the cased well with designed cement channeling. To guarantee the stability of the calculation, the time step should meet:

1

t 

(12)

2

vmax x  y 2  z 2

To guarantee the convergence of the calculation, the axis step should be constrained as below: max  x, y, z   vmin / 4 f max (13) To guarantee the accuracy of the calculation, the maximum axial wave number should meet:

(2)

k z max 

2π 3πf max  z vf

(14)

(3)

2. The research result of acoustic field in cased well

(4)

2.1. Comparison of numerical simulation method with calibration wells

(5)

Fig. 3 is the velocity spectrum in x-y plane at different cement channeling angles of 0°, 90°, 180° and 360°. It can be seen the figure can reflect the true cement channeling situation. The numerical simulation was based on the real borehole size, cement parameters and formation parameters of the calibration wells. The detailed parameters are listed in Table 1. Fig. 4 is the acoustic full waveform comparison of 2.5-D

Medium

Model of non-axisymmetric casing well.

(8)

Introducing monopole acoustic source into the equations: g jk  F  t    r   jk (11)

Table 1.

Fig. 2.

(7)

Txy

Non-axisymmetric acoustic field



(6)

Parameters of the numerical simulation. P-wave velocity/(m·s1)

Shear wave Density/ Outer divelocity/(m·s1) (kg·m3) ameter/mm

Liquid in borehole Casing

1 500

0

1 000

124.26

5 400

3 300

7 800

139.70

Cement

3 406

2 018

2 095

216.0

Formation

6 733

3 892

2 781

∞

 516 

TANG Jun et al. / Petroleum Exploration and Development, 2016, 43(3): 514–521

Fig. 3.

Velocity spectrum in x-y plane at different cement channeling angles.

2.2. Impact of sector cement channeling on acoustic field

Fig. 4. Comparison of simulated full waveform with full waveform from CBL/VDL logging data.

finite differential simulation result with the real CBL/VDL logging data when the borehole is fully cemented in limestone formation. It can be seen from this figure that the first waveform arrival time from 2.5-D finite differential simulation is the same as the real logged waveform from CBL/VDL, and the first 3 waveforms match with each other very well, proving the numerical simulation method is reliable.

The full acoustic waveforms at different cement channeling angles of 22.5°, 45°, 90°, 180° and 360° were obtained by numerical simulation method. Fig. 5 is the cross plot of cement channeling angle with the amplitude of the casing arrival. The normalized amplitude of casing arrival is the ratio of the amplitude of onsite casing arrival with the amplitude of free pipe. It can be seen from Fig. 5 that the denser the cement, the faster the attenuation of the amplitude of casing arrival will be as the cement channeling angle decreases. When the cement channeling angle is between 90° and 270°, there is obvious difference on the attenuation of the amplitude of casing arrival under different cement densities. Despite the changes in cement density, when cement channeling angle is less than 45°, the change of the amplitude of casing arrival is ignorable. That is to say the lower limit of the cement channeling angle which can be identified by acoustic logging is 45°. The numerical simulated results can match with the real logging data in Well 3, proving the accuracy of the numerical simulation method.

 517 

TANG Jun et al. / Petroleum Exploration and Development, 2016, 43(3): 514–521

Fig. 5. Relationship between channeling angle and the amplitude of the casing arrival by numerical simulation.

2.3. Effect of bond interface II quality on the acoustic field

Cementing quality bond interface II is affected by cement sheath and formation factors, and there is no uniform acoustic evaluation method and standard so far in the industry. Acoustic field of bond interface II in sandstone and limestone formation was numerically simulated with real axis integrated method. According to Hu[8] and Liu’s[18] previous research, the velocity of limestone is normally faster than the velocity of casing arrival. When casing, cement and formation are well bonded with each other and there is enough transmitter to receiver spacing in the acoustic tool, formation waveform will arrive earlier than casing arrival, which is favorable for the theory research of formation waveform arrival and cementing quality of bond interface II. Figs. 6 and 7 are the waveform and spectrum of bond interface II in limestone formation when the T-R spacing is 1524 mm and cement density is 1.5 g/cm3. It can be seen from Fig. 6 that formation waveform arrives the receiver earlier than casing arrival when the width of the bond interface II is around 0 mm. When the width is between 0.5 to 20 mm, the amplitude of the first formation arrival decreases, while the later coming arrivals mix with the other either formation waveform or casing arrivals. It is difficult to pick up the formation first arrivals signal in time domain. Fig. 7 is the same waveform but in frequency domain. It is clear

Fig. 7. II .

Frequency spectrum at varying width of bond interface

that when the cement channel width is around 0 mm, there is no casing arrivals and the full waveform can represent the formation waveform. The main frequency is the formation arrival frequency which is around 15-17 kHz. When the width of bond interface II annulus increases but is still less than 5 mm, the main frequency is still around 15-17 KHz, but there are some other confusing frequency higher than 17 KHz in the waveform. When the width is bigger than 5 mm, the formation arrival will disappear in the waveform. The main frequency now is the frequency of casing arrivals (around 17-18 KHz). In addition, based on the simulation results, it is difficult to pick up the formation arrivals in time domain in sandstone formation, so, the frequency analysis on the full waveform is the effective method to evaluate cementing quality of bond interface II.

3. New cement bond quality evaluation standard based on CBL/VDL logging There are two different cement bond quality evaluation standards in the industry. One is evaluating the bond relationship of casing, cement and formation in lateral based on cement strength, cementing strength and logging data. The other is evaluating the isolation capacity of the cement in vertical direction along the borehole axis since the cement can prevent fluid flow. A lot of oil and gas companies in China have their own cement evaluation standard and most of them are based on the cement bond quality valuation standard for cased well with acoustic logging [19]. But this standard, only using the waveform amplitude, can't evaluate the cementing quality of bond interface II. A new evaluation standard based on the cased well CBL/VDL acoustic field research is proposed in this paper. 3.1.

Evaluation parameters

The definition of interface I cementing index is:

BI1 

Fig. 6.

Full waveform at varying width of bond interface II.

lg Cmax  lg C lg Cmax  lg Cmin

(15)

The definition of the ratio of the bonded cement with cement annulus is:  518 

TANG Jun et al. / Petroleum Exploration and Development, 2016, 43(3): 514–521

Fig. 8.

The relationship between cementing index and ratio of the bonded cement with cement annulus.

I c   360    / 360

(16)

Fig. 8a is the cross plot of bond interface I cementing index with ratio of the bonded cement with cement annulus at 4 different cement densities based on the cased well acoustic field research and formula 15 and 16. The cross plot shows an obvious linear relationship between bond interface I cementing index and the ratio. Generally, cementing quality is considered good when the ratio of bonded cement with cement annulus is higher than 0.8 (which means the cement channeling angle is less than 72°). From Fig. 8a, when cement density is 1.2 g/cm3, the ratio of bonded cement with cement annulus is higher than 0.75, indicating good cementing. When cement density is 1.89 g/cm3, the ratio of bonded cement with cement annulus is higher than 0.8, indicating good cementing quality. When cement density is 2.25 g/cm3, the ratio of bonded cement with cement annulus is higher than 0.82, indicating good cementing quality too. That is to say, when cement density is higher, the evaluation standard should be higher, while cement density is low, the standard should be lower. When the cementing quality of bond interface I is good, the formation waveform is closely related to the cementing quality of bond interface II. Due to the interference of casing arrival and surface wave arrival, it is difficult to pick up formation arrivals directly from time domain. The method in reference [20] was used to calculate the amplitude of formation arrival, which was then corrected by lithology. The definition of bond interface II cementing index is:

BI 2 

lg A  lg Amin lg Amax  lg Amin

(17)

According to the results of cased well acoustic field research in this paper, the cement channeling angle at the bond interface II has a strong impact on the amplitude of the formation waveform, so we can transform the amplitude of the formation wave into bond interface II cementing index and the cement channeling angle into the ratio of bonded cement with cement annulus to find out their relationship. It can be seen from Fig. 8b that this two factors are in linear relationship. When the ratio of bonded cement with cement annulus of

higher than 0.8 is considered good cementing quality, the bond interface II cementing index should be higher than 0.78. If the ratio of bonded cement with cement annulus of lower than 0.5 is considered poor cementing quality, the bond interface II cementing index of less than 0.45 is considered poor cementing quality. 3.2.

New evaluation standard

The new cementing quality evaluation standard is based on the real CBL/VDL logging data in calibration wells and the numerical simulation results. The standard integrates the waveform amplitude, bond interface I cementing index and bond interface II cementing index. Tables 2 and 3 are the detailed evaluation standard. Table 2.

Cementing quality evaluation standard in conventional

cement density (1.51.8 g/cm3) Waveform Cementing index Cementing index Evaluation results amplitude/% of interface I of interface II <15 0.81.0 0.81.0 Poor cementation Good cementation of interface I <15 0.81.0 <0.8 Poor cementation of interface II Moderate 1530 0.50.8 0.50.8 cementation >30 <0.5 <0.5 Poor cementation Table 3.

Cementing quality evaluation standard in lower ce-

ment density (<1. 2 g/cm3) Waveform Cementing index Cementing index Evaluation results amplitude/% of interface I of interface II <25 0.751.00 0.81.0 Good cementation Good cementation of Interface I <25 0.751.00 <0.8 Poor cementation of interface II Moderate 2545 0.450.75 0.50.8 cementation >45 <0.45 <0.5 Poor cementation

 519 

TANG Jun et al. / Petroleum Exploration and Development, 2016, 43(3): 514–521

4.

Conclusions

Cmin—casing amplitude in cement well;

The cased well acoustic field has been investigated by combining the real logging data from the calibration wells with the numerical simulation. The cased well acoustic field can be classified into axisymmetric and non-axisymmetric problems. The axisymmetric acoustic field was simulated by real axis integral method, while the non-axisymmetric acoustic field was simulated by 2.5-D finite differential method. The amplitude of casing first arrival with channeling angle simulated by 2.5-D finite differential varies in the same trend with the results from logging, proving the numerical simulation is reliable. Both of the real acoustic logging data and the numerical simulation show that the cement channeling only can be detected by acoustic tool when the cement channeling angle is higher than 45°. Meanwhile, the amplitude of the casing arrival varies at different degrees with the cement channeling angle at different cement densities. When the borehole situation and the acoustic tool are suitable, the bond interface I cementing quality can be evaluated by the casing arrivals, while the bond interface II cementing quality can be evaluated by the formation arrivals. In this research, when the width of the annulus at bond interface II is less than 5 mm wide, the formation arrival signal can be taken as first arrival, it is easily recognized on time spectrum in limestone formation and closely related to the width of the annulus at bond interface II. When the annulus at bond interface II is more than 5 mm wide, the formation arrival in limestone formation cannot be identified and cannot be used to evaluate the cementing quality of bond interface II either. The new standard presented in this paper is based on the real CBL/VDL logging data in calibration wells and numerical simulation results. The evaluation standard includes the bond interface I cementing quality evaluation and bond interface II cementing quality evaluation at different cement densities.

d—space between acoustic source and receiver, m; fmax—the highest sound source frequency, Hz; F(t)—source time-domain function; gjk—the monopole sound source function matrix; Gxx, Gyy, Gzz—the sound source function of Fourier transform along z axis, which are all function of x, y, t, Kz, Pa/s; I0—the first kind of zero-order Bessel function of imaginary argument; Ic—the ratio of the bonded cement with cement annulus, f; k—wave number, m1; kr—the wave number component along radial direction, m1; kz—the wave number component along z axis, m1; Kz—z of Fourier transform; p—pressure response, Pa; r—distance from borehole axis, m; r—Vector distance from borehole axis, m; t—time, s; Txx, Tyy, Tzz, Txy, Txz, Tyz—the stress components of Fourier transform along z axis, which are all function of x, y, t, Kz, Pa; vf—acoustic velocity, m/s; vmax, vmin—the maximum and minimum velocity, m/s; Vx, Vy, Vz—the velocity of Fourier transform along x, y, z axis, m/s; x, y, z—rectangular coordinate, m; X(ω)—function of frequency spectrum; δ—unit-step function; δjk—unit-step function matrix; Δt—time interval, s; Δx, Δy, Δz—space interval, m; θt—channel angel (°); λ—first order Lame constant, Pa; μ—second order Lame constant, Pa; ρ—density, kg/m3; ω—angular frequency, Hz.

References

Acknowledgement

[1]

The authors thank CNPC XIBU Drilling Engineering Co., LTD for their support and assistance in providing calibration wells’ acoustic logging data.

ZHANG Chengguang, JIANG Wanzhe, PAN Heping. Acoustic logging and application. Beijing: Petroleum Industry Press, 2009.

[2]

LI Tao. Solid expandable tubular patching technique for hightemperature and high-pressure casing damaged wells. Petro-

Nomenclature

leum Exploration and Development, 2015, 42(3): 374–378. [3]

A—the area of extreme value in formation amplitude spectrum in

BIOT M A. Propagation of elastic waves in a cylindrical bore containing a fluid. Journal of Applied Physics, 1952, 23(9):

current layer, m2;

997–1005.

Amax—the area of extreme value in formation amplitude spectrum

[4]

2

in cased well, m ;

BIOT M A. Theory of propagation of elastic waves in a fluid-saturated porous solid(II): Higher frequency range.

Amin—the area of extreme value in formation amplitude spectrum

Journal of the Acoustical Society of America, 1956, 28(2):

in bond interface II not bonded, default value is 1, m2;

179–191.

A1—reflection coefficient;

[5]

WHITE J E, ZECHMAN R E. Computed response of an

[6]

CHENG C H, TOKSOZ M N. Elastic wave propagation in a

BI1, BI2—bond interface I, II cementing index;

acoustic logging to0l. Geophysics, 1968, 33(2): 302–310.

C—casing amplitude;

fluid filled borehole and synthetic acoustic logs. Geophysics,

Cmax—free casing amplitude;

 520 

TANG Jun et al. / Petroleum Exploration and Development, 2016, 43(3): 514–521

[14] HAN Wei, MAO Jie, JIN Shijie. A thickness determination

1981, 46(7): 1042–1053. [7]

ZHANG Hailan, LI Mingxuan, HAILAN Z. Numerical study of acoustic field of borehole in slow formation. CJ GeophysHU Wenxiang, QIAN Menglu. Synthetic waveforms of the acoustic field in cased boreholes and their time-frequency dis-

microannulus thickness on capacity of acoustic wave-long tool. Oil Geophysical Prospecting, 2003, 38(5): 540–542. [16] XU Yanfeng, HU Wenxiang. Ultrasonic imaging for appear-

tribution. ACTA Acoustic, 2002, 27(3): 223–228. [9]

frequency ultrasound. ACTA Acoustic, 2014, 39(4): 467–472. [15] DIAO Shun, QIAO Wenxiao, DU Guangsheng. Influence of

ics, 1993, 36(1): 137–144. [8]

method of thin layer between casing and cement using low

LIN Weijun, ZHANG Chengyu, ZHANG Hailan, et al. Acoustic field in a cased well with a sectorial crossing chan-

ance of vertical slot by reverse time migration. Acta Physica Sinica, 2014, 63(15): 154302. [17] CHU Wei, SHEN Jiyun, YANG Yunfei, et al. Calculation of

nel. ACTA Acoustic, 2005, 30(1): 9–14. [10] SONG R L, LIU J X, YAO G J. Parallel finite difference

micro-annulus size in casing-cement sheath-formation system

modeling of acoustic fields in nonaxisymmetric cased hole.

under continuous internal casing pressure change. Petroleum Exploration and Development, 2015, 42(3): 379–385.

Chinese Journal of Geophysics, 2010, 53(6): 2767–2775. [11] SONG R L, LIU J X, HOU C H. Numerical simulation of

[18] LIU Jisheng, WANG Kexie. Studying each mode of ascoutic

sector bond log and improved cement bond image. Geophys-

full-wavetrains using frequency wavenumber analysis. Well

ics, 2012, 77(4): 95–104.

Logging Technology, 2000, 24(3): 198–202.

[12] CHEN Dehua, WANG Xiuming, ZHANG Hailan, et al. The

[19] National Development and Reform Commission. Procedure

effects of cement density and casing dimension on casing

for cement evaluation: SY/T 6592-2004. Beijing: Petroleum Industry Press, 2004.

waves in oil wells. ACTA Acoustic, 2008, 33(1): 15–20. [13] SHI Fangfang, WU Xianmei, ZHANG Bixing. Application of

[20] TANG Jun, ZHANG Chengguang. Application study on ce-

cylindrical linear phased array in casing borehole. Chinese

ment bond quantitative evaluation by MAK-Ⅱwaveform data.

Journal of Acoustics, 2010, 29(1): 65–72.

Well Logging Technology, 2011, 35(3): 266–269.

 521 