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.

References

References
1.
Mura
,
T.
,
1987
,
Micromechanics of Defects in Solids
,
Martinus Nijhoff, Leiden, The Netherlands
.
2.
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
.
3.
Eshelby
,
J. D.
,
1959
, “
The Elastic Field Outside an Ellipsoidal Inclusion
,”
Proc. R. Soc. London, Ser. A
,
252
(
1271
), pp.
561
569
.
4.
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
.
5.
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
.
6.
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
.
7.
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
.
8.
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
.
9.
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
.
10.
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
.
11.
Ghabezloo
,
S.
,
2015
, “
A Micromechanical Model for the Effective Compressibility of Sandstones
,”
Eur. J. Mech. A/Solids
,
51
, pp.
140
153
.
12.
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
.
13.
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
.
14.
Nemat-Nasser
,
S.
, and
Hori
,
M.
,
1999
,
Micromechanics: Overall Properties of Heterogeneous Materials
,
Elsevier
,
Amsterdam
.
15.
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
.
16.
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
.
17.
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
.
18.
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.
19.
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
.
20.
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
.
21.
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
.
22.
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
.
23.
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.
24.
Bedayat
,
H.
, and
Dahi Taleghani
,
A.
,
2015
, “
Two Interacting Ellipsoidal Inhomogeneities: Applications in Geoscience
,”
Comput. Geosci.
,
76
, pp.
72
79
.
25.
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
.
26.
Ahmadi
,
M.
,
Dahi Taleghani
,
A.
, and
Sayers
,
C. M.
,
2014
, “
Direction Dependence of Fracture Compliance Induced by Slickensides
,”
Geophysics
,
79
(
4
), pp.
C91
C96
.
27.
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
.
28.
Crampin
,
S.
,
1994
, “
The Fracture Criticality of Crustal Rocks
,”
Geophys. J. Int.
,
118
(
2
), pp.
428
438
.
29.
Hudson
,
J. A.
,
1981
, “
Wave Speeds and Attenuation of Elastic Waves in Material Containing Cracks
,”
Geophys. J. Int.
,
64
(
1
), pp.
133
150
.
30.
Nur
,
A.
, and
Simmons
,
G.
,
1969
, “
Stress-Induced Velocity Anisotropy in Rock: An Experimental Study
,”
J. Geophys. Res.
,
74
(
27
), pp.
6667
6674
.
31.
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
.
32.
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
.
33.
Berryman
,
J. G.
,
1992
, “
Effective Stress for Transport Properties of Inhomogeneous Porous Rock
,”
J. Geophys. Res.
,
97
(
B12
), pp.
17409
17424
.
34.
Cheng
,
A. H.-D.
,
1997
, “
Material Coefficients of Anisotropic Poroelasticity
,”
Int. J. Rock Mech. Min. Sci.
,
34
(
2
), pp.
199
205
.
35.
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
.
36.
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
.
37.
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
.
38.
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
.
39.
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
.
40.
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
.
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