Rocks underground often have pores and bedding planes, which are appropriate to be described by the transversely isotropic poroelastic constitutive model. Drilling boreholes in these rocks must be careful, since stresses and pore pressure would change with time, because of the inherent time dependent property of poroelasticity as well as pore fluid diffusion. In order to correlate the behavior of transversely isotropic poroelastic model of borehole in plane strain with the behavior of isotropic poroelastic model, an equivalent isotropic material is built with carefully chosen material constants, and correlation rules are successfully developed. With the solutions for the borehole problem in an isotropic model obtained previously, the solutions to transversely isotropic model can be obtained. Two cases of tensile failure and six cases of shear failure for the borehole are considered. As a result, the allowable borehole working pressure range is formulated by explicit expressions. The failure case, time, and location could also be obtained for any given drilling pressure. Results obtained from the Hooke’s traditional elastic model are compared, and it is found that poroelastic model is necessary in borehole safety check, while Hooke’s model is not on the safe side.

References

References
1.
Fjaer
,
E.
,
Holt
,
R.
,
Raaen
,
A.
,
Risnes
,
R.
, and
Horsrud
,
P.
,
2008
,
Petroleum Related Rock Mechanics
,
2nd ed.
,
Elsevier
,
Amsterdam, The Netherlands
.
2.
Biot
,
M. A.
,
1941
, “
General Theory of Three-Dimensional Consolidation
,”
J. Appl. Phys.
,
12
(
2
), pp.
155
164
.
3.
Biot
,
M. A.
, and
Willis
,
D. G.
,
1957
, “
The Elastic Coefficients of the Theory of Consolidation
,”
ASME J. Appl. Mech.
,
24
, pp.
594
601
.
4.
Biot
,
M. A.
,
1955
, “
Theory of Elasticity and Consolidation for a Porous Anisotropic Solid
,”
J. Appl. Phys.
,
26
(
2
), pp.
182
185
.
5.
Biot
,
M. A.
,
1972
, “
Theory of Finite Deformations of Porous Solids
,”
Indiana Univ. Math. J.
,
21
(
7
), pp.
597
620
.
6.
Biot
,
M. A.
,
1973
, “
Nonlinear and Semilinear Rheology of Porous Solids
,”
J. Geophys. Res.
,
78
(
23
), pp.
4924
4937
.
7.
Gao
,
Y.
,
Liu
,
Z.
,
Zhuang
,
Z.
, and
Hwang
,
K.-C.
,
2017
, “
A Reexamination of the Equations of Anisotropic Poroelasticity
,”
ASME J. Appl. Mech.
,
84
(
5
), p.
051008
.
8.
Thompson
,
M.
, and
Willis
,
J. R.
,
1991
, “
A Reformation of the Equations of Anisotropic Poroelasticity
,”
ASME J. Appl. Mech.
,
58
(
3
), pp.
612
616
.
9.
Cheng
,
A. H.-D.
,
1997
, “
Material Coefficients of Anisotropic Poroelasticity
,”
Int. J. Rock Mech. Min. Sci.
,
34
(
2
), pp.
199
205
.
10.
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
.
11.
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. Geomech. Abstr.
,
25
(
3
), pp.
171
182
.
12.
Gao
,
Y.
,
Liu
,
Z.
,
Zhuang
,
Z.
,
Hwang
,
K.-C.
,
Wang
,
Y.
,
Yang
,
L.
, and
Yang
,
H.
,
2016
, “
Cylindrical Borehole Failure in a Poroelastic Medium
,”
ASME J. Appl. Mech.
,
83
(
6
), p.
061005
.
13.
Cui
,
L.
,
1995
, “
Poroelasticity With Application to Rock Mechanics
,” Ph.D. thesis, University of Delaware, Newark, DE.
14.
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
.
15.
Howard
,
G. C.
, and
Fast
,
C. R.
,
1957
, “
Optimum Fluid Characteristics for Fracture Extension
,”
Drilling and Production Practice
,
American Petroleum Institute
,
New York
, pp.
261
270
.
16.
Detournay
,
E.
, and
Cheng
,
A. H.-D.
,
1993
, “
Fundamentals of Poroelasticity
,”
Analysis and Design Method, Vol. II of Comprehensive Rock Engineering: Principles, Practice and Projects
,
Pergamon Press
,
Oxford, UK
, pp.
113
171
.
17.
Muskhelishvili
,
N. I.
,
1953
,
Some Basic Problems of the Mathematical Theory of Elasticity
,
Noordhoff
,
Groningen, The Netherlands
.
18.
Cheng
,
A. H.-D.
,
2016
,
Poroelasticity
(Theory and Applications of Transport in Porous Media), Vol.
27
,
Springer International Publishing
,
Cham, Switzerland
.
19.
Jaeger
,
J. C.
,
Cook
,
N.
, and
Zimmerman
,
R.
,
2007
,
Fundamentals of Rock Mechanics
,
4th ed.
,
Blackwell Publishing
,
Malden, MA
.
20.
Aoki
,
T.
,
Tan
,
C.
, and
Bamford
,
W.
,
1993
, “
Effects of Deformation and Strength Anisotropy on Borehole Failures in Saturated Shales
,”
Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
,
30
(
7
), pp.
1031
1034
.
21.
Chen
,
X.
, and
Gao
,
D.
,
2017
, “
The Maximum-Allowable Well Depth While Performing Ultra-Extended-Reach Drilling From Shallow Water to Deepwater Target
,”
SPE J.
, epub.
22.
Abate
,
J.
, and
Valkó
,
P. P.
,
2004
, “
Multi-Precision Laplace Transform Inversion
,”
Int. J. Numer. Methods Eng.
,
60
(
5
), pp.
979
993
.
You do not currently have access to this content.