March 1997--Coke Drum Life

**Coke drums are often the large pressure vessels you see in a refinery with
a drilling rig derrick sitting on the top. Coke drums are both waste disposal
systems for high residual, tarry oils, and they are also significant gross
margin contributors to the financial performance of refineries. Volatile fumes
from the coke drums are recycled to make useful products such as gasoline and
the solid material deposited in the coke drum is sold as coke for many
purposes. The drilling rig on top of the drum is used with water under high
pressure to fracture the solid coke bed so the coke can be removed for sale.**

__The Problem__

Richard Boswell of Stress Engineering Services, Houston, TX presented a paper
at the **1997 Energy Week Conference** (sponsored by ASME and API
Technical Societies) in Houston called **Remaining Life Evaluation of
Coke Drums**. His co-authors were Tom Farraro
and Michael J. Sober both of CITGO Petroleum Corp.

Their paper showed both axial and hoop stresses were nearly the same (!?strange event for a pressure vessel?!) due
to convolutions in the 20 foot diameter vessel which began its life as a
smooth, circular cylinder. In Figure 5 of the paper, they presented the maximum
__axial__ stress in a histogram. The data consisted of 126 production
cycles. The vessel is known to have a finite life. Remaining coke drum life is
now a major economic issue for most refineries around the world.

The maximum stress produced in coke drums usually occurs during the quench cycle. The stress is dependent upon how the operator executes the quench cycle from ~900 degrees F to ambient temperature. Fast quench cycles produce higher stresses. Slower quench cycles produce lower stresses. Also some coke drums have major stress problems in the skirt area which support the ~20 foot diameter vessel which is ~60 feet tall.

Here is a tabulation of the stresses measured with high temperature strain gages and the number of occurrences recorded. Stresses are recorded in ksi and occurrence are counts (for example the first data point is a stress level of 12.5 ksi with 4 occurrences of this maximum stress recorded):

12.5* 4 17.5*4
22.5*14 27.5*12
32.5*17 37.5*11,

42.5*12 47.5*11 52.5*9
57.5*6 62.5*5
67.5*7,

72.5*4 77.5*3
82.5*3 87.5*3
112.5*1

The data can be entered in WinSMITH Weibull using a frequency table format, i.e., 12.5*4--which means you'll only have 17 rows of data shown in one column. This is a very efficient method for inputting data into a spreadsheet.

__Questions:__

1) Which statistical distribution best describes the stresses produced during
the coking cycle?

a) Weibull _______ b) Log-normal
_______ c)

2) Is the data well behaved? Base the decision on the
rank regression correlation coefficient (a measure of goodness of fit).
Compared the actual results to the critical correlation coefficient [ccc]. The ccc is the value
expected to be obtained 90% of the time from a well behaved rank regression)?

a) Yes ____ b) No _____

3) Based on a likelihood ratio estimate, what are the 90% confidence limits for
the characteristics of the "best" curve fit of the data?

a) eta, muAL, mu _________ (The
measure of central tendency)

b) beta, sigF, std __________ (The
shape factor for the distribution)

4) What percentage of the cycles can be expected to exceed:

20 ksi ______ 30 ksi ______ 40 ksi
______ 50 ksi ______

60 ksi ______ 70 ksi ______ 80 ksi
______ 90 ksi ______

5) For coke drums which have remaining life, if you limit the stresses to a
value of "X", how would you find the remaining life of the vessel as
a result of limiting the remaining peak stresses?

6) If you know the operating costs/gross margins produced by the coker, and the number of cycles remaining, how can you find
the most economical operating condition to maximize operating profit based on
the remaining life of coke drums?

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__Solutions:__

Start the analysis by entering the 126 data points into WinSMITH Weibull using the
frequency table format. Use the rank regression technique. Click on the
distribution analysis icon and find the following results for question #1.

**Answer For Question #1:**

Weibull Results [t0 = None, 2
Parameter]

Correlation, r = .978, r^2 = .957, ccc^2 =
.9717, (r^2-ccc^2) = -.0147, (Bad!)

Characteristic Value = 48.580, Weibull
Slope = 2.741, Method = rr

Weibull Results [t0 = 8.35,
3 Parameter]

Correlation, r = .987, r^2 = .976, ccc^2 =
.9852, (r^2-ccc^2) = -.0092, (Bad!)

Characteristic Value = 39.668, Weibull
slope = 1.954, Method = rr/t0^

** ****LogNorm**** Results [t0 = None, 2 Parameter}
Correlation, r = .990, r^2 = .981, ccc^2 =
.984, (r^2-ccc^2) = **

Log-Mean Antilog = 39.465, Std. Dev. Factor = 1.596, Method = rr

Normal+ Results [t0 = None,
2 Parameter}

Correlation, r = .974, r^2 = .949, ccc^2 =
.984, (r^2-ccc^2) = -.035 (Bad!)

Mean = 43.730, Std. Deviation = 19.363,
Method = rr

Choose the distribution with (r^2-ccc^2) = **largest value**. Select the
l**og-normal distribution **as shown in the probability plot for coke drum
axial stresses as shown on the curve along the left margin.

The actual r^2 = coefficient of determination for the coke drum axial stress lies just a smidgen outside of the desired value and this is the reason for the (Bad!) label.

**Answer For Question #2:
**No,

**Answer For
Question #3:
**The measure of central tendency is

This elliptical-shaped curve is found by making the calculations in WinSMITH Weibull by clicking on 90% confidence intervals and the likelihood ratio method found under the confidence limit icon. Save the calculations to a file. Plot the file in WinSMITH Visual to get the results shown to the right. The 90% confidence limits are shown by the red triangles. The central triangle represents the point estimates for MuAL = 39.465 and SigF = 1.596

**Answer For Question #4:
**Click on the predict icon in WinSMITH Weibull when the data is in the plot
with the log-normal equation activated. Verify the statistical model is
log-normal by clicking on the PC icon. Input the information on the datum (such
as 20 ksi), and read the information shown below to
find the percentage of loads exceeding a value:

20 ksi -> **92.7%**
30 ksi -> **72.2%**
40 ksi -> **48.9%**
50 ksi -> **30.6%
** 60 ksi ->

**Answer For Question #5:
**Find the remaining life by building a

a) Draw random stresses from the distribution to equal the number of cycles recorded by the unit.

b) For each random stress drawn from the simulation solve the S-N equation for the number of allowable cycles.

Remember to derate the simple S-N curve for state of stress, stress concentrations, surface finish, corrosions, etc.

Where the simulated stress is less than the "knee" of the S-N curve make the allowed number of cycles very large (say ~10E100).

c) For each simulated stress for a cycle, compute Miner's equation component (1 cycle)/(allowed cycles).

d) Sum components for Miner's equation for all iterations.

e) If the summation of Miner's equation components is greater than 1 the system fails. If less than one success.

f) Calculate reliability = successes/(successes + failures) for each group of iterations.

g) Increase the number of cycles from the present life to a future life and calculate reliability--repeat the process many times to find the central tendency.

h) Now repeat the simulations with "circuit breaker" limitations on the maximum stress --observe the increases in expected life.

**Answer For Question #6:
**Build several decision trees. Use the chances for success and the chances
for failure (found from the simulations) to compute the gross profits for
different maximum stress levels. Use the case producing the greatest net
present value using a life cycle cost strategy. Consider the initial
installation and the major repair costs and lost production occurring during
repairs.

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**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 and a list of technical papers.

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.

** 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 converted into $'s and time so you
have answers that will interest your management team!**

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