The risk target is a function of the owner-user’s corporate philosophy for making risk decisions. Some companies are more risk adverse than others, and this will have a direct impact on the inspection planning results.
Rearranging Equation (1.68), the maximum acceptable POF for any bundle as a function of the consequence of tube failure and the risk target specified by the user is as follows:
,max tube tgt
f tube
f
P Risk
= C (1.69)
From this and the equation for POF in time, (see Equations (1.56)), a target inspection date can be determined.
This target date is the date at which the risk for the bundle meets the risk target specified by the User.
8.6.2 Example
Using the example risk target and Ctubef calculated in Section 8.4.2, Equation (1.70) yields a maximum or target POF that may be used in inspection planning as follows:
75,000 150,000 0.5
tube f,max
P = = (1.70)
8.6.3 Inspection Planning Without Inspection History (First Inspection Date) a) General
To plan inspections, the risk at any point in time must be calculated. Figure 8.2 provides the POF curve for the example problem or Section 8.4.2 using the matching heat exchanger bundles from the reliability database. Using the value of Pftube,max that was calculated in Equation (1.70) and using the risk target, the risk as a function of time can be determined.
b) Introduction of Uncertainty and its Effect on Risk
Without a large sampling of inspection data for the bundle, there is a degree of uncertainty associated with whether or not the matching set of exchanger bundles from the failure database accurately represents the bundle being evaluated. To account for inaccuracies and biases that are inherent in the failure database, additional uncertainty is introduced into the statistics. A default value for additional uncertainty of 50% is used. Figure 8.3 shows the curve from the example problem shifted to the left as a result of the addition of the 50% uncertainty.
If the bundle has no inspection record and no knowledge exists as to the condition of the bundle, the 50%
uncertainty curve is used to predict the POF as a function of time for the bundle. The calculated risk for a bundle without any inspection knowledge will be higher than for a bundle which has inspection records.
Although the action of inspection does not in itself reduce risk, this agrees with governing RBI principles stating that the more knowledge obtained for a piece of equipment, the less uncertainty exists, resulting in a reduction of the calculated risk.
Without any inspection, the recommended length of service for the bundle in the example problem as a function of time may be determined using the 50% additional uncertainty (AU) curve on Figure 8.3 or may be obtained from Table 8.3.
In the example problem, the maximum acceptable POF, Pftube,max, as calculated per Equation (1.70), was determined to be 0.5 (or 50%). Based on this, the recommended first inspection would be 7.1 years after installation. This compares to a predicted value of 14.7 years if the raw data (90% LBC) representing the matching set of bundles in the reliability database was used. This shows the direct effect that inspection uncertainty has on the calculated risk and the subsequent inspection plan.
8.6.4 Inspection Planning with Inspection History a) Effect of Inspection on POF
The information gained from an inspection of the tube bundle can be used to assess the actual condition of the bundle and to make adjustments to the POF rate curves as necessary.
An inspection provides two things:
1) Reduction in uncertainty due to the effectiveness of the inspection resulting in the use of a more accurate failure rate curve, e.g., moving from a 50% AU curve (no inspection history) to a curve 20%
AU curve (usually effective inspection). See Section 8.6.4.b) for a discussion of inspection effectiveness.
2) Knowledge of the true condition of the bundle. This can result in a shift of the failure rate curve to the right or to the left. The current condition of the bundle could either be quantified by remaining wall thickness data or by an estimate of the remaining life that comes directly from an actual inspection, see Section 8.6.4.c).
b) Reduction in Uncertainty Due to Inspection Effectiveness
If the tube bundle has been inspected, the uncertainty is reduced (the POF curve moves to the right) and the POF at any time decreases. In this way, inspection knowledge reduces the POF and the calculated risk.
At this point, the concept of inspection effectiveness is introduced, similar to the methodology used in other modules. As improved inspection techniques are used, the amount of uncertainty decreases and the Weibull plot shifts to the right. Using this concept will result in more rigorous inspection techniques being implemented as the bundle reaches end of life.
In the example bundle problem, the impact of more rigorous inspection techniques can be seen by evaluating the predicted duration as a function of inspection effectiveness in Error! Reference source not found..
The discussion of inspection effectiveness is continued in Annex 2.C.
c) Shift of POF Curve Due to Knowledge of True Bundle Condition 1) General
Not only does an inspection reduce the uncertainty in the data, it also provides knowledge of the current condition of the bundle. It may be determined that the bundle is in excellent condition and that the curve being used for the POF is too conservative. Conversely, it may also be determined that the bundle is in worse condition than what has been predicted using data from bundles in similar service.
Where general corrosion is the controlling damage mechanism in the bundle, the average measured tube thickness data may be used to predict the future bundle failure date. For other damage mechanisms (vibration, tube end thinning, etc.) or where measured thickness data does not exist, a qualitative estimate of the remaining life can be used to predict the future bundle failure date.
Whichever method is used to calculate a future failure date based on an inspection record, the predicted future failure data can be used to modify the base POF curve.
2) Predicted Future Failure Date Based on Measured Thickness Data
The thinning rate of the tube bundle may be determined using the average furnished wall thickness and the average wall thickness as measured at the last inspection as follows:
orig insp rate
dur
t t
t t
= − (1.71)
With the failure point defined as a fraction of remaining wall thickness,RWTf, the predicted bundle life adjusted for inspection, PBLadj, can be calculated using Equation (1.72).
f orig adj
rate
RWT t
PBL t
= ⋅ (1.72)
As an example, let’s assume that the example bundle from Section 8.4.2 had the following inspection details:
i) Installation Date – January 1992 with original wall thickness, torig, of 0.12 inches.
ii) June 2000 – Bundle had minor general corrosion throughout on outside diameter (OD), 10% of the tubes were sampled using Elliot gages/calipers and found to have an average wall thickness of 0.11 inches (8.5% wall loss). Bundle was hydrotested without leaks. Inspection effectiveness graded as “C.”
iii) September 2003 – Bundle showed minor wall loss to 0.104 inches average thickness (13% wall loss). Bundle was hydrotested without leaks. Inspection effectiveness graded as “C.”
iv) A failure definition of 50% remaining wall thickness is used, i.e., RWTf = 0.5.
For the example problem, the bundle was inspected in September 2003 after 11 3/4 years in service.
Over this time period, the average measured wall thickness went from 0.12 inches down to 0.104 inches.
The thinning rate is calculated using Equation (1.73) as follows:
0.12 0.104
0.001362 11.75
trate = − = inches/year (1.73)
The predicted bundle life adjusted for inspection, PBLadj, is then calculated using Equation (1.74).
0.5 0.12
44.1 years 0.001362
PBLadj = ⋅ = (1.74)
At this rate, the average wall thickness would reach 50% of the original wall thickness or the remaining wall thickness (RWTf) in 44.1 years, or in September of 2047. This bundle is in better condition than predicted by bundles in similar service.
d) Predicted Future Failure Date Based on Estimated Remaining Life
As an alternative, when tube wall thickness data is unavailable for calculation of a bundle tube thinning rate, or when the damage mechanism is something other than general corrosion, the estimated remaining life (ERL) of the bundle from the last inspection can be used to calculate predicted bundle life.
adj dur
PBL = t + ERL (1.75)
e) Adjustment to Failure Rate Curve Based on Actual Condition of Bundle
Once the predicted bundle life based on the last inspection has been determined using either Equation (1.72) or (1.74), a modified characteristic life (Weibull η parameter) for the bundle may be determined using Equation (1.76). It is modified by adding the adjusted predicted life of the bundle as an additional failure point as follows:
1
1
1 N
mod i
i
r t
β β
η
=
=
(1.76)
For the example bundle with matching data of Table 8.2, a modified η parameter, ηmod, is calculated by adding the 44.1 year predicted failure life to the original data set as follows:
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
1
2.568 2.568 2.568 2.568 2.568 2.568
2.568 2.568 2.568 2.568 2.568
18 22 16 10 12
1 27.2 years
6 13 14 25 8 (44.1)
ηmod = + + + + + =
+ + + +
(1.77)
Plotting this as the failure point on the Weibull diagram results in a shift to the right as shown in Figure 8.4. Note that the β parameter (Weibull slope parameter) was kept the same as the original curves from data obtained from similar bundles. This is the basis of Weibaye’s analysis that assumes that similar failure mechanisms will produce similar slope values.
The new POF curve in Figure 8.3 (second from left) shows the impact of the September 2003 inspection. In the example problem, two adjustments to the right were made. The uncertainty was reduced from 50% (no inspection) to 30% (“C” Inspection) as a result of the Elliot gauging/calipers measurements taken to estimate the remaining wall thickness. Additionally, the base curve containing the raw data was shifted to the right of the original raw data curve because the bundle was not in as poor condition as was expected using the initial curve.
As a result, the recommended inspection interval at the maximum acceptable POF of 50% for the bundle was increased from 7.1 years to 17.1 years or to February 2009. This calculation can be made using Equation (1.78) as follows:
( ln 1 tube )1 27.2 ( ln 1 0.5 [ ] )2.5681 17.1
int mod f,max
t = η ⋅ − − P β = ⋅ − − = years (1.78)
8.6.5 Effects of Bundle Life Extension Efforts
In general, during an inspection, only minor repairs and cleaning operations are performed on exchanger bundles. Bundles are not returned to an “as new” condition and therefore, the bundle POF is typically calculated at a service duration (i.e., time in service) based on the bundle’s original installation date.
However, there are several life extension methods that may be made to a bundle during shutdowns that serve to return the bundle back into service in an improved (not as-new) condition. In these situations, it would be too conservative to calculate the future bundle POFbased on the original service date, so an adjustment is made to the start date for calculation purposes. Table 8.5 provides a list of life extension methods and the credit given as represented by the life extension factor, LEF. An adjusted service duration,tadjdur, is then calculated using the
LEF in accordance with Equation (1.79).
( 1 )
dur dur
tadj = − LEF t (1.79)
In Equation (1.80), the actual service duration,tdur, is calculated as the time period (years) calculated from the bundle original installation date to the inspection date when the life extension method was performed.
tdur = Inspect Date Install Date − (1.80)
The adjusted installation date from which all subsequent POF calculations are made is determined by subtracting the adjusted service duration, tadjdur(years), from the date when the life extension method was performed as shown in Equation (1.81).
New install date = Inspect Date tadj − dur (1.81)
8.6.6 Future Inspection Recommendation
Using the inspection adjusted failure rate curve as defined by the new Weibull parameters, the target date for the next inspection can be determined. This will be the date at which the risk calculated using Equation (1.68) exceeds the risk target, Risktgt, specified by the user. To maintain a risk level below the risk target, an inspection will be required prior to that date. The question that needs to be answered is what level of inspection is required to ensure that the risk target will not be exceeded during operation of the equipment.
This may best be illustrated using Figure 8.6. This figure shows the effect that inspections have had on the bundle in our example problem. With scheduled turnarounds March 2008 and March 2012, inspection will be required at the March 2008 shutdown since the target risk (or Pf,maxtube ) will be exceeded in February 2009. If a “C”
inspection is planned for the March 2008 shutdown, there is no guarantee that the slope of the curve will be modified enough to reduce the calculated risk below the target value by the March 2012 shutdown. Therefore, a level “B” inspection is recommended. Figure 8.5 shows the effect that the level “B” inspection has on the risk curve.