Porochemothermoelastic Solution for an Inclined Borehole in a Transversely Isotropic Formation
Publication: Journal of Engineering Mechanics
Volume 131, Issue 5
Abstract
A generalized anisotropic poromechanics formulation for chemically active poroelastic media under nonisothermal conditions, termed as porochemothermoelastic, is presented. The pore fluid is modeled as a two-species constituent comprised of the solute and the solvent. Governing equations are developed and applied to obtain the analytical solution for an inclined borehole in chemically active transversely isotropic formation subjected to a three-dimensional state of stress and nonisothermal conditions. Numerical examples are presented to demonstrate the thermochemical effects on stress and pore pressure distributions in the vicinity of the borehole and their potential impacts on borehole stability.
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Acknowledgments
The writers would like to thank Dr. Rajesh Nair and Dr. Mazen Kanj for the discussion pertaining to the results and constructive suggestions in preparing this paper. The financial support from the Rock Mechanics Consortium, at the PoroMechanics Institute, is also acknowledged.
References
Abousleiman, Y., Cheng, A. H.-D., Jiang, C., and Roegiers, J.-C. (1996). “Porovis-coelastic analysis of borehole and cylinder problems.” Acta Mech., 119, 199–219.
Abousleiman, Y., and Cui, L. (1998). “Poroelastic solutions in transversely isotropic media for wellbore and cylinder.” Int. J. Solids Struct., 35(34/35), 4905–4929.
Abousleiman, Y., and Cui, L. (2000). “The theory of anisotropic poroelasticity with applications.” Modeling and applications in geomechanics, M. Zaman, J. Booker, and G. Gioda, eds., Wiley, New York, 559–593.
Abousleiman, Y., and Ekbote, S. (2004). “Solutions for the inclined borehole in a porothermoelastic transversely isotropic medium.” J. Appl. Mech., 72, 102–114.
Abousleiman, Y., Ekbote, S., and Tare, U. (2001). “Time-dependent wellbore stability predictions.” J. Pet. Technol., February, 29–30.
Abousleiman, Y., Kanj, M., and Ekbote, S. (2002). “Tools in Poromechanics.” Proc., 2nd Biot’s Conf. on Poromechanics, Grenoble, France.
Bear, J., and Corapcioglu, M. Y. (1981). “A mathematical model for consolidation in a thermoelastic aquifer due to hot water injection or pumping.” Water Resour. Res., 17(3), 723–736.
Biot, M. A. (1941). “General theory of three-dimensional consolidation.” J. Appl. Phys., 12, 155–164.
Biot, M. A. (1955). “Theory of elasticity and consolidation of a porous anisotropic solid.” J. Appl. Phys., 26, 182–185.
Biot, M. A., and Willis, D. G. (1957). “The elastic coefficients of the theory of consolidation.” J. Appl. Mech., 24, 594–601.
Bird, R. B., Stewart, W. E., and Lightfoot, E. N. (1960). Transport phenomena, Wiley, New York.
Coussy, O. (1989). “A general theory of thermoporoelastoplasticity for saturated porous materials.” Transp. Porous Media, 4, 281–293.
Coussy, O. (1991). Mécanique des milieux poreux, Editions Technip, Paris.
Coussy, O. (1995). Mechanics of porous continua, Wiley, New York.
Cui, L., Abousleiman, Y., Cheng, A. H.-D., and Roegiers, J.-C. (1999). “Time-dependent failure analysis of inclined boreholes in fluid saturated formations.” J. Energy Resour. Technol., 121, 31–38.
Cui, L., Cheng, A. H.-D., and Abousleiman, Y. (1997). “Poroelastic solution of an inclined borehole.” J. Appl. Mech., 64, 32–38.
Ekbote, S. (2002). “Anisotropic poromechanics of the wellbore coupled with thermal and chemical gradients.” PhD dissertation, The University of Oklahoma, Norman, Okla.
Ekbote, S., and Abousleiman, Y. (2003a). “Incorporating chemical effects in a porothermoelastic formulation and application to inclined boreholes.” The 2003 IUTAM Symposium on the Mechanics of Physicochemical and Electromechanical Interactions in Porous Media, Rolduc, Kerkrade, The Netherlands.
Ekbote, S., and Abousleiman, Y. (2003b). “Stability analyses of inclined boreholes in chemically active formations under non-isothermal conditions.” The 16th ASCE Conf. on Engineering Mechanics (CD-ROM), Seattle, Wash.
Heidug, W. K., and Wong, S. W. (1996). “Hydration swelling of water-absorbing rocks: A constitutive model.” Int. J. Numer. Analyt. Meth. Geomech., 20, 403–430.
Huyghe, J. M., and Janssen, J. D. (1999). “Thermo-chemo-electro-mechanical formulation of saturated charged porous solids.” Transp. Porous Media, 24, 129–141.
Katsube, N. (1988). “The anisotropic thermomechanical constitutive theory for fluid-filled porous materials with solid/fluid outer boundaries.” Int. J. Solids Struct., 24(4), 375–380.
Li, X., and Li, X. (1992). “On the thermoelasticity of multicomponent fluid-saturated reacting porous media.” Int. J. Eng. Sci., 30(7), 891–912.
McTigue, D. F. (1986). “Thermoelastic response of fluid-saturated porous rock.” J. Geophys. Res., [Solid Earth Planets], 91(B9), 9533–9542.
McTigue, D. F. (1990). “Flow to a heated borehole in porous, thermoelastic rock: Analysis.” Water Resour. Res., 26(8), 1763–1774.
Mitchell, J. K. (1993). Fundamentals of soil behavior, Wiley, New York.
Mody, F. K., and Hale, A. H. (1993). “A borehole model to couple the mechanics and chemistry of drilling fluid shale interaction.” Proc., SPE/IADC Drilling Conf., The Society of Petroleum Engineers, Richardson, Tex., paper 25728.
Onaisi, A., Audibert, A., Bieber, M. T., Bailey, L., Denis, J., and Hammond, P. S. (1993). “X-ray tomography visualization and mechanical modeling of swelling shale.” J. Pet. Sci. Eng., 9, 313–329.
Sherwood, J. D. (1993). “Biot poroelasticity of a chemically active shale.” Proc. R. Soc. London, Ser. A, 440, 365–377.
Sherwood, J. D. (1994a). “A model of hindered solute transport in a poroelastic shale.” Proc. R. Soc. London, Ser. A, 445, 679–692.
Sherwood, J. D. (1994b). “A model for the flow of water and ions into swelling shale.” Langmuir, 10, 2480–2486.
Sherwood, J. D. (1995). “Ionic transport in swelling shale.” Adv. Colloid Interface Sci., 61, 51–64.
Sherwood, J. D., and Bailey, L. (1994). “Swelling shale around a cylindrical wellbore.” Proc. R. Soc. London, Ser. A, 444, 161–184.
Stehfest, H. (1970). “Numerical inversion of Laplace transforms.” Commun. ACM, 13, 47–49 and 624.
Yeung, A. T., and Mitchell, J. K. (1993). “Coupled fluid, electrical and chemical flows in soil.” Geotechnique, 43(1), 121–134.
Yuan, Y. G., Abousleiman, Y., and Roegiers, J.-C. (1995). “Fluid penetration around a borehole under coupled hydro-electro-chemico-thermal potentials.” The 46th Annual Technical Meeting of The Petroleum Society of CIM, Alberta, Canada, paper 95–72.
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© 2005 ASCE.
History
Received: Mar 17, 2003
Accepted: Jun 4, 2004
Published online: May 1, 2005
Published in print: May 2005
Notes
Note. Associate Editor: Alexander H.-D. Cheng
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