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TECHNICAL PAPERS

Solutions for the Inclined Borehole in a Porothermoelastic Transversely Isotropic Medium

[+] Author and Article Information
Younane Abousleiman, Shailesh Ekbote

Mewbourne School of Petroleum and Geological Engineering, School of Civil Engineering and Environmental Science, PoroMechanics Institute, The University of Oklahoma, Norman, OK 73019

J. Appl. Mech 72(1), 102-114 (Feb 01, 2005) (13 pages) doi:10.1115/1.1825433 History: Received January 21, 2004; Revised March 18, 2004; Online February 01, 2005
Copyright © 2005 by ASME
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References

Biot,  M. A., 1941, “General Theory of Three-Dimensional Consolidation,” J. Appl. Phys., 12, pp. 155–164.
Biot,  M. A., 1955, “Theory of Elasticity and Consolidation of a Porous Anisotropic Solid,” J. Appl. Phys., 26, pp. 182–185.
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), pp. 723–736.
Kurashige,  M., 1989, “A Thermoelastic Theory of Fluid-Filled Porous Materials,” Int. J. Solids Struct., 25(9), pp. 1039–1052.
Coussy,  O., 1989, “A General Theory of Thermoporoelastoplasticity for Saturated Porous Materials,” Transp. Porous Media, 4, pp. 281–293.
Coussy, O., 1995, Mechanics of Porous Continua, Wiley, New York.
Katsube,  N., 1988, “The Anisotropic Thermomechanical Constitutive Theory for Fluid-Filled Porous Materials With Solid/Fluid Outer Boundaries,” Int. J. Solids Struct., 24(4), pp. 375–380.
Utsugida, Y., 1985, “Coupled Analysis of Flow and Heat Around a High-Level Nuclear Waste Repository,” in Proc. 5th Int. Conf. Numerical Methods in Geomechanics, Nagoya, Balkema, Rotterdam, pp. 711–716.
Brownell,  D. H., Garg,  S. K., and Pritchett,  J. W., 1977, “Governing Equations for Geothermal Reservoirs,” Water Resour. Res., 13, pp. 929–934.
Rice,  J. R., and Cleary,  M. P., 1976, “Some Basic Stress Diffusion Solutions for Fluid-Saturated Elastic Porous Media With Compressible Constituents,” Rev. Geophys. Space Phys., 14(4), pp. 227–241.
Thompson,  M., and Willis,  J. R., 1991, “A Reformulation of the Equations of Anisotropic Poroelasticity,” ASME J. Appl. Mech., 58, pp. 612–616.
Wang, H., 2000, Theory of Linear Poroelasticity With Applications to Geomechanics and Hydrogeology, Princeton University Press, Princeton.
Booker,  J. R., and Savvidou,  C., 1984, “Consolidation Around a Spherical Heat Source,” Int. J. Solids Struct., 20, pp. 1079–1090.
Booker,  J. R., and Savvidou,  C., 1985, “Consolidation Around a Point Heat Source,” Int. J. Numer. Analyt. Meth. Geomech., 9, pp. 173–184.
McTigue,  D. F., 1986, “Thermoelastic Response of Fluid-Saturated Porous Rock,” J. Geophys. Res., 91(B9), pp. 9533–9542.
McTigue,  D. F., 1990, “Flow to a Heated Borehole in Porous, Thermoelastic Rock: Analysis,” Water Resour. Res., 26(8), pp. 1763–1774.
Kurashige,  M., 1992, “Thermal Stresses of a Fluid-Saturated Poroelastic Hollow Cylinder,” JSME Int. J.,35(4), pp. 386–391.
Kodashima,  T., and Kurashige,  M., 1996, “Thermal Stresses in a Fluid-Saturated Poroelastic Hollow Sphere,” J. Therm. Stresses, 19, pp. 139–151.
Cheng,  A. H.-D., 1998, “Material Coefficients of Anisotropic Poroelasticity,” Int. J. Rock Mech. Min. Sci., 34, pp. 183–193.
Abousleiman, Y., and Cui, L., 2000, “The Theory of Anisotropic Poroelasticity With Applications,” Modeling and Applications in Geomechanics, edited by M. Zaman, J. Booker, and G. Gioda, Wiley, New York.
Abousleiman,  Y., Cheng,  A. H.-D., Cui,  L., Detournay,  E., and Roegiers,  J.-C., 1996, “Mandel’s Problem Revisited,” Geotechnique, 46(2), pp. 187–195.
Abousleiman,  Y., and Cui,  L., 1998, “Poroelastic Solutions in Transversely Isotropic Media for Wellbore and Cylinder,” Int. J. Solids Struct., 35(34/35), pp. 4905–4929.
Li,  X., 1992, “A Generalized Theory of Thermoelasticity for an Anisotropic Medium,” Int. J. Eng. Sci., 30(5), pp. 571–577.
Sharma,  J. N., and Kumar,  V., 1996, “On the Axisymmetric Problems of Generalized Anisotropic Thermoelasticity,” J. Therm. Stresses, 19, pp. 781–794.
Sharma,  J. N., and Kumar,  V., 1997, “Plane Strain Problems of Transverse Isotropic Thermoelastic Media,” J. Therm. Stresses, 20, pp. 463–476.
Nowacki, W., 1962, Thermoelasticity, Addison-Wesley, Reading, MA.
Nowinski, J. L., 1978, Theory of Thermoelasticity With Applications, Sijthoff & Noordhoff, Groningen.
Ekbote, S., Abousleiman, Y., and Zaman, M. M., 2000, “Porothermoelastic Solution for an Inclined Borehole in Transversely Isotropic Porous Media,” Fourth North American Rock Mechanics Symposium. Seattle, WA, Sept. 5–10.
Ekbote, S., 2002, “Poromechanics Wellbore Stability: Theory and Applications,” Ph.D. dissertation, The University of Oklahoma.
Abousleiman, Y., and Ekbote, S., 1999, “Porothermoelasticity in Transversely Isotropic Porous Materials,” The IUTAM Symposium on Theoretical and Numerical Methods in Continuum Mechanics of Porous Materials. Stuttgart, Germany, Sept. 5–10, pp. 145–152.
Bird, R. B., Stewart, W. E., and Lightfoot, E. N., 1960, Transport Phenomena, Wiley, New York.
Cui,  L., Cheng,  A. H.-D., and Abousleiman,  Y., 1997, “Poroelastic Solution of an Inclined Borehole,” ASME J. Appl. Mech., 64, pp. 32–38.
Cheng,  A. H.-D., 1997, “On Generalized Plane Strain Poroelasticity,” Int. J. Rock Mech. Min. Sci., 35, pp. 199–205.
Li,  X., Cui,  L., and Roegiers,  J.-C., 1998, “Thermoporoelastic Modeling of Wellbore Stability in Non-Hydrostatic Stress Field,” Int. J. Rock Mech. Min. Sci., 34(3/4), pp. 829–835.
Nair,  R., Abousleiman,  Y., and Zaman,  M. M., 2002, “A Finite Element Porothermoelastic Model for Dual-Porosity Media,” Int. J. Numer. Analyt. Meth. Geomech., 28(9), pp. 875–898.
Carslaw, H. S., and Jaegar, J. C., 1959, Conduction of Heat in Solids, Oxford University Press, New York.
Stehfest,  H., 1970, “Numerical Inversion of Laplace Transforms,” Commun. ACM, 13, pp. 47–49; 13, p. 624.

Figures

Grahic Jump Location
(a) Schematic of an inclined borehole; (b) Far-field stresses in the xyz coordinate system
Grahic Jump Location
Pore pressure varying with r/R along θ=90 deg at t=0.001 day for different values of ΔT
Grahic Jump Location
Effective radial stress varying with r/R along θ=90 deg at t=0.001 day for different values of ΔT
Grahic Jump Location
Effective tangential stress varying with r/R along θ=90 deg at t=0.001 day for different values of ΔT
Grahic Jump Location
Effective tangential stress around the wellbore at r/R=1 for different values of ΔT and αss. Curves generated using data given by Li et al., 1998 (Table 2).
Grahic Jump Location
Pore pressure varying with r/R along θ=90 deg at t=0.001 day
Grahic Jump Location
Pore pressure varying with r/R along θ=90 deg at t=0.001 day
Grahic Jump Location
Effective radial stress varying with r/R along θ=90 deg at t=0.001 day
Grahic Jump Location
Effective tangential stress varying with r/R along θ=90 deg at t=0.001 day
Grahic Jump Location
Stress clouds at r/R=1 and t=0.001 day
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Stress clouds at r/R=1 and t=0.001 day
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Effective tangential stress varying with θ at r/R=1 and t=0.001 day
Grahic Jump Location
Pore pressure varying with r/R for αmm=0.1, 1.0, for t=0.001, 0.01, and 0.1 day
Grahic Jump Location
Effective radial stress varying with r/R for αmm=0.1, 1.0, for t=0.001, 0.01, and 0.1 day
Grahic Jump Location
Effective tangential stress varying with r/R for αmm=0.1, 1.0, for t=0.001, 0.01, and 0.1 day
Grahic Jump Location
Pore pressure varying with r/R at t=0.001 day for different combinations of E/E, ν/ν′ , and αmm
Grahic Jump Location
Effective radial stress varying with r/R at t=0.001 day for different combinations of E/E, ν/ν′ , and αmm
Grahic Jump Location
Effective tangential stress varying with r/R at t=0.001 day for different combinations of E/E, ν/ν′ , and αmm

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