Numerical simulation of acoustic field in logging-while-drilling borehole generated by linear phased array acoustic transmitter

Regarding the actual acoustic LWD tool, the main frequency of the excitation signal applied to each element (f₀), the spacing between adjacent elements (d) and the delay time between the excitation signals applied to adjacent elements (Δτ) were the same in all numerical simulations. In this study, f₀ was 15 kHz and d was 6 cm. The model was 1.5 m × 5 m in size. The source and receiver were both mounted on the exterior interface of the collar. The central point of the source position was at 4 m in the z-direction. Table 1 lists the elastic parameters and dimensions of the media, where V_p and V_s are the velocities of the compression (P) and shear (S) waves, respectively; ρ is the density; and r is the outer radius.

Figure 6.

Energy distribution graphs of the P wave in the fluid generated by the LPA acoustic transmitters: (a) normalized and (b) unnormalized amplitudes.

Figure 9.

Energy distribution graphs of the P wave in the fluid generated by the LPA acoustic transmitters: (a) normalized and (b) unnormalized amplitudes.

Table 1.

Elastic parameters and dimensions of media in the calculation model.

Type	\|${V_p}$\| (m s⁻¹)	\|${V_s}$\| (m s⁻¹)	\|$\rho $\| (kg m⁻³)	\|$r$\| (m)
Fluid	1500	0	1000	0.027
Collar	5860	3130	7800	0.09
Fluid	1500	0	1000	0.117
Formation	3000	1800	2000	−

Type	\|${V_p}$\| (m s⁻¹)	\|${V_s}$\| (m s⁻¹)	\|$\rho $\| (kg m⁻³)	\|$r$\| (m)
Fluid	1500	0	1000	0.027
Collar	5860	3130	7800	0.09
Fluid	1500	0	1000	0.117
Formation	3000	1800	2000	−

Table 1.

Elastic parameters and dimensions of media in the calculation model.

Type	\|${V_p}$\| (m s⁻¹)	\|${V_s}$\| (m s⁻¹)	\|$\rho $\| (kg m⁻³)	\|$r$\| (m)
Fluid	1500	0	1000	0.027
Collar	5860	3130	7800	0.09
Fluid	1500	0	1000	0.117
Formation	3000	1800	2000	−

Type	\|${V_p}$\| (m s⁻¹)	\|${V_s}$\| (m s⁻¹)	\|$\rho $\| (kg m⁻³)	\|$r$\| (m)
Fluid	1500	0	1000	0.027
Collar	5860	3130	7800	0.09
Fluid	1500	0	1000	0.117
Formation	3000	1800	2000	−

2.2 The calculation method

The finite-difference method (FDM) is a useful technique for studying the propagation of elastic waves in complex models. In this study, we applied the FDM in a 2-D cylindrical coordinate system (Randall et al. 1991; Wang & Tang 2003; He et al. 2013) to simulate the acoustic fields generated by the different transmitters in the LWD borehole. The stress–velocity elastic wave equations in isotropic media are as follows:

\begin{eqnarray*} \rho \frac{{\partial {v_r}}}{{\partial t}} &=& \frac{{\partial {\sigma _{rr}}}}{{\partial r}} + \frac{1}{r}\left( {{\sigma _{rr}} - {\sigma _{\theta \theta }} + m{\sigma _{r\theta }}} \right) + \frac{{\partial {\sigma _{rz}}}}{{\partial z}} + {f_r} \nonumber \\ \rho \frac{{\partial {v_\theta }}}{{\partial t}} &=& \frac{{\partial {\sigma _{r\theta }}}}{{\partial r}} + \frac{1}{r}\left( {2{\sigma _{r\theta }} - m{\sigma _{\theta \theta }}} \right) + \frac{{\partial {\sigma _{\theta z}}}}{{\partial z}} + {f_\theta } \nonumber \\ \rho \frac{{\partial {v_z}}}{{\partial t}} &=& \frac{{\partial {\sigma _{rz}}}}{{\partial r}} + \frac{1}{r}\left( {{\sigma _{rz}} + m{\sigma _{\theta z}}} \right) + \frac{{\partial {\sigma _{zz}}}}{{\partial z}} + {f_z} \nonumber \\ \frac{{\partial {\sigma _{rr}}}}{{\partial t}} &=& (\lambda + 2\mu )\frac{{\partial {v_r}}}{{\partial r}} + \lambda \frac{1}{r}\left( {{v_r} + m{v_\theta }} \right) + \lambda \frac{{\partial {v_z}}}{{\partial z}} + {g_{rr}} \nonumber \\ \frac{{\partial {\sigma _{\theta \theta }}}}{{\partial t}} &=& \lambda \frac{{\partial {v_r}}}{{\partial r}} + (\lambda + 2\mu )\frac{1}{r}\left( {{v_r} + m{v_\theta }} \right) + \lambda \frac{{\partial {v_z}}}{{\partial z}} + {g_{\theta \theta }} \nonumber \\ \frac{{\partial {\sigma _{zz}}}}{{\partial t}} &=& \lambda \frac{{\partial {v_r}}}{{\partial r}} + \lambda \frac{1}{r}\left( {{v_r} + m{v_\theta }} \right) + (\lambda + 2\mu )\frac{{\partial {v_z}}}{{\partial z}} + {g_{zz}}\nonumber \\ \frac{{\partial {\sigma _{\theta z}}}}{{\partial t}} &=& \mu \left( { - \frac{1}{r}m{v_z} + \frac{{\partial {v_\theta }}}{{\partial z}}} \right) + {g_{\theta z}} \nonumber \\ \frac{{\partial {\sigma _{rz}}}}{{\partial t}} &=& \mu \left( {\frac{{\partial {v_z}}}{{\partial r}} + \frac{{\partial {v_r}}}{{\partial z}}} \right) + {g_{rz}} \nonumber \\ \frac{{\partial {\sigma _{r\theta }}}}{{\partial t}} &=& \mu \left[ {\frac{{\partial {v_\theta }}}{{\partial r}} + \frac{1}{r}\left( { - {v_\theta } - m{v_r}} \right)} \right] + {g_{r\theta }} , \end{eqnarray*}

(1)

where |${v_r}$|⁠, |${v_\theta }$| and |${v_r}$| are the velocity components; |${\sigma _{rr}}$|⁠, |${\sigma _{\theta \theta }}$|⁠, |${\sigma _{zz}}$|⁠, |${\sigma _{r\theta }}$|⁠, |${\sigma _{rz}}$| and |${\sigma _{\theta z}}$| are the stress components; |$\rho $|⁠, |$\lambda $| and |$\mu $| are the density and Lamé coefficients, respectively; and |$m$| takes values of 0, 1 and 2 for monopole, dipole and quadrupole sources, respectively. Further, |$g$| and |$f$| are source terms. When |$m = 0$|⁠, the velocity and stress components are related to r and z only, and |${\sigma _{r\theta }}$|⁠, |${\sigma _{\theta z}}$| and |${f_\theta }$| are zero. Under such conditions, the stress–velocity elastic wave equations can be rewritten as follows:

\begin{eqnarray*} \rho \frac{{\partial {v_r}}}{{\partial t}} &=& \frac{{\partial {\sigma _{rr}}}}{{\partial r}} + \frac{1}{r}\left( {{\sigma _{rr}} - {\sigma _{\theta \theta }}} \right) + \frac{{\partial {\sigma _{rz}}}}{{\partial z}} + {f_r}\nonumber \\ \rho \frac{{\partial {v_z}}}{{\partial t}} &=& \frac{{\partial {\sigma _{rz}}}}{{\partial r}} + \frac{1}{r}{\sigma _{rz}} + \frac{{\partial {\sigma _{zz}}}}{{\partial z}} + {f_z}\nonumber \\ \frac{{\partial {\sigma _{rr}}}}{{\partial t}} &=& (\lambda + 2\mu )\frac{{\partial {v_r}}}{{\partial r}} + \lambda \frac{1}{r}{v_r} + \lambda \frac{{\partial {v_z}}}{{\partial z}} + {g_{rr}}\nonumber \\ \frac{{\partial {\sigma _{\theta \theta }}}}{{\partial t}} &=& \lambda \frac{{\partial {v_r}}}{{\partial r}} + (\lambda + 2\mu )\frac{1}{r}{v_r} + \lambda \frac{{\partial {v_z}}}{{\partial z}} + {g_{\theta \theta }}\nonumber \\ \frac{{\partial {\sigma _{zz}}}}{{\partial t}} &=& \lambda \frac{{\partial {v_r}}}{{\partial r}} + \lambda \frac{1}{r}{v_r} + (\lambda + 2\mu )\frac{{\partial {v_z}}}{{\partial z}} + {g_{zz}}\nonumber \\ \frac{{\partial {\sigma _{rz}}}}{{\partial t}} &=& \mu \left( {\frac{{\partial {v_z}}}{{\partial r}} + \frac{{\partial {v_r}}}{{\partial z}}} \right) + {g_{rz}} . \end{eqnarray*}

(2)

The source terms are defined as follows (Coutant et al. 1995):

\begin{eqnarray*} {f_r}\left( {r,z,t} \right) &=& 0\nonumber \\ {f_z}\left( {r,z,t} \right) &=& 0\nonumber \\ {g_{rr}}\left( {r,z,t} \right) &=& \sum\limits_{i = 1}^m {{s_i}\left( t \right)\delta \left( {r - {r_i}} \right)\delta \left( {z - {z_i}} \right)} \nonumber \\ {g_{\theta \theta }}\left( {r,z,t} \right) &=& \sum\limits_{i = 1}^m {{s_i}\left( t \right)\delta \left( {r - {r_i}} \right)\delta \left( {z - {z_i}} \right)} \nonumber \\ {g_{zz}}\left( {r,z,t} \right) &=& \sum\limits_{i = 1}^m {{s_i}\left( t \right)\delta \left( {r - {r_i}} \right)\delta \left( {z - {z_i}} \right)} \nonumber \\ {g_{rz}}\left( {r,z,t} \right) &=& 0 , \end{eqnarray*}

(3)

where |$s$| is the excitation signal function, |$\delta $| is the unit impulse function, |${r_i}$| and |${z_i}$| are the coordinates of the ith element, and |$i$| is the serial number of the element. Note that |$s$| is defined as follows:

\begin{eqnarray*} {s_i}\left( t \right) = {a_i}\left[ {1 - 2{{\left( {\pi {f_0}t - \pi {f_0}{\tau _i}} \right)}^2}} \right]{\mathrm{ e}^{ - {{\left[ {\pi {f_0}\left( {t - {\tau _i}} \right)} \right]}^2}}}, \end{eqnarray*}

(4)

where |${\tau _i}$| is the total delay time of the excitation signal applied to the ith element and |${a_i}$| is the amplitude of the excitation signal applied to the ith element.

2.3 Characteristics of different waves

Fig. 2 shows the waveforms in the LWD borehole generated by the monopole acoustic transmitter. Under the calculation conditions employed in this study, the monopole acoustic transmitter generates four waves in the LWD borehole: the collar wave, the gliding P wave, the gliding S wave and the Stoneley (ST) wave. The arrival times of the collar and gliding P waves are earlier than those of the gliding S and ST waves, and the amplitudes of the collar and gliding P waves are considerably smaller than those of the gliding S and ST waves. The slowness–time correlation (STC; Kai & Esmersoy 1992) and slowness–frequency correlation (SFC; Wang et al. 2012) methods were utilized to further analyse the received waveforms in the time and frequency domains, respectively. Fig. 3 shows the results obtained from these two methods. The colour data represent the correlation values, and the distribution characteristics corresponding to the maximum correlation values indicate the true properties of the different waves. According to the STC diagram, the velocities of the collar, gliding P, gliding S and ST waves are approximately 5250, 2950, 1790 and 1300 m s⁻¹, respectively. According to the SFC diagram, the collar wave has a high dispersion property, the gliding P and S waves have a negligible dispersion property and the ST wave has a slight dispersion property. The collar wave is a guided wave propagating along the drill collar. The characteristics of the collar wave are similar to those of guided waves in elastic cylinders and cylindrical shells. The collar wave velocity is between the P- and S-wave velocities of the drill collar, and higher than the velocities of the most formations. Therefore, the collar wave adversely affects the measurement of formation velocities in actual monopole acoustic LWD.

Figure 2.

Waveforms in the LWD borehole generated by the monopole acoustic transmitter. The offsets were 2, 2.2, 2.4, 2.6, 2.8 and 3 m, respectively. Because the amplitudes of the collar and gliding P waves were considerably smaller than those of the gliding S and ST waves, the former two waves are displayed in (a), and the latter two waves are displayed in (b). Note that (a) and (b) present the same waveform data, but with different display scales.

Figure 3.

Results of waveforms generated by the monopole acoustic transmitter using the STC and SFC methods. (a) STC diagram and (b) SFC diagram.

Fig. 4 shows the waveforms in the LWD borehole generated by the LPA acoustic transmitter. Δτ is 20 μs and n is 12. Compared to the monopole transmitter, the guided waves in the LWD borehole generated by the LPA acoustic transmitter have the same type but different relative amplitude, and the amplitude ratio of the gliding P wave to the collar wave is obviously increased when using the LPA acoustic transmitter. The received waveforms are also further analysed using the STC and SFC methods, with results shown in Fig. 5. The velocities and dispersion properties of the guided waves generated by the LPA acoustic transmitter are similar to those of the waves generated by the monopole acoustic transmitter. However, the gliding P wave generated by the LPA acoustic transmitter has better correlation. Thus, the velocity of the gliding P wave can be obtained more easily and accurately.

Figure 4.

Waveforms in the LWD borehole generated by the LPA acoustic transmitter. The offsets were 2, 2.2, 2.4, 2.6, 2.8 and 3 m, respectively. Because the amplitudes of the collar and gliding P waves were considerably smaller than those of the gliding S and ST waves, the former two waves are displayed in (a), and the latter two waves are displayed in (b). Note that (a) and (b) present the same waveform data, but with different display scales.

Figure 5.

Results of waveforms generated by the LPA acoustic transmitter using the STC and SFC methods. (a) STC diagram and (b) SFC diagram.

3 INFLUENCE OF THE LPA PARAMETERS ON DIFFERENT WAVES IN THE LWD BOREHOLE

3.1 Relationship between delay time and critical angle

When a plane wave is incident from a fluid into a solid, reflection and refraction occur on the fluid–solid interface, obeying the law of refraction:

\begin{eqnarray*} \frac{{\sin \theta }}{{\sin {\theta _f}}} = \frac{c}{{{c_f}}}, \end{eqnarray*}

(5)

where c_f is the velocity of the incident wave in the fluid, c is the velocity of the refracted wave in the solid, θ_f is the incident angle, and θ is the refracted angle. When θ_f is equal to the critical angle, θ is equal to 90°; this phenomenon is called total reflection. According to eq. (5), the critical angle of the collar wave is θ_f₀=16.60°; the critical angle of the gliding P wave (the first critical angle of formation) is θ_f₁=30°; the critical angle of the gliding S wave (the second critical angle of formation) is θ_f₂=56.44°; the ST wave has no critical angle because its velocity is less than that of the fluid P wave. The value of Δτ affects the deflection angle (|$\theta _{fd}$|) of the main radiated acoustic beam in the borehole, obeying the following equation:

\begin{eqnarray*} \Delta \tau = \frac{{d\sin {\theta _{fd}}}}{{{c_f}}}. \end{eqnarray*}

(6)

When θ_fd is equal to the critical angle of a certain wave, the energy of that wave can be greatly enhanced on the fluid–solid interface. According to eq. (6), when Δτ is equal to 11.4, 20 and 33.3 μs, θ_fd is equal to θ_f₀, θ_f₁ and θ_f₂, respectively.

3.2 Influence of delay time

We first studied the influence of Δτ on the different waves in the LWD borehole. Table 2 lists the parameters of each LPA acoustic transmitter and Fig. 6 shows the energy distribution of the P wave in the fluid generated by the LPA acoustic transmitters. By adjusting the delay time of the LPA acoustic transmitter, the deflection angle of the main radiated acoustic beam can be controlled.

Table 2.

LPA acoustic transmitter parameters.

Code name	\|$n$\|	\|$\Delta \tau $\| (μs)
4-(0)	4	0
4-(4)	4	4
4-(8)	4	8
4-(11.4)	4	11.4
4-(16)	4	16
4-(20)	4	20
4-(33.3)	4	33.3
4-(40)	4	40
4-(50)	4	50

Table 2.

LPA acoustic transmitter parameters.

Code name	\|$n$\|	\|$\Delta \tau $\| (μs)
4-(0)	4	0
4-(4)	4	4
4-(8)	4	8
4-(11.4)	4	11.4
4-(16)	4	16
4-(20)	4	20
4-(33.3)	4	33.3
4-(40)	4	40
4-(50)	4	50

Fig. 7 shows the waveforms in the LWD borehole generated by the LPA acoustic transmitters with the different delay times, when n is 4. As Δτ is increased from 0 to 50 μs, the amplitudes of the collar, gliding P and gliding S waves are first increased and then decreased, whereas the amplitude of the ST wave is increased continuously. When Δτ are 11.4, 20 and 33.3 μs, θ_fd are equal to θ_f₀, θ_f₁ and θ_f₂, and the maximum amplitudes of the collar wave, gliding P wave and gliding S wave are obtained, respectively.

Figure 7.

Waveforms in the LWD borehole generated by the LPA acoustic transmitters with different delay times. The element number n = 4 and the offset is 3 m. The collar and P waves are displayed in (a), and the gliding S and ST waves are displayed in (b). Note that (a) and (b) present the same waveform data, but with different display scales.

Fig. 8 shows a comparison of the waveforms in the LWD borehole generated by the monopole acoustic transmitter and the LPA acoustic transmitters. Compared to the monopole acoustic transmitter, the amplitudes of the gliding P and S waves in the LWD borehole generated by the LPA acoustic transmitter are not enhanced obviously when Δτ is 0. However, the amplitude of the gliding P (or S) wave in the LWD borehole generated by the LPA acoustic transmitter is obviously enhanced when Δτ is set such that θ_fd is equal to θ_f₁ (or θ_f₂). This is because, when Δτ is 0, the radiation direction of the main radiated acoustic beam in the borehole is perpendicular to the well axis. Therefore, rather than being reflected back into the borehole, most of the energy is incident on the formation. When Δτ is set such that θ_fd is equal to θ_f₁ (or θ_f₂), the main radiated acoustic beam in the borehole is incident along the direction most favourable for generating the gliding P (or S) wave. Thus, most of the energy forms the gliding P (or S) wave.

Figure 8.

Comparison of waveforms in the LWD borehole generated by the monopole acoustic transmitter and the LPA acoustic transmitters. The offset was 3 m. Comparison of (a) gliding P and (b) gliding S waveforms.

3.3 Influence of element number

Next, we studied the influence of n on the different waves in the LWD borehole. Table 3 lists the parameters of each LPA and Fig. 9 shows the energy distribution graphs of the P wave in the fluid generated by the LPA acoustic transmitters. By adjusting the element number of the LPA acoustic transmitter, the angle width of the main radiated acoustic beam can be controlled.

Table 3.

LPA acoustic transmitter parameters.

Code name	\|$n$\|	\|$\Delta \tau $\| (μs)
1	1	-
4-(20)	4	20
4-(33.3)	4	33.3
8-(20)	8	20
8-(33.3)	8	33.3
12-(20)	12	20
12-(33.3)	12	33.3

Table 3.

LPA acoustic transmitter parameters.

Code name	\|$n$\|	\|$\Delta \tau $\| (μs)
1	1	-
4-(20)	4	20
4-(33.3)	4	33.3
8-(20)	8	20
8-(33.3)	8	33.3
12-(20)	12	20
12-(33.3)	12	33.3

Fig. 10 shows the waveforms in the LWD borehole generated by the LPA acoustic transmitters for different element numbers, when Δτ (20 μs) is set such that θ_fd is equal to θ_f₁. The amplitude of the gliding P wave is increased constantly as the element number increases. The amplitude of the collar wave is increased first and then remains basically unchanged as the element number increases. However, the amplitudes of the gliding S and ST waves show almost no dependence on the element number. Further, we calculated the relative values of the different waves by dividing the peak-to-peak values for n > 1 by that for n = 1. Fig. 11 shows the relationships of the various waves between the relative value and the element number when Δτ is 20 μs. The amplitude of the gliding P wave is increased linearly as the element number increases when Δτ (20 μs) is set such that θ_fd is equal to θ_f₁.

Waveforms in the LWD borehole generated by LPA acoustic transmitters with different element numbers. Δτ (20 μs) is set such that θfd is equal to θf1 and the offset is 3 m. The collar and gliding P waves are displayed in (a), and the gliding S and ST waves are displayed in (b). Note that (a) and (b) present the same waveform data, but with different display scales.

Figure 10.

Waveforms in the LWD borehole generated by LPA acoustic transmitters with different element numbers. Δτ (20 μs) is set such that θ_fd is equal to θ_f₁ and the offset is 3 m. The collar and gliding P waves are displayed in (a), and the gliding S and ST waves are displayed in (b). Note that (a) and (b) present the same waveform data, but with different display scales.

Figure 11.

Relationships of various waves between relative value and element number when Δτ is 20 μs.

Figure 12.

Waveforms in the LWD borehole generated by the LPA acoustic transmitters with different element numbers. Δτ (33.3 μs) is set such that θ_fd is equal to θ_f₂ and the offset is 3 m. The collar and gliding P waves are displayed in (a), and the gliding S and ST waves are displayed in (b). Note that (a) and (b) present the same waveform data, but with different display scales.

Fig. 12 shows the waveforms in the LWD borehole generated by the LPA acoustic transmitters for different element numbers, when Δτ (33.3 μs) is set such that |$\theta _{fd}$| is equal to θ_f₂. The amplitude of the gliding S wave is increased constantly as the element number increases, whereas the amplitudes of the collar, gliding P and ST waves show almost no dependence on the element number. We calculated the relative values of the different waves using the same method. Fig. 13 shows the relationships of the various waves between the relative value and the element number when Δτ is 33.3 μs. The amplitude of the gliding S wave is increased linearly as the element number increases when Δτ (33.3 μs) is set such that θ_fd is equal to θ_f₂.

Figure 13.

Relationships of various waves between relative value and element number when Δτ is 33.3 μs.

4 CONCLUSIONS

During actual monopole acoustic LWD, a strong tool wave propagates along the drill collar, which adversely affects the measurement of formation velocities. Based on the FDM, the acoustic field generated by the LPA acoustic transmitter in the LWD borehole was studied, and the effect of the LPA acoustic transmitter applied to acoustic LWD was analysed. The findings of this study provide a new approach for next-generation acoustic LWD tool design.

By adjusting the parameters of the LPA acoustic transmitter, the angle width and deflection angle of the main radiated acoustic beam in the borehole could be controlled. When the parameters of the LPA were set such that the gliding P (or S) wave stacked in the same phase, the amplitude of the gliding P (or S) wave was greatly enhanced. The application of the LPA acoustic transmitter could effectively improve the reliability of the acoustic LWD tool in measuring formation velocities.

Methods to weaken the collar wave amplitude were not employed in this study. When the collar wave velocity was close to the formation wave velocity, use of the LPA acoustic transmitter could not increase the amplitude ratio of the formation wave to the collar wave. Therefore, the combination of the LPA acoustic transmitter and groove-cutting (or variable-size collar) techniques has a better application prospect.

In addition, the LPA acoustic transmitter can also be applied to reflection acoustic LWD. The technology to directionally enhance the energy in the formation is significant for the exploration of geological structures outside the borehole.

ACKNOWLEDGEMENTS

The authors would like to thank the editors and reviewers for their valuable comments. This work is supported by the National Natural Science Foundation of China (41874210 and 11734017), the National Science and Technology Major Project (2017ZX05019001 and 2017ZX05019006), the Petro China Innovation Foundation (2016D-5007-0303) and the Science Foundation of China University of Petroleum, Beijing (2462016YJRC020).

REFERENCES

Aron

J.

,

Chang

S.K.

,

Dworak

R.

,

Hsu

K.

,

Lau

T.

,

Masson

J.P.

,

Plona

T.L.

,

1994

.

Sonic compressional measurements while drilling

, in

Proceedings of the SPWLA 35th Annual Logging Symposium

,

Society of Petrophysicists and Well-Log Analysts

, Tulsa, Oklahoma.

10.1007/s12182-014-0352-3

Che

X.

,

Qiao

W.

,

Wang

R.

,

Zhao

Y.

,

2014

.

Numerical simulation of an acoustic field generated by a phased arc array in a fluid-filled cased borehole

,

Pet. Sci.

,

11

,

385

–

390

.

Che

X.H.

,

Qiao

W.X.

,

Ju

X.D.

,

Wang

R.J.

,

2016a

.

Azimuthal cement evaluation with an acoustic phased-arc array transmitter: numerical simulations and field tests

,

Appl. Geophys.

,

13

,

194

–

202

.

10.1007/s11770-016-0537-1

Che

X.H.

,

Qiao

W.X.

,

Ju

X.D.

,

Lu

J.Q.

,

Wu

J.P.

,

Cai

M.

,

2016b

.

Experimental study of the azimuthal performance of 3D acoustic transmitter stations

,

Pet. Sci.

,

13

,

52

–

63

.

10.1007/s12182-015-0073-2

Coutant

O.

,

Virieux

J.

,

Zollo

A.

,

1995

.

Numerical source implementation in a 2D finite-difference scheme for wave-propagation

,

Bull. seism. Soc. Am.

,

85

,

1507

–

1512

.

Cui

Z.W.

,

2004

.

Theoretical and numerical study of modified Biot's models, acoustoelectric well logging and acoustic logging while drilling excited by multipole acoustic sources, PhD thesis

,

Jilin University, China

.

Guan

W.

,

Hu

H.

,

Zheng

X.

,

2013

.

Theoretical simulation of the multipole seismoelectric logging while drilling

,

Geophys. J. Int.

,

195

,

1239

–

1250

.

He

X.

,

Hu

H.

,

Wang

X.

,

2013

.

Finite difference modelling of dipole acoustic logs in a poroelastic formation with anisotropic permeability

,

Geophys. J. Int.

,

192

,

359

–

374

.

Joyce

B.

,

Patterson

D.

,

Leggett

J.

,

Dubinsky

V.

,

2001

.

Introduction of a new omnidirectional acoustic system for improved real-time LWD sonic logging-tool design and field test results

, in

Proceedings of the SPWLA 42rd Annual Logging Symposium

,

Society of Petrophysicists and Well-Log Analysts

, Houston, Texas, .

Kai

H.

,

Esmersoy

C.

,

1992

.

Parametric estimation of phase and group slownesses from sonic logging waveforms

,

Geophysics

,

10

,

978

–

985

.

Kinoshita

T.

,

Dumont

A.

,

Hori

H.

,

Sakiyama

N.

,

Morley

J.

,

Garcia-Osuna

F.

,

2010

.

LWD sonic tool design for high-quality logs

, in

Proceedings of the SEG Annual Meeting

,

Society of Exploration Geophysicists

, Denver, Colorado.

Leggett

J.V.

,

Dubinsky

V.

,

Patterson

D.

,

Bolshakov

A.

,

2001

.

Field test results demonstrating improved real-time data quality in an advanced LWD acoustic system

, in

Proceedings of the SPE Annual Technical Conference and Exhibition

,

Society of Petroleum Engineers

, New Orleans, Louisiana.

Randall

C.J.

,

Scheibner

D.J.

,

Wu

P.T.

,

1991

.

Multipole borehole acoustic waveforms: synthetic logs with beds and borehole washouts

,

Geophysics

,

56

,

1757

–

1769

.

Sinha

B.K.

,

Simsek

E.

,

Asvadurov

S.

,

2009

.

Influence of a pipe tool on borehole modes

,

Geophysics

,

74

,

E111

–

E123

.

Su

Y.

,

Tang

X.

,

Liu

Y.

,

Xu

S.

,

Zhuang

C

,

2015b

.

Extensional-wave stopband broadening across the joint of pipes of different thickness

,

J. acoust. Soc. Am.

,

138

,

EL447

–

EL451

.

Su

Y.D.

,

Tang

X.M.

,

Xu

S.

,

Zhuang

C.X.

,

2015a

.

Acoustic isolation of a monopole logging while drilling tool by combining natural stopbands of pipe extensional waves

,

Geophys. J. Int.

,

202

,

439

–

445

.

Tang

X.M.

,

Cheng

C.H.A.

,

2004

.

Quantitative Borehole Acoustic Methods

,

Elsevier Science Publishing

.

Tang

X.M.

,

Wang

T.

,

Patterson

D.

,

2002

.

Multipole acoustic logging-while-drilling

, in

Proceedings of the SEG Annual Meeting

,

Society of Exploration Geophysicists

, Salt Lake City, Utah.

Wang

R.

,

Qiao

W.

,

Ju

X.

,

2012

.

A multi-channel acoustic logging signal dispersion analysis method

,

Well Logging Technol.

,

36

,

135

–

140

.

Wang

T.

,

Tang

X.

,

2003

.

Finite-difference modeling of elastic wave propagation: a nonsplitting perfectly matched layer approach

,

Geophysics

,

68

,

1749

–

1755

.

Wu

J.

,

Qiao

W.

,

Che

X.

,

Ju

X.

,

Lu

J.

,

Wu

W.

,

2013

.

Experimental study on the radiation characteristics of downhole acoustic phased combined arc array transmitter

,

Geophysics

,

78

,

D1

–

D9

.

10.1190/geo2012-0114.1

Yang

Y.

,

Guan

W.

,

Hu

H.

,

Xu

M.

,

2017

.

Numerical study of the collar wave characteristics and the effects of grooves in acoustic logging while drilling

,

Geophys. J. Int.

,

209

,

749

–

761

.

Zhang

B.

,

Tang

X.M.

,

Su

Y.D.

,

Qi

X.

,

2016

.

An acoustic logging while drilling technique using the dual source of opposite polarity

,

Chin. J. Geophys.

,

59

,

1151

–

1160

.