Published

2023-11-10

Multivariable Regression 3D Failure Criteria for In-Situ Rock

Criterio de falla tridimensional por regresión multivariable en rocas in-situ

DOI:

https://doi.org/10.15446/esrj.v27n3.105872

Keywords:

3D failure criterion, Non-linear failure criterion, Linear regression, Polynomial multivariable regression, Geomechanics, In-situ stresses, Principal stresses (en)
criterio de falla tridimensional, criterio de falla no lineal, regresión lineal, regresión polinomial multivariable, geomecánica, tensiones in-situ, tensiones principales (es)

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Authors

  • Mohatsim Mahetaji Department of Petroleum Engineering, School of Energy Technology, Pandit Deendayal Energy University- PDEU, Gandhinagar, Gujarat, India https://orcid.org/0000-0002-2442-8891
  • Jwngsar Brahma Department of Mathematics, School of Technology, Pandit Deendayal Energy University- PDEU, Gandhinagar, Gujarat, India
  • Rakesh Kumar Vij Department of Petroleum Engineering

Wellbore stability problems increase with the exploration and development of oil and gas reservoirs. A new 3D non-linear failure criterion is proposed as a trigonometric function considering the intermediate principal stress (2)  on the triaxial compression test data. Mohr-Coulomb and Hoek-Brown are well-known failure criteria, but they do not consider the influence of (2) on rock strength. This new criterion produces a concave surface on the principal stress space (1,2, 3) with the influence of intermediate principal stress. In this study, sensitivity analysis for the variable is also done to understand the significant influence of parameters on the accuracy of the proposed criterion. Further validation of this non-linear criterion on three principal stresses (1,2, 3) was done compared with linear regression and second-degree polynomial regression results. It has been observed that the new non-linear 3D criterion with five material parameters reveals a good fit compared to linear regression and second-degree polynomial regression, which have four and six material parameters, respectively. The new non-linear criterion was further validated by comparison with existing criteria like the Priest, Drucker-Prager, and Mogi-Coulomb. It has been observed that the new 3D non-linear criterion shows a more accurate result than these existing criteria as certain rock types exhibit coefficient of determination (DC) values near one, precisely 0.95 for inada granite, 0.94 for orikabe monzonite, and 0.91 for KTB amphibolite. In contrast, other rock types have DC values ranging from 0.7 to 0.9. The new 3D non-linear criterion also yields lower root means square error (RMSE) values than the Mogi-Coulomb criterion for seven rock types. Specifically, the RMSE values by the new criterion are as follows: KTB amphibolite - 40.03 MPa, Dunham dolomite - 15.16 MPa, Shirahama sandstone - 9.08 MPa, Manazuru andesite - 22.14 MPa, Inada granite - 35.47 MPa, and Coconino sandstone - 19.047 MPa. This new 3D criterion gave precise predictions of the failure of the formation under in-situ stresses and was further helpful for the simulation of the wellbore in the petroleum industry. The variable in the new 3D criterion should be calculated from triaxial compression test data for each formation rock before applying this criterion to the wellbore stability problem and the sand production problem.

Los problemas de estabilidad de un pozo se incrementan con la exploración y el desarrollo de los reservorios de petróleo y gas. En este trabajo se propone un nuevo criterio de falla tridimensional y no lineal como una función trigonometrica que considera la tensión principal intermedia (2) en la información para la evaluación de compresión triaxial. Los criterios de falla de Mohr-Coulomb y Hoek-Brown son bien conocidos, pero estos no consideran la influencia de la tensión principal intermedia en la dureza de la roca. Este nuevo criterio produce una superficie cóncava en el espacio de las tensiones principales máxima, intermedia y mínima (1,2, 3) con la influencia de la tensión principal intermedia. Para este trabajo también se hizo el análisis de sensibilidad con el fin de entender la influencia de los parámetros en la exactitud del criterio propuesto. Se realizó una validación adicional de este criterio en las tres tensiones principales (máxima, intermedia y mínima) y se comparó con los resultados de la regresión lineal y la regresión polinómica de segundo grado. En este proceso se observó que el criterio tridimensional no lineal con cinco parámetros materiales revela un buen ajuste en comparación con las regresiones lineal y polinómica de segundo grado, que se trabajaron con cuatro y seis parámetros materiales, cada una. El nuevo criterio no lineal se validó adicionalmente con criterios existentes como el de Priest, Drucker-Prager y Mogi-Coulomb. Los autores observaron que el nuevo criterio tridimensional no lineal muestra un resultado más exacto que aquellos de los criterios existentes ya que ciertos tipos de roca exhiben valores en los coeficientes de determinación cerca de uno. Precisamente, 0.95 para granito inada, 0.94 para monzonita orikabe, y 0.91 para anfibolitas KTB. En contraste, otros tipos de rocas tienen valores en los coeficientes de determinación que van de 0.7 a 0.9. El nuevo criterio tridimensional no lineal también produce valores de error cuadrático medio (RMSE) más bajos que el criterio Mogi-Coulomb en siete tipos de rocas. Específicamente, los valores RMSE para el nuevo criterio son los siguientes: anfibolitas KTB = 40.03 MPa; dolomitas Dunham = 15.16 MPa; arenisca Shirahama = 9.08 MPa; andesita Manazuru = 22.14 MPa; granito inada = 35.47 MPa, y arenisca Coconino = 19.047 MPa. Este nuevo criterio tridimensional ofreció predicciones precisas de falla de la formación bajo tensiones in-situ y luego fue útil en la simulación de pozos en la industria petrolera. La variable en el nuevo criterio tridimensional debe de ser calculada con información de la evaluación de compresión triaxial en cada formación rocosa antes de aplicar este criterio en los problemas de estabilidad de pozos y en los problemas de producción de arena.

References

Aadnoy, B., & Looyeh, R. (2019). Petroleum rock mechanics: drilling operations and well design. Gulf Professional Publishing.

Al-Ajmi, A. M., & Zimmerman, R. W. (2005). Relation between the Mogi and the Coulomb failure criteria. International Journal of Rock Mechanics and Mining Sciences, 42(3), pp.431-439 doi.org/10.1016/j.ijrmms.2004.11.004

Bou-Hamdan, K. F. (2022). A 3D semianalytical model for simulating the proppant stresses and embedment in fractured reservoir rocks. Journal of Porous Media, 25(6). doi.org 10.1615/JPorMedia.2022041752

Brannon, R. M., Fossum, A. F., & Strack, O. E. (2009). KAYENTA: theory and user's guide (No. SAND2009-2282). Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States). doi.org/10.2172/984159

Bui, D., Nguyen, T., Nguyen, T., & Yoo, H. (2023). Formation damage simulation of a multi-fractured horizontal well in a tight gas/shale oil formation. Journal of Petroleum Exploration and Production Technology, 13(1), 163–184. https://doi.org/10.1007/S13202-022-01544-8/TABLES/6

Chang, C., & Haimson, B. (2000). True triaxial strength and deformability of the German Continental Deep Drilling Program (KTB) deep hole amphibolite. Journal of Geophysical Research: Solid Earth, 105(B8), 18999-19013. doi.org/10.1029/2000JB900184

Colmenares, L. B., & Zoback, M. D. (2002). A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks. International Journal of Rock Mechanics and Mining Sciences, 39(6), 695-729. doi.org/10.1016/S1365-1609(02)00048-5

Culshaw, M. G. (2015). The ISRM suggested methods for rock characterization, testing and monitoring: 2007–2014. In: Ulusay, R (ed.). Bulletin of Engineering Geology and the Environment, 74(4), 1499-1500. DOI: 10.1007/978-3-319-007713-0

Drucker, D. C., & Prager, W. (1952). Soil mechanics and plastic analysis or limit design. Quarterly of applied mathematics, 10(2), 157-165. https://www.jstor.org/stable/43633942

Ewy, R. T. (1999). Wellbore-stability predictions by use of a modified Lade criterion. SPE Drilling & Completion, 14(02), 85-91. doi.org/10.2118/56862-PA

Ghassemi, A. (2017). Application of rock failure simulation in design optimization of the hydraulic fracturing. Porous Rock Fracture Mechanics, 3-23. https://doi.org/10.1016/B978-0-08-100781-5.00001-4

Haimson, B., & Chang, C. (2000). A new true triaxial cell for testing mechanical properties of rock, and its use to determine rock strength and deformability of Westerly granite. International Journal of Rock Mechanics and Mining Sciences, 37(1-2), 285-296. doi.org/10.1016/S1365-1609(99)00106-9

Hoek, E., & Brown, E.T. (1997). Practical estimates of rock mass strength. International journal of rock mechanics and mining sciences, 34(8), 1165-1186. doi.org/10.1016/S1365-1609(97)80069-X

Hoek, E., Carranza-Torres, C., & Corkum, B. (2002). Hoek-Brown failure criterion-2002 edition. Proceedings of NARMS-Tac, 1(1), 267-273.

Jiang, H., & Yang, Y. (2020). A three‐dimensional Hoek–Brown failure criterion based on an elliptical Lode dependence. International Journal for Numerical and Analytical Methods in Geomechanics, 44(18), 2395-2411. doi.org/10.1007/s00603-014-0691-9

Kim, M., & Lade, P. (1984). Modelling rock strength in three dimensions. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 21(1), 21-33. https://doi.org/10.1016/0148-9062(84)90006-8

Lee, Y. K., Pietruszczak, S., & Choi, B. H. (2012). Failure criteria for rocks based on smooth approximations to Mohr–Coulomb and Hoek–Brown failure functions. International Journal of Rock Mechanics and Mining Sciences, 56, 146–160. https://doi.org/10.1016/J.IJRMMS.2012.07.032

Lian, J., Sharaf, M., Archie, F., & Münstermann, S. (2013). A hybrid approach for modelling of plasticity and failure behaviour of advanced high-strength steel sheets. International Journal of Damage Mechanics, 22(2), 188-218. doi.org/10.1177/1056789512439319

Ma, X., & Haimson, B. C. (2016). Failure characteristics of two porous sandstones subjected to true triaxial stresses. Journal of Geophysical Research: Solid Earth, 121(9), 6477-6498. 10.1002/2016JB012979

Mahetaji, M., Brahma, J., & Sircar, A. (2020). Pre-drill pore pressure prediction and safe well design on the top of Tulamura anticline, Tripura, India: a comparative study. Journal of Petroleum Exploration and Production Technology, 10(3). https://doi.org/10.1007/s13202-019-00816-0

Mahetaji, M., Brahma, J., & Vij, R. K. (2023). A new extended Mohr-Coulomb criterion in the space of three-dimensional stresses on the in-situ rock. Geomechanics and Engineering, 32(1), 49–68. https://doi.org/10.12989/GAE.2023.32.1.049

Mogi, K. (1971). Fracture and flow of rocks under high triaxial compression. Journal of Geophysical Research, 76(5), 1255-1269. doi.org/10.1029/JB076i005p01255

Mogi, K. (2006). Experimental rock mechanics (Vol. 3). CRC Press.

Ottosen, N. S. (1977). A failure criterion for concrete. Journal of the Engineering Mechanics Division, 103(4), 527-535. doi.org/10.1061/JMCEA3.0002248

Pan, X. D., & Hudson, J. A. (1988). A simplified three dimensional Hoek-Brown yield criterion. ISRM International Symposium. ISRM-IS-1988-011

Priest, S. D. (2005). Determination of shear strength and three-dimensional yield strength for the Hoek-Brown criterion. Rock Mechanics and Rock Engineering, 38(4), 299-327. doi.org/10.1007/s00603-005-0056-5

Shvarts, A., & van Helden, G. (2022). Embodied learning at a distance: From sensory-motor experience to constructing and understanding a sine graph. Mathematical Thinking and Learning, 1-29. doi.org/10.1080/10986065.2021.1983691

Singh, M., Raj, A., & Singh, B. (2011). Modified Mohr–Coulomb criterion for non-linear triaxial and polyaxial strength of intact rocks. International Journal of Rock Mechanics and Mining Sciences, 48(4), 546-555. doi.org/10.1016/j.ijrmms.2011.02.004

Takahashi, M., & Koide, H. (1989). Effect of the intermediate principal stress on strength and deformation behavior of sedimentary rocks at the depth shallower than 2000 m. ISRM international symposium. ISRM.

Yi, X., Ong, S., & Russell, J. E. (2006). Quantifying the effect of rock strength criteria on minimum drilling mud weight prediction using polyaxial rock strength test data. International Journal of Geomechanics, 6(4), 260-268. doi.org/10.1061/(ASCE)1532-3641(2006)6:4(260)

Yi, X., Valkó, P. P. & Russell, J. E. (2005). Effect of rock strength criterion on the predicted onset of sand production. International Journal of Geomechanics, 5(1), 66-73. doi.org/10.1061/(ASCE)1532-3641(2005)5:1(66)

Yi, X., Valkó, P. P., & Russell, J. E. (2005). Effect of rock strength criterion on the predicted onset of sand production. International Journal of Geomechanics, 5(1), 66-73. doi.org/10.1061/(ASCE)1532-3641(2005)5:1(66)

Zhang, J. J. (2019). Applied petroleum geomechanics. Gulf Professional Publishing.

Zhang, L. (2008). A generalized three-dimensional Hoek–Brown strength criterion. Rock mechanics and rock engineering, 41(6), 893-915. doi.org/10.1007/s00603-008-0169-8

Zhang, L., & Zhu, H. (2007). Three-dimensional Hoek-Brown strength criterion for rocks. Journal of Geotechnical and Geoenvironmental Engineering, 133(9), 1128-1135. doi.org/10.1061/(ASCE)1090-0241(2007)133:9(1128)

How to Cite

APA

Mahetaji, M., Brahma, J. and Kumar Vij, R. (2023). Multivariable Regression 3D Failure Criteria for In-Situ Rock. Earth Sciences Research Journal, 27(3), 273–287. https://doi.org/10.15446/esrj.v27n3.105872

ACM

[1]
Mahetaji, M., Brahma, J. and Kumar Vij, R. 2023. Multivariable Regression 3D Failure Criteria for In-Situ Rock. Earth Sciences Research Journal. 27, 3 (Nov. 2023), 273–287. DOI:https://doi.org/10.15446/esrj.v27n3.105872.

ACS

(1)
Mahetaji, M.; Brahma, J.; Kumar Vij, R. Multivariable Regression 3D Failure Criteria for In-Situ Rock. Earth sci. res. j. 2023, 27, 273-287.

ABNT

MAHETAJI, M.; BRAHMA, J.; KUMAR VIJ, R. Multivariable Regression 3D Failure Criteria for In-Situ Rock. Earth Sciences Research Journal, [S. l.], v. 27, n. 3, p. 273–287, 2023. DOI: 10.15446/esrj.v27n3.105872. Disponível em: https://revistas.unal.edu.co/index.php/esrj/article/view/105872. Acesso em: 21 feb. 2024.

Chicago

Mahetaji, Mohatsim, Jwngsar Brahma, and Rakesh Kumar Vij. 2023. “Multivariable Regression 3D Failure Criteria for In-Situ Rock”. Earth Sciences Research Journal 27 (3):273-87. https://doi.org/10.15446/esrj.v27n3.105872.

Harvard

Mahetaji, M., Brahma, J. and Kumar Vij, R. (2023) “Multivariable Regression 3D Failure Criteria for In-Situ Rock”, Earth Sciences Research Journal, 27(3), pp. 273–287. doi: 10.15446/esrj.v27n3.105872.

IEEE

[1]
M. Mahetaji, J. Brahma, and R. Kumar Vij, “Multivariable Regression 3D Failure Criteria for In-Situ Rock”, Earth sci. res. j., vol. 27, no. 3, pp. 273–287, Nov. 2023.

MLA

Mahetaji, M., J. Brahma, and R. Kumar Vij. “Multivariable Regression 3D Failure Criteria for In-Situ Rock”. Earth Sciences Research Journal, vol. 27, no. 3, Nov. 2023, pp. 273-87, doi:10.15446/esrj.v27n3.105872.

Turabian

Mahetaji, Mohatsim, Jwngsar Brahma, and Rakesh Kumar Vij. “Multivariable Regression 3D Failure Criteria for In-Situ Rock”. Earth Sciences Research Journal 27, no. 3 (November 10, 2023): 273–287. Accessed February 21, 2024. https://revistas.unal.edu.co/index.php/esrj/article/view/105872.

Vancouver

1.
Mahetaji M, Brahma J, Kumar Vij R. Multivariable Regression 3D Failure Criteria for In-Situ Rock. Earth sci. res. j. [Internet]. 2023 Nov. 10 [cited 2024 Feb. 21];27(3):273-87. Available from: https://revistas.unal.edu.co/index.php/esrj/article/view/105872

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