Hydrocarbon Processing - March 2021 - 62

Heat Transfer
pipe, resulting in a strong tendency toward stratified flow with resulting higher
temperature on the upper pipe surface.
The major sources of temperature
non-uniformity result from an unavoidable combination of geometry and physics. The burner flames and hot flue gas
transfer more radiant heat to the flamefacing surface of the coil. Heaters with
burners mounted on one or both sides of
the coil exhibit this non-uniformity. The
measure of this non-uniformity is known
as the circumferential flux factor and has
been well-characterized. As combustion
releases heat from the burner flame, an
additional longitudinal flux factor exists.
Engineers have been unable to characterize the longitudinal flux factor in a general sense because it is heater and burner
dependent. FIG. 3 shows an example of
single-fired tubes with a high-longitu-

dinal variation in flux and the resulting
peak-to-average flux ratio of 2.3. This flux
ratio translates to a 16.1°C (61°F) higher
film temperature and a 37.8°C (100°F)
higher tube metal temperature in example calculations.
Variation in heat transfer to the process fluid comes from both within and
without the process coil. So, what is to be
done? Variation in the physical properties
of the fluid that are driven by vaporization inside the coil plays a strong role in
the local tube metal temperature. It is also
apparent that physics and geometry of the
flue gas side drive non-uniformity from
the outside the coil. A common method
of increasing homogeneity in a process
is to increase the mixing of the constituents. One can show through simulation
that properly designed tube inserts can
improve process homogeneity. This im-

provement can, in turn, be used to reduce
tube metal temperatures, increase yield
and increase heater capacity.
Simulation results: Improved area
goodness factor for tube inserts. In-

creasing the mixing inside a process coil
comes at a cost: the pressure drop through
the system also increases. The process
fluid diffusion inside the heater tube can
be estimated by using heat transfer as a
surrogate measure. To measure the relative effectiveness of various inserts, stepchange designs were simulated in combination with automated optimization for
thousands of combinations of geometric
parameters. The relative merit of each
design was judged by comparing the area
goodness factor, or the Colburn factor (j)
divided by the Fanning friction factor ( f ).
The final optimized design has a 30%
increase in area goodness factor vs. traditional twisted tapes. The practical implication is that by using an optimized design,
more process mixing with lower pressure
drop can be achieved. A key parameter in
twisted tape design is the twist-pitch, or
the number of pipe diameters required
for the twisted tape to make a helical
revolution within a length of the tape. FIG.
4 shows a comparison in the simulated
area goodness factor for both traditional
twisted tapes and the optimized design vs.
increasing twist pitch.
Simulation results: Multiphase flow
through a horizontal return. Simula-

tions comparing the optimized design to
an empty tube demonstrate that the incoil mixing translates to increased process homogeneity for multiphase flows.
FIG. 5 shows the predicted convection
heat transfer coefficient over the entire
tube surface and liquid volume frac-

FIG. 2. An example heat transfer coefficient vs. temperature differential for a multiphase
horizontal pipe and flow regime.

Circumferential flux factor, CFF
Refractory
wall

Tubes

Longitudinal flux factor, CFF

Average heat flux
(␾)

Tubes

Radiating
plane
␾ 60°
␾ average = 1.8

MARCH 2021 | HydrocarbonProcessing.com

Average flux profile
(␾)

␾ max
␾ average = up to 2.4

2.3 peak/average flux

Actual flux
profile

FIG. 3. Flux factors used in heater tube temperature calculations.

Average heat flux
(␾)

␾ max
␾ average = 1.05 to 1.3

Actual flux
profile

1.8 CFF

Overall flux non-uniformity

1.3 LFF

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Hydrocarbon Processing - March 2021

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