reservoir geomecanics

313 Wellbore stability
a.
b. c.
6.5 7 7.5 8 8.5
5.5 6 6.5 7 7.5 8
Required P m Required P m
5
5.5 6 6.5
Required P m
Figure 10.8. Wellbore stability as a function of mud weight. In each of these figures, all parameters
are the same except rock strength. For a UCS of 7000 psi (a), a required mud weight of ∼8.6 ppg
(slightly overbalanced) is needed to achieve the desired degree of stability in near-vertical wells
(the most unstable orientation). For a strength of 8000 psi (b), the desired degree of stability can be
achieved with a mud weight of ∼8 ppg (slightly underbalanced). If the strength is 9000 psi (c) a
stable well could be drilled with a mud weight of ∼7.3 ppg (appreciably underbalanced).
consider how uncertainty of one parameter affects wellbore stability in terms of the
mud weight required to achieve a desired degree of wellbore stability. In the case
of underbalanced drilling, we are obviously interested in how much one could lower
mud weight without adversely affecting well stability. More generally, QRA allows us
to formally consider the uncertainty associated with any of the parameters affecting
wellbore stability.
Figure 10.9 shows an example of the application of QRA, where the input parameter
uncertainties are given by probability density functions (from Moos, Peska et al. 2003)
that are specified by means of the minimum, the maximum, and the most likely values
of each parameter. The probability density functions shown here are either normal
or log-normal curves depending on whether the minimum and maximum values are
symmetrical (e.g. S v , S Hmax , S hmin , and P p )orasymmetrical (as shown for C 0 ) with
respect to the most likely value. In both cases, the functional form of the distribution is
defined by the assumption that 99% of the possible values lie between the maximum
and minimum input values.
Once the input uncertainties have been specified, response surfaces for the wellbore
collapse (Figure 10.10) and the lost circulation pressures (not shown) can be
defined. These response surfaces are assumed to be quadratic polynomial functions of
the individual input parameters. Their unknown coefficients in the linear, quadratic and
interaction terms are determined by a linear regression technique that is used to fit the