Fired Heater Design

Fired Heater Design

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HEAT TRANSFER IN THE RADIANT SECTIONOF PETROLEUM HEATERS *

By Walter E. Lobo (Member) and James E. Evans! (Non-Member)

ABSTRACT

A brief review of empirical equations for predicting heat transfer in the combustion chambers of steam boilers and petroleum heaters is followed by a study of eighty-fiveperformance tests on nineteen furnaces differing widely in amount and arrangement of refractory cold surfaces. Operating conditions are available on furnaces with andwithout air preheat, with and without flue gas recirculation, fired with refinery cracked gas or oil fuel, and with a wide range of variation of excess air. The data arecorrelated by means of a theoretical equation and the deviations are no greater than the probable errors in the test data, and consistently less than those obtained by theempirical equation of Wilson, Lobo and Hottel. For simplicity of calculation the equation is presented in graphical form. An illustrative design problem has been included.

SUMMARY

In view of the trend of the petroleum industry toward ever-increasing radiant heat transmission rates, as well as higher tube skin temperatures andhigher percentages of heat-receiving surface per unit of refractory surface, this investigation has been initiated to study the effect of these variablesand to find a means of allowing for their effect in the design of tubular oil heaters.

Eighty-five tests of nineteen different furnaces have been analyzed in this study. The test data include furnaces with and without air preheat andrecirculation of flue gas. Excess air varied from 6% to over 170%, and average radiant rates from 3,000 to 54,000 Btu per hour per sq, ft. ofcircumferential tube area. The furnaces themselves were square, rectangular, or cylindrical in shape and varied widely in arrangement of surfaces; theratio of effective refractory surface to equivalent cold plane surface varied from 0.45 to 6.55. Refinery cracked gas was the most common fuel, but anumber of tests were made using oil fuel.

In this report a general and simple theoretical treatment is presented which satisfactorily correlates all the data. The deviations from the observedradiant section duties are well within the probable accuracy of the data. The average deviations of the predicted heat to the oil in the radiant sectionfrom the observed are 5.3% as compared to 6.85% when using the Wilson, Lobo, and Hottel empirical equation. The maximum deviation has beenreduced from 33% to 16%. The data indicate that the larger deviations occurring when using the empirical equation are partly due to break-down ofthe equation below average radiant rates of 5,000 and above 30,000 Btu per hour per sq. ft. of circumferential area. It is likely that the empiricalequation is seriously in error when applied to furnaces operating tube skin temperatures above 1000° F., as well as in furnaces having a lowpercentage of refractory surface and low values of PL, the product of partial pressure of the radiating constituents of the flue gas and the mean beamlength of the radiating beam. The data available do not indicate any restriction which should be placed on the use of the theoretical equation hereinpresented.

*This paper is printed prior to presentation at the Thirty-Second Annual Meeting, Providence, Rhode Island, November 15, 16, and 17, 1939, in order to encouragediscussion both verbal at the time of presenting and written.Written discussion should be sent to the Secretary's Office promptly as it will be submitted to the author before publication. Written discussion received prior toNovember 10th will be read at time of presentation.Discussion on this paper will be printed in Volume 36, No. 2, only.!The M. W. Kellogg Company, New York City.

INTRODUCTION

In view of the trend of the petroleum industry toward ever-increasing radiant heat transmission rates, as well as higher tube skin temperatures and

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Fired Heater Design


higher percentages of heat-receiving surface per unit of refractory surface, this investigation has been initiated to study the effect of these variablesand to find a means of allowing for them in the design of tubular oil heaters.

Although the exact mechanism of heat transmission in the radiant section of furnaces is complicated by factors about which little is known, certaingeneralizations and fundamental principles are fairly well established and can be used to advantage in solving radiant heat transfer problems. Some ofthese factors and their bearing on heat transfer problems are discussed below.

The major transfer of heat in the radiant section of a furnace is due to radiation from the hot gas cloud to the ultimate heat-receiving surface and byheat re-radiated from from the hot refractory surfaces to the cold surface. Some of the heat is also transferred at the instant of chemical union of themolecules in the flame. Of the radiation from the gas cloud, the major part is due to radiation from the carbon dioxide and water molecules present init. Incandescent soot particles are a source of some radiation, but with fuels and burners commonly used in the petroleum industry, combustionusually results in a practically non-luminous flame. Oil fuels tend to give a more luminous flame than refinery gas at the usual percentages of excessair because of the cracking of the oil particles to soot during the combustion period. Data are not available on the exact degree of luminosity of oilflames, but it is probably a function of burner design, the amount of steam used in atomization and the percent excess air used.

In modern furnaces increasing amounts of heat are transmitted directly from the gas mass and lesser amounts are transmitted by the way of therefractory because the current trend is to fill the radiant section with cold tube surface in the interest of economy. Since the radiating constituents inthe flue gas are the H2O, CO2 and SO2 molecules present, the amount of heat radiated by them will be a function of their number and the temperatureof the gas and cold surfaces. One measure of their number is their partial pressure. Another measure of their number is the mean length of theradiating beam in the gas mass. Hottel 1 has shown that the product PL, atmospheres-feet, expresses these two facts and permits the data on theradiation from gases to be correlated. For any given fuel, P is a function of the excess air used and L is a function of the furnace alone. An equation,to be valid for a wide variety of sizes and shapes of furnaces, must take into account the effect of PL on furnace performance.

Heat transfer by convection to the tubes in the radiant section of petroleum heaters accounts for only a small amount of the heat transferred, especiallyin high radiant rate furnaces. This convection transfer is more important in low rate furnacesbecause heat transfer by convection is proportional to thetemperature difference Tg - Ts, between flue gas and cold surface, whereas the radiant heat transfer is proportional to the difference T4

g - T4s where

the temperatures are expressed as degrees Rankine.

In view of the complexity of the problem, numerous investigators have correlated furnace performance by means of empirical equations. To illustratethe basic approach several of these empirical treatments are briefly summarized and their outstanding limitations described. A more complete reviewof this earlier lititure has been made in a previous publication.2

EMPIRICAL FURNACE EQUATIONS

The following empirical equations have been classified into two major groups according to whether they are similar to the Hudson or the DeBaufretype equation.

Hudson3 correlated the data on several types of steam-boiler furnaces by the simple equation:

(1)

m = fraction of total heat input to the furnace (above the steam temperature) which is absorbed by the ultimate heat receiver.G = air-fuel ratio, lbs. air / lb. fuel firedC = pounds of fuel per hour per sq. ft. of water-cooled surface.

Fired Heater Design


(2)

m = fraction of heat transferred above atmospheric temperatureG = air-fuel ratio, lbs. air / lb. fuel firedCo = pounds of equivalent good bituminous coal per hour per sq. ft. of water-cooled surface.

Wilson, Lobo and Hottel 2 modified the Orrok equation and correlated the performance on ten of twelve furnaces. Their recommended equation is :

(3)

m = fraction of total heat input above 60°F. absorbed by the cold surfacea Acp = effectiveness of tube surface as compared to a continuous cold plane, sq. ft.Q = net heat liberated from combustion of the fuel, B.t.u. per hourG = air-fuel ratio, lbs. air per lb. fuel fired.

Hottel 5 has proposed the following type of equation :

(4)

H = total net heat input from all sources, B.t.u. per hourN = the hourly mean heat capacity of the flue gas between the temperature of the gas leaving the chamber and a base temperature of 60° F.B.t.u./hour/°F.f = an overall exchange factor defined by the equation :

(5)

whereq = heat transferred by radiation, B.t.u./hourTg = temperature of the gas or hot surface, °F. + 460Ts = temperature of cold surface, °F. + 460.

The overall exchange factor makes allowance for variation in effective flame emissivity, arrangement of refractory and non-black conditions in thefurnace chamber. The constants in the above equation are very tentative so that it is only to be considered as illustrating a method. The f concept hasbeen satisfactorily used in the equation presented in this paper and has been defined and discussed under the derivation of the theoretical equation.

Fired Heater Design


DeBaufre 6 proposed an empirical equation which is similar to the basic Stefan-Boltzmann equation :

(6)

q = heat transferred, B.t.u./hourAo = total tube surface exposed to radiation, sq. ft.Tg = temperature of the products of combustion leaving the furnace chamber, °F. + 460Ts = temperature of cold surface, °F. + 460E = effectiveness factor of the cold surface.

DeBaufre attempted to correlate E as a function of the rate of heat liberation per unit of furnace volume but the correlation was poor. For black bodyconditions E would have a maximum value of 0.173, the Stefan-Boltzmann constant.

Mekler 7 proposes the equation :

(7)

q = heat transferred by radiation, B.t.u./hourSe = equivalent "effective" heating surface, sq. ft.C = an empirical coefficient depending on the temperature used for TgTg = exit gas or theoretical flame temperature, °F. + 460Ts = temperature of cold surface, °F. + 460.

In contrast to DeBaufre, however, he evaluates Se as a function of the "fraction cold" of the furnace. An approximate graphical method is used forsolving the DeBaufre type of equation. No cognizance is taken of the effect of PL on the heat transferred, and furnaces having the same geometricshape but widely different volumes are presumed to have the same fractional heat absorbtion. The effect of excess air on flame emissivity is likewiseneglected.

GENERAL LIMITATIONS OF THE EMPIRICAL EQUATION

If a series of furnaces operate on fuels whose heating value varies between comparatively narrow limits and whose ultimate heat-receiving surfacetemperatures are nearly constant, the performance of these furnaces may be adequately described by a simple empirical equation. However, asconditions deviate from those used to determine the constants of the equation its validity will be questionable. For example, a valid equationdetermined for tubes at a low temperature will certainly be invalid when the tube temperature is increased to a much higher value because as thistemperature is increased it becomes more difficult to transfer a given amount of heat in a given furnace. In other words, to maintain a definite radiantrate in a furnace with a high tube temperature, more fuel must be fired.

Another disadvantage of the empirical equation is the difficulty of allowing for the effect of excess air unless a fuel of approximately constant heatingvalue is used. If, for example, an air-fuel ratio is used to measure the effect of air addition, large values of the ratio are commonly associated withhigh percentages of excess air and low available heats. Conversely, small values of the ratio are associated with low percentages of excess air and highavailable heats. The danger involved in the indiscriminate use of an air-fuel ratio is best illustrated by an example. For theoretical combustion an

Fired Heater Design


average blast furnace gas would have an air-fuel ratio of approximately 0.73 lbs. air per lb. fuel gas and a natural gas might have a ratio of 15.9, yetthe theoretical flame temperature of the blast furnace gas would be only 2800° F. as compared to 3580° F. for the natural gas. If the excess air in thecase of the combustion of the blast furnace gas were increased until the air-fuel ratio became 15.9, the theoretical flame temperature would drop to atemperature much lower than 2800° F. If the the tube temperature was then increased, a point would be reached where no heat could be transferred tothe tubes. However, with the same net heat liberation, natural gas fuel would transfer a finite amount of heat.

Realizing the limitations of the purely empirical approach it was decided to develop a theoretical radiant heat equation, simplified by assumptions, ifnecessary, and to test it by the application to* data obtained on furnace performance.

*It should be remembered, however, that in many furnaces the usual measurement of the temperature of the gases leaving the radiant section does not give Tg directly, buta value usually less than Tg depending on the quantity of heat lost by the flue gases to the convection section by radiation at the point of measurement.

DEVELOPMENT OF THE THEORETICAL RADIANT EQUATION

By a proper definition of terms the heat transferred in the radiant section could be predicted exactly by a Stefan-Boltzmann type equation.

(8)

q' = net heat transferred by radiation to the tubes, B.t.u./hourT'g = mean temperature of the hot gases in the furnace, °F. + 460T's = mean tube skin temperature, °F. + 460. a Acp = area of a plane which will absorb the same as the actual cold surface in the furnace, sq. ft.f = an overall exchange factor correcting for flame emissivity, arrangement of the refractory, volume of the combustion chamber, etc. This factor willbe discussed in detail later.

In the combustion chamber Tg, the mean temperature of the hot gases in the furnace and the temperature of the exit gases will undoubtedly differ, butrun somewhat parallel. However, it was assumed that T'g

could be replaced by the exit temperature, Tg.* This assumed interchangeability introduces, of course, a degree of empiricism into the equation whichwill be justified, however, if the results are satisfactory.

All the net heat transferred to all the surfaces in the radiant section, i.e., the heat lost by the flame, is given by the following equation :

(9)

A'r = area of refractory in furnace, sq. ft.Ao = circumferential tube surface, sq. ft.hc = convection coefficient, B.t.u./hour/sq.ft./°F.

Fired Heater Design


Since both the external losses from the furnace and the net heat transferred to the refractory by convection, given by the term hcA'r(Tg - Tr), areusually small, the two may be assumed equal without appreciably affecting the results. Equation (9) may then be rewritten to give instead the heatreceived by the oil :

(10)

The second term represents the heat transferred to the tubes by convection and it may be approximated as its magnitude is usually much smaller thanthe first term of equation (10).

By making the assumptions that :1. The convection coefficient lies normally between 2 and 3 B.t.u./hour/sq.ft./°F.;2. In most furnaces Ao equals (2a Acp) approximately;

3. The overall exchange factor f has a value of about 0.57;the terms hc and Ao in equation (10) can be expressed in terms of a Acp and f, thus :

(11)

Making this substitution in equation (10) :

(12)

Of the various ways that equation (12) representing the heat transfer relation can be combined with the equation representing a heat balance on thecombustion chamber, the following graphical procedure is suggested :

LetH = the total net heat input to the furnace from all sources; i.e., combustion of the fuel, sensible heat in the air and fuel, sensible heat inrecirculated flue gases, etc., B.t.u./hr.q = the total net heat absorbed in the radiant section by the ultimate heat-receiving surface, B.t.u./hr.N = the hourly heat capacity of the flue gas evaluated at the temperature of the gasses leaving the section, B.t.u./hr./°F. = (mols/hours) (mean MCpbetween tg and 60°F.) (see Figure No. 15 in Appendix)

b = fraction of total net heat input lost from the external furnace wallstg = temperature of the gases leaving the section, °F.

bH = total heat losses, B.t.u./hr.

The heat balance equation may be written : (Datum temperature = 60° F.)

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(13)

By multiplying both sides of the equation by H(1 - b) we obtain :

(14)

Then

(15)

This may be transposed to :

(16)

The merit of such a relation is that the term in parentheses in the brackets is dependent on the fuel characteristics, excess air, air preheat, etc., and maybe separately evaluated. After its value is determined, it may be used to establish the simple graphical relation among H((1 - b))/aAcp, q/aAcp, tg, inaccordance with the following construction :

Since the term (t'f - 60) is, from its method of construction the theoretical temperature the gases would attain (a) if combustion were adiabatic exceptfor the loss of the fraction b of the enthalpy of the fuel and (b) if the products of combustion had a mean specific heat equal to their mean value from

Fired Heater Design


tg down to the base temperature, the term t'f may be thought of as a sort of flame temperature, referred to hereafter as the pseudo-flame temperaturefor short.

If now a plot is constructed with the coordinates q/aAcp and tg' a series of lines representing equation (12) may be placed on the plot; one for eachvalue of surface temperature ts (see Figures 1 and 2). On the same diagram a straight line through the value t'f (completely determined by fuelcharacteristics, and presented for varying conditions of operation in Figures 3 and 4 in which the radiant section external losses have been taken as2% of the total net heat input to the furnace) drawn through a point on the family of curves corresponding to the correct tube skin temperature, ts, andfor q/aAcp or tg (according to which of these is fixed) when extended to the left, will intersect the line tg=60° at the value of H((1 - b))/aAcp.

Fired Heater Design


In design calculations the temperature, tg, of the flue gases leaving the radiant section must be estimated before the pseudo-flame temperature can beobtained. This assumed or provisional t'f must be revised if the assumed bridge wall temperature is found to be considerablely in error. Thedescriptive example included at the end of this section illustrates the method of calculation.

EVALUATION OF THE EQUIVALENT SURFACE, aAcp

Acp is the area of a continuous plane replacing the row of tubes and may be taken as the product of the exposed tube length, and center to centerdistance between tubes, and the number of tubes in the exposed radiant row. a is the ratio of reception by the actual surface to reception by acontinuous plane. Then the term aAcp is the tube area expressed as equivalent cold plane surface, i.e., the area of a plane which will absorb the sameas the actual cold surface in the furnace.

Fired Heater Design


Hottel8 gives a as a function of the ratio

as in Figure 5.

The following example illustrates the method of calculating aAcp.Assume a radiant section of the following characteristics :

Size of tubes 5" outside diameterCenter to center distance of tubes 10"Exposed length of tube 30 ft.Total number of tubes 60Arrangement of tubes, 2 rows on equilateral triangular spacingNumber of tubes per row 30

a=0.984, i.e., total to 2 rows

aAcp=0.984(750)=738 sq.ft. equivalent cold plane surface.

Fig. 5 Distribution of Heat to One or Two Rows of Tubes Mounted onRefractory Wall and Irradiated from One Side.

Tubes on equalateral triangular centers; ordinate expressed on basis of heat transfered from a plane to a plane replacing tubes, or to infinite number ofrows of tubes. These curves are a good approximation for tubes placed on rectangular or square centers

Fired Heater Design


EVALUATION OF THE FLAME EMISSIVITY, Pf

By definition, the emissivity of the flame is the ratio of the heat actually transmitted from the flame to the cold surface to the heat which would havebeen transmitted had the flame and the cold surface been perfect radiators. An illustrative example of this calculation is available in the literature.11

Figure No. 6 gives Pf in terms of (PCO2+PH2O)L, tg, and ts for cracked gas fuel and a tube emissivity of 0.90. This plot is also a good approximationfor fuel oil. The radiation cjharts of Hottel9 which were used in this calculation are included in the Appendix as Figures Nos. 13 and 14.

PCO2 = partial pressure of carbon dioxide in the flue gas, atmospheresPH2O = partial pressure of water vapor in the flue gas, atmospheresL = mean length of radiant beam in the combustion chamber, feetPL = atmospheres-feet

Values of PCO2 + PH2O and the air-fuel ratio for typical cracked gas and oil fuels have been plotted on Figure No. 7. The analysis of the fuels onwhich these calculations are based are indicated in the Appendix.

MEAN LENGTH OFRADIANT BEAMS

The mean length, L, of the radiant beam in the combustion chamber may be estimated from Table I.

Fired Heater Design


Table I.-Mean Length of Radiant Beams inVarious Gas Shapes12

From the values given by Hottel12 for the mean length, L, of radiant beamsin various gas shapes, the following approximate values have been

derived for use in practical oil heater design. These valuesmay be used until more exact methods are available.

Dimensional Ratio(length, width, height L

in any order)Rectangular Furnaces

1. 1-1-1 to 1-1-31-2-1 to 1-2-4 2/3(Furnace Volume)1/3

2. 1-1-4 to 1-1-inf 1 x smallest dimension3. 1-2-5 to 1-2-8 1.3 x smallest dimension4. 1-3-3 to 1-inf-inf 1.8 x smallest dimension

Cylindrical Furnaces5. d x d 2/3 x diameter6. d x 2d to d x inf 1 x diameter

EVALUATION OF THE OVERALL ECHANGE FACTOR, fLetAt = total area of furnace surfaces in the radiant section=

Acp + refractory surfaces unprotected by tubes, sq. ft

aAcp = equivalent cold plane surface, sq.ft.Ar = effective refractory surface, sq.ft. (Ar = At - aAcp)Pc = emissivity of the ultimate heat-receiving surface, assumed

=0.90Pf = emissivity of the flame.Frc = fraction of all the radiation emitted from all the refractory

in all directions, which, if not absorbed by the gas,would hit cold surface aAcp

The overall exchange factor, f, as defined by Hottel9, is then :

(18)

Where

Fired Heater Design


(19)

Af = Area of the flame bundle, sq. ft.In commercial furnaces Af may be considered equal to At, and equation (19) may be simplified to the form used in this study :

(20)

The exact evaluation10 of Frc is rather tedious. In an effort to simplify the evaluation of this factor, more than twenty furnaces differing as widely aspossible in design were studied, using the exact technique referred to above. It was found that for ratios of Ar/aAcp from 0 to 1, the value of Frc wasadequately given by the ratio aAcp/At. For ratios of Ar/aAcp from 3 to 6.5, Frc was very nearly equal to aAcp/Ar. Figure No. 8 embodies these resultsand gives f directly as a function of the ratio Ar/aAcp and the flame emissivity Pf.

Before discussing the results which prove the validity of the assumptions made in the development of the radiant equation, a descriptive example willbe given to illustrate the use of the general method.

EXAMPLE

Find the total net heat input (i.e., the enthalpy of the incoming fuel and air above 60° F., water as vapor) to the following furnace :

DataDimensions of combustion chamber 15' x 30' x 40'Tube outside diameter 5: O.D.Center to center spacing 10"Number of tubes in section 90 arranged in a single rowCircumferential tube surface 4710 sq. ft.Total wall area, Ar 4300 sq. ft. *

ConditionsNet heat input to oil 70,650,000 B.t.u./hr.Desired radiant rate 15,000 B.t.u./hr./sq.ft. circumferential surfaceCracked gas fuel 20,000 B.t.u./lb. (L.H.V.)Excess air 30%Temperature of air leaving preheater 460° F.Estimated tube skin temperature 1000° F.

Calculation of effective surface, aAcp Reference

Fired Heater Design


Center to center distance/tube O.D. 2a to one row 0.88 Fig. 5Acp = (90 tubes)(10"C/12)(40' long) 3,000 sq.ft. of Acp

aAcp = 0.88(3000) 2,640 sq.ft. of aAcp

Calculation of exchange factor, fRadiant section dimension ratio, 15/15 x 30/15 x 40/15 = 1 x 2 x 2.67L = 2/3(volume)1/3 = 2/3(15x30x40)1/3 17.5 feet Table IP, partial pressure CO2 + H2O 0.22 atmospheres Fig. 7PL = 0.22(17.5) 3.84 (atm.) (ft.)Assume tg (temp. flue gas leaving) 1,800° F.PF, flame emissivity 0.495 Fig. 6AR = Ar-aAcp = 4300-2640 1,660 sq.ft.AR/aAcp = 1600/2640 0.63f = 0.56 Fig. 8q/aAcpf = 15,000(4710/2640)(1/0.56) 47,900 B.t.u./hr./aAcpf

Calculation of Total Net Heat Input Results Referencetg 1,850° F. Fig. 2PF, as previously calculated ** is close enough 0.495t'F at 30% excess air, 460-60=400°air preheat, 1850° F. tg 3,620° F. Fig. 30.98 H/aAcpf 94,000 B.t.u./hr./aAcpf Fig. 2H/aAcp (94,000/0.98) x 0.56 53,700 B.t.u./hr./aAcp

H = Total net heat input (53,700)(2,640) 142,000,000 B.t.u./hr.* Area of opening to convection section equals 200 sq.ft. so Ar = 4500-200.** When assumed temperature of flue gases leaving radiant section is inerror by 100° or more, PF and f should be revised.

RESULTS

The results of the investigation are summarized in Tables II and III. Table II gives the characteristics of the furnaces studied and the ratio of the actualheat to the oil to that calculated by the proposed theoretical equation, as well as by the empirical equation of Wilson, Lobo and Hottel. Sketches of thegeneral types of furnaces studied are shown in Figures 16 through 22 in the Appendix. These should be considered as diagrammatic only.

Table II. - Characteristics of Furnaces and TestsTotal Total Mean Ratio:

Tube Circum Effective Furnace Effective LengthOutside Tube ferential Tube Wall Refractory Ratio Radiant Air Flue Gas No.of Actual/Calculated

Furnace Diameter Spacing TubeArea Area Surface Surface AR/Acp Beam Preheat Recirculation Fuel Tests Heat to Oil(h) (g)

Fired Heater Design


Symbol General O.D. C-C Ac aAcp AT AR L Empirical Theoretical

Unit Type Inches Inches Sq.Ft. Sq.Ft. Sq.Ft. Sq.Ft. Feet Equation Equation

*1 A 5 10 2,389 1,340 3,080 1,740 1.30 14.3 Yes &No Yes & No Gas 16 1.03 1.02

*2 B 4 6.75 1,496 756 3,271 1,515 2.00 19.6 Yes No Oil 17 0.93 0.94*3 C 5 10 2,945 2,255 3,855 1,600 0.71 17.0 No Gas 10 0.95 0.994 B 5 10 2,394 1,343 4,277 2,934 2.18 17.8 Yes No Gas 7 0.94 0.97*5 D 5 17.3(a) 4,443 2,303 3,362 1,059 0.46 24.0(c) Yes No Gas 3 0.92 1.00

6(d) E 5 9 3,060 1,608 3,174 1,566 0.97 12.8 No No Gas 2 1.02 0.997(d)#1 E 5.5 9.75 12,467(b) 3,610 6,560 2,950 0.82 22.2 No No Gas 1 1.18 1.117 #2 E 5 9.25 7,153 3,698 6,560 2,862 0.77 22.2 No No Gas 1 1.11 1.14*8 F 4 8.75 284 216 1,628 1,412 6.55 11.2 No No Gas 7 1.04 0.989 B 5 8.75 4,775 1,844 2,976 1,132 0.61 14.7 Yes No Gas 4 1.04 1.0310 G 4 8.75 1,347 465 1,875 1,410 3.04 11.2 No No Oil 3 0.94 0.9911 G 4 8.75 1,466 498 1,608 1,110 2.23 8.28(e) No No (f) 3 0.77 1.0712 B 5 8.75 2,314 1,197 3,423 2,226 1.86 15.9 No No Oil 2 0.98 1.0813 D 5 10.25 5,780 2,108 3,333 1,225 0.58 22.5(c) Yes No Gas 1 1.02 0.9914 D 5 10.25 5,780 2,108 3,049 941 0.45 22.5(c) Yes No Gas 1 0.94 0.9115 D 5 10.25 2,890 1,928 3,067 1,139 0.59 22.5(c) Yes No Gas 1 0.99 0.9316 D 5 10.25 5,780 2,108 3,049 941 0.45 22.5(c) Yes No Gas 1 0.99 0.9817 B 5 8.75 1,718 887 2,369 1,482 1.67 13.2 No No Gas 1 0.92 0.9418 B 5 8.75 1,867 965 2,143 1,178 1.22 12.6 No No Gas 3 0.96 1.0219 E 5.5 9.25 3,616 1,820 3,885 2,065 1.14 17.1 No No Oil 1 0.90 1.08

FOOTNOTES :(a) Two rows with center lines 2.62 inches apart.(b) Double row of tubes.(c) Circular furnace, L = diameter.(d) Double radiant type furnace.(e) L = 1.8 (minimum distance).(f) Products of combustion from furnace No. 10.(g) Wilson, Lobo, and Hottel Empirical Equation.(h) For sketches of general type of furnace see Figs. 16 through 22 in the Appendix.* Furnaces used by Wilson, Lobo and Hottel (2).

Table III. - Test Data and Calculations(b) RadiantSection (c) Rate of Heat Ratio:Actual/Calculated

Average (a) Bridge Temperatures Average (d) (e) Input Absorption Heat to OilRadiant Excess Wall Tube Overall TotalNet Hourly Pseudo- Heat (g)

Symbol Furnace RateTo Air Temper- Oil Oil Skin Flame Exchange Heat Heat Flame into 0.98H q Empirical TheoreticalUnit Fuel Test FirstRow ture In Out Temp. Emissivity Factor Input Capacity Temp. Oil aAcpf aAcpf Equation Equation

B.t.u./hr./ t'g ts H N t'f q

Sq.Ft. % °F. °F. °F. °F. Pf f 106B.t.u./hr.Btu/hr/

°F °F. 106B.t.u./hr. 106B.t.u./hr.

1 Gas 1 4,760 17.3 1,140 728 850 820 0.525 0.675 53.04 34,643 1,562 11.4(f) 57.40 12.60 1.04 1.012 6,440 113.8 1,220 700 865 817 0.415 0.585 42.21 21,528 1,980 15.4 52.80 19.60 1.04 1.14

Fired Heater Design


3 7,190 80.8 1,250 680 868 805 0.456 0.621 37.68 16,692 2,275 17.2 44.50 20.60 1.24 1.124 7,650 72.3 1,250 675 875 809 0.460 0.625 37.55 15,246 2,475 18.3 43.80 21.80 1.12 1.115 9,110 51.0 1,230 645 875 788 0.480 0.645 35.25 10,196 3,455 21.8 40.40 25.35 1.07 1.067 8,900 48.9 1,180 648 872 794 0.494 0.650 36.18 9,672 3,720 20.8 40.60 23.35 0.99 0.948 7,990 32.4 1,180 660 870 794 0.514 0.665 36.57 11,942 3,060 19.1 40.35 21.43 1.01 0.979 7,480 61.1 1,200 660 858 790 0.480 0.640 35.86 11,548 3,100 17.9 40.70 20.85 1.05 0.9310 6,440 122.0 1,215 680 850 795 0.419 0.590 38.05 17,211 2,225 15.4 47.10 19.43 0.98 1.0411 6,260 141.3 1,225 685 850 797 0.412 0.585 39.22 16,438 2,395 15.0 49.10 19.10 1.04 0.9212 5,440 178.0 1,225 700 843 803 0.395 0.565 44.32 22,715 1,970 13.0 57.00 17.07 0.94 0.9315 9,560 33.3 1,360 650 858 780 0.498 0.655 44.46 14,954 2,960 22.9 49.60 26.50 1.04 1.0616 11,030 30.5 1,440 650 885 793 0.485 0.641 51.22 16,889 3,040 26.4 58.40 30.75 0.99 1.0517 10,700 26.0 1,360 655 885 800 0.505 0.660 47.49 16,499 2,880 25.6 52.70 29.00 1.01 1.1218 6,470 24.4 1,250 728 865 822 0.520 0.670 65.32 36,228 1,823 15.5 71.15 17.24 0.91 0.9519 10,200 42.1 1,270 655 875 795 0.485 0.642 45.72 12,843 3,550 24.4 52.00 28.35 0.95 0.96

Avg .... 1.03 1.022 Oil 1 7,160 114 1,270 681(b) 717 0.49 0.720 24.58 10,300 2,395 10.73 44.10 19.72 0.99 1.00

2 4,200 184 1,260 688 715 0.501 0.780 20.94 11,300 1,873 6.30 37.10 11.70 0.77 0.873 4,840 154 1,225 689 717 0.494 0.725 19.55 9,560 2,065 7.24 34.90 13.18 0.87 0.914 7,720 38 1,415 692 726 0.585 0.772 23.55 7,640 3,080 11.58 39.40 19.78 0.91 0.905 7,520 30 1,410 694 725 0.643 0.800 22.16 7,060 3,130 11.24 35.80 18.59 0.92 0.916 7,890 51 1,450 702 735 0.570 0.770 25.46 8,690 2,935 11.80 42.90 20.20 0.91 0.897 7,600 74 1,420 703 733 0.556 0.763 26.71 10,180 2,535 11.39 45.20 19.70 0.89 0.948 7,590 83 1,440 704 735 0.541 0.750 27.78 10,540 2,640 11.36 47.70 20.00 0.89 0.899 4,800 175 1,175 699 730 0.512 0.735 19.28 10,000 1,950 7.18 33.80 12.89 0.94 0.9810 5,100 167 1,205 702 736 0.502 0.730 20.23 10,200 2,002 7.64 35.95 13.82 0.94 0.9711 4,920 69 1,200 680 716 0.585 0.772 14.58 5,650 2,590 7.37 24.40 12.61 0.94 0.9512 5,180 48 1,205 677 717 0.610 0.785 14.30 5,080 2,820 7.75 23.60 13.02 0.95 0.9613 5,050 100 1,185 692 728 0.557 0.763 16.13 6,860 2,363 7.55 27.40 13.08 0.95 0.9614 5,320 120 1,225 698 735 0.517 0.740 17.84 7,820 2,300 7.96 31.20 14.20 0.96 0.9715 6,500 106 1,270 694 726 0.525 0.743 23.40 10,120 2,323 9.73 40.70 17.30 0.94 0.9616 6,780 42 1,230 679 716 0.584 0.770 18.54 6,340 2,920 10.14 31.15 17.40 0.99 0.9917 6,740 68 1,300 684 720 0.561 0.768 20.64 7,630 2,720 10.09 35.15 17.48 0.97 0.96

Avg .... 0.93 0.943 Gas 1 8,360 55 1,390 749 927 884 0.475 0.557 46.93 15,300 3,060 24.66 36.60 19.60 0.98 0.99

2 8,000 105 1,430 765 923 889 0.425 0.517 56.41 22,700 2,493 23.61 47.40 20.25 0.95 0.993 9,010 35 1,490 758 947 900 0.492 0.570 50.32 14,900 3,380 26.61 38.40 20.75 0.94 0.944 9,160 33 1,490 762 944 900 0.495 0.573 51.86 15,820 3,270 27.03 39.40 20.95 0.93 0.955 8,860 66 1,430 764 944 898 0.450 0.538 56.90 21,100 2,700 26.17 46.00 21.58 0.94 1.006 11,850 89 1,455 752 948 897 0.490 0.570 64.96 20,300 3,200 34.93 49.50 27.18 1.03 1.047 10,520 50 1,440 749 948 896 0.475 0.557 62.22 21,050 2,960 31.04 48.60 24.73 0.98 1.028 9,650 55 1,430 746 948 894 0.474 0.556 60.56 21,200 2,860 29.36 47.40 23.40 0.96 1.0111 6,760 119 1,400 742 878 853 0.410 0.505 49.03 20,620 2,395 19.92 42.20 17.50 0.89 0.9612 7,990 92 1,450 753 878 857 0.430 0.520 52.50 19,920 2,645 23.56 43.90 20.08 0.93 0.98

Avg .... 0.95 0.994 Gas 1 7,840 44 1,454 711 937 842 0.492 0.740 38.33 12,254 3,120 18.78 36.95 18.90 0.95 0.92

Fired Heater Design


2 7,990 62 1,432 718 914 833 0.466 0.720 41.84 14,698 2,840 19.13 42.40 19.80 0.97 0.923 7,160 71 1,401 714 909 826 0.466 0.720 39.09 14,408 2,295 17.17 40.40 17.70 0.94 1.044 6,360 72 1,389 712 906 823 0.466 0.720 34.65 12,841 2,290 15.25 35.10 15.79 0.92 1.025 9,900 75 1,454 749 937 871 0.466 0.720 54.94 20,772 2,335 23.68 55.50 24.50 1.02 1.146 7,340 78 1,463 740 933 859 0.455 0.710 44.59 17,127 2,550 17.58 46.90 18.42 0.89 0.887 7,550 81 1,472 716 934 847 0.455 0.710 46.11 18,009 2,560 18.09 47.50 18.96 0.90 0.89

Avg .... 0.94 0.975 Gas 1 4,510 101 1,466 803 1,001 949 0.485 0.530 50.57 20,627 2,465 21.11 40.75 17.27 0.89 0.97

2 4,800 103 1,473 825 1,025 969 0.485 0.530 54.41 22,310 2,450 22.40 44.00 18.30 0.91 0.983 5,610 88 1,477 836 1,049 988 0.495 0.535 57.96 22,040 2,625 26.27 46.00 21.25 0.97 1.04

Avg .... 0.92 1.006 Gas 1 14,910 5.1 1,781 666 1,004 986(j) 0.470 0.595 88.56 22,740 3,840 45.66 90.60 47.80 1.04 1.00

2 14,840 6.4 1,789 664 1,006 990 0.470 0.595 90.04 23,344 3,840 45.46 92.10 47.40 1.03 0.98Avg .... 1.02 0.99

7 Gas 1 12,053 22 1,507 672 920 845 0.586 0.660 184.7 51,910 3,550 104.6 75.00 43.80 1.18 1.112 9,300 41 1,433 753 948 903 0.570 0.650 138.6 43,875 3,160 74.1 52.40 30.85 1.11 1.14

Avg .... 1.15 1.138 Gas 1 16,970(i) 128 598 818 880 0.323 0.762 21.45 16,958 2,090 4.82(f) 127.90 29.30 0.86 0.96

2 23,800 64 510 788 872 0.365 0.788 19.85 11,491 2,750 6.77 114.20 39.80 1.01 0.953 28,800 50 494 778 884 0.375 0.795 23.05 11,582 2,970 8.16 131.80 47.50 1.04 0.944 36,700 34 480 789 929 0.370 0.790 30.28 16,994 3,290 10.43 174.00 61.10 1.04 0.915 39,000 52 497 786 941 0.360 0.780 34.40 20,122 2,950 11.10 200.00 65.80 1.11 1.006 42,500 53 512 786 958 0.360 0.780 38.44 18,442 2,870 12.09 224.00 71.60 1.10 1.077 50,900 33 473 775 980 0.368 0.788 44.72 18,163 3,220 14.45 258.00 85.00 1.09 1.00

Avg .... 1.04 0.989 Gas 1 12,470 26 1,725 749 978 990(j) 0.480 0.545 81.56 21,200 3,823 44.60 79.50 44.50 1.05 1.03

2 12,450 32 1,652 745 973 995 0.471 0.540 83.01 23,000 3,600 44.63 81.60 44.90 1.08 1.073 11,900 16 1,786 741 977 1,000 0.480 0.545 79.07 20,150 3,910 42.71 77.00 42.50 1.01 1.004 11,530 46 1,711 759 975 1,007 0.445 0.516 85.90 25,850 3,320 41.48 88.30 43.50 1.03 1.04

Avg .... 1.04 1.0310 Oil 1 21,200 26 1,705 670 914 898 0.430 0.750 30.99 9,252 3,340 14.55 87.00 41.65 0.95 0.99

2 20,400 21 1,695 677 912 898 0.437 0.753 28.47 8,187 3,475 13.98 79.90 39.83 0.95 0.983 21,600 38 1,740 691 910 900 0.420 0.742 34.57 11,168 3,100 14.82 98.00 42.90 0.93 1.00

Avg .... 0.94 0.9911 (k) 1 3,140 111 1,037 573 670 682 0.390 0.665 15.82 11,701 1,388 8.67 46.90 11.10 0.67 1.08

2 4,320 74 1,038 570 677 686 0.425 0.691 13.92 8,312 1,702 5.07 39.65 14.72 0.87 1.163 3,840 91 1,103 593 691 703 0.395 0.667 19.06 12,276 1,585 5.35 56.25 13.51 0.77 0.98

Avg .... 0.77 1.0712 Oil 1 10,780 45 1,457 474 750 716 0.490 0.706 48.48 16,209 2,990 24.88 56.10 29.50 0.95 1.04

2 8,770 63 1,399 470 729 689 0.475 0.695 41.66 15,531 2,690 20.03 49.20 24.10 0.91 1.02Avg .... 0.93 1.03

13 Gas 1 9,300 17 1,560 712 915 897 0.590 0.631 56.36 13,786 4,060 34.53 41.45 25.90 1.02 0.9914 Gas 1 7,060 28 1,700 738 903 897 0.560 0.595 46.10 11,626 3,940 26.09 36.00 20.80 0.94 0.9115 Gas 1 9,150 15 1,750 734 901 894 0.580 0.630 52.46 12,080 4,310 31.01 42.35 25.50 0.99 0.9316 Gas 1 9,300 26 1,623 704 898 883 0.565 0.595 58.46 14,630 3,980 34.45 45.60 27.45 0.99 0.98

Fired Heater Design


Avg .... 0.98 0.9617 Gas 1 9,810 59 1,505 712 892 872 0.415 0.630 42.19 15,000 2,815 16.89 74.00 30.20 0.92 0.9418 Gas 1 9,330 57 1,480 737 950 925 0.417 0.580 39.99 14,062 2,850 17.41 70.10 31.20 0.97 1.00

2 9,350 59 1,482 735 960 930 0.417 0.580 40.60 14,402 2,820 17.46 70.50 31.20 0.96 1.013 8,310 86 1,415 685 905 870 0.395 0.560 39.79 16,222 2,460 15.52 72.10 28.75 0.95 1.05

Avg .... 0.96 1.0219 Oil 1 9,120 95 1,382 825 850 879 0.45 0.596 87.50 37,350 2,360 32.97 79.00 30.38 0.90 1.08

Grand Avg .... 0.969 0.992

(a) At bridge wall. Average Deviation ................ 6.85 % 5.30 %(b) With high velocity thermocouples. Maximum Deviation ................ 33 % 16 %(c) Estimated from average oil temperature, inside coefficient with allowance for coke deposit. % of Tests Between 0 and 2 % Deviation.... 17.7 % 31.8 %(d) Net heat input from combustion of the fuel, air preheat, and recirculation if any. 0 and 4 % Deviation.... 36.5 % 53.0 %(e) Based on flue gas duty, except for Furnaces Nos. 1 and 8.(f) Estimated from oil side. Applies only to furnaces Nos. 1 and 8.(g) Wilson, Lobo, and Hottel Empirical Radiant Equation.(h) Temperatures for Furnace No. 2 are average oil temperatures.(i) Based on exposed tube surface.(j) Actual tube skin thermocouple measurements.(k) Fuel = Products of combustion from Furnace No. 10.

The actual heat to the oil is obtained by subtracting the enthalpy of the flue gas leaving the radiant section from the enthalpy of the entering fuel and air, and then subtracting the estimated external losses, plus the direct radiant heatfrom the combustion chamber absorbed by the first rows of the convection section. The latter item is obtained by a convection section heat balance , gas side versus oil side, in which the heat lost by the gas is considered between theactually measured true gas temperature of the gases entering and leaving the section. A summary of the test data required and a short outline of the method of calculation are included in the Appendix.

Table III gives a summary of the test data and calculations for all eighty-five tests which have been used as an independent check on the validity of the derived theoretical equation. The ratio of the actual heat absorbed by the oil in theradiant section to that predicted by both the empirical and theoretical equations is given for each of the individual tests. The deviations of any test from the average deviations for a given furnace can thus be readily seen.

DISCUSSION OF RESULTS

In order to arrive at a definite conclusion regarding the respective merits of the Wilson, Lobo and Hottel empirical equation and the theoretical equation, the heat absorbed by the oil in the radiant section as predicted by these twoequations has been compared to the actually observed heat absorption.

Fired Heater Design


The radiant section will be defined as that section in which the heat is liberated and in which the heat transfer is primarily by radiation from the hot gas mass and the hot refractory surfaces. The cold or ultimate heat-receiving surfaceis considered to consist of those tubes which can "see" to a greater or less extent the main gas mass. This emphasis has been made because in the case of certain furnaces the first rows of tubes in the convection section can see themain gas mass. The plane area * of these tubes, Acp, must be considered as a part of the radiant section equivalent cold plane surface, aAcp. In furnaces where the convection section is placed behind a bridge wall, out of sight of themain gas mass, the projected area of the convection section is not considered to be part of the radiant section cold surface.

*In a bank of three or more rows of tubes a = 1.0, and Acp = aAcp.

It may be seen from Table III that in practically every case the equation presented in this paper correlates the test data better than the empirical equation even though the furnace tests used to determine the constants of the empiricalequation are included in the present data. The maximum deviation has been reduced from 335 to 16%. These facts are perhaps best illustrated by Figures Nos. 9 and 10, which show the spread of the data using both methods ofcorrelation. Inasmuch as the data represent plant tests, it is suspected that the larger deviations may be due to inaccuracies in the data and not to any fundamental fault in the radiant equation. It is significant that using the theoreticalequation the greatest deviations are not confined to any one furnace but seem to be well distributed. Again, furnace No. 4, the worst case, shows deviations of -11% and -12% and +14%, indicating that the data on this one furnace areprobably less reliable than the average. Actually, the temperature of the gases leaving the radiant section of this furnace was determined at only two points instead of by a complete traverse. Since in many cases it is difficult to judgeexactly the accuracy of the plant data, no attempt has been made to segregate and give more weight to the better data. The number of tests available for this study is hardly large enough for a rigid statistical analysis, but for somegeneralizations are justified. For instance, considering the data in their entirety, Figures Nos. 10 and 12(A) indicate that the deviations between the observed and the calculated heat absorption occur in a random manner and are notpeculiar to any one fiurnace, even though the ratio of effective refractory to effective cold surface, (Ar/aAcp), varied fourteen-fold for the furnaces investigated.

Figure 11 (B) (C) (D) and Figure 12 (B) (C) (D) are given in order to permit visualizing the effect of some of the variables on the results obtained by the two correlations.

The effect of excess air is shown in Figures 11 (B) and 12 (B). It should be remembered that although the percentage of excess air varied less than 10% to more than 170%, other factors may likewise have been varying at the sametime. In general, the empirical equation appears to predict correctly the heat absorption by the oil in the radiant section in the excess air range from 10% to 80%, the more usual commercial range. Above 80% it predicts heatabsorptions which are 10% to 13% too high. Over this range, 10% to 170%, the theoretical equation shows no significant trend. As previously pointed out, the use of an air-fuel ratio is open to criticism and the trend may be due tothis factor.

Figures 11 (C) and 12 (C) classify the data according to average radiant rate based on circumferential tube surface, B.t.u. per hour per sq. ft. In those furnaces with a double row of radiant tubes, the rate has been taken as the averagefirst row rate. Here, again, the theoretical equation shows no significant trend over the range 3,000 to 51,000 B.t.u. per hour per sq. ft. The empirical equation shows signs of breaking down at rates below 4,000 and predicts radiantsection heat absorption 10% in excess of the true figure at that point. Only two tests are available at rates between 3,000 and 4,000 but they confirm the trend and indicate that the heat absorbed by the oil, as calculated by theempirical equation, may be almost 40% high in this range.

Figures 11 (D) and 12 (D) give another indication of the range of the furnace data, but have significance only in that they give an indication of the theoretical flame temperature. These figures show that over the wide range of t'f, the

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pseudo-theoretical flame temperature, the deviations have no definite trend. It is obvious, therefore, that petroleum heaters can be designed by means of the new equation for fuels of widely different heating values as a low pseudo-flame temperature may mean either a fuel of low grade, or a high heating value fuel degraded with excess air or recirculated inert gas. Since most of these tests have been made with very similar fuels, the trend shown in Figure 11 (D)is probably due to the composite effect of rate and excess air discussed above.

CONCLUSIONS AND RECOMMENDATIONS

The theoretical radiant equation as developed in this paper is recommended for the solution of heat transfer problems in the radiant section of tubular heaters using fuel oil or gaseous fuel.

The equation is believed to be valid for any condition of air preheat, inert gas recirculation, percentage of excess air, or radiant rate. The effect of furnace volume on the amount of heat liberation necessary to maintain any given radiantrate is adequately handled by the use of the flame emissivity as outlined previously. The results indicate that the f plot represents an accurate and simple method of simultaneously allowing for the effect of flame emissivity and theamount of refractory surface present in the radiant section.

The Wilson, Lobo, and Hottel empirical equation is not recommended for use on furnaces differing widely from those used to determine the constants of the equation. However, the equation may be used with safety on box-type heaters(see Figures 16, 17, 18, 20 and 21) when the greatest accuracy is not required and subject to the following qualifications :

1. Fuel oil or cracked refinery gas as fuel;2. Radiant rates between 5,000 and 30,000 B.t.u./hr./sq.ft. of circumferential tube area ;3. Per cent excess air between 5% and 80%;4. Tube skin temperatures not closer than 400° F, to the temperature of the flue gas leaving the radiant section ;5. Length of the radiant beam, L, greater than 15 feet.

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NOMENCLATURE

Ao = total outside tube area exposed to radiation, sq.ft.AR = effective refractory area, sq.ft.A'R = actual refractory area, sq.ft.AT = total wall area in combustion section, sq.ft.Acp = area of plane replacing tubes, sq.ft.C = actual firing rate of fuel/sq.ft. of exposed tube area, lbs./hr./sq.ft.Co = equivalent firing rate of good bituminous coal/sq.ft. of projected tube area, lbs./hr./sq.ft.CA = firing rate based on projected tube area, lbs./hr./sq.ft.E = effectiveness factor of the cold surfaceFrc = fraction of all the radiation emitted from all the refractory in all directions, which, if not absorbed by the gas, would hit cold surface, aAcp

FS = angle-emissivity factorG = air-fuel ratio, lbs. air /lb. of fuelH = total net heat input to combustion chamber, B.t.u./hr.hc = convection coefficient, B.t.u./hr./sq.ft./°F.L = mean length of radiant beam, feetN = hourly heat capacity, B.t.u./hr./°F.Pe = emissivity of tube surfacePf = emissivity of flamePCO2 = partial pressure of CO2, atmospheresPH2O = partial pressure of water vapor, atmospheresMCPavg. = mean molal heat capacity between 60° and temperature, tgQ = net heat liberated from combustion of the fuel, B.t.u./hourq = heat transferred to oil, B.t.u./hourq' = heat transferred by radiation, B.t.u./hourq" = net heat transferred to all surfaces in the radiant section, B.t.u./hourSe = equivalent "effective" heating surface, sq.ft.Tg = temperature of products of combustion leaving combustion chamber, °F. + 460°Ts = tube skin temperature, °F. + 460°t = temperature, °F.tg = temperature of flue gas leaving combustion chamber, °F.t'f = Pseudo-flame temperature, °F.a = factor by which Acp must be reduced to obtain effective cold surface, aAcp (effective tube area)

b = fraction of total net heat input lost from the external furnace wallsf = overall exchange factorm = fraction of heat available above 60° F. absorbed by cold surfaces in the combustion chamber

Fired Heater Design


LITERATURE CITED1. Hottel, Trans. A.I.Ch.E. 19, 173 (1927); Ind. Eng. Chem. 19, 888 (1927)2. Wilson, Lobo, Hottel, Ind. Eng. Chem. 24, 486 (1932)3. Hudson, Engineer 70, 523 (1890)4. Orrok, Trans. A.S.M.E. 1148 (1925)5. Hottel, Unpublished notes on Radiant Heat Transmission, Mass. Inst. of Tech. (1938)6. DeBaufre, Trans. A.S.M.E. 53 (14), 253 (1931)7. Mekler, Nat. Pet. News 30 (30), R355 (1938)8. Hottel, Trans. A.S.M.E., Fuels Steam Power 53 (14), 265 (1931)9. Hottel, Unpublished notes on Radiant Heat Transmission, Mass. Inst. of Tech. (1938)10. Hottel, in Chem. Eng. Handbook 1, 888 (1934)11. Hottel, Ibid. 1, 910 (1934)12. Hottel, Ibid. 1, 892 (1934)

ACKNOWLEDGMENT

The authors gratefully acknowledge the helpful suggestions offered during the course of the investigation by Mr. J. H. Rickerman.

APPENDIXSTANDARD FUEL COMPOSITION

STANDARD CRACKED GAS FUEL

Component Mol PerCentCH4 ................................... 37.0

C2H4 ................................... 4.0C2H6 ................................... 22.0C3H6 ................................... 8.0C3H8 ................................... 23.0C4H10 ................................... 6.0

____100.0

Lower heating value per lb. at 60° F. 20,557 B.t.u. (Higher heating value 22,400 B.t.u.)Specific gravity relative to air, 1.06Specific volume at 60° F. and 14.7 lb./sq.in. 0.0807 lb./ft.3Combustion calculations are based on air at 60° F. and 50% relative humidity.

OIL FUEL

Component Wt. PerCentC ................................... 85.0H2 ................................... 12.0S ................................... 1.5

O2 ................................... 0.7N2 ................................... 0.8

Fired Heater Design


____100.0

Lower heating value per lb. at 60° F. 17,130 B.t.u.Steam for atomization, 0.3 lb./lb. fuel oilAir at 60° F. and 50% relative humidity.

TEST DATA REQUIRED FOR DETERMINATION OF HEAT ABSORBED

BY OIL IN RADIANT SECTION

A. Quantities:1. Fuel.2. Oil through furnace.3. Steam used for atomization, if any.

B. Temperatures:1. Oil to and from various sections of furnace.2. Flue gas from radiant section, determined by high velocity couple traverse, reading being taken about every two feet across furnace.

3. Flue gas from convection section or after bank of convection tubes through which combustion gases first pass, determined by high velocitycouple traverse.

4. Air, both atmospheric and preheated, if any.5. Fuel.6. Surface of furnace for estimation of radiant losses.7. Steam used for atomization, if any.

C. Analysis:1. Fuel, heating value and proximate analysis.

2. Flue gas from radiant section by Orsat analysis of samples drawn through water-cooled sampling tube at intervals comparable to those used intemperature measurements.

3. Flue gas from same convection section section bank after which temperature (3) was measured, sample taken and analized as above.D. Humidity of Atmospheric Air.

METHOD OF CALCULATION

Due to the fact that in petroleum heaters it is often difficult to determine accurately the heat absorbed by the oil in the radiant section from the oil side because of unknown heat of reaction, vaporization, etc., it is essential in mostcases to obtain this figure by heat balance from the flue gas side, determining also by heat balance, as mentioned in the paper, any direct radiation from the combustion box to the convection section. Thus, the balance may be shown asfollows:

Heat Input:1. Heat of combustion of fuel.2. Heat in air used for combustion.3. Heat in steam used for atomization, if any.4. Heat in recirculated flue gases, if any.

Fired Heater Design


Heat Output:1. Heat in flue gases leaving radiant section.2. Heat to oil in radiant section (determined by difference).3. Heat to external losses.4. Heat radiated from combustion box to convection section (determined by heat balance on part or all of convection section).

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