The wavefield of acoustic logging in a cased-hole with a single casing – Part I: a monopole tool

The wavefield of acoustic logging in a cased-hole with a single casing – Part I: a monopole tool SUMMARY The bonding quality of the seal formed by the cement or collapse material between casing and formation rock is critical for the hydraulic isolation of reservoir layers with shallow aquifers, production and environmental safety, and plug and abandonment issues. Acoustic logging is a very good tool for evaluating the condition of the bond between different interfaces. The understanding of the acoustic logging wavefields in wells with single casing is still incomplete. We use a 3-D finite difference method to simulate wireline monopole wavefields in a single cased borehole with different bonding conditions at two locations: (1) between the cement and casing and (2) between the cement and formation. Pressure snapshots and waveforms for different models are shown, which allow us to better understand the wave propagation. Modal dispersion curves and data processing methods such as velocity–time semblance and dispersion analysis facilitate the identification of propagation modes in the different models. We find that the P wave is submerged in the casing modes and the S wave has poor coherency when the cement is replaced with fluid. The casing modes are strong when cement next to the casing is partially or fully replaced with fluid. The amplitude of these casing modes can be used to determine the bonding condition of the interface between casing and cement. However, the limited variation of the amplitude with fluid thickness means that amplitude measurements may lead to an ambiguous interpretation. When the cement next to the formation is partially replaced with fluid, the modes propagate in the combination of steel casing and cement and the velocities are highly dependent on the cement thickness. However, if the cement thickness is large (more than 2/3 of the annulus between casing and rock), the arrival time of the first arrival approximates that of the formation compressional wave when cement is good. It would highly likely that an analyst could misjudge cement quality because the amplitudes of these modes are very small and their arrival times are very near to the formation P arrival time. It is possible to use the amplitude to estimate the thickness of the cement sheath because the variation of amplitude with thickness is strong. While the Stoneley mode (ST1) propagates in the borehole fluid, a slow Stoneley mode (ST2) appears when there is a fluid column in the annulus between the casing and formation rock. The velocity of ST2 is sensitive to the total thickness of the fluid column in the annulus independent of the location of the fluid in the casing annulus. We propose a full waveform method, which includes the utilization of the amplitude of the first arrival and also the velocity of the ST2 wave, to estimate the bonding condition of multiple interfaces. These two measurements provide more information than the current method that uses only the first arrival to evaluate the bonding interfa next to the casing. Defects, Downhole methods, Numerical modelling, Guided waves, Wave propagation 1 INTRODUCTION The condition of the bond in a cemented cased well is very critical to borehole integrity. It affects the production efficiency as well as production and environmental safety (Lecampion et al.2011). It is thus essential to accurately evaluate the material bonding behind casing. In a single cased hole, there are two bonding interfaces, bonding interface I: interface between the casing and material next to the casing, bonding interface II: interface next to the formation. The methods for cement bonding evaluation are most often applied at these two bonding interfaces. Acoustic wireline logging methods, including the sonic at around 20 kHz source frequency (Pardue et al.1963; Eyl et al.1991; Zhang et al.2011; Haldorsen et al.2016a; Wang et al.2016a) and ultrasonic at around a few hundred kHz source frequency (Hayman et al.1991; Viggen et al.2016) are the most commonly used methods for evaluating the cement bonding condition and they are widely used during the well construction. The interpretation of the acquired data is designed for material evaluation behind single casing strings. Currently, the most commonly used sonic method in the industry is cement bond logging (CBL), in which the attenuation factor is measured from the first arrival amplitude only, whereas variable density logging (VDL) uses the amplitude of the full waveform (Walker 1968). Sonic data are usually combined with the ultrasonic methods to estimate the cement bonding condition, especially when evaluating for gas invasion (Schlumberger 1989).The interpretation of sonic data uses the relationship between the amplitude of the casing wave and the fluid column thickness (e.g. Jutten & Corrigall 1989; Liu et al.2011; Tang et al.2016), and the time of the first arrival (Zhang et al.2011). The attenuation value is also inversely proportional to the azimuth cement coverage (Song et al.2013). Measurements made on the first arrival can be ambiguous because it often has small amplitude. In particular, if interface I is not cemented, the CBL/VDL cannot tell the bonding condition of interface II. Although the newly developed pitch-catch method at the ultrasonic frequency range (He et al.2014; Viggen et al.2016; Wang et al.2016a) show the possibility to evaluate the bonding condition at interface II, it is still challenged by eccentering of the casing and roughness of the interface (van Kuijk et al.2005; Haldorsen et al.2016b). To improve methods for evaluating cement integrity, it is useful to study the sonic wavefields in the single casing situation to determine the possibility of evaluating the bonding condition by using full waveforms rather the currently used time of first arrival method (Zhang et al.2011) or first arrival amplitude (Jutten & Corrigall 1989; Liu et al.2011; Song et al.2013; Tang et al.2016). Although a number of studies have been conducted for single casing strings (e.g. Tubman et al.1984; Zhang et al.2016), the understanding of the sonic wavefields in the single casing model is still incomplete. Because the 3-D finite difference (3DFD) method can conveniently simulate the complex geometry of the cased hole (such as eccentered tool and casing) and also can help us understand the dynamic wave propagation, we use a 3DFD method (Wang et al.2015) to simulate the monopole wavefields in single cased borehole models with different bonding conditions. We investigate the different modes propagating in the borehole in the wireline environment by analysis of the simulated 3-D wavefield records. By using data processing methods, we attempt to identify a relationship between fundamental mode propagation and the condition of the cement bonds. 2 METHOD AND MODELS Although analytical or semi-analytical methods can get accurate solutions for simple models, they cannot get the solutions for models with complicated geometries. For complex models such as having tool and casing eccentering, azimuthal variation in the replacement of cement with fluid, we must appeal to numerical methods such as 3DFD. We use the 3DFD code that has previously been used by Wang et al. (2015) to simulate wave propagation in boreholes with a single casing string. The code is second order in both space and time, which allows reliable results even for models that have high impedance contrast between fluid and solid. Prior to using our 3DFD code, we must confirm its reliability for modelling situations where the steel casing is present in the model. Our single cased borehole model consists of multiple concentric cylinders. The innermost cylinder is the borehole fluid and the second is the steel casing. The outermost cylinder is the formation (e.g. sandstone in Table 1). An industry standard $${9{^{5}}\!/\!{_{8}}}$$ inch (1 inch = 2.54 cm) casing is used in the model, where the casing thickness is 14 mm. The material filling the cylinder between the casing and formation is cement. The cement may be partially or fully replaced with fluid. Table 1 lists the geometries and elastic parameters of an example fully cemented cased hole (shown in Fig. 1). In this study, we only change the geometry and filling material of the cement cylinder to investigate the effect of different bonding conditions on full waveforms. Figure 1. View largeDownload slide A cased well model with good bonding. (a) Side view. (b) Top-down view. Figure 1. View largeDownload slide A cased well model with good bonding. (a) Side view. (b) Top-down view. Table 1. Elastic parameters for the model used in our study. Medium  Vp (m s−1)  Vs (m s−1)  Density (kg m−3)  Radius (mm)  Fluid  1500  0  1000  108  Steel  5500  3170  8300  122  Cement  3000  1730  1800  170  Sandstone  4500  2650  2300  300  Medium  Vp (m s−1)  Vs (m s−1)  Density (kg m−3)  Radius (mm)  Fluid  1500  0  1000  108  Steel  5500  3170  8300  122  Cement  3000  1730  1800  170  Sandstone  4500  2650  2300  300  View Large For the code validation, we investigate the case of sonic logging in a hole in which the cement outside the steel casing is completely replaced by fluid. A ring source is approximated by 36 point sources embedded on the outer boundary of the casing. Although the source loading is different from that for sonic logging in a cased hole, which is a centralized source in the inner fluid, we choose this model because we can easily generate validation waveforms using the Discrete Wavenumber integration method (DWM; Byun & Toksöz 2003) that has been further developed for an ALWD model (Wang & Tao, 2011; Wang et al.2015). We use a 10 kHz Ricker wavelet as a monopole source, because the wide frequency range of the Ricker wavelet includes the frequency band of the most common sonic logging tools. Although the centre frequency of the CBL is 20 kHz, the ST wave is most strongly excited at frequencies lower than 10 kHz (Wang et al.2015), and the 10 kHz Ricker wavelet includes this frequency range. Fig. 2 shows the simulations obtained using both 3DFD and DWM. The grid sizes of 1 mm in x and y, and 2 mm in z directions are used in the 3DFD code. The array waveforms (Fig. 2a) show a nearly perfect match between the FD and DWM excepting the difference that appears in the later part of the waveform (after 1 m s) due to the numerical dispersion of FD in the z direction. This late-arriving mode corresponds to the ST (Stoneley) wave propagating in the fluid column between casing and formation (marked as ST2). More explanation of the ST2 will be presented in Figs 3 and 4. The casing mode, S and pR (pseudo Rayleigh) and ST1 (Stoneley in the fluid column inside the steel casing) waves can be easily found and are identified with lines marked according to their arrival times and in the velocity–time semblance plot (Fig. 2b). Figure 2. View largeDownload slide Comparison between the 3DFD and DWM simulations in a free casing model: (a) array waveforms; (b) velocity–time semblance plot for the array waveforms in (a). Figure 2. View largeDownload slide Comparison between the 3DFD and DWM simulations in a free casing model: (a) array waveforms; (b) velocity–time semblance plot for the array waveforms in (a). Figure 3. View largeDownload slide (a) X–Z profile of the model: (a) Single casing model with a perfect cement bond. Colours blue, red, light blue and orange are fluid, steel casing, cement and formation, respectively. Source position is marked with a yellow dot. Pressure snapshots for situations where the (b) cement is perfectly bonded, (c) free casing and (d) casing immersed in fluid. Figure 3. View largeDownload slide (a) X–Z profile of the model: (a) Single casing model with a perfect cement bond. Colours blue, red, light blue and orange are fluid, steel casing, cement and formation, respectively. Source position is marked with a yellow dot. Pressure snapshots for situations where the (b) cement is perfectly bonded, (c) free casing and (d) casing immersed in fluid. Figure 4. View largeDownload slide (a) Waveforms acquired on a centralized receiver array for a centralized point source in a borehole with a casing that is surrounded by fluid. (b) Frequency–velocity semblance plot made from (a) and modal dispersion curves calculated for the model. (c) and (d) are the calculated modal dispersion curves for casing with of varying inner (IR) and outer (OR). Figure 4. View largeDownload slide (a) Waveforms acquired on a centralized receiver array for a centralized point source in a borehole with a casing that is surrounded by fluid. (b) Frequency–velocity semblance plot made from (a) and modal dispersion curves calculated for the model. (c) and (d) are the calculated modal dispersion curves for casing with of varying inner (IR) and outer (OR). 3 NUMERICAL SIMULATIONS Here we use our 3DFD simulator to investigate the full waveforms and wave propagation characteristics by examining wavefield snapshots for three different models: (1) casing immersed in fluid, (2) free casing in a borehole and (3) perfect cement bonding between casing and formation. For the model with the casing immersed in a fluid, the cement and formation are completely replaced with fluid. We use this model to understand the modes propagating in the casing. For the free casing model, only the cement between casing and formation rock is replaced with fluid. In the simulations, the effect of the tool is ignored and a centralized point source with 10 kHz Ricker wavelet is used. Fig. 3(a) shows side views of the borehole model with good cement between casing and formation. The pressure snapshots at 1.0 ms on an x–z profile are shown in Fig. 3(b) (good bond), Fig. 3(c) (free casing) and Fig. 3(d) (casing immersed in fluid). Fig. 3(d) can help us understand the modes in the casing. As has been shown in non-destructive testing, there are three types of guided wave in casings: L (longitudinal), F (flexural) and T (torsional) modes (Cawley et al.2002; Edwards & Gan 2007). T modes are associated with pipe rotation and would be found in the drilling pipe. L modes are monopole modes in the casing that axis-symmetrically expand and contract the casing. They are similar to the extensional modes in the collar in acoustic logging-while-drilling (Wang et al.2016b, 2017). F modes are dipole or quadrupole (or even higher order) modes in the casing that are similar to the flexural, or screw modes on the collar in acoustic logging-while-drilling. Here we find casing modes (L modes) at offsets of about 1.5 to 4 m while the ST wave follows and both modes leak into the region both inside and outside of the casing as leaky modes that can be seen in Fig. 3(d). We use a dense receiver array with a 0.1 mm interval to record the waveforms from the source position to the top of the model along the z axis to understand the wave modes. Fig. 4(a) shows an example for the case of casing immersed in fluid. We find three visible modes as marked with lines. Comparing the extracted frequency–velocity semblance contour plot (Rao & Toksöz 2005; Wang et al.2015) from the array waveforms with the calculated modal dispersion curves shown as solid lines (Tubman et al.1984; Zhang et al.2016) in Fig. 4(b), we find that the modes seen in the waveforms are the casing modes (L1–L5), ST1 and an additional ST2 (slow ST in Plona et al.1992). Although the ST2 mode mainly propagates outside of the casing, it penetrates the casing and can be received in the inner fluid column due to its low frequency. To investigate the properties of the ST2 wave in more detail, Figs 4(c) and (d) show the modal dispersion curves for various inner or outer radii of the casing. It can be seen that increasing the outer radius (labelled as OR in the plots) causes the L modes to shift slightly towards lower frequency (Fig. 4c). The velocity of the ST2 mode increases with increasing outer radius thus reducing the difference in velocity of ST1 and ST2 (Fig. 4c). Decreasing the inner radius moves the L modes to higher frequency (Fig. 4d). At the same time the velocity of the ST2 wave becomes larger. We infer that increasing outer and decreasing inner radii, which are equivalent to increasing the thickness of the casing, will increase the ST2 wave velocity and reduce the phase velocity gap between the two ST waves. Another issue that should be noted is that effect of changing the inner radius is stronger than that of changing the outer radius. Generally, the ratio between the inner radius and casing thickness affects the ST2 wave velocity, where the smaller ratio generates a larger velocity. Other modes including P, S and pR (pseudo Rayleigh) modes are marked in Figs 3(b) and (c). Although the wave front of the casing modes propagate the fastest in the pressure snapshots, the modes do not leak and are trapped in the casing when the casing is well cemented, which makes them invisible both in the borehole and formation (as shown in Fig. 3b). The formation P and S waves can be detected by a centralized array receiver. However, the casing mode leaks into the fluid when the cement coupling is not good as seen in the free casing model shown in Fig. 3(c). In this situation, the first arrival in the borehole is the strong leaky casing mode and the formation P wave is submerged within the multiple order casing L modes. Thus the formation P wave is hardly discerned in the borehole fluid when cement is poor. Fig. 5 shows the array waveforms obtained from a centralized receiver in the models (displayed the same way as Fig. 4a) and the related velocity analysis in the time (Kimball & Marzetta 1986) and frequency domains. Figs 5(a)–(c) are for the well cemented cased hole. The waveforms have a time sequence of P, S, pR, ST and pR modes in Fig. 5(a). Several pR modes appear and they propagate at different velocities. The waveforms at offsets of 3–3.7 m (interval of 0.1 m) are used for calculating velocity–time semblance (Fig. 5b) and dispersion (Fig. 5c). From the plots, we discern the P, S, multiple orders of pR, and ST modes, respectively. For the case where the cement is completely replaced with fluid, Fig. 5(d), the waveforms are very different from the case where good cement is present. The wave modes in time sequence are casing L, a rather poorly discerned S (Paillet & Cheng 1991), clear ST, and the strongly dispersive pR waves. Figure 5. View largeDownload slide (a) Waveforms acquired in a well cemented cased hole with a centralized receiver array and a centralized point source located in the borehole fluid (b) time–velocity plot, (c) frequency–velocity plot. (d)–(f) are the same as (a)–(c) except for the case where cement is completely replaced with fluid. Figure 5. View largeDownload slide (a) Waveforms acquired in a well cemented cased hole with a centralized receiver array and a centralized point source located in the borehole fluid (b) time–velocity plot, (c) frequency–velocity plot. (d)–(f) are the same as (a)–(c) except for the case where cement is completely replaced with fluid. The phase velocities of the casing L modes, S, and ST waves can be obtained from the velocity analysis of the waveforms in both the time (Fig. 5e, method described in Kimball & Marzetta 1986) and frequency (Fig. 5f, method described in Rao & Toksöz 2005) domains. It is obvious that there are two ST modes in Fig. 5(f) corresponding to an ST inside the casing with a higher velocity and an additional ST in the fluid column between casing and formation. The additional ST mode is similar to the one found in the vertical seismic profile (VSP) data such as in Marzetta & Schoenberg (1985) and Daley et al. (2013) that is not present when there is good cement between the casing and formation. For sonic logging data in a cased hole, the additional ST2 mode can also be found in some published field data such as in Haldorsen et al. (2016a). However, this additional mode is not clearly visible when the source frequency is around 10 kHz. To investigate the influence of the source frequency on the amplitudes of different modes in the model with fluid replacing cement, we plot the simulated waveforms obtained at different source frequencies in Fig. 6. Modes are marked in the plots according to their arrival times. It is easy to find the relationship between the source frequency and the amplitude of modes. The casing mode is weak below 3 kHz. We get much more obvious ST modes at low frequency. However, if the frequency is below 3 kHz, we cannot identify ST2 wave from the waveforms because of its large wavelength at low frequency. According to Figs 5(f) and 6, we find that if the source frequency is set at around 6 kHz, it is easy to distinguish the two obvious ST modes. Figure 6. View largeDownload slide Waveforms at different source frequencies in the free casing model. (a) Normalized waveforms (normalized by waveform amplitude at 2 kHz) at source frequency from 2 to 5 kHz; (b) normalized waveforms (normalized by waveform amplitude at 6 kHz) at source frequency from 6 to 10 kHz. Figure 6. View largeDownload slide Waveforms at different source frequencies in the free casing model. (a) Normalized waveforms (normalized by waveform amplitude at 2 kHz) at source frequency from 2 to 5 kHz; (b) normalized waveforms (normalized by waveform amplitude at 6 kHz) at source frequency from 6 to 10 kHz. 4 PARTIALLY BONDED MODELS Based on the dispersion curves and waveforms for the free casing model, we find the newly identified ST2 mode that provides another way to distinguish whether there is good versus bad cement behind the casing. In the following sections, we discuss the wavefields of the partially cemented models to determine the possibility of evaluating the bonding condition by using full waveforms including the current method based on the first arrival (e.g. Walker 1968; Zhang et al.2011) and the phase velocity of the ST2 wave. By investigating the detail of the wavefields for models with different thicknesses of fluid and cement, we hope to get a direct method to determine the bonding condition including that between the outer casing interface and the formation by using data acquired by a commonly used array acoustic logging tool with a source having sonic frequencies (e.g. Zhang et al.2011). 4.1 Fluid between steel casing and cement We first consider models in which some of the cement next to the casing (bonding interface I) is replaced with fluid. Fig. 7 shows a schematic diagram (top-down view) of a partially cemented borehole model. R1, R2, RCI and Rh are the inner radii of the casing, fluid column, cement and borehole wall. The fluid thickness is equal to RCI–R2. With R2 of 122 mm (Table 1), we investigate the wavefields in the models with RCI of 122, 122.5, 123, 124, 126, 130, 138, 154, 162 and 170 mm, which correspond to the models with fluid thickness of 0 (fully cemented), 0.5, 1, 2, 4, 8, 16, 32, 40 and 48 mm (no cement) next to the casing. Figure 7. View largeDownload slide Schematic diagrams (top-down view) of a partially cemented borehole model (bad bonding for interface I). R1, R2, RCI and Rh are the inner radii of casing, fluid column, cement and borehole wall. The fluid thickness is equal to RCI—R2. R1, R2 and Rh are given in Table 1. Figure 7. View largeDownload slide Schematic diagrams (top-down view) of a partially cemented borehole model (bad bonding for interface I). R1, R2, RCI and Rh are the inner radii of casing, fluid column, cement and borehole wall. The fluid thickness is equal to RCI—R2. R1, R2 and Rh are given in Table 1. We calculate the modal dispersion curves for the models and find that they vary with the fluid thickness for the ST2 and casing modes (as shown in Fig. 8) while other modes such as ST1 and pR have no change. Fig. 8(a) shows the dispersion curves for ST2 with various fluid thicknesses. We find that the ST2 mode is very sensitive to the fluid thickness. The velocity of ST2 increases with the fluid thickness. This means that the ST2 wave velocity could be a good indicator for cement bond evaluation. Figure 8. View largeDownload slide Dispersion curves of ST2, L and pR modes with various fluid thicknesses between casing and cement (bonding interface I). (a) ST2 modes, fluid thicknesses are marked; (b) L and pR modes, the legends for different lines are given and the black dot lines are the free bonding case (the fluid thickness of 48 mm). Figure 8. View largeDownload slide Dispersion curves of ST2, L and pR modes with various fluid thicknesses between casing and cement (bonding interface I). (a) ST2 modes, fluid thicknesses are marked; (b) L and pR modes, the legends for different lines are given and the black dot lines are the free bonding case (the fluid thickness of 48 mm). There is very small difference in velocity of the L modes with fluid thicknesses (shown in Fig. 8b). The black dotted lines, denoting the modes in the free casing model (the fluid thickness of 48 mm), are almost the same as the modes in the cases with partial cement except at the inflection points at lower frequencies (marked with a solid line) for different L modes. These small variations are very hard to observe from field data because it would require a high performance dispersion analysis method having high resolution. We simulate the full waveforms for most of the models (the fluid thickness of 0, 4, 8, 16, 32, 40 and 48 mm) as shown in Fig. 9 (traces for source–receiver spacing of 3 m are shown). In Fig. 9(a), we see the clear casing mode as the first arrival when the cement is partially replaced with fluid. Walker (1968) was the first to give the relationship between the amplitude of the casing modes and the thicknesses of cement sheath. The current methods for cement evaluation are mostly based on his relationship by using the amplitude of the casing modes. However, the small dependence of the amplitude of the first arrival with fluid thickness, shown in Fig. 9(a), challenges the tool design and data processing. The added uncertainty from working in the down-hole environment, such as the limited dynamic range of the acquisition system, the high temperature and high pressure that can adversely impact the electronic components, and the electronic noise, contributes to the difficulty. The P wave is submerged in the casing modes and cannot be discerned. This is similar to the case of P wave measurements in fast-fast formations in acoustic logging-while-drilling situations (Wang et al.2017). The difficult to discern arrival time of S wave makes the S wave velocity measurement difficult when fluid exists next to the casing. The ST1 and ST2 modes are hard to discern due to the strong interference from the pR wave. As we found in Fig. 6, we get a visible ST2 mode when the source frequency is set at around 6 kHz. Fig. 9(b) shows traces that have been filtered using a 5–8 kHz bandpass filter. The arrival times of the ST2 mode at different fluid thicknesses are marked by arrows. The velocity analyses in time and frequency domains (based on the filtered data for the case with the fluid thickness of 16 mm) are given in Fig. 10. Although the waveforms for fluid thickness of 0.5 and 1 mm are not simulated due to computational limitations (the large memory requirements), we are confidential that it is possible to identify the ST2 wave from array waveforms even for fluid thickness below 1 mm. Figure 9. View largeDownload slide Synthetic waveforms for the models with fluid of various thicknesses between the casing and cement (bonding interface I). Traces with source–receiver spacing of 3 m are plotted. (a) Original waveforms; (b) waveforms filtered with a bandpass filter from 5 to 8 kHz. Arrows in the plot show the arrival time of ST2 mode at different fluid thickness cases. Figure 9. View largeDownload slide Synthetic waveforms for the models with fluid of various thicknesses between the casing and cement (bonding interface I). Traces with source–receiver spacing of 3 m are plotted. (a) Original waveforms; (b) waveforms filtered with a bandpass filter from 5 to 8 kHz. Arrows in the plot show the arrival time of ST2 mode at different fluid thickness cases. Figure 10. View largeDownload slide Velocity analysis in time and frequency domains for the synthetic waveforms with the fluid thickness of 16 mm (the spacing between the source and the nearest and furthest receivers are 3 and 3.7 m, respectively, and the axial receiver interval is 0.1 m). (a) Time semblance result; (b) dispersion analysis, the modal dispersion curves are also plotted (dotted lines). Figure 10. View largeDownload slide Velocity analysis in time and frequency domains for the synthetic waveforms with the fluid thickness of 16 mm (the spacing between the source and the nearest and furthest receivers are 3 and 3.7 m, respectively, and the axial receiver interval is 0.1 m). (a) Time semblance result; (b) dispersion analysis, the modal dispersion curves are also plotted (dotted lines). We easily find casing, S and pR, ST1 and ST2 modes from the velocity–time semblance plot (Fig. 10a). However, the separation between the latter two modes is larger than that in the free casing model (Fig. 5e) due to the slower ST2. With the help of the modal dispersion curves (dotted lines in Fig. 10b), the dispersion analysis of the different modes can be easily identified from the contour plot in Fig. 10(b), where the ST modes are clear. The velocity analyses illustrate the possibility of using the later part of the waveform to determine the fluid thickness next to the casing rather than the relatively small amplitude dependence of the first arrival on thickness. If we find casing modes, we can infer that the interface between casing and cement (interface I) is filled with fluid and then we can use the ST2 to determine the thickness of the fluid column. 4.2 Fluid between cement sheath and formation The primary objective of a cement job is to hydraulically isolate the formation and prevent escape of fluids inwards to the borehole annuli avoiding industrial accidents (e.g. Deepwater Horizon on 2010 [Deepwater Horizon Study Group 2011]). This requires that the diagnostic for well integrity must provide the formation sealing status across producing intervals. In this case, the bonding condition at the interface between the cement and formation (bonding interface II) is more important than that at interface I. The current sonic/ultrasonic measurements provide some information about the geometry of defects that can be observed using the range of source frequency. However, validating hydraulic isolation means that one must prove that there is no flow behind the pipe regardless of the type of bonding material including: cement, collapsed formation, formation cracks and barite. In this case, sonic/ultrasonic methods are part of solution rather than a complete solution of the hydraulic isolation question. The current ultrasonic/sonic evaluation methods can be combined with other sources of information to provide more complete information about hydraulic isolation. In this section, we will investigate the possibility of using the sonic method to evaluate the bonding condition at interface II. Fig. 11 shows a schematic diagram (top-down view) of a partially cemented borehole model. R1, R2, RCO and Rh are the inner radii of casing, cement, fluid column and borehole wall, respectively. The fluid thickness is equal to Rh—RCO. We investigate the wavefields in the models with RCO of 170, 169.5, 169, 168, 166, 162, 154, 138, 154, 130 and 122 mm, which correspond to models with the fluid thickness of 0 mm (fully cemented), 0.5, 1, 2, 4, 8, 16, 32, 40 and 48 mm (no cement) next to the formation. Since the dispersion characteristics in the models with fluid next to the formation are similar to those in Fig. 8, where there are fluids at the interface between the casing and cement (interface I), we do not display them. The only difference of the dispersion characteristics from those shown in Fig. 8 is that the L modes have lower speed and the inflection points move to the lower frequency. The reason for the lower velocity of the casing L modes is they propagate in a material consisting of steel casing and cement, which has a lower velocity than the steel casing. The cement next to casing enlarges the effective radius of the casing and moves the inflection points to lower frequencies. The trend of the dispersion curves of these modes is that with more cement, velocity decreases and the inflection point shifts towards lower frequency. We cannot find any difference in dispersion for the mode ST2 from that shown in Fig. 8(a) for the corresponding fluid thickness cases. This suggests that ST2 cannot be used as indicator for the location of where the fluid column exists. However, at a minimum, we can know whether interface II is bonded well by using the arrival time and velocity of the L modes when interface I is boned (Zhang et al.2011). Then we can determine the thickness of the fluid column next to the formation by using the ST2 mode. Figure 11. View largeDownload slide Schematic diagram (top-down view) of a partially cemented borehole model. R1, R2, RCO and Rh are the inner radii of casing, cement, fluid column and borehole wall. The fluid thickness is equal to Rh—RCO. Figure 11. View largeDownload slide Schematic diagram (top-down view) of a partially cemented borehole model. R1, R2, RCO and Rh are the inner radii of casing, cement, fluid column and borehole wall. The fluid thickness is equal to Rh—RCO. We display the full waveforms calculated for different fluid-layer thickness in Fig. 12 in the same manner as Fig. 9. In the detailed display of the waveforms in Fig. 12(c) we see a clear casing mode (a combination of casing and cement modes) as the first arrival between the labelled casing and P arrivals when the cement is partially replaced with fluid. Although the P wave is submerged in the casing mode and cannot be discerned when the fluid column is large, if the fluid column thickness is as small as 4 mm to about 16 mm, or the cement thickness is large, for example above 2/3 of the annulus, the arrival time of the first arrival approximates the formation P wave arrival time for the good cement case. Interpretation of the result from the first arrival method would lead to the incorrect conclusion that cement is good rather than that the condition at interface II is poor. Fortunately, we find a clear ST2 in the waveforms, especially those that have been filtered, which can help us avoid the misinterpretation from the arrival time of the first arrival (Zhang et al.2011). Similar to the case of bonding interface I, we suggest the use of a tool with a large source–receiver spacing to separate the ST2 modes for the thin (4–8 mm) fluid column cases. Figure 12. View largeDownload slide Synthetic waveforms for models with fluid of various thicknesses in front of formation (bonding interface II). Traces having source–receiver spacing of 3 m are plotted. (a) Original waveforms. (b) Waveforms that have been filtered with a bandpass filter from 5 to 8 kHz. (c) Unfiltered waveforms from 0 to 2 ms of (a). Figure 12. View largeDownload slide Synthetic waveforms for models with fluid of various thicknesses in front of formation (bonding interface II). Traces having source–receiver spacing of 3 m are plotted. (a) Original waveforms. (b) Waveforms that have been filtered with a bandpass filter from 5 to 8 kHz. (c) Unfiltered waveforms from 0 to 2 ms of (a). Fig. 13 shows the velocity–time semblance (Fig. 13a) and dispersion analysis (Fig. 13b) contour plots for the case of 16 mm of fluid at interface II. In Fig. 13(a), we clearly find a casing-cement mode with a velocity nearly the same as the P velocity. We also find the S, ST1 and ST2 modes. As mentioned, if we only use the first arrival (amplitude or arrival time) to determine the bonding condition, we will definitely misjudge the bonding condition as indicating very good cement even for the fluid column thickness of 16 mm in front of formation. However, the good coherence for ST2 (from the filtered waveforms in Fig. 12b) in Fig. 13(a) gives us an opportunity to avoid the misjudgement. The dispersion analysis plot in Fig. 13(b) gives us another view for mode identification that can also be used to eliminate the misjudgement. The modal curves (solid lines) for the model with fluid column thickness of 16 mm next to the casing are also plotted to illustrate the difference from Fig. 10(b). We find the dispersion characteristics of pR, ST1, and ST2 are the same as those in Fig. 10(b). The casing-cement modes, which will likely be identified as P waves, have slower velocities than the P wave and the L modes in Fig. 10(b). Figure 13. View largeDownload slide Velocity analysis in time and frequency domains for synthetic waveforms with the fluid thickness of 16 mm calculated using spacing between the source and the nearest and furthest receivers are 3 and 3.7 m, respectively, and an axial receiver interval of 0.1 m. (a) Time semblance result; (b) dispersion analysis, the modal dispersion curves from Fig. 10(b) are also plotted (dotted lines). Figure 13. View largeDownload slide Velocity analysis in time and frequency domains for synthetic waveforms with the fluid thickness of 16 mm calculated using spacing between the source and the nearest and furthest receivers are 3 and 3.7 m, respectively, and an axial receiver interval of 0.1 m. (a) Time semblance result; (b) dispersion analysis, the modal dispersion curves from Fig. 10(b) are also plotted (dotted lines). Our results show that it is necessary to use the full waveform, especially the later part of the waveforms, to estimate the cement bonding condition when a fluid column exists next to the formation. Dispersion analysis is also a good tool to eliminate misinterpretation. In field applications, dispersion analysis may be impractical due to the time it requires. Time semblance would also be helpful because we could get velocity information about the ST2 mode, which can be a very good indicator of bonding condition. 4.3 Cement inside the fluid columns To give more detail about the relationship between the waveforms and the thickness and location of the fluid column and cement sheath, we separate the annulus between casing and formation into three parts with each part being a different medium (cement or fluid) with different thickness. By using this model, we simulate the waveforms in models with cement partially replacing fluid columns both next to the casing and the formation. All the waveforms are shown in Fig. 14(a) and the names for different models are also listed on the waveforms. The letters ‘f’ and ‘c’ are fluid and cement, respectively. The number before the letter is the thickness (units in mm) of the medium. For example, ‘4f16c28f’ means the annulus consists of 4 mm and 28 mm fluid columns next to the casing and in front of the formation, respectively. In addition, a 16 mm thick cement layer is placed between the two fluid columns. The arrival times for different modes are marked by lines. The casing, P, and S waves are expanded and shown in Fig. 14(b). Because a fluid column exists next to the casing, the arrival time of the casing mode is the same independent of the thickness of the fluid column. The amplitude of the casing wave changes a little with the changing thickness of the fluid next to the casing. The current cement bonding evaluation method is based on the relationship between the amplitude of the casing wave and the fluid column thickness (e.g. Jutten & Corrigall 1989; Liu et al.2011; Tang et al.2016). However, this method strongly depends on measurements of the amplitude of the first arrival and could lead to misinterpretation because the amplitude dependence on fluid column thickness is not strong. Another issue is that we cannot infer the bonding condition of the interface between the cement and formation if the cement next to the casing is partially replaced with fluid. Figure 14. View largeDownload slide Waveforms and dispersion analysis for models with cement next to the casing and the formation partially replaced by fluid. (a) Waveforms at 3 m offset. Names for models are listed on the waveforms. The letters ‘f’ and ‘c’ are fluid and ‘cement’, respectively. The number before the letter is the thickness (in mm) of the medium. For example, ‘4f16c28f’ means the annulus consists of 4 mm and 28 mm fluid columns next to casing and in front of formation, respectively. In addition, cement with 16 mm is between the two fluid columns. (b) Frist 2 ms of the normalized waveforms. (c–g) Dispersion analysis plots for the waveforms for different models. The green lines are the dispersion curves for the model (Fig. 7) with a 32 mm fluid column between casing and cement. The black lines are the dispersion curves for models (Fig. 7) with the fluid thickness of 4 mm (c), 8 mm (d), 16 mm (e), 24 mm (f) and 28 mm (g). Figure 14. View largeDownload slide Waveforms and dispersion analysis for models with cement next to the casing and the formation partially replaced by fluid. (a) Waveforms at 3 m offset. Names for models are listed on the waveforms. The letters ‘f’ and ‘c’ are fluid and ‘cement’, respectively. The number before the letter is the thickness (in mm) of the medium. For example, ‘4f16c28f’ means the annulus consists of 4 mm and 28 mm fluid columns next to casing and in front of formation, respectively. In addition, cement with 16 mm is between the two fluid columns. (b) Frist 2 ms of the normalized waveforms. (c–g) Dispersion analysis plots for the waveforms for different models. The green lines are the dispersion curves for the model (Fig. 7) with a 32 mm fluid column between casing and cement. The black lines are the dispersion curves for models (Fig. 7) with the fluid thickness of 4 mm (c), 8 mm (d), 16 mm (e), 24 mm (f) and 28 mm (g). We also find little difference in the ST waves (inside the rectangle in Fig. 14a) with various fluid thicknesses. The dispersion analysis (contour) plots for the waveforms from different models are shown in Figs 14(c)–(g). We do not calculate the modal dispersion curves for the models we simulated here. However, we plot the modal dispersion curves for the model in Fig. 7. The green lines are the dispersion curves for a model (Fig. 7) with a 32 mm fluid column between casing and cement. The black lines are the dispersion curves for a model (Fig. 7) with the fluid thickness of 4 mm (Fig. 14c), 8 mm (Fig. 14d), 16 mm (Fig. 14e), 24 mm (Fig. 14f) and 28 mm (Fig. 14g). It is obvious that the green lines for mode ST2 match the dispersion contour plots for all fluid column thicknesses. This suggests that the ST2 wave can be used to determine the total thickness of the fluid column in the annulus and it is not just sensitive to the fluid thickness next to the casing if there is another fluid column between cement and formation. This may be considered to be a limitation of the application of the ST2 wave. However, it would be a great supplement for the current first arrival amplitude method. We can use the amplitude of the casing wave to determine the fluid thickness next to the casing although sometimes this method will not work very well. We can get the total fluid thickness in the annulus by comparing the velocity or dispersion curves with the modal cases. Then we can know the distribution of the fluid in the annulus. This overcomes the limitation of the current amplitude method on the bonding condition of the interface between cement and formation and can also reduce uncertainty of interpretation. 4.4 Fluid inside cement sheath We also consider models having a fluid column of varying thickness inside the cement sheath that is otherwise well bonded to the casing and formation. Fig. 15 shows the waveforms and dispersion analysis for different models. The placement of the subfigures is the same as Fig. 14. Model names are as described for Fig. 14. Fig. 15(a) shows the full waveforms (3 m offset) for different models and the first 2 ms waveforms are zoomed in and shown in Fig. 15(b). We find that the thickness of cement next to the casing will definitely affect the arrival time (marked by circles in Fig. 15b) and amplitude of the first arrival (the mode propagating in the combined casing and cement of different thickness). As we discussed in the previous section, the arrival time (velocity) method (Zhang et al.2011) will not work well when the cement sheath thickness is large (e.g. 24c16f8c in Fig. 15b). However, the variation in the first arrival amplitude can be easily discerned and this can be used as an indicator for thickness of the cement sheath next to the casing. We find that the ST waves (marked with a rectangle in Fig. 15a) are sensitive to the cement sheath thickness, which means the ST2 wave is not sensitive to the location of the fluid column. The dispersion contour plots are shown in Figs 15(c)–(g) (modal dispersion curves for 16 mm fluid column existing in interface I is plotted with back lines). We find that the dispersion contours of ST2 wave overlap those for the model shown in Fig. 11 (the fluid column thickness of 16 mm). This overlap leads us to infer that the ST2 wave is only sensitive to the fluid thickness not the fluid location. Figure 15. View largeDownload slide Waveforms and dispersion analysis for different models plotted in a manner similar to that in Fig. 14. (a) Waveforms at 3 m offset. (b) First 2 ms of the normalized waveforms. Arrival times of the first arrival are marked with circles. (c–g) Dispersion analysis plots for the waveforms for different models. Figure 15. View largeDownload slide Waveforms and dispersion analysis for different models plotted in a manner similar to that in Fig. 14. (a) Waveforms at 3 m offset. (b) First 2 ms of the normalized waveforms. Arrival times of the first arrival are marked with circles. (c–g) Dispersion analysis plots for the waveforms for different models. 5 FLOW CHART FOR CEMENT BOND EVALUATION USING FULL WAVEFORMS Based on the above investigations of the full waveform for different models, we propose a full waveform method to evaluate the cement bonding condition at different interfaces, where both the first arrival and ST2 wave are used in a combined interpretation. Fig. 16 shows a flow chart of the full waveform method. The data required are the full waveforms and the thickness (D) of the annulus between the casing and the formation rock. Using the wellbore geometry, one calculates the arrival time tc of the casing wave. The first arrival t0 is picked on the waveform and compared to tc. If the two times match, interface I is not well cemented and a further interpretation of the bonding condition at interface II requires a comparison of the calculated fluid thickness (d0) next to the casing from first arrival amplitude A0 and the total fluid thickness in the annulus from the ST2 velocity. If the thicknesses match, the interface II has good cement, otherwise there is another fluid column behind interface I. If the two times do not match, interface I has good cement and the existence of the ST2 phase is determined by performing velocity analysis for the further interpretation. If there is no ST2 phase, the cement is good. If the ST2 phase exists, the amplitude of the first arrival is measured and used to estimate the thickness of cement next to the casing (L1c). If L1c matches the difference between the annulus thickness D and total fluid thickness d2 in the annulus, interface II has poor cement. Otherwise, there is another fluid column between interfaces I and II. In addition interface II probably has poor cement. Figure 16. View largeDownload slide Flow chart diagram of the full waveform cement bonding evaluation method. Figure 16. View largeDownload slide Flow chart diagram of the full waveform cement bonding evaluation method. 6 CONCLUSIONS We have used a 3DFD method to simulate wave propagation from a monopole source in a single cased borehole with different bonding conditions. Pressure snapshots of the wavefields give us a direct way to evaluate wave excitation and propagation for different models. Evaluation of the full wavefield helps improve understanding of the application not only to a single cased hole but also to underwater cables, and oil and chemical pipelines. Data processing methods such as velocity–time semblance and dispersion analysis facilitate the identification of the modes in the different models. Our conclusions are as follows: The formation modes can be easily discerned when the casing is well bonded. However, the P wave is submerged in the casing mode and the S wave has poor coherence when the cement is replaced with fluid. The amplitude of casing L modes can be used to determine the bonding condition of the interface between casing and cement. However, the small variation of first arrival amplitude with thickness of fluid between casing and cement could introduce ambiguity in the interpretation. When using only the arrival time (velocity) of the first arrival, it would be highly likely that the presence of fluid between the casing and the cement would be misjudged as good cement. The amplitude of the first arrival is a much better indicator. The slow Stoneley (ST2) mode can be used to evaluate the total thickness of the fluid column in the annulus no matter where the fluid column is located even when there are two fluid columns. Analysis of the full waveform by combining the first arrival and the slow ST waves can be used eliminate the ambiguity about cement condition and improve cement evaluation reliability compared to the current method using only first arrival measurements. ACKNOWLEDGEMENTS This study is supported by the Founding Members Consortium of the Earth resources Laboratory at MIT. We thank two anonymous reviewers whose comments substantially improved the presentation of our work. REFERENCES Byun J., Toksöz M.N., 2003. 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Astron. , 59( 2), 624301, doi:10.1007/s11433-015-5756-6. https://doi.org/10.1007/s11433-015-5756-6 Google Scholar CrossRef Search ADS   © The Authors 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geophysical Journal International Oxford University Press

The wavefield of acoustic logging in a cased-hole with a single casing – Part I: a monopole tool

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Abstract

SUMMARY The bonding quality of the seal formed by the cement or collapse material between casing and formation rock is critical for the hydraulic isolation of reservoir layers with shallow aquifers, production and environmental safety, and plug and abandonment issues. Acoustic logging is a very good tool for evaluating the condition of the bond between different interfaces. The understanding of the acoustic logging wavefields in wells with single casing is still incomplete. We use a 3-D finite difference method to simulate wireline monopole wavefields in a single cased borehole with different bonding conditions at two locations: (1) between the cement and casing and (2) between the cement and formation. Pressure snapshots and waveforms for different models are shown, which allow us to better understand the wave propagation. Modal dispersion curves and data processing methods such as velocity–time semblance and dispersion analysis facilitate the identification of propagation modes in the different models. We find that the P wave is submerged in the casing modes and the S wave has poor coherency when the cement is replaced with fluid. The casing modes are strong when cement next to the casing is partially or fully replaced with fluid. The amplitude of these casing modes can be used to determine the bonding condition of the interface between casing and cement. However, the limited variation of the amplitude with fluid thickness means that amplitude measurements may lead to an ambiguous interpretation. When the cement next to the formation is partially replaced with fluid, the modes propagate in the combination of steel casing and cement and the velocities are highly dependent on the cement thickness. However, if the cement thickness is large (more than 2/3 of the annulus between casing and rock), the arrival time of the first arrival approximates that of the formation compressional wave when cement is good. It would highly likely that an analyst could misjudge cement quality because the amplitudes of these modes are very small and their arrival times are very near to the formation P arrival time. It is possible to use the amplitude to estimate the thickness of the cement sheath because the variation of amplitude with thickness is strong. While the Stoneley mode (ST1) propagates in the borehole fluid, a slow Stoneley mode (ST2) appears when there is a fluid column in the annulus between the casing and formation rock. The velocity of ST2 is sensitive to the total thickness of the fluid column in the annulus independent of the location of the fluid in the casing annulus. We propose a full waveform method, which includes the utilization of the amplitude of the first arrival and also the velocity of the ST2 wave, to estimate the bonding condition of multiple interfaces. These two measurements provide more information than the current method that uses only the first arrival to evaluate the bonding interfa next to the casing. Defects, Downhole methods, Numerical modelling, Guided waves, Wave propagation 1 INTRODUCTION The condition of the bond in a cemented cased well is very critical to borehole integrity. It affects the production efficiency as well as production and environmental safety (Lecampion et al.2011). It is thus essential to accurately evaluate the material bonding behind casing. In a single cased hole, there are two bonding interfaces, bonding interface I: interface between the casing and material next to the casing, bonding interface II: interface next to the formation. The methods for cement bonding evaluation are most often applied at these two bonding interfaces. Acoustic wireline logging methods, including the sonic at around 20 kHz source frequency (Pardue et al.1963; Eyl et al.1991; Zhang et al.2011; Haldorsen et al.2016a; Wang et al.2016a) and ultrasonic at around a few hundred kHz source frequency (Hayman et al.1991; Viggen et al.2016) are the most commonly used methods for evaluating the cement bonding condition and they are widely used during the well construction. The interpretation of the acquired data is designed for material evaluation behind single casing strings. Currently, the most commonly used sonic method in the industry is cement bond logging (CBL), in which the attenuation factor is measured from the first arrival amplitude only, whereas variable density logging (VDL) uses the amplitude of the full waveform (Walker 1968). Sonic data are usually combined with the ultrasonic methods to estimate the cement bonding condition, especially when evaluating for gas invasion (Schlumberger 1989).The interpretation of sonic data uses the relationship between the amplitude of the casing wave and the fluid column thickness (e.g. Jutten & Corrigall 1989; Liu et al.2011; Tang et al.2016), and the time of the first arrival (Zhang et al.2011). The attenuation value is also inversely proportional to the azimuth cement coverage (Song et al.2013). Measurements made on the first arrival can be ambiguous because it often has small amplitude. In particular, if interface I is not cemented, the CBL/VDL cannot tell the bonding condition of interface II. Although the newly developed pitch-catch method at the ultrasonic frequency range (He et al.2014; Viggen et al.2016; Wang et al.2016a) show the possibility to evaluate the bonding condition at interface II, it is still challenged by eccentering of the casing and roughness of the interface (van Kuijk et al.2005; Haldorsen et al.2016b). To improve methods for evaluating cement integrity, it is useful to study the sonic wavefields in the single casing situation to determine the possibility of evaluating the bonding condition by using full waveforms rather the currently used time of first arrival method (Zhang et al.2011) or first arrival amplitude (Jutten & Corrigall 1989; Liu et al.2011; Song et al.2013; Tang et al.2016). Although a number of studies have been conducted for single casing strings (e.g. Tubman et al.1984; Zhang et al.2016), the understanding of the sonic wavefields in the single casing model is still incomplete. Because the 3-D finite difference (3DFD) method can conveniently simulate the complex geometry of the cased hole (such as eccentered tool and casing) and also can help us understand the dynamic wave propagation, we use a 3DFD method (Wang et al.2015) to simulate the monopole wavefields in single cased borehole models with different bonding conditions. We investigate the different modes propagating in the borehole in the wireline environment by analysis of the simulated 3-D wavefield records. By using data processing methods, we attempt to identify a relationship between fundamental mode propagation and the condition of the cement bonds. 2 METHOD AND MODELS Although analytical or semi-analytical methods can get accurate solutions for simple models, they cannot get the solutions for models with complicated geometries. For complex models such as having tool and casing eccentering, azimuthal variation in the replacement of cement with fluid, we must appeal to numerical methods such as 3DFD. We use the 3DFD code that has previously been used by Wang et al. (2015) to simulate wave propagation in boreholes with a single casing string. The code is second order in both space and time, which allows reliable results even for models that have high impedance contrast between fluid and solid. Prior to using our 3DFD code, we must confirm its reliability for modelling situations where the steel casing is present in the model. Our single cased borehole model consists of multiple concentric cylinders. The innermost cylinder is the borehole fluid and the second is the steel casing. The outermost cylinder is the formation (e.g. sandstone in Table 1). An industry standard $${9{^{5}}\!/\!{_{8}}}$$ inch (1 inch = 2.54 cm) casing is used in the model, where the casing thickness is 14 mm. The material filling the cylinder between the casing and formation is cement. The cement may be partially or fully replaced with fluid. Table 1 lists the geometries and elastic parameters of an example fully cemented cased hole (shown in Fig. 1). In this study, we only change the geometry and filling material of the cement cylinder to investigate the effect of different bonding conditions on full waveforms. Figure 1. View largeDownload slide A cased well model with good bonding. (a) Side view. (b) Top-down view. Figure 1. View largeDownload slide A cased well model with good bonding. (a) Side view. (b) Top-down view. Table 1. Elastic parameters for the model used in our study. Medium  Vp (m s−1)  Vs (m s−1)  Density (kg m−3)  Radius (mm)  Fluid  1500  0  1000  108  Steel  5500  3170  8300  122  Cement  3000  1730  1800  170  Sandstone  4500  2650  2300  300  Medium  Vp (m s−1)  Vs (m s−1)  Density (kg m−3)  Radius (mm)  Fluid  1500  0  1000  108  Steel  5500  3170  8300  122  Cement  3000  1730  1800  170  Sandstone  4500  2650  2300  300  View Large For the code validation, we investigate the case of sonic logging in a hole in which the cement outside the steel casing is completely replaced by fluid. A ring source is approximated by 36 point sources embedded on the outer boundary of the casing. Although the source loading is different from that for sonic logging in a cased hole, which is a centralized source in the inner fluid, we choose this model because we can easily generate validation waveforms using the Discrete Wavenumber integration method (DWM; Byun & Toksöz 2003) that has been further developed for an ALWD model (Wang & Tao, 2011; Wang et al.2015). We use a 10 kHz Ricker wavelet as a monopole source, because the wide frequency range of the Ricker wavelet includes the frequency band of the most common sonic logging tools. Although the centre frequency of the CBL is 20 kHz, the ST wave is most strongly excited at frequencies lower than 10 kHz (Wang et al.2015), and the 10 kHz Ricker wavelet includes this frequency range. Fig. 2 shows the simulations obtained using both 3DFD and DWM. The grid sizes of 1 mm in x and y, and 2 mm in z directions are used in the 3DFD code. The array waveforms (Fig. 2a) show a nearly perfect match between the FD and DWM excepting the difference that appears in the later part of the waveform (after 1 m s) due to the numerical dispersion of FD in the z direction. This late-arriving mode corresponds to the ST (Stoneley) wave propagating in the fluid column between casing and formation (marked as ST2). More explanation of the ST2 will be presented in Figs 3 and 4. The casing mode, S and pR (pseudo Rayleigh) and ST1 (Stoneley in the fluid column inside the steel casing) waves can be easily found and are identified with lines marked according to their arrival times and in the velocity–time semblance plot (Fig. 2b). Figure 2. View largeDownload slide Comparison between the 3DFD and DWM simulations in a free casing model: (a) array waveforms; (b) velocity–time semblance plot for the array waveforms in (a). Figure 2. View largeDownload slide Comparison between the 3DFD and DWM simulations in a free casing model: (a) array waveforms; (b) velocity–time semblance plot for the array waveforms in (a). Figure 3. View largeDownload slide (a) X–Z profile of the model: (a) Single casing model with a perfect cement bond. Colours blue, red, light blue and orange are fluid, steel casing, cement and formation, respectively. Source position is marked with a yellow dot. Pressure snapshots for situations where the (b) cement is perfectly bonded, (c) free casing and (d) casing immersed in fluid. Figure 3. View largeDownload slide (a) X–Z profile of the model: (a) Single casing model with a perfect cement bond. Colours blue, red, light blue and orange are fluid, steel casing, cement and formation, respectively. Source position is marked with a yellow dot. Pressure snapshots for situations where the (b) cement is perfectly bonded, (c) free casing and (d) casing immersed in fluid. Figure 4. View largeDownload slide (a) Waveforms acquired on a centralized receiver array for a centralized point source in a borehole with a casing that is surrounded by fluid. (b) Frequency–velocity semblance plot made from (a) and modal dispersion curves calculated for the model. (c) and (d) are the calculated modal dispersion curves for casing with of varying inner (IR) and outer (OR). Figure 4. View largeDownload slide (a) Waveforms acquired on a centralized receiver array for a centralized point source in a borehole with a casing that is surrounded by fluid. (b) Frequency–velocity semblance plot made from (a) and modal dispersion curves calculated for the model. (c) and (d) are the calculated modal dispersion curves for casing with of varying inner (IR) and outer (OR). 3 NUMERICAL SIMULATIONS Here we use our 3DFD simulator to investigate the full waveforms and wave propagation characteristics by examining wavefield snapshots for three different models: (1) casing immersed in fluid, (2) free casing in a borehole and (3) perfect cement bonding between casing and formation. For the model with the casing immersed in a fluid, the cement and formation are completely replaced with fluid. We use this model to understand the modes propagating in the casing. For the free casing model, only the cement between casing and formation rock is replaced with fluid. In the simulations, the effect of the tool is ignored and a centralized point source with 10 kHz Ricker wavelet is used. Fig. 3(a) shows side views of the borehole model with good cement between casing and formation. The pressure snapshots at 1.0 ms on an x–z profile are shown in Fig. 3(b) (good bond), Fig. 3(c) (free casing) and Fig. 3(d) (casing immersed in fluid). Fig. 3(d) can help us understand the modes in the casing. As has been shown in non-destructive testing, there are three types of guided wave in casings: L (longitudinal), F (flexural) and T (torsional) modes (Cawley et al.2002; Edwards & Gan 2007). T modes are associated with pipe rotation and would be found in the drilling pipe. L modes are monopole modes in the casing that axis-symmetrically expand and contract the casing. They are similar to the extensional modes in the collar in acoustic logging-while-drilling (Wang et al.2016b, 2017). F modes are dipole or quadrupole (or even higher order) modes in the casing that are similar to the flexural, or screw modes on the collar in acoustic logging-while-drilling. Here we find casing modes (L modes) at offsets of about 1.5 to 4 m while the ST wave follows and both modes leak into the region both inside and outside of the casing as leaky modes that can be seen in Fig. 3(d). We use a dense receiver array with a 0.1 mm interval to record the waveforms from the source position to the top of the model along the z axis to understand the wave modes. Fig. 4(a) shows an example for the case of casing immersed in fluid. We find three visible modes as marked with lines. Comparing the extracted frequency–velocity semblance contour plot (Rao & Toksöz 2005; Wang et al.2015) from the array waveforms with the calculated modal dispersion curves shown as solid lines (Tubman et al.1984; Zhang et al.2016) in Fig. 4(b), we find that the modes seen in the waveforms are the casing modes (L1–L5), ST1 and an additional ST2 (slow ST in Plona et al.1992). Although the ST2 mode mainly propagates outside of the casing, it penetrates the casing and can be received in the inner fluid column due to its low frequency. To investigate the properties of the ST2 wave in more detail, Figs 4(c) and (d) show the modal dispersion curves for various inner or outer radii of the casing. It can be seen that increasing the outer radius (labelled as OR in the plots) causes the L modes to shift slightly towards lower frequency (Fig. 4c). The velocity of the ST2 mode increases with increasing outer radius thus reducing the difference in velocity of ST1 and ST2 (Fig. 4c). Decreasing the inner radius moves the L modes to higher frequency (Fig. 4d). At the same time the velocity of the ST2 wave becomes larger. We infer that increasing outer and decreasing inner radii, which are equivalent to increasing the thickness of the casing, will increase the ST2 wave velocity and reduce the phase velocity gap between the two ST waves. Another issue that should be noted is that effect of changing the inner radius is stronger than that of changing the outer radius. Generally, the ratio between the inner radius and casing thickness affects the ST2 wave velocity, where the smaller ratio generates a larger velocity. Other modes including P, S and pR (pseudo Rayleigh) modes are marked in Figs 3(b) and (c). Although the wave front of the casing modes propagate the fastest in the pressure snapshots, the modes do not leak and are trapped in the casing when the casing is well cemented, which makes them invisible both in the borehole and formation (as shown in Fig. 3b). The formation P and S waves can be detected by a centralized array receiver. However, the casing mode leaks into the fluid when the cement coupling is not good as seen in the free casing model shown in Fig. 3(c). In this situation, the first arrival in the borehole is the strong leaky casing mode and the formation P wave is submerged within the multiple order casing L modes. Thus the formation P wave is hardly discerned in the borehole fluid when cement is poor. Fig. 5 shows the array waveforms obtained from a centralized receiver in the models (displayed the same way as Fig. 4a) and the related velocity analysis in the time (Kimball & Marzetta 1986) and frequency domains. Figs 5(a)–(c) are for the well cemented cased hole. The waveforms have a time sequence of P, S, pR, ST and pR modes in Fig. 5(a). Several pR modes appear and they propagate at different velocities. The waveforms at offsets of 3–3.7 m (interval of 0.1 m) are used for calculating velocity–time semblance (Fig. 5b) and dispersion (Fig. 5c). From the plots, we discern the P, S, multiple orders of pR, and ST modes, respectively. For the case where the cement is completely replaced with fluid, Fig. 5(d), the waveforms are very different from the case where good cement is present. The wave modes in time sequence are casing L, a rather poorly discerned S (Paillet & Cheng 1991), clear ST, and the strongly dispersive pR waves. Figure 5. View largeDownload slide (a) Waveforms acquired in a well cemented cased hole with a centralized receiver array and a centralized point source located in the borehole fluid (b) time–velocity plot, (c) frequency–velocity plot. (d)–(f) are the same as (a)–(c) except for the case where cement is completely replaced with fluid. Figure 5. View largeDownload slide (a) Waveforms acquired in a well cemented cased hole with a centralized receiver array and a centralized point source located in the borehole fluid (b) time–velocity plot, (c) frequency–velocity plot. (d)–(f) are the same as (a)–(c) except for the case where cement is completely replaced with fluid. The phase velocities of the casing L modes, S, and ST waves can be obtained from the velocity analysis of the waveforms in both the time (Fig. 5e, method described in Kimball & Marzetta 1986) and frequency (Fig. 5f, method described in Rao & Toksöz 2005) domains. It is obvious that there are two ST modes in Fig. 5(f) corresponding to an ST inside the casing with a higher velocity and an additional ST in the fluid column between casing and formation. The additional ST mode is similar to the one found in the vertical seismic profile (VSP) data such as in Marzetta & Schoenberg (1985) and Daley et al. (2013) that is not present when there is good cement between the casing and formation. For sonic logging data in a cased hole, the additional ST2 mode can also be found in some published field data such as in Haldorsen et al. (2016a). However, this additional mode is not clearly visible when the source frequency is around 10 kHz. To investigate the influence of the source frequency on the amplitudes of different modes in the model with fluid replacing cement, we plot the simulated waveforms obtained at different source frequencies in Fig. 6. Modes are marked in the plots according to their arrival times. It is easy to find the relationship between the source frequency and the amplitude of modes. The casing mode is weak below 3 kHz. We get much more obvious ST modes at low frequency. However, if the frequency is below 3 kHz, we cannot identify ST2 wave from the waveforms because of its large wavelength at low frequency. According to Figs 5(f) and 6, we find that if the source frequency is set at around 6 kHz, it is easy to distinguish the two obvious ST modes. Figure 6. View largeDownload slide Waveforms at different source frequencies in the free casing model. (a) Normalized waveforms (normalized by waveform amplitude at 2 kHz) at source frequency from 2 to 5 kHz; (b) normalized waveforms (normalized by waveform amplitude at 6 kHz) at source frequency from 6 to 10 kHz. Figure 6. View largeDownload slide Waveforms at different source frequencies in the free casing model. (a) Normalized waveforms (normalized by waveform amplitude at 2 kHz) at source frequency from 2 to 5 kHz; (b) normalized waveforms (normalized by waveform amplitude at 6 kHz) at source frequency from 6 to 10 kHz. 4 PARTIALLY BONDED MODELS Based on the dispersion curves and waveforms for the free casing model, we find the newly identified ST2 mode that provides another way to distinguish whether there is good versus bad cement behind the casing. In the following sections, we discuss the wavefields of the partially cemented models to determine the possibility of evaluating the bonding condition by using full waveforms including the current method based on the first arrival (e.g. Walker 1968; Zhang et al.2011) and the phase velocity of the ST2 wave. By investigating the detail of the wavefields for models with different thicknesses of fluid and cement, we hope to get a direct method to determine the bonding condition including that between the outer casing interface and the formation by using data acquired by a commonly used array acoustic logging tool with a source having sonic frequencies (e.g. Zhang et al.2011). 4.1 Fluid between steel casing and cement We first consider models in which some of the cement next to the casing (bonding interface I) is replaced with fluid. Fig. 7 shows a schematic diagram (top-down view) of a partially cemented borehole model. R1, R2, RCI and Rh are the inner radii of the casing, fluid column, cement and borehole wall. The fluid thickness is equal to RCI–R2. With R2 of 122 mm (Table 1), we investigate the wavefields in the models with RCI of 122, 122.5, 123, 124, 126, 130, 138, 154, 162 and 170 mm, which correspond to the models with fluid thickness of 0 (fully cemented), 0.5, 1, 2, 4, 8, 16, 32, 40 and 48 mm (no cement) next to the casing. Figure 7. View largeDownload slide Schematic diagrams (top-down view) of a partially cemented borehole model (bad bonding for interface I). R1, R2, RCI and Rh are the inner radii of casing, fluid column, cement and borehole wall. The fluid thickness is equal to RCI—R2. R1, R2 and Rh are given in Table 1. Figure 7. View largeDownload slide Schematic diagrams (top-down view) of a partially cemented borehole model (bad bonding for interface I). R1, R2, RCI and Rh are the inner radii of casing, fluid column, cement and borehole wall. The fluid thickness is equal to RCI—R2. R1, R2 and Rh are given in Table 1. We calculate the modal dispersion curves for the models and find that they vary with the fluid thickness for the ST2 and casing modes (as shown in Fig. 8) while other modes such as ST1 and pR have no change. Fig. 8(a) shows the dispersion curves for ST2 with various fluid thicknesses. We find that the ST2 mode is very sensitive to the fluid thickness. The velocity of ST2 increases with the fluid thickness. This means that the ST2 wave velocity could be a good indicator for cement bond evaluation. Figure 8. View largeDownload slide Dispersion curves of ST2, L and pR modes with various fluid thicknesses between casing and cement (bonding interface I). (a) ST2 modes, fluid thicknesses are marked; (b) L and pR modes, the legends for different lines are given and the black dot lines are the free bonding case (the fluid thickness of 48 mm). Figure 8. View largeDownload slide Dispersion curves of ST2, L and pR modes with various fluid thicknesses between casing and cement (bonding interface I). (a) ST2 modes, fluid thicknesses are marked; (b) L and pR modes, the legends for different lines are given and the black dot lines are the free bonding case (the fluid thickness of 48 mm). There is very small difference in velocity of the L modes with fluid thicknesses (shown in Fig. 8b). The black dotted lines, denoting the modes in the free casing model (the fluid thickness of 48 mm), are almost the same as the modes in the cases with partial cement except at the inflection points at lower frequencies (marked with a solid line) for different L modes. These small variations are very hard to observe from field data because it would require a high performance dispersion analysis method having high resolution. We simulate the full waveforms for most of the models (the fluid thickness of 0, 4, 8, 16, 32, 40 and 48 mm) as shown in Fig. 9 (traces for source–receiver spacing of 3 m are shown). In Fig. 9(a), we see the clear casing mode as the first arrival when the cement is partially replaced with fluid. Walker (1968) was the first to give the relationship between the amplitude of the casing modes and the thicknesses of cement sheath. The current methods for cement evaluation are mostly based on his relationship by using the amplitude of the casing modes. However, the small dependence of the amplitude of the first arrival with fluid thickness, shown in Fig. 9(a), challenges the tool design and data processing. The added uncertainty from working in the down-hole environment, such as the limited dynamic range of the acquisition system, the high temperature and high pressure that can adversely impact the electronic components, and the electronic noise, contributes to the difficulty. The P wave is submerged in the casing modes and cannot be discerned. This is similar to the case of P wave measurements in fast-fast formations in acoustic logging-while-drilling situations (Wang et al.2017). The difficult to discern arrival time of S wave makes the S wave velocity measurement difficult when fluid exists next to the casing. The ST1 and ST2 modes are hard to discern due to the strong interference from the pR wave. As we found in Fig. 6, we get a visible ST2 mode when the source frequency is set at around 6 kHz. Fig. 9(b) shows traces that have been filtered using a 5–8 kHz bandpass filter. The arrival times of the ST2 mode at different fluid thicknesses are marked by arrows. The velocity analyses in time and frequency domains (based on the filtered data for the case with the fluid thickness of 16 mm) are given in Fig. 10. Although the waveforms for fluid thickness of 0.5 and 1 mm are not simulated due to computational limitations (the large memory requirements), we are confidential that it is possible to identify the ST2 wave from array waveforms even for fluid thickness below 1 mm. Figure 9. View largeDownload slide Synthetic waveforms for the models with fluid of various thicknesses between the casing and cement (bonding interface I). Traces with source–receiver spacing of 3 m are plotted. (a) Original waveforms; (b) waveforms filtered with a bandpass filter from 5 to 8 kHz. Arrows in the plot show the arrival time of ST2 mode at different fluid thickness cases. Figure 9. View largeDownload slide Synthetic waveforms for the models with fluid of various thicknesses between the casing and cement (bonding interface I). Traces with source–receiver spacing of 3 m are plotted. (a) Original waveforms; (b) waveforms filtered with a bandpass filter from 5 to 8 kHz. Arrows in the plot show the arrival time of ST2 mode at different fluid thickness cases. Figure 10. View largeDownload slide Velocity analysis in time and frequency domains for the synthetic waveforms with the fluid thickness of 16 mm (the spacing between the source and the nearest and furthest receivers are 3 and 3.7 m, respectively, and the axial receiver interval is 0.1 m). (a) Time semblance result; (b) dispersion analysis, the modal dispersion curves are also plotted (dotted lines). Figure 10. View largeDownload slide Velocity analysis in time and frequency domains for the synthetic waveforms with the fluid thickness of 16 mm (the spacing between the source and the nearest and furthest receivers are 3 and 3.7 m, respectively, and the axial receiver interval is 0.1 m). (a) Time semblance result; (b) dispersion analysis, the modal dispersion curves are also plotted (dotted lines). We easily find casing, S and pR, ST1 and ST2 modes from the velocity–time semblance plot (Fig. 10a). However, the separation between the latter two modes is larger than that in the free casing model (Fig. 5e) due to the slower ST2. With the help of the modal dispersion curves (dotted lines in Fig. 10b), the dispersion analysis of the different modes can be easily identified from the contour plot in Fig. 10(b), where the ST modes are clear. The velocity analyses illustrate the possibility of using the later part of the waveform to determine the fluid thickness next to the casing rather than the relatively small amplitude dependence of the first arrival on thickness. If we find casing modes, we can infer that the interface between casing and cement (interface I) is filled with fluid and then we can use the ST2 to determine the thickness of the fluid column. 4.2 Fluid between cement sheath and formation The primary objective of a cement job is to hydraulically isolate the formation and prevent escape of fluids inwards to the borehole annuli avoiding industrial accidents (e.g. Deepwater Horizon on 2010 [Deepwater Horizon Study Group 2011]). This requires that the diagnostic for well integrity must provide the formation sealing status across producing intervals. In this case, the bonding condition at the interface between the cement and formation (bonding interface II) is more important than that at interface I. The current sonic/ultrasonic measurements provide some information about the geometry of defects that can be observed using the range of source frequency. However, validating hydraulic isolation means that one must prove that there is no flow behind the pipe regardless of the type of bonding material including: cement, collapsed formation, formation cracks and barite. In this case, sonic/ultrasonic methods are part of solution rather than a complete solution of the hydraulic isolation question. The current ultrasonic/sonic evaluation methods can be combined with other sources of information to provide more complete information about hydraulic isolation. In this section, we will investigate the possibility of using the sonic method to evaluate the bonding condition at interface II. Fig. 11 shows a schematic diagram (top-down view) of a partially cemented borehole model. R1, R2, RCO and Rh are the inner radii of casing, cement, fluid column and borehole wall, respectively. The fluid thickness is equal to Rh—RCO. We investigate the wavefields in the models with RCO of 170, 169.5, 169, 168, 166, 162, 154, 138, 154, 130 and 122 mm, which correspond to models with the fluid thickness of 0 mm (fully cemented), 0.5, 1, 2, 4, 8, 16, 32, 40 and 48 mm (no cement) next to the formation. Since the dispersion characteristics in the models with fluid next to the formation are similar to those in Fig. 8, where there are fluids at the interface between the casing and cement (interface I), we do not display them. The only difference of the dispersion characteristics from those shown in Fig. 8 is that the L modes have lower speed and the inflection points move to the lower frequency. The reason for the lower velocity of the casing L modes is they propagate in a material consisting of steel casing and cement, which has a lower velocity than the steel casing. The cement next to casing enlarges the effective radius of the casing and moves the inflection points to lower frequencies. The trend of the dispersion curves of these modes is that with more cement, velocity decreases and the inflection point shifts towards lower frequency. We cannot find any difference in dispersion for the mode ST2 from that shown in Fig. 8(a) for the corresponding fluid thickness cases. This suggests that ST2 cannot be used as indicator for the location of where the fluid column exists. However, at a minimum, we can know whether interface II is bonded well by using the arrival time and velocity of the L modes when interface I is boned (Zhang et al.2011). Then we can determine the thickness of the fluid column next to the formation by using the ST2 mode. Figure 11. View largeDownload slide Schematic diagram (top-down view) of a partially cemented borehole model. R1, R2, RCO and Rh are the inner radii of casing, cement, fluid column and borehole wall. The fluid thickness is equal to Rh—RCO. Figure 11. View largeDownload slide Schematic diagram (top-down view) of a partially cemented borehole model. R1, R2, RCO and Rh are the inner radii of casing, cement, fluid column and borehole wall. The fluid thickness is equal to Rh—RCO. We display the full waveforms calculated for different fluid-layer thickness in Fig. 12 in the same manner as Fig. 9. In the detailed display of the waveforms in Fig. 12(c) we see a clear casing mode (a combination of casing and cement modes) as the first arrival between the labelled casing and P arrivals when the cement is partially replaced with fluid. Although the P wave is submerged in the casing mode and cannot be discerned when the fluid column is large, if the fluid column thickness is as small as 4 mm to about 16 mm, or the cement thickness is large, for example above 2/3 of the annulus, the arrival time of the first arrival approximates the formation P wave arrival time for the good cement case. Interpretation of the result from the first arrival method would lead to the incorrect conclusion that cement is good rather than that the condition at interface II is poor. Fortunately, we find a clear ST2 in the waveforms, especially those that have been filtered, which can help us avoid the misinterpretation from the arrival time of the first arrival (Zhang et al.2011). Similar to the case of bonding interface I, we suggest the use of a tool with a large source–receiver spacing to separate the ST2 modes for the thin (4–8 mm) fluid column cases. Figure 12. View largeDownload slide Synthetic waveforms for models with fluid of various thicknesses in front of formation (bonding interface II). Traces having source–receiver spacing of 3 m are plotted. (a) Original waveforms. (b) Waveforms that have been filtered with a bandpass filter from 5 to 8 kHz. (c) Unfiltered waveforms from 0 to 2 ms of (a). Figure 12. View largeDownload slide Synthetic waveforms for models with fluid of various thicknesses in front of formation (bonding interface II). Traces having source–receiver spacing of 3 m are plotted. (a) Original waveforms. (b) Waveforms that have been filtered with a bandpass filter from 5 to 8 kHz. (c) Unfiltered waveforms from 0 to 2 ms of (a). Fig. 13 shows the velocity–time semblance (Fig. 13a) and dispersion analysis (Fig. 13b) contour plots for the case of 16 mm of fluid at interface II. In Fig. 13(a), we clearly find a casing-cement mode with a velocity nearly the same as the P velocity. We also find the S, ST1 and ST2 modes. As mentioned, if we only use the first arrival (amplitude or arrival time) to determine the bonding condition, we will definitely misjudge the bonding condition as indicating very good cement even for the fluid column thickness of 16 mm in front of formation. However, the good coherence for ST2 (from the filtered waveforms in Fig. 12b) in Fig. 13(a) gives us an opportunity to avoid the misjudgement. The dispersion analysis plot in Fig. 13(b) gives us another view for mode identification that can also be used to eliminate the misjudgement. The modal curves (solid lines) for the model with fluid column thickness of 16 mm next to the casing are also plotted to illustrate the difference from Fig. 10(b). We find the dispersion characteristics of pR, ST1, and ST2 are the same as those in Fig. 10(b). The casing-cement modes, which will likely be identified as P waves, have slower velocities than the P wave and the L modes in Fig. 10(b). Figure 13. View largeDownload slide Velocity analysis in time and frequency domains for synthetic waveforms with the fluid thickness of 16 mm calculated using spacing between the source and the nearest and furthest receivers are 3 and 3.7 m, respectively, and an axial receiver interval of 0.1 m. (a) Time semblance result; (b) dispersion analysis, the modal dispersion curves from Fig. 10(b) are also plotted (dotted lines). Figure 13. View largeDownload slide Velocity analysis in time and frequency domains for synthetic waveforms with the fluid thickness of 16 mm calculated using spacing between the source and the nearest and furthest receivers are 3 and 3.7 m, respectively, and an axial receiver interval of 0.1 m. (a) Time semblance result; (b) dispersion analysis, the modal dispersion curves from Fig. 10(b) are also plotted (dotted lines). Our results show that it is necessary to use the full waveform, especially the later part of the waveforms, to estimate the cement bonding condition when a fluid column exists next to the formation. Dispersion analysis is also a good tool to eliminate misinterpretation. In field applications, dispersion analysis may be impractical due to the time it requires. Time semblance would also be helpful because we could get velocity information about the ST2 mode, which can be a very good indicator of bonding condition. 4.3 Cement inside the fluid columns To give more detail about the relationship between the waveforms and the thickness and location of the fluid column and cement sheath, we separate the annulus between casing and formation into three parts with each part being a different medium (cement or fluid) with different thickness. By using this model, we simulate the waveforms in models with cement partially replacing fluid columns both next to the casing and the formation. All the waveforms are shown in Fig. 14(a) and the names for different models are also listed on the waveforms. The letters ‘f’ and ‘c’ are fluid and cement, respectively. The number before the letter is the thickness (units in mm) of the medium. For example, ‘4f16c28f’ means the annulus consists of 4 mm and 28 mm fluid columns next to the casing and in front of the formation, respectively. In addition, a 16 mm thick cement layer is placed between the two fluid columns. The arrival times for different modes are marked by lines. The casing, P, and S waves are expanded and shown in Fig. 14(b). Because a fluid column exists next to the casing, the arrival time of the casing mode is the same independent of the thickness of the fluid column. The amplitude of the casing wave changes a little with the changing thickness of the fluid next to the casing. The current cement bonding evaluation method is based on the relationship between the amplitude of the casing wave and the fluid column thickness (e.g. Jutten & Corrigall 1989; Liu et al.2011; Tang et al.2016). However, this method strongly depends on measurements of the amplitude of the first arrival and could lead to misinterpretation because the amplitude dependence on fluid column thickness is not strong. Another issue is that we cannot infer the bonding condition of the interface between the cement and formation if the cement next to the casing is partially replaced with fluid. Figure 14. View largeDownload slide Waveforms and dispersion analysis for models with cement next to the casing and the formation partially replaced by fluid. (a) Waveforms at 3 m offset. Names for models are listed on the waveforms. The letters ‘f’ and ‘c’ are fluid and ‘cement’, respectively. The number before the letter is the thickness (in mm) of the medium. For example, ‘4f16c28f’ means the annulus consists of 4 mm and 28 mm fluid columns next to casing and in front of formation, respectively. In addition, cement with 16 mm is between the two fluid columns. (b) Frist 2 ms of the normalized waveforms. (c–g) Dispersion analysis plots for the waveforms for different models. The green lines are the dispersion curves for the model (Fig. 7) with a 32 mm fluid column between casing and cement. The black lines are the dispersion curves for models (Fig. 7) with the fluid thickness of 4 mm (c), 8 mm (d), 16 mm (e), 24 mm (f) and 28 mm (g). Figure 14. View largeDownload slide Waveforms and dispersion analysis for models with cement next to the casing and the formation partially replaced by fluid. (a) Waveforms at 3 m offset. Names for models are listed on the waveforms. The letters ‘f’ and ‘c’ are fluid and ‘cement’, respectively. The number before the letter is the thickness (in mm) of the medium. For example, ‘4f16c28f’ means the annulus consists of 4 mm and 28 mm fluid columns next to casing and in front of formation, respectively. In addition, cement with 16 mm is between the two fluid columns. (b) Frist 2 ms of the normalized waveforms. (c–g) Dispersion analysis plots for the waveforms for different models. The green lines are the dispersion curves for the model (Fig. 7) with a 32 mm fluid column between casing and cement. The black lines are the dispersion curves for models (Fig. 7) with the fluid thickness of 4 mm (c), 8 mm (d), 16 mm (e), 24 mm (f) and 28 mm (g). We also find little difference in the ST waves (inside the rectangle in Fig. 14a) with various fluid thicknesses. The dispersion analysis (contour) plots for the waveforms from different models are shown in Figs 14(c)–(g). We do not calculate the modal dispersion curves for the models we simulated here. However, we plot the modal dispersion curves for the model in Fig. 7. The green lines are the dispersion curves for a model (Fig. 7) with a 32 mm fluid column between casing and cement. The black lines are the dispersion curves for a model (Fig. 7) with the fluid thickness of 4 mm (Fig. 14c), 8 mm (Fig. 14d), 16 mm (Fig. 14e), 24 mm (Fig. 14f) and 28 mm (Fig. 14g). It is obvious that the green lines for mode ST2 match the dispersion contour plots for all fluid column thicknesses. This suggests that the ST2 wave can be used to determine the total thickness of the fluid column in the annulus and it is not just sensitive to the fluid thickness next to the casing if there is another fluid column between cement and formation. This may be considered to be a limitation of the application of the ST2 wave. However, it would be a great supplement for the current first arrival amplitude method. We can use the amplitude of the casing wave to determine the fluid thickness next to the casing although sometimes this method will not work very well. We can get the total fluid thickness in the annulus by comparing the velocity or dispersion curves with the modal cases. Then we can know the distribution of the fluid in the annulus. This overcomes the limitation of the current amplitude method on the bonding condition of the interface between cement and formation and can also reduce uncertainty of interpretation. 4.4 Fluid inside cement sheath We also consider models having a fluid column of varying thickness inside the cement sheath that is otherwise well bonded to the casing and formation. Fig. 15 shows the waveforms and dispersion analysis for different models. The placement of the subfigures is the same as Fig. 14. Model names are as described for Fig. 14. Fig. 15(a) shows the full waveforms (3 m offset) for different models and the first 2 ms waveforms are zoomed in and shown in Fig. 15(b). We find that the thickness of cement next to the casing will definitely affect the arrival time (marked by circles in Fig. 15b) and amplitude of the first arrival (the mode propagating in the combined casing and cement of different thickness). As we discussed in the previous section, the arrival time (velocity) method (Zhang et al.2011) will not work well when the cement sheath thickness is large (e.g. 24c16f8c in Fig. 15b). However, the variation in the first arrival amplitude can be easily discerned and this can be used as an indicator for thickness of the cement sheath next to the casing. We find that the ST waves (marked with a rectangle in Fig. 15a) are sensitive to the cement sheath thickness, which means the ST2 wave is not sensitive to the location of the fluid column. The dispersion contour plots are shown in Figs 15(c)–(g) (modal dispersion curves for 16 mm fluid column existing in interface I is plotted with back lines). We find that the dispersion contours of ST2 wave overlap those for the model shown in Fig. 11 (the fluid column thickness of 16 mm). This overlap leads us to infer that the ST2 wave is only sensitive to the fluid thickness not the fluid location. Figure 15. View largeDownload slide Waveforms and dispersion analysis for different models plotted in a manner similar to that in Fig. 14. (a) Waveforms at 3 m offset. (b) First 2 ms of the normalized waveforms. Arrival times of the first arrival are marked with circles. (c–g) Dispersion analysis plots for the waveforms for different models. Figure 15. View largeDownload slide Waveforms and dispersion analysis for different models plotted in a manner similar to that in Fig. 14. (a) Waveforms at 3 m offset. (b) First 2 ms of the normalized waveforms. Arrival times of the first arrival are marked with circles. (c–g) Dispersion analysis plots for the waveforms for different models. 5 FLOW CHART FOR CEMENT BOND EVALUATION USING FULL WAVEFORMS Based on the above investigations of the full waveform for different models, we propose a full waveform method to evaluate the cement bonding condition at different interfaces, where both the first arrival and ST2 wave are used in a combined interpretation. Fig. 16 shows a flow chart of the full waveform method. The data required are the full waveforms and the thickness (D) of the annulus between the casing and the formation rock. Using the wellbore geometry, one calculates the arrival time tc of the casing wave. The first arrival t0 is picked on the waveform and compared to tc. If the two times match, interface I is not well cemented and a further interpretation of the bonding condition at interface II requires a comparison of the calculated fluid thickness (d0) next to the casing from first arrival amplitude A0 and the total fluid thickness in the annulus from the ST2 velocity. If the thicknesses match, the interface II has good cement, otherwise there is another fluid column behind interface I. If the two times do not match, interface I has good cement and the existence of the ST2 phase is determined by performing velocity analysis for the further interpretation. If there is no ST2 phase, the cement is good. If the ST2 phase exists, the amplitude of the first arrival is measured and used to estimate the thickness of cement next to the casing (L1c). If L1c matches the difference between the annulus thickness D and total fluid thickness d2 in the annulus, interface II has poor cement. Otherwise, there is another fluid column between interfaces I and II. In addition interface II probably has poor cement. Figure 16. View largeDownload slide Flow chart diagram of the full waveform cement bonding evaluation method. Figure 16. View largeDownload slide Flow chart diagram of the full waveform cement bonding evaluation method. 6 CONCLUSIONS We have used a 3DFD method to simulate wave propagation from a monopole source in a single cased borehole with different bonding conditions. Pressure snapshots of the wavefields give us a direct way to evaluate wave excitation and propagation for different models. Evaluation of the full wavefield helps improve understanding of the application not only to a single cased hole but also to underwater cables, and oil and chemical pipelines. Data processing methods such as velocity–time semblance and dispersion analysis facilitate the identification of the modes in the different models. Our conclusions are as follows: The formation modes can be easily discerned when the casing is well bonded. However, the P wave is submerged in the casing mode and the S wave has poor coherence when the cement is replaced with fluid. The amplitude of casing L modes can be used to determine the bonding condition of the interface between casing and cement. However, the small variation of first arrival amplitude with thickness of fluid between casing and cement could introduce ambiguity in the interpretation. When using only the arrival time (velocity) of the first arrival, it would be highly likely that the presence of fluid between the casing and the cement would be misjudged as good cement. The amplitude of the first arrival is a much better indicator. The slow Stoneley (ST2) mode can be used to evaluate the total thickness of the fluid column in the annulus no matter where the fluid column is located even when there are two fluid columns. Analysis of the full waveform by combining the first arrival and the slow ST waves can be used eliminate the ambiguity about cement condition and improve cement evaluation reliability compared to the current method using only first arrival measurements. ACKNOWLEDGEMENTS This study is supported by the Founding Members Consortium of the Earth resources Laboratory at MIT. We thank two anonymous reviewers whose comments substantially improved the presentation of our work. REFERENCES Byun J., Toksöz M.N., 2003. 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Geophysical Journal InternationalOxford University Press

Published: Jan 1, 2018

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