Chemical Engineering June 2018 - 74

= K / Wg
ln[(Tg1-ts) / (Tg2-ts)] = K1n0.2/Wg
0.2
0.2
(16)
Where n is the tube count. The effect
of gas properties is neglected in
this simplified approach. If tube count
does not change, then K1n0.2 can
be replaced by K, another constant.
These simplifications work well for
clean gases and when direct radiation
from flame or high non-luminous
heat transfer coefficients are absent.
Using the above equation, one can
predict several aspects of a fire-tube
waste-heat boiler performance:
1. Effect of steam pressure
2. Effect of plugging of tubes
3. Effect of change in gas flow
4. Effect of gas inlet temperature.
Example 4
A fire-tube waste-heat boiler generating
steam from hot air has been
purchased with the parameters as
shown in Table 12, Column 1. However,
the plant is operating as shown
in Column 2 at a lower steam pressure
and at lower capacity due to
various reasons. Tube geometry data
are available as shown. How can we
find out if the boiler is performing well
or sized properly using the simplified
approach? In Case 3, 15% of the
tubes were plugged for leaks. What
will be the performance then with the
design gas flow?
Solution: Typically steam side flow
measurements and low temperature
gas, fluid temperatures are more reliable
than gas flow or high temperature
measurements. Hence, in such
simulation studies, the fluegas flow is
typically worked out from energy balance.
This example also shows how
one can find out the effect of steam
pressure on an evaporator performance.
Case
2: The values shown are as
measured in the field. Using these
we have to check if the design case
performance can be achieved. 4.93
million Btu/h is the energy absorbed
by steam using the steam flow and
enthalpy data with zero blowdown.
For a quick estimate of airflow in
operating case, from Appendix 3, we
can estimate the gas specific heat
at the average gas temperature of
Examples of using these correlations are given in references 1 and 2.
Finned tube bundles
(1,000 + 525) / 2 = 763˚F as 0.2592
Btu/lb˚F.
Correlations for finned tube bundles are more involved and shown in references 1
with worked out examples.
The gas property factor affecting gas side heat transfer is given by [1,2,4]
Fg = k0.67 Cp0.33/µ0.32
Then gas flow will be: 4.93 × 106/
[0.2592 / (1,000-525)] = 40,040 lb/h
Let us first compute K.
ln[(1,000-448) / (525-448)] =
K/40,0420.2 or K = 16.4.
Use this to check if design perforAPPENDIX
C: PROPERTIES OF GASEOUS MIXTURES
mance can be achieved. Let us see
if exit gas temperature of 615˚F can
be obtained with the stated gas flow
of 70,000 lb/h at 1,200˚F and at 615
psia.
(7)
Using Equation (16) again,
ln[(1,200-489 / (Tg2-489)] = 16.4 /
700,000.2 or Tg2 = 611˚F
Examples of using these correlations are given in references 1 and 2.
Finned tube bundles
Correlations for finned tube bundles are more involved and shown in ref
with worked out examples.
The gas property factor affecting gas side heat transfer is given by [1,2,4
Fg = k0.67 Cp0.33/µ0.32
The supplier has given 615˚F,
which is close. The measured gas
pressure drop between the boiler
inlet and exit is 1.0 in. wc. The design
pressure drop will be approximately
(70,000/40,000)2 × 1 = 3.1
in. wc across the tubes. Considering
the higher average gas temperature
the gas pressure will be higher, close
to the 3.4 in wc, the design value
stated. Hence the design/proposal
data are reasonable, assuming the
measurements in case 2 are good.
(7)
Hence using such simplified estimates
backed up by one set of good
field data, one can get a good idea
of off-design performance of fire tube
or water tube boilers.
APPENDIX 1
Tube-side heat-transfer coeffiAPPENDIX
C: PROPERTIES OF GASEOUS MIXTURES
cient. Simplified estimates for heat
transfer coefficients of single-phase
fluids inside tubes are presented in
The duty or steam flow after plugging
will be (1,200-619) / (1200-611)
= 0.986 × 100 = 98.6% of design
value. The gas pressure drop will be
about (425/361)2 × 3.4 = 4.6 in wc.
Gas pressure drop will be a major
concern rather than decrease in duty
with 15% plugging.
Case 3: If 15% of tubes are
plugged, what will happen to the
duty and gas pressure drop with the
design gas flow and inlet gas temperature?
Let
us check the revised K value
for the original design. K = 16.4 ×
(361/425)0.2 = 15.88
Using Equation (16), ln[(1,200489)
/ (Tg2-489)] = 15.88/70,0000.2
= 1.705 or Tg2 = 619˚F
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