Heaters Film and Bulk

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For any differential portion of heat-transfer surface area ( dA), the differential rate of heat transferred ( dQ)may be related to the temperature difference between the fluid film temperature in contact with the insideheating surface ( T f) and the bulk fluid temperature ( T) at that same location.

dQ h idA i(T fT)

(1)

For any localized area we have:

dQ/dA i q i h i(T fT) h iT f

(2)

In Equation (2), the heat transferred per unit inside heat-transfer area ( dQ/dA i) is defined as the heat flux ( q

i). The difference between the fluid film temperature and the bulk temperature ( T fT) is usually referred to asthe film temperature rise ( T f). The inside, film heat-transfer coefficient is, by definition, equal to q i T f.

Therefore, the fluid film temperature may be calculated as follows:

T f T + T f T + q i/h i

(3)

In the process equipment industry it is customary to express the heat flux as q o Q A orather than q i. Thatis, the heat flux is expressed as the heat transfer rate per unit of external heat-transfer surface area. With

these definitions, q i q oA o A i, and Equation (3) becomes:

T f= T + (q o/h i)(A o/A i) = T + q o/h io

( )

Equation ( ) is the working equation for film temperature. It is common to use the form with h io (defined as h iA i A o, the inside, film heat-transfer coefficient referenced to the outside surface area). For round tubes, h io

h id i d o.

A typical temperature profile in a thermal-fluid-heater tube is shown in Figure 1. To estimate the fluid filmtemperature at any given location in a thermal f luid heater, all that is required is an estimate of T, q oand h ioat that location.

Dont be fooled by common misconceptions. It is important to dispel a few oversimplified notions that are oftenrepeated in the industry literature. The film temperature rise is equal to q o h io, the ratio of heat flux to heat-

transfer coefficient. No one variable by itself determines the film temperature.

Nevertheless, it is common to find comments such as "film temperature will not be a p roblem if q ois less than10,000 Btu (ft 2 h)" or "use oversized radiant-heat-transfer area to assure low film temperature" or "filmtemperature can be kept low by maintaining a fluid velocity of at least 7 ft s". In fact, for any given film-temperature limit, the allowable amount of T fdepends strongly on the bulk temperature ( T). If a fluid isused at a bulk temperature well below its allowable film temperature, more film-temperature rise is allowed.And there can never be any single heat-flux limit or fluid velocity requirement that will assure low filmtemperature. It is always the ratio of q o h io that determines the film temperature rise, and all three variablesT, q o and h iothat determine the film temperature.

Determination of film temperature at any given location in a t hermal fluid heater requires knowledge of thevalues of T, q oand h io at that location. Heat fluxes averaged over an entire heater will give no meaningfulresult if it is the maximum film temperature that is of interest.

Next, well consider how to estimate T, q oand h io at key locations in a thermal fluid heater.

Radiant zone heat flux

In a thermal fluid heater, the overall average heat flux is easily calculated. It is simply the total heat dutydivided by the total heat-transfer surface area. Unfortunately, this overall average is of little use in theestimation of maximum film temperature. Before proceeding with the calculation of local-maximum filmtemperatures, we will take a look at a few of the more common types of fired heater designs and determinethe average heat flux in the radiant zone. If the average radiant-zone heat flux is known, there are reasonableempirical methods to estimate maximum local flux.

In every heater type, there is a zone of heat transfer where the primary mode of heat transfer is radiant. In this

zone, heat transfer by radiation typically accounts for over 80 of the total heat transferred (except in theconvective heater style, discussed later, where heat transfer may be predominantly convective even in thehottest tube rows). Let us now consider the distribution of radiant and convective heat in the radiant zone of athermal fluid heater.

Tangent-tube helical-coil heaters. For tangent-tube helical-coil heaters of the type shown in Figure 2, theradiant zone is considered to be the inner side of the cylinder formed by successive turns of the helical coil.For a two-pass single-helical heater, the radiant zone is slightly less than 50 (typically 5 8 ) of the totalcoil surface area. In the case o f a three-pass double-helical heater, the area of the radiant zone is typically 20

23 of the total. Since the surface area is easily calculated for any given heater, the value ofA ofor theradiant zone can be readily determined in any case.

Page 2 of 24Cover Story Part 1: Heat Flux And Film Temperature In Fired, Thermal-Fluid Heaters...

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The radiant zone duty ( Q r) must be determined so that an average radiant-zone heat flux ( q r) may becalculated. In general, the calculation of Q rdepends upon many factors, including the furnace geometry,combustion conditions and fluid temperature. Detailed procedures for radiant zone calculations are beyond thescope of this article, but the re are well-established, quasi-theoretical techniques for determining radiant-zoneperformance [ 2].

The heater vendor must calculate Q rin order to properly design a heater or rate its performance, and thevalues of Q rand A o(or at least q r Q r A o) should be reported to the poten tial purchaser for evaluation andcomparison of bids. Due to the numerous variables that apply to radiant calculations, the calculation of radiantheat transfer has some inherent uncertainties. Nevertheless, in most applications the radiant-zone, exittemperature of the fluegas can usually be predicted to within 100F, so that the radiant zone duty (as apercentage of the total duty) can be predicted within 3 percentage points. The radiant zone duty in a two-pass heater can account for anywhere from 0 to 85 of the total heat-transfer duty (a typical value is 72 ).In a three-pass heater, it is sometimes possible to achieve more convective duty, especially for applications

with low fluid-inlet temperature. When this is the case, the radiant duty is usually in the range of 50 to 75 ofthe total (a typical value is 2 ).

So, if the overall average heat flux for the heater is, say ,000 Btu (ft 2 h) in a given two-pass heater, theaverage heat flux in the radiant zone may exceed 1 ,000 Btu (ft

2 h), see Example 1. Three-pass heaters

always have much more convective surface area than radiant area, so the disparity between average radiant-zone flux and overall average flux tends to be higher. Consider the heater in Example 2, where the overallaverage heat flux is only 7,1 0 Btu (ft 2 h) but the radiant zone average is 1 , 00 Btu (ft 2 h).

API-style heaters. Heaters built in accordance with American Petroleum Institute (API) Standard 5 0 alwayshave tubes that are spaced at some distance apart, usually twice the nominal tube diameter. In API thermal

fluid heaters (Figure 3), an overall heat-flux calculation is seldom even reported, as it has little relation to theradiant zone flux. The convective section typically utilizes both bare tubes and extended surface tubes (fins orstuds), with the result that t he convective zone often has a large, external surface area that would skew anyaverage based on total surface. In these heaters, the convective surface area does not have any fixed relationto the radiant area and is varied for each particular application. (In contrast, in a tangent-tube helical-coilheater the area ratio of radiant and convective surface is fixed for any given coil diameter.) Because of thisvariation, the radiant duty can vary from 0 to 85 of the total duty. adiant-zone and convective-zone heatduties, areas and heat fluxes must be reported separately in order to achieve a proper evaluation of a design

(Example 3). A good rule of thumb for API heaters in thermal fluid service is to assume that 75 of the duty isoccurring in the radiant zone.

Local-maximum heat flux and maximum film temperature

After determining the average heat flux in the radiant zone, it is a simple matter to calculate the average fluid-

film-temperature rise in the radiant zone. It is the average radiant-zone heat flux divided by the average valueof h io. (More on the calculation of h iowill be presented later.) Calculation of the maximum film temperaturerequires a bit more work.

Tangent-tube, helical coil heaters. First we will consider the case of t angent-tube helical coils. By simplegeometrical considerations, it is easily shown that the radiant heat flux at the coil surface directly normal to the




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radius of the radiant cylinder is higher than the average over the entire curved surface by a factor of 21.57. This is the tube-circumference, heat-flux variation factor, F C. Strictly speaking, this factor applies todirect radiation only. A portion of the radiant zone duty is convective, and it does not necessarily vary by thissame ratio. However, it is to be expected that the washboard surface of the coil has a higher convectivecoefficient at the portion normal to the cylinder radius than in the curved triangular space where the tubestouch. Since the convective contribution is a relatively small portion of the radiant zone flux, the ratio ofmaximum to average flux around the half-tube circumference is generally taken to be 1.57.

In addition to circumferential flux variation around the tube surface, there is also a variation in heat fluxlongitudinally in the radiant zone. This longitudinal flux is difficult to quantify accurately, as it depends on thefuel characteristics, flame length, and excess air levels. Some typical profiles of this factor ( F L) are given inFigure . For gas-fired heaters with a flame length equal to 50 0 of the radiant cylinder length, the peak

flux occurs at a distance of about 33 of the radiant zone length from the burner. At this location thelongitudinal heat flux factor ( F L) will be in the range of 1.05 to 1. 0, with 1.10 being a typical value for asingle, long-flame forced-draft burner.

Finally, the localized heat flux is affected to some extent by the localized temperature of the tube surface

being irradiated. The factor accounting for this effect of tube-surface temperature variation ( F T) is generallyclose to unity in a thermal fluid heater. A typical value for F T is 0. at the location of maximum heat flux.Details on how to estimate F Tmore precisely are given in ef. [ 5].

Putting all the factors together, the maximum radiant-zone heat flux may be related to the average as follows:

q m F CF LF Tq r

(5)

Assuming F C 1.57, F L 1.10, and F T 0. , the localized maximum heat flux will exceed the average by a

factor of 1.71.

If we know Tand h io at this location, we can now calculate the film temperature. eep in mind, though, thatthe fluid is not at its final outlet temperature at this point of maximum heat flux.

To be sure to determine the maximum film temperature properly, the film temperature must also be calculatedat the heater outlet. The calculation procedure is the same, except that in this case F L is evaluated at the coiloutlet location, typically at one end or the other of the radiant zone, and Tis now the fluid outlet temperature.

See Example 5 for a calculation of maximum film temperature in a two-pass, helical-coil heater.

API-style heaters. The estimation of the maximum, radiant-zone heat flux in these heaters is similar to thecase for tangent-tube heaters, but the procedure is slightly more complicated. Consider first that in the case oftangent-tube, coil heaters, the radiant surface is considered to be the semicircular portion of the coilcircumference facing the flame. In API heaters, by contrast (Figure 5), the tubes are spaced apart withreradiating refractory behind the tubes. Therefore, the average flux calculation for API heaters is based on theentire tube circumference and the distribution of radiant heat around the tube is a function of tube spacing.

Because of the tube spacing and the f luegas flow pattern in this type of heater, the convective component ofheat transfer is significant (typically about 15 of the total radiant-zone flux), and tends to be morepronounced behind the tubes.

Heat flux distribution around the circumference of fired heater tubes has been studied in depth over the years,and various authors have presented data and estimation techniques to quantify the heat distribution [ 3, 4].The procedure has been more or less standardized in API Standard 530, Appendix C [ 5]. The workingequation for calculating the maximum heat flux at any point in the coil is as follows:

q m F CF LF T( q r q rc) q rc

( )

For Equation ( ), F C, F Land F Tare the heat-flux variation factors already discussed in the previous sectionon tangent-tube helical coils. Since the entire tube circumference (as opposed to only half for tangent-tubehelical-coil heaters) is considered in calculating q rfor an API heater, it is not surprising that F Ctends to besomewhat higher for an API heater. The value of F Cvaries with tube spacing, but typically ranges from 1.85to 1. 5 for tubes made of standard pipe sizes that are spaced at twice the nominal pipe diameter. A graph of F

Cversus tube spacing is presented in Figure . The term F Ccan tend to be an overestimate, as it assumes

that refractory surfaces absorb all incident radiation. eflections will tend to reduce the actual value of F C.




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Note that the convective component of the radiant-zone heat flux is subtracted from the average beforecorrecting for variation in the radiant component of the flux. In the API 530 procedure, the convective term inEquation ( ) is assumed to be a constant around the tube circumference. In fact, studies have shown that the

convective effect tends to be greatest in the areas around the circumference where the direct radiant f lux islowest (that is, between the tubes and the refractory) [ 3]. Consequently, Equation ( ) is slightly conservative,producing a slight overestimation of the true maximum radiant flux.

See Example an illustration of the use of Equation ( ).

Convective heaters

For convective thermal-fluid heaters (Figure 7), the maximum heat flux usually occurs near the hot, gas-inletend of the coil, either at the first bare-tube row or at t he first finned-tube row. For the first bare row of tubes,the heat flux may be calculated using Equation ( ). The radiant portion of the flux is generally a smallerfraction of the total in this case, as the tubes have no direct view of the flame. Nevertheless, the nonluminousgas radiation from the gas volume beneath the coil can produce substantial heat flux at the first tube row,usually exceeding the convective flux. The fraction of the total heat radiated by the hot gas that is absorbed ineach tube row may be calculated as described by Ganapathy [ 6]. In this case, F Cis slightly higher than for afurnace with refractory behind the tubes, and F L 1.0.

Usually, however, convective heaters are specifically designed to operate at reduced gas temperatures where

radiative heat transfer is a smaller fraction of the total in relation to other fired heater types. The maximumheat flux often occurs at the row of finned tubes exposed to the hottest fluegas and in this area the heattransfer is predominantly convective. To determine the maximum film t emperature in a convective heater, theheat flux and film temperature should be checked at the hot, gas-inlet end and at any tube row where the findensity is increased.

When calculating peak heat flux in a convective bundle, it must be considered that the convective heat-transfer coefficient at the leading edge (gas inlet) of a given tube row is about 1.5 times the circumferentialaverage coefficient, and the gas temperature to be used in calculating the peak flux is the inlet gastemperature for that tube row, not the average.

Calculating film temperature

Once the maximum, radiant-zone heat flux is determined, the film temperature can be calculated. The firststep is calculation of h i.

Calculation of h iis straightforward. The value of h imay be calculated by various correlations available inliterature. One widely used correlation is the Dittus-Boelter Equation [ 7]:

h i 0.02 3( k d i) e0.8 Pr 0. ( w)

0.1

(7)

Equation (7) applies to straight tubes, but it is also recommended for calculating peak film temperature inhelical coils. Although the circumferential-average h iis greater in a helical coil than in a straight tube by thefactor (1 3.5 d i D coil), studies have shown that the enhancement in h ioccurs at the outer radius of the coil.In studies of flow in curved channels, the local value of h iat the inner coil radius is typically less than thecircumferential average [ 9], and since that is where the maximum radiant flux occurs, it is recommended notto credit any enhancement in h ifor helical flow at the point of peak heat flux.

The factor ( w)0.1

is generally very close to unity and may be assumed to be 1.0 for most calculations. Therest of the fluid properties needed to calculate h imay be found in the fluid vendor s literature. Havingcalculated h i, h io is then calculated by h io h id i d o.




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Checking the result

T f.

Calculate the ratio of the estimated T fto the allowable maximum value of T f. T f

If T fis more than 80% of the allowable, investigate more carefully.

Be extra cautious about any design that uses high radiant heat flux to make up for a large, allowable T f.

Consider future process changes.

Install tube thermocouples in any application where film temperature is a concern.

Summing up

Demand quantitative information from the vendor.

For any type of heater, the radiant and convective duties, surface areas, and heat fluxes must be reportedseparately.

The average and local-maximum radiant heat fluxes should be reported.

The film temperature at any location is a function of three variables: bulk fluid temperature, heat flux, and filmheat-transfer coefficient.

In helical coil heaters, whether of the tangent-tube or API type, the maximum-heat-flux location may not

coincide with the maximum film temperature.

For prospective purchasers: Question the heater manufacturer!

If film temperature appears to be critical (if it approaches the limit closely) measure it!

Edited by Rebekkah Marshall

Example 1

Q r

q QA o

q r Q rA o,r




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Example

q QA o

q r

Q r

A o,r

Example

Q

q QA o

q b QA o,b

q r

Q r

A o,r

Example

d o F cF L F T

q rc q m

q m F cF LF T(q rq rc) q rc

q r

Example

d i

h i h io

S m l nits Maximum lux rea eater utlet

Location of maximum heat flux: C L T

q m F CF LF Tq r

T

h io

T f T q m h io 561F

Coil outlet:F L

q m

T

hio

T f T q m h io 609F




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menclature

A i

A o

A o,b

A o,r

C p

D coil

d i

d o

F C

F L

F T

h i

h io

h o

k

k w

Pr C p k

Q

Q r

q i

q m

q o

q r

q rc

Re d iv

R film,o h io

R fouling

R wall

r i

r o

T

T f

T f

T fouling

T w

v

uth r

Robert Pelini

e erences

Process Heating

Chem. Eng.

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Pet.

Refiner

Hydrocarbon Process.

Int. J. Heat Mass Transfer

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Heaters Film and Bulk