Acoustic Anisotropy Measurements and Interpretation in Deviated Wells

Acoustic Anisotropy Measurements and Interpretation in Deviated Wells X. M. Tang, and D. Patterson, Houston Technology Center, Baker Atlas, Houston, Texas, USA ABSTRACT Many acoustic anisotropy measurements using cross-dipole tools have been made in deviated/high-angle wells. Interpreting the acoustic anisotropy data becomes an important task in reservoir exploration and formation evaluation. We present theoretical analyses and case study examples to characterize the deviated well acoustic anisotropy data. The results demonstrate that the measured anisotropy is controlled by two major factors: formation stress and (TI) anisotropy. A general trend is that stress-induced anisotropy is mostly measured in stress-sensitive rocks (e.g., sandstones), while the TI-anisotropy is usually found in rocks with finely-aligned micro-scale structures (e.g., shales and silts). Using this trend as a guideline allows us to correctly interpret the anisotropy data in connection with well configuration and the geological environment. INTRODUCTION A current trend in petroleum exploration and production is that more and more deviated, and even horizontal, wells are drilled, especially for deep water reservoirs. The issue of anisotropy is especially important for deviated wells penetrating soft sediments of deep water reservoirs. In sedimentary formations, shales can be highly anisotropic due to mineral alignment associated with their deposition, and the sands can also be anisotropic due to their sensitivity to formation stresses. Interpreting the acoustic anisotropy data from a deviated well can be very complicated (Patterson and Tang, 2005). Figure 1 illustrates the deviated well, cross-dipole measurement in an anisotropic formation. In a deviated well, the well trajectory is neither perpendicular to, nor parallel with, the formation bedding planes. Consequently, the measured anisotropy is not the true formation anisotropy, but an apparent anisotropy at a given well deviation. Besides, several anisotropy parameters (e.g., Thomsen parameters) are needed to characterize the formation anisotropy while the cross-dipole measures only one of them directly in a horizontal well. Nevertheless, the variation of the anisotropy and its associated azimuth with the well trajectory and formation structure contains the information about the anisotropy parameters. By analyzing the anisotropy data in conjunction with the well configuration, we can characterize the anisotropy properties. By combining the data with lithology, we can also distinguish stress-induced anisotropy from other sources of anisotropy. The result is an improved characterization of formation anisotropy and its geologic environment. TI-ANISOTROPY IN A DEVIATED WELL Many anisotropic rocks (such as shales, silts, etc.) can be modeled as TI, or transversely isotropic, media. The anisotropy has a symmetry axis (generally normal to the bedding plane), which, when aligned with vertical, is known as VTI. The VTI is characterized by three Thomsen parameters: γ, ε, and δ (Thomsen, 1986). The first two parameters represent, respectively, shear and compressional wave anisotropy between vertical and horizontal directions. The last parameter, δ, controls the shape of wavefront in the VTI medium. In the VTI formation, two 1

shear waves, SH and qsv, polarize, respectively, in the horizontal and vertical planes. The cross-dipole tool measures the wave velocities V sh and V qsv at a given deviation angle (Sinha et al., 2006) and determines their polarization relative to the well trajectory. Using the Thomsen parameters, the compressional (called quasi-p or qp) and shear velocities in a VTI medium can be expressed by the following approximate (for qp and qsv) but sufficiently accurate formulae (Chi and Tang, 2003). V V V qp qsv sh ( ) ( ) 2 2 2 2 ε δ sin θcos θ 1 2εsin θ P0 2 = V + 2 2 2 V 2 ε δ sin θcos θ P0 1 S 0 2 2 V 1+ 2εsin θ / f S 0 = V + 2 = V 1+ 2γ sin θ S 0 1+ 2εsin θ / f (1) 2 2 where f = 1 V V ; V S0 P0 P0 andv S 0 are respectively the P- and S-wave velocity in the vertical direction. The difference ε - δ, as appearing in Eq. (1), strongly influences wave propagation characteristics in the VTI medium. For example, ε = δ corresponds to an elliptically shaped qp wavefront, while ε > δ and ε < δ correspond, respectively, to positive and negative anellipticity. This difference parameter has been a subject of study (Berryman et al., 1997) and is also a useful parameter in seismic processing (Alkhalifah and Tsvankin, 1995; Tsvankin and Thomsen, 1994). A VTI formation can be classified into three categories: 1) ε is significantly smaller than δ, 2) ε and δ are about the same order, and 3) ε is significantly greater than δ. Figure 2 illustrates the characteristic change of SH and qsv wave velocities V sh and V qsv as a function of the well deviation angle. The V sh curve increases from V S0 at 0 o to V SH at 90 o deviation. The V qsv curve, however, may show a pronounced maximum, or almost no variation, or a pronounced minimum, depending on to which category the formation belongs. The apparent anisotropy calculated using the relative difference between V sh and V qsv, as measured from a cross-dipole tool, exhibits different characteristics depending on the ε - δ parameter. If ε and δ are about the same order, the apparent anisotropy increases monotonously with deviation to reach the γ value at 90 o. For ε significantly greater than δ (or more rigorously, under the 2 2 condition ε > δ + γ V V, as can be S0 P0 approximately derived from Eq. (1), assuming f~1), the anisotropy is negative (V sh < V qsv ) at small angles. The anisotropy vanishes at a certain transition angle (this angle depends on the value of ε δ relative to γ, see Eq. (1); for the set of parameters used in Figure 2, this angle is about 45 o ), and becomes positive at large angles. The characteristic variation of V sh and V qsv with the deviation angle is used to interpret cross-dipole data in deviated wells. STRESS-INDUCED ANISOTROPY AROUND BOREHOLE A formation rock subjected to an unbalanced stress field exhibits anisotropic characteristics (Tang and Patterson, 2001). This phenomenon can be well explained by the rock physics of a porous rock containing elongated pores and/or microcracks (e.g., sandstones). The application of an oriented stress will close/suppress the pores/cracks normal to the stress and preserve/initiate cracks along the stress direction. The resulting alignment of the pores/cracks produces an anisotropy equivalent to that of a TI medium, whose axis 2

of symmetry is parallel with the minimum stress direction (Tang and Cheng, 2004). In contrast to sandstones, shales usually do not exhibit the stress-induced TI-anisotropy behavior (Rai and Hanson, 1988), mainly because the two types of rock have different micro-scale structures. As will be demonstrated later, the distinctly different stress-sensitivity between sand and shale provides a guideline for interpreting anisotropy measurement in deviated wells. DATA ANALYSES AND INTERPRETATION In the following, we will apply the above theoretical analyses and results to interpret some cross-dipole anisotropy data measured in deviated wells. The first two examples relate to VTI anisotropy measured in deviated wells and the variation of the measured anisotropy with deviation. The last two examples combine the TI- and stress-induced anisotropy effects to provide interpretation that is consistent with formation lithology and geological setting of the measurement environment. Example 1: Anisotropy azimuth vs. well azimuth Comparing either the fast shear azimuth and the well azimuth or the fast shear azimuth relative to the high side of the borehole can determine whether the fast shear corresponds to SH or qsv waves, as shown in Figure 3 for a deviated well. Track 1 shows gamma-ray (GR) and well deviation (DEV) log curves across a 200-ft interval. The well deviation ranges from 55 o at the bottom to 40 o at the top. The formation is a massive shale (See GR log). Tracks 2 through 5 show the cross-dipole anisotropy measurement results. The anisotropy, shown as shaded curves in Track 2, includes both the (high resolution) receiverarray anisotropy, plotted left to right, and the source-to-array anisotropy, plotted right to left. The anisotropy curves show that the measured anisotropy is fairly large, ranging from 6-12% as the well deviation increases. Tracks 3 and 4 show the anisotropy analysis referenced to magnetic north. Track 3 shows the distribution of the fast shear (yellow) along with the well trajectory (blue) over every 50-ft. interval. Track 4 is an image presentation combining the anisotropy magnitude with the fast shear polarization azimuth. Tracks 5 and 6 again show the anisotropy analysis, this time being referenced to the high side of the borehole. Track 5 displays the distribution of the fast shear (yellow) referenced to the high side of the borehole (red) over every 50-ft. interval, and Track 6 shows the anisotropy map for the high-side reference. As we can see, there is a difference of roughly 45 o between fast-shear azimuths with the two different points of reference. This illustrates the need to understand the reference of the fast-shear azimuth. If magnetic north is used as reference, the well trajectory will directly impact the fast shear direction, as opposed to the high-side reference where the well direction does not have this impact. De and Schmitt (2005) discussed scenarios and conditions for selecting the reference point for a deviated well. The azimuth data in both reference methods reveal an interesting phenomenon: the fast shear polarization is perpendicular to the well trajectory and the high side of the hole. This means that the fast shear wave, with its polarization normal to the vertical plane containing borehole axis, is an SH wave polarizing in the horizontal plane. In fact, this situation is consistent with the theoretical modeling results shown in Figure 2. At high deviation angles, the cross-dipole-measured fast shear wave is always the SH wave, for all 3

the three ε ~δ scenarios of the VTI formation. This comparison of the anisotropy azimuth with the well azimuth therefore indicates that the measured anisotropy reflects the VTI anisotropy of the shale formation, and, for this high-angle well, the anisotropy magnitude is approaching the true VTI shear-wave anisotropy. Example 2: Anisotropy azimuth change at a transition point The anisotropy azimuth change with borehole deviation in a VTI formation is also related to the VTI properties. The example in Figure 4 shows the behavior of the cross-dipolemeasured anisotropy (Tracks 2 through 5) passing through a transition point of the SH and qsv waves in a shale formation. The well deviation (dashed curve DEV in Track 1) is approximately 45 o and gradually increases from the upper to lower section of the well. The anisotropy magnitude is generally small but unambiguously determined, as is indicated by the well-defined fast and slow shear wave splitting in Track 5. The anisotropy map shows an almost 90 o azimuth difference between upper and lower intervals. Theoretical modeling is used to interpret the abrupt azimuth change with deviation. In the upper interval, the fast shear azimuth coincides with the well azimuth (Track 4), showing that the qsv wave is the fast wave (scenario marked by left bar in right figure of the theoretical curves, where V qsv is greater than V sh ). As the well angle increases, V qsv drops below V sh (scenario marked by the right bar in right figure) and the SH wave becomes the fast shear. This is evidenced by the fact that in the lower interval the polarization of the fast shear (now the SH wave) is normal to the well azimuth lying in the horizontal plane. The analysis suggests that the anisotropy of the subject formation belongs to the ε > δ category. Note also that the small measured anisotropy magnitude does not mean that formation TI-anisotropy is small. It mainly reflects that for VTI anisotropy with ε > δ, the anisotropy undergoes an SH- and qsv-wave transition point at approximately 45 o deviation. Example 3: VTI and stress effects at sandshale boundary In this example, we demonstrate the effects of VTI and formation stress on measured anisotropy data. Combining the two effects allows us to correctly interpret the measurement result. Figure 5 shows the anisotropy measurement results in the vicinity of a sand-shale boundary in a highly deviated well (deviation is 76 o ). The lithology of the formation is indicated in Track 1 with a gamma-ray (GR) curve. A massive sand formation is above a shale formation. Anisotropy is well-determined in both formations. The fast- and slow-shear waves show well-identified splitting (Track 4). The three shaded quality-control curves also indicate the well-determined anisotropy (left curve for anisotropy, middle curve for crossto-inline shear-wave energy ratio, and right curve for fast-shear azimuth, see Tang and Chunduru, 1999). The anisotropy magnitude (Track 5), however, is quite different for the two formations, as is also shown by the fast and slow shear slowness curves in Track 4. The anisotropy in sand is about 5-6%, and becomes greater than 20% in the lower shale. Of particular interest is the switch between fast (solid curve) and slow (dashed curve) shear polarization azimuths at the sand-shale boundary, as demonstrated in Track 6. Below is an interpretation of the anisotropy result based on the lithology and well configuration. It is well known that stress-induced anisotropy commonly occurs in sandstone formations and is rarely observed in shale formations. This 4

happens because sand has much higher stress sensitivity than shale (Rai and Hanson, 1988). Based on the observation, it is reasonable to hypothesize that the anisotropy measured in the sand formation is caused by stress and that in the shale formation it is caused by VTI anisotropy. This hypothesis is supported by the fast and slow polarization angle switch shown in Track 6. If the anisotropy in sand is stressinduced, then the fast shear polarization should be along the maximum stress direction. For this nearly horizontal well (deviation = 76 o ), the maximum stress around the borehole should be the overburden pressure and the fast shear polarization should be close to vertical, or pointing to the high side of the borehole, as indicated in Track 6. For the high-angle well, the fast shear in the VTI shale should the SH wave with a polarization lying in the horizontal plane (see Figures 1, 2, and 3). This change of anisotropy caused from overburden stress in the upper sand to VTI in the lower shale naturally explains the nearly 90 o jump in the fast shear polarization at the sand-shale boundary. The demonstrated abrupt switch of fast polarization at sand-shale boundaries is frequently observed in deviated wells drilled through sediments of deepwater reservoirs. We have observed this phenomenon even in wells with lower deviation angles (~40 o ). Example 4: Interpreting anisotropy data near a salt dome The alternating effects of stress and TI in sand and shale can also be observed in anisotropy data measured in the vicinity of salt domes. In this geologic environment, the local stress field is controlled by the salt body which in turn affects the anisotropy measurement. This scenario is demonstrated in the following example. Figure 6 shows anisotropy measurement results in the vicinity of an up-thrust salt dome. The lithology of the formation, as indicated by the gamma-ray (GR) curve in Track 1, is mostly sand (low GR values) and shale (high GR values). Significant anisotropy (10-15%) is observed in sand bodies and lower anisotropy (4-8%) is measured in shales. The reliability of the anisotropy, whether it is in sand or in shale, is quite good, as indicated by the good waveform data quality and the well identified fast-slow shear-wave splitting in Track 5. The smaller anisotropy in shales can be explained by the apparent dip angle of the formation beds relative to borehole. Because the (vertical) well is near the salt flank, formation beds were uplifted by the upthrust of the dome, resulting in a structural dip of approximately 50 o in the depth section shown in Figure 6. For this dipping bed situation, the well-to-bedding configuration is similar to that of a deviated well through horizontal beds. This 50 o bed angle relative to borehole is perhaps the reason for the small anisotropy values in shales. As shown in Figure 4, the apparent anisotropy near the qsv SH transition point around 45 o is small, with SH being the fast shear wave. An interesting observation is that again we see the characteristic 90 o jump of the anisotropy azimuth (i.e., fast shear angle) between sand and shale formations, as shown by the rose diagrams in Track 2 and anisotropy map in Track 4. This phenomenon is again linked to the alternating effects of stress and TI effects that are present respectively in sand and shale formations. An interpretation is illustrated in the lower figure of Figure 6, as explained below. In the vicinity of an up-thrust salt dome, the maximum horizontal compressive stress arises from the pushing from the center of the dome. This stress field induces anisotropy around 5

borehole and, in the stress-sensitive sand formation, is detected by the anisotropy measurement. The fast shear polarization should therefore point to the center of the dome. Whereas in the shale formation that is insensitive to the stress-induced anisotropy, the fast shear is an SH wave whose polarization direction is horizontal and is normal to the borehole. This SH-wave polarization is therefore along the perimeter of the salt dome. Thus, the two fast shear directions (one in sand and another in shale) are perpendicular to each other. This interpretation is consistent with the available information about the lithology, structural dip, and the geologic environment of the formation surrounding the borehole. In passing we mention that the near-salt dome phenomenon, as demonstrated in Figure 6, has been observed in various offshore reservoirs, e.g., the Gulf of Mexico, West Africa, etc. CONCLUSIONS Cross-dipole anisotropy measurement in deviated wells is generally affected by TI property of the formation and by the ambient stress field. The stress-induced anisotropy exists mainly in stress-sensitive rocks (e.g., sandstones) and is rarely observed in shales, whereas the TI-anisotropy exists mainly in rocks with fine alignment of microstructures/minerals (e.g., shales). This lithology-related anisotropy occurrence allows us to distinguish the cause of anisotropy in the measurement data. The anisotropy magnitude and fast shear variation, and their variation with well deviation, lithology, and geologic environment, in connection with the two major causes of anisotropy, are important bases for interpreting the anisotropy data. A typical phenomenon demonstrating the alternating effects of stress and TI is the 90 o jump at sandshale boundaries, as are commonly observed in deviated wells and in wells near a salt dome. REFERENCES Alkhalifah, T. and Tsvankin, I., 1995, Velocity analysis for transversely isotropic media: Geophysics, Soc. of Expl. Geophys., 60, 1550-1566. Berryman, J. G., Grechka, V. and Berge, P. A., 1997, Analysis of Thomsen parameters for finely layered VTI media, 67th Ann. Internat. Mtg: Soc. of Expl. Geophys., 941-944. Chi, S. H., and Tang, X. M., 2003, Accurate approximations to qsv and qp wave speeds in TIV media and Stoneley wave speed in general anisotropic media, in 44 th Society of Professional Well Log Analysts Annual Logging Symposium, paper OO. De, D. S., and Schmitt, D. P., 2005, Issues with shear-wave azimuthal anisotropy in highly deviated wells, paper 17647, Offshore Technology Conference, Houston, TX, May, 2005. Rai, C. S., and Hanson, K. E., 1988, Shearwave velocity anisotropy in sedimentary rocks: A laboratory study: Geophysics, 53, 800-806. Sinha, B. K., E. Simsek, and Q.-H. Liu, 2006, Elastic-wave propagation in deviated wells in anisotropic formations: Geophysics, 71, no.6, D191-D202. Tang, X. M., and C. H. Cheng, 2004, Quantitative borehole acoustic methods, Elsevier Science Publishing, Inc. Tang, X. and Chunduru, R. K., 1999, Simultaneous inversion of formation shearwave anisotropy parameters from cross-dipole acoustic-array waveform data: Geophysics, Soc. of Expl. Geophys., 64, 1502-1511. 6

Tang, X. M., and Patterson, D., 2001, Shear wave anisotropy measurement using crossdipole acoustic logging: An overview: Petrophysics, 42, 107-117. Patterson, D., and Tang, X., 2005, Pitfalls in Dipole Logging-Anisotropy: Cause of Discrepancy in Borehole Acoustic Measurements, Paper 17644, OTC annual conference. Thomsen, L., 1986, Weak elastic anisotropy: Geophysics, Soc. of Expl. Geophys., 51, 1954-1966. Tsvankin, I. and Thomsen, L., 1994, Nonhyperbolic reflection moveout in anisotropic media: Geophysics, Soc. of Expl. Geophys., 59, 1290-1304. ACKNOWLEDGEMENT We thank Baker Hughes for permitting publication of this paper. qsv VTI axis SH Transmitter Figure 1. Diagram illustrating cross-dipole anisotropy measurement in a deviated well penetrating a VTI formation. 7

Figure 2: Shear-wave (SH and qsv) velocity (upper figure) and apparent anisotropy (lower figure) vs. deviation angle for various ε δ scenarios. 8

Figure 3: Large anisotropy across a shale section in a deviated well comparing the anisotropy fast azimuth with two different reference directions. Tracks 3 and 4 show the fast azimuth compared to the well azimuth relative to magnetic north. Note the direction is perpendicular to the well direction and is influenced by the well direction. The two tracks on the right (Tracks 5 and 6) show the fast azimuth relative to the high side of the borehole which is not affected by the well direction. 9

DEV 40 50 Anis. Anisotropy Map 0 (%) 6 Azimuth diagram Fast & Slow Waves 0 (%) 40 0 (deg) 360 1 (ms) 6 V SH GR CAL Well AZ Apparent Anisotropy Shear Velocity V S0 V sh V qsv, ε > δ γ ε > δ 0 0 Angle (deg) 90 Figure 4: Anisotropy characteristics through the transition angle (see the 90 azimuth change in left figure). Below this angle, the fast shear is the qsv wave. Above the angle, the fast shear becomes the SH wave, as explained by the theoretical curves in the right figure. 10

Depth (m) GR 50 1 50 QC Ind. DTS 440 (μs/ft) 140 Shear waveform 1 Time (ms) 8 ANISOTROPY 60 (%) Azimuth 0 (deg) 180 440 Slowness 140 440 (μs/ft) 240 Dipole (μs/ft) SAND SHALE Slow Fast Fast Slow Wireline Fast Slow Borehole High Hide σ max SH Figure 5: Anisotropy data across a sand-shale contract in a 76 o -deviation well. Note the abrupt jump in the fast (slow) shear azimuth at the contact (circled area in Track 6). The bottom diagram illustrates the interpretation for this phenomenon: in the upper sand the fast shear points to the (vertical) overburden stress while in the lower shale the fast shear is an SH wave with a horizontal polarization. 11

GR (api) 20 170 Fast Az Aniso. 0 (%) 40 Anisotropy Map 0 (deg) 360 Fast & Slow waves 0 (ms) 5 X020 m X100 M Upthrust Dome σ max sand shale Figure 6: Anisotropy data in the vicinity of a salt dome. Note the 90 o jump of fast azimuth (Tracks 2 and 3) between sand and shale. The bottom diagram illustrates the interpretation for this phenomenon: In sand the fast shear points to the (radial) compressive stress while in shale the fast shear is an SH wave with a polarization along perimeter of the dome. 12