ISSN : 2277-1328 (Online) - ISRM

Study of Wellbore Stresses and Stability based on a Hollow Cylinder Model
13
The three failure criteria mentioned above, i.e., Mohr-
Coulomb, Drucker-Prager and Modified Lade criterion,
have been used in the analysis outlined above to predict
the critical collapse pressure and tensile failure criterion
has been used to predict the critical fracturing pressure.
Then the results obtained from different failure criteria
have been compared. Furthermore, the parametric
analysis about the stress state and critical pressures has
been conducted. Two ratios, the ratio of external and
internal radius and the ratio of external and internal
pressure, have been identified as crucial parameters that
have significant influence on the critical internal pressure.
To assess the influence of pore pressure on stability, the
critical internal pressures have been estimated for two
scenarios: with and without the pore pressure, and the
big difference between these two cases has been
observed. The set of rock strength and in situ stress
data from one oilfield in the UAE has been used in
calculations. It is shown in Table 1 where σ h
is the in-situ
horizontal stress, σ v
is the vertical stress, and analysis
has been performed in terms of two parameters α and β
defined as
R o
= αR i
and P i
= βP o
...(15)
Table 1 : Rock properties and in situ stress data
Depth σ h
σ v
P p
S o
β
(m) (MPa/ (MPa/ (MPa/ (MPa) (degree)
100m) 100m) 100m)
2134 1.39 2.35 1.13 11.2 32.7
3.1 Maximum Shear Stress
The wellbore stresses σ r
, σ θ
and σ z
were obtained by
solving Eqs. 12-14. The three principal stresses σ 1
, σ 2
and σ 3
were identified based on their magnitudes. Then,
the maximum shear stress τ max
was calculated as τ max
=
(σ 1
-σ 3
)/2. Fig. 4 shows the variation of τ max
with the radius
ratio α. As α increases, the maximum shear stress
decreases, sharply at first and then remains approximately
constant. Thus, the maximum shear stress τ max
is very
sensitive to wall thickness if the hollow cylinder is thin.
Then a tiny increment in wall thickness can result in
significant shear stress reduction. However, the maximum
shear stress τ max
is much less sensitive to wall thickness
for the thick-walled cylinder. This can provide guidelines
for scaling the laboratory hollow cylinder stress data into
the real wellbore situation where α is infinite.
Fig. 4 also shows the impact of β on τ max
. As β decreases
from 1.0 to 0, τ max
will increase accordingly. In other words,
the larger the difference between P i
and P o
is, the greater
the τ max
is. Therefore, if P o
is fixed (such as in-situ horizontal
stresses) and the internal well pressure continues
decreasing (such as mud weight-related drilling pressure),
τ max
in the inner wall will continuously increase until shear
failure will occur.
Fig. 4 : Maximum shear stress at R i
as function of α and β.
3.2 Minimum Internal Well Pressure
Figs. 5 and 6 show the influence of failure criteria, radius
ratios and pore pressure on the lower bound mud weight,
which is the minimum internal well pressure required to
maintain wellbore stable. Firstly, the influence of failure
criteria on minimum internal pressure becomes quite
obvious through comparing the two sets of curves. The
Mohr-Coulomb criterion is the most conservative criterion
and the Drucker-Prager criterion is the most nonconservative
one. The Mohr-Coulomb criterion predicts
the highest critical β. That is mainly because the Mohr-
Coulomb criterion is a two-dimensional criterion that only
considers σ 1
and σ 3
. Therefore, the strengthening effect
of the intermediate principal stress is ignored and borehole
strength is underestimated. However, the Drucker-Prager
criterion gives us the lowest critical β. That is mainly due
to its overestimation of the intermediate principal stress
strengthening effect. The Modified Lade criterion is a
moderate one that is between the above two extreme
criteria as it seems to properly account for the influence
of σ 2
on rock strength. These results are consistent with
the results obtained by Zhang et al [14] .
Fig. 5 : The effect of failure criterion on β-collapse
including pore pressure effects
Volume 1 No. 2 July 2012