Hydrocarbon Processing - August 2021 - 72

Heat Transfer
Qr, max = Fc
where,
FC
FT
× FL × FT × Qr, avg
= Circumferential heat flux variations
FL = Longitudinal heat flux variations
= The effect of tube metal temperature on the radiant
heat flux
Qr, avg = The average radiant heat flux for the outside surface
Qr, max = The maximum radiant heat flux for the outside
surface.
Estimation of factors impacting peak heat flux calculation.
Descriptions of factors follow below.
Circumferential heat flux factor (FC
). Circumferential
heat flux is a function of coil geometry, layout and firing arrangement
(single-fired vs. double-fired), shown in FIG. 2, and
is estimated from Figure B.1, " Ratio of maximum local to average
heat flux, " provided in API 530.1
value of FC
This graph provides the
outside diameter. Note: Single-fired tubes have higher FC
from the ratio of tube center-center spacing to tube
compared
to double-fired tubes-in single firing, both sides are not
exposed to the same intensity of radiations, leading to higher
temperatures on one side of the tube.
Longitudinal heat flux factor (FL
path, as discussed above, and depends on tube length, tube layout
and flame profile. Vertical tube heaters have higher FL
). As defined in API 530,1
FL is used to account for variations in heat flux along the flame
compared
to horizontal heaters where burners are provided along the tube
length. Common values between 1 and 1.5 are used, depending
on the firebox dimensions and flame aspect ratios. Computational
fluid dynamics (CFD) modeling, as shown in FIG. 3, may
also be used to estimate this factor for new heater configurations.
Tube metal temperature factor (FT
). API 530 provides the
following correlation (Eq. 2) for estimating the tube metal temperature
factor FT
FT = (Tg,ave
4 - Ttm
for most applications:
4) / (Tg,ave
4 - Ttm,ave
4)
(2)
(1)
where,
Tg,ave
Ttm
= the average flue-gas temperature, expressed in
Kelvin (°R), in the radiant section
= the TMT, expressed in Kelvin (°R), at the point
under consideration
Ttm,ave = the average TMT, expressed in Kelvin (°R),
in the radiant section.
It is important to note that:
* FT
* FT > 1 near areas of lower TMT.
For most applications, FT
< 1 near the coil outlet or areas of maximum TMT
is estimated to be in the range of
0.9-1. However, for certain applications, dependent on the service-more
precisely, the process fluid temperature difference
at the inlet and outlet of the radiant section-FT
as 0.7. Therefore, ignorance of FT
can result in providing a huge
heat transfer area and subsequently limiting heater turndown.
To illustrate FT
are elaborated.
Case study 1. A hydrogen heater in a hydroprocessing unit is
considered for evaluation of the FT
factor. The heater has an inlet
and outlet temperature of 326°C (619°F) and 566°C (1,051°F),
respectively. The heater is designed for an average radiant heat
flux of 7,800 Btu/hr/ft2
for double-firing arrangement. The
tube size is a 5.563-in. outer diameter (OD) and tubes are
placed at 2D center-center spacing. The tubes are placed vertically
at the center of the cylindrical furnace in a cruciform-type
arrangement. The outlet temperature is considered as the bulk
fluid temperature for calculation. The weld-weld tube length is
47 ft. The peak flux for this heater is estimated as:
* FC
factor = 1.2
° Tubes are placed in 2D spacing in a double-fired
arrangement
° Tube OD/tube spacing = 10/5.563 = 1.8
° Refer to API 530 Figure B.1 to calculate FC
* FL factor = 1.4
Flame radiation
Peak flux/average
heat flux = 1.8
Flame radiation
Flame radiation
Peak flux/average
heat flux = 1.2
Refractory wall
Tubes
Single-fired heater
FIG. 2. Circumferential heat flux distribution in fired heaters.
72 AUGUST 2021 | HydrocarbonProcessing.com
Tubes
(°F)
Double-fired heater
FIG. 3. Sample CFD modeling TMT contours
in a horizontal box heater.
985
970
955
940
925
910
895
880
865
850
as 1.2.
significance, the following two case studies
can be as low
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