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Heat Exchanger IRIS Wall Thickness And Gumbel Smallest Distribution Paul Barringer, P.E. Barringer & Associates, Inc. P.O. Box 3985 Humble, TX 77347-3985 Phone: 281-852-6810 FAX: 281-852-3749 Email: [email protected] Web: http://www.barringer1.com

January 24,2002

© Barringer & Associates, Inc. 2002

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What’s The Issue? How To Resolve? • Heat exchanger is 17 years old—460 tubes • At turnaround eddy current wall thickness inspection occurred—we’re worried • Did an IRIS inspection on 10% of tubes—now we’re more worried—what does the data say? • Retube now? Retube next turnaround in 3 years (age 20 years)? Retube at second turnaround in 6 years (age 23 years)? © Barringer & Associates, Inc. 2002

Time Issues

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What Are Cost Consequences? • Failure is dependent on outside temperatures: – – – –

Summer failure = $750,000 lost margins & retube Fall failure = $500,000 lost margins & retube Winter failure = $100,000 lost margins & retube Spring failure = $250,000 lost margins & retube

• Another key issue is environmental impact along with the cost issues if failure occurs Money Issues © Barringer & Associates, Inc. 2002

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Why Did They Inspect? • Rule of thumb for this facility– Inspect tubes if wall thickness has been reduced by 1/3, i.e. from 0.083” to 0.055” – Consider retubing heat exchangers when tube wall thickness has been reduced to ½ of original wall thickness, i.e. from 0.083” to 0.0415”

• This exchanger has environmental concerns © Barringer & Associates, Inc. 2002

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Eddy Current vs IRIS Inspection • Eddy current inspection is a quick and inexpensive inspection of each tube—min wall is reported for each tube • IRIS inspection is a more detailed and more expensive inspection with a rotating head ultrasonic tool—min wall is reported for each tube and tube ID’s must be very clean © Barringer & Associates, Inc. 2002

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What Did IRIS Inspection Find? • The minimum wall thickness report shows: Wall*qty 0.050*1 0.055*1 0.056*2 0.058*2 0.059*1 0.061*6

0.063*9 0.064*9 0.065*4 0.066*5 0.067*2 0.069*4

Wall thickness measured in inches

• Minimum allowed wall thickness is 0.036” © Barringer & Associates, Inc. 2002

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Competing Models: Weibull or Gumbel Distributions? Weibull Distribution with rank regression & inspection option Data stacks from course measurements ∴use inspection option for regression

Small risk of wall thickness R= Coefficient © Barringer & Associates, Inc. 2002 of regression less than min allowed ccc= critical correlation coefficient

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Competing Models: Weibull or Gumbel Distributions? Gumbel- Distribution with rank regression

Bigger than for Weibull distribution ∴ use Gumble-

R= Coefficient Higher risk of wall thickness less than & Associates, © Barringer Inc. 2002 of regression ccc= critical correlation coefficient min allowed ∴more conservative

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PDF Curves

Note the Gumbel- distribution says to expect more occurrences with thinner walls


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Why Gumbel Lower Distribution?

F( x) := 1 − e

F( x) := e

−e

−e

results in the smaller sizes ( x− Ψ ) Emphasizes Use for minimum wall thicknesses, etc. Extreme Value δ

Gumbel Smallest or Lower Extreme Cumulative Distribution Function

− ( x− Ψ ) δ

Emphasizes results in the larger sizes Use for gust loads and floods, etc.

Extreme Value Gumbel Largest Extreme Cumulative Distribution Function


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The Gumbel smallest extreme value CDF is given by: ( t− ψ )

F( t)

1−e

δ

−e

Rearanging the equations to read ( t− ψ )

1 − F( t)

e

−e

( t− ψ )

δ

1

Or

( t− ψ )

e

1 1 − F( t)

e

e

δ

δ

e

Taking the log of both sides you get: ( t −ψ )

 e  1 − F( t) 

ln

1

δ

Again, taking the log of both sides you get: ln ln

1    1 − F( t)  

(t − ψ )

t

δ

δ

+

ψ δ

Gumbel- Distribution has uniform X-axis

This has the equation form of y = mx+b for a straight line where the Y-axis is the same as for the Weibull distribution which has the following form for a straight line equation

Same Y-axis

ln ln

1    1 − F( t)  

β ⋅ ln( t) − β ⋅ ln( η )

Weibull Distribution has logarithmic X-axis

So you could get from the Gumbel smallest plot to the Weibull plot with some math complications.


Heat Exchanger IRIS Inspection Data

99 95

90

G-/rr/insp1

Occurrences CDF %

70 50

40 30 20 10

Ψ =0.06427

5

δ

2

Area is 1% hi by 0.01” wide

Area is 1% hi by 0.01” wide

Year 17

80 60

11

Xi Del r^2 n/s 0.06427 0.00316 0.989 46/0

1 .03

.04

.05

.06

.07

.08

.09

.1

.11

Tube Wall Thickness (inches) © Barringer & Associates, Inc. 2002

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95

Occurrence CDF %

80

Heat Exchanger IRIS Inspection Data 99

G-/rr/insp1 Year 17

90

70 60 50 40 30 20 10 5 2 1 .5

Assumes new tube with tmin = 0.083” and tmax = 0.101” for ~6*σ = 99.8%

Year ?? Min Allowed Wall = 0.036”

99.9

Year 0

Note ~parallel slopes ∴ general corrosion Xi Del r^2 n/s 0.06427 0.0031573 0.989 46/0 0.09706 0.0020362

.2 .1 .03

.04

.05

.06

.07

.08

.09

.1

.11

Tube Wall Thickness (inches) © Barringer Associates, Inc. 2002 Corrosion rate = & (0.09706-0.06427)/17 = 0.00193”/yr

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Retube Or Not Retube Now? • At year 20 (next turnaround) the characteristic wall thickness will decline to 0.05848” • The risk for falling below 0.036” min wall is 8.075E-04 • The $risk exposure = 8.075E-04*$750,000 = $606 Time & Money Issues Converge • ∴ take the risk for running 3 more years —do not retube now and run to TA at yr 20. © Barringer & Associates, Inc. 2002

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Retube Or Not Retube To Reach Yr 23? • At year 23 (2nd turnaround) the characteristic wall thickness will decline to 0.0527” • The risk for falling below 0.036” min wall is 5.036E-03 Time & Money Issues Converge • The $risk exposure = 5.036E-03*$750,000 = $3,777 which is OK for business risk but maybe not OK for environmental risk • ∴ retube at year 20 if risk adverse, run to year 23 if the organization is a risk taker © Barringer & Associates, Inc. 2002

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Now, For Grins • Consider a case of the Gumbel larger distribution for Houston


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Remember June 9, 2001?


Peak Annual Stream Flows-Gage Height (feet) USGS 08074000 Buffalo Bayou at Houston, Texas

99.9

G+/rr

Note: Gage Datum: -1.36 feet above sea level

Altitude for 100 yr flood comes from the return period = 1/(1-p). When RP = 100, then p = 99%

Forecasted One Hundred Year Flood Gage Height

95 June 9, 2001

Occurrence CDF (%)

99

90 80 60

17

70

50 40 30 20 10 5 21 .2.5.1

Xi Del r^2 n/s 17.2 5.99 0.978 67/0 0

10

20

30

40

44.76 50

60

70

80

Peak Gage Height (feet) © Barringer & Associates, Inc. 2002

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Assumed Houston Flood Cost

4

2

1

100 year flood will be a 2X $ problem

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June 9, 2001

Assumed Flood Cost US ($ Billion)

5

0 10

20

30

40

50

Gage Height (feet) © Barringer & Associates, Inc. 2002

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Want More Details? • Got to http://www.barringer1.com • Look at Problems of the Month • For software to make the calculations, look at WinSMITH Weibull (which also includes Gumbel large and small distributions) • Also look at the biography of Dr. Weibull and Dr. Abernethy (the world’s leading expert in Weibull analysis—formerly with Pratt & Whitney Engines) • Dr. Weibull got many of his ideas on extreme values while working at Bofors Steel in Sweden—you can see Bofors antiaircraft guns at the Museum of the Pacific in Fredricksburg, TX. © Barringer & Associates, Inc. 2002

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