Page 244 - Chemical Process Equipment - Selection and Design

214 HEAT TRANSFER AND HEAT EXCHANGERS

EXAMPLE 8.13 tube spacings the peak temperatures are:
Peak Temperatures
An average flux rate is 12,00OBtu/(hr)(sqft) and the inside film Center-to-center/diameter 1 1.5 2 2.5 3
coefficient is 200 Btu/(hr)(sqft)("F). At the position where the Peak ("F) 1036 982 958 948 9.22
average process temperature is 850"F, the peak inside film For heavy liquid hydrocarbons the upper limit of 950°F often is
temperature is given by T = 850 + 12,000"R/200. At the several adopted.

convection, and heat recovery sections of the heater to the heat Pertinent equations and other relations are summarized in
released by combustion. The released heat is based on the lower Table 8.16, and a detailed stepwise procedure is listed in Table
heating value of the fuel and ambient temperature. With standard 8.17. A specific case is worked out in detail in Example 8.15.
burners, efficiencies may be in the range 60-80%; with radiant Basically, a heater configuration and size and some aspects of the
panels, 8042%. Within broad limits, any specified efficiency can be performance are assumed in advance. Then calculations are made
attained by controlling excess air and the extent of recovery of of the heat transfer that can be realized in such equipment.
waste heat. Adjustments to the design are made as needed and the process
An economical apportionment of heat absorption between the calculations repeated. Details are given in the introduction to
radiant and convection zones is about 75% in the radiant zone. This Example 8.16. Figures 8.20, 8.21, and 8.22 pertain to this example.
can be controlled in part by recirculation of flue gases into the Some of the approximations used here were developed by
radiant chamber, as shown in Figure 8.19(b). Wimpress (1963); his graphs were converted to equation form for
Because of practical limitations on numbers and possible convenience. Background and more accurate methods are treated
locations of burners and because of variations in process notably by Lobo and Evans (1939) and more briefly by Kern (1950)
temperatures, the distribution of radiant flux in a combustion and Ganapathy (1982). Charts of gas emissivity more elaborate than
chamber is not uniform. In many cases, the effect of such Figure 8.23 appear in these references.
nonuniformity is not important, but for sensitive and chemically An early relation between the heat absorption Q in a radiant
reacting systems it may need to be taken into account. A method of zone of a heater, the heat release Qf, the effective surface A, and
estimating quickly a flux distribution in a heater of known the air/fuel ratio R lb/lb is due to Wilson, Lobo, and Hottel [Znd.
configuration is illustrated by Nelson (1958, p. 610). A desired Eng. Chem. 24,486, (1932)l:
pattern can be achieved best in a long narrow heater with a
multiplicity of burners, as on Figure 17.16 for instance, or with a (8.45)
multiplicity of chambers. A procedure for design of a plug flow
heater is outlined in the Heat Exchanger Design Handbook (1983, Although it is a great simplification, this equation has some utility in
3.11.5). For most practical purposes, however, it is adequate to appraising directional effects of changes in the variables. Example
assume that the gas temperature and the heat flux are constant 8.16 considers changes in performance with changes in excess air.
throughout the radiant chamber. Since the heat transfer is Heat transfer in the radiant zone of a fired heater occurs largely
predominantly radiative and varies with the fourth power of the by radiation from the flue gas (90% or so) but also significantly by
absolute temperature, the effect of even substantial variation in convection. The combined effect is represented by
stock temperature on flux distribution is not significant. Example
8.14 studies this problem. (8.46)

DESIGN OF FIRED HEATERS where Tg and T, are absolute temperatures of the gas and the
receiving surface. The radiative properties of a gas depend on its
The design and rating of a fired heater is a moderately complex
operation. Here only the completely mixed model will be treated. chemical nature, its concentration, and the temperature. In the
For this reason and because of other generalizations, the method to thermal range, radiation of flue gas is significant only from the
be described affords only an approximation of equipment size and triatomic molecules H,O, CO,, and SO,, although the amount of
performance. Just what the accuracy is, it is hard to say. Even the the last is small and usually neglected. With fuels having the
composition C,H,,
the ratio of partial pressures is pHzo/pcOz = 1.
relatively elaborate method of Lobo and Evans (1939) is able to In Figure 8.23, the emissivity of such a gas is represented as a
predict actual performance only within a maximum deviation of function of temperature and the product PL of the partial pressures
16%.
of water and carbon dioxide and the path of travel defined by the
mean beam length. Item 8 of Table 8.16 is a curve fit of such data.
When other pertinent factors are included and an approxima-
tion is introduced for the relatively minor convection term, the heat
EXAMPLE 8.14 transfer equation may be written
Effect of Stock Temperature Variation
A combustion chamber is at 2260"R, a stock enters at 1060"R and Q/aA,F = 1730[(T,/1000)4 - (z/1000)4] + 7(T, - q). (8.47)
leaves at 1360"R. Accordingly, the heat fluxes at the inlet and outlet
are approximately in the ratio (2.264 - 1.064)/2.264 - 1.364) = Here the absorptivity depends on the spacing of the tubes and is
1.095. The small effect of even greater variation in flux on a mild given by item 5 of Table 8.16. The cold plane area A, is the
cracking operation is illustrated in Figure 8.22. product of the number of tubes by their lengths and by the
center-to-center spacing. The combination aA, is equal to the area
of an ideal black plane that has the same absorptivity as the tube