Part I Heat Transfer Fouling

8/17/2019 Part I Heat Transfer Fouling

http://slidepdf.com/reader/full/part-i-heat-transfer-fouling 1/27

P RT

I

H T

TR NSF R

FOULING





— —

pr

es

su

re dro

ps m

ay

in

cr

eas

e

gr

ea

ter t

empe

ratu

re

d

if

fer

en

ce

s

m

ay b

e

re

qu

ir

ed

to

main

tain

the s

ame

d

uty

shu

t—d

own

an

d

cl

e ni

ng

co

sts be

come

ex

ces

si

ve

Hea

t

t

ran

sf

er

f

ou

lin

g

invo

lves

si

mult

aneo

us

h

ea

t m

ass

a

nd

m

ome

ntum

tra

ns

fe

r

with

che

mica

l

and

bi

olo

g

ica

l pro

cesse

s

a

lso

ta

king

pla

ce

A

lthou

gh

the

litera ture

on

fouling

is

found

in a

wide

variety

of

journals

the

subject

ap

pears

to fa

ll

int

o

t

he

d

is

ci

pli

ne o

f ch

emic

al

e

ng

in

ee

rin

g

et

iled

re

view

s of

h

e t

t

ran

sf

er

fo

ul

in

g r

e

few an

d

far

be

twee

n

In

9 8

Bad

ger

an

d

B

an

ch

er

o

3

r

evie

wed

sca

li

ng

in

d

es

ali

na

tio

n

In

96

8 W

a

tk

in

son

e

view

ed

t

he

su

bj

ec

t

of

fo

uli

ng

b

rie

fly

I

n

9

69

ot

t5

re

view

ed

in d

et

ail

t

he

fo

u

lin

g of

h

eat

ex

chan

ge

e

quipm

ent

with

sp

ec

ia

l r

ef

ere

nc

e

t

o

co

olin

g

wa

ter

syst

ems

In 9

7

t

t

6

al

so

rev

iew

ed

ga

s

side

fo

uli

ng

in

h

e t exc

han

ge

s

ystem

s; air

—co

oled

h

eat

ex

changers

and

oil—fired

heaters

In

97 Bott

and

W

al

ke

r

d

iscus

sed

f

ou

lin

g

in

heat

t

ra

nsf

er equi

pme

nt

in

g

en

era

l

In 97

Ta

borek

e

t

l

c

onsi

dere

d

f

ou

lin

g

i

n

coo

ling

wa

ter

syst

ems and

men

tion

ed

the

othe

r mai

n

ty

pes

of

fo

uli

ng

In 973

o

pk

in

s

7

and

W

alk

er

O

rev

iewe

d

fo

uling

in g

en

er

al

In

975

ot

tO

s

urve

yed

he t

tra

ns

fer f

ou

lin

g In

976

S

ui

to

r et

l

revi

ewed

the

his

to

ry

a

nd

sta

tu

s

o

f

rese

rch

in

fou

li

ng

of he

at

e

xcha

nger

s

in

co

oling

wat

er

s

erv

ic

e



3

C

LAS

SIFiC

AT

ION

2

1

I

ntr

od

uc

tio

n

M

ost

he

at

t

ran

sf

er

pr

oc

es

ses

at s

ol

id

su

rf

ac

es

a

re

su

bje

ct

ed

to

fou

li

ng

i

n o

ne

w

ay

o

r a

no

th

er. M

o

re

ov

er

num

erous

pro

ce

ss

es

res

ul

t

in

th

e

ac

cu

m

ul

ati

on and

fo

rm

a

tio

n of

m

at

eri

als

a

t

su

rfa

ce

s w

ith

o

ut

h

ea

t

tr

an

sfe

r ev

en

ta

ki

ng

p

lac

e.

Fo

r e

xa

m

ple

pa

rti

cle

su

sp

en

sio

ns an

d s

up

er

sat

ur

ate

ds

ol

uti

on

s

m

ay

r

es

ul

t

in

de

po

si

tio

n

o

n

un

he

at

ed

su

rf

ac

es.

The

te

rm

s

f

ou

lin

g

and

de

po

si

tio

n a

re

the

re

fo

re

us

ed in

te

rc

ha

ng

ab

ly in

man

y in

sta

nc

es

.

Fo

ul

ing

a

s d

ef

in

ed

ab

ov

e

r

efe

rs t

o

th

e

acc

um

u

la

tio

n

an

d

fo

rm

a

tio

n

o

f

su

b

sta

nc

es

th

at

a

ff

ec

t

t

he

t

he

rm

al

p

erf

or

m

an

ce of

s

ur

fa

ces

.

A

lt

ho

ug

h t

he de

po

si

tio

n

of

m

at

er

ial

s a

t

u

nh

ea

ted s

urf

ac

es do

es

no

t

st

ri c

tly

c

on

sti

tut

e

fo

uli

ng

th

e

ba

sic a

cc

um

u

la

tio

n

p

ro

ce

ss

es

in man

y

c

as

es

m

us

t

be

es

se

nti

al

ly the

sam

e

Be

ca

us

e

f

ou

lin

g

i

s

su

ch

a

co

m

pl

ex p

heno

meno

n

it

m

ust

be

w

or

th

w

h

ile

t

o at

tem

p

t

som

e c

las

si

fic

at i

on

to

id

en

tif

y a

re

as

o

f

co

nc

er

n and

s

tim

u

lat

e

fur

th

er

e

xp

er

im

en

ta

l

s

tud

ie

s.

T

hi

s w

as

rec

o

gn

ise

d

by

Bo

tt

an

d

W

a

lke

r

and T

ab

or

ek e

t

l

th

at l

ist

ed

s

ome b

ro

ad

ca

teg

o

rie

s

o

f

f

ou

lin

g

an

d m

e

nt

ion

ed

th

e m

a

in

va

ria

bl

es

.

im

p

ort

an

t co

ns

ide

ra

tio

n m

us

t

a

ls

o be

t

he fi

eld

o

f

a

ct

ivi

ty

or

in

du

str

y

w

he

re de

po

sit

io

n

a

nd

fo

uli

ng

o

cc

ur

2 2

Type

s

o

f

F

ou

li

ng

On

e

fa

ct

or

t

ha

t

is

i

mp

or

ta

nt

i

n fou

li

ng

is

th

e

m

ode

o

f

h

ea

t

tra

ns

fe

r;

in

vo

lvi

ng

se

ns

ibl

e

or

1

at

er

t he

ats

.

F

ou

lin

g

by a s

in

gle

ph

as

e

flu

id i

s

l

ike

ly

to dif

fe

r

fro

m th

at

of a

bo

ilin

g o

ne

H

owe

ver

f

or

th

e

pr

es

en

t p

urp

o

ses

f

ou

li

ng

at

b

oi

lin

g

and

n

on

b

oi

lin

g s

ur

fac

es

w

il

l

be

co

ns

id

ere

d

to

ge

th

er. I

t

sh

ou

ld

be

ap

pr

ec

iat

ed

t

ha

t m

o

st r

ea

l

de

po

si

ts c

on

ta

in

fou

la

nt

s a

ris

in

g

fro

m s

ev

er

al

s

ou

rc

es

; so

lub

il

ity

p

art

icu

la

te

re

ac

ti

on

e

tc

. N

ev

ert

he

le

ss

it

is

c

o

nv

en

ien

t

to d

is

tin

gu

ish b

et

we

en

th

e f

oll

ow

in

g mai

n

t

yp

es

:

So

lu

bil

ity f

ou

iin

c

o

cc

ur

s

w

hen a

su

bs

ta

nc

e co

mes

ou

t

o

f

s

olu

ti

on

d

ue to

he

at

ing

or

co

oli

ng

.

Th

e d

ep

os

iti

on

o

f

i

nv

er

se

s

ol

ub

ili

ty

ino

rg

an

ic s

al

ts

on

he

at

ed

sur

fa

ce

s

us

ua

lly

ca

fle

d

s

ca

lin

g’

be

lon

g

s

to

t

his

ty

pe

of

fo

u

lin

g.

S

ca

lin

g

is

cc

m

on

i

n b

oi

le

r

s

l

c

o

oli

ng

w

at

er s

y

s

t

m

s

0

7

8

de

sa

lin

at

io

n

p

r

o

ce

s

se

s

8

7

an

d

oil

w

ell

op

e

ra

t

io

n

s

9

S

u

bs

tan

ce

s

inv

es

tig

at

ed

i

nc

lud

e

cal

ci

um

c

r

b

o

n

t

e

7

5

4

8

c

alc

iu

m

su

l

ph

a

te

9

an

d

mag

nesiu

m

h

y

ro

xi

e

In

or

ga

ni

c

s

ub

st

an

ces

wi

th

norm

l

s

olu

bi

lit

y

de

po

si

t

on

c

oo

le

d

s

ur

fac

es

; s

ili

ca

in

g

eo

the

rm

al

waters

is

such

a

syst m

a

ra

ffi

n

waxe

s

in c

ru

de

oil

s

and

h

y

dro

ca

rb

on so

lv

en

ts

als

o

dis

pl

ay

n

orm

al



—4

solub

ility

nd

give rise

to

b

oth

d

epos

ition and

fou li

ng

p

robl

ems

8

9

7

.

eth

ods

to

red

uce fou

ling are both

che

mica

l

a

nd me

chan

ical

in

n tu

re

8

Pa

rticu

late

fou

ling

i

s

wher

e

par

tic le

s

susp

ende

d

i

n liqu

ids

or g

ases d

epos

it

out

a

nd

adh

ere

to

surf

aces. Co

nside

rable wo

rk ha

s been don

e

on

aero

sol

deposition on

unheated

surf ces

8

Studies

at

heated

surfaces

have

also

b

een

p

erfo

rmed

678

.

The de

posit

ion and

fou

ling

of

partic

ulat

e

cor

rosio

n

pro

duct

s in b

oile

r w

aters

and

reac

tor

c

oolan

ts

h

ave

been

exten

sive

ly

studi

ed

9

9

Pa

rticu

late

foul

ing syst

ems stu

died

inc

lude

s

and-

wate

r

susp

nsio

ns5

part

icles

in

gas

o l

s46

h

ema

tite in

w te

r77

an

d

s

ome

d

esali

natio

n

s

ys

te

ms

2

8

.

P

articu

late

de

posit

ion

inc lu

des

se

di m

enta

tion

.

Reaction

fouling

occurs

when

chemical

reaction transformation

occurs

at

he

at

tra

nsfe

r su

rfac

es

a

nd fo

rm dep

osits

. C

okin

g

the ther

mal

deco

mpo

sition

of

heav

y

hydr

ocar

bons

occ

urs

wi

dely

in in

dust

ry

0

6

R

eact

ion f

oulin

g i

s

co

rmo

n

in

th

e p

etro

leum in

u

st

ry

l’

0

8

9

Freo

ns are k

now

n

to form

de

posi

ts

b

y

therm

al

de

com

posit

ion

i

n

poo l

o

iling

.

Biolo

gica

l

fou

ling is w

hen or

gani

sms

grow

n

at

hea

t

tra

nsfe

r

surf

aces.

Thi

s

type

of

foul

ing is

co

niiio

n

i

n coo

ling

wa

ter

syst

erns

m.

Co

rros

ion fo

uling

o

ccurs

wh

en

heat tr

ansfe

r s

urfac

es

corro

de

and

chan

ge th

ei r

th

erm

al

c

hara

cteri st

ic s.

2

.3

V

aria

bles

T

he

m

ain var

iable

s t

ha t a

ffec

t

d

eposi

tion and

f

oulin

g have

been d

iscu

ssed

by

seve

ral

u

tho

rs

7

80

The

mos

t

ge

neral

obs

ervat

ion

is tha

t

fo

ulin

g of

h

eat

e

xcha

nger

s

incr

ease

s with ti

me us

ually in a

n

a

sym

ptoti

c fash

ion.

n

c.s t

of

the

ob iished

studies

fouling

is

d

irect

ly

proportiona

l

to

fou

lant

c

once

ntra

tion. ow

ever

the

str

ength

of co

olin

g

w

ater depo

sits

has be

en

s

hown

t

o de

c’ees

e with

de

creas

ing depo

sit puri

ty

The

effe

cts of

t

emp

eratu

re

in

d

ecsit

ioc an

d

fou

ling

de

pend grea

tly

o the typ

e

of foul

ing oc

curin

g.

In

s

u ty

fo ul

in g fo

r exam

ple

th

e

te

mpe

ratur

e

dif f

erenc

e

be

twee

n

b

ulk

n

d

su rfa

ce

resu

lt

in

th

e co

ncen

tratio

n

d

rivin

g

f

orce

c

aus i

ng e

posi

tion

emp

erat

ure

ofte

n

en te

rs d

ep os

ition

rate

s

in

n

rrhe

nius—

typ

e

ex

pres

sion

6 7

1

4 27

95

Flui

d

v

eloci

ty

i

s

pro

bably th

e

most

imp

ortan

t

var

iable

when s

tudy

ing depo

sitio

n



—

—

and

f

ou

lin

g

.

It

eff

ec

ts

bo

th

the

con

vect

ive

tra

ns

po

rt

of

fou

la

nt

s

t

owar

d

s

ur

fa

ces

an

d

the

she

ar

st

res

se

s

w

hich

d

ep

os

its

are

s

ubje

cted

t

o.

The

ov

era

ll

ef

fec

t is th

ere

fo

re co

mple

x a

s

w

ill be

in

dic

at

ed in S

ectio

n

belo

w.

O

ther

v

ar

ia

ble

s

of in

ter

es

t in

clud

e

hea

t

fl

ux

tub

e

dia

mete

r

and

sur

fa

ce

rou

ghne

ss

p

ar

tic

le di

am

e

ter

flu

id and

fo

ul

an

t

ch

emi

stry

an

d

th

e us

ual

ph

ysica

l

p

ro

pe

rti

es

.

2.4

I

nd

us

tri

es of I

nte

re

st

Sinc

e

f

ou

li

ng oc

curs

in so

m

any

in

du

str

ie

s p

roba

bly

all

pro

cess

in

du

st

rie

s it

is

p

erhap

s

re

le

va

nt to co

nside

r

the

main

fi

eld

s

of

ac

tiv

ity whe

re th

e

phe

nom

ena

may

a

ct a

s

a c

on

st

ra

int

on t

he

ce

ntr

al

pr

oc

ess

. D

epo

sition

a

nd

fo

uli

ng

occu

r

in

the

foll

owin

g main

f

ie

lds

Po

wer

gene

ratio

n

whe

re

high

qu

ali

ty feed

w

ater

s

giv

e

ris

e to

fo

uli

ng

w

hen s

ubje

cted to

hi

gh t

empe

ratu

re

c

o

nd

itio

n

s.

C

omb

ustio

n

products may

also

cause

fouling

. D

es

ali

na

tio

n wher

e

r

aw

or tr

ea

ted

sea

—w

aters

giv

e

ri

se

to

fo

ul

ing at mo

st

co

nd

iti

on

s.

Pet

roleu

m

in

du

st

ry

wher

e d

ep

os

iti

on

occ

urs in

flo

w

lin

es

and

f

oulin

g

in th

e

vari

ous hy

droc

arbo

n

p

ro

ces

se

s.

Coo

ling

s

er

vic

e

as

p

ra

cti

ce

d

in

almo

st e

very

i

nd

us

try

.

Raw an

d tr

ea

ted

cool

ing

w

ater

s

are use

d e

xt

en

siv

el

y and

giv

e

r

ise

to

fo

u

lin

g

a

t n

orm

al

o

pera

ting

co

nd

it

ion

s.

Air cool

ed

ex

chan

gers

m

ay

giv

e

ris

e

to

p

ar

tic

ul

ate fo

ul

ing

.

In r

ec

en

t ye

ars ener

gy

cons

erva

tion

h

as

be

come

m

ore

and

mo

re

im

por

tant

in

industry

One

way

of

conserving

ener

gy

is

to exc

hang

e h

eat

b

etwe

en

pro

cess

str

ea

is ; hot r

ej

ec

t

h

eats

cold

in

le

t Va

riou

s

w

aste

s m

ay

also

be

comb

uste

d to ex

tr

ac

t e

nerg

y.

o

wev

er

m

any

en

ergy

c

onse

rvati

on meas

ures

m

ay

be

s

ub

je

ct

to

fo

uli

ng

.

F

ouli

ng m

ay a

lso

put

a

c

on

st

rai

nt

on

alt

er

na

tiv

e en

ergy

s

ourc

es. G

eothe

rma

l flu

id

s c

onta

in

c

on

si

de

ra

ble amo

unts of

si l

ica

t

ha

t d

ep

o

sit

on c

old

s

urf

ac

es durin

g

he

at ex

tr

ct

io

n

The e

xtr

ac

tio

n

of

energ

y

f

rom

ocea

n

th

erma

l g

ra

di

en

ts

c

ould

b

e

li

m

ite

d

by

sea

wat

er

f

ou

l

in

g

Th

e

m

ain

foul

ing

ef

fe

cts in

i

nd

us

try

; pres

sure

drop

i

nc

rea

se

s

and

g

re

at

er

te

mper

ature

differences required for some

duty

will

in

some

cases

also

result

in

increased

u

se o

f en

ergy

.

T

here

fore

f

ou

lin

g

mu st

be

an

i

mpo

rtant

co

ns

tra

in

t

o

n

en

ergy

c

on

se

rva

tio

n

.

n

t

he

da

iry i

nd

us

try

f

oulin

g

in

m

ilk

trea

tmen

t

pro

cess

es i

s of

g

re

at

p

rac

ti

cal

im

p

ort

n

ce

l



PRE

VIO

US STU

DIES

3

I

nt

rod

u

cti

on

I

n the p

re

se

nt s

ec

tio

n,

only

th

ose s

tu

die

s

deali

ng

sp

ec

ifi

c l

ly

with h

ea

t

tr

n

sfe

r

f

ou

lin

g

wil

l be

co

nside

red

Non

-foul

ing

stu

di

es

suc

h

as

ae

rosol

d

ep

os

iti

on

, are

b

et

ter

c

onsi

dere

d

s

ep

ar

ate

ly

. Pre

viou

s s

tud

ie

s

on hea t

t

r

ns

fer

f

ou

lin

g

wi

ll be

co

nsid

ered

i

n two

gro

ups;

d

ep

os

iti

on

-r

ele

as

e

st

ud

ies

and

gene

ral

s

tu

die

s.

Th

e fo

rme

r

gr

oup

dea

ls

with he

at

t

r

nsf

er

fo

ul

ing w

here

th

e

fo

ul

an

t bu

ild u

p

m

ay b

e re

pr

es

en

ted b

y

a

simp

le m

ass

b

alanc

e

in

th

e

fo

rm

of

two

fu

nc

ti

on

s; d

ep

os

itio

n and

r

ele

as

e.

Th

e

gene

ral

s

tud

ie

s

gr

oup

d

eals

with

the

rem

ainin

g

s

itu

t

io

ns

The

d

ep

o

sit

ion

-r

ele

as

e

app

roac

h

h

as

m

et

w

ith

so

me

succ

ess

in pr

ed

ict

in

g

h

ea

t

t

r n

sf

er

fo

ul

ing

.

This

su

ccess

see

ms

t

o ar

gue

f

or

fu

rth

er

d

evelo

pme

nts

o

f

sui

ta

ble

mo

dels.

3.

2

D

e

po

sit

io

n-r

el

ea

se

Kern

and

S

ea

to

n

2

o

bser

ved

th

at

the f

ou

lin

g

r

esi

sta

nc

e

of

man

y he

at

exc

hang

ers

in

oi

l

re

fin

er

ies a

ppea

red

t

o

inc

re

as

e

as

ym

pt

ot

ica

lly

w

ith

tim

e.

Th

ey

su

gges

ted

th

t t

he

tim

e d

epen

denc

e

of

the

f

ou

lin

g

re

si

sta

nc

e co

uld

be

appr

oxim

ated

by

th

e e

mpir

ical

ex

pres

sion

:

Rf

[

ex

p -

St

)]

2

wh

ere

Rf

a

nd

w

ere

the fo

ul

in

g r

es

ist

an

ce

s

t

an

y t

ime t a

nd

a

t

a

sym

ptoti

c

co

nditi

ons

r

es

pe

cti

ve

ly

,

a

nd

a

c

on

st

an

t.

o

exp

erim

ental

data

we

re

p

resen

ted

but

it

was

sta

te

d

t

h

t t

he

flu

id

v

el

oc

ity

was

an

i

mpor

tant

va

ria

bl

e

eff

ec

tin

g

fo

u

lin

g.

Kern n

Seato n

proposed

a

theoretical

fouling

model

where

the

net

rate

of

as

e

xpre

ssed

as

th

e

d

if

fer

en

ce

betw

een

the

r t

e

o

f

de

po

sit

io

n and

th

e

rat

e

o

r

e

as

e.

Th

e mo

del

was es

sen

ti

ll

y

a

m

ass b

alan

ce

e

xp

res

si

on

:

k

k

wher

e:

de

po

si

tio

n

c

oe

ffi

cie

nt

k

release

coefficient

x

d

ep

os

it

thi

ckne

ss



—

—

c

fo

ulan

t

conc

entra

tion

m

ass fl

ow ra

te

r

sh

ear stre

ss

a

t

wall

By

ass

umin

g

c and

cons

tant

an

d

x<<

d

tub

e

d

iam

eter

, K

ern and

Seat

on w

ere

able

to

in

tegra

te

E

quat

ion 3 a

nd ob

tained

a

n

expression

tha t

gave

the

deposit

thi

ckne

ss

as a fun

ctio

n of

tim

e:

k

c

x

[

exp

-

k

4

k

Th

is

exp

ress

ion is of t

he

sam e ge

nera

l

fo

rm

a

s

Equ

ation

i.

T

he

i

nit ia

l

ra

te o

f dep

ositi

on

and

the

asym

pto

tic fou

ling

resi

stanc

e we

re

obtained

by putting

x

and

dx/dt

in Equation

3,

respectively.

‘

....

5

\d

tj

k

c

6

K

ern

and Se

aton

l

sho

wed

that

w

hen

th

e

dep

osit

thi

ckne

ss

x w

as

signi

fican

t

in rela

tio n

to tube

di

amet

er

d,

Equ

ation 3

is no

t

d

irect

ly

inte

grab

le.

Ke

rnl

has

d

erive

d the

appr

opri

ate solu

tion

of

th

e

dep

osit

ion-r

eleas

e

ex

pres

sion for

the

ca

se o

f co

nstan

t

pr

essu

re

drop

an

d c

once

ntrat

ion

bu

t

v

ariab

le

ma

ss

fl

owra

te.

W

atk

inson

C

stud

ied the fou

ling

o

f

a

heate

d

stai

nless

ste

el tub

e

by

a

h

eavy

ga

s

oi 9

6

a

nd a sa

nd-w

ater

s

usp

nsion

Th

e

ma

in

pu

rpos

e of t

he

e

xper

imen

ts

was

to

inve

stiga

te

the

eff

ec t

o

f mas

s

flo

wra

te

on

f

oulin

g. W

atk

inso

n

oun

d th

at,

at

the

ex

perim

ent

al

c

ondi

tions

g

iven

in

Tabl

e 1,

the h

eated

tub

e

f

ouled

in a

n asym

ptot

ic fash

ion.

he

f

oulin

g resi

stanc

e

was

c

orrel

ated

to

Eq

uatio

n

2,

an

d

in Tabl

e

the mai

n relat

ionsh

ips

are gi

ven.

T

he

h

eat fl

ux was

no

t speci

fied.

Add

ition

al

exp

erim

ents

w

ere c

arrie

d ou

t

to

inv

estig

ate

t

he

effec

t

of tube

wa

ll temp

eratu

re

on

g

as

o

il f

oulin

g a

t co

nsta

nt

m

ass

flow

c

ondi

tions

. T

he in i

tial

rat

e of depo

sitio

n wa

s

c

orrel

ated

to

t

empe

ratu

re

by

an

Arr

heni

.s-typ

e

exp

ress

ion.

Th

e eff

ec t

of f

lowr

ate on san

d-wa

ter

foul

ing w

as

fo

und

to b

e mor

e

c

omp

lex

th

an in

dica

ted

i

n

T

able

When

0.1

36

kg

/s,

bo

th

S

and

dR

f/dt

to

we

re

fo

und to decrease

d

rastic

ally wit

h flow

rate.

This

criti

cal

i

o;ira

te

was

eq

uiva

lent

to

bulk

velo

city

2.

29

rn s

and m

ass

flu

x



8

2341 kg/m However,

R showed the

same

flowrate

dependence

at al l values.

TABLE

Experimental

Conditions l

roperty

Gas Oi l

Sand-water

c

mg/kg

15

T

°C 100

60

Tw

°C 146

77

kg/s 0.081

0.353

0.067

0.248

tmax

h

390

132

d mm 8.6

8.6

d pm 5O 15

TABLE

Experimental

RelationshipsO

erm

Gas

Oil

Sand—water

wi.

/dR

\

i—-I

W’

\dt

/t=o

R

W

W ’

Watkinson4 developed

a

new deposition—release model

in

an attempt to

ratizna]ize the experimental results

The

following model

was

proposed:

=

k

N

k r

7

where

the

deposition

function

includes particle

stickability

sand

mass flux

towards the wall

N. Other

symbols as before.

The

release

funct ion is that

of Kern and Seaton l l

The

terms

in

the

deposition function

were

expressed

by:



9

k

exp -E/R

T

s=

g

f u

N

=

h

Cb

c

•

9

h=

12 Sc

where:

k

= constant

E

= activation

energy

Rg

=

universal

gas

constant

T

=

tube wall

temperature

f = friction factor

u = fluid

bulk

velocity

h

=

mass

transfer coefficient

Cb

=

foulant

bulk concentration

c = foulant wall

concentration

w

Sc

=

foulant

Schmidt

number

WatkinsonC

assumed

x<<d

and

derived

a

general

expression

that

gave

the

deposit

thickness

x as

a function

of

time. Tw o limiting

cases

were considered;

mass transfer controlled

and

adhesion

controlled.

In the

former

s ‘

and

c, such that:

= k

u

Cb

exp -k

f

U2t

11

12 Sc f u

where

in the

release function has

been

replaced by

k

f

u

the latter,

the

deDos-ition

process was controlled

by

the

chemistry

of adhesion

and:

—

k exp -E/R

T

—

k

f

w

exp -k f

u

t

12

where K

is a

concentration

dependent

coefficient. Table

3

shows how the main



relationships

depend

on the

fluid

bulk

velocity. The

corresponding

relationships

from the Kern-Seaton

model

are

also

given. The

sand-water

fouling

was

therefore mass

transfer

controlled

and

the

gas

oil

fouling

more

adhesion

controlled.

Watkinson l

has

also developed deposition—release

expressions

where

deposit

thickness

was

sufficient

to affect

fouling.

TABLE

Model

RelationshipsO

22

erm

Kern—Seaton

Mass transfer Adhesion

fu

fu fu

/dR\

_i

U

U

\dt

/

t=o

R

fu ’

/fu ’

fu2 1

Char1esworth

studied

the

deposition

of

particulate corrosion products

in

a boiling water

reactor.

It

was suggested

that

a

modified Kern-Seaton

expression

might

describe

the

build-up

of

corrosion

products

on

heated

and

unheated surfaces.

k c-k

w

dt

where

w

was

the weight

of

deposit

per

unit

area

and

other

symbols

as before.

In

this

model

fluid

velocity does not

affect

the deposit build-up.

TaDrek

e:

performed extensive

and

systematic experimental work

on

pure

ir’;erse solbility

salt

solutions

and

a

variety

of

cooling waters. A

desi:n —

release model was

developed

for

fouling by treated cooling

tower

water with

low

suspended

solids

content.

The

model

described mixed

crystallisation

fouling of inverse

solubility

salts. The main solid depositing

was calcium

carbonate. The following deposition-release

expression was

proposed:

dR

=

A exp -E/R T

k

xm

14

dt

gs



whe

re:

s

st ic

kabil

ity

w

t r chara

cter

izatio

n fac

tor

exp

onen

t

T

de

posit

surf

ace tem

perat

ure

deposit

characterization factor

m

exp

onen

t

No

prac

tical e

xper

imen

tal da

ta

were

give

n

nor

a

ny

valu

es

of

the va

riou

s

te

rms

in

volv

ed

i

n

the

depo

sitio

n and rele

ase

fun

ction

s T

he fou

lant

conc

entr

ation

w

as

c

hara

cteris

ed

by

the

Lan

geli

er

satu

ratio

n

inde

x

a

nd

the

s

ticka

bility

wa

s

de

term

ined

em

piric

ally

as:

s

k

e

xp

u

1

5

The depo

sit struc

ture

w

as as

sum

ed

to d

epen

d

on

th

e

fluid v

eloc

ity

s

uch

tha t

:

k

Ua

16

w

here th

e e

xpo

nent a

2

.

Th

e fouli

ng

resi

stanc

e again

st

time

was

g

iven b

y:

k k

A

exp

Rf

k

xp

k

t

1

7

w

here

th

e expo

nent

b

2. A

cco

rding to

this

mo

del

the

de

pend

ence

of

f

d

Rf/d

t to

and

R

f

on

fluid

velo

city ar

e mo

re

com

plex

than

in

prev

ious

mo

dels.

The

expo

nen

t

in

wa

s

assum

ed

u

nity

when corr

elatin

g

the

mod

el

to expe

rime

ntal

data

Watk

inso

n and r

tin

z

hav

e

stud

ied

the

fou

ling

o

f

a

cons

tant

wall

te

mpe

ratur

e

e

xcha

nger b

y a sy

nthet

ic

calc

ium

ca

rbon

ate sol

ution

.

T

he

va r

iable

s

in

vest

igate

d we

re fl

uid v

eloc

ity,

bu

lk

tem

per

ature

a

nd tube

d

iame

ter.

T

he

w

ater

con

taine

d

3Q00

mg

kg diss

olved

s

olid

s a

nd 4

m

g kg

parti

culat

e matte

r

I

t was

estab

lishe

d tha

t ca

lcium

ca

rbon

ate d

epos

ited

fr

om solu

tion

.

I

n the

e

xpe

rimen

ts

inv

estig

ating

th

e

eff

ec ts o

f

velo

city

and

di

ame

ter,

the bulk

inle

t te

mpe

ratur

e

wa

s

57°

C

and

the

t

ube

wa

ll temp

erat

ure 10

3°C

.

A

sym

ptoti

c co

ndit

ions were

reac

heá

in

less

t

han

ho

urs,

duri

ng

wh

ich

the d

epo

sit su

rface

te

mpe

ratur

e

—

2

—



decreased

5°C

typically.

Experimental

data

at

constant

bulk

and wall

temperature

for Re

<

2 were correlated

to the asymptotic

fouling

resistance

by:

R

ci d°3

u’3 ..

.. 18

Watkinson

and

M artinez7 developed

a

deposition—release

model

where the

deposition function

was written in terms

of

inverse

solubil ity salt

crystalli

zation

while

the

release

function was

as in

the

Kern—Seaton

model.

dx

n

kl cb

c

k

x T

19

dt

S

The constant k

was

a

crystallization

rate

constant

and n

an

exponent. Foulant

concentration in

bulk and

at

deposit surface

were

given

by

cb

and

respectively.

It was assumed

that the

solubility

of

calcium

carbonate

was

linear

with

temperature:

cb

c

= k

T

Tb

20

and the

heat

transfer

situation

that

of a steam condenser

such that:

R

>>R R

21

This meant

that:

-T

T T

=

w

b

s

b

1 Rf/R

wnere

T ,

Tb

and

T

refer

to

the temperature

at deposit surface,

fluid

bulk

and

tube Eetai

wall,

respectively.

ne

crysta1Hzaton rate

constant

was

given

by:

k

= k exp _E/Rg

T

23

The following

deposition—release model

resulted.

/

-E/R\

=

k

k

exp

kT

24

dt

\Tb c/

13



where:

T

w

b

1 R

f/R .

The

depo

sitio

n-rel

ease

model

was not

in

tegrated,

but

an expression for the

asym

pto

tic

f

ouli

ng

re

sista

nce

was

given and

used

to

compare

the

e

xper

imen

tal

data

to

the

model.

It

was

found

that the model

corr

ela te

d

th

e data

well

when

n

2.

General

Experimental

s

tudi

es into hea

t

tr

ansfe

r

fo

ulin

g no

t

spe

cific

ally

d

ealt

with

el

sewh

ere in

the

Th

esis, w

ill

be

co

nsid

ered b

rie fly

in

th

e

p

rese

nt sec

tion.

McCabe and

R

obins

on

proposed

tha

t th

e

amount

of

scal

e

formed

in

ev

apor

ators

was

prop

ortio

nal

to

the

amount

of

l

iquid

eva

pora

ted

It

was

assumed

that

the

te

mper

ature

d

iffer

ence

T

b

remained

co

nsta

nt with

time

The

fo

llow

ing

eq

uatio

n give

s

the ov

erall he

at tra

nsfe

r

resis

tanc

e

w

ith

tim

e:

R

2

+ k

t

26

where

Rc

is

the

overall heat

transfer

resis tance at

clean

conditions and

k

a

co

nstan

t.

This equ

ation

has

been v

erifi

ed

f

or ev

apor

ator sc

alin

g.

I

l as s

onO

has developed

an

expr

essio

n

for

heat exchanger

sca

ling

. The

e

xpre

ssion corre

lated calcium

c

arbo

nate

d

epo

sition da

ta

at low f

luid

v

eloc

ities

where

no

dep

osit re

lease

oc

curre

d.

Reit

zer H

S

has d

erive

d

a

simi

lar

e

xpre

ssio

n.

Reitzer assumed

tha t

heat

exchanger

scaling

depended

on the

foulant

su

persa

tura

tion,

raise

d

to

th

e

power

n.

At

cons

tant

T5

Tb

the

over

all

hea

t t

ransf

er

res

istan

ce was

given

by:

ik \

k

AT \

+

n + 1

—

ç

t

27

h

and

a

t

c

onsta

nt

heat

flux

co

ndit

ions:

14



k

k

R +

t

28

k

where:

k

d

iffus

ion—

rea

ction coef

ficie

nt

k

deposit

thermal

conductivety

k

co

nsta

nt

p

= depo

sit den

sity

h ins

ide h

eat trans

fer c

oeffi

cient

Gonionskiy

et

4

have discu

ssed the

bove

relat

ions

hips

and

developed

an

exp

ress

ion

for th

e ove

rall hea

t tran

sfer

re

sistan

ce

wi

th time

. The scal

ing

process

was

ssumed

to

depend

on

the average

fluid

temperature

in

the

boundary

l

ayer

Calcium

s

ulph

ate

d

epos

ition

d

ata

was

co

rrela

ted by the de

rive

d ex

pres

sion

Hasson

et

al

5

stud

ied

the

for

mati

on of calcium

c

arbo

nate

s

cales

in

a

c

onst

ant hea

t flux exch

ange

r.

Experiments

were

performed

at

Reynolds number

13000

to

42000.

D

eposi

tion inc

rease

d

li

neari

ly with

ti

me. It

was

found

that

the

rat

e

of depo

sit io

n

was

d

iffus

ion

c

ontro

lled

and

t

hat:

°

8

29

dt

sson

and

Za

havi

s

tudie

d

th

e dep

osit

ion

of ca

lcium

sul

phate on he

ated

su

rface

s

I

t was found that

dep

ositi

on was

g

reat

es t

a

t the downstream

end

of

the

ex

chan

ger

d

ecrea

sing

rap

idly

toward

the

upstream

regio

n

Palen

and

W

est

wate

r stu

died

calcium

sulph

ate

d

epos

ition

in

a

pool

b

oile

r

and

found

it

proportional

to

the

heat

flux

squared.

Galloway

has

studied

tne

forna

tion

o

f

ino

rgani

c

sc

ales

by an e

lect

roche

mica

l

method and

obtai

ned

an

exp

ress

ion

fo

r

the

d

ime

nsion

less

dep

osit th

ickn

ess w

ith

tim

e. Walker

and

Bo

ttO

a.

e

e:D

Hed

curve

fitt

ing

methods

to

foul

ing

data

K

onak

26

has d

iscu

ssed the

pre

di io

n

of fou

ling

curv

es in

hea

t

tra

ns fe

r

equipment.

Fis

her

et

a

l7

have

disc

usse

d some

tec

hniq

ues

used

t

o

measure

foul

ing

Morse

and

Knud

sen

stud

ied

th

e e

ffect

o

f

alk

alin

ity on

t

he sca

ling

of sim

ula

ted

co

oling

tower

wa

ter

Fou

ling

i

ncre

ased

as

ymp

totic

ally with

time

and

was g

reate

r

a

t

high

alka

linit

y

val

ues

D

epo

sit

s

tren

gth

was found

to be

a funct

ion

of

t

he

non

calci

um

carb

onat

e

components.

15



Hopkins

and

Hopkins

and

pstein

investigated

the

fouling

of

heated

stainless

steel

tubes

by ferric

oxide

in

water.

The

experimental

conditions

were as follows:

concentration 15-3750

mg kg

Reynolds

number 10100 — 37600

heat

flux

0—292

kw/m

average bulk temperature

60°C

tube

wall

temperature

60-90°C

tube

internal diameter

8.71

mm

p 6.2

The

ferric

oxide

hematite

consisted

of”.’0.2 pm fundamental

particles

that

agglomerated

into particles

>

10 pm

in diameter. No measurable

fouling

occurred

at

concentrations

c<750 mg kg and

reproducable

results

were

obtained only

if

c>1750

mg/kg.

Most runs were

performed

at a

standard

concentration

of

2130

mg/kg.

Fouling

increased with

concentration.

The

build-up of deposits was

asymptotic

and

reached steady conditions

in

2-4

hours. The

following relationships

were

derived:

R f

a

30

dR

_Z

a

31

dt

It

was

found that deposition

decreased

with

heat

flux;

deposition was

greatest

at zero heat f lux conditions. It

was

suggested

that thermophoresis

might

play

an important

role

in the deposition

process.

hypothesis

was

presented

according

to

w i

the fouling behaviour

is

controlled

by the rate

at

which

crevice corrosion

of

the

stainless

steel

occurs.

16

—



NOMENCLATURE

A

Heat

transfer

area

m

a Exponent

b

Exponent

c

Foulant

concentration mg/kg

D

Diffusivity

of

particulate

foulant

s

d

Tube

diameter

m or

mm

d Particle diameter

m

or

pm

E

Activation

energy

kJ

f

Friction

factor

=

pu

h

Heat

transfer coefficient

kW/m2OC

k

Constants

and

coefficients

m

Exponent

N

n Exponent

Rate

of

heat

transfer

kW

q

Heat

flux kW/m

R

Heat transfer

resistance

kW m

OC _1

Rf

Fouling

resistance

kW m

°C ’

R

Universal

gas

constant

=

8.3143

J/mole

°K

Re

Reynolds

number

=

ud/’

s

Stickability

Sc

Schmidt number of

particulate foulant

=

/D

Teerature

°C

or

°K

e

s

Temperature difference

°C

u Fluid

bulk velocity

m/s

W

Mass flowrate

kg/s

w

Weight

of

deposit mg/cm

x

Deposit

thickness

mm

or pm

—

—



Heat transfer

factor

°C

onstant

Deposit

characterization

factor

Water characterization factor

Kinematic

viscosity

rn

s

p

Fluid density

kg/rn

Shear

stress at

wall

N/rn

Subscripts

b

Bulk

c

lean

i

Inside

o

Outside

s

Surface

w

Wall

Superscript

symptotic

It:S



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P RT

P R FFIN

W X

EPOSITION

N

FOULING

Documents

Part I Heat Transfer Fouling