Chemical Engineering June 2018 - 73

Q = 0.561 × 53,643 × (1,472-508) = 29 × 106 Btu/h
Exit gas temperature = 29 × 106/ (176,000 × 0.99
× 0.3051) = 926˚F and exit steam temperature is 29 x
106/132,000 / 0.676 = 833˚F.
It can be shown that the maximum tube wall temperature
is far less than 900˚F and hence, tubes will not fail.
However, the duty is lower. This is not a bad idea if a
plant is willing to accept the lower duty of superheater as
a temporary measure.
It can be shown that if the steam flow was reduced
to 105,000 lb/h, then in parallel flow, one can achieve
an exit steam temperature of 890˚F. The maximum tube
wall temperature will be less than 950˚F and still acceptable.
This exercise is left to the reader. Table 9 shows the
results.
Example 3
A petroleum refinery is planning to install a thermal fluid
heater (paratherm1) utilizing energy from a gas turbine
exhaust to preheat the fluid from 250 to 550˚F. It has obtained
quotes from two suppliers and the data are shown
here. Both offer the same duty and same exit fluid temperature.
Both vendors use T11 tubes. Cross-section is
the same. Plant wants to evaluate the two designs. The
vendors have not offered more information. Prices were
comparable. In fact, vendor 1 was 5% less in price.
Solution: The first thing that struck the plant engineers
was the vast difference in surface areas. Vendor 1 appeared
to be attractive as the price was also slightly lower.
However, some process engineers felt that more surface
area in finned tubes can be misleading as explained in
references 1 and 4. Higher ratio of fin surface to tube
surface lowers the gas-side heat-transfer coefficient. The
product of (UA) will be the same if the duty and LMTD are
same. Some plant engineers referred to the literature on
the fluid and found that the maximum film temperature
allowable was 650˚F. Hence a calculation was done to
check the film temperature in both cases. Let us assume
both vendors have sized the exchanger with proven correlations.
In other words, let us assume that the surface
areas given by them will perform the duty.
In order to compute the maximum film temperature,
the maximum heat flux has to be computed. This required
computation of tube side heat transfer coefficient
at the fluid exit as also the U value.
The average U = Q/A/LMTD. LMTD in both cases is
350˚F. Hence U1= 15.94 × 106 / 7,740 / 350 = 5.89 Btu/
ft2h˚F and U2 = 15.94 × 106 / 350 / 4,895 = 9.30 Btu/
ft2h˚F.
Fluegas properties at 950˚F and 750˚F (maximum and
average fluegas temperatures are shown below. Tubeside
properties at average fluid temperature and maximum
fluid temperature are also shown below.
At average paratherm 1 temperature of 400˚F, Cp = 0.67,
µ = 1.9, k = 0.055 and at 550˚F, Cp = 0.77, μ = 0.58, k
= 0.055.
Hence, average fluid-transfer coefficient = 2.44 ×
(80,000/5)0.8 × (0.67/1.9)0.4 × 0.0550.6/1.771.8 = 233
72
Btu/ft2h˚F
And maximum fluid heat transfer coefficient at 550˚F is:
2.44 × (80,000/5)0.8 × (0.77/0.58)0.4 × 0.0530.6 / 1.771.8
= 387 Btu/ft2h˚F
Maximum heat flux inside tubes: vendor 1:
6.21 × (950-550) × 7,740 × 12 / (3.14 × 1.77 × 15 ×
10 × 8.5) = 32,550 Btu/ft2h and for vendor 2, it is 23,257
Btu/ft2h (average gas-side heat-transfer coefficients
were corrected for gas temperature at inlet)
One has to be careful using vendor 1, because the film
temperature is close to the limit of 650˚F. Small variations
in U around tube periphery, non-uniformity in fluegas flow
or temperatures can cause film temperature to be easily
exceeded. Hence, the plant can consider vendor 2 a
better and safer design. Vendor 1 may be asked to use
smaller fin density and quote again. It may be noted that
film temperatures cannot be measured. More often, they
are calculated as shown. If the issue of film temperature
had not been addressed, plant would have purchased
vendor 1's design and would have run into problems in
operation later. Plants will do better to ask fluid heater
vendors to provide film temperature calculations.
Example of a fire tube boiler performance
In order to obtain the performance of any boiler components,
the U value must be obtained first. This is a rather
tedious calculation, if done manually, because fluid properties
vary with temperature and analysis. Hence, a simplified
approach is in order. Plant engineers are advised
to start with these simplified calculations and with programming
skills, develop calculation modules for boilers
in their plants. This article gives several examples of how
using the simplified approach plant engineers can check
the accuracy of any water tube or fire tube boiler design
or components such as superheater and economizer or
a fluid heater.
One of the reasons the simplified approach works well
in many boiler applications is that the gas-side heattransfer
coefficient governs the overall heat transfer coefficient
U, as shown earlier, and hence, manipulating
the variables connected with gas-side variations alone
will help evaluate the performance with acceptable accuracy
of any evaporator, superheater or economizer
or fluid heater. Sometimes calculation of the tube inside
or outside coefficient becomes a necessity and hence,
Appendices 1, 2 and 3 are provided. The simplified approach
for fire-tube waste-heat boiler evaluation will be
of interest to plant engineers.
ln [(Tg1-ts)/(Tg2-ts)] = UA/(WgCpg)
(14)
As gas side governs U, for a given tube geometry
(length, number, tube sizes) we can write:
UA = K1 (Wg/n)0.8 n / (WgCpg)
(14a)
Where K1 is a constant for the given geometry, considering
the tube length and diameter and gas properties
Equation (14) becomes:
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