Problem Of
The Month
June 1997--Pipe Wall Thickness And Risk Based Inspection
Pipe wall thickness is an issue of mechanical integrity and plays a role in risk based inspections. A data set is shown below. The usual questions and answers follow the data. Page down for the problem statement. Return to the list of monthly problems by clicking here. Bypass the background information and go directly to the problem statement by clicking here.
Background
Equipment inspection for mechanical integrity is a major nondestructive testing
issue to verify that equipment is capable for use to prevent or minimize the
consequences of catastrophic release of toxic, reactive, flammable, or
explosive chemicals as required by OHSA 1910.119 -- Process Safety Management
of Highly Hazardous Chemicals. Risk based inspection is a program/methodology
for developing decisions about risk--how much risk, where is the risk, and when
to inspect/re-inspect for controlling risk. With facts from a risk based
inspection program, the details can be prioritized for determining the risk for
individual equipment in a plant by identifying the likelihood for failure (the
probability of failure) and the consequence of failure ($s if the event
occurs). The desired action of a risk based inspection program is to
simultaneous get lower risks and lower costs.
A portion of the issue is to establish procedures for process safety management that will protect employees by preventing or minimizing the consequences of chemical accidents involving highly hazardous chemicals. The purpose of risk based inspection is to identify the risk and verify the equipment is safe for eliminating or mitigating the consequences of the release of hazardous chemicals. The mechanical integrity issue involving inspection and testing requires performing inspection and tests on process equipment following recognized and generally accepted good engineering practices. The frequency of inspection and tests of process equipment must be consistent with applicable manufacturers' recommendations, good engineering practices, and experience from prior operating experience.
Each company establishes and defines a plan for their mechanical integrity
inspections and tests. The plan must address:
1) Type of inspection and tests to be performed,
2) The extent of inspections and tests,
3) The frequency or intervals of inspections and tests,
4) The preparations required,
5) The personnel qualifications and responsibilities, and
6) The acceptance criteria.
Mechanical equipment integrity covers:
1) Pressure vessels,
2) Heat exchangers,
3) Storage tanks,
4) Fired heaters,
5) Piping,
6) Maintenance materials and spare parts,
7) Rotating equipment,
8) Instruments and controls,
9) Relief devices,
10) Fire protection systems, and
11) Electrical equipment.
Equipment may be covered even if it does not contain a highly hazardous
chemical---if the equipment can contribute to severe problems.
Mechanical integrity programs for risk assessment help:
1) Define and measure risk,
2) Allow periodic reviews to measure the safety program in a
cost-effective manner,
3) Systematically reduce the probability of failures, and
4) Help with a reliability improvement program for plant equipment.
Risk based inspection is required because:
1) Most inspection codes and standards are based on the likelihood
of failure rather than the cost of failure,
2) A need exists to reduce the risk of high consequences of failure
using a Pareto sorting process to control the vital few cost issues,
3) Improvements are needed in the cost effectiveness of inspection
programs by shifting resources to attack the vital few issues, and
4) Quantification is required to understand what are the risks and
how to measure the effects of reductions of risk from inspection
programs/practices.
Several well-known inspection codes and standards are in use or in
preparation for use. They include:
1) API 581 Base Resource Document on Risk-based Inspection,
2) API-RP-580 Risk Based Inspection (In preparation),
3) API 510 Pressure Vessel Inspection Code,
4) API-570 In-Service Piping Inspection Code,
5) API-653 Storage Tank Inspection Standard,
6) ASME I00311 Risk-Based Inspection-Development Of Guidelines
Volume 1-General Document.
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The Problem
Pipe wall thickness inspection data, shown below in Table 1, has been acquired
at a specific location for years.
|
Table 1: Wall Thickness measurements (inches) |
||||||||
|
Location |
YR1 |
YR2 |
YR4 |
YR6 |
YR8 |
YR 10 |
YR 12 |
YR 14 |
|
1 |
0.311 |
0.311 |
0.311 |
0.314 |
0.309 |
0.308 |
0.308 |
0.305 |
|
2 |
0.316 |
0.318 |
0.310 |
0.315 |
0.305 |
0.300 |
0.302 |
0.298 |
|
3 |
0.308 |
0.300 |
0.298 |
0.301 |
0.295 |
0.291 |
0.295 |
0.292 |
|
4 |
0.305 |
0.305 |
0.302 |
0.304 |
0.295 |
0.294 |
0.290 |
0.289 |
|
5 |
0.318 |
0.311 |
0.304 |
0.305 |
0.300 |
0.299 |
0.295 |
0.285 |
|
6 |
0.321 |
0.318 |
0.313 |
0.313 |
0.308 |
0.305 |
0.300 |
0.295 |
|
Maximum |
0.321 |
0.318 |
0.313 |
0.315 |
0.309 |
0.308 |
0.308 |
0.305 |
|
Minimum |
0.305 |
0.300 |
0.298 |
0.301 |
0.295 |
0.291 |
0.290 |
0.285 |
|
Mean |
0.3132 |
0.3105 |
0.3063 |
0.3087 |
0.3020 |
0.2995 |
0.2983 |
0.2940 |
The measurements occur at the same spot on the pipe. This specific location is considered the worst location for corrosion on this pipe loop.
The data contains the usual measurement errors. Notice the average wall thickness is getting smaller as the pipe ages.
This service for this pipe has a high risk for fire and lost production from the plant along with a high probability of injury to a large number of people and death to a few people. The financial consequence of a failure has the potential for a total loss of $85,000,000--including business interruption. For business purposes, the risk for this condition must be controlled to less than $10,000. Since human fatalities are likely, the maximum allowed probability of failure permitted is 0.01%.
A straightforward calculation of the probability of failure (POF) using Risk$ = POF*$Consequences shows the POF = $10,000/$85,000,000 = 0.00012 = 0.012%. For human life at risk--the probability of failure is desired at less than 0.01% (or 99.99% reliability). Thus the POF for loss of human life, i.e., 0.01%, must prevail in the calculations.
The minimum wall thickness needed for pressure containment is estimated from Barlow's stresses at 0.047" with an additional estimated 0.033" for bending stresses, plus and estimated 0.051" for miscellaneous small abuses for a total estimate of 0.131". This minimum estimate, as judged by members of the assessment team, may be too low for some unusual conditions by a factor of 1.8 (this multiplier is a statement of confidence) to cover unknown conditions. Thus the practical minimum wall thickness estimate is 0.131*1.8 = 0.236".
*
Questions:
1) Using the wall thickness data, how has risk varied with time?
2) When will end of useful life occur?
3) When should the next inspection for wall thickness occur based on no
substantial change in operating practice?
4) When end of useful predicted life is reached and plant management
wants to avoid the expenditure of funds for replacement, how to do you determine
if a life extension is possible?
5) Can WinSMITH
Weibull's new "Parameter As Function Of Engineering
Variable" answer the question about end of useful life?
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Solutions:
Answer For Question #1: Using the wall thickness data, how has risk
varied with time?
Figure 1
shows a Weibull plot of all wall thickness by year of inspection--the data is
fairly orderly because the same spot is measured at each inspection. Notice how
the log scale has been expanded to cover the range of interest between
0.236" and 0.325". Remember the Weibull method starts with discrete
data to aid in forming a continuous model of wall thickness.
Each of the actual lines modeling the wall thickness is projected to the
minimum allowed wall thickness of 0.236" and the probability value is
calculated when the intersection occurs. The calculated probability of failure
is shown in Table 2.
|
Table 2: Probability of Failure
(%) For A |
|||||||
|
Yr 1 |
Yr 2 |
Yr 4 |
Yr 6 |
Yr 8 |
Yr 10 |
Yr 12 |
Yr 14 |
|
1.2E-05 |
1.4E-05 |
2.6E-05 |
1.2E-05 |
9.8E-05 |
3.7E-05 |
3.2E-04 |
2.7E-03 |
Note that a Weibayes line has been drawn through the critical value in
Figure 1 at minimum allowed wall thickness (0.236") and maximum allowed
probability of failure (0.01%) with a slope of the line at a beta of 45.65
which forms another critical value for eta at 0.2885"--this will be used
later in the analysis.
Answer For Question #2: When will end of useful life occur?
Preparing a trend line of probabilities from Table 2 is not helpful in projected the end of life.
A Probit probability
plot of the data from Table 2 would be very helpful in relating the CDF with
time. WinSMITH Weibull will only plot values greater than 0.001%. This
condition excludes six out of the eight values and thus a Probit chart for this
data is not possible.
Figure 2 shows a trend line of the characteristic thickness values described by eta. Values of eta decline with age of the pipe and form a smooth trend line which is projected to intercept the critical value of eta (see Figure 1 and the Weibayes line for a critical estimate of eta = 0.2885".
From Figure 2, the useful life is reached in 20.6 years where the probability of failure is projected to reach the critical value of 0.01% at a critical wall thickness of 0.236".
Answers For Question #3: When should the next inspection for wall
thickness occur based on no substantial change in operating practice?
The current operating time on the pipe is 14 years. End of useful life based on risk and wall thickness is projected to occur in 20 years. For a prudent method, perhaps the next inspection should occur at the remaining half-life which is three years into the future. Schedule the next wall thickness survey for year 17.
If you're really nervous, then maybe the next measurement should occur at the 1/4 life which would occur 1.5 years into the future. Remember in general, pipe wall thickness evaluation efforts often puts the cart before the horse. Too much testing and inspection is performed when risks are very low (in this case year 2-10) and too little testing occurs near end of life (year ~17-20) because the inspection effort becomes boring in not finding any problems.
If operating conditions change substantially or errors occur in severity of materials within the pipe, the inspection plan should be altered. Use shorter periods if conditions are more severe. Use longer periods if conditions are less severe. For example, if poor operating practices occur and corrosion rates rise, it would not be prudent to ignore the deteriorating effects to sustain a calculated half-life for the next inspection.
The argument for the next inspection period is to perform the inspection at a cost effective interval without exceeding the risk budget. You will never have enough data for a risk free decision!
Answers For Question #4: When end of useful predicted life is reached and plant management wants to avoid the expenditure of funds for replacement, how to do you determine if a life extension is possible?
Notice the calculation for the minimum wall includes a factor to improve the confidence of the allowed minimum wall thickness. The multiplier is a factor of 1.8 to cover the indecision and discomfort level of not knowing God's true value for the minimum. If a survey of stresses in the piping is conducted and a survey of the wall thickness within the remaining pipe is conducted, then perhaps the factor can be reduced and made closer to unity. Removal of unknowns in the stress level can permit a smaller critical wall thickness and thus permit a logical extension of life based on facts.
Answers For Question #5: Can WinSMITH Weibull's "Parameter
As Function Of Engineering Variable" answer the question about end of
useful life?
The parameter as a function of engineering variable takes the family-of-curves which are grouped according to ages of use. The program requires the use of a maximum likelihood estimate (MLE) method and solves for one slope that would theoretically fit all data sets. An exponential curve fit was selected (options are an exponential, power or Arrhenius) as producing the most logical fit. Look at the help file in WinSMITH Weibull for details on this new feature.
The age to predicted end of useful life is 28.4 years. Remember this method uses the MLE method for fitting the data and as Abernethy describes in The New Weibull Handbook, 2nd editon, 1996, Section 2.21 pages 2-18 & 2-19, "MLE has a bias error toward steep betas for small samples....". The best slope calculated by the MLE is 52.77 and when the parameter is selected at 28.4 years, a line is drawn through the critical value at 0.01% risk and 0.236" wall thickness.
The answer is yes, the Parameter As Function Of Engineering Variable is helpful in providing ANOTHER estimate for end of useful life. Remember the Weibayes line shown above used a flatter beta = 45.65 as often corrosion data develops more scatter in thickness readings over longer periods of time and thus engineering judgement out trumps mathematical calculations for this case.
Comments:
In the land of the blind, a one-eyed man is king. These techniques help provide THE one eye which is important in making decisions. When in doubt, use good judgement. No one method answers all questions!!
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