Abstract

In the existing models of wellbore stability, the borehole wall is idealized as either a fully permeable or a completely impermeable surface. However, the widely observed fact that a shale borehole is permeable to solvent molecules but impermeable to solutes suggests that the borehole wall should be considered as a non-ideal semi-permeable medium. When the wellbore is exposed to the drilling fluid, the dynamic modification of pore pressure on the borehole surface is required to account for fluid entering the formation. In this paper, we present an analytical solution for a semi-permeable borehole subjected to a non-hydrostatic stress in a poroelastic medium, where a Robin boundary condition for pore pressure is adopted, with the fluid flux into the rock matrix being proportional to the pore pressure difference across the borehole wall. Integral transform and load decomposition techniques are employed to assist in the derivation of analytical solutions. The results reveal that, compared to the permeable and impermeable borehole models, the semi-permeable model predicts a sharp difference in the stress and pore pressure fields.

References

1.
Haimson
,
B.
, and
Fairhurs
,
C.
,
1969
, “
Hydraulic Fracturing in Porous-Permeable Materials
,”
J. Pet. Technol.
,
21
(
7
), pp.
811
817
.
2.
Selvadurai
,
A.
,
2007
, “
The Analytical Method in Geomechanics
,”
ASME Appl. Mech. Rev.
,
60
(
3
), pp.
87
106
.
3.
Kanfar
,
M. F.
,
Chen
,
Z.
, and
Rahman
,
S. S.
,
2016
, “
Fully Coupled 3D Anisotropic Conductive-Convective Porothermoelasticity Modeling for Inclined Boreholes
,”
Geothermics
,
61
, pp.
135
148
.
4.
Gao
,
J.
,
Deng
,
J.
,
Lan
,
K.
,
Feng
,
Y.
,
Zhang
,
W.
, and
Wang
,
H.
,
2017
, “
Porothermoelastic Effect on Wellbore Stability in Transversely Isotropic Medium Subjected to Local Thermal Non-Equilibrium
,”
Int. J. Rock. Mech. Min. Sci.
,
96
, pp.
66
84
.
5.
Carter
,
J. P.
, and
Booker
,
J. R.
,
1982
, “
Elastic Consolidation Around a Deep Circular Tunnel
,”
Int. J. Solids Struct.
,
18
(
12
), pp.
1059
1074
.
6.
Detournay
,
E.
, and
Cheng
,
A. H. D.
,
1988
, “
Poroelastic Response of a Borehole in a Non-Hydrostatic Stress Field
,”
Int. J. Rock Mech. Min. Sci.
,
25
(
3
), pp.
171
182
.
7.
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
.
8.
Abousleliman
,
Y.
, and
Ekbote
,
S.
,
2005
, “
Solutions for the Inclined Borehole in a Porothermoelastic Transversely Isotropic Medium
,”
ASME J. Appl. Mech.
,
72
(
1
), pp.
102
114
.
9.
Selvadurai
,
A.
,
2008
, “
Interface Porosity and the Dirichlet/Neumann Pore Fluid Pressure Boundary Conditions in Poroelasticity
,”
Transp. Porous Media
,
71
(
2
), pp.
161
172
.
10.
Wang
,
Y. L.
, and
Dusseault
,
M. B.
,
2003
, “
A Coupled Conductive-Convective Thermo-Poroelastic Solution and Implications for Wellbore Stability
,”
J. Pet. Sci. Eng.
,
38
(
3–4
), pp.
187
198
.
11.
Chen
,
G. Z.
, and
Ewy
,
R. T.
,
2005
, “
Thermoporoelastic Effect on Wellbore Stability
,”
SPE J.
,
10
(
2
), pp.
121
129
.
12.
He
,
L.-W.
, and
Jin
,
Z.-H.
,
2011
, “
Effects of Local Thermal Non-Equilibrium on the Pore Pressure and Thermal Stresses Around a Spherical Cavity in a Porous Medium
,”
Int. J. Eng. Sci.
,
49
(
3
), pp.
240
252
.
13.
Ding
,
L.
,
Wang
,
Z.
,
Wang
,
Y.
, and
Liu
,
B.
,
2020
, “
Thermo-Poro-Elastic Analysis: The Effects of Anisotropic Thermal and Hydraulic Conductivity on Borehole Stability in Bedding Formations
,”
J. Pet. Sci. Eng.
,
190
, p.
107051
.
14.
Cui
,
L.
,
Ekbote
,
S.
,
Abousleiman
,
Y.
,
Zaman
,
M.
, and
Roegiers
,
J.
,
1998
, “
Borehole Stability Analysis in Fluid Saturated Formations With Impermeable Boundary
,”
Int. J. Rock. Mech. Min. Sci.
,
35
(
4/5
), pp.
582
583
.
15.
Bai
,
B.
, and
Li
,
T.
,
2009
, “
Solutions for Cylindrical Cavity in Saturated Thermoporoelastic Medium
,”
Acta Mech. Solida Sin.
,
22
(
1
), pp.
85
94
.
16.
Fan
,
Z.
, and
Parashar
,
R.
,
2020
, “
Transient Flow to a Finite-Radius Well With Wellbore Storage and Skin Effect in a Poroelastic Confined Aquifer
,”
Adv. Water Resour.
,
142
, p.
103604
.
17.
Abousleiman
,
Y. N.
, and
Chen
,
S. L.
,
2010
, “
Poromechanics Response of an Inclined Borehole Subject to In-Situ Stress and Finite Length Fluid Discharge
,”
J. Mech. Mater. Struct.
,
5
(
1
), pp.
47
66
.
18.
Chen
,
S. L.
,
2019
, “
Three-Dimensional Analytical Poromechanical Solutions for an Arbitrarily Inclined Borehole Subjected to Fluid Injection
,”
Proc. R. Soc. A-Math. Phys. Eng. Sci.
,
475
(
2221
), p.
20180658
.
19.
Fan
,
Z. Q.
,
Eichhubl
,
P.
, and
Gale
,
J. F. W.
,
2016
, “
Geomechanical Analysis of Fluid Injection and Seismic Fault Slip for the M(w)4.8 Timpson, Texas, Earthquake Sequence
,”
J. Geophys. Res.-Solid Earth
,
121
(
4
), pp.
2798
2812
.
20.
Fan
,
Z.
,
Eichhubl
,
P.
, and
Newell
,
P.
,
2019
, “
Basement Fault Reactivation by Fluid Injection Into Sedimentary Reservoirs: Poroelastic Effects
,”
J. Geophys. Res.-Solid Earth
,
124
(
7
), pp.
7354
7369
.
21.
Huang
,
C.
, and
Chen
,
S. L.
,
2019
, “
Stress Analysis of an Inclined Borehole Subjected to Fluid Discharge in Saturated Transversely Isotropic Rocks
,”
Int. J. Geomech.
,
19
(
11
), p.
04019118
.
22.
Huang
,
C.
, and
Chen
,
S. L.
,
2021
, “
Study of Wellbore Breakdown Under Fluid Injection in Transversely Isotropic Poroelastic Formations
,”
SPE J.
,
26
(
1
), pp.
394
411
.
23.
Fan
,
Z.
, and
Parashar
,
R.
,
2019
, “
Analytical Solutions for a Wellbore Subjected to a Non-Isothermal Fluid Flux: Implications for Optimizing Injection Rates, Fracture Reactivation, and EGS Hydraulic Stimulation
,”
Rock Mech. Rock Eng.
,
52
(
11
), pp.
4715
4729
.
24.
Mehrabian
,
A.
, and
Abousleiman
,
Y. N.
,
2013
, “
Generalized Poroelastic Wellbore Problem
,”
Int. J. Numer. Anal. Meth. Geomech
,
37
(
16
), pp.
2727
2754
.
25.
Fan
,
Z. Q.
,
Parashar
,
R.
, and
Jin
,
Z. H.
,
2020
, “
Impact of Convective Cooling on Pore Pressure and Stresses Around a Borehole Subjected to a Constant Flux: Implications for Hydraulic Tests in an Enhanced Geothermal System Reservoir
,”
Interpretation
,
8
(
2
), pp.
SG13
SG20
.
26.
Wang
,
Y.
,
Li
,
W.
, and
Dusseault
,
M. B.
,
2021
, “
THM Response of a Borehole in Naturally Fractured Media
,”
J. Pet. Sci. Eng.
,
205
, p.
108941
.
27.
Zhai
,
X.
, and
Atefi-Monfared
,
K.
,
2020
, “
Explanation of Early Failure in Porous Media Confined With Flexible Layers, Considering Thermo-Osmosis, Thermal-Filtration and Heat Sink From Fluid Dilation
,”
Comput. Geotech.
,
122
, p.
103501
.
28.
Rajapakse
,
R.
,
1993
, “
Stress Analysis of Borehole in Poroelastic Medium
,”
J. Eng. Mech.
,
119
(
6
), pp.
1205
1227
.
29.
Zhai
,
X.
, and
Atefi-Monfared
,
K.
,
2021
, “
Thermo-Poroelasticity Under Temporal Flux in Low Permeable Layer Confined With Flexible Sealing Media
,”
Int. J. Numer. Anal. Meth. Geomech.
,
45
(
3
), pp.
382
410
.
30.
Li
,
J.
,
Qiu
,
Z.
,
Zhong
,
H.
,
Zhao
,
X.
, and
Huang
,
W.
,
2020
, “
Analysis of Chemo-Poro-Thermo-Mechanical Effects on Wellbore Strengthening
,”
ASME J. Energy Resour. Technol.
,
142
(
12
), p.
123005
.
31.
Wei
,
J.
,
Cheng
,
Y.
, and
Yan
,
C.
,
2020
, “
Two-Dimensional Pore Pressure Distribution Model to Evaluate Effects of Shale Semipermeable Membrane Characteristics
,”
ASME J. Energy Resour. Technol.
,
142
(
1
), p.
012902
.
32.
Nguyen
,
K.
,
Mehrabian
,
A.
,
Santra
,
A.
, and
Phan
,
D.
,
2022
, “
Tensile Failure and Fracture Width of Partially Permeable Wellbores With Applications in Lost Circulation Material Design
,”
SPE J.
,
27
(
1
), pp.
465
487
.
33.
Wang
,
H. F.
,
2010
,
Theory of Linear Poroelasticity With Applications to Geomechanics and Hydrogeology
,
Princeton University Press
,
Princeton, NJ
.
34.
Cheng
,
A.-D.
,
2016
,
Poroelasticity
,
Springer
,
Switzerland
.
35.
Song
,
Y.
, and
Rudnicki
,
J. W.
,
2016
, “
Plane-Strain Shear Dislocation on a Leaky Plane in a Poroelastic Solid
,”
ASME J. Appl. Mech.
,
84
(
2
), p.
021008
.
36.
Heimisson
,
E. R.
,
Rudnicki
,
J.
, and
Lapusta
,
N.
,
2021
, “
Dilatancy and Compaction of a Rate-and-State Fault in a Poroelastic Medium: Linearized Stability Analysis
,”
J. Geophys. Res.-Solid Earth
,
126
(
8
), p.
e2021J
37.
Zoback
,
M.
,
2010
,
Reservoir Geomechanics
,
Cambridge University Press
,
Cambridge, UK
.
You do not currently have access to this content.