17-9 june 2003inverse problem in engineering symposium topic fouling probe development for tubular...

7-9 June 2003 Inverse Problem in engineering Symposium 1

Topic

FOULING PROBE DEVELOPMENT FOR TUBULAR HEAT EXCHANGERS:

A first step

Laetitia PEREZ

P. TOCHONB. LADEVIE

UMR CNRS 2392J.C. BATSALE

UMR CNRS 8508


Overview

1. Industrial context

2. The Probe

3. Direct model

- theoretical sensitivity analysis

4. Experimental device

5. Experimental results

- experimental sensitivity analysis

6. Conclusions


Industrial context

- heat exchangers in the power and process industries

- performance degradation

- thermal resistance increase

- pressure drop increase

- heat coefficient decrease


Industrial context

Economic problems:

- oversizing equipment

- high maintenance costs

- energy expense

It is necessary to:

- detect the onset of fouling

- follow its development over time

Effectiveness of heat exchangers optimization


The Probe

probeExchanger parts

TeflonReheater

Stainless steel

Transient heatflux

Recording of the temperature evolution Thermocouple

probeExchanger parts

TeflonReheater

Stainless steel

Transient heatflux

Recording of the temperature evolution Thermocouple


Direct model

2 2 2

2 2 2 2

1 1 1T T T T T

r r r r x z a t

33

, , , if 0 otherwise 0

T r x z tr r z b

r

6

66 6

¨

, , , where air air air

r r

T r x z tr r h x S T S r L

r

0

, , ,0 0

z

T r x z tz

dz

, , , 0z L T r x L t

0 0 , , , 0r r T r x z t

even function in T x

0 00 , , ,0 where is the steady state temperaturet T r x z T T

Transient heat equation in cylindrical coordinates:

Boundary conditions:hair

hwater

r

zb

Cylinder axis

r0

r1

r2

r3r4

r5

r6

L

Exchanger part

Symetrie axis

hair

hwater

r

zb

Cylinder axis

r0

r1

r2

r3r4

r5

r6

L

Exchanger part

Symetrie axis

Stainless steel

Teflon

Reheater (sensor)

Stainless steel

Teflon

Reheater (sensor)


Direct model

0 0 0

, , , , , , cos cos

12with where ,

L ptn n

n

r k p T r x z t z kx e dzdxdt

nn k

L

2 2

22 2

, , , , , ,1, , , 0n n

n n

d r k t d r k t k pr k t

dr r dr r a

0 0 0

*

*

, , , cos cos

, , , 0 for and

sin,0, , for n and 0

b ptn n

n

nn

n

r k p z kx e dzdxdt

r k p n k

br p k

p

,

, , , , , ,

, , , , , ,in outin out

n n

n nr rr r

r k p r k pA B

r k p r k pC D


Direct model

1

1 1 23 3

1 1 2

,0, , ,0, ,air airn n

air air

C D h S Ar p r p

A B h S B

3 30

2, , , ,0, , cos

N

n nn

T r x z p r p zL

Finally, the temperature in the Laplace-Fourier space is:

The temperature in the real space is:

Too many approximations hard to check

Harsh industrial conditionsDirect model


Sensitivity analysis

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0-0 .2

0

0 .2

0 .4

0 .6

0 .8

1

1 .2

3

31

, 0 ,

1, 0 ,

N

nn

T r z t

T r z tN

3

31

, 0 ,

1, 0 ,

a ira ir

N

nn

T r z th

h

T r z tN

3

31

, 0 ,

1, 0,

pp

N

nn

T r z tC

C

T r z tN

t (s )

, , , ,i

ii

i

T r x z tX t


Experimental device

Air at 323 K

with particles

Cooling water

AirFoulant particles generator

Heat exchanger parts and probe

Industrial water

sewer

Air at 323 K

with particles

Cooling water

AirFoulant particles generator

Heat exchanger parts and probe

Industrial water

sewer


Experimental results

In clean conditions:

t (s)

Exp

erim

enta

l tem

pera

ture

s(°

C)

100 200 300 400 500 600 700 800 900 10008.5

9

9.5

10

Increase of air flow rate 50 Nm3/h

60 Nm3/h 70 Nm3/h 80 Nm3/h 90 Nm3/h 100 Nm3/h

t (s)

Exp

erim

enta

l tem

pera

ture

s(°

C)

100 200 300 400 500 600 700 800 900 10008.5

9

9.5

10

Increase of air flow rate 50 Nm3/h

60 Nm3/h 70 Nm3/h 80 Nm3/h 90 Nm3/h 100 Nm3/h

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

1 . 2

t ( s )

e x p 3

e x p 31

, 0 , ,

1, 0 , ,

e r i m e n t a ln o r m N

e r i m e n t a ln

T r z t QT Q

T r z t QN

n o r m n o r mi jT Q T Q

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

1 . 2

t ( s )

e x p 3

e x p 31

, 0 , ,

1, 0 , ,

e r i m e n t a ln o r m N

e r i m e n t a ln

T r z t QT Q

T r z t QN

n o r m n o r mi jT Q T Q


Experimental sensitivity analysis

3, 0, .airT r z t f h g t

3 0, 0, .air airair

fT r z t f h h g t

h

1

3

32 1

1

, 0,

1. , 0,

T T

air

N

n nNn

nn

f h g t g t g t T r z t

g t T r z tg t

The temperature response can be written by:

For a little heat transfer coefficient variation:

the signal amplitude variation can be calculated by:


12cov

T

air Tf h g t g t

40 50 60 70 80 90 100 1109.3

9.4

9.5

9.6

9.7

9.8

9.9

10

10.1

Standard deviationin considering only the steady state (t>100s)

Standard deviation in considering allthe signal

Q (Nm3/h)

f(h

air)

40 50 60 70 80 90 100 1109.3

9.4

9.5

9.6

9.7

9.8

9.9

10

10.1

Standard deviationin considering only the steady state (t>100s)

Standard deviation in considering allthe signal

Q (Nm3/h)

f(h

air)

Experimental sensitivity analysis


Experimental results

In fouled conditions:

Cooling water

Air flow

with particles

Deposit pattern around the probe

- Fouling detection after 22h

- Fouling thickness after 78h : efouling = 2 mm

t = 22 ht = 35 ht = 40 ht = 70 ht = 78 h

0 100 200 300 400 500 600 700 800 900 1000

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

Growing fouling

0norm fouling norm foulingT e T e

t (s)


Conclusions

- Fouling probe development

-direct model :

-sensitivity analysis

-experimental device :

-experimental sensitivity analysis

f(hair)

f(efouling)

17-9 june 2003inverse problem in engineering symposium topic fouling probe development for tubular...

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