Chemical Engineering June 2018 - 61

Surface
Gas temp in ±5°C
Gas temp out ±5°C
TABLE 2. DETAILED BOILER PERFORMANCE - AT 100% LOAD
Screen
1,360
1,072
Final SH
1,072
892
Gas spec. heat, Kcal/kg°C
Duty, MM Kcal/h
U, Kcal/m2h°C
Surface area, m2
LMTD, °C
0.3328
11.78
117.81
105
953
Gas pressure drop, mm wc 55.22
Max gas velocity, m/s
Tube wall temp ±5°C
Fin tip temp ±5°C
Weight, kg
51
322
322
Fluid temp in, ˚C
Fluid temp out ±5°C
Pressure drop, kg/cm2
Fluid velocity, m/s
Fluid heat transfer coeff.
Fouling factor, gas
Fouling factor, fluid
Spray, kg/h
2,774
222
256
0.00
9780
0.0002
0.0002
3,260
need it in the future.
I have experienced this problem
when plants contact me to solve
problems related to underperforming
steam systems and lower-thanexpected
efficiency. The problems
include boiler circulation issues, superheater
or economizer tube failures,
or underperforming steam generators
and waste heat boilers. The
tube geometry data are either unavailable
or are not clear and have to
be " made up " in order to evaluate the
thermal performance. In some cases,
I have also seen drawings that should
show tube spacing or the number of
streams, but nevertheless is not provided.
In other cases, the thermal performance
information given is sketchy
and without details. This situation is
like buying a gadget without an owner's
manual and trying to figure out a
solution when the gadget fails.
There is a clear need for process
and plant engineers to become more
familiar with basic boiler calculations,
as well as with the data that they
should demand to obtain from boiler
and HRSG suppliers.
Basic energy-transfer equations
The basic equation for energy transfer
in a boiler component is given by
Equations (1) and (2).
Q = UA∆T
(1)
∆T is log mean temperature difference
(LMTD; nomenclature on p. 58).
If A is based on the tube inner sur60
face,
then U should also be based
on tube inner surface. Expressed as
a equation, it would be the following:
UiAi = UoAo = Q/∆T
(2)
If a heat-transfer component receives
external radiation from the
furnace or cavity, then:
Q - Qr = Qc + Qn = UA∆T
(3)
The energy lost by the hot fluegas
stream is absorbed by the colder
fluid (steam or water), as shown in
the equation below:
Wh ∆hh = Wc ∆hc = Q
(4)
This equation neglects heat losses
from the casing, which are typically
0.5 to 1.0%. Generally, the higher
the boiler duty, the lower the heat
loss percentage.
In all sizing or performance calculations,
U (the overall heat-transfer
coefficient) must be computed. For
tubes with extended surfaces, the
following equations apply:
1/Uo = (At/Ai)/hi + ffi(At/Ai) + ffo +
(At/Aw) (d/24Km) ln(d/di) + 1/hoη
(5)
If plain tubes are used, Equation
(5) may be simplified to the following
Equation (6):
1/Uo = d/di/hi + ffi(d/di) + (d/24Km)
ln (d/di) + ffo + 1/ho
(6)
0.3244
7.16
109.29
103
639
83.47
49
511
511
3,298
286
400
0.50
24.4
1299
0.0002
0.0002
Pry SH
892
778
0.3163
4.44
104.92
77
550
54.63
43
386
386
2,473
256
313
0.71
26.9
1799
0.0002
0.0002
Evaporator
778
465
0.3024
11.60
105.23
322
343
97.00
33
284
284
8,506
222
256
0.00
9780
0.0002
0.0002
Cleaver Brooks
Economizer
465
154
0.2815
10.78
40.61
2395
111
45.10
16
123
136
16,071
116
222
0.93
1.7
9390
0.0002
0.0002
FIGURE 4. The photograph shows the exterior of an
elevated-drum steam generator for large capacity
The above equations may be
used while sizing or evaluating the
performance of water-tube boilers,
superheaters, economizers and firetube
boilers.
Which coefficient governs U?
The gas-side heat-transfer coefficient
governs the performance
of boiler components, such as the
evaporator, economizer, superheater
and gas-fluid heaters. Why is this
important to know? When simulating
the performance of boiler components
or of the boiler as a whole,
the effect of gas-side parameters
will govern the overall performance,
while the steam-water-side parameters
will have minimal impact. Therefore,
concentrating on gas-side data
will enable engineers to perform the
analysis for off-design performance
rather quickly, instead of having to
evaluate both gas- and steam-side
heat-transfer coefficients.
In a typical fire tube for example,
the gas-side heat-transfer coefficient
ranges from 10 to 20 Btu/ft2h°F,
while the boiling steam-side or waterside
coefficient ranges from 1,500
to 3,000 Btu/ft2h°F, depending on
steam pressure and heat flux [1, 2]. If
d = 2 in., di = 1.7 in., ffi = ffo = 0.001,
and Km = 25 Btu/ft h°F, then the following
calculation can be made:
1/Uo = (2/1.7)/15 + 0.001 × (2/1.7)
+ 0.001 + 1/1,500 + (2/24/25)
ln (2/1.7) = 0.07843 + 0.001176
+ 0.001 + 0.000667 + 0.00054 =
0.0818, or Uo = 12.22 or Ui = 12.22
× 2/1.7 = 14.38 Btu/ft2h°F or Ui =
0.958 hi
Similarly, in a water-tube boiler, steam
is boiling inside the tubes and hence,
hi = 1,500-4,000 Btu/ft2h°F, while fluegas
flows outside and ho ranges from
10-20 Btu/ft2h°F. It can be shown from
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