Corrosion Problems, Inspection Data, And The Gumbel Lower Distribution
The Issue:
We
have a column operating in a severe environment. Corrosion inside of the column is occurring
in irregular zones. The zones are due to
uneven flows inside the column.
Production wants to know when they should cease operation because of
potential leaks. Production also wants
to make the decision based on inspection data taken from outside of the low
pressure vessel.
Bottom
line issues of concern:
1) How much longer can we operate?, and
2) When should we shut down?
Data:
What
do we know from the data? We’ve been
using ultrasonic wall thickness readings in the marked-off “thin” zones which
are defined by a grid marked on the outside diameter of the vessel. Of course the coordinates marked on the
vessel include both thick areas and thin areas.
How do we make the data speak to us so we can make a cost effective
decision. Clearly we won’t have a
calamity from the thick areas, but the thin areas of the column will cause us
misery.
First,
simply plot the minimum wall thicknesses to see where we are based on our last
inspection results. Figure 1 shows the
results and the curved plot shows evidence of a mixture of thin sections and
thick section.
|
Figure 1: Wall Thickness Raw Data From Ultrasonic
Inspections |
|
|
Thick
walls are safe. Thin walls are our
concern. Based on engineering judgment, we
must separate the thick walls from the thin walls and make further analysis
based on the thin walls. The dividing
line between thick/thin areas is ~63.2% dividing line. Notice the inspection team is concerned about
movement of wall thickness from thick to thin as evidenced by the frequent
inspection data over the past 9 months.
The
thin walls are plotted below in Figure 2.
|
Figure 2: Thin Wall
Thickness Raw Data From Ultrasonic Inspections |
|
|
Observations:
What
does Figure 2 tell us?
The
line at time = 0 is not determined by inspection, but it is set by the mill
tolerance. At time=0, the lower wall
thickness is set at 0.1% occurrence and the upper limit to wall thickness is
set at 99.9% occurrence and this is seen to cross the characteristic value at
Xi=50.56 which in real thickness units is 0.5056 inches. If the wall thickness
marched to the left from the zero time line with a family of parallel lines we
would describe this as general corrosion. If the family of curves moves to the left AND
flattens in slope, we would observe both general corrosion and accelerated
corrosion as the accelerated corrosion adds more variability to the wall
thickness data.
From
Figure 2 you can see most of the problem is due to a high rate of general
corrosion follow by a smaller component of accelerated corrosion. After only 966 days in service, the wall
thickness readings of the sample inspection data forecasts that somewhere in
the vessel you should expect to find slightly more than 0.1% chance the wall
thickness will be less than 0.240 inches allowed by ASME’s
tmin allowed wall thickness. We have now crossed onto the thin ice! Risks are now increasing beyond the zone of
prudence as ASME factor of safety ~3 is growing smaller if the vessel is
operated at it’s maximum allowed pressure rating (i.e., we’ve gone from a
reliability of the vessel of 0.9999 to 0.999).
Six
months later the vessel is again inspected because we’re worried. The criteria for success are now based on API
579 specification for fitness of service which allows use of a lower
safety factor. The wall thickness limit
is set at 0.180 inches where the safety factor is ~ x/0.191 = 3/0.240 or x=2.4,
and we are approaching 0.1% chance the wall thickness somewhere in the vessel
will show less than 0.180 inch wall thickness.
Because
we’re really worried about loss of wall, another inspection was conducted one
month later on February 7, 2006 and the wall thickness was slightly less. It says ~15% of wall thickness readings
should be less than ASME’s tmin
and we are running into the limit of API’s fitness for service limit.
Should
we take the risk and run longer or should we reject the risk and purchase a
replacement vessel of better grade material with and expected longer life? So what’s involved in the risk? Several people work in the area and could be
exposed to a vigorous corroding material and if a leak occurs we must shut down
the system and take a big loss in margin. The total financial consequences will exceed
$30,000,000 for vessel failure.
If
we’re risk adverse, we would use the probability of failure = 15% set by
prudent ASME limits which society has used as a standard for over 100 years
[i.e., 15%*$30,000,000 = $4,500,000 exposure]. If we’re risk accepting, we would use the probability
of failure as ~1% using API limits for fitness of service which has been in use
by society for ~15 years [i.e., 0.1%*$30,000,000 = $30,000 exposure].
Both
risks (ASME & API) are rising quickly with more time in service. Order a new column from better grades of
material and procure it on an accelerated basis as the risks are too high for
most organizations. Consider taking the
column out of service immediately to reduce the risk of a failure. We have crossed into the zone of thin ice (we’ve
busted ASMEs tolerance) and we’re about to break
through the thin ice (we’re about to bust APIs tolerance) as we move into the
zone of imprudence!
You
might ask what result occurred following this analysis. A one page slide was presented to management using
Figure 2 along with the risk assessment in monetary form. Management agreed the risk was too high. The process was shut down in an orderly
manner as a measure of prudence. The column
was replaced before it failed which would have cause severe personnel issues
and severe environmental issues.
Why The Gumbel Lower
Distribution And Why The Inspection Routine?
The
Gumbel lower distribution was selected because it’s made for using the smallest
recorded data. The Gumbel lower
distribution is one of the double exponential equations of the extreme. Note the Gumbel lower distribution has a
Weibull Y-axis and the X-axis is uniformly divided which makes it easier for
many people to interpret the results.
The
inspection routine in WinSMITH
Weibull probability plots regress the trend line through the top data point
of stacks of data. We clearly have
stacks of data obtained from rounding the data for recording purposes—this is
Sherwin’s Method of regression.
Comments:
Refer to the caveats on the Problem
Of The Month Page about the limitations of the following solution.
Maybe you have a better idea on how to solve the problem. Maybe you find where
I've screwed-up the solution and you can point out my errors as you check my
calculations. E-mail your comments, criticism, and corrections to: Paul
Barringer by 
clicking
here. Return
to top of page.
You can download this as a PDF file.
Return to Barringer
& Associates, Inc. homepage