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On the Road to Understanding Heat Exchangers: A FewStops Along the WayJOE W. PALEN aa Heat Transfer Research, Inc, College Station, Texas, USAPublished online: 27 Apr 2007.

To cite this article: JOE W. PALEN (1996) On the Road to Understanding Heat Exchangers: A Few Stops Along the Way, HeatTransfer Engineering, 17:2, 41-53, DOI: 10.1080/01457639608939872

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On the Road toUnderstandingHeat Exchal1gers: A FewStops Along the Way

JOE W. PALEN

Heat Transfer Research, Inc., College Station, Texas, USA

INTRODUCTION: WHAT IS SO DIFFICULT?

My mother, who passed away this year, askedme on a recent visit, "Well, are you still workingon the same thing?" On assuring her my thing wasstill heat transfer, she replied, "There must be alot involved with it." This got me to thinking: Justwhy is it so difficult to determine how to size heatexchangers that I would spend some 30 years at itand still have a lot of uncertainties to deal with?

There are a lot of nontechnical reasons forthat, but sticking to the safer ground, I would saythe real difficulties come from two sources: sharpturns, and intermolecular force gradients. Let meback into this to explain what I mean. Suppose wehave an ideal gas flowing at laminar velocity in astraight line along a flat plate, which is infinitelylong and wide and is slightly heated. By a numberof different approaches, depending on how rigor­ous we needed to be, we could solve the Navier­Stokes equations and obtain an accurate answerfrom first principles, with no expensive experimen­tation required. Notice that for this example there

This article is the text of the Kern lecture given by the author atthe 30th National Heat Transfer Conference, August 1995, in Port­land, Oregon.

Address correspondence to Joseph W. Palen, PhD, HTRI, 1500Research Parkway, Suite 100, College Station, TX 77845.

heat transfer engineering

are no sharp turns, and the intermolecular forcesare the same throughout the fluid.

The problem is that there are almost no oppor­tunities in the processes for making gasoline, plas­tic, or anything else worth buying to heat or coolanything under such analytically superb condi­tions. And it takes only the variation of physicalproperties (intermolecule force gradient) to beginto cause real problems with the analytical solu­tion. Add to this a bank of tubes protrudingthrough baffles that reverse the flow, and webegin scrambling for some shortcuts to try andestimate a heat exchanger size. Of course, thisscramble is nothing new; engineers who have neverwritten down the Navier-Stokes equations havespecified working heat exchangers for decades(more about that later, under the topic of "Foul­ing"). However, sizing heat exchangers in thismanner does take a different thought process.

I was fortunate to have come from school,knowing practically nothing of immediate useful­ness, into a group of process engineers who hadalready spent some time struggling with what KenBell calls "sufficient conclusions from insufficientdata." One of them once mentioned as his thoughtprocess, "Now if I were a molecule in this situa­tion, what would I do?" I have thought about thiswhimsical musing a number of times and in recentyears it is making sense to me. The answer toextra-Navier-Stokes solutions may be just that: (1)

vol. 17 no. 2 1996 41

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Figure 1 Shell-side flow distribution.

SHELL-SIDE FLOW: SHARP TURNS

(2)MTD = of LMTD

Figure 1 illustrates the problem, which was firstrecognized by Tinker [1]. The most extreme flowmaldistribution is seen in laminar flow; however,the phenomenon is significant in all flow regimes.Flow maldistribution is caused by the existence ofa number of different possible flow paths in theexchanger and the different flow resistances ineach path due mostly to different momentumchanges (sharp turns). It is possible to estimatethe amount of flow in each parallel stream bysetting up equations for the pressure drop of eachstream in terms of the flow resistance coefficientsand solving simultaneously. The resistance coeffi­cients, of course, are the secret to success. Devel­opment of these required a succession of twowell-defined expensive research programs, one atthe University of Delaware and one at HTRI,which were designed to isolate the effects of thevarious resistances in full-size and scaled modelheat exchangers. It was found that typically onlyabout 60-70% of the total stream actually flowedacross the tube bundle in turbulent flow, and onlyabout 40-50% in laminar flow, for typical ex­changer geometries. The remainder of the streamleaked through clearances in the baffle or by­passed around the bundle between the tubes andthe shell.

A consequence of there being several shell-sidestreams is the existence of several different tem­perature profiles, as shown in Figure 2. This re­quires that the heat exchanger mean temperaturedifference (MTD) receive a second modificationin addition to the elassical F factor for noncoun­tercurrent flow. This new factor was termed thedelta factor and was applied as follows:

The term (5 is developed from a straightforwardheat balance on each of the streams, but involves"mixing factors" determining the amount of directcontact heat transfer between the various streams.This, of course, also requires a lot of data.

LAMINAR FLOW: INTERMOLECULAR FORCE'GRADIENTS

Believe in molecules; and (2) try to visualize howthey would behave under the conditions in ques­tion.

No matter what approach is used, it is not easyto predict heat transfer rates in case of sharpturns and intermolecular force gradients. Andwe also have to worry about pressure losses asan equally important part of the economics. Thefollowing sections discuss some of the work done-"stops along the way."

Here is an area that at first did not seem toneed a stop: (I) "Laminar flow is easy to predict";and (2) "not applicable in industry-just design tohigher velocity." Wrong on both counts! Takingthe second research objection first, there are manycases in industrial processing where the fluid is soviscous that it is impossible to produce turbulentflow without exceeding process limits on eitherpressure drop or velocity. It so happens that theseare the cases of extreme interest because the heattransfer coefficient is so low that investment usu­ally is significant. Here, the viscosity and densitygradients at the wall caused the confusion. Even­tually, the solution came not by more rigorousNavier-Stokes solutions, but by including two moredimensionless groups in the empirical correlation:a Grashof number to account for density gradient,and a ratio of wall to bulk viscosity. Of course,when we do it this way, a lot of representativedata arc required. It is frustrating, tedious, andbecoming increasingly expensive to get good heattransfer and pressure drop data from a fluid thatis solid at room temperature. At one time indus­trial companies had no choice but to take on suchtasks. However, one of the earliest examples of"outsourcing" was to assign Heat Transfer Re­search, Inc. (later also Heat Transfer and FluidFlow Services) such jobs.

Empirical correlations developed for laminarflow did a reasonably good (adequate) job if thelocal bulk velocity could be accurately calculatedin all parallel flow channels. A typical correlationwas of the form

However, early experimentation with realisticshell-side geometries showed that the problemwas more difficult for shell-side flow.

42 heat transfer engineering vol. 17 no. 2 1996

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f---ITso

"E" Stream

pressure drop using a semiempirical exponent, m,to adjust to specific geometry and second-orderphysical property effects. The exponent m nor­mally ranges between about 0.4 and 0.5.

(4)

Exchanger Length

Figure 2 Shell-side stream temperature profiles. Major ("Determinative'') Flow Regimes

A rule of thumb suggested in [2] is to use Eq. (4) ifj; is greater than 1.5 and Eq. (6) if j* is less than0.5. In typical process condensers, otten both theNusselt falling-film and the two-phase convective

vol. 17 no. 2 1996 43

1. Condensation:Shear-controlled flowGravity-controlled flow

2. Boiling:Wet wallDry wall

Flow regimes can be important because theycan determine which heat transfer mechanismsare in operation under the particular local condi­tions (which can change throughout the exchangerfor condensers and vaporizers). Some of the typesof flow regimes that can be characterized areillustrated in Figures 3 and 4.

For the purpose of selecting mechanisms, the"determinative" regimes are as follows.

(5)Gu

[gDpu( PI - p)JO.5

If velocities are high enough that the shear forceis much larger than the gravity force, "shear­controlled flow" prevails, and if the wall is wet,Eq. (4) represents the operative heat transfermechanism for either condensation or boiling.

. ~f velocities are low and gravity forces are sig­nificant compared to shear forces, "gravity-con­trolled flow" prevails, and the liquid and vaporphases tend to separate, with the liquid phaseflowing in the direction of the gravity force.

A parameter developed by Wallis, j;, is usefulto determine whether gravity separation of thephases will occur. This factor is proportional tothe square root of the ratio of shear to gravityforce:

Most two-phase friction calculations for bothtube-side and shell-side flow are now based on thepioneering "separated flow" model of Martinelliand co-workers, in which the pressure drops of thetwo phases are equated and the interface effectsare handled by a single "constant," C, which maybecome a function of flow regimes and exchangergeometry.

If the wall is covered with liquid and nucleationis suppressed (see below), two-phase heat transfercan be expressed in terms of an analogy with

Friction-Based Relationships

heat transfer engineering

If it were not for intermolecular force gradi­ents, there would be no two-phase flow (to thegreat joy of some and unemployment of many).The basic difficulty in dealing with two-phase flowis due to the great difference in intermolecularforces in the liquid and vapor, producing inter­faces and causing large differences in physicalproperties. Here we see the importance of criticalpressure in boiling and condensation calculations,since the intermolecular forces in both phasesbecome the same as the pressure approaches thecritical. The distance from the critical then deter­mines how much acceleration the molecule expe­riences as it goes from one phase to the other, andhow much shear is exerted on the interface for agiven total flow rate. The difference in inter­molecular forces in the liquid and vapor forms thebasis for surface tension forces, which are of ma­jor importance for nucleate boiling.

TWO-PHASE (GAS-LIQUID) FLOW: MOREINTERMOLECULAR FORCE GRADIENTS

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1. Low liquid loading,vapor at wall

1- - ........

I

--- ..........

Tubeside Mist

2. Low liquid loading,liquid at wallct::J.. '...... . -, ~ -

-," "- - .. -- . -

Tubeside Annular or Mist Annular

3. High liquid loading

Tubeside High Velocity Bubble Flow

Horizontal Tubeside Flow Patterns in the Shear-Controlled Flow Regime

1. Low liquid loading 2. High liquid loading 3. Transition

Horizontal TubesideWave and Stratified

Horizontal Tubeside Low VelocitySlug and Plug Flow

Horizontal Tubeside High VelocitySlug Flow and Semiannular Flow

Horizontal Tubeside Flow Patterns in the Gravity-Controlled and Transitional Flow Regimes

Figure 3 Tube-side flow patterns.

mechanisms arc significant and are prorated ac­cording to the flow regime factor.

transfer to the liquid film. For horizontal tubes,this basic form is

Graoity-Controlled Films(6)

In condensation and falling-film vaporization, amodification of the original theory by Nusselt isused to determine the film thickness and heat

The factor Fg can be either greater or less than1.0, depending on the orientation of the surfaceand the condition of the interface.

3. High Liquid Loading2. Low liquid Loading,Liquid at Wall

O?:QD

•a

vap~low = ~ Vap~low. ~

1. Low Liquid Loading,Vapor at Wall

696Qg09096Shellside Mist Shellside Annular or Shellside High Velocity

Mist Annular Bubble Flow

Horizontal Tubeside Flow Patterns In the Shear-Controlled Flow Regime

1. Low Liquid Loading 2. Very High Liquid Loading 3. Transition

Vapor Flow- Vapor Flow-Nusselt Condensing Regime

(Wavy-Stratified on Map)Shellside Low Velocity

Slug FlowShellside Transition Flow

with Liquid Dropout

Horizontal Tubeslde Flow Patterns in the GraVity-Controlled and Transition Flow Regime

Figure 4 Shell-side flow patterns.

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Nucleate Boiling

In vaporization, when the wall superheat is highenough, nucleate boiling occurs at the wall andthis mechanism adds to the two-phase heat trans­fer, sometimes dominating. The general form nor­mally used was originated independently by Chen[3] and by Fair [4]:

heat of the vapor phase is very small compared tothe latent heat involved in phase change. How­ever, the heat transfer coefficient is also verysmall, so normally it is good practice to proratethe liquid-phase and vapor-phase resistances withrespect to the ratio of the duties. In its mostsimple form this approach may be expressed asfollows:

45

(11)

V+L-• Vertical Upflow Best

~ Double segmentalor Rod Baffle

V+L .• Vertical Baffle Cut Separation

Figure 5 Separation in shell-side two-phase flow.

vol. 17 no. 2 1996

V+L• Horizontal baffle cut• Mixed flow• Must be shear controlled• High pressure drop

Heat transfer to vaporizing or condensing mix­tures provides one of the most interesting butleast understood areas of process heat transfer.

Shell-Side Flow Separation

All of the above tactics are involved in solvingthe intermolecular force gradient problems. How­ever, for shell-side flow, the problem of two-phaseflow is accentuated by sharp turns, and manyunknowns still exist.

One of the most troublesome practical prob­lems involving shell-side two-phase flow is phaseseparation in horizontal "feed-effluent" exchang­ers, which are vaporizing hydrocarbons on theshell side in the presence of gas, mostly hydrogen.This can result in a considerable portion of theexchanger in the dry wall regime, causing poorperformance. Figure 5 illustrates the problem andsuggests two solutions, the better of which is avertical exchanger.

MIXTURES: STILL MORE INTERMOLECULARFORCE GRADIENTS

(10)

The nucleate boiling heat transfer coefficient,hnb' can be calculated by a number of correla­tions. One of the best dimensionless group repre­sentations is by Stephan and Abdelsalam [5]. Asimple correlation by Mostinski [13] will give ap­proximate results if corrected for mixture effectsby the factor FC' as described later.

hnb = 0.00658Pcqo7FpFc (8)

With P, in Ibf / in.2 abs and q in Btu z'hr ft2, h mb

is given in Btuy'hr ft2 OF. For pure fluids,

heat transfer engineering

(P )o.17 (P)1.2 (P)

Fp = 1.8 Pc' + 4 Pc + 10 Pc (9)

Gas-Phase Heat Transfer

So far nothing has been said about heat trans­fer to the vapor (or gas) phase. Often the sensible

If Eq. (10) is used, h n becomes hnb' hb becomesh cb ' and a is set equal to 1.0. A value of m = 2 isconsistent with [6].

For mixtures, it is better to eliminate the last twoterms of Eq. (9) to compensate for the massdiffusion limit at high pressures, unless aSchliinder-type method is used, as described later.

The term a (nucleate boiling suppression fac­tor) is a function of the amount of superheatrequired for nucleation in the presence of super­imposed two-phase forced flow. This term origi­nally was correlated for tube-side boiling by Chen[3], and no better practical method is currentlyavailable. Evaluation of the effect for shell-sideflow is a current research topic. An alternativemeans of superimposing parallel heat transfermechanisms has also been used in both condensa­tion and boiling, and has been shown to agreewith a large quantity of convective boiling data bySteiner and Taborek [6]:

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Liquid Film Interlace Boundary Layer Bulk Vapor

Figure 6 Condensation of mixtures.

BulkUquld

Temperature Profile

Figure 7 Boiling of mixtures.

Vapor Bubble

Ught .j. .component~

Heavy . ~-;.~)-~~~:;'~?Component .......

course in both situations the more stirring orrruxmg that can take place at the interface, theeasier it is for the trapped light (or heavy, in thecase of boiling) molecules to diffuse back to thebulk and eliminate the problem. It is interesting tonote that because of the direction of flow to theinterfaces, the vapor-side diffusion is controllingin condensation, while in boiling the liquid-sidediffusion is controlling.

Determining how to deal practically with theseproblems was much more difficult than to visual­ize them. There had been an early understandingthat even small amounts of inert gas greatly dete­riorate condenser performance, and classicaltreatments for the cases of a single condensingcomponent and for a condensing binary are wellknown, due to Colburn and co-workers [7, 8]. Forindustrial design of both multicomponent reboil­ers and condensers, the correction was much lessscientific. It was noticed that such units were notperforming up to design, so for future designs alarger fouling factor was assigned. This inadver­tent correction has left residual effects in designtoday, as discussed later.

One of the first attempts to relate the deterio­ration of boiling performance of mixtures tosomething other than a fouling factor was throughan empirical relation to the fluid boiling range [9].It was noticed that for the pool boiling data ofCichelli-Bonilla and of Sternling-Tichacek, the de­crease in measured heat transfer coefficient com-

The reason for the problems is traceable tomolecular size gradients set up by the phase­change process; the same problems do not existfor sensible (no-phase-change) heat transfer tomixtures. Most phase change in the process indus­tries takes place due to required separations.Chemical reactors produce a large variety ofmolecular species in addition to the particular onerequired. The heart of the separation process isthe train of distillation columns, each of whiehrequires a reboiler and condenser operating on amixture. In addition, the feed to the reactor nor­mally is mixture, which is partially vaporizedagainst a similar condensing mixture in a "feed-ef­fluent" heat exchanger, previously described.Therefore, mixture vaporizers and condensersabound in the process industries, and it is notpossible (as one of my academic friends oncesuggested) to substitute a single-component fluidto provide a simpler solution. .

Here is a case where both the Navier-Stokesand the molecular telepathy (guess) models havebeen put to use. The best solution so far seems tobe a combination of the two. First, instead ofwriting down the differential equations for eachmolecular species, let us try to visualize what isgoing on. The basic processes for condensationand boiling of mixtures are illustrated in Figures 6and 7.

Taking first a condensing case, Figure 6, wehave a cold wall on which is forming a condensatefilm composed of the heavier molecules and someof the lighter molecules of the condensing vapor.The vapor, consisting of a mixture of molecules, isrushing to the interface to make up the massbalance for the molecules condensed. However, atthe interface a preponderance of the heavymolecules is condensing according to equilibriumconditions at the interface, so the lighter moleculesare concentrating in the vapor at the interface.These then try to flow back to the bulk vapor(diffuse) against the total flow of vapor to theinterface, and the extent to which they are suc­cessful determines how much decrease in heattransfer will be seen as compared to condensationwhen the molecules are all the same size (purefluid). This decrease in heat transfer rate is due tothe fact that the equilibrium temperature of theinterface decreases with the increase in concen­tration of light molecules at the interface.

An exactly analogous scenario is equally validfor the liquid side of the interface in boilingexcept that the heavy molecules concentrate andincrease the interface temperature, Figure 7. Of

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where

This work currently is receiving further attentionas a promising compromise for design calcula­tions. The missing element is determination ofeffective mass transfer coefficients, {3/, which logi-

100 .....Tetradecene

---.... _ _ _ _ _ ;- Weighted Average

------

/0n-Pentane

Figure 9 Boiling of mixtures: comparison of Schliindcrmethod with data.

cally are functions of the amount of agitation atthe interface.

For condensation, the same type of formulationshould apply, theoretically. The original Colburn­Drew work for a condensing binary can also beexpressed in a form analogous to that of Schliinderfor boiling. A theoretical treatment for multicorn­ponent mixtures was formulated by Krishna andStandart [12]. However, for practical use in designof condensers with multicomponent mixtures, aproration of liquid-phase and gas-phase heattransfer coefficients is used as shown in Eq. (1I).This method was proposed in its most frequentlyused form by Bell and Ghaly [22]. It also has beenempirically modified to account better for flowregime, exchanger geometry, and molecular diffu­sion resistance in proprietary studies. It is conceiv­able that an approach using an effective averagemass transfer coefficient for certain classes offluids would be a practical solution for condensa­tion, as it is proving to be for boiling, and hope­fully a unified method that applies for both boil­ing and condensation will be possible in the fu­ture.

(13)

(12)

pared to that for the pure fluids decreased as theboiling range was increased and a preliminarycorrection was proposed, as shown in Figure 8.This was later improved using data from actualreboilers, taking into account that only the nucle­ate boiling mechanism of Eq. (6) was significantlyaffected by the diffusion problem.

Schliinder [10] was the first to simplify thedifferential equations for the composition bound­ary layer enough to provide a practical method forboiling of binary mixtures. The method containeda mass transfer coefficient, which he found couldbe approximated as a constant for a large range ofmixtures. Figure 9 shows an example prediction ofthe nucleate boiling heat transfer coefficient for amixture of n-pentane and tetradecene.

However, application to multicomponent mix­tures in industrial design was still impractical.Recently, Thorne and co-workers [11] have shownhow the boiling-range approach and the Schliinderboundary-layer approach could be combined toprovide an approximate method easily applicablefor the first time to industrial mixtures. The equa­tion form for this approach is

Figure 8 Mixture correction: early empirical correlation.

heat transfer engineering

CRITICAL (MAXIMUM) HEAT FLUX

There are a number of "rules of thumb" thatdeal with situations for which there is really nogood analysis or for which a real analysis would bevery involved, when all that is needed is somereminder to use engineering judgment. Such thingsinclude maximum velocity, maximum (Ju 2

, maxi­mum pressure drop for phase change, maximumweight fraction vaporized for thermosiphons, etc.One rule of thumb that has been made into asomewhat more definite limit by analysis and com-

47vol. 17 no. 2 1996

18080 120 160

Boiling Range, F40°

.00.8c-EO.6EJ::,,0.4oLLO.2

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where

for such a purpose is the ratio of the heatercross-sectional area for vapor escape to the totalsurface area. This ratio, '!tb', is equal to(1TDb L )/ A b and is exactly 1.0 for a single tube.Data for a wide range of bundle geometriesshowed that the maximum heat flux for bundlescould be approximated by multiplying by a con­stant times the factor, '!tb'

parison with data is that of maximum heat flux forprocess reboilers. For pool boiling outside a singletube, the tube surface begins to become blanketedby a vapor above a certain (critical) heat flux,depending on the strength of the intermolecular

. forces in the liquid and the difference between inthe strength of the intermolecular forces in theliquid and in the vapor. This combination of de­pendencies has the effect that a maximum valueof the critical heat flux in pool boiling is observedat a reduced pressure of about 0.2 for all fluids,being lower at both very low pressure and veryhigh pressure. This effect is illustrated qualita­tively for a vertical thermosiphon reboiler in Fig­ure 10.

(14)

Effect of Bundle Geometry

The maximum heat flux phenomenon has beencorrelated for pool boiling with single tubes byboth the reduced pressure empirical method ofMostinski [13] and by the hydrodynamic model ofKutateladze [] 4] and of Zuber [15]. However, fortube bundles it was known that the limiting heatflux was far less than that for a single tube and,since no one knew exactly why, a rule of thumbwas imposed that the critical heat flux should notexceed 12,000 Btuy hr ft 2 (38,000 W/m2 ) for hy­drocarbon reboilers. The initial attempt to im­prove on this used the "molecular telepathy"approach rather than the Navier-Stokes approach.It was reasoned [9] that the surrounding tubesimpeded flow of vapor from, and flow of liquid to,any given tube, and therefore the decrease ofcritical heat flux should be some function of thenumber of tubes. One logical geometric function

7

N

E 5

~3

2

104

.001 .01 PIPe.1 1.0

Figure 10 Maximum heat flux in reboilers.

48 heat transfer engineering

The above equation indicates that for '!tb > 0.323,the bundle maximum heat flux is the same as for asingle tube. This would be the equivalent of about6 tubes on a l-in-square pitch, and indicates thatfor very small bundles there is no significant effectof the bundle geometry on single tube perfor­mance. This is consistent with available data. Theeffect of bundle geometry on critical heat flux, aswell as on average boiling heat transfer coeffi­cient, for which there is an opposite effect, isshown qualitatively by Figure 11.

Boiling In Tubes

Critical heat flux for boiling inside tubes can bedue to any of three phenomena:

1. Mist flow2. Film boiling3. Instability.

Temperature DifferencenDbL~ =Bundle ClreumferencelHeat Transfer Area

Figure 11 Effect of tube bundle geometry.

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Drops Liquid

Vapor on Wall Vapor on Wall

Film Boiling

Figure 12 Dry wall regimes: in tube.

Instability is a hydrodynamically induced phe­nomenon and will be discussed later. The othertwo limitations are due to dry wall regimes, whichare illustrated in Figure 12.

Mist flow occurs when the weight fraction vaporis high (nominally greater than about 0.6) and themass velocity is high enough to strip the liquidfrom the wall. This condition can be estimated bythe J. R. Fair [4] correlation:

(15)

For Eq. 15, G'mist is in lb Zhr ft2.Film boiling occurs when the intermolecular

forces in the liquid become very small and a layerof vapor is formed on the wall. This condition canoccur at any vapor fraction above the criticaltemperature difference for film boiling. In fact,due to the constrictive nature of the tube, it isrecommended that the maximum temperature dif­ference for nucleate boiling not be exceeded. Avariation of the method for bundles is currently inprogress but is still unpublished. In general, filmboiling is more likely to occur in practice at highreduced pressures. The best method currentlyavailable in the literature for critical heat flux fortube-side boiling is by Katto and Ohno [16].

For vertical thermosiphon reboilers, an empiri­cal correlation for critical heat flux is given in [17]:

(D

2)1l.35 (P)O.25( P)qb.max = 16,080 -t p cO.

61Pc 1 - Pc

(16)

For Eq. (16), D, and L are in feet, Pc is in psia,and qb max is in Btu z'hr ft '.

Instability occurs when the' vapor accelerationloss temporarily exceeds the driving head for for­ward flow, and newly formed vapor is forced back­ward against the net flow. This can happen only atlow pressures (when the vapor intermolecularforces are much weaker than the liquid inter-

molecular forces). A simplified model which givesa reasonable prediction is that of Boure [18].

FOULING

The subject of fouling is included in this articlenot because the author knows' much about itbut because of its unique position as a roadblockto further progress. Several decades ago, JerryTaborek and a large number of HTRI peoplepublished an article entitled "Fouling-The Ma­jor Unresolved Problem in Heat Transfer" [19].Today another article by the same title could justas well appear. The sad fact is that, even though agreat amount of research has been done on foul­ing since then, there has been little real progress!At least there has been very little that can betranslated into improved practical design applica­tions. Typically we still see the same fouling fac­tors being used and the same 30-50% overdesigndevoted to fouling with no relationship to whetherfouling actually has been a problem in the past ornot.

The Real Problem

So, what is so difficult about fouling? It is notintermolecular force gradients and sharp turns. Itis not even the very nonlinear nature of the depo­sition function, nor the unpredictability of thedeposit strength and removal stress. What is sohard about fouling is that: (1) it is about 90% anontechnical matter, and (2) it is an issue no onefeels responsible to take on. Yet it is an issue that,more than any other, directly affects the eco­nomics of the heat exchanger investment of anyplant.

Let me elaborate. It is not uncommon for theoverall design heat transfer coefficient of HTRI(or HTFS) programs to change as improved corre­lations are developed from new data. A commonscenario is for a customer to call and point outsomething like the following: Previously the unitthat he is about to build was 2% oversurfaced andnow with the new program modifications it is 11%oversurfaced, or (a bigger problem) previously itwas 5% over and now it is 1% under. During thediscussion the percent surface devoted to thespecified fouling factor normally comes up andtypically is in the range 35-60%. In many casesthese can be condensers or other light hydrocar-

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Design Implications

bon exchangers with no known fouling history.Nevertheless, the manufacturer is adamant thathe cannot change the fouling factor since it isspecified by the processor, and therefore the de­sign must be altered.

The question then is, where did the processorget his fouling factor? Almost always from theTEMA tables. Since a committee including TEMAand HTRI members reviewed the TEMA foulingfactors in the last decade, we might ask what iswrong with that? What is wrong falls under theabove two reasons why improvement is difficult,all of which can be summarized in one sentence:There is no relationship between operating condi­tions, actual fouling history, design methods used,overall economics, and the fouling factor speci­fied, and no one seems to be in any position to doanything about it.

The impact of this situation on the develop­ment of design methods provides an interestingaspeet of this frustrating situation. There are infact several types of examples. However, let usconcentrate on two of the most significant: boilingand condensing of fairly wide-boiling-range lighthydrocarbon mixtures. The issue here is how foul­ing factor specifications should be related tomethods developments. In both cases the originaldesign methods (as given, of course, in Kern'sbook [23]) did not consider the very significantdiffusion resistance penalty to the heat transfercoefficient. However, the fouling factors used (alsogiven in Kern's book, and being too high) made upfor the faet that the heat transfer coefficientswere calculated too low. In fact, since light hydro­carbon reboilers and condensers normally operatewithout significant fouling, the entire surface de­voted to fouling was actually just a make-up forthe heat transfer coefficient misguesses, probablyevolved from plant observations.

Now, enter the developer of a new method forthe heat transfer coefficient of light hydrocarbonreboilers and condensers, one that takes into ac­count the mass transfer resistance missing in theprevious accepted methods. The safety factors inthe form of fouling factors are no longer neces­sary. Unfortunately, this new bit of informationwas not transferred to the fouling faetor specifica­tion process, nor could it have been since nomechanism exists for adjustment of fouling factorsbased on development of new correlations. There-

50 heat transfer engineering

fore, the same fouling factors are still used, andthe reboilers and condensers now become furtheroverspeeified by as much as 50%. C. H. Gilmour,in his 1965 article, "No Fooling-No Fouling"[20], advocated better design and much lower foul­ing factors, and he explained how use of largefouling faetors actually contributes to fouling. Onthe other hand, A. C. Mueller [21] contends thatthe TEMA tables are better than nothing andhave the advantage of many years of use with nocomplaints. This can easily mean that they are fartoo conservative.

I do not mean to say that all fouling factors aresafety factors that will disappear when we havecompletely reliable design correlations. There ob­viously are process situations that foul badly.However, what is needed is to recognize the truefouling situations and begin to see how designconditions can be altered to provide a lower levelof fouling. The TEMA fouling factors do nothingto help with this situation. So, what do we recom­mend? The easiest thing is to continue to saynothing can be done about fouling, so let's acceptthe TEMA factors and get on with our business. Ifthis is the case, it may be out of proportion tospend millions of additional dollars on heat trans­fer research, since the amount of improvement ineconomics is not nearly as great as can be madeby a business decision to reduce the fouling factor.However, we can do better: What is needed is adifferent approach.

PRESENT APPROACH VERSUS NEW DESIGNAPPROACH

Present Approach

Presently, the design procedure is to calculateshell-side and tube-side heat transfer coefficient,specify fouling factors, calculate an overall heattransfer coefficient, and determine the heat trans­fer area required based on specified conditions,which set the temperature difference available.The problem with this is that even if the foulingfactors are "real," the unit is clean on startup andthe run conditions must be adjusted by the opera­tor, sometimes severely, to produce the required,rather than excess, duty. Two classic examples arebrought to mind:

Condensers: The condensation rate is too high,column pressure is falling, so cooling water rate

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is decreased. This has the two effects of (1)decreasing the velocity, and (2) increasing thewall temperature at the exit. Both of theseeffects increase the fouling rate, so that thespecified fouling factor (or greater) is achievedafter all.

Reboilers: The reboiler is started up with full de­sign steam pressure, as required by the specifi­cation sheet giving an overall temperature dif­ference of 7SOF at a required heat flux of 10,000Btuy'hr ft2. However, with a condensation heattransfer coefficient of 2,000 Btuy hr ft2 of and atotal fouling factor of 0.004 hr ft 2of/Btu, theboiling-side temperature difference was sup­posed to be 30°F and the boiling regime wassupposed to be nucleate. However, since thefouling did not exist, at least for startup, theactual boiling-side temperature difference was70°F and the boiling regime was film boiling. Ifthe heat transfer coefficient for film boiling inthe bundle were about 140 Bru z'hr ft? F, not anuntypical value, the duty would be exactlymatched and all would be well except for twothings: (1) There is not operating room forfouling in case it does occur; and (2) the walltemperature is much hotter than design, sofouling logically would be more rapid than ex­pected. The logical result would be to assumefouling was greater than design and assign aneven larger fouling factor next time, thus com­pounding rather than recognizing the problem.What would be better?

New Approach

One possible approach would be a two-partdesign:

1. Clean operation2. Fouled operation

This requires a knowledge of how the unit will becontrolled as the overall heat transfer coefficientis changed. Presently, the designer sometimeschecks for clean operation, but more often thannot he or she has no knowledge of the controlscheme to be used, so this is not possible. Prefer­ably the design should be made around the clean,not the fouled, condition, since we know thiscondition will occur and the other one is specula­tive. The trick, then, would be to devise controlchanges required in case of different levels offouling factor.

Kettle Reboiler

Assume that the critical heat flux for the condi­tion is calculated to be 20,000 Btuy'hr ft2 and it iselected to design to 70% of the critical or 14,000Btu z'hr ft2. Assume that the boiling temperatureis 200°F, and the calculated boiling heat transfercoefficient at this heat flux is 400 Btuy hr ft2 OF.Assume steam at a maximum available pressure of150 psig, with a maximum saturation temperatureof 365°F, and that a condensing heat transfercoefficient is calculated as 1,600 Btuyhr ft2 OF. If awall resistance of 0.0002 is calculated and a ratioof outside to inside tube area is 1.2, the overallclean heat transfer coefficient is 290 Btu/hrft 2°F

and the required temperature difference is 48°F.Therefore the required clean condition steam sat­uration temperature is 248°F and the correspond­ing steam pressure is 44 psig. If the control systemwill be a valve in the steam line, this is no prob­lem: The valve can close to a position producing44 psig steam at a temperature of 365°F with117°F superheat. Heat will be transferred at thesaturation temperature rather than at the super­heat temperature, and the required operationshould be achieved for the clean condition.

Next, the fouled conditions should be investi­gated. For each 0.001 additional fouling factor,the temperature difference at this design heat fluxis increased by 0.001 X 14,000 or 14°F. Since 14°Fincrease in saturation temperature adds roughly 8psig to the steam pressure in this range, we cansee that for an improbably high total fouling resis­tance of 0.004 hr ft 2of/Btu, the required steampressure is 44 + 32 or 77 psig. Since this is still farbelow the maximum available steam pressure, thisreboiler design is satisfactory, and conditions arealready set to begin operation.

Horizontal Shell-Side Condenser

The condenser case is less straightforward, sincethere is not a recommended design heat flux.Water-cooled condenser design should begin withthe water velocity and temperature. Maximumcooling-tower water temperature should be wellbelow 120°F, and minimum water velocity shouldbe above 5 ft/sec. Given the condensing duty, thewater rate can be calculated based on a maximumallowable water temperature rise, say, 80°F to110°F. Based on the 5 ft/sec limit, the number oftubes per pass can be calculated. If a maximumlength is known and an overall heat transfer coef-

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heat transfer engineering vol. 17 no. 2 1996

ficient can be roughly estimated, the total numberof tubes and number of tube passes can be esti­mated. This tentative clean design can then berated on a commercial condenser rating programand geometry adjusted for final match.

Next the fouled conditions arc estimated. Thisstep can be done entirely using the commercialrating program, by specifying total fouling factorsof 0.001, 0.002, and 0.003, respectively, and deter­mining the required increase in water rate anddecrease in temperature rise to achieve requiredduty at each level. The maximum allowable foul­ing level can then be seen based on requiredpressure drop as compared with available pump­ing power. This maximum allowable fouling levelis then judged acceptable or not acceptable basedon data for fouling of the type of cooling waterused (the condensing-side fouling factor normallycan be considered zero, unless an unusual foulingcondition is known to exist).

SUMMARY

In summary, we can state the following:

I. Empirical conditions are still necessary for pre­diction of heat transfer and pressure drop inreal industrial situations, due to thenonideali­ties of "sharp turns" and "intermolecular forcegradients."

2. Most "rough spots in the road" involve thefollowing areas:Flow maldistributionTwo-phase flow regimesCritical heat fluxMulticomponent vaporization and condensa­

tion3. In practical design the "rough road" is mainly

still handled by a large fouling factor, the "bigdetour."This practice is wasteful and self-defeating.A new approach to design is needed.

NOMENCLATURE

A" bundle heat transfer area, ft2 (rn")BR boiling range, dew point-bubble point,

OF (OC)

C I constantC 2 constantC3 constantD tube diameter, ft (rn)

52

hi

LLMTDMTD

nNuPPcq

ql,max

a.;

q,Re

bundle diameter, ft (rn)inside tube diameter, ft (m)mean temperature difference correctionfactorcorrection for diffusion resistance inboiling of mixturesempirical correction to the Nusselt solu­tion, gravity-controlled condensationpressure function in nucleate boilingacceleration of gravity, ftjhr (rnys)mass velocity of liquid phase flowingalone, Ibjhr (kgys)mass velocity for vapor phase flowingalone, lbjhr (kgy's)heat transfer coefficientheat transfer coefficient, mechanism "a,"Btujhr ft 2OF (W jm2 K)heat transfer coefficient, mechanism "b,"Btujhr ft2 OF (W jm2 K)heat transfer coefficient, convective boil­ing, Btujhr ft2 OF (W jm2 K)heat transfer coefficient, liquid-phaseconvection, Btujhr ft 2 OF (W jm2 K)heat transfer coefficient, boiling mixture,Btujhr ft 2 OF (W jm2 K)heat transfer coefficient, nucleate boil­ing, Btujhr ft2 OF (W jm2 K)heat transfer coefficient, natural convec­tion, Btujhr ft 2OF (W jm2 K)heat transfer coefficient, convective boil­ing, Btujhr ft 2 OF (W jm2 K)heat transfer coefficient, two-phase,shear-controlled, Btujhr ft 2OF(Wjm 2 K)dimensionless gas velocitythermal conductivity of liquid,BtujhrftOFtube length, ft (rn)log mean temperature difference, OF (OC)true mean temperature difference, OF(OC)

empirical exponentNusselt numberpressure, psia (kPa)critical pressure, psia (kl'a)heat flux, Btujhr ft2 (W jm2 K)critical (maximum) heat flux, single tube,Btujhr ft 2 (W jm2 K)critical (maximum) heat flux, bundle,Btujhr ft2 (W jm2 K)sensible heat flux, vapor Btujhr ft 2

(Wjm 2 K)total heat flux, Btujhr ft2 (W jm2 K)Reynolds.number

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REFERENCES

[I) Tinker, T., Shell Side Characteristics of Shell and TubeHeat Exchangers, Gel/era/ Discussion of Heal Transfer,Proc. lnst. Mech. Eng., London, 1951.

[2] Palen, J. W., Breber, G., and Taborek, J., Prediction ofFlow Regimes in Horizontal Tubeside Condensation,Hear Transfer Eng., vol. 1, no. 2, pp. 47-57.

[3] Chen, J. C, A Correlation for Boiling Heat Transfer toSaturated Fluids in Convective Flow, Ind. Eng. Chem.Proc. Des. Deu., vol. 5, no. 3, pp. 322-329, 1966.

[4] Fair, J. R., What You Need to Design ThermosiphonReboilers, Petroleum Refiner, vol. 39, no. 2, pp. 105-123,1960.

[5] Stephan, K., and Abdelsalam, M., Heat Transfer Corre­lations for Natural Convection Boiling, Int. J. Heat MassTransfer, vol. 23, pp. 73-87, 1980.

[6] Steiner, D., and Taborek, J., Flow Boiling in TubesCorrelated as an Asymptotic Model, Heat Transfer Eng.,vol. 13, no. 2, pp. 43-69, 1992.

[7] Colburn, A P., and Hougen, O. A, Design of Cooler­Condensers with Mixtures of Vapors with Non-con­densing Gases, Ind. Eng. Chem., vol. 26, pp. 1178-1182,1934.

[8] Colburn, A P., and Drew, T. 8., The Condensation ofMixed Vapors, Trans. AIChE, vol. 33, pp. 197-215, 1937.

[9] Palen, J. W., and Small, W. M., A New Way to DesignKettle and Internal Reboilers, Hydrocarbon Processing,vol. 43, no. 11, p. 199, 1964.

[10] Schliinder, E. U., Heat Transfer in Boiling of Mixtures,1111. Chem. Eng., vol. 23, no. 4, pp. 589-599, 1983.

[11] Thome, J. R., and Shakir, S., A New Correlation for

Joseph W, Palen is a senior consultant atHeat Transfer Research Inc. (HTRIl. Hewas the 1994 recipient of the Donald Q.Kern award for his groundbreaking work indeveloping design methods for heat exchang­ers, largely conducted at HTRI. A fellow ofthe American Institute of Chemical Engi­neers, he has served for many years on theexecutive committee of that organization's

Heat Transfer and Energy Conversion Division and taught a designcourse in its continuing education program. Dr. Palen served for twoyears as an adjunctprofessor at the BandungInstitute of Technologyin Indonesia. At HTRI, he hopes to bring design methodsfor boilingand condensation of multicomponent mixtures to a more satisfactoryreconciliation with fundamental theory and to contribute to the useof smaller, more realistic "fouling factors."

Nucleate Pool Boiling of Aqueous Mixtures, AIChESymp. Ser., vol. 83, no. 257, pp. 46-51, 1987.

[12] Krishna, R., and Standart, G. L., A MulticomponentFilm Model Incorporating a General Matrix Method ofSolution to Maxwell-Stefan Equations, AIChE J., vol. 22,pp. 383-389, 1976.

[13] Mostinski, I. L., Application of the Rule of Correspond­ing States for the Calculation of Heat Transfer andCritical Heat Flux, Teploenergetika, vol. 4, p. 66, 1963,English Abstract: Br. Chern. Eng., vol. 8, no. 8, p. 580,1963.

[14] Kutateladze, S. 5., A Hydrodynamic Theory of Changesin the Boiling Process under Free Convection Condi­tions, Izu. Akad. Nauk SSSR, Old. Tekh. Nauk, no. 4, pp.529-536, 1951.

[15] Zuber, N., Stability of Boiling Heat Transfer, Trans.ASME, vol. 80, p. 711,1958.

[16] Katto, Y" and Ohno, H., An Improved Version of theGeneralized Correlation of Critical Heat Flux for ForcedConvective Boiling in Uniformly Heated Tubes, Int. J.Heat Mass Transfer, vol. 27, no, 9, pp. 1641-1648, 1984.

[17] Palen, J. W., Shih, C C, Yarden, A., and Taborck, J.,Performance Limitations in a Large Scale ThermosiphonReboiler, Proc. 51h Int. Heat Transfer Con]; Tokyo, vol.5, pp. 205-208, 1974.

[18] Boure, J., The Oscillatory Behavior of Heated Channels,CEA R-3049, June 1966.

[19] Taborek, J., Aoki, T., Ritter, R. 8., Palen, J. W., andKnudsen, J. G., Fouling-The Major Unresolved Prob­lem in Heat Transfer, Chem. Eng. Prog., vol. 68, no. 2,pp. 59-67, no. 7, pp. 69-78, 1972.

[20] Gilmour, C H., No Fooling-No Fouling, Chem. Eng.Prog., vol. 61, no. 7, pp. 49-54,1965.

[21] Mueller, A. C, Section F. Fouling, Handbook of HeatTransfer Applications, 2d ed., pp. 4-139, 4-142, McGraw­Hill, New York, 1985.

[22] Bell, K. J., and Ghaly, M. A, An Approximate General­ized Design Method for Multicornponent Zf'artial Con­densers, AIChE Symp. SeL, vol. 69, no. 131, pp. 72-79,1973.

[23] Kern, D. Q. Process Heat Transfer, McGraw-Hili, 195I.

saturation temperature, of (OC)wall temperature, of (OC)Martinelli parameter, ratio of liquidpressure drop to vapor pressure drop forboth phases turbulentnucleate boiling suppression factormass transfer coefficient, liquid phase,ftjhr (my's)MTD profile distortion factorpressure drop, liquid flowing alone, psia(kPa)pressure drop, two-phase flow, psia (kl'a)pressure drop, vapor flowing alone, psia(kPa)mass transfer resistance functionlatent heat, Btujlb (W jm2

)

viscosity, liquid phase, Ibjft hr (N sjm2)

viscosity, vapor phase, lby'ft hr (N sjm2)

density, liquid phase, Ibjft 2 (kgjm2)

density, vapor phase, lbjft 2 (kg z'rn")bundle geometry factor

a

/31

OmA

/-LI/-LvPIPv'l'h

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