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.

 

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Last revised 11/14/2006
© Barringer & Associates, Inc. 2006