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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-five performance tests on nineteen
furnaces differing widely in amount and arrangement of refractory
cold surfaces. Operating conditions are available on furnaces with
and without 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 are correlated 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 the empirical 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 and higher percentages of heat-receiving
surface per unit of refractory surface, this investigation has been
initiated to study the effect of these variables and 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 and recirculation 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. of circumferential tube area. The furnaces
themselves were square, rectangular, or cylindrical in shape and
varied widely in arrangement of surfaces; the ratio 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 a number
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 observed radiant section duties are well within
the probable accuracy of the data. The average deviations of the
predicted heat to the oil in the radiant section from the observed
are 5.3% as compared to 6.85% when using the Wilson, Lobo, and
Hottel empirical equation. The maximum deviation has been reduced
from 33% to 16%. The data indicate that the larger deviations
occurring when using the empirical equation are partly due to
break-down of the 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 empirical equation is seriously in error when
applied to furnaces operating tube skin temperatures above 1000° F.,
as well as in furnaces having a low percentage of refractory surface
and low values of PL, the product of partial pressure of the
radiating constituents of the flue gas and the mean beam length of
the radiating beam. The data available do not indicate any
restriction which should be placed on the use of the theoretical
equation herein presented.
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 higher percentages of heat-receiving
surface per unit of refractory surface, this investigation has been
initiated to study the effect of these variables and 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, certain generalizations and fundamental principles are fairly
well established and can be used to advantage in solving radiant
heat transfer problems. Some of these 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 by heat 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 the molecules 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 in it.
Incandescent soot particles are a source of some radiation, but with
fuels and burners commonly used in the petroleum industry,
combustion usually results in a practically non-luminous flame. Oil
fuels tend to give a more luminous flame than refinery gas at the
usual percentages of excess air 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 oil flames, 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 the refractory because the current trend is to fill the
radiant section with cold tube surface in the interest of economy.
Since the radiating constituents in the 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
temperature of the gas and cold surfaces. One measure of their
number is their partial pressure. Another measure of their number is
the mean length of the radiating beam in the gas mass. Hottel 1 has
shown that the product PL, atmospheres-feet, expresses these two
facts and permits the data on the radiation 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, especially in high radiant rate furnaces. This
convection transfer is more important in low rate furnacesbecause
heat transfer by convection is proportional to the temperature
difference Tg - Ts , between flue gas and cold
surface, whereas the radiant heat transfer is proportional to the
difference T4g - 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 illustrate the basic approach several of these empirical
treatments are briefly summarized and their outstanding limitations
described. A more complete review of this earlier lititure has been
made in a previous publication.
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