Chemical Engineering June 2018 - 63

Equation (6) above that Uo = 14.18 Btu/
ft2h°F or Uo = 0.945 ho.
Now, consider a finned tube evaporator
with the following tube geometry:
d = 2 in., di = 1.77 in., fins/in. =
2, fin height = 0.75 in., fin thickness
= 0.049 in. The ratio of outside to inside
area is 5.9.
Let us say ho = 15 Btu/ft2h°F and
hi = 2,500 Btu/ft2h°F.
In this situation, the calculation
goes as follows:
1/Uo = 5.9/2,500 + 0.001 × 5.9 +
0.001 + 5.9 × (2/24/25) ln(2/1.77)
+ 1/(0.73 × 15) = 0.00236 + 0.0059
+.001 + 0.0024 + 0.0913 = 0.109,
or Uo
= 9.18 Btu/ft2h°F or Uo =
9.18/0.73/15 = 0.84hoη (fin effectiveness
is 0.73; Refs. 1 and 2 give
details of their evaluation).
For a case in which there is a higher
fin density and lower tube-side coefficient
(such as a superheater), the
ratio will be lower (around 0.75 hoη.
Hence, for finned tubes, depending
on fin geometry, Uo = 0.75 to 0.8
hoη. In this case, ho still governs Uo.
The gas-side heat-transfer coefficient,
ho, consists of convective and
non-luminous coefficients. Procedures
for estimating convective and
non-luminous heat-transfer coefficients
in boiler components are given
in Ref. 1. Fluid pressure drops inside
and outside tubes may also be obtained
from Ref. 1. This article does
not deal with the estimation of fluegas
or steam-water-side pressure
drops, only thermal performance.
ho = hc + hn
(7)
The expanded online version of
this article (at www.chemengonline.
com/performance-prediction-industrial-boilers)
describes the procedure
for computing heat transfer
coefficients for flow inside and outside
plain tubes. The expanded version
also provides an idea of how
the fluegas transport properties can
be obtained for a gas mixture. If one
can obtain the steam-side heattransfer
coefficient hi inside a superheater
tube, it will help in evaluating
tube wall temperatures, as shown in
an example also included in the longer
online version of this article. In
a fire tube boiler, hi helps to determine
the size of the boiler or predict
62
Yes
End
FIGURE 5. Following a logic tree, such as the one shown here for off-design performance of a simple HRSG,
can help plant engineers evaluate the effects of various operating conditions
Boiler load, %
Boiler duty
Excess air
Fluegas recirculation
Fuel input (hhv)
Heat relative rate(HHV)
Heat relative rate(HHV)
Steam flow
Steam pressure
Steam temperature
TABLE 3. STEAM GENERATOR PERFORMANCE AT VARIOUS LOADS
100
75
Ambient temperature
Relative humidity
64.68
21.1
60
15
77.58
823,241
546,978
99,819
42.2
399
Feedwater temperature 116
Water temp. leaving eco. 222
Blowdown, %
1
Boiler exit gas temp.
Eco. exit gas temp.
Air flow
Fluegas flow
Spray flow
Air moisture loss
Fuel moisture loss
Casing loss
Unacceptable/margin
Efficiency, LHV
Efficiency, HHV
Furnace backpressure
% vol. CO2
H2O
N2
O2
SO2
fuel flow
469
158
116,909
122,934
3,260
Fluegas analysis, losses, efficiency, %
Dry gas loss
4.62
0.09
10.55
0.50
0.50
92.56
83.75
370
8.56
17.30
71.65
2.48
6,024
48.51
21.1
60
15
57.89
614,296
408,152
74,864
42.2
399
116
207
1
417
143
87,237
91,733
1,869
4.14
0.08
10.45
0.67
0.50
93.03
84.17
201
8.56
17.30
71.65
2.48
4,494
its performance, as it governs U, as
shown above.
For gas temperatures below
1,500ºF, neglecting hn may not lead
to significant errors. In fire-tube boilers,
since the beam length is tube
50
32.34
21.1
60
15
38.52
408,750
271,584
49,909
42.2
399
116
190
1
359
132
58,047
61,039
492
3.74
0.07
10.36
1.00
0.50
93.21
84.33
86
8.56
17.30
71.65
2.48
2,990
25
15.98
21.1
60
35
19.36
205,403
136,476
24,955
42.2
386
116
183
1
306
125
34,243
35,746
4.18
0.08
10.31
2.00
0.50
91.67
82.94
28
7.38
15.12
72.51
4.99
1,502
inner diameter, hn, will be small and
can be neglected. Then hi = hc.
Two calculation categories
In general, calculations carried out
in boiler practice can be divided into
CHEMICAL ENGINEERING WWW.CHEMENGONLINE.COM
JUNE 2018
Units
Million Kcal/h
°C
%
%
%
Million Kcal/h
Kcal/m3h
Kcal/m2h
kg/h
kg/cm2g
±5°C
±5°C
±5°C
%
±5°C
±5°C
kg/h
kg/h
kg/h
%
%
%
%
%
%
%
mm wc
Start
tg1
ts2
Input Wg, tg1, gas, analysis,
steam pressure, tw1, A1, A2, A3
Assume Ws
Assume ts2
Compute Qa
Compute tg2
Compute Qt
Q1 = Qt
No
(Qa-Qt)/Qa
<0.01
Yes
Compute Q2, tg3
Wc=Ws
No
(Qa-Qt)/Qa
<0.01
Yes
Q3 = Qt
Compute Wc using
Q1, Q2, Q3, ts2
(Ws-Wc)/Ws
<0.01
Notes: Unfired performance, NTU method
used for solving all surfaces
A1, A2, A3 = surface areas of superheater
(SH), evaporator (evap.), economizer (eco.)
Wg, Ws = gas, steam flows
Q1, Q2, Q3 = duty of superheater, evaporator
and economizer
Assume tw2
compute Qa, tg4
compute Qt
tg2
ts
tw2
tg3
tw1
tg4
Wg
SH evap. eco.
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Chemical Engineering June 2018

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