Problem Of The Month
July 1997--Monte Carlo Reliability Model
Starting With WinSMITH Weibull Data
WinSMITH Weibull software can assemble random data into a very compact form. The software will provide a useful probabilistic information for many purposes as was illustrated in the March '97 problem of the month. This problem shows how to estimate the fatigue life of a pressure vessel--in this case a very large diameter coke drum.
The next question is "What can you do with the information"? Answers for questions below are graphically illustrated with GIF files for clarity--these six files are 122 K in size and may take a few moments to load.
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
Refer to the background information for the March '97 problem of the month
to show how stress data is converted into a statistical format for a process
which is behaving in a probabilistic manner.
The name
The
The
Many arguments occur about the "goodness" of the random number generator. For practical purposes, the random number generator in most modern PCs is pretty good and certainly good enough for solving practical engineering problems where we're trying to achieve answers to 10% accuracy or better. We'll save the perfect answer for the scientist to find--if they can live long enough.
Return to the list of monthly problems by clicking here. Return to top of this problem statement by clicking here.
The Problem
Discrete stress measurements of circumferential and axial stress on coke drums can
be used to improve coke drum design by converting the experimental data into a
statistical format. This technique was shown in the March '97 problem of the month
using high temperature experimental stress data from Richard Boswell of Stress Engineering Services in
Actual stresses collected during normal operation of coke drums at ~900F (480C) can be used to simulate future expected stress loads on the drum. Each drum is expected to exhibit its own unique stress patterns and locations based on operating conditions, etc. which requires a physical stress assessment of actual conditions over a period of 6-12 months to calibrate the model.
The stress simulations follow accepted
Questions:
1) How will the algorithm be established for finding the life of a coke
drum which is a pressure vessel with high thermal and crushing stresses
randomly imposed on the stresses from internal pressure?
2) Using experimental stresses collected on the surface of coke drum what is the expected life?
3) How does wall thickness vary with end of life under these stress
loading conditions?
4) What effect would limiting the stresses have on fatigue life?
5) If stresses are limited, how many cutbacks can production expect based
on a specified stress level.
Return to the list of monthly problems by clicking here. Return to top of this problem statement by clicking here.
Solutions:
Answer to Question 1) How will the algorithm be established for finding
the life of a coke drum which is a pressure vessel with high thermal and
crushing stresses randomly imposed on the stresses from internal pressure?
Figure 1 shows a coke drum model starting with actual experimental stresses and the S-N curve expected for the material. The methodology is shown in the lower left hand corner of the figure. By randomly selecting stresses to simulate the stresses which would occur during operation, a case history is forecasted by simulation to calculate end of fatigue life.
Answer to Question 2) Using experimental stresses collected on the surface
of coke drum what is the expected life?
Using Miner's rule for fatigue stresses, individual load steps are
accumulated until Miner's rule sums to 1.0 for fatigue failure. For this
specific case, fatigue life is reached at 4960 cycles ±~350 cycles based on use
of Miner's rule for fatigue--of course end of life by rupture will be longer.
For this particular model, the chronological age to failure is 27.6 years. The
figure below shows one example of how Miner's rule accumulates by Monte Carlo
simulation as the actual curve oscillates around the straight line until it
reach end of life at the failure point of 1.0. This curve was generated from a
The
Answer to Question 3) How does wall thickness vary with end of life under
these stress loading conditions?
Figure 2 shows an example of using the model to forecast wall thickness requirements for a variety of cycles until end of life. The thickness requirements are helpful for design of new drums or repair of damaged sections. For this case, adding 20% to the wall thickness would double the number of cycles until reaching the fatigue limit.
Answer to Question 4) What effect would limiting the stresses
have on fatigue life?
Limiting peak drum stresses is another alternative to increase fatigue life.
This alternative requires continuously monitoring the drum and moderating peak
operating conditions by minutes/hours to avoid life-robbing peak stresses. This
condition can help extend life of existing drums by projecting the end of life
under present conditions and forecasting the improvement by stress control
procedures by simulation modeling as shown in Figure 3.
Answer to Question 5) If stresses are limited, how many cutbacks can
production expect based on a specified stress level.
Figure 4 shows the number of normal cycles per cutback expected when a maximum
stress level is specified.
Of course the final question involves life cycle costing to find cost-effective
actions to arrive at a solution most effective for the stockholders.
Return to the list of problems by clicking here. Return to top of this problem statement clicking here.
Other Industry Sources For Coke Drums-
Technical comments distributed on a CD to an American Petroleum Industry conference on coke drums in May 2001 are available at http://www.stress.com/servicetier3.php?sid=5&pid=206 by Stress Engineering Services who perform experimental stress analysis and conduct extensive FEA computer studies of coke drums.
CIA Inspection Inc. performs extensive inspection of the interior of on-line delayed coke drums without blinding or scaffolding to obtain a detailed interior profile of the vessel using laser range imaging and video inspection. The site has links to coke drum related sites at http://www.cia-inspection.com/industrylinks.htm .
Comments:
Here are a few quotations that might make this idea about
If you bet on a horse, that's gambling.
If you bet you can make three spades, that's entertainment.
If you bet the structure will survive for a hundred years, that's engineering.
See the difference? Ephraim
Suhir, Applied Probability for Engineers and Scientists,
McGraw-Hill, 1997, page xix.
The man with a new idea is a crank
until the idea succeeds. Mark Twain Following
the Equator, ch. 32, "Pudd'nhead Wilson's New Calendar" (1897).
Traditional scientific method has always
been at the very best, 20-20 hindsight. It's good for seeing where
you've been. It's good for testing the truth of what you think you know, but it
can't tell you where you ought to go.
Robert M. Pirsig Zen and the Art of Motorcycle
Maintenance, pt. 3, ch. 24 (1974).
The real accomplishment of modern science
and technology consists in taking ordinary men, informing them narrowly and
deeply and then, through appropriate organization, arranging to have their
knowledge combined with that of other specialized but equally ordinary men.
This dispenses with the need for genius. The resulting performance, though less
inspiring, is far more predictable. John
Kenneth Galbraith The New
Refer to the caveats on the Problem
Of The Month Page about the limitations
of the above 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.
Technical tools are only interesting toys for engineers until results are converted into a business solution involving money and time. Complete your analysis with a bottom line which converts $'s and time so you have answers that will interest your management team!
You can download this problem as a PDF file by clicking here.
