0
Research Papers: Petroleum Engineering

Anisotropic Inhomogeneous Poroelastic Inclusions: With Application to Underground Energy-Related Problems

[+] Author and Article Information
Houman Bedayat

Bureau of Economic Geology,
University of Texas at Austin,
Austin, TX 78758
e-mail: houman.bedayat@gmail.com

Arash Dahi Taleghani

Department of Petroleum Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: a_dahi@lsu.edu

1Corresponding author.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received November 30, 2015; final manuscript received December 21, 2015; published online January 21, 2016. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 138(3), 032905 (Jan 21, 2016) (7 pages) Paper No: JERT-15-1455; doi: 10.1115/1.4032449 History: Received November 30, 2015; Revised December 21, 2015

Understanding the stress change in a reservoir generated by fluid production/injection is important for field development purposes. In this paper, we provide the Eshelby solution for stress and strain distribution inside and outside of an anisotropic poroelastic inhomogeneity due to pore pressure changes inside the inhomogeneity. The term anisotropic inhomogeneity refers to an inhomogeneity with anisotropic poroelastic constants. Some graphical results for strain and stress ratios for different material properties and geometries are presented as well. Anisotropy in elastic properties has been studied extensively in the last century; however, anisotropy in poroelastic properties, despite its potential significant impact in different engineering problems, has not been explored thoroughly. The results show how neglecting the effect of anisotropic poroelastic properties may result in large differences in calculated stresses. Due to the authors' primary interest in geomechanical problems, the discussions and examples are chosen for applications involving fluid withdrawal/injection into hydrocarbon reservoirs.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Topics: Stress , Pressure
Your Session has timed out. Please sign back in to continue.

References

Mura, T. , 1987, Micromechanics of Defects in Solids, Martinus Nijhoff, Leiden, The Netherlands.
Eshelby, J. D. , 1957, “ The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems,” Proc. R. Soc. A, 241(1226), pp. 376–396. [CrossRef]
Eshelby, J. D. , 1959, “ The Elastic Field Outside an Ellipsoidal Inclusion,” Proc. R. Soc. London, Ser. A, 252(1271), pp. 561–569. [CrossRef]
Eshelby, J. D. , 1961, “ Elastic Inclusions and Inhomogeneities,” Progress in Solid Mechanics, Vol. 2, I. N. Sneddon and R. Hill , eds., North-Holland, Amsterdam, pp. 89–140.
Li, S. , Sauer, R. A. , and Wang, G. , 2007, “ The Eshelby Tensors in a Finite Spherical Domain—Part I: Theoretical Formulations,” ASME J. Appl. Mech., 74(4), pp. 770–783. [CrossRef]
Shodja, H. M. , Rad, I. Z. , and Soheilifard, R. , 2003, “ Interacting Cracks and Ellipsoidal Inhomogeneities by the Equivalent Inclusion Method,” J. Mech. Phys. Solids, 51(5), pp. 945–960. [CrossRef]
Zou, W. , He, Q. , Huang, M. , and Zheng, Q. , 2010, “ Eshelby's Problem of Non-Elliptical Inclusions,” J. Mech. Phys. Solids, 58(3), pp. 346–372. [CrossRef]
Malekmotiei, L. , Samadi-Dooki, A. , and Voyiadjis, G. Z. , 2015, “ Nanoindentation Study of Yielding and Plasticity of Poly(Methyl Methacrylate),” Macromolecules, 48(15), pp. 5348–5357. [CrossRef]
David, E. , and Zimmerman, R. , 2011, “ Compressibility and Shear Compliance of Spheroidal Pores: Exact Derivation Via the Eshelby Tensor, and Asymptotic Expressions in Limiting Cases,” Int. J. Solids Struct., 48(5), pp. 680–686. [CrossRef]
Meng, C. , Heltsley, W. , and Pollard, D. D. , 2012, “ Evaluation of the Eshelby Solution for the Ellipsoidal Inclusion and Heterogeneity,” Comput. Geosci., 40, pp. 40–48. [CrossRef]
Ghabezloo, S. , 2015, “ A Micromechanical Model for the Effective Compressibility of Sandstones,” Eur. J. Mech. A/Solids, 51, pp. 140–153. [CrossRef]
Khoshgofta, M. , Najarian, S. , Farmanzad, F. , Vahidi, B. , and Ghomshe, F. T. , 2007, “ A Biomechanical Composite Model to Determine Effective Elastic Moduli of the CNS Gray Matter,” Am. J. Appl. Sci., 4(11), pp. 918–924. [CrossRef]
Malekmotiei, L. , Farahmand, F. , Shodja, H. M. , and Samadi-Dooki, A. , 2013, “ An Analytical Approach to Study the Intraoperative Fractures of Femoral Shaft During Total Hip Arthroplasty,” ASME J. Biomech. Eng., 135(4), p. 041004. [CrossRef]
Nemat-Nasser, S. , and Hori, M. , 1999, Micromechanics: Overall Properties of Heterogeneous Materials, Elsevier, Amsterdam.
Zhou, K. , Hoh, H. J. , Wang, X. , Keer, L. M. , Pang, J. H. L. , Song, B. , and Wang, Q. J. , 2013, “ A Review of Recent Works on Inclusions,” Mech. Mater., 60, pp. 144–158. [CrossRef]
Bedayat, H. , and Dahi Taleghani, A. , 2015, “ Pressurized Poroelastic Inclusions: Short-Term and Long-Term Asymptotic Solutions,” Rock Mech. Rock Eng., 48(6), pp. 2359–2367. [CrossRef]
Rudnicki, J. W. , 2002, “ Alteration of Regional Stress by Reservoirs and Other Inhomogeneities: Stabilizing or Destabilizing?” Ninth International Congress on Rock Mechanics (ISRM), Paris, France, Aug. 25–29, pp. 1629–1637.
Rudnicki, J. W. , 2002, “ Eshelby Transformations, Pore Pressure and Fluid Mass Changes, and Subsidence,” Poromechanics II: 2nd Biot Conference on Poromechanics, Grenoble, France, Aug. 26–28, pp. 307–312.
Chen, Z. R. , 2011, “ Poroelastic Model for Induced Stresses and Deformations in Hydrocarbon and Geothermal Reservoirs,” J. Pet. Sci. Eng., 80(1), pp. 41–52. [CrossRef]
Soltanzadeh, H. , and Hawkes, C. D. , 2012, “ Evaluation of Caprock Integrity During Pore Pressure Change Using a Probabilistic Implementation of a Closed-Form Poroelastic Model,” Int. J. Greenhouse Gas Control, 7, pp. 30–38. [CrossRef]
Bedayat, H. , and Dahi Taleghani, A. , 2013, “ The Equivalent Inclusion Method for Poroelasticity Problems,” Poromechanics V, C. Hellmich , B. Pichler , and D. Adam , eds., American Society of Civil Engineers, Reston, VA, pp. 1279–1288.
Taleghani, A. D. , and Klimenko, D. , 2015, “ An Analytical Solution for Microannulus Cracks Developed Around a Wellbore,” ASME J. Energy Resour. Technol., 137(6), p. 062901. [CrossRef]
Heidari, M. , Nikolinakou, M. , Flemings, P. , and Hudec, M. , 2015, “ A Simplified Analysis of Stresses in Rising Salt Domes and Adjacent Sediments,” 49th U.S. Rock Mechanics/Geomechanics Symposium, San Francisco, CA, June 28–July 1, Paper No. ARMA-2015-159.
Bedayat, H. , and Dahi Taleghani, A. , 2015, “ Two Interacting Ellipsoidal Inhomogeneities: Applications in Geoscience,” Comput. Geosci., 76, pp. 72–79. [CrossRef]
Ghabezloo, S. , and Hemmati, S. , 2011, “ Poroelasticity of a Micro-Heterogeneous Material Saturated by Two Immiscible Fluids,” Int. J. Rock Mech. Min. Sci., 48(8), pp. 1376–1379. [CrossRef]
Ahmadi, M. , Dahi Taleghani, A. , and Sayers, C. M. , 2014, “ Direction Dependence of Fracture Compliance Induced by Slickensides,” Geophysics, 79(4), pp. C91–C96. [CrossRef]
Shao, J. F. , Chau, K. , and Feng, X. , 2006, “ Modeling of Anisotropic Damage and Creep Deformation in Brittle Rocks,” Int. J. Rock Mech. Min. Sci., 43(4), pp. 582–592. [CrossRef]
Crampin, S. , 1994, “ The Fracture Criticality of Crustal Rocks,” Geophys. J. Int., 118(2), pp. 428–438. [CrossRef]
Hudson, J. A. , 1981, “ Wave Speeds and Attenuation of Elastic Waves in Material Containing Cracks,” Geophys. J. Int., 64(1), pp. 133–150. [CrossRef]
Nur, A. , and Simmons, G. , 1969, “ Stress-Induced Velocity Anisotropy in Rock: An Experimental Study,” J. Geophys. Res., 74(27), pp. 6667–6674. [CrossRef]
Hu, D. W. , Zhou, H. , and Shao, J. F. , 2013, “ An Anisotropic Damage-Plasticity Model for Saturated Quasi-Brittle Materials,” Int. J. Numer. Anal. Methods Geomech., 37(12), pp. 1691–1710. [CrossRef]
Rice, J. R. , and Cleary, M. P. , 1976, “ Some Basic Stress Diffusion Solutions for Fluid-Saturated Elastic Porous Media With Compressible Constituents,” Rev. Geophys., 14(2), pp. 227–241. [CrossRef]
Berryman, J. G. , 1992, “ Effective Stress for Transport Properties of Inhomogeneous Porous Rock,” J. Geophys. Res., 97(B12), pp. 17409–17424. [CrossRef]
Cheng, A. H.-D. , 1997, “ Material Coefficients of Anisotropic Poroelasticity,” Int. J. Rock Mech. Min. Sci., 34(2), pp. 199–205. [CrossRef]
Tan, X. , and Konietzky, H. , 2014, “ Numerical Study of Variation in Biot's Coefficient With Respect to Microstructure of Rocks,” Tectonophysics, 610, pp. 159–171. [CrossRef]
Silvestri, V. , Soulie, M. , Marche, C. , and Louche, D. , 1985, “ Effect of Soil Anisotropy on the Wave-Induced Pore Pressures in the Seabed,” ASME J. Energy Resour. Technol., 107(4), pp. 441–449. [CrossRef]
Dokhani, V. , Yu, M. , Miska, S. Z. , and Bloys, J. , 2015, “ The Effects of Anisotropic Transport Coefficients on Pore Pressure in Shale Formations,” ASME J. Energy Resour. Technol., 137(3), p. 032905. [CrossRef]
Abousleiman, Y. N. , and Ekbote, S. , 2005, “ Solutions for the Inclined Borehole in a Porothermoelastic Transversely Isotropic Medium,” ASME J. Appl. Mech., 72(1), pp. 102–114. [CrossRef]
Morrow, D. A. , Haut Donahue, T. L. , Odegard, G. M. , and Kaufman, K. R. , 2010, “ Transversely Isotropic Tensile Material Properties of Skeletal Muscle Tissue,” J. Mech. Behav. Biomed. Mater., 3(1), pp. 124–129. [CrossRef] [PubMed]
Feng, Y. , Okamoto, R. J. , Namani, R. , Genin, G. M. , and Bayly, P. V. , 2013, “ Measurements of Mechanical Anisotropy in Brain Tissue and Implications for Transversely Isotropic Material Models of White Matter,” J. Mech. Behav. Biomed. Mater., 23, pp. 117–132. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

A single inclusion embedded in an infinite medium. Ω1 and C1 indicate inclusion domain and its elastic moduli tensor, respectively. Ω and C represent the surrounding matrix and its elasticity moduli tensor, respectively.

Grahic Jump Location
Fig. 2

(a) Strain ratio and (b) stress ratio due to a pressure change inside an isotropic poroelastic inhomogeneity. Both graphs are plotted against the inhomogeneity aspect ratio, e. It is assumed that g is a shear modulus ratio, G1/G; αij1=δij (isotropic case); and ν0=ν1=0.2. However, the dependence of the solution on ν0 is weak. These graphs are in exact agreement with Figs. 4 and 7 in Rudnicki [17].

Grahic Jump Location
Fig. 3

Stress ratio against inhomogeneity aspect ratio, e, for various shear modulus ratio (g=G1/G0) and Poisson's ratio. The solid lines indicate vertical stress ratio σ33/p, whereas the dotted lines indicate lateral stress ratio σ11/p.

Grahic Jump Location
Fig. 4

Stress ratio for different α331 values. g=(G1/G0);ν0=ν1=0.2;a1=a2=a3=1. (a) σ33/p if α331=0.1; (b) σ33/p if α331=1; (c) σ33d/p, difference of (a) and (b); (d) σ11/p if α331=0.1; (e) σ11/p if α331=1; and (f) σ11d/p, difference of (d) and (e).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In