Remaining Life In
Pressure Relief Valves
The
Weibull User’s Conference is held every two years for the purpose of describing
new findings from various Weibull experts working on advancing the
technology. On March 8-9, 2007 the
Conference was held in
What
is the remaining life in relief valves that are surviving in service after 24
months.
The Issue:
“You
have 10, special purchase, high-temperature, relief valves in service. The test data for life is a Weibull model
fitted to their laboratory, high temperature, time-to-failure data which
indicates:
characteristic life Eta = 72 months and Weibull shape factor Beta = 2.6.
The
recommended scheduled replacement interval is 2 years of service. The valves have completed 24 months of
service and none have failed. The
reliability for 24 months of service starting from time zero is 94.4% using the
original Weibull model. You want to
demonstrate a minimum reliability of 95% for continued operation. The big question for these surviving safety
relief valves:
How
much longer can you keep these valves in service before you need to replace
them?”
Facts:
Weibull
characteristic life, h = 72 months. The Weibull shape
factor, b = 2.6 based on laboratory test.
Ten values have already survived 24 months without failure. The minimum reliability desired is 95%.
The questions:
1) How much longer will the valves survive (given they have already survived for 24
months without failure) and you want them to demonstrate 95% reliability at
removal from service?
2) What method would you use for finding the
remaining life to achieve 95% reliability for the 10 survivors who at still
alive at 24 months?
The answer:
The
current survivors are expected to survive for 6 more months (24+6=30 months)
and the chance for survival is 95%.
Please note: reliability +
unreliability = 1 where unreliability is often called the probability of
failure and for this case we have a 5% chance for failure in the next 6
months. Why is reliability important?—it
sets the risk levels. If the
consequences of pressure vessel failure is $1,000,000 and the probability of
failure is 5% then we have $Risk = pof*$Consequence =
5%*$1,000,000 = $50,000. Don’t take more
risk than you can afford, it will wreck your business and get you fired. Don’t take too little risk, if wasted good
money. You’ve got to get the risk
correct: Not too much risk and not too
little risk—it’s got to be just right, and different businesses allow different
risks. When you speak of reliability you
speak about the sweet side of the coin, when you speak about unreliability, you
speak about the sour side of the coin—by the way, when you know one, you also
know the other.
Please
note that survivors that have completed the planned, scheduled, replacement
interval does not always require instant removal from service for testing—from
the answer below, you’ll see that a grace period can exist. It’s a conditional reliability issue.
How to get the answer:
a) The easy way
to an answer-
1. Go to WinSMITH Weibull software (you
can download a demo version
which will solve this problem as you will not have to supply data into the data
spreadsheet which would result in some randomization of the data
spreadsheet).
2. Open the calculator
icon (top row, 6th from the left hand side).
3. Open the menu option for life remaining after no (zero) failures.
4. Input the known information of:
beta [2.6],
eta
[72 months],
present age [24 months], and
probability of failure (pof = 1- reliability) [5%].
5. Read the results as expected remaining life
usage [6.67
months]. Round the answer down to be
conservative to get 6 months.
b) The hard way to an answer-
1. Reliability at 24 months was expected to be
R(24) = exp(-(t/h)b )= exp(-(24/72)2.6
)= exp(-(0.333)2.6 )= exp(-0.0573) =94.4144776%
Whereas
the valves have show no failures to compromise reliability.
2. Conditional reliability equation is
R(24+x)/R(24) = 95%
Where
(24 + x) is the current surviving age and x is the additional number of months
of life to achieve a conditional reliability of 95%. This means the future reliability will be
R(24+x) = 89.6937537% given the parts are alive today at time 24 months. Why use conditional reliability
calculations??—it’s because the valves have already survived to the current
time of 24 months without failure (given an expected reliability at 24 months
of 94.4144776% at starting time zero).
3. Open Excel, click on Tools, click on Options,
click on Calculations, in the dialog box
click on Iteration, change maximum
Iterations to 10000, change maximum Change to 0.00001.
This
sets-up conditions for use of the Excel tool called Goal Seek so we get an
accurate answer.
4. In Excel cell A1 input the trial value for x as
1
This is done so that Excel will have a starting guess value for iterating the
correct value for x.
5. In Excel cell A2 and write (or copy/paste the equation below) the conditional
reliability equations:
=(exp(-1*((24+a1)/72)^2.6))/exp(-1*(24/72)^2.6)
6. In Excel, click on Tools,
click on Goal Seek, in the dialog box
set cell $a$2 (the equation) to value 95% by changing cell $a$1 (the guess number).
7. Get the answer in cell A1 =
6.673
months rounded down to 6 months.
8. Yes, we could have solved for time
mathematically this way:
R(24 + x) =e-((24+x)/h)b
e((24+x)/h)b = 1/(R(24+x))
((24+x)/h)b = ln(1/(R(24+x)))
(24+x)/h = {ln(1/(R(24+x)))}1/b
24 + x = h*{ln(1/(R(24+x)))}1/b
x = -24 +h{ln(1/(R(24+x)))}
1/b
= -24 + 72*(ln(1/89.6937537% ))1/2.6
= -24+72*(ln(1.114904839))0.384615
= -24+72*(0.426015604)
= -24 +30.67312352
= 6.673
months rounded down to 6 months as shown above in step 7.
Additional facts of life about relief valves:
You
can only determine pressure relieve valve failure in the
dangerous direction by periodic pressure testing. Testing lets you learn what you don’t know
until proven by a high pressure test. Of
course, if the pressure under the valve continues to stay below the maximum
allowed pop pressure, the relived valve overpressure failure is benign because the valve is
not demanded to pop open to relive the high pressure.
If
pressure under the relief valve exceeds the maximum allowed pop pressure the valve
has failed in the dangerous direction. If a relief valve is called to perform its
duty at high pressure and it won’t open, then a benign failure can become a
failure in the dangerous direction. Dangerous failures can become time bombs
because of the unknowns.
If
pressure under the valve is less than the minimum allowed pop pressure,
pressure relief valves can leak because of valve simmer from the slow
leak then the valve has failed in the safe direction. Simmering safety valves are observable failures. Simmering relief valves usually get removed
from service for service/replacement to prevent leakage.
A
safety valve may appear unfailed only because it has not been stressed from
pressure below the valve. It may appear
unfailed because it has not been tested periodically to show it’s capabilities
for relieving pressure safely within the allowed safe range.
Safety
relief valves in very clean service, where pressures are controlled by system
restrains, can have very long life, free from sticking, and blockage. Clean service occurs in service with refrigeration pressure relief
valves as an example. When clean
valves with pressures well below the control limit are tested coming back from the
field for periodic verification, a large percentage (about 95%) of relief
valves will pass the outgoing standard.
The valves must be tested as received from the field (not cleaned-up and
not reassembled before testing). The pop
open pressure data must be recorded in variable format (actual pop pressure
recorded in appropriate units with comparison to the outgoing standard for
acceptable/non-acceptable performance), and the pop pressures should not
be recorded in attribute format (pass/fail).
Safety
relief valves in dirty/sticky/gummy/high-temperature/low-temperature service
can have very short life due to sticking and blockage as occurs in refineries
or chemical plants and these problems are called failures. Failure problems are especially true where
the maximum pressures to be sealed are very near the maximum allowed by the
relief valve as the valve may chatter open and sit down in its own sticky
refuse in the valve which will act like “glue” to stifle clean operation of the
valve to break over and relive pressures from damaging equipment.
In
dirty/sticky/gummy pressure service the roughness of loading problems occurs
with surges and dynamic loads which can contaminate relief valves from the
fluids/gasses to be sealed. The
roughness of pressure loads on pressure relief valves has the same type effect
on safety factors as occurs with mechanical loads on materials with the
resulting condition of varying safety factors on the dangerous side because of
interference of load-strength
conditions.
Often
the dirty/sticky/gummy pressure relief valves don’t open inside the hi/lo
limits. In fact, they simply don’t open
at any reasonable pressure! This failure
to open and relive pressure becomes a time bomb waiting for a call for duty,
and they can’t perform the intended function for which the pressure relief
valve exists.
An
example of the early open problems (about
20%), open within the normal allowed range (about 60%), and open in the dangerous direction (about 20%) are described in a normal probability
plot, Figure 3, page 316 of Trans IChemE, Vol. 60, 1982 from the article “Reliability Assessment Of Safety/Relief
Valves” by R. J. Aird (pages 314-318) as shown in
Figure 1. Based on test valve test data
I have observed, I agree with Aird’s observations,
unless the operation is unusually clean service.
|
|
|
Figure 1: About 60% of
Relief Valves Open Within The Allowed Range |
Some
times the solution to a contamination problem for relief values is to use a
rupture diaphragm between the high pressure and the safety relief valve. The rupture diaphragm and the relief valve
become a function series reliability model requiring a higher relief valve
reliability to achieve the expected system reliability for service.
The
inferior practice of disassembling pressure relief valves removed from service,
cleaning the valve and reassembling the valve before performing the
pressure test will not discover the blockage from sticking/blockage. Thus a successful pressure test obtained from
this practice is a false success staged for eye-wash.
Age
in service to failure is important—here is a time keeping problem. A relief valve has been in service for 3
years. It is removed from service,
tested as passing the min/max pop pressures.
The valve is disassembled, cleaned, and placed back into service (with
the presumption of being restored to zero time). At the second 3 year interval it is removed
from service, tested and it fails the second pop test. The age to failure is 3 years (the age to
failure IS NOT 6 years because the valve has been cleaned and restored to zero
time for the second campaign). Time
keeping of ages to failure is very important for making decisions about life in
service.
The perception:
Suppose
we have a relief valve that must pop at 300 psi and
we are allowed ±5% for the pop range. That means the valve must open between 285 psi and 315 psi. Unfortunately, the high side of pressure
relief is measured with rubber rulers which are stretched to fit a political
agenda. The political agenda does not
reduce the risks to the business.
Allowed relief ranges should be handled without excuses and without use
of rubber rulers. Why?—the inferior
logic becomes if it is OK to steal pennies from the cash register till, then
it’s OK to steal nickels, and if OK to steal nickels, then it’s OK---you’ve got
the picture! Don’t handle upside
exceptions from an Enron perspective! Be
squeaky clean and follow a rigid procedure.
If peak pressures vary and
pressure relief valves relieve at variable pressures how will you know where
you are:
You
can have load-strength
interference problems that will decrease reliability of the system. How do
you get the loads?—collect the maximum daily pressures recorded on the system
and make a Gumbel upper
probability plot for the load. Take the
pop pressures from a family of similar values and make a Weibull probability
plot for the strength. Use the two
probability models to find the % interference.
Relief Valve Resources:
ASME
Consolidated Safety Relief Valve Code
Excerpts SRV-1
ANSI/API
RP 520, Part 1 Sizing and Selection,
Sizing, Selection, and Installation Of Pressure-Relieving Devices in Refineries
ANSI/API
RP 520, Part 2 Installation, Sizing,
Selection, and Installation Of Pressure-Relieving Devices in Refineries
API
RP 521, Guide for Pressure-Relieving and
Depressuring Systems
ANSI/API
527, Seat Tightness of Pressure Relief
Valves
ANSI/API
RP 576, Inspection of Pressure-Relieving
Devices
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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