CONTINUOUS STATISTICAL INDICATOR OF STRESS-INDUCED DIPOLE FLEXURAL WAVE ANISOTROPY

Transcription

1 SPWLA 52 nd Annual Logging Symposium, May 14-18, 2011 CONTINUOUS STATISTICAL INDICATOR OF STRESS-INDUCED DIPOLE FLEXURAL WAVE ANISOTROPY A. Syed, A. Bertran, A. Donald, B. Sinha, and S. Bose, Schlumberger Copyright 2011, held jointly by the Society of Petrophysicists and Well Log Analysts (SPWLA) and the submitting authors This paper was prepared for presentation at the SPWLA 52nd Annual Logging Symposium held in Colorado Springs, Co, USA, May 14-18, ABSTRACT Anisotropy from dipole flexural wave data can be attributed to various mechanisms, such as structural layering or stress-induced effects. Layering or intrinsic anisotropy is generally quantified by Thomsen parameters that describe differences in compressional or shear stiffnesses normal and parallel to the bedding planes. However, stress-induced effects in sonic data acquired in clastic formations have been traditionally identified in terms of dipole dispersion crossovers. To use acoustic data for determining the maximum horizontal stress direction and magnitude, a method is required to first identify depth intervals that exhibit the stress-induced anisotropy dominating the sonic data. A new technique is presented for extracting a continuous statistical indicator for the degree of confidence in the presence of stress-induced dipole flexural anisotropy. Examples demonstrate its use in three different logging environments. The proposed technique uses flexural dispersion curve estimates extracted from the rotated fast and slow dipole waveforms over the entire measured frequency band. Differences between low-frequency asymptotes of the fast and slow dipole dispersion estimates are used to generate indicators of shear slowness anisotropy; relative changes between the fast and slow dipole dispersions at higher frequencies are analyzed to conclude whether the two dispersions are nonintersecting, implying intrinsic anisotropy, or exhibit a crossover, suggesting the presence of stressinduced anisotropy dominating the sonic data. In actual field data, the extracted dispersion curves are subject to measurement errors, so a statistical approach is taken to quantify such errors and use them in conjunction with the measured differences to test for the hypothesis of a dipole dispersion crossover. The 1 corresponding test statistic can then be viewed as a probabilistic indicator for the presence of anisotropy resulting from differences between the maximum and minimum horizontal stresses in the borehole crosssectional plane. Such an indicator is more stable and appropriate to use as a continuous log to flag zones where such stress-induced anisotropy is dominating the data. Three case studies are presented demonstrating evaluation of this new technique in both slow and fast formations from the North Sea; Arkansas, USA; and Colorado, USA. The North Sea data illustrate a slow formation (DTshear ~ 300 us/ft) at shallow depths where the sand is plastic in the logged interval. The first example from North America is from tight gas sands in a fast formation (DTshear ~ 150 us/ft), where both the natural and drilling-induced fractures exist in the same logged interval. The second example from North America is from a stiff shale gas reservoir where the rock exhibits stress-induced as well as intrinsic anisotropy. INTRODUCTION It is well known that in the presence of any anisotropy, either that due to azimuthal stress imbalance or to azimuthal variation in rock properties, shear waves emitted from a cross-dipole source split in two orthogonal directions, one traveling faster than the other. The azimuth of faster shear polarization depends on the physical mechanism causing the anisotropy. Figure 1 displays four cross-dipole signatures associated with different formation characteristics. In a homogeneous and isotropic rock, no shear splitting occurs and the flexural waves overlay each other over the entire frequency band. In the case of an inhomogeneous but isotropic rock, flexural wave slownesses for the fast and slow waves still overlay each other at low frequencies but exhibit larger slownesses at higher frequencies from the model flexural wave dispersion appropriate for a

2 SPWLA 52nd Annual Logging Symposium, May 14-18, 2011 homogeneous isotropic formation. If the anisotropy is caused by stress imbalance (inhomogeneous anisotropic) in the borehole cross-sectional plane, the azimuth of fast shear is aligned with the direction of far-field stress. This fact has been used for estimating the direction of horizontal stress in vertical wells for a long time (Sinha et al., 2000). In such cases, crossdipole dispersions exhibit a crossover at an intermediate frequency. Finally, if the anisotropy is caused by fractures, the flexural waves split in the orthogonal borehole axial planes that are perpendicular and parallel to the strike of fractures, with the faster shear traveling parallel to the strike of dominant fractures. In this case, flexural dispersions from the rotated dipole waveforms are nonintersecting over the entire frequency band (homogeneous anisotropic). The intrinsic anisotropy in shales caused by the layering or predominant clay particle alignment makes it transversely isotropic, with axis of symmetry perpendicular to the layering in shales. Intersection of such shales at a relative angle with respect to the well trajectory causes a parallel split on the flexural waves that is similar in behavior to that caused by fractures. See Figure 2. Figure 1. Schematic signatures of cross-dipole dispersions. Analyses of dispersion curves provide useful input to many geophysical, petrophysical, and geomechanical applications. Anisotropy caused by stress imbalance, and the possibility of determining the stress directions from it, has implications for drilling, wellbore stability, and other geomechanical applications. The anisotropy caused by fractures, and the dependence of azimuth on 2 fracture strike, has implications for field development. The study of anisotropy caused by shales is useful for geophysical applications. Flexural dispersion curves are extracted from the rotated fast and slow dipole waveforms over the entire measured frequency band. Differences in lowfrequency asymptotes of the fast and slow dispersions are indicators of shear slowness anisotropy. Relative changes between the fast and slow dispersion curves at higher frequencies are analyzed to conclude whether the two dispersions are nonintersecting, implying intrinsic anisotropy, or exhibit a crossover, suggesting the presence of stress-induced anisotropy dominating the sonic data. Dipole dispersion crossovers occur in the presence of differential stress in the plane of the borehole cross section. Perturbations in the nearwellbore stress distributions are then also reflected in the crossover in the acoustic shear radial profiles in the fast and slow directions. Traditionally, the analyst must review the sonic dispersion curves frame by frame and analyze them in detail to determine the zones where sonic anisotropy is predominant and then to determine the cause of anisotropy. Since in actual field data the extracted dispersion curves are subject to measurement errors, a raw comparison may lead to spurious indicators of anisotropy and dispersion crossovers. Therefore, we propose a statistical approach to quantify errors in the cross-dipole dispersion estimates and then use them in conjunction with the measured differences to solve a hypothesis testing problem. The test statistic supporting the hypothesis of a difference in the low-frequency asymptotes estimates along with a crossover at the intermediate frequencies then becomes, after suitable normalization, a probabilistic indicator for the presence of anisotropy resulting from the differences between maximum and minimum stresses in the plane of the borehole cross section. Such an indicator is more stable and appropriate to use as a continuous log to flag the zones where such stress-induced anisotropy is dominating the data. BACKGROUND Usually the direction of fast shear azimuth is determined from Alford rotation. However, a new algorithm has been introduced (Bose et al., 2007) that

3 SPWLA 52 nd Annual Logging Symposium, May 14-18, 2011 exploits the flexural wave propagation physics incorporating the flexural dispersion over a wide bandwidth including the energetic Airy phase region. This processing, called Dipole Anisotropy Four Components (DAFC), does not assume any particular rock model for the formation. It is therefore applicable in the presence of anisotropy caused by either aligned fractures or formation stresses, and even in the presence of mechanical alteration in the borehole vicinity. In contrast to the traditional Alford rotation, this new technique determines the direction of fast shear azimuth from the low-frequency limit of the extracted dispersion estimates of the fast and slow flexural wave slownesses. Since this technique uses the flexural wave over the entire band width, an anisotropy mechanism indicator is also generated identifying the presence of stressinduced anisotropy resulting in a crossover of the fast and slow flexural wave dispersions at some intermediate frequency. A statistical test is constructed to normalize differences in the dispersion estimates by using the uncertainties in those estimates for both the anisotropy (difference in shear slowness) indicator, AI, and the mechanism (dispersion crossover) indicator, CI, so as to flag only those zones where these differences are statistically significant. The anisotropy flag thus generated is a reliable indicator of anisotropy because it is based on slowness difference. This methodology has been applied in a tight shale gas field in Arkansas, USA, fractured tight sandstone in Colorado, USA, and also in the overburden sediments of the North Sea. It has been found to be of great help in identifying stress-induced anisotropy for hydraulic fracturing and cuttings-injection operations. EXAMPLES The anisotropy and crossover indicators were generated for both slow and fast formations from the North Sea and North America. Case History 1: Arkansas Shale Gas The formation evaluation objective for this well was to evaluate and characterize the borehole sonic anisotropy within a potential shale gas reservoir (Walsh et al., 2006). The rock exhibits both stress-induced as well as intrinsic anisotropy from natural fractures. The technique was used for a reliable first estimate of 3 differentiating types of shear-wave anisotropy. When the results of this technique were compared to the dispersion analysis, it was found that the proposed technique flagged the anisotropic zones automatically without much input from the user. The crossover indicator identified stress-induced anisotropy more reliably than manual visual picks. However, in zones where the dispersion curves are influenced by multiple phenomena that is, both fractures, stress and bedding more data were needed for correct interpretation. For example, in Figure 3 the DAFC algorithm has correctly flagged Interval A as anisotropic. Analysis of dispersion curves indicates most of this anisotropy is driven by fractures. A 50% confidence crossover flag is also generated. Note that it is hard to pick the crossover from the dispersion plot itself. However, when the low-frequency section is compared with the higher-frequency section, it is clear that there is a tendency toward crossover as the slow and fast dispersion plots start to overlay. The statistical algorithm does recognize that the crossover is not full, and on a scale of 0 to 1 grades the CI flag between 0.5 and 1, mostly below 1. In the same well, higher within the stiff organic-rich section, the crossover in the dispersion curves becomes clearer and the crossover indicator identifies the stressinduced anisotropy and flags it to 1 (see Figure 4). Dispersion plots show the crossover and also a significant amount of shale layering; the Stoneley shear stiffness is much larger than the vertical shear stiffness from the flexural waves. This event was described by Walsh et al. (2006) as orthotropic anisotropy, or a low degree of symmetry whereby C66 > C55 > C44. Case History 2: Colorado Tight Sandstone The algorithm was run on a well in Colorado. The objective of this well was to detect and evaluate the presence of fractures and natural gas. There are large differences in the minimum and maximum horizontal stresses throughout the region, along with variations in the concentration of existing natural fractures. The average porosity ranges from 3% to 7% with corresponding microdarcy matrix permeability. Most of the production requires hydraulic fracture stimulation if not enough natural fractures are encountered (Donald and Bratton, 2006).

4 SPWLA 52nd Annual Logging Symposium, May 14-18, 2011 The observed acoustic anisotropy is caused by fractures and stress. Figure 5 shows the outputs of DAFC algorithm. Both stress crossover and fracture anisotropy were observed on the dispersion curves. In Zone A, dispersion curves indicate mostly HTI (Horizontally Transverse Isotropic) type of anisotropy where the fast and slow shear waves have split parallel and perpendicular to the fracture strike. No crossover or stress effect is evident on the dispersion curves. The AI and CI indicators correctly pick the anisotropy. In Zone B, the crossover indicator is observed. Dispersion plots still show fracture effect at the low frequency but also show a subtle stress crossover, which may have been missed by visual checks. Comparing Zones B and A, it is evident that the large slowness anisotropy in Zone A has been completely dominated by natural fractures. There may also have been some stress effect in Zone A; however, if so, it is masked by the dominating presence of natural fractures. Zone C, on the other hand, shows isotropic behavior where there is no detectable anisotropy from stress or fractures. Identifying the isotropic zones is important for stimulation design and perforation placement. This zone may be difficult to break down during the initial stages of hydraulic fracturing; the rock may not have a preferential orientation for propagation of the induced fracture. Zone D is similar to Zone B in the top section, where the fractures are not intersecting the borehole and hence no fractures could be identified from the Stoneley data analysis. However, away from the borehole, fractures are present and are manifested in the slowness anisotropy at low frequencies. When there are competing sources of anisotropy, the crossover indicator is useful in quantifying the amount of stressrelated anisotropy in the wellbore. Case History 3: North Sea The objective of formation evaluation for this well was to establish rock properties and stress orientation for use in a program to inject cuttings into weak sandstone formation in the overburden. The sandstone was weak and unconsolidated with shear slowness in the range of 350 us/ft, which causes some energy loss at higher frequencies. However, despite this, significant energy concentration at low frequencies gives confidence in results. The top Eocene sand was not very stress sensitive, and although the shear anisotropy was observed, the crossover was never clear. The bottom Eocene sand showed more stress sensitivity and a crossover flag was raised. An anisotropy and crossover flag was raised in Interval A in the Oligocene sands shown in Figure 5. The dispersion analysis confirmed the finding. The direction of horizontal stress is NE61 from the fast shear azimuth in this interval. Shales in Interval B exhibit typical intrinsic anisotropy. The anisotropy flag is raised, but the crossover flag remains at 0. A review of dispersion analysis confirmed this zone is transversely isotropic. CONCLUSION The new DAFC algorithm can be used as an alternative to Alford rotation. One advantage of this algorithm is that it reviews the full dispersion curves for each depth and generates a statistical indicator of acoustic anisotropy (AI). If a dipole crossover is also observed, a crossover flag (CI) is also generated. The algorithm was useful in picking the anisotropy caused by fractures and stress in the case histories described in this paper. If multiple mechanisms are influencing the dispersion curves, the statistical nature of the algorithm enables generation of a spurious low-confidence crossover flag. In such cases, careful interpretation of the dispersion curves is necessary using other data such as fracture identification from the Stoneley reflection data. The results from this process can be readily used in geomechanical modeling for identifying zones with stress-related anisotropy or the presence of natural fractures. Direct applications to hydraulic fracturing or cuttings-injection programs in hard or soft rock have been illustrated. ACKNOWLEDGEMENTS The authors thank the corporations that provided data for this study and Schlumberger for permission to publish this work. 4

5 SPWLA 52 nd Annual Logging Symposium, May 14-18, 2011 REFERENCES Bose, S., Sinha, B.K., Sunaga, S., Endo, T., and Valero, H.P., 2007, Anisotropy processing without matched Cross-Dipole transmitters: presented at SEG San Antonio annual meeting. Donald, A. and Bratton, T., 2006, Advancement in acoustic techniques for evaluating open natural fractures: presented at SPWLA 47th Annual Logging Symposium, 4 7 June. Sinha, Bikash K., Kane, Michael R., and Frignet, Bernard, 2000, Dipole Dispersion Cross Overs and Sonic Logs in a Limestone Reservoir: Geophysics, 65 (2). Walsh, J., Sinha, B., and Donald, A Formation Anisotropy Parameters Using Borehole Sonic Data: presented at SPWLA 47th Annual Logging Symposium, 4 7 June. ABOUT THE AUTHORS Anzar Syed is a senior geomechanics engineer working with Schlumberger Data & Consulting Services in Aberdeen, UK. He has 15 years experience with Schlumberger working in the upstream oil and gas industry. He started his career as a wireline field engineer and has worked in Pakistan, Oman, Abu Dhabi, Indonesia, and UK. He has extensive experience in wireline field operations and management, log quality control and acquisition planning, petrophysical interpretation, and geomechanics. Since 2007 he has been involved in wellbore stability modeling and sanding analysis for various North Sea fields. Anzar holds an electrical engineering degree from NED University of Engineering and Technology, Karachi, Pakistan. Amelie Bertran is a petrophysicist working at the Schlumberger Montpellier Technology Center in France. She joined Schlumberger in 2005 as a wireline field engineer working in Holland. In 2007, she moved to Stavanger, Norway, where she was a petrophysicist in the Data Services team, mainly focusing on processing and interpretation. Since 2011, she has worked at the technology center on the implementation of sonic processing and geomechanics in a wellbore 5 analysis platform. She holds a Master s degree in geodynamics from the University of Chambery, France, and a Master s degree in geology from the National Museum of Natural History in Paris, France. Adam Donald is a Schlumberger principal geomechanics and acoustics engineer and is also the team leader for the North Sea. Adam has 12 years experience with Schlumberger; he joined the wireline group in 1998 as a field engineer and worked on land and offshore Canada projects. In 2004 he moved to Denver, where he focused on tight gas evaluation using acoustics and petrophysics. His current focus in the North Sea is wellbore stability, rock mechanics testing, and completion optimization. He received his Bachelor s degree in geological engineering from the University of Waterloo in Ontario, Canada (1998) and a Master s degree in mining engineering from Dalhousie University in Nova Scotia, Canada (2004). Adam holds two patents in areas of borehole acoustics and geomechanics. He is a registered Professional Engineer in the Province of Alberta, Canada, and an active publishing member of SPWLA, SPE, and SEG. Bikash Sinha is a scientific advisor and program manager at Schlumberger-Doll Research. Since joining Schlumberger in 1979, he has contributed to many sonic logging innovations for geophysical and geomechanical applications, as well as to development of high-precision quartz pressure sensors for downhole measurements. He is currently involved in sonic data analysis for the characterization of formation anisotropy, fractures, and stresses. Bikash has received a B.Tech. (Hons.) degree from the Indian Institute of Technology, Kharagpur, and an M.A.Sc. degree from the University of Toronto, both in mechanical engineering, and a PhD in applied mechanics from Rensselaer Polytechnic Institute, Troy, New York. He has authored or coauthored more than 170 technical papers and has received 31 U.S. patents. An IEEE fellow, he received the 1993 Outstanding Paper Award for an innovative design and development of a quartz pressure sensor published in the IEEE Transactions on UFFC. He is a member of SEG, SPE, and SPWLA. Sandip Bose is a principal research scientist at Schlumberger-Doll Research, where he has been working on developing signal-processing algorithms for borehole acoustic tools. Since joining Schlumberger in

6 SPWLA 52nd Annual Logging Symposium, May 14-18, , he has made numerous contributions to the commercial data processing for borehole sonic and ultrasonic tools with both wireline and logging-whiledrilling conveyances and has over a dozen patent and patent filings. Sandip holds a B.Tech degree from the Indian Institute of Technology, Kanpur, and a PhD from Cornell University, both in electrical engineering. He is a member of the IEEE and the SEG. Figure 2. Schematic diagram of stress-induced, transversely isotropic (TI), vertically aligned fractures that can be identified in terms of cross-dipole dispersion signatures. 6

7 SPWLA 52 nd Annual Logging Symposium, May 14-18, 2011 Figure 3. Dispersion crossovers and the anisotropy indicators in a log from a Tight Shale Gas well in Arkansas. Track 1 includes density (red, scale 1.95 to 2.95 g/cm3) and neutron porosity (blue, scale 0.45 to -.15 p.u). AI in Track 4 is the anisotropy indicator. CI in Track 5 is the crossover flag. In Track 6, the shaded green area is the slowness anisotropy, brown is fast shear, cyan is slow shear, and black is compressional; all are presented on scales of 200 to 0 us/ft. 7

8 SPWLA 52nd Annual Logging Symposium, May 14-18, 2011 Figure 4. Arkansas well. The crossover becomes clearer and the flag reads 1. Low-frequency analysis of the dispersion curves indicates fractures or shales are also influencing the anisotropy. Color legends are same as those of Figure 3. 8

9 SPWLA 52 nd Annual Logging Symposium, May 14-18, 2011 Figure 5. Anisotropy and crossover indicators in a log for a Colorado well showing a combination of stress and fracture features. Color legends are same as those of Figure 3. Additionally, the green shading on the right side of Track 6 indicates fracture width as measured from Stoneley data. 9

10 SPWLA 52nd Annual Logging Symposium, May 14-18, 2011 Figure 6. Crossover indicator in the log from unconsolidated overburden sands and shales in the North Sea. In Track 6, black is compressional, brown is the fast shear, and cyan is the slow shear. 10