Fouling of Heat Ex Changers (1995)

8/6/2019 Fouling of Heat Ex Changers (1995)

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Fouling of Heat Exchangers

by T. R. Bott

ISBN: 0444821864

Pub. Date: April 1995

Publisher: Elsevier Science & Technology Books


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P R E F A C E

There a re m any t ex tbooks devo ted to hea t t rans fe r and the des ign o f hea texchange rs ranging from the ext reme theoret ica l to the very practical . Thepurp ose of these publ ica t ions i s to provide im proved u nders tanding of the sc ienceand to g ive guidance on the des ign and opera t ion o f process h eat exchangers . Inmany o f these texts the problem of the accum ulat ion of deposi ts on heat t ransfersurfaces is ignored or at best , dealt with through the tradit ional fouling resistance.I t i s common knowledge that th is approach is severe ly l imi ted and inaccurate andmay lead to gro ss er rors in des ign. Fur the rmo re the very arbi t rary choice offoul ing res is tance more than offse ts the accuracy of corre la t ions and sophis t ica tedmethods , for the appl ica t ion o f fundamental heat t ransfer knowledge.

Li t t le a t tent ion was paid to the heat exchanger foul ing and the associa tedinefficiencies o f heat e xch ang er op eration t i ll the so-called "oil crisis" o f the 1970s,wh en i t becam e vi tal to m ake efficient use o f available energy. He at ex chang erfoul ing of course reduces the oppo r tuni ty for heat recovery wi th i t s a t tendanteffect on primary energy demand s. Since the oil crisis there has been a m od estin teres t in obta ining know ledge regarding a ll aspects o f heat exchang er foul ing, but

the inves tment is no wh ere n ear as large as in the f ield o f heat transfer as a wh ole.Al though books have appeared f rom t ime to t ime s ince the 1970s , address ing

the quest ion o f heat exch anger fouling, they are largely based on co nferences andmeet ings so that there i s a genera l lack of cont inui ty. The p urpo se o f th is boo ktherefore, i s to p resent a comprehensive appraisa l o f current kn ow ledge in allaspects o f heat e xchang er fouling including fundam ental sc ience , m athemat icalmod els such as they are , and aspects o f the pract ica l app roach to deal wi th theproblem of foul ing throug h des ign and opera t ion of heat exchangers . Thetechniqu es o f on an d off-l ine cleaning o f heat ex chan gers to re store efficiency arealso described in some detail .

The ph i losophy o f the book is to p rov ide a wide range o f da ta in suppor t o f thebasic concepts associa ted wi th heat exchanger foul ing, but wri t ten in such a waythat the non-mathemat ica l novice as wel l as the exper t , may f ind the text ofinterest.

T.R. Bot tDecember 1994


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oo

v i i

A C K N O W L E D G E M E N T S

The autho r wishes to record his sincere gratitude for the skill, dedicationand persistence of Jayne Olden, without w hich this boo k w ould never have beencompleted.

All the diagrams and figures in this book were drawn by Pauline Hill andher considerable effort is acknowledged.


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ix

N O M E N C L AT U R E

Note: In the use of equations it will be necessary to use consistent units unlessotherwise stated

Area or area for heat transfer

A~ Constant

A n Hamaker constant

a+, a o aD, ar Vector switches associated with the dimensionless depositionparameters N I, N o N o and N r respectively

B Correction term Equation 12.28

C Circulation rate

C Cunningham coefficient or a constant

c Concentration

cb

C m

Concentration in bulk blowdown water

Concentration in make up water

cp Specific heat

%

c~

Specific heat of solid

Concentration of cells in suspension

D Diffusion coefficient or dimensionless grouping as described byEquation 10.50

D c Collector diameter

d

Diffusion coefficient for particles

Diameter

E Activation energy or dimensionless grouping as described byEquation 10.49


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Fouling o f Heat E xchangers

Eo

F

Eddy diffusivity

Shear force

F~ Adhesion parameter

F~ Repulsion force

FS Slagging index

F . Van der Waals force

f Friction factorf~ Ball frequency (Balls/h)

Lifshitz - van d er Waals co nstant

K Transfer coefficient or Co nstant

x~ M ass tran sfer coefficient o f species A

x~ Deposition coefficient

x .

Mass transfer coefficient allowing for sticking probability

Mass transfer coefficient

M ass transfer coefficient of macro-mo lecules

xo Constant in Equation 10.31

X,o Solubility product

x , Transport coefficient

Kt Dim ensionless transpo rt coefficient

k~

Rate constants Equation 12.10

Rate constant

Length

t . Characteristic length

M M ass flow rate

M * Asym ptotic deposit mass


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N o m e n c l a t u r e xi

m~m

M ass of fouling deposit

Mass

N Dimensionless deposit ion parameter (Equation 7.40)

N~ M ass flux of cells

Dim ensionless interception deposit ion pa ram eter

Dim ensionless diffusion deposit ion pa ram eter o r ma ss flux awayfrom reaction zone

N, Dimensionless impaction deposit ion parameter

N~

N~

N~

M ass f lux of m acro-molecules

M ass flux of reactants or precursors

Dimensionless thermophoresis deposit ion parameter

Particle num ber density

Integer on concentration factor

P Sticking probability

e,

Po

P~

Probability of scale formation

Sticking probability for impacting mechanisms

Sticking probabili ty for non-impacting mechan isms

Ov erall sticking probability

P Pressure

Ap

O

Pressure drop

Ra te o f heat transfer

Heat flux

R Universal gas constant or param eter defined in Equ ation 9.14

Fouling resistance or Fouling potential (see Chap ter 16)Overall fouling resistance

Fouling resistance at t ime t


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o~

X l l Fouling o f Heat Exchangers

a ,

R T

R|

Slagging propensity

Total resistance to heat transfer

Asymptotic fouling resistance

t" Radius

Rate of oxygen supply

r~ Rate of corrosion

Rate of oxygen supplyStopping distance o r param eter defined by Equa tion 9.13

SR Silica ratio

Temperature

L Cloud point temperature

T c v Tem perature of critical viscosity

r l

r ,

t

Freezing temperature

Pou r point temperature

Time

Induction time

U

Av erag e ball circulation time

Electrophoretic mobili ty o f charged particles

Overall heat transfer coefficient fo r clean conditions

Overall heat transfer coefficient fo r fouled con ditions

Velocity

U o Init ial velocity or velocity in the absence of thermo phoresis

/ / r

U T

Radial velocity

Stokes terminal velocity

/A t Velocity due to thermopho resis


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N o m e n c l a t u r e xii i

U*

f ,

Fric t ion veloci ty

M ean pa r t i c le vo lum e

V Volum et r ic f low

v,

Ene rgy assoc ia t ed wi th doub le l aye r s

To ta l e ne rgy o f adsorp t ion

Ene rgy assoc ia t ed wi th van de r W aa l s fo rces

Elect rophore t ic mobi l i ty

X N um ber o f ce ll s pe r un i t a rea

N um ber o f ce ll s to co ver com ple te ly uni t a rea

Thickness or d is tance

Subscripts

A v Av e r a g e

B u l k

B~o Biomass

C Cold or c lean

Crit ical

Crys ta l face

f Foulant , or f reezing

g G a s o r g r o w t h

H H o t

I m p a c t

Induction, or ini t iat ion, or interference or inside

/n Inhibitory

i r r Irreversible


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xiv F o u l i n g o f H e a t E x c h a n g e r s

m Mean , o r me ta l

m a x M a x i m u m

P Par t ic le or s t i ck ing probabi l i ty

p P re s su re

r e v Revers ib le

Sca le, sur face or so l id , sa tura t ion

t Time

w W al l o r sur face

x ~ A d s o r b e d c ell s

Asympto t ic or in f in i te

D i m e n s i o n l e s s n u m b e r s

R e = d v p R e y n o l d s n u m b e rr/

Pr = cp ~ Prand t l number

S t = ~ S tan to n n u m ber17vcp

a dN u = N u s s e l t n u m b e r

S c = r / Schmid t num berpO

S h = K I . S h e r w o o d n u m b e rD

B i = a /~ B io t num ber2


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N o m e n c l a t u r e xv

G r e e k

a

P

r/o

~ t o t

P

2"*

.(2

H eat transfer coefficient

Time constant

Distance over which diffusion takes place

Induced EMF

Viscosity

Particle collection efficiency

Com bined collection efficiency for non-impacting mechan isms

Ov erall particle collection efficiency

Fraction of surface

Thermal conductivity

Therm al conductivity of foulant deposit

Therm al conductivity o f scale

Kinem atic viscosity

Dimensionless group described by Equation 10.48

Densi ty

Foulant density

Shear stress o r particle relaxation t ime

Dim ensionless particle relaxation t ime

Rate of deposi t ion

Particle flux

Particle volume

Particle volume function (see Equation 7.45)

Rate o f removalScale strength factor

W ater qual i ty factor


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Table of Contents

Preface

Acknowledgements

Nomenclature

1 Introduction 1

2 Basic Principles 7

3 The Cost of Fouling 15

4 General Models of Fouling 23

5 Fluid Flow and Mass Transfer 33

6 Adhesion 45

7 Particulate Deposition 55

8 Crystallisation and Scale Formation 97

9 Freezing Fouling or Liquid Solidification 137

10 Fouling Due to Corrosion 149

11 Chemical Reaction Fouling 185

12 Biological Growth on Heat Exchanger Surfaces 223

13The Design, Installation, Commissioning and Operation of

Heat Exchangers to Minimise Fouling269

14 The Use of Additives to Mitigate Fouling 287


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15 Heat Exchanger Cleaning 357

16Fouling Assessment and Mitigation in Some Common

Industrial Processes409

17 Obtaining Data 479

Index 517


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C H A P T E R 1

I n t r o d u c t i o n

The accum ulat ion o f unw anted d eposi ts on the surfaces of heat excha ngers i susual ly referred to as fouling. The presence o f these deposi ts represents ares istance to the t ransfer of heat and therefore reduce s the effic iency of theparticular heat exchanger. The foulant may be crystall ine, biological material , theprodu cts of chemical react ions including corros ion, or par ticula te mat ter. Thecharacter o f the dep osi t depends on the f lu id (l iquid or gas) pass ing throug h theheat exchanger. I t may be the bulk fluid i tse l f that causes the problem of deposi tformat ion, e .g . the decom posi t ion o f an organic liquid under the tem peraturecondi t ions wi thin the heat exchanger. Far m ore of ten than not , the foul ing problemis produced by some form of contaminant wi thin the f lu id , of ten a t very lowconcentration, e.g. solid part icles or micro-organisms.

Foul ing can occur as a result of the f lu ids being handled and thei r con st i tuents incombinat ion wi th the operat ing condi t ions such as temperature and veloci ty.Almost any solid or semi solid material can become a heat exchanger foulant, but

some mater ia ls that are com monly enc ountered in industr ial operat ions as foulantsinclude:Inorganic materials

Airborne d usts and gr i tW aterborne mud and s il tsCalc ium and ma gnesium sal tsI ron oxide

Organic mater ia lsBiological substances, e.g. bacteria, fungi and algaeOils, waxes and greasesHeavy organic deposits , e .g. polymers, tarsCarbon

Fig. 1 .1 is a photog raph of the tube pla te of a shel l and tube heat ex change rfouled wi th par t icula te mat ter deposi ted f rom high temperature f lue gases pass ingthroug h the tubes.

The problems associa ted wi th heat exchanger foul ing have been known s incethe f irs t heat exchang er wa s invented. The m om entum of the industr ial revolut ion

depended on the ra is ing of s team, usually f rom coal combust ion. In the ear ly daysser ious problems aro se in steam ra is ing equipment on ac count of the accu mulat ionof deposi ts on the wate r s ide of boilers . The presence of these deposi ts , usual lycrystall ine in character originating from the dissolved salts in the feed water,


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caused the skin temperature of the boiler tube to reach dangerous levels allowingfailure to occur. Dev elopm ent of suitable feed wa ter treatm ent program me showever has largely eliminated the problem in modem boiler operating technology.

FIGU RE 1.1. A fouled tube plate of a shell and tube boiler

In general the ability to transfer heat efficiently remains a central feature ofmany industrial processes. As a conseq uence much attention has been paid toimproving the understanding of heat transfer mechanisms and the development ofsuitable correlations and techniques that may be applied to the design of heatexchangers. On the othe r hand relatively little consideration has been given to th eproblem o f surface fouling in heat exchangers. A review [Some rscales 1988] thattraces the history of heat exchanger fouling suggests four epochs in thedevelopment of an understanding of the problem of fouling. The ch ronologyfollows in general, the development of science and measurement techniques overthe same timescale. In the first period up to abou t 1 92 0, conc ern wa s directedtowa rds observing the phenomenon and devising methods of reducing the problemwith less emphasis on the scientific understanding of the mechanisms involved.

The second period from 1920 - 19 35 covered development in the me asurement o ffouling and representation. The following ten years from 1935 - 1945 sa w theextende d use of the so-called "fouling factor". The fouling factor ma y be definedas the adverse thermal effects of the presence of the deposit, expressed innumerical terms. Fouling factors or fouling resistance is discussed in mo re detail inChapter 2. From 194 5 to the present time a more scientific approach to theproblem of fouling has been introduced with detailed investigations into themechanisms that underline the problem of heat exchang er fouling. Ch apters 7 - 12detail the physical and chemical conditions and interactions that lead to heatexcha nger surface fouling.

The review by Somerscales [1988] demonstrates how little has been donetoward s a better understanding of the problem since the early 1800s except insteam raising technology. It is indeed an anomaly that the accurac y of man ysophisticated design techniques is restricted by a lack of understanding of the


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Introduction 3

foul ing process l ikely to be associa ted wi th the par t icular process underconsideration.

Energ y con servat ion is often a factor in the ec onom ics of a par t icular process .At the same t ime in re la tion to the remainder o f the proce ss equipment , theprop ortion of capital that is required to install the ex chan gers is relat ively low. I t isprobably for th is reason that heat exchanger foul ing has been neglected as mostfouling problems are unique to a par t icular process and heat ex change r des ign.

The p roblem o f heat exchanger fouling therefore represents a chal lenge [ 'Bo a1992] to designers, tech nologists and scientists , not only in term s o f heat tran sfertechnology but a lso in the wider aspects of economics and environmentalacceptabil i ty and the human dimension.

The pr incipal purpose of th is boo k is to provide some insight in to the pro blemof foul ing f rom a sc ienti fic and technological s tandpoint . Impro ved un ders tandingof the m echanisms that lead to the accum ulat ion o f deposi ts on surfaces wi llprovide opportunit ies to reduce or even eliminate, the problem in certain si tuations.Three basic stages may be visualised in relat ion to deposit ion on surfaces from amo ving fluid. The y are:1 . The di ffus ional t ranspor t o f the foulant or i ts precursors across the boun dary

layers adjacen t to the solid surface within the f low ing fluid.

2. Th e adhesion o f the deposit to the surface and to itself .

3 . The t ranspor t o f mater ia l away f rom the surface .

The sum of these bas ic com ponents represen t s the g row th o f the depos i t on thesurface.

In mathemat ical terms the ra te of ' deposi t gro w th m ay be regarded as thedifference betw een

~D -~ R (1 .1)

w here #~ and #R are the rates o f depo sit ion and rem oval respectively.

The extent of the adhesion w ill influence #R-

Fig. 1 .2 shows an idealised asymptot ic graph o f the ra te of grow th of a deposi ton a surface. In region A the proc ess of adhesion is initiated. In some foulingsi tuat ions the condi t ioning (or induct ion) per iod can take a long t ime, perhaps ofthe order o f several weeks . In other exam ples of foul ing the in it ia t ion per iod m ay

be only of the order of minutes or even seconds.Reg ion B represents the s teady grow th of the deposi t on the surface . U nde r

these c i rcumstances there is comp et i tion betw een deposi t ion and removal . Therate o f deposi t ion gradua l ly fa lls whi le the ra te o f removal of depo si t gradual ly


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G, I

w

.4,,..

. 4 . -o,.....V l

0sW

r~

Time

FIGU RE 1 .2. The change in deposit thickness with time

increases. Finally the rate of remov al and the rate of deposition m ay becom e equalso that a plateau steady state or asym ptote is reached (Region C) wh en the depositthickness remains virtually constant.

Many system variables will affect the extent of the various stages and these willbe discussed in subsequent chapters.

The world consumption of energy is large, taking into account all sources andm ethod s of utilisation. Fossil fuels are of course, extensively used for thegeneration of heat used to raise steam for the production of electrical power.Under these circumstances a large fraction of the heat released from the fuel istransferred across various heat exchangers to the cold utility (cooling water).Under the prevail ing conditions of operation there is ample opportunity for heattransfer surfaces to become fouled with attendant reductions in the efficiency of

energy utilisation. In other processes the primary fuels, coal, oil or natural gas areused for process stream heating. Fo r instance the crude oil vapo risers in petroleumrefining are usually heated by m eans o f fuel oil combu stion.

Red uced efficiency of the heat exch angers due to fouling, represe nts an increasein fuel consumption with repercussions not only in cost but also in the conservationof the world's energy resources. The necessary use o f additional fossil fuels tomake good the shortfall in energy recovered due to the fouling problem, will alsohave an impact on the environment. The increased carbon dioxide prod uce dduring com bustion w ill add to the "global warming" effect.

Although reduced heat transfer efficiency is of prime importance there may alsobe pressure drop problems. The presence of the foulant will restrict f low thatresults in increased pressure drop. In severe examp les of fouling the exc hang ermay become inoperable because of the back pressure. Indeed the pressure dropproblem s may have a more pron oun ced effect than the loss of thermal efficiency.


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Introduction 5

In o rde r to he lp reduce o r ove rcom e the p rob lem of fou l ing , add i t ives m ay beused . For ins t ance a who le indus t ry has bu i lt up a round the t r ea tm en t o f w a te rused for cool ing purposes . The var ious chem icals added to the w ater fal l in to threecategor ies , i .e . cont ro l o f b io logica l grow th, p reven t ion of sca le format ion andcor ros ion inh ib it ion . Care ful cho ice o f t r ea tmen t p rog ram m es wil l do m uch toreduce the accum ula t ion o f depos i ts on hea t exchange su rfaces . The add i tion o fchem icals how ever, br ings wi th it problem s for the en vironme nt .

I t i s oRen the case tha t the water used for cool ing i s re turned to i t s source , e .g .a five r o r lake . Ev en w a te r t aken f rom som e o the r source such as a bore ho le wi lleventual ly be re turned to the natura l envi ronm ent . Th e presence of the addi t ivescan rep resen t a haza rd fo r the env i ronment s ince many o f the chem ica ls ma y be

regarded as toxic .De spi te the bes t e fforts of engineers and technolog is ts to reduc e or e l iminate

heat ex chan ger foul ing the grow th o f depos i ts wi ll s til l occ ur in som e ins tances .Per iodic c leaning of the heat exch angers wi l l be nec essary to res tore the h eatexch ange r to eff ic ient opera t ion . I f the deposi ts a re d ifficult to rem ove byme chanical m eans chem ical c leaning m ay be required . The ch em icals used for th ispurpose wi l l of ' ten be aggress ive in character and represent an eff luent problemaf ter the c leaning opera t ion . Unless th is eff luent is proper ly t rea ted i t could a lsorepresen t an env i ronmenta l p rob lem. Eve n wa te r used fo r c l eaning can becom econtaminated and may require sui table t rea tment before d ischarge .

O f d i rec t conce rn to the opera to r o f p rocess eq u ipmen t a re the eco nom icaspects o f heat e xcha nger foul ing s ince th is wi ll a ffec t the opera t ing co s ts tha t inturn affec ts the prof i tabi li ty of the ope ra t ion as a whole . In the f irs t ins tance theheat exc hang er is genera l ly overdes igned to a l low for the inc idence o f fouling .Increas ing the s ize o f the exch anger wi l l of course , increase the in it ia l capi ta l co s tand henc e the annua l capi ta l charge .

The re s t r i c tion to f low imposed by the p resence o f the depos i t m eans tha t fo r agiven throu ghp ut the veloci ty wi ll have to increase . Th e increased veloci tyrepresen ts an inc rease in pum ping ene rgy and hence an inc rease in cos ts . M any

pum ps are e lec t r ica l and so the increased ene rgy requirem ent i s in te rm s o f themo re expensive secondary ene rgy. Othe r ope ra t ing cos t s can acc rue f rom thepresence o f the depos i ts such as inc reased m a in tenance requ i rement s o r r edu cedou tpu t. Em ergen cy shu tdow n as a d i rec t re su l t o f hea t exchang er fou l ing can bepar t icular ly expensive . In m any exam ples of severe foul ing the f requency ofc lean ing ma y no t co incide wi th ~ th e p lanned pe r iod ic p lan t shu tdow n fo rmaintenance (annual bas is ) and i t might be necessary to ins ta l l s tandby heatexchangers fo r use when the c l ean ing o f hea t exchangers beco m es necessa ry.Addi t ional heat t ransfer capaci ty provided by s tandby equipment represents an

addit ional capital charge.F ina l ly, bu t by no means l eas t , t he re i s the human d imens ion to the p rob lem offouling. Seve re foul ing can lead to the loss of em ployee mora le [Bot t 1992] . Th erepeated and pers is tent need to shut down the p lant to c lean heat exchangers , ordi ff icult ies in mainta in ing the des i red o utpu t d ue to the a ccum ulat ion o f deposi ts


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will inevitably lead to frustration o n the part o f those emp loyees w hos e duty i t is tomaintain prod uction and produ ct quality. Th e problem is com pou nde d if f inancialincentives are l inked to quali ty and volum e of production. Rep eated subjection tothese difficult working conditions can lead to an indifferent att i tude that cancomp ound the unsatisfactory character of product ion brou ght abo ut by theparticular fouling problem.

The foul ing of heat exchangers is a wide ranging topic covet ing many aspects o ftechnolog y. I t represents a challenge not simply in terms o f reducing pro du ct co st ,and hence competit iveness in the market place, but also with the concerns ofm od em society in respect o f conservat ion of l imited resources, for the environm entand the natural world, and for the improv eme nt o f industrial w orkin g conditions.

I t i s the pu rpose of this book to provide a backg round and basis that wi l l enable thereader to face up to the chal lenges presented by the problem of heat exchangerfouling.

R E F E R E N C E S

Bo tt, T .R., 19 92 , He at exchang er fouling. The challenge, in: Boh net, M ., Bott ,T.R., Karabelas, A.J., Pilavachi, P.A., S6m6ria, R. and Vidil, R. eds.Fouling Mechanisms - Theoretical and Practical Aspects. EditionsEurop6ennes Thermique et Industrie, Pads, 3 - 10.

Som erscales, E.F.C., 198 8, Fouling o f heat transfer surfaces: an historical review.25th Nat . Heat. Trans . Conf . ASM E. H ouston.


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C H A P T E R 2

Basic Principles

The accumulation of deposits on the surfaces of a heat exchanger increases theoverall resistance to h eat flow. Fig. 2.1 illustrates how the tem peratu re d istributionis affected by the presence o f the individual fouling layers.

FIGURE 2.1. Temperature distribut ion across fouled heat exchanger surfaces

T1 and T6 represent the te mpe ratures o f the bulk h ot and cold fluids respectively.Unde r turbulent flow conditions these temperatures extend almost to the bou ndarylayer in the respective fluids since there is good mixing and the heat is cardedphysically rather than by condu ction as in solids or slow mov ing flui ds . Theboundary layers (the regions between the deposit and the fluid), because of theirnear stagnant conditions offer a resistance to heat flow. In general the thermal

conductivity of foulants is low unlike that o f metals which are relatively high. Fo rthese reasons, in order to drive the heat through the deposits relatively largetemp erature differences are required, wh ereas the temp erature difference across themetal wall is comparatively low.


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Fouling o f Heat Exchangers

Therm al conduct iv it ies o f some com m on foulant- like mater ia ls are g iven inTable 2 .1 that a lso includes data for comm on co nst ruct ion mater ia ls . The effectsof even th in layers of foulant m ay be readily apprecia ted .

TABLE 2.1

Some thermal conductivities of foulants and metals

Mater ia l Therm al conduct iv i tyW/mK

Alumina 0 .42Biofi lm (effectively wa ter) 0.6Carbon 1 .6Calc ium sulphate 0 .74Calc ium carbonate 2 .19M agnes ium ca rbona te 0 .43Ti tanium oxide 8Wa x 0 . 2 4

C o p p e r 4 0 0

Brass 114Mone l 23Ti tanium 21M ild steel 27.6

The resistance to heat f low across a solid surface is given as

x

-~- (2.1)

w here x is the solid thickness

and 2 is the therma l con ductivity o f the part icular solid.

Referr ing to the d iagram (Fig . 2 .1) the res is tances o f the solids to heat f low are:

F o r D ep os it 1 x---Lwh ere 2~ is the thermal conduct iv i ty of Deposi t 121

Fo r Dep osi t 2 xz wh ere 22 is the thermal conduct iv i ty of Dep osi t 2


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B a s i c P r i n c i p l e s

and for the m etal wall xm wh ere ,;1,m s the thermal con duct ivi ty o f the m etal

Fo r s teady s ta te condi t ions the heat f lux q

q = T 2 - T 3 = T 3 - T 4 =T 4 - T 5 ( 2 . 2 )

A lso q = a , ( ~ - g ) = a , ( ~ - ~ ) (2.3)

where a~ and tz2 are the h eat transfer coefficients for the h ot and cold fluidsrespectively.

Equ at ion (2 .3) can be rewri tten as

~ - ~ _ ~ - ~(2.4)

1 1and

a l a 2

respectively.

represent the resistance to heat f low o f the ho t and co ld fluids

The total resistance to heat f low will be the sum o f the individual resistances, i .e .R r the total therm al resistance will be given by

R r ( x ~ ) ( x ~ 2 2 ) ( x ~ . ) 1 1+ + + ~ 4 -a I a 2

(2.5)

The overal l temperature dr iving force to accomplish the heat t ransfer between thehot and cold fluids is the sum o f the individual tem pera ture differences

i . e . ( ~ - r ~ ) + ( ~ - ~ ) + ( ~ - ~ ) + ( r , - ~ ) + ( ~ - ~ )

o r T I - T 6

.' . q - T~-T6 (2.6)ev


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10 F o u l in g o f H e a t E x c h a n g e r s

If the he at exch ange area required for the required heat transfer is A, then the rateof heat transfer Q

ev(2.7)

In general the design of heat exchangers involves the determination of therequired area A. The necessary heat transfer, the tempera tures and the fluids aregenerally known from the process specification, the individual heat transfercoefficients of the fluids may be calculated, and values of the fouling resistances oneither side of the heat excha nger wo uld have to be estimated. It is the latter thatcan be d ifficult and if the resista nces are inc orrectly e stima ted d ifficulties insubsequ ent ope ration may be manifest.

At first sight it may be thou ght possible to calculate the fouling resistance, i.e.

x:12:

where x: i s the deposit thickness

and 2 is the foulant thermal conductivity

The difficulty is however, that this involves a knowledge of the likely thicknessof the deposit laid dow n on the heat exchanger surfaces and the correspondingthermal conductivity. In general these data are not available. It is therefo renecessary to assign values for the fouling resistance in order that the heatexcha nger m ay be designed.

An alternative way o f writ ing Equation 2.6 for clean conditions when the heattransfer surfaces are clean, is:

q = Uc(T~ - T6) (2.8)

where Uc represents the overall heat transfer coefficient for clean conditions, i.e.

g c + ~ - t -al a2(2.9)

and allowing for the fouling resistances on either side of the heat transfer surface

1 x~ x 2 x , . + ~ + ~ ( 2 . 1 0 )

uo +

Rew riting Equ ation 2.8 for fouled conditions, to give the heat flux


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B a s i c P r i n c i p le s 11

q = U o ( T~ - T6 ) (2 .11)

Because the temperature dr iv ing force across the heat exchanger usual ly var iesa long the length of the heat exchanger, i t i s necessary to emp loy som e m ean valueof the tem pera ture d i fference in us ing Equa t ions 2 .8 and 2 .11.

I f ATt and A T2 are the temp erature d i fference betwee n the h ot and cold f lu ids a te i the r end o f the hea t exchanger then the t empera tu re d i ffe rence may be t aken asthe ari thmetic mean, i .e .

AT,,, = A Te- A T (2.1 2)2

but m ore usual ly the log mea n temp erature d i fference is used, i .e .

AT,,, = AT~ - A T (2 .1 3)

l n ( A ~

For mo re backgrou nd to the use o f mean t empera tu re d i fferences in the des ignof heat exchangers the reader i s referred to such texts as Hew it t , Shires and Bot t[1994].

The mean temperature d i fference may be subst i tu ted in Equat ion 2 .11 to g ivethe heat f lux

q = U o A T~ (2 .14)

and i f the to ta l avai lable heat t ransfer area A is taken in to accou nt

Q = U o A A T ~ (2 .15)

In the des ign of heat exchangers A is usual ly unkn ow n, so rearranging E qua t ion2.15 p rovides a mean s o f est imat ing the required heat t ransfer area , i .e .

A = Q ( 2.1 6 )

The choice o f the individual foul ing res is tances for the ca lcula tion o fU o canhave a mark ed inf luence on the s ize of the heat ex chang er and hen ce the capi ta l

cost .For a heat exchanger t ransferr ing heat f rom one l iquid to another wi th the

individual l iquid heat t ransfer coeff ic ients o f 2150 and 294 0W / m Z Kand foul ing


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12 Fouling of Heat Exchangers

res i s tances o f 0 .00015 and 0 .0002 m2/WK on the sur faces of the hea t exchanger,the to ta l res i s tance to hea t f low is

1 1

2 1 5 0 2 9 4 00 .00015 + 0 .0002 m2/WK

= 0 .00047 + 0 .00034 + 0 .00015 + 0 .0002 m2/WK

= 0 .00116 m2K/W

For the g iven des ign condi t ions , i . e . thermal load and tempera ture d i fference

th is foul ing res is tance represents an increase in the requi red hea t exchanger a reaover and above the c lean area requi rements of

0 . 0 0 0 3 5

0 .00081x 100% = 43 .2%

i.e . the c os t o f the hea t exchan ger wi l l be increased con s iderably due to thepresence of the foul ing on the hea t exchanger.

I f the sam e foul ing res is tances a re applied to a hea t exchang er t ransfer r ing h ea tbe tween two gases where the indiv idual hea t t ransfer coeff ic ien ts a re much lowerdue to the low therm al conduct iv i ty of gases , say 32 .1 and 7 9 .2W/m2K, thesituation is quite different.

U nde r these condi t ions the to ta l thermal res i s tance i s

1 1+, + 0 .00035 m2K/W

32.1 79.2

= 0 .0312 + 0 .0126 + 0 .00035 m2K/W

= 0 .0442 m2K/W

In these c i rcumstances the increase in requi red area in compar ison to the c leancondi t ions i s

0 .00035

0 .0438x 100% = 0 .8%

Fo r the l iquid / liquid exchanger the choice o f foul ing res is tances rep resents acons iderable increase in the requi red sur face in compar ison wi th in the c lean


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B a s i c P r i n c i p l e s 1 3

condi tions . Using the same foul ing res is tances for a gas /gas heat exchange rrepresents negligible addit ional capital cost .

The t radi tional metho d o f des igning heat exch angers i s to consider the potent ia lfoul ing problem and ass ign a sui table foul ing res is tance to co rrespond. In orde r toass is t wi th th is se lec t ion, organisa t ions such as the Tubular ExchangerM anufacturers Asso cia t ion (T EM A) issue tables of foul ing res is tances for specia lappl ica t ions . The f irs t edi t ion appeared in 1941. Fro m t ime to t ime these data arereviewed and revised. A review wa s carried out in 1988 and mad e available[Chenoweth 1990] .

The pr incipal d i ff iculty in th is approa ch to des ign is the prob lem o f choice . Atbes t the tables of foul ing resis tances g ive a range of m ean foul ing res is tances , but

in genera l there i s no informat ion on the condi t ions a t which these values apply.Fo r ins tance there i s genera l ly no inform at ion of f lu id veloci ty, tempe rature ornature and conce ntra t ion of the foulant. As wi l l be seen la ter these fac torsamon gs t o the rs , can have a p ronou nced e ffec t on the deve lopmen t o f fou lingres is tance . Proba bly the larges t am ount o f informat ion conta ined in the tables isconcerned wi th wa te r. Tab le 2 .2 p resen t s the re levan t da ta pub li shed by TE M Abased on a careful review and the appl ica t ion of sound engineer ing acumen by agrou p o f kno wled geab le engineers , involved in the des ign and o pera t ion of shel land tube heat exchangers .

TABLE 2.2

Fouling resistances in wa ter systems

W ater type Foul ing res is tance104 m2K /W

Sea wa te r (43~ maxim um ou t le t )Brack i sh wa te r (43~ maxim um ou t le t )Trea ted coo l ing tower w a te r

(49~ maxim um ou t l et )Art if ic ial spray pon d (49~ max imum out le t )Closed loop t r ea ted w a te rRiver wa te rEngine j acke t w a te rDis t il led wa ter o r c losed cycle conden sateTreated boi ler feedwaterB o i le r b l o w d o w n w a t e r

1 . 7 5 - 3 . 53.5 - 5.31.75 - 3.5

1.75 - 3.51.753 . 5 - 5 . 31 . 7 5

0 .9 - 1 .750 .93.5 - 5.3

Ch enow eth [ 1990] g ives the assum pt ions under ly ing the d ata con ta ined in Table2.2 . Fo r tubes ide , the veloci ty of the s t ream is a t leas t 1 .22m /s (4 f l / s ) fo r tubes o fnon-ferrous a l loy and 1 .83m /s (6 f t / s ) for tubes fabr ica ted f rom carbon s tee l andothe r ferrous al loys. Fo r shell-side f low the ve locity is at least 0.61m /s (2f t / s ) . In


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14 Fouling o f Heat Exchangers

respect o f temp erature i t i s assumed that the tempe rature o f the surface on w hichdeposi t ion is taking place does not exceed 71~ (160~ I t i s a lso assume d thatthe water is suitably treated so that corrosion fouling and fouling due to biologicalactivity do not contribute significantly to the overall fouling. Ch eno w eth [1990]com me nts on the fur ther res t ric t ions of these data . He observes that fouling bytreated w ater is know n to be a funct ion of the prevail ing velocity, the surfacetem pera tu re , and thepH and is of ten characterised by reaching an asy m ptote (seeFig. 1.2). Altho ugh asym ptotic values could be identified in the tables, the typicalvalues l isted for design, reflect a reasonable cleaning cycle and heat exchangeroperat ion without operat ing upset . The severe l imita tions imposed by theassumptions will be readily appreciated.

I t has to be said however, that wi thout other informat ion, these publ ished dataare of value in making an assessment of the potent ia l fouling resis tance. At thesame t ime d ata on foul ing res is tances have to be t reated with caut ion, they can onlybe regard ed as a guide. A further l imitation is that these value s only apply to shelland tube heat exchangers . Condi t ions in pla te heat exchan gers for ins tance, couldbe quite different.

A fundamental f law in the use of f ixed foul ing res is tances as suggested by theTEMA tables is that they impose a s ta t ic condi t ion to the dynamic nature offouling. In fundamental terms the use of Equ at ion 2 .5 in conjunct ion with the

tables are not soun d unless steady state has been reached. Fig. 1.2 show s that it isonly after the lapse of t ime that a steady fouling resistance is obtained. In othe rwords the heat exchanger does not suddenly become fouled when i t i s put onstream. Fo r a period of t ime the heat exchanger wil l over perform becau se theoverall resistance to heat f low is low er than that used in the design. To allow forthis overdesign the heat exchanger operator may adjust condi t ions that inthemselves could exacerbate the fouling problem. Fo r instance, the veloci ty maybe reduced , in turn this could accelerate the rate of deposit ion. I t is possible thatthe imposed conditions could lead to fouling resistances that are subsequently,gre ater than those used in the design with attendan t operating difficult ies. Effects

of this kind will be d iscussed in more detail later.

R E F E R E N C E S

Chen oweth, J . , 1990, Final repor t of the HT R I/TE M A joint com mit tee to reviewthe fouling section of TE M A standards. Heat. Trans. Eng. 11, No . 1, 73.

Hewitt , G.F., Shires, G.L. and Bott , T.R., 1994, Process Heat Transfer. CRCPress , Boca Raton.


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15

C H A P T E R 3

The Cos t o f Fou l ing

3 . 1 I N T R O D U C T I O N

In Chapter 1 some o f the factors that con tr ibute to the cost o f foul ing we rement ioned. I t is the purp ose of th is chapter to give more detai l in respect o f thesecosts.

At tem pts hav e been mad e to m ake es t imates of the overall costs of foul ing interms o f par t icular processes or in par ticular countr ies . In a very extensive s tudyo f refinery fouling costs published in 1981 [van N ostra ndet a l 1981] a typicalf igure was given as being o f the orde r o f $107 US per annu m for a ref ineryproce ssing 105 barrels of crud e oil per day. Allowing for inflation this f igure wou ldbe som ething l ike $2 - 3 x 107 in 1993. The se authors also report the ad van tagesof us ing anti foulant chemicals. For ins tance on the crude uni t the use of anadditive reduces the annual cost at tr ibutable to fouling by almost 50%, even taking

into acco unt th e cost of the antifoulant.About the same t ime i t was suggested [Thackery 1979] that the overal l cost offouling to industry in the U K wa s in the range s - 5 x 108 per annum . Translatingthis into costs for 1993 the probable range wo uld be s - 14 x 18 s. An overall costof foul ing for the US publ ished a few years ago [Garret t -Pr iceet a l 1985] was $8 -10 x 109 per annum. The correspond ing f igures for 1993 w ould be in the rang e$ 1 5 - 20 x 109 per annum. A recent study [Chaudag ne 1992] for French indu stryreco rded an overall co st o f fouling in Fran ce to be aro und 1 x 10 ~~ Fren ch Fran csper annum. Pi lavachi and Isdale [1992] conclude over the Eu rop ean C om mu nityas a who le the co st of heat exchanger foul ing a t the t ime o f wri t ing, w as of theorder o f 10 x 109 EC U and o f th is to ta l 20 - 30% was due to the co st o f addi t ionalenergy. I t is clear from these l imited data that fouling costs are substantial and anyreduct ion in these costs would be a welcome contr ibut ion to prof i tabi l i ty andcompetit iveness.

3 .2 I N C R E A S E D C A P I TA L I N V E S T M E N T

In order to make a l lowance for potent ia l foul ing the area for a given heattransfer is larger than for clean conditions as described in Ch apte r 2. Fo r the

liquid/l iquid exchanger discussed in Chapter 2 i t was shown that the required areafor the given fouling conditions was 1.43 times that for clean conditions. Alth ou ghthe cost of heat exchangers is not str ict ly pro rata in relation to area i t will beapprecia ted that for a large complex containing several heat exchangers the


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addi t ional capi ta l cos t for a l l the exchangers wi l l represent a considerable sum ofmoney.

In addi t ion to the ac tual s ize of the hea t exchan ger o ther increased capi tal cos tsare likely. Fo r ins tance w here i t i s ant ic ipated that a par t icular heat exc han ger i sl ikely to suffer severe or diff icult fouling, provision for off- l ine cleaning will berequired. The locat ion of the heat exchan ger for easy access for c leaning m ayrequire addi t ional p ipe work and larger pumps compared wi th a s imi lar heatexch anger opera t ing w i th li tt le or no foul ing placed a t a mo re con venient locat ion.

Fur the rm ore i f the p rob lem of fou ling is though t to be excessive i t migh t benecessary to ins ta l l a s tandby exchanger, wi th a l l the associa ted pipe workfoundat ions and suppor ts , so that one heat exchanger can be opera ted whi le the

other is being c leaned and serviced. Un der these c i rcumstances the addi t ionalcapi ta l cos t i s l ike ly to more than double and wi th a l lowances for heavy deposi tsthe f inal cos t could be 4 - 8 t imes the cos t o f the corresp onding excha nger runn ingin a clean condit ion.

A ddit ional cap ital costs for injection equipm ent wil l also be inv olved if i t isthought necessary to dose one or both s t reams wi th addi t ives to reduce the foul ingproblem. Con sidera t ion of on- l ine c leaning (see Ch apter 15) such as the Ta pro gg esystem for coo ling w ater, wil l also involve addit ional capital. I t has to be saidhowever, tha t on- l ine c leaning can be very effect ive and that the addi t ional capi ta lcos t can of ten be jus t if ied in terms of reduced opera t ing cos ts .

I t i s important that as the des ign of a par t icular heat exchanger evolves tocom pens ate for the problem o f fouling, each addi t ional incremen t in capi ta l cos t i sexam ined careful ly in order that it m ay be jus ti f ied . The indiscriminate use offouling resistances for instance, can lead to high capital costs , special ly whereexot ic and expensive mater ia ls of const ruct ion are required. Fu r therm ore the wa yin wh ich the addi t ional area i s acco mm oda ted, can affect the ra te of fouling. Fo rinstance if the addit ional area results say, in reduced velocit ies, the fouling ra te m aybe higher than ant ic ipated (see Ch apter 13) and the value of the addi t ional areama y be largely offse t by the effec ts of heavy deposi ts.

3 .3 A D D I T I O N A L O P E R AT I N G C O S T S

A num ber of contr ibutory opera t ing co s t fac tors that resul t f rom theaccum ulat ion of unw anted deposi ts on heat exchan ger surfaces can be identi f ied .

The funct ion o f a heat excha nger as the nam e impl ies , is to t ransfer hea t energ ybetw een s t reams. The pr ime reason for th is i s to con serve heat which is usual ly acos t ly comp onen t o f any p rocess . Redu ced e ff ic iency has to be com pensa ted insom e way in the process . I f heat is not recov ered the shor t fa ll wi l l have to be m ade

up perh aps by the consu mp t ion of mo re pr imary fuel such as o il , coal or gas . Inother opera t ions i t i s necessary to ra ise the temperature of a par t icular s t ream tofaci l i ta te a chemical react ion, for example hydrocracking in ref inery opera t ions toproduc e low er molecu la r we igh t p roduc t s. In pow er s t a t ions the e ff ic iency o f thes team condensers a t the out le t f rom the turbines has a d i rec t effec t on the cos t of


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The Cost of Fouling 17

the e lect ric ity produ ced (see Cha pter 1 6) . I f the cool ing of po we r s ta t ioncon den sers is inefficient i t will mean that not all the p ressu re energ y available in thes team p ass ing throug h the turbines may be ut il ised.

Ap ar t f rom the problem of reduced energy eff ic iency other problem s m ayaccrue. Fo r example i f the tem perature of the feed to a chemical reactor i s low erthan the opt imum cal led for in the des ign, the yie ld f rom the reactor may bereduced. The qual i ty of the prod uct may not be acceptable and addit ionalprocess ing m ay be required to im prove the specif ica t ion of the pro duct .

In the operat ion of a d is ti llat ion column w here the feed p reheater exchan gesheat between the bot tom product and the feed, ineff ic ient heat exchange wi l l meanaddit ional heat requirem ents in the reboiler. In turn this repres ents a greate r "boil

up" rate in the colum n betw een the reboiler and the feed inlet that co uld affect theefficiency of the s t r ipping sect ion o f the colum n d ue to drople t en t ra inmen t andchannel ling. Such condi tions may affect produ ct qual i ty or throu ghp ut m ay haveto be reduced to mainta in product specif ica tion. These effects represent a reducedreturn on investmen t in terms of the dis ti lla tion column. M ore ov er becau se theheat removed f rom the bot tom product i s reduced addi t ional cool ing may berequired (a t fur ther cost ) before the bot tom product i s pumped to s torage.Additional cooling requirements will put an extra load on the cold uti l i ty and mayadversely affect i ts operating cost .

The p resence o f deposi ts on the surface o f heat exchan gers res t r ic ts the f lowarea . As a conseq uence for a g iven throug hpu t the veloci ty of f low increases . Inapproximate terms.

Ap a u 2 (3 .1)

wh ere Ap is the loss of pressure throug h the exchanger

and u is the fluid velocity

so that even small changes in velocity can represent substantial increases in Ap.Foul ing deposi ts are usual ly rough in comparison wi th s tandard heat exchangersurfaces. Th e roughn ess increases the fr iction experien ced by the fluid f lowingacross the surface so that for a given velocity Ap is greater than in the cleancondi tion. The larger the Ap the higher the pump ing energy required and hence agrea ter pumping cost . A more extensive discuss ion of pressure drop is g iven inChapter 5 .

The presenc e o f foul ing on the surface of heat exchang ers may be the cau se o faddi tional maintenance costs . The m ore obvious resul t of course , i s the need to

clean the heat excha nge r to return i t to efficient operation. N ot only will thisinvolve labour costs but i t may require large quanti t ies of cleaning chemicals andthere may be effluent problems to be overcom e that add to the cost. I f the c leaningagents are hazardous or toxic , e laborate safe ty precaut ions wi th a t tendant costs ,


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may be required. Cleaning of heat exchangers i s d iscussed in mo re deta i l inChapter 15.

Addi t ional maintenance costs may der ive f rom the higher pressure drop acrossthe exchange r due to the presence of the deposit . The higher in le t pressu re maycause fa ilure of jo ints and place a heavier load on the associa ted pum p. I t isposs ible that the presence o f the depo si t wi ll accelera te co rros ion of the heatexchanger. In turn th is may lead to ear l ier replacement o f the whole exch ange r ora t leas t , heat exchange r components . Fai lure of heat exchan ger jo ints m ay lead tohazard ous condi t ions due say to leaking f lamm able or toxic substances.

Th e presence o f a deposit on the "cold side" o f h igh tem peratu re heatexchangers such as might be found in s team ra is ing plant , may give r ise to high

metal temp eratures that can increase corros ion or even loss of in tegr i ty o f themetal wi th co st ly consequences .

The f requent need to dismant le and c lean a heat exchanger can affect thecont inued in tegri ty of the equipment , i.e. com ponen ts in shel l and tube excha ngerssuch as baff les and tubes may be damaged or the gaskets and pla tes in pla te heatexchan gers may becom e faul ty. The damag e may also agg ravate the foul ingproblem by causing res t r ic t ions to f low and upset t ing the required temperaturedistribution.

3 .4 L O S S O F P R O D U C T I O N

The effects of foul ing on the through put of heat exchang ers due to res t r ic t ionsto f low and inefficient heat transfer, have already been m entioned. Th e need toresto re f low and heat excha nger efficiency will necessitate cleaning. O n a planne dbasis the in terrupt ions to produ ct ion may be m inimised but even so i f the remaind erof the p lant is operat ing correct ly then th is wil l const i tu te a loss o f outpu t that , i fthe rem ainder o f the equipm ent i s running to capaci ty s ti ll represents a loss o fprof i t and a reduced contr ibution to the overal l cos ts of the par t icular s ite. Theconsequ ences o f enforced shu tdow n du e to the effects of fouling are of course

much m ore expens ive in t e rms o f ou tpu t . M uch depends on a recogni tion o f thepotent ia l foul ing a t the des ign s tage so that a proper a l lowance is made toaccom mo date a sa t is factory c leaning cycle . W hen the ser iousness of a foul ingprob lem goes unrecognised dur ing des ign then unscheduled o r even emergencyshutdow n, may be necessary. Fo r example , in the par t icular foul ing s ituat ionil lustrated by Fig. 1.1, three heat exchan gers were d esigned an d installed. I t w asant ic ipated that two would be operat ing whi le the other was being c leaned on a s ixmo nth cycle. Un der th is ar rangeme nt product ion wo uld have been mainta ined a t asa t is factory and cont inuous level. In the event the heat exchangers required

cleaning every 1 0 - 14 days! Th e prob lem becam e so difficult that at certain timesall three exchang ers were o ut o f operat ion w i th severe penal ties in term s of costand loss o f product ion.


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The Cost o f Fou ling 19

Product ion t ime lost through the need to c lean a heat exchanger can never berecovered and it could in certain situations, mean the difference between profit andloss.

3 .5 T H E C O S T O F R E M E D I A L A C T I O N

Th e use o f additives to eliminate or redu ce the effects of fouling has alreadybeen mentioned. An example o f the effect iveness of an anti foulant on the preheatstream o f a crude oil distil lation unit has been d escribed [van No stran det al 1981 ].These data sh ow that considerable mit igat ion o f the foul ing can be achieved by thismethod. Fig. 3.1 demo nstrates the fal l off in heat duty with and with out

antifouling additives. At the t ime of publication (1981 ) the annual cost o f thesechemicals w as $1.55 x 105 for a crude unit handling 100,000 barrels per day.

1 7 0

1 4 8

L~

~ . 1 2 7

" v 1 0 6

" - 8 5

_ , , N o f o u l i n g .

_ W i f h o u f o n f i f o u l a n f

, I ~ 1 . .. .. I I , i I I t ,

0 2 4 6 8 10 12

N o n f h s o n s f r e o m

FIGURE 3.1. The reduction of heat duty with and without antifoulant

Treatment of cool ing wa ter to combat corrosion, scale formation and b iofoul ingcan be achieved by a suitable programm e. The cost m ay be high and for a mod estcool ing w ater system the cost m ay run into tens of thousand s o f pounds.

If the foul ing problem cannot be relieved by the use of addi t ives i t ma y benecessary to m ake modifications to the plant. M odification to allow on-linecleaning of a heat exchanger can represent a considerable capital investment.Before capita l can be comm it ted in this way, some assessment of the effect ivenessof the modif ication must be made. In some exam ples of severe foul ing problemsthe decision is straightforward, and a pay back time of less than a year could beanticipated. In other exam ples the decision is mo re com plex and the financial r isksinvolved in making the m odification will have to be ad dressed.


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The Cost o f Fouling 21

FIGUR E 3.3. Change in costs with fouling for 600 MW pow er station with a h eavily loaded turbine

These data show that for a lightly loaded turbine wh ere the extent o f the foulingresistance is 5 times higher than the design figure, the annual total cost penalty is$8.4 rn and $4.7 rn for lightly and heavily loaded turbines respectively. Themagnitude of these figures are indicative o f the degree of effort justified to reducetube fouling on an existing condenser.

3 .7 CONC LUDING COMMENTS ON THE COST OF FOULING

A number of contributions to the cost of fouling have been identified, howeversome o f the costs will remain hidden. Although the cost of cleaning and loss ofproduction may be recognised and properly assessed, some o f the associated costsmay not be attributed directly to the fouling problem. Fo r instance the cost ofadditional maintenanc e o f ancillary equipme nt such as pumps and pip ewo rk, will

usually be lost in the overall maintenance charges. The additional energy used toaccommodate the increased pressure drop or the shortfall in heat recovery thatrequires an additional energy input, are unlikely to be recognised. Fur ther mo rebecause the fouling process is dynamic, i.e. the fouling effects generally increasewith time, the effect on the associated services, e.g. hot and cold utilities may notbe apparent for a considerable time.

REFERENCES

Chau dagne , D., 1992, Fouling costs in the field of heat ex chang e equipm ent in theFrench Market, in: Bohnet, M., Bott, T.R., Karabelas, A.J., Pilavachi, P.A.,S6m6ria, R. and Vidil, R. eds. Fouling Mechanisms - Theoretical andPractical Aspects. Editions Europ6ennes Thermique et Industrie, Paris.


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Cud ett, P.L. and Impagliazzo, A.M., 198 1, The imp act of condenser tube foulingon power plant design and enconomics, in: Chenoweth, J.M. andImpagliazzo, A .M . eds . Fouling in He at Exc hange Equipment. H TD , Vol.17, ASME.

Garrett-Price, B.A.et al, 19 85 , Fouling o f Heat Exchangers, Characteristics,Costs, Prevention, Control, Removal. Noyes Publications, New Jersey.

van N ostran d, W .L., Leach, S.H . and Haluska, J.L., 19 81 , in: Som erscales, E.F.C .and Knudsen, J.G. eds . Fouling of Heat T ransfer Equipment. H em ispherePublishing C orp. W ashington.

Thack ery, P.A., 19 79 , The co st o f fouling in heat ex chang er plant, in: Fou ling -Science or Art? Inst. Corrosion Science and Technology and Inst. Chem.

Engineers, Guildford.


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16V~12 (4 .5)

i.e. a fourfold increase in velocity.

The corresponding Reynolds number wi l l be

d 1 16 V P i . e . 8 V p2 ad , 2 r/ ad, r/

w her e r /a nd p are the fluid viscosity and density respectively

Com pared wi th the o r ig ina l Reynolds num ber

4V .p_p_i.e 4Vp

i .e . the Rey nolds num ber has been doubled due to the presence of the depo si t.

In addit ion the rough ness o f the depo sit surface will be different from the cleanheat exc hange r surface roughn ess (usual ly greater) w hich wi ll result in a change inthe level of turbulence par ticular ly near the surface . Gre ater rough ness wi l lprod uce g reater turbulence wi th i ts enhancement of heat t ransfer or a smo othersurface may reduce the level of turbulence. An a l ternative s ta tement descr ibing theeffects of foul ing m ay be m ade on th is basis [Bot t and W alker 1971 ] .

Change in = Change due to + Change due + Change dueheat t ransfer thermal to roughn ess to change incoefficient resistance o f o f foulant Re caused by

foulant the presenceof the foulant

(4 .6)

The purpose of any foul ing model i s to ass is t the des igner or indeed theope rator of heat exchangers , to make an assessment o f the impact o f foul ing onheat exchan ger performan ce given cer ta in operat ing condi tions . Ideal ly amathem at ical in terpreta t ion o f Equ at ion 4 .6 wo uld p rovide the bas is for such anassessment but the inclusion of an extensive se t of condi t ions in to onemathematical model would be at best , diff icult and even impossible.

Fig . 1 .2 provided an idealised pic ture of the developm ent of a deposi t w i th time.O ther possibil it ies, st il l ideal , are possible and these are show n on Fig. 4.1. Cu rveC represents the asymptot ic curve of Fig . 1 .2 . Curve A rep resents a s t ra ight l inere la t ionship o f deposi t th ickness w i th t ime, i .e . the ra te of develop me nt


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General Models of Fouling 25

V l

t ArC

t ./o 1 , . i

4 1 - .

. 4 . -. m

t / t0

rs

Ti m e tI n i t i a t i o nper iod

FIGURE 4.1. Idealised deposition curves

of the foul ing layer is constant once the in i tia tion o f the pro cess has taken place .Cu rve B on the o th er hand, repres ents a fa ll ing ra te of deposi t ion once in i tia t ionhas occurred. I t is poss ible that in effect , Cu rve B is essent ia l ly par t of a s imi larcurve to C and i f the p rocess o f depos i tion w ere a l lowed to p rogress su ffi ci en t ly anasympto te would be p roduced .

General m odels of the foul ing proc ess are essentia l ly the f it t ing o f equat ions tothe curves il lus t ra ted in Fig . 4 .1 . Th e curves A, B and C on Fig . 4 .1 a re sho wn tohave an in i tia tion or indu ct ion per iod, b ut in some exam ples o f foul ing, e .g . the

depos i tion o f wa x f rom w axy hy drocarbons dur ing a coo l ing p rocess , the in i ti a tionper iod m ay be so shor t as to be negl ig ible . I t is of ten ext rem ely di fficult orimpossible to predic t the in i tia tion per iod even wi th the benef i t o f exper ience , sothat most mathemat ica l models that have been developed ignore i t , i .e . foul ingbegins as soon as f lu id f lows through the heat exchanger.

The inaccuracY in ignor ing the in it iat ion per iod is not l ikely to be great . Fo rsevere foul ing problem s the in i tia tion of foul ing is usual ly rapid . W her e thees tabl ishm ent o f the foul ing takes long er it i s usual ly accom panied by a mod est ra teof foul ing . U nde r these c i rcumstances whe re long pe riods be tween hea t exchangercleans are poss ible , the induct ion per iod represents a re la t ively smal l percentage ofthe cycle. Er rors in ignor ing i t a re therefore smal l par t icularly in the l ight of theother uncer ta in t ies associa ted wi th the foul ing process . Typical in i t ia t ion per iodsmay be in the range 50 - 400 hours .


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26 Fou l ing o f H eat Exchangers

4 .2 A S I M P L E G E N E R A L M O D E L

The s imples t model i s that of Curve A in Fig . 4 .1 but ignor ing the induct ionper iod and wou ld have the fo rm

d rxI =-~ - . t (4 .7)

wh ere x is the th ickness of deposi t a t time t .

If the indu ction t ime (or init iat ion p eriod) is t~ then th e Eq uatio n 4.7 b eco m es

x y = ~ t ( t - t i ) (4 .8)

The di ff icul ty of course in us ing th is model i s that wi thout exper imental workd x / d ti s unk now n and the use o f x to determine the foul ing res is tance to heattransfer is also a prob lem since the thermal co ndu ctivity o f the fou lant is no tusual ly know n (see Chapter 2) . In terms o f foul ing res is tance Equat ion 4 .8 wo uldtake the form

_dRR ~ - - - ~ ( t - t~) (4 .9)

wh ere R~ is the fouling therm al resistance at time t and

x~ (4 .10)R1~= 2 I

wh ere x~ is the th ickness and t ime t

Even in this form the model is diff icult to use unlessd R / d ti s known f romexper imental determinat ions the condi t ions o f which can a lso be appl ied to thefoul ing p roblem in hand.

4 .3 A S Y M P T O T I C F O U L I N G

On e of the s implest models to expla in the fouling process w as pu t forw ard byKern and Seaton [ 1959].

R~ =Rioo( 1 - e ~ ) (4 .11)


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G e n e r al M o d e l s o f F o u l i n g 27

w here R~ is the foul ing thermal res is tance a t t ime t

RI, is the fouling resistance at infinite time - the a sym ptotic value.

f l i s a constant depen dent o n the sys tem prop er t ies

The m odel i s essent ia l ly a mathem at ica l in terpre ta t ion of the asym ptot ic foul ingcurve, Fig. 1.2 (or Cu rve C on Fig. 4.1, but igno ring the ini t iat ion t ime). I t is anideal ised model and does l i t t le for the des igner of a heat exchanger unless speci f icvalues for RI~ and f l a re to hand. The actual values o f these c onstants w i ll depen dup on the type of foul ing and the opera t ing condi t ions . In genera l there wi l l be nowa y o f p red ic t ing these va lues un less som e de ta il ed exper imenta l w ork has beencomp leted. Such research is o t 'ten t ime consu ming and therefore , expensive . TheKern and Sea ton m ode l does, however, p rov ide a ma themat ica l exp lana t ion o f thes imple fou ling concep t. A com promise so lu tion was p rop osed [Bot t and W alker1973] which employs l imi ted data gathered over a much shor ter t ime span, but theresul ts of such an approach would need to be t rea ted wi th caut ion.

Kern and Sea ton [1959] p roposed a mathemat ica l r e s t a tement o f Equ a t ion 4 .1with tubu lar f low in mind o f the form

dx l = K~c' M - K2 rx ~ (4 .12)d t

w h e r e K~c'M i s the ra te of deposi t ion term s imi lar to a f irs t order react ion

K2x~ is the ra te of removal (or eros ion) term

and K~ and K 2 are con stants

c ' is the foulant concentrat ion

M is the m ass f low ra te

x, is the fo ulant layer thickness at t ime t

r is the she afing stress= f p u 2

wh ere f i s a so-cal led f r ic t ion fac tor (see Chapter 5 for more deta i l )

By assum ing that c' and M are constant which is reasonable for a s teady s ta tef low heat exchanger, and x the th ickness , i s very mu ch less than the tube diam eterfor depo si t ion in a tube , i t is poss ible to in tegra te Eq uat ion 4 .12.


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K ~ c ' M ( 1 - e - X ~ " ) (4.13)

The equat ion i s s imi lar to equat ion 4 .11 in form wi thK~c'M a cons tan t fo r a

g iven se t o f ope ra t ing equa t ions and i s equ iva len t t oRy| in Eq uat ion 4 .11 . K 2 i sa lso a cons tan t an d equ ivalent to ti-

The ini ti al r a te o f depos i tion and the a sym pto t i c fou l ing r e s i s tance can b e

ob ta ined by pu t t ing x = 0 and d ry = 0 in Equ a t ion 4 .12 .dt

t h e n ( - -] t _ _ o = K l C ' M (4 .14 )K~c'M i s a cons tan t fo r a cons tan t s e t o f ope ra t ing cond i t ions

The a sympto t i c th i cknessxro =

c 'M

(4 .15 )

and i s a lso cons tant for g iven condi t ions

Kern and Sea ton [1959] deve loped the theory fu r the r us ing the B las iusre l a t ionsh ip , t o make a l lowance fo r the change in f low a rea caused by thedepos i t ion p rocess.

_ r__r__ K / R e . . 2 5 (416). e. w her e f - Pu 2 = .

w h e r e K: i s the Blas ius co ns tant

dand Ap = 4 ~ (4 .17 )

d p 2 g

w her e d~ i s the ins ide d iame ter of the tube

I i s the len gth o f tube in the d i rec t ion o f f low

Un der these cond i t ions fo r tu rbu len t f low


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General M odels o f Fouling 29

(4.18)

Ap~ is the pressu re dro p a t the asy mp tot ic value o f the foulant th ickness

K~c' charac terises the fou ling qualit ies of the f luid and g enerally wil l remainK~

constant . Sho uld practical data be available for one set o f condit ions, th e thicknessof the asym ptot ic value o f the foul ing th ickness a t a d i fferent se t of condi t ions may

be obtained from the rat io"

x I ~ , _ ~ | ~ _ o., ~ ,

xe .~ - [ p M ~ ] g - ~ | L~,JL J~ 4 1

(4 .19)

The subscr ip ts 1 and 2 refer to the tw o se ts of condi tions .

The model which Kern and Seaton proposed is an a t tempt to provide ageneralised equation for fouling; that is to say with no reference to the mechanismof deposit ion. In general , it can be assumed that the mechanism of removal wi ll besimilar in most si tuations since i t wil l depend upon the condit ions at thefluid/foulant interface, al thoug h the coh esive streng th o f the foulant layer will bedifferent in different examples.

A genera l ised equat ion for asymptot ic foul ing for any mechanism based on the"dr iv ing force" for deposi t development has been proposed [Konak 1973] ; the"dr iv ing force" i s suggested as the d i fference between the asymptot ic foul ing

resistance an d the fou ling resistance at t im e t . , i .e . the driving force = (RI~- R~).Assuming a power law funct ion

dR~ =K (R I~_ R ~ ) . (4 .20)dt

wh ere K is a constant

n is an exponen t

The f inal equat ion b ecom es


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30 F o u l i n g o f H e a t E x c h a n g e r s

[_ R~ _ I= K RI| t (4 .21 )

f o r n ~ l

w h e n n = 1

( 4 . 2 2 )

Bo th Equ a t ions 4 .21 and 4 .22 sa ti sfy the boun dary cond i t ion x ~ 1 and t ~ oo

Equ a t ion 4 .22 i s a fo rm o f Equ a t ion 4 .11 p ropo sed by Kern and Sea ton [ 1959]

4 .4 FA L L I N G R AT E F O U L I N G

Ep ste in [1988] prese nts a mathem at ica l analysis of fal ling ra te fou l ing asexempl i fi ed by Curve B on F ig . 4 .1 . He a s sumes tha t

dRI i s p rop or t ion to ( som e d r iv ing fo rce ) "d t

(4 .23 )

i .e . propor t ional to q" ( 4 . 2 4 )

wh ere n i s an exponen t

q i s the heat f lux

Fo r con s tan t su r face coe ff i ci en t o f hea t tr ans fe r a , t he hea t f lux is g iven by

q = U o A T = ~AT

( 4 . 2 5 )

w h e r e Uo i s the o vera l l hea t t ransfer coeff ic ient for fouled con di t ions

R c is the res is tance to hea t t ran sfer for c lean cond i t ions

and R c is 1 _ 1 wh en no fou l ing has occur reda

w h e r e Uc i s the overa l l hea t t ransfer coeff ic ient for unfouled condi t ions


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G e n e r a l M o d e l s o f F o u l i n g 31

Assuming that the overal l temperature di fference remains constant wi th t ime acomb inat ion of Equ at ion 4 .24 and 4 .25 yields

dR y = K (4 .26)a t +R:)"

wh ere K is a constant

t - t dR R/ K

In teg ra tin g f ~ - f/=o a t ~. (R c )"

(4 .27)

i .e . ( P c +R : ) " + 'P c " + . = K ( n - 1 ) t (4 .28)

which yields a non-asymptotic fal l ing rate curveR : v s t

An a l ternat ive w ay o f wri t ing Equ at ion 4 .28 is

1 1= K t (4 .29)TT n+ l TT n+ l

" D " C

The values o f K and n that wil l be necessary to a l low an assessment o f foul ingto be m ade, wi ll depend on the mechanism responsible for the fouling, e .g . whe theror not the fouling is caused by chemical reaction or mass transfer of part icles.Such data are n ot in general , readily available.

4 .5 C O N C L U D I N G R E M A R K S

Attempts have been made to develop the general ised models that were devised

several decades ago. Fo r ins tance Tab oreke t a l [ 1972] too k the gen eral equ at ion

dm= #n - #s (4 .30)

d t

wh ere rn is the mass deposi t

and a t temp ted to wri te equat ions that could be the basis of a determinat ion o f rand ~R- Th ese autho rs recognised that a specific fouling m echanism m ust mo dify

the general equat ion, and proc eeded to out l ine the form o f the equat ions that m ightbe used to take accoun t of th is fact . Thu s they in t roduced express ions that too kaccoun t of chemical reaction, mass transfer and se t tl ing. The rem oval term w aswri t ten in terms of f lu id shear and the b ond res istance in the deposi t that affected


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removal. De spite these refinements howev er, these mo dels sti ll lei~ a great deal tobe assum ed abo ut the particular fouling problem unde r consideration.

The use of general mod els for fouling analysis has m any attractions but w ith thepresent state of knowledge and the severe l imitations on the generation of suitabledata, their application to specific problems is unlikely to be significant at least inthe imm ediate future. The fact that the references to general models are roughly inthe period 1960 - 1975, with little published since that time is not withoutsignificance. Th e rece nt initial w or k o f An jorin and Feidt [ 1992] on the analysis o ffouling using entropy concepts how ever, show s promise. The next two chaptersillustrate the com plexities that are "hidden" in the term s ~z~ and ~ As the w or k onfouling develops, in the longer term, generalised relationships may assume more

importance.The present development o f general theories to the problem of fouling,

however, has the very definite advantage that i t has drawn attention to theunderlying phen om ena and seeks to m ake a logical analysis of the problem. Theundoub ted w orth of this approach is to emphasise the factors which need to beconsidered in any developm ent of a theory and m odel o f any particular system.

Specific models that have been developed for particular mechanisms will bediscussed in the a ppropriate chapters.

R E F E R E N C E S

Anjorin, M. and Feidt, M., 1992, Entropy analysis applied to fouling - a newcriteria, in: Bohnet, M., Bott, T.R., Karabelas, A.J., Pilavachi, P.A.,S6m6ria, R. and Vidil, R., eds. Fouling Mechanisms Theoretical andPractical Aspects. Editions Europ6 ennes T hermique et Industrie, Paris, 69 -77.

Bott , T.R. and Walker, R.A., 1971, Fouling in heat transfer equipment. Chem.Engr. No. 251,391 - 395.

Bo tt , T.R. and W alker, R.A., 197 3, An app roach to the prediction of fouling inheat exchang er tubes from existing data. Trans. Inst . Chem. E ngrs. 51, No .2, 165.

Kern, D .O. and S eaton, R.E., 1959, A theoretical analysis of thermal surfacefouling. Brit. Chem. Eng. 14, No. 5, 258.

Ko nak, A.R., 1973. Prediction of fouling curves in heat transfer equipment. Trans.Inst . Chem. Engrs. 51,377.

Epstein, N., 1981, in: Somerscales, E.F.C. and Knudsen, J.G. eds. Fouling of He atTransfer Equipment. Hem isphere Publishing Corp. W ashington.

Taborek, J., Aoki, T., Ritter, R.B., Palen, J.W. and Knudsen, J.G., 1972,

Predictive methods for fouling behaviour. Chem. Eng. Prog. 68, No. 7, 69 -78.


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33

C H A P T E R 5

F l u id F l o w a n d M a s s T r a n s f e r

5 . 1 I N T R O D U C T I O N

H eat ex change rs are des igned to handle flu ids , e i ther gases or l iquids . I t is to beexpected therefore , tha t the f low o f the f lu ids throug h the e xcha nger wi l l inf luenceto a lesser or grea ter degree , the laying dow n o f deposi ts o n the su rfaces of heatexchangers . In par t icular the behaviour of f lu ids in respect o f the t ranspo r t o fmater ia l, whe ther i t be par tic les , ions, m icrobes or o ther con taminat ing co m pon ent ,wi ll a ffec t the extent and the ra te o f deposi t accumu lat ion.

A shor t r~sum~ of the bas ic con cepts of f lu id f low and mass t ransfer wi l l begiven here as a basis for further d iscussion in depth, of the different foulingmechanisms.

5 .2 T H E F L O W O F F L U I D S

Tw o p roper t ies o f f lu ids influence the way f lu ids behave. Th ey are densi ty andviscosity. M ost gases have a re lat ively low densi ty and low viscosi ties . On theoth er hand l iquids can display a range o f densit ies and viscosities, for instan ce thedensity and viscosity of l ight organic l iquids are relat ively low, but other l iquidssuch as mercury have a h igh densi ty and l iquids wi th a h igh viscosi ty include fueloils and treacle.

Visc osity is not a ppa rent t il l the f luid is in mo tion. Fo r a f luid in m otio n a forceis required to m ainta in flow. In order to spread a v iscous paint on a sol id surfacethe necessary force is appl ied by the paint brush. In s imple terms the b ot to m of the

paint adheres to the surface whi le the layers of paint remo te f rom the surfaceadhere to the brush. The force applied throu gh the brush - a shear force -mainta ins the layers of paint betw een the brush and the surface in mo t ion. Thebrush m ay be m ove d a t constant speed, bu t the layers of paint mov e a t d i fferentspeeds . I t may be visual ised that the mo lecules of paint adjacent to the surface ares ta t ionary wh i le there i s a gradual increase in veloci ty throu gh the individual layerst il l the layer in contac t wi th the brush mo ves a t the speed (or veloci ty) o f the b rush.In o ther w ord s a veloci ty gradient i s es tablished throug hou t the layers.

The veloci ty gradient i s propor t ional to the shear force per uni t

d ui .e . r a ~ (5 .1)d r


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wh ere r i s the shear force

u is the velocity

x is the distance perpendicular to the surface.

In order to m ake re la tionship 5 .1 in to an equat ion a constant of propor t ional i ty isrequired, i.e.

d u, = , 7 ( 5 . z )

a x

wh en r / i s termed the coeff ic ient o f v iscosity (or m ore usual ly " the viscosity" of thefluid).

The viscosi ty is def ined as the shear force per uni t area necessary to achieve avelocity gradient o f unity. Eq uatio n 5.2 applies to the majori ty of f luids, and theyare general ly known as Newtonian f lu ids , or f lu ids that d isplay Newtonianbehav iour. Th ere are exceptions, and som e fluids (usually l iquids) do not con formto Equat ion 5 .2 , and these are general ly c lass i f ied as non-Newtonian f lu ids

although within this grouping there is a sub classif ication with dist inctly different"viscosity" behaviour for the f luids within the different groups.Osb orn R eynolds in 1883 in a c lass ical experiment , observed two kinds o f f lu id

f low within a p ipe namely laminar or s t reamline f low (somet imes cal led viscousf low) and turbulent f low. In the form er a th in f ilament of dye in the centre of thepipe remained coherent , w hereas for turbulent f low the f ilament of dye was b roke nup by the act ion of the turbulence or turbulent eddies .

The cr i ter ion for whether the f lu id is f lowing under laminar or turbulentcondi t ions is the so-cal led Reyno lds num ber(Re)for p ipe f low def ined as

R e - d u p (5 .3)

wh ere d is the inside pipe diameter

and p is the fluid den sity

Th e physical significance of the Rey nold s nu m ber is essential ly that i t represe ntsthe ra t io

m o m e n tu m f o rc e sviscous forces


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Flu id F low andM ass Trans fe r 35

B e l o w a b o u t R e = 2000 the flow is streamline aboveR e 3000 the f low isturbulent . The region betwee nR e = 2000 and 3000 is more uncer ta in and isusually called the transit ion region.

I t wil l be apparent h ow the f lu id proper t ies inf luence the m agni tude of theRey nold s num ber. In general terms for instance, a liquid with a high viscosity willhave a low R eynolds n um ber and hence i t is likely to f low un der laminarcondit ions, and a l iquid with a high density is l ikely to be turbulent under f lowingcondit ions.

The veloci ty dis t ribut ion is d i fferent und er these two regimes. Un der laminarcondit ions the velocity profi le is a parabola (see Fig. 5.1) and the mean velocity off low is hal f the veloci ty a t the centre o f the tube ( the maximu m v elocity) . Un der

turbulent condi t ions the veloci ty prof i le i s no longer parabol ic but i s as shown onFig. 5.2. Fo r turbulent f low the me an velocity of the f luid in the pipe is 0.82 x thevelocity at the centre.

Even under turbulent condi t ions there remains near the f lu id/sol id in terface as low moving layer (usual ly referred to as the viscous sub- layer) resul t ing f rom the"drag" between the fluid and the solid surface.

O Ju

cc l

. 4 - -I / I

~

r - ~

ii i

9 9 - - ' 1 1 3 ( ~

Velocityl l U I L p I ~ ' -

FIG UR E 5 .1 . Ve loc i t y p ro f i l e i n a tube w i th l amina r f l ow

(I /ud:::l::::l

, ,4, . - .q l l )

. n

O

ii i

VelocityFIG UR E 5 .2 . Ve loc i t y p ro f i l e i n a t ube w i th t u rbu l en t f l ow

~_L I

4 .


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In addi t ion to heat t ransfer, of concern to des igners and op era tor s of heatexchangers i s the pressure drop exper ienced in the f lu id as i t passes through theexchanger. Of ten it i s the increased pressure drop b roug ht abo ut by the presen ceof deposi ts , ra ther than the reduc ed heat t ransfer effic iency that forces the shutdow n of a hea t exchanger fo r ma in tenance and c lean ing ( see Ch ap te r 3 ) .

If the shear stress at the w all of a pipe is r the fr ict ional force at the wa ll is givenby

F = r n d l ( 5. 4)

wh ere I i s the length of the p ipe

In order for f lu id to f low this must be balanced by the force dr iv ing the f lu idthro ug h the p ipe , i .e .

7/~ 2

: A o - - T - ( 5 . 5 )

~ 2

.'. A p ~ = rnd l (5 .6 )4

4 dor Ap = -- if- (5.7)

The d imens ion less g roup ~ - i s dependen t on Reyno lds number and fo r tu rbu len t

condi t ions a lso on the rou ghness of the surface .

5 .3 M A S S T R A N S F E R

The t ranspo r t of materia l tow ards a surface that is being fouled depen ds u ponthe pr inciples of mass t ransfer. W hen a concentra t ion gradient of a par t icularcomponent wi th in a f lu id exis ts there i s a tendency for that component to move soas to reduce the concen tra t ion gradient. The process is kno w n as mas s t ransfer. Ina stat ionary f luid or a f luid f lowing under streamline condit ions, with aconce ntra t ion gradient of a com pon ent a t f ight angles to the d i rec t ion of f low, th emass t r ans fe r occurs a s a r e su l t o f the rando m mo t ion o f the molecu les wi th in thef lu id sys tem. The mot ion is of ten referred to as "Brow nian mo t ion" . In aturbu lently f lowing fluid the si tuation is quite different. U nd er these con dit ions"eddy diffus ion" is super imp osed on the Bro wn ian mot ion. Ed dy di ffusion resultsf rom the rando m phys ica l mo vem ent o f pa r ti c le s o f f lu id b rou gh t abou t by theturbulent condi t ions . The "parcels" o f f lu id physically t ransfer molecu les o f thediffus ing component down the concentra t ion gradient .


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F l u i d F l o w a n d M a s s Tr a n sf e r 37

If w e co nsider a mixture in wh ich com pon ent A is d i ffus ing throug h a f lu id Btow ards a surface. Diffus ion is at f ight angles to the genera l f low of f lu id B, andby Fick 's La w [Fick 1855] .

D dcA= - ( 5 . 8 /

w h e r e N a i s the ra te o f d iffusion of m olecules o f A

ca i s the concen tra t ion o f A a t a d is tance x f rom the surface

DABis the "diffusivity" o f A t hro ug h B

The di ffus ion of A th roug h B wi l l depend not o nly on the physical prop er t ies o f Aand B but also the prevail ing f luid f low condit ions.

I f the f low is turbulent then the d i ffusivity of A in B is augme nted by ed dydiffus ion. U nde r these condi t ions Eq uat ion 5 .8 . beco m es

N~=-(DAB +Eo)dcAd x

(5 .9)

w here E D is the eddy di ffus ion

In genera l for turbulent f lowE o >> DAB and the lat ter can o ften be neg lected inthe assessm ent o f mass t ransfer.

N ot only wi ll the t ransfer of a foulant to a heat exchang er surface dep end up onthe physical proper t ies of the const i tuents o f the sys tem, it wi l l a lso depend u

Documents

Fouling of Heat Ex Changers (1995)