700

750

800

850

900

950

1000

1050

1100

1150

10/18/2012 12/7/2012 1/26/2013 3/17/2013 5/6/2013 6/25/2013 8/14/2013 10/3/2013 11/22/2013 1/11/2014

Tem

pera

ture

(F

)

390

400

410

420

430

440

450

460

470

480

490

500

510

520

530

540

550

Pre

ssu

re (

psig

)

Coil Inlet PressureProcess Outlet Temperature

Tube Metal Temperature

Accelerated

Creep Range

Convection Section

Tubes 1 – 18

Roof SectionTubes 19 – 30

Radiant Section

Tubes 31 – 50

P = 476 psig

Inlet Pressure

P = 105 psig

Outlet Pressure

TI

TI

TI

TI

TI

TI

Smart Pig performed November 2012

• 0% Creep (Diametrical Growth)

• Baseline thickness readings

Tube Pressure

(Simulated)

Deterministic Remaining Life Analysis for Single Tube #31

Tube Metal Temperature

(Simulated)

• Calculate future expected creep damage by simulating coking runs based on historical pressure, temperature, and corrosion

rates.

• Use methods of API 530 & API 579 to find cumulative Partial

Damage Fraction based on Larson-Miller parameter.

• API 579 recommends tube retirement at PDF > 0.80

• PDF is a function of temperature, pressure, and tube thickness

),()(

10

2424

20460

10001

thicknesspressurefstressfLMP

FailuretoTimePDFPDF

n

n

T

LMPnn

==

=+=

−

+

⋅−

Assumed Operating Conditions

psig361

F1121

psig343

F986

150

/58.9

oo

=

=

=

=

=

=

EOR

EOR

SOR

SOR

P

T

P

T

daysLengthRun

yearinRateCorrosion

What input values to use for model?Answer: Monte Carlo Simulation

900

950

1000

1050

1100

1150

10/18/2012 12/7/2012 1/26/2013 3/17/2013 5/6/2013 6/25/2013

Tem

pera

ture

(F

)

Tube Metal Temperatures & Run Length

Co

nvecti

on

Secti

on

Tu

bes 1

–18

TI

TI

TI

TI

TI

TI TI

TI

TI

TI

TI

TI

Coil 5 Coil 6

Ro

of

Secti

on

Tu

bes 1

9 –

30

Rad

ian

t S

ecti

on

Tu

bes 3

1 –

50

Radiant TubesTemperature profile based on TI readings

Roof TubesTemperature profile based on adjusted IR readings

Maximum recorded IR temperatures are scaled from the

measurement date to SOR and EOR using the Rankine

energy scale and TI measured values.

SOR Temperature

EOR Temperature

Pressure Profile & Corrosion Rates

Co

nvecti

on

Secti

on

Tu

bes 1

–18

TI

TI

TI

TI

TI

TI TI

TI

TI

TI

TI

TI

Coil 5 Coil 6

Ro

of

Secti

on

Tu

bes 1

9 –

30

Rad

ian

t S

ecti

on

Tu

bes 3

1 –

50

100

150

200

250

300

350

400

450

500

0 5 10 15 20 25 30 35 40 45 50

Tu

be P

ressu

re (

psig

)

Pressure Profile P_SOR P_EOR

R2 = 0.8666

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20 25 30 35 40 45 50

Co

rro

sio

n R

ate

(in

/year)

Pressure ProfileInlet Pressures Scaled to Fit Hydraulic Pressure Drop Model

Corrosion RatesCalculated for Each Tube from Install Date

P = 476 psig

Inlet Pressure

P = 105 psig

Outlet Pressure

Roof Tubes

Installed 1991

Material Properties – Larson Miller Parameter

API 530 provides Average and Minimum value curves for the Larson

Miller Parameter as a function of stress for 9Cr-1Mo metallurgy

• Minimum LMP is considered unrealistically conservative by industry for

remaining life analysis

• Average LMP is more realistic but it is possible to have material properties

below this value

For Monte Carlo analysis we can construct a random normal distribution

of LMP values in between the Average and Minimum curves

Curve fits for LMPmin and LMPave are given in API 579

Stress

LMP

API 530 Average

LMP Curve

API 530 Minimum

LMP Curve Introduce LMP Multiplier

( )35.0,5.0 == σµN

( ) ( )444 3444 21 3

5.0minmin ,5.0 ==⋅−+= σµNLMPLMPLMPLMP ave

×⋅−=

×⋅−=

9min

9

101ln14465.3

102ln07692.3

stressLMP

stressLMPave

LMP Percent = Normal random variable

approximately between 0 and 1

Monte Carlo Simulation – Setup

Utilized the R statistical computing language to write two functions

• tube_life() generates one deterministic run of simulated creep damage for a

single tube based on the parameters passed to it until PDF > 0.80 and returns the

expected remaining life.

tube_life(run_length,tube_OD,tube_thickness,corrosion_rate,P_SOR,P_EOR,T_

SOR,T_EOR,LMP_percent,partial_damage_fraction) { … return(remaining_life)}

• tube_mc() runs the Monte Carlo simulation by generating random normal

distributions of size n for SOR/EOR temperature, run length, and LMP percent.

The SOR/EOR pressure, tube thickness, and corrosion rate data is retrieved from

a csv file for the given tube_number and tube_life() is called to make n runs of the

simulation. The resulting distribution of remaining_life is written to output.csv.

tube_mc(tube_number,n)

Start of run Pressure: P_SOR

End of run Pressure: P_EOR

Tube Outer Diameter: tube_OD

Measured Thickness: tube_thickness

Corrosion Rate: corrosion_rate

Roof Tube Temperature Zone

T_SOR: N(µ=911.66,σ=39.13)

T_EOR: N(µ=1113.49,σ=44.88)

Radiant Tube Temperature Zone

T_SOR: N(µ=960.1,σ=14.159)

T_EOR: N(µ=1151.46,σ=19.97)

Run length : N(µ=163.7,σ=32.95)

LMP Percent: N(µ=0.5,σ=0.5/3)

Deterministic VariablesRandom Variables

coil_data.csv

EOR Temperature Sensitivity - Tube #24Coil 5 average values for all parameters

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34

1000 1020 1040 1060 1080 1100 1120 1140 1160 1180 1200 1220 1240 1260 1280 1300 1320 1340

End of Run Temperature (F)

Rem

ain

ing

Lif

e (

years

)Monte Carlo Simulation – Results

• Monte Carlo simulation results show that Tube #24 in

Coil 5 is the first tube expected to reach a partial damage

fraction of 0.80 in 3.73 years at the 99% confidence level.

• We can safely continue to operate the heater until August

2016 (3.73 years from 11/15/12) with less than a 1%

probability of mechanical failure. There should be no

issues to make it to the planned January 2016 turnaround.

• Increasing end of run temperatures significantly reduces

tube life at an exponential rate.

Coker Heater Remaining Life Monte Carlo Simulation99% confidence interval (n=10,000)

0123456789

101112131415161718192021222324252627282930313233

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

Tube Number

Rem

ain

ing

Lif

e (

years

)

Coil 5

Coil 6

Coil 5 - Tube #24

3.73 years (Aug 2016)

Tube #50 Distribution of Remaining Life

1% Probability Failure

Monte Carlo Simulation – Coil 5 Run Comparisons

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

13000

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

Tube Number

Re

ma

inin

g L

ife

(d

ay

s)

n=10,000 n=1000 Minimum LMP (LMP Percent = 0) Average LMP (LMP Percent = 1)

#clear all

rm(list = ls(all = TRUE))

for(i in 1:200){cat("\n")}

getwd()

tube_life <-

function(run_length,tube_OD,tube_thickness,corrosion_rate,P_SOR,P_EOR,T_SOR,T_EOR,LMP_percen

t,partial_damage_fraction){

T_daily_increase = (T_EOR-T_SOR)/run_length

P_daily_increase = (P_EOR-P_SOR)/run_length

remaining_life = 0

T = T_SOR

P = P_SOR

while (partial_damage_fraction < 0.80) {

stress = P/2*(tube_OD/tube_thickness-1)

LMP_ave = -1*log(stress/2e+09)*1/0.325

LMP_min = -1*log(stress/1e+09)*1/0.318

LMP = LMP_min + (LMP_ave-LMP_min)*LMP_percent

time_to_rupture = 10^(LMP/(T+460)*10^3-20)

partial_damage_fraction = 24/time_to_rupture + partial_damage_fraction

T = T + T_daily_increase

P = P + P_daily_increase

tube_thickness = tube_thickness - corrosion_rate

remaining_life = remaining_life + 1

if (T > T_EOR) {

T = T_SOR

P = P_SOR

}

}

return(remaining_life)

}

tube_mc <- function(tube_number,n){

tube_data = read.csv("coil 6 data.csv")

pressure = tube_data[tube_number,]$pressure

P_SOR = tube_data[tube_number,]$P_SOR

P_EOR = tube_data[tube_number,]$P_EOR

tube_OD = tube_data[tube_number,]$tube_OD

tube_thickness = tube_data[tube_number,]$tube_thickness

corrosion_rate = tube_data[tube_number,]$corrosion_rate/(1000*365)

RND_T_SOR = rnorm(n, mean=T_SOR_mean, sd=T_SOR_sd)

RND_T_EOR = rnorm(n, mean=T_EOR_mean, sd=T_EOR_sd)

RND_run_length = rnorm(n, mean=run_length_mean, sd=run_length_sd)

RND_LMP_percent = rnorm(n, mean=0.5, sd=0.5/3)

life_dist =

mapply(tube_life,run_length=RND_run_length,tube_OD=tube_OD,tube_thickness=tube_thickness,cor

rosion_rate=corrosion_rate,P_SOR=P_SOR,P_EOR=P_EOR,T_SOR=RND_T_SOR,T_EOR=RND_T_EOR,LMP_perce

nt=RND_LMP_percent,partial_damage_fraction=0)

hist(life_dist,nclass=20)

percentiles = quantile(life_dist,probs=seq(0,1,.01))

percentiles = c(tube_number,n,percentiles)

names(percentiles)[1] = "tube_number"

names(percentiles)[2] = "n"

print(percentiles)

output = data.frame(t(percentiles))

names(output) = names(percentiles)

if (file.exists("output.csv")) {

output_file = read.csv("output.csv")

names(output_file) = names(percentiles)

output_file = rbind(output_file,output)

write.table(output_file, sep = ",", file = "output.csv")

} else write.table(output, sep = ",", file = "output.csv")

}

run_length_mean = 163.7

run_length_sd = 32.95

#roof tubes

T_SOR_mean = 911.66

T_SOR_sd = 39.13

T_EOR_mean = 1113.49

T_EOR_sd = 44.88

tube_mc(19,10000)

tube_mc(20,10000)

tube_mc(21,10000)

tube_mc(22,10000)

tube_mc(23,10000)

tube_mc(24,10000)

tube_mc(25,10000)

tube_mc(26,10000)

tube_mc(27,10000)

tube_mc(28,10000)

tube_mc(29,10000)

tube_mc(30,10000)

#radiant tubes

T_SOR_mean = 960.1

T_SOR_sd = 14.159

T_EOR_mean = 1151.46

T_EOR_sd = 19.97

tube_mc(31,10000)

tube_mc(32,10000)

tube_mc(33,10000)

tube_mc(34,10000)

tube_mc(35,10000)

tube_mc(36,10000)

tube_mc(37,10000)

tube_mc(38,10000)

tube_mc(39,10000)

tube_mc(40,10000)

tube_mc(41,10000)

tube_mc(42,10000)

tube_mc(43,10000)

tube_mc(44,10000)

tube_mc(45,10000)

tube_mc(46,10000)

tube_mc(47,10000)

tube_mc(48,10000)

tube_mc(49,10000)

tube_mc(50,10000)