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Is it necessary to install a downhole safety valve in a subsea oil/gas well?
Even if the mathematical model is correct the data applied will not be perfect for the specific
situation. Data books often pool data from a number of samples that all have individual
differences in construction and operating environment. These data are applied to the new
model and may not be valid there. Data books normally leave out environmental and
operational effects when assigning reliability values to components.
Reliability data
During the process of selecting a data set applicable for reliability quantification, the data
sources have been carefully examined. As a result of different data collection approaches,
reliability data often vary significantly from one data source to another. For some components
in the barrier system the data is scarce. An estimation is therefore done in understanding with
Marvin Rausand, supervisor [19]. The reliability input data used in the reliability calculations
are presented by data dossiers in appendix D. Reliability data used in this study mainly
originates from platform wells and are found in SINTEF reports and the OREDA handbook.
5.4.2 Calculations done in CARA
The fault trees of the case example are constructed by the use of a computerised fault tree
analysis package, CARA (Computer Aided Reliability Analysis). This program may also be used
for unavailability calculations. CARA assumes an exponentially distributed lifetime with
constant failure rates for the components is.
CARA calculates the unavailability of the ‘TOP’ event by using approximation formula 5-2 for
tested barriers and Equation 5-4 for the non-tested barriers. The fault trees of appendix C, with
reliability values found in the data dossiers of appendix D, perform the basis for the
calculations. The results of the CARA-calculations are presented in subsection 5.4.4.
5.4.3 Calculations done by hand
The general MFDT formula (Equation 5-1) is applied when finding the unavailability of tested
barriers. The non-tested barriers make use of Equation 5-4 and Equation 5-5. Some of the
examined cut sets consist of combinations of tested and non-tested barriers. Dividing the
combined cut set into two parts solves this problem. The unavailability of the combined cut set
is found as the product of the unavailability of each part. The results of the calculations are
presented in subsection 5.4.5.
The non-tested barriers that are given a lifetime t=131400 hours (15 years). When applied to
the cut sets this generates the most conservative value of unavailability. Periodically tested
barriers are tested with time distribution τ=4380 hours (6 months). In these calculations
components are assumed to be “as good as new” when tested. The methods also consider the
barriers to have constant failure rates and be independent of each other.
Ex. 1 Unavailability of two tested barriers
The calculation of two tested barriers of a parallel structure will be done here. The reliability
function is derived from the structure function of the parallel structure as shown in Figure 5-6.
Diploma thesis, NTNU 2002
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