Characterization of Anisotropic Elastic Moduli and Stress for Unconventional Reservoirs Using Laboratory Static and Dynamic Geomechanical Data (includes associated erratum)
- Farrukh Hamza (Halliburton) | Cheng Chen (Halliburton) | Ming Gu (Halliburton) | John Quirein (Halliburton) | Vladimir Martysevich (Halliburton) | Luis Matzar (Halliburton)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- May 2018
- Document Type
- Journal Paper
- 392 - 404
- 2018.Society of Petroleum Engineers
- ANNIE model, dynamic-to-static correlation, Anisotropy, Laboratory Geomechanics, Ultrasonic measurements
- 1 in the last 30 days
- 380 since 2007
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Erratum Notice: This paper has been modified from its original version to include erratum SPE-175907-ER (https://doi.org/10.2118/175907-ER); correction to the captions of Figs. 2 and 3 on pages 395 and 396.
In a vertically transverse isotropic (VTI) medium, accurate prediction of the vertical and horizontal Young’s moduli (E) and Poisson’s ratios (ν) is crucial to predicting minimum horizontal stress (σhmin) and hence selecting drilling mud, cement weights, and perforation locations. Fully characterizing the geomechanical properties of VTI shale requires five independent stiffness coefficients. In a vertical well, two of them are directly calculated from the velocity of the vertically propagating compressional waves (P-waves) and shear waves (S-waves), whereas a third is estimated from the Stoneley-wave velocity. To obtain the last two stiffness coefficients, an empirical model must be used. This study integrates laboratory mechanical and sonic measurements to evaluate the ANNIE and modified- ANNIE models and extend the dynamic-to-static conversion equations. The ANNIE model is a three-parameter empirical model proposed by Schoenberg et al. (1996) to interpret anisotropic stiffness coefficients.
Laboratory static and dynamic geomechanical experiments were applied to multiple core plugs extracted at different depths from a target shale play. Using a laboratory ultrasonic scanner, velocities were measured in different directions to obtain the five stiffness coefficients. To compare the performance of the two empirical models, three stiffness coefficients were then applied along with the ANNIE or modified-ANNIE models for estimating the dynamic Young’s modulus and Poisson’s ratio. The static elastic moduli were measured using triaxial compression experiments; horizontal and vertical core plugs were tested to account for anisotropy.
Static and dynamic results illustrated that horizontal Young’s moduli were predominantly higher than vertical Young’s moduli, which suggested a horizontal layered structure. Vertical Poisson’s ratios can be greater or smaller than horizontal Poisson’s ratios, which is consistent with the prediction of the modified-ANNIE model. Conversely, the ANNIE model always predicts ν (vertical) ≥ ν (horizontal). Static and dynamic data illustrated that the anisotropic σhmin (minimum horizontal stress) was predominantly higher than the isotropic σhmin. This implied that using an isotropic model to predict laminated shale will underestimateσhmin. The elastic moduli measured from the dynamic method were consistently higher than those measured from the static method. The dynamic and static data were used to fit the widely used dynamic-to-static conversion equations: the Canady (2011) and Morales and Marcinew (1993) equations. The Canady (2011) equation was extended to the “very hard” (greater than 70-GPa or 10.2-Mpsi Young’s modulus) regime, whereas the Morales and Marcinew (1993) equation was extended to the regime of porosity less than 10%. Mpsi¼1,000 psi. Finally, the results of σhmin predicted by the isotropic and two anisotropic models (ANNIE and modified-ANNIE) were compared with the values of σhmin calculated using full ultrasonic data measured in the laboratory, showing that modified-ANNIE improved the prediction by solving the stress-underestimation issue of the ANNIE and isotropic models.
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Belikov, B. A. 1970. Elastic Properties of Rock Minerals and Rocks. Moscow: Nauka.
Canady, W. 2011. A Method for Full-Range Young’s Modulus Correction. Presented at the North American Unconventional Gas Conference and Exhibition, The Woodlands, Texas, 14–16 June. SPE-143604-MS. https://doi.org/10.2118/143604-MS.
Chertov, M. 2012. Closed-Form Solution for Vertical Fracture Width in Anisotropic Elastic Formations. Int. J. Rock Mech. Min. 53 (July): 70–75. https://doi.org/10.1016/j.ijrmms.2012.04.006.
Eissa, E. A. and Kazi, A. 1988. Relation Between Static and Dynamic Young’s Moduli of Rocks. Int. J. Rock Mech. Min. 25 (6): 479–482. https://doi.org/10.1016/0148-9062(88)90987-4.
Gorjainov, N. L. 1979. Seismic Methods in Engineering Geology. Moscow: Nedra.
Gu, M., Quirein, J., Murphy, E. et al. 2016. Method for Acoustic Anisotropy Interpretation in Shales When the Stoneley-Wave Velocity is Missing. Petrophysics 57 (2): 140–155. SPWLA-2016-v57n2a5.
Higgins, S. M., Goodwin, S. A., Donald, A. et al. 2008. Anisotropic Stress Models Improve Completion Design in the Baxter Shale. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 21–24 September. SPE-115736-MS. https://doi.org/10.2118/115736-MS.
Hows, A. M., Hofmann, R., and Gonzalez, E. F. 2013. Characterization of Anisotropic Dynamic Mechanical Rock Properties in Shale Gas Plays. Presented at the 47th US Rock Mechanics/Geomechanics Symposium, San Francisco, 23–26 June. ARMA-2013-604.
Lacy, L. L. 1997. Dynamic Rock Mechanics Testing for Optimized Fracture Designs. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 5–8 October. SPE-38716-MS. https://doi.org/10.2118/38716-MS.
Mavko, G., Mukerji, T., and Dvorkin, J. 2009. The Rock Physics Handbook, second edition. Cambridge, UK: Cambridge University Press.
McCann, D. M. 1992. Determination of Young’s Modulus of the Rock Mass from Geophysical Logs. Geol. Soc. London 65 (1): 317–325. https://doi.org/10.1144/GSL.SP.1992.065.01.24.
Morales, R. H and Marcinew, R. P. 1993. Fracturing of High-Permeability Formations: Mechanical Properties Correlations. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 3–6 October. SPE-26561-MS. https://doi.org/10.2118/26561-MS.
Murphy, E., Barraza, S. R., Gu, M. et al. 2015. New Models for Acoustic Anisotropic Interpretation in Shale. Presented at the SPWLA 56th Annual Logging Symposium, Long Beach, California, 18–22 July. SPWLA-2015-WWWW.
New England Research. 2016. AutoScan, http://www.ner.com/site/systems/autoscan.html (accessed 26 April 2017).
Norris, A. N. and Sinha, B. K. 1993. Weak Elastic Anisotropy and the Tube Wave. Geophysics 58 (8): 1091–1098. https://doi.org/10.1190/1.1443493.
Nye, J. F. 1985. Physical Properties of Crystals: Their Representation by Tensors and Matrices. New York: Oxford University Press.
Quirein, J., Eid, M., and Cheng, A. 2014. Predicting the Stiffness Tensor of a Transversely Isotropic Medium When the Vertical Poisson’s Ratio is Less Than the Horizontal Poisson’s Ratio. Presented at the SPWLA 55th Annual Logging Symposium, Abu Dhabi, 18–22 May. SPWLA-2014-OOOO.
Schoenberg, M., Muir, F., and Sayers, C. 1996. Introducing Annie: A Simple Three-Parameter Anisotropic Velocity Model for Shales. J. Seism. Explor. 5 (1): 35–49.
Sone, H. 2012. Mechanical Properties of Shale Gas Reservoir Rocks and Its Relation to the In-Situ Stress Variation Observed in Shale Gas Reservoirs. PhD dissertation, Stanford University, Stanford, California.
Thiercelin, M. J. and Plumb, R. A. 1994. Core-Based Prediction of Lithologic Stress Contrasts in East Texas Formations. SPE Form Eval 9 (4): 251–258. SPE-21847-PA. https://doi.org/10.2118/21847-PA.
Thomsen, L. 1986. Weak Elastic Anisotropy. Geophysics 51 (10): 1954–1966. https://doi.org/10.1190/1.1442051.
Vernik, L. and Nur, A. 1990. Ultrasonic Velocity and Anisotropy of Petroleum Source Rocks: The Bakken Formation. Proc., SEG Technical Program Expanded Abstracts 1990, 845–848. https://doi.org/10.1190/1.1890358.
Voigt, W. 1928. Lehrbuch der Kristallphysik, first edition (repr.). Leipzig, Germany: B. G. Teubner Verlag.
Wang, Z. 2000. Dynamic Versus Static Elastic Properties of Reservoir Rocks. In Seismic and Acoustic Velocities in Reservoir Rocks: Recent Developments, ed. Z. Wang and A. Nur, 531–539. Tulsa: Society of Exploration Geophysicists.
Waters, G. A., Lewis, R. E., and Bentley, D. 2011. The Effect of Mechanical Properties Anisotropy in the Generation of Hydraulic Fractures in Organic Shales. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 30 October–2 November. SPE-146776-MS. https://doi.org/10.2118/146776-MS.
Zoback, M. D. 2007. Reservoir Geomechanics, first edition. Cambridge, UK: Cambridge University Press.
Zoback, M. D., and Byerlee, J. D. 1975. The Effect of Cyclic Differential Stress on Dilatancy in Westerly Granite Under Uniaxial and Triaxial Conditions. J. Geophys. Res. 80: 1526–1530. https://doi.org/10.1029/JB080i011p01526.