Technical Papers
Jan 9, 2020

Poroelastoplastic Borehole Modeling by Tangent Stiffness Matrix Method

Publication: International Journal of Geomechanics
Volume 20, Issue 3

Abstract

The stability of borehole is a major concern in petroleum and geotechnical engineering. Subsurface fossil fuel and thermal energy extraction, deep geologic carbon/energy storage, and waste disposal require sophisticated borehole modeling. In many instances in deep well drilling, rock exhibits a plastic behavior rather than a pure linear elastic behavior. Rock is a porous material consisting of a compressible solid matrix and number of compressible fluids occupying the pore space, so numerical analysis of complex borehole problems based on nonlinear poromechanics is indispensable. In computer methods for nonlinear poromechanics, it is expected that the tangent stiffness method is more efficient than the constant stiffness method because the number of iterations can be reduced; however, the speculation has not been corroborated, especially when applied in borehole engineering. To investigate the computational efficiency of the two methods, fully coupled poroelastoplastic borehole modeling was implemented by both the tangent stiffness and initial (or constant) stiffness methods. Results showed that the two calculation methods are consistent, and the computational performance of the tangent stiffness method is superior to the initial stiffness method based on borehole modeling, reflected in the significantly reduced number of iterations and total running time required.

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Data Availability Statement

The models in the “Numerical Experiments” section and associated codes used during this study are confidential in nature.

References

Acar, B. Y., H. T. Durgunoglu, and M. T. Tumay. 1982. “A bipolar analytical and parametric finite element method analysis of surface loading in semi-infinite mass with a circular opening.” Math. Modell. 3 (3): 259–278. https://doi.org/10.1016/0270-0255(82)90029-X.
Biot, M. A. 1941. “General theory of three-dimensional consolidation.” J. Appl. Phys. 12 (2): 155–164. https://doi.org/10.1063/1.1712886.
Bowen, R. M. 1980. “Incompressible porous media models by use of the theory of mixtures.” Int. J. Eng. Sci. 18 (9): 1129–1148. https://doi.org/10.1016/0020-7225(80)90114-7.
Carter, J. P., and J. R. Booker. 1982. “Elastic consolidation around a deep circular tunnel.” Int. J. Solids Struct. 18 (12): 1059–1074. https://doi.org/10.1016/0020-7683(82)90093-2.
Carter, J. P., and J. R. Booker. 1983. “Creep and consolidation around circular openings in infinite media.” Int. J. Solids Struct. 19 (8): 663–675. https://doi.org/10.1016/0020-7683(83)90063-X.
Carter, J. P., and J. R. Booker. 1984. “Elastic consolidation around a lined circular tunnel.” Int. J. Solids Struct. 20 (6): 589–608. https://doi.org/10.1016/0020-7683(84)90030-1.
Chai, J. C., and Y. Zhou. 2018. “Method for considering the effect of nonuniform consolidation.” Int. J. Geomech. 18 (2): 04017151. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001078.
Chen, G., and L. Yu. 2015. “Consolidation around a tunnel in a general poroelastic medium under anisotropic initial stress conditions.” Comput. Geotech. 66 (May): 39–52. https://doi.org/10.1016/j.compgeo.2015.01.007.
Coussy, O. 1989. “A general theory of thermoporoelastoplasticity for saturated porous materials.” Transp. Porous Media 4 (3): 281–293. https://doi.org/10.1007/BF00138040.
Cui, L., A. H. D. Cheng, and Y. Abousleiman. 1997. “Poroelastic solution for an inclined borehole.” J. Appl. Mech. 64 (1): 32–38. https://doi.org/10.1115/1.2787291.
Desai, C. S. 2001. Mechanics of materials and interfaces: The disturbed state concept. Boca Raton, FL: CRC Press.
Desai, C. S., and Z. Wang. 2003. “Disturbed state model for porous saturated materials.” Int. J. Geomech. 3 (2): 260–265. https://doi.org/10.1061/(ASCE)1532-3641(2003)3:2(260).
Detournay, E., and A. H. D. Cheng. 1988. “Poroelastic response of a borehole in a non-hydrostatic stress field.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 25 (3): 171–182. https://doi.org/10.1016/0148-9062(88)92299-1.
Drucker, D. C., and W. Prager. 1952. “Soil mechanics and plasticity analysis of limit design.” Quart. J. Appl. Math. 10 (2): 157–165. https://doi.org/10.1090/qam/48291.
Fox, P. J., and J. D. Berles. 1997. “CS2: A piecewise-linear model for large strain consolidation.” Int. J. Numer. Anal. Methods Geomech. 21 (7): 453–475. https://doi.org/10.1002/(SICI)1096-9853(199707)21:7%3C453::AID-NAG887%3E3.0.CO;2-B.
Fox, P. J., and H. Pu. 2012. “Enhanced CS2 model for large strain consolidation.” Int. J. Geomech. 12 (5): 574–583. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000171.
Gambolati, G., M. Ferronato, P. Teatini, R. Deidda, and G. Lecca. 2001. “Finite element analysis of land subsidence above depleted reservoirs with pore pressure gradient and total stress formulations.” Int. J. Numeric. Analytic. Meth. Geomech. 25 (4): 307–327. https://doi.org/10.1002/nag.131.
Geertsma, J. 1957. “A remark on the analogy between thermoelasticity and the elasticity of saturated porous media.” J. Mech. Phys. Solids 6 (1): 13–16. https://doi.org/10.1016/0022-5096(57)90042-X.
Hall, K. M., and P. J. Fox. 2018. “Large strain consolidation model for land subsidence.” Int. J. Geomech. 18 (11): 06018028. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001267.
Lanzoni, L., E. Radi, and A. Nobili. 2018. “Stress and pressure fields around two wellbores in a poroelastic medium.” Meccanica 53 (3): 639–657. https://doi.org/10.1007/s11012-017-0683-4.
Lewis, R. W., and B. A. Schrefler. 1998. The finite element method in the static and dynamic deformation and consolidation of porous media. New York: Wiley.
Li, B., Y. G. Fang, and Z. F. Ou. 2018. “Asymptotic solution for the one-dimensional nonlinear consolidation equation including the pore evolution effect.” Int. J. Geomech. 18 (10): 04018125. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001239.
Manoharan, N., and S. P. Dasgupta. 1995. “Consolidation analysis of elasto-plastic soil.” Comput. Struct. 54 (6): 1005–1021. https://doi.org/10.1016/0045-7949(94)00403-P.
Meng, M., Z. Zamanipour, S. Miska, M. Yu, and E. M. Ozbayoglu. 2019. “Dynamic stress distribution around the wellbore influenced by surge/swab pressure.” J. Pet. Sci. Eng. 172 (Jan): 1077–1091. https://doi.org/10.1016/j.petrol.2018.09.016.
Neto, E. S., D. Peric, and D. Owen. 2008. Computational methods for plasticity. Chichester, UK: Wiley.
Ouria, A., C. S. Desai, and V. Toufigh. 2015. “Disturbed state concept-based solution for consolidation of plastic clays under cyclic loading.” Int. J. Geomech. 15 (1): 04014039. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000336.
Rice, J. R., and M. P. Cleary. 1976. “Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents.” Rev. Geophys. Space Phys. 14 (2): 227–241. https://doi.org/10.1029/RG014i002p00227.
Shao, J. F., G. Duveau, F. Bourgeois, and W. Z. Chen. 2006. “Elastoplastic damage modeling in unsaturated rocks and applications.” Int. J. Geomech. 6 (2): 119–130. https://doi.org/10.1061/(ASCE)1532-3641(2006)6:2(119).
Siriwardane, H. J., and C. S. Desai. 1981. “Two numerical schemes for nonlinear consolidation.” Int. J. Numer. Methods Eng. 17 (3): 405–426. https://doi.org/10.1002/nme.1620170309.
Terzaghi, K. 1923. “Berechnung der Durchlassigkeitsziffer des Tones aus dem Verlauf der hydrodynamischen Spannungserscheinungen.” Sitzungsberichte Mathematisch-naturwissenschaftlicheKlasse 132 (Part 11A): 125–138.
Terzaghi, K., B. R. Peck, and G. Mesri. 1999. Soil mechanics in engineering practice. 3rd ed. New York: Wiley.
Wong, C. K., R. G. Wan, and C. K. Wong. 2018. “Methodology for estimating creep deformation from consolidation deformation in 1D compression.” Int. J. Geomech. 18 (6): 04018042. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001162.
Yin, S. 2008. “Geomechanics-reservoir modeling by displacement discontinuity-finite element method.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Waterloo.
Yin, S., L. Rothenburg, and M. B. Dusseault. 2006. “3D coupled displacement discontinuity and finite element analysis of reservoir behavior during production in semi-infinite domain.” J. Transp. Porous Media 65 (3): 425–441. https://doi.org/10.1007/s11242-006-0003-2.
Zhang, H., S. Yin, and B. S. Aadnoy. 2018. “Poroelastic modeling of borehole breakouts for in-situ stress determination by finite element method.” J. Pet. Sci. Eng. 162 (12): 674–684. https://doi.org/10.1016/j.petrol.2017.10.085.
Zhu, B. 2018. The finite element method. Beijing: Wiley, Tsinghua University Press.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 20Issue 3March 2020

History

Received: Nov 28, 2018
Accepted: Sep 3, 2019
Published online: Jan 9, 2020
Published in print: Mar 1, 2020
Discussion open until: Jun 9, 2020

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Ph.D. Candidate, Dept. of Petroleum Engineering, Univ. of Wyoming, Laramie, WY 82071. Email: [email protected]
Associate Professor, Dept. of Civil and Environmental Engineering, Univ. of Waterloo, Waterloo, ON, Canada N2L 3G1 (corresponding author). ORCID: https://orcid.org/0000-0002-4854-693X. Email: [email protected]

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