ISSN : 2277-1328 (Online) - ISRM

Study of Wellbore Stresses and Stability based on a Hollow Cylinder Model
15
the mud weight window is getting wider, so it is easier to
avoid instability problems. Note that the minimum and
maximum mud weights change only slightly and stay
approximately constant when α is greater than a certain
value, such as 3 or 4. This phenomenon can be used to
predict the wellbore stability problems by virtue of hollow
cylinder testing.
Fig. 9 : The required mud weight without pore pressure
4. CONCLUSIONS
A hollow cylinder model was used in this paper to conduct
the parametric analysis of wellbore stresses and stability
in terms of three major parameters that have significant
influence on the critical internal wellbore pressure, such
as radius ratio α, pressure ratio β, and pore pressure P p
.
Different values of these parameters give rise to different
stress distributions in the hollow cylinder and,
subsequently, affect the critical internal pressures. In
addition, the critical internal pressure also depends on
the failure criterion and three popular failure criteria such
as Mohr-Coulomb, Drucker-Prager, and the Modified Lade
criterion have been considered in this paper. Several
conclusions can be drawn from this work.
Firstly, the radius ratios a has great impact on the minimum
and maximum critical internal pressure. As this ratio
increases, the minimum internal pressure decreases and
the maximum internal pressure increases. In other words,
the safe mud weight window will be widened if the radius
radio increases. In addition, the minimum and the maximum
mud weights change only slightly and remain approximately
constant when a is greater than a certain value. This
phenomenon can be used to scale the lab hollow cylinder
test data up to the scale of wellbore stability problems. It
also means that, from stress point of view, it is easier to
control stability of an oilfield well than of a small hollow
cylinder sample tested in laboratory environment.
Secondly, pore pressure also plays an important role in
borehole stability analysis and mud weight design. It can
significantly weaken the rock by reducing confining stress,
thus narrowing down the safe mud weight window to a
great degree. When pore pressure effects and effective
stresses are considered, the safe mud weight window is
much narrower than when compared to the dry rock case.
Hence, neglecting pore pressure (or inaccurate pore
pressure estimation) will have misleading effect on safe
mud weight choices and may result in triggering wellbore
instability problems.
Finally, this analysis confirms the differences and
characteristics of the three yield criteria considered in this
paper. The Mohr-Coulomb criterion is apparently
conservative. It is a two-dimensional failure criterion that
does not account for the intermediate principal stress
strengthening effect. The Drucker-Prager criterion is
apparently non-conservative and over predicts the s 2
strengthening effect. The Modified Lade criterion is a
moderate one, between the extremes of the other two criteria.
Thus, it can provide reasonable mud weight predictions.
Acknowlegdements : Support from the Petroleum
Institute and local operating companies for the work
covered in this paper is gratefully acknowledged.
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Volume 1 No. 2 July 2012