A method to determine the strike of interface outside of borehole by monopole borehole acoustic reflections

Journal of Petroleum Science and Engineering 133 (2015) 304–312

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Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol

A method to determine the strike of interface outside of borehole by monopole borehole acoustic reflections Hua Wang a,b,n, Guo Tao c, xuefeng Shang b a

State Key Lab of Petroleum Resources and Prospecting, China Univ. of Petroleum, Beijing, China Earth Resources Lab, MIT, Cambridge, MA, USA c The Petroleum Institute of Abu Dhabi, United Arab Emirates b

art ic l e i nf o

a b s t r a c t

Article history: Received 8 January 2015 Received in revised form 21 April 2015 Accepted 13 May 2015 Available online 23 June 2015

We use a 3-dimensional finite difference method (3DFD) to study acoustic reflection wavefields generated by a monopole-logging tool in a fluid-filled borehole surrounded by formations with a tilted interface away from the borehole in both wireline and logging-while-drilling (LWD). Different strikes of a tilted interface are considered in simulations. The simulation results demonstrate the arrival times of reflections in different azimuth receivers of the monopole tool are different, from which we can tell the strike of the reflector. Although more works need to be done on the suitable receiver pairs, the phase differences of the waveform in different receiver pairs are definitely helpful for the determination of the strike. Acoustic reflections in LWD case have advantages of deeper depth of investigation and higher resolution than that in wireline case for imaging of the structures away from borehole. & 2015 Elsevier B.V. All rights reserved.

Keywords: Strike determination Acoustic reflection logging Monopole logging-while-drilling

1. Introduction With the development of unconventional oil and gas reservoirs such as shale gas plays, more attention of well logging is paid to the geometry of the formation bedding around the borehole, which is crucial in geo-steering. Conventional sonic logging method however is inadequate due to the limitation of lateral depth of investigation. Most of acoustic logging utilize the energy trapped in the fluid-filled borehole which acts as a non-perfect wave guide, such as traveling as P wave, S wave, Stoneley wave and pseudo-Rayleigh wave (pR.) in the monopole case. On the other hand, less than 1% of the energy excited by the acoustic source leaks into the formation as body waves that can be used to determine the formation bedding geometry (He, 2005). Fig. 1 depicts the propagation of the leaky modes in the formation and the reflection waves back off an interface into the borehole. Such subtle signals can be extracted to image the geometry of the geological structures near the borehole. Recent studies of this socalled borehole acoustic reflection logging have shown that it can detect about 10–20 m away from borehole. In addition, we can use such a method in acoustic logging-while-drilling (ALWD) operations for geo-steering (Tang et al., 2007). The first prototype of the acoustic reflection tool is Evaluation of Velocity and Attenuation (EVA) developed in 1982 (Fortin et al., n Corresponding author at: State Key Lab of Petroleum Resources and Prospecting, China Univ. of Petroleum-Beijing, China.

http://dx.doi.org/10.1016/j.petrol.2015.05.025 0920-4105/& 2015 Elsevier B.V. All rights reserved.

1991). Schlumberger developed their first acoustic reflection tool (BARS: Borehole Acoustic Reflection Survey) in 1998, and released a new tool (Sonic Scanner) in 2005. Published papers and reports show the tool can detect the structure around the borehole to a distance of 20 m in 3 dimensions (Pistre et al., 2005, Hirabayashi et al., 2010). However, the details of data processing methods and software are still not clear to the industry. Baker Hughes developed dipole shear measurements to infer the strike information of the structures far from the borehole (Tang et al., 2007; Wei and Tang, 2012). Bohai Drilling of CNPC developed an acoustic reflection logging tool and the data processing software in 2007, which are similar to BARS (Li et al., 2014). Although acoustic reflection imaging tools are available for nearly a decade (Esmersoy et al., 1998; Tang, 2004; Pistre et al., 2005; Hirabayashi et al., 2010), some problems still exist. The most difficult one is to extract the very weak reflection from the dominant borehole-guided signal trains. Stacking and migration of monopole data can enhance the reflection signal, and infer the dip angle of the reflector outside the borehole (Li et al., 2014). The strike direction is usually determined from the dipole data using the different sensitivity of the SH and SV reflections to the azimuth of structure (Tang et al., 2007). Compared with monopole data, however, the amplitude from dipole is much smaller and sensitive to the noise level. In this paper, we propose a new method to determine the strike of the formation bedding outside of the borehole from monopole data. 3 Dimensional finite difference method (3DFD) is employed to simulate large-scale and complex geometrical models for

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305

Fig. 1. Schematic of the acoustic reflection image well logging.

acoustic reflection logging. Both wireline and LWD cases are considered in this study.

2. Features of 3DFD in the study To simulate the 3D wavefield of acoustic reflection logging, a large-scale model and Cartesian coordinate system will be used in the simulations. The staggered grid will be used in the code with second-order accuracy in both space and time domain (Wang et al., 2015). More details about the 3DFD method can be found in Cheng (1994) and Tao et al. (2008). The high-performance absorbing layer boundary method, the Complex Frequency Shifted Perfectly Matched Layer (CFS-PML), is employed to simulate the large-scale model for acoustic reflection logging. By applying the CFS-PML, the reflectivity of the truncated boundary will be less than one in ten thousand and therefore the interfering reflections due to the artificial boundaries can be effectively suppressed.

3. Simulations of acoustic reflections with 3DFD Firstly, the acoustic reflection data are simulated by 3DFD. For the cases of acoustic wave in a fluid-filled borehole surrounded by a formation (formation I in Table 1) without a reflection, a discrete wavenumber integration method (DWM) (Cheng and Toksoz, 1981) simulations are performed to benchmark the results from 3DFD. The parameters and geometry of the models are shown in Table 1. For the wireline case, a point source and azimuthal array receivers are located in the center of the borehole with radius of 10 cm. The radius of the borehole in the ALWD case is 11.7 cm. Radius of the inner and outer edges of the drill collar are 2.7 cm and 9 cm, respectively. The ring source, which consists of 36 point sources, and array receivers are embedded on the outer edge of the drill collar (Fig. 1). The point source and ring source are used as monopole sources in the wireline case and LWD case, respectively. The configuration of borehole for ALWD can refer to Fig. 1 in Wang and Tao (2011). The grid size in the 3DFD is 5 mm and 3 mm for

Table 1 Parameters for the borehole models.

Borehole fluid Collar Outer fluid Formation I Formation II

Vp (m/s)

Vs (m/s)

Density (g/cm3)

1470 5860 1470 4500 3000

– 3300 – 2650 1800

1.00 7.85 1.00 2.40 2.00

Vp and Vs are the velocity of compressional and shear wave, respectively.

wireline and ALWD simulations, with time step size of 5
10  7 s and 2.5
10  7 s. The PML thickness is 10 grid cells in the simulations. The grid size, time step size and PML thickness will not be changed in the following study. The comparisons of the results from both 3DFD and DWM for non-reflection model (only formation I exists outside the borehole ) are shown in Fig. 2, in which Fig. 2(a) and (b) are simulation results at 10 kHz for monopole cases in wireline and ALWD, respectively. From these comparisons, it can be seen that the 3DFD and DWM are in very good agreement in these cases and show only very small divergence due to the numerical dispersion of 3DFD. These results demonstrate the validity and applicability of our 3DFD source code in studies of acoustic wireline and LWD logs.

4. Acoustic reflection imaging log of a formation interface away from borehole for wireline monopole case The size of the model is 5.5 m (x)
0.6 m (y)
15 m (z). The fluid-filled borehole with radius of 10 cm is located at x ¼1 m, y¼0.3 m and parallel to z direction. The angle between the borehole axis and the normal of the interface between formation I (around borehole) and formation II (far away from borehole) is 85°, which means the dip of the interface is 5°. The interface with azimuth angle of 0° and strike of 0° intersects with x-axis at (4.8 m, 0 m, and 0 m). Here the strike means the angle between y axis and the interface (anti-clockwise). The top view of the model as shown in Fig. 3 illustrates the geometry of the model. In the figure, the strike α and the azimuth θ are anti-clockwise angles

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Fig. 2. Comparisons for 3DFD and DWM in acoustic logging model (a) waveform of monopole measurements with the source central frequency of 10 kHz; (b) waveform of LWD monopole measurements with the source central frequency of 10 kHz.

Fig. 3. Schematic diagrams of the formation interface model. In the figure, angles α and φ are the strike and azimuth of the reflector. The strike of the reflector would change with rotation around its symmetric axis in the study. Azimuth receivers, which are numbered as 1, 2, and 3, and so on, are also shown in the figure to describe the azimuth angle of the reflector.

relative to the y axis and x axis, respectively. In this study, we will change the strike of the reflector with rotation around its symmetric axis. Simulations on the acoustic reflection image logging for the formation interface with different strikes (0, 30 and 45°) are done here. Azimuth receivers, which are numbered as 1, 2, 3, and so on, are also shown in the figure to describe the azimuth angle of the reflector. Here, we could find the relationship between

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the strike and the azimuth, which means the strike equal to the azimuth. The monopole source is a Ricker wavelet of 10 kHz with excitation amplitude of 1
104 and locates at (1 m, 0.3 m, 0.835 m). Fig. 4 shows the array full waveform (Fig. 4a) and reflections in the array receivers in the borehole (Fig. 4b) (strikes of 0°) with maximum amplitude of Stoneley wave of about 3
106. The centralized point source and array receivers are used here. The reflections are the difference between the full waveform and modes in the same size model, in which the modes are from the model without interface. In the wave propagation of the reflection image logging, the leaky energy from the borehole traveling as P- and S-wave in the formation will be reflected back into the borehole or be refracted after they meet the geological structure. There are four kinds of reflections and four kinds of refractions. The reflections are P–P reflection, S–S reflection and two kind of converted reflections, P– S and S–P reflections, and the refractions are P–P, P–S, S–P and S–S. The different reflections and refractions will be received according to the relative location of the tool and structures. The four kinds of reflections with maximum amplitude of about 4
104 have a hyperbolic relationship between the arrival time and offset (shown in Fig. 4b). P–P reflection with arrival time between 1.5 ms and 2 ms and S–S reflection with arrival time after 3 ms can be observed clearly. The converted reflections P–S and S–P are located between P–P and S–S, in which the S–P reflection is buried in the

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Fig. 4. Array full waveform (a) with maximum amplitude about 3
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Fig. 5. (a) The top view of the configuration of source and azimuth receivers (10 receivers in azimuth). (b) and (c) are the reflections after subtraction of azimuth receivers at 3 m and 7 m spacing, respectively. The black-, blue-, and red-plot line are the waveforms from the interface case with strikes of 0, 30 and 45°, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

later stretching of the P–S reflection and cannot be discerned. To investigate the sensitivity of monopole data to the strike of the interface, the waveforms in azimuth receivers for different strikes are also given as follows. The configuration of centralized point source and 10 azimuth receivers are shown in Fig. 5a. We define the angle (RAZ) of the receivers relative to the receiver 1 as azimuth of the receiver (as shown in Fig. 5a). The radius of azimuth receivers is 40 mm, which is similar to the radius of the wireline acoustic tool. Here we give the reflections after subtraction of two different spacing to illustrate the effect of strike of interface on the received waveform. Fig. 5b and c are the waveforms of azimuth receivers at 3 m and 7 m spacing, respectively. The two figures are on the same scale of amplitude. In the two figures, the black-, blue-, and red-plot lines are the waveform from the interface case with strikes of 0, 30 and 45°, respectively. It is evident that the S–S reflection dominates in the waveforms at the spacing of 7 m, which tells us further that the suitable spacing would be helpful for the usage of some reflection (especially for S– S reflection). From Fig. 5b and c, we also find that the arrival time of the head wave for the large strike of the interface would be much later than that of a small strike case. Fig. 6a and b show the reflections at azimuth receivers for strikes of 0° at 3 m (for P–P head wave) and 7 m (for S–S head wave) spacing, respectively. Fig. 6c–f are the corresponding waveforms at two different spacings of the strikes of interfaces of 30 and 45°. According to the relationship between locations of the azimuth receivers and the place of the reflector, the difference of the arrival time of the reflections should exist among different azimuth receivers. For the strike of 0°, the corresponding arrival time of the waveforms in sequence are R1, R2, R3, R10, R4, R9, R5, R8, R7, and R6. We also find that some changes appear in the arrival time of the head waves with an increase of the strike of the interface. Some details are as follows: the differences of the arrival time between R1 and R2, R10 and R4, R9 and R5, and R7 and R6 get smaller and smaller for both near (3 m) and far (7 m) spacings. In particular, the arrival time of the head wave in R4, R5, and R6 would be ahead of that in R10, R9 and R7 for the large strike case (e.g. 45° case) respectively. Therefore, we expect phase difference between receiver pairs to be helpful for the determination of the strike of the interface (Wang et al., 2013). According to the location of azimuth receivers shown in Fig. 5a, we could get the phase difference of the head reflections between R1 and other receivers. Follow Wang et al. (2013), we can the formulation for phase difference between receiver i and j: Δψij(ω)¼ [ψi(ω)  ψj(ω)]/2, in which the phase

could be obtained by ψ(ω) ¼tan  1[imag(W(ω))/real(W(ω))], and W(ω) is the Fourier transform of the signal w(t). The frequency spectrums of reflection waveforms in 3 m spacing for the strike of 0° case are shown in Fig. 7a. We find the main frequency of reflections under the concentrated distribution area of between 8 kHz and 20 kHz. Here we choose a frequency range from 8 kHz to 15 kHz as a display area for phase difference for all the strike cases. Fig. 7b shows the phase difference between R1 and R2 for different strike of the interface. We similarly display the phase differences between R1 and R3, R1 and R10, R1 and R4, R1 and R9, R1 and R5, R1 and R8, R1 and R7, R1 and R6. From Fig. 7, we can tell the effects of the strikes of the interfaces on the phase differences of different receiver pairs. Obviously, the receiver pairs chosen here are not the most suitable pairs. More work should be focused on the data processing for choosing suitable receiver pairs. However, we can conclude that the strike of the interface can be determined by the phase difference between waveforms in different receiver pairs.

5. Acoustic reflection imaging log in LWD of a formation interface away from borehole for LWD monopole case Development of the acoustic reflection logging in LWD case can pave the way for geo-steering, the most advanced technology of logging. Nakken et al. (1995) had proposed a geo-steering system with one transmitter and two receivers, in which the center frequency of the source is between 1 kHz and 4 kHz and the depth of investigation is about 20 m away from the borehole. We now apply the 3DFD to study the acoustic reflection responses of an interface away from the borehole model. The model is the same as the interface model in the wireline case, with only a little difference existing in the borehole with the collar occupied. The parameters of the medium are given by Table 1. The top view of the ring sources and the configuration of 36 azimuth receivers are shown in Fig. 7a. The simulation result for the strike of 0° of the interface is given here first. The wave traces with the maximum amplitude of ST wave of 2.7
105 from the receivers 1 (R1) and 24 (R24) are shown in Fig. 8. Very little difference can be discerned from the full waveform plot. Therefore, we only need to show the full waveform of the R1 here to illustrate the arrivals. It can be seen from Fig. 8b that the three obvious events in the array waveform are collar wave, S wave and Stoneley (ST) wave, respectively. Fig. 8c and d display the reflections with the maximum amplitude of 700 for R24 and R1 with the arrival time of the

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Fig. 6. (a), (c) and (e) are the reflections from azimuthal receivers in 3 m spacing for the strikes of the interfaces of 0, 30 and 45°, respectively; (b), (d) and (f) are the waveforms from azimuthal receivers in 7 m spacing for strikes of the interfaces of 0, 30 and 45°, respectively.

reflections of R24 marked, respectively. The P–PP and S–S reflections are very clear in the array reflections. However, the converted reflection S–P is buried in the later part of the P–S and therefore hard to distinguish. The amplitude of reflections is variable, with offset (spacing) from the array reflections. In particular, we could get the S–S reflection with maximum amplitude by choosing a suitable spacing, which will be helpful for the extracting of the S–S reflection from the full waveform. Additional information can be derived if we compare the reflections in the wireline and LWD cases. There is nearly only one circle in each reflection waveform in the LWD case while there are about 6–8 circles in the wire line case. The fewer oscillations there are, the less interference there would be with the quality of imaging process. By frequency analysis (as shown in Fig. 9) we find that there are two peaks in the spectrum of the reflections in the wireline case:

one is at about 17 kHz, and the other is at about 9 kHz. However, most of the frequency of the reflections in LWD is less than 8 kHz, which indicates that the depth of investigation by the reflection logs in LWD case is deeper than that in wireline case. On the other hand, although the absolute amplitude of the reflection in wireline case is less than that in LWD case, the relative amplitude or reflectivity of the wireline case is larger than the LWD case, which implies the difficulty for exacting reflections from the LWD case. Form Fig. 8, we see that the arrival times of the reflections in R1 are obviously earlier than those in R24. This kind of difference of arrival time in different azimuth receivers is clearer than that in wireline cases, which illustrates the phase differences between different receiver pairs would be more suitable for the determination of the azimuth of the interface in LWD case. The phase difference method is also expected to be useful for the determination of the strike of the interface by choosing

H. Wang et al. / Journal of Petroleum Science and Engineering 133 (2015) 304–312

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Fig. 7. (a) Frequency spectrum of waveforms in azimuthal receivers at 3 m spacing, (b) (j) phase difference of waveforms for different strike cases at 3 m spacing between R1 and R2, R1 and R3, R1 and R10, R1 and R4, R1 and R9, R1 and R5, R1 and R8, R1 and R7, R1 and R6, respectively.

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Fig. 8. The full waveform with the maximum amplitude of ST wave of 9
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suitable receiver pairs. Here we show the phase differences between different receivers and receiver 1 with different strikes of interface changing. Only some examples are shown here in Fig. 10, which are the phase differences of the R1 and R6, R1 and R10, R1 and R13, R1 and R18, R1 and R24, R1 and R27, R1 and R31, R1 and R34. From Fig. 10, we could also consider that although the phase differences are expected to be helpful for the determination of the strikes of interface, the inconspicuous characteristic of the phase difference between receiver 1 and other receivers cannot tell the

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6. Conclusions In the paper, we apply the 3DFD method to simulate the acoustic reflection image logging for both wireline and LWD cases with a tilted interface at different strikes away from borehole. From the the simulation results, the main conclusions and

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strikes clearly and the more suitable receiver pairs should be chosen by much more studies.

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Fig. 9. The comparison of the reflections from wireline and LWD cases. (a) The reflections; (b) the frequency spectrum.

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Frequency (kHz)

4

6

8

10

12

14

16

18

20

Frequency (kHz)

Fig. 10. (a)  (h) Phase difference of waveforms for different strike cases at 3 m spacing between R1 and R6, R1 and R10, R1 and R13, R1 and R18, R1 and R24, R1 and R27, R1 and R31, R1 and R34, respectively.

suggestions are as follows:

 The configuration of azimuth receivers is sensitive for the strike of the structure away from borehole.

 Arrival time of reflections in different azimuth receivers of monopole tool is different, from which we can tell the strike of



the reflector and the phase difference of the waveform in different receiver pairs will be helpful for the determination of the strike of the reflect structure; Acoustic reflections in LWD case have advantages of deeper depth of investigation and higher resolution for imaging of the structures away from borehole.

H. Wang et al. / Journal of Petroleum Science and Engineering 133 (2015) 304–312

312

 Further works will focus on the choosing of suitable receiver pairs for the determination of strike and complex drilling environments, such as off center tool.

Acknowledgments This study is supported by, NSFC (nos. 41174118 and 41404100), a China Post-doctoral Science Foundation (no. 2013M530106) and The International Postdoctoral Exchange Fellowship Program.

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