Chemical Engineering June 2018 - 65

TABLE 8. EFFECTIVENESS FACTORS FOR EXCHANGERS
Parallel-flow, single-pass
Counter-flow, single-pass
Shell-and-tube (one shell pass;
two, four, six and so on, tube
passes)
Shell-and-tube (n shell pass; 2n,
4n, 6n, and so on, tube passes)
Cross-flow, both streams unmixed
can also be evaluated by the NTU
method. Simply change the tube
geometry of the heat exchanger to
match the desired performance, and
then freeze the design. Following
that, the off-design performance is
evaluated for several cases. Hence,
the NTU method can be used for a
design calculation or an off-design
calculation. Effectiveness, ε, is the
most important factor in these calculations
and once it is arrived at,
the duty of the exchanger can be
obtained.
Table 8 shows the effectiveness
factor for various arrangements. It
is sufficient if the fluid flows and the
hot and cold fluid inlet temperatures
are known. In that case, the following
equations apply.
Cross-flow, both streams mixed
Q = εCmin (T1 - t1)
Cmin = (WCp)min
Cmax = (WCp)max
C = Cmin/Cmax
Cross-flow, streams Cmin unmixed
Cross-flow, streams Cmax unmixed
and the exit hot- and cold-side fluid
temperatures.
These
calculations
are applicable for single-phase fluids
only and no external radiation is assumed
to be present.
Conventional method. The procedure
for the conventional method is
as follows:
* Assume the exit temperatures of
the hot gas stream (T2, T1, t1) are
known
* Compute the assumed duty Qa
= WhCph (T1 - T2) (Wh, Wc are
known)
* Compute the exit temperature of
the cold fluid t2 using t2 = t1 + Qa/
Wc/Cpc
* Compute the LMTD, since all four
temperatures are known
* Compute U using equations discussed
in the online section of
this article and in Refs. 1 and 2.
Compute the transferred duty Qt
= UA∆T
* If both Qa and Qt are within a
small range (~0.5%), then we may
stop the iteration. If not, change T2
in Step 1 and repeat the protocol
until the difference is 0.2% or less.
64
Quick convergence logic may be
used to speed up the calculations.
Each time the gas or steam/water
temperature is corrected, the corresponding
gas and fluid properties,
and also the heat-transfer coefficients,
will change. A computer
program is ideal for such an exercise,
because the manual calculations
become tedious. However,
engineers should know how to do
these calculations manually in order
to develop a computer program.
Ref. 1 also contains numerous
manually calculated examples for
various types of boiler equipment.
NTU method of performance
evaluation. The Number of Transfer
Units (NTU) method is the most
widely used method in the chemical
process industries (CPI), as it " directly "
solves for the duty, although
a few iterations will help to improve
the accuracy. U is dependent on
the average gas temperature or film
temperature and on the fluid properties,
which impact the heat-transfer
coefficients with changing temperatures.
A new equipment design also
NTU = UA/(WCp)min
(8)
(9)
(10)
(11)
(12)
These terms may be used in the
equations shown in Table 8 to estimate
ε for the exchanger configuration
in question. Once ε is obtained,
the duty may be obtained. Thereafter,
the exit fluid temperatures are
obtained. Using multiple iterations
will improve the accuracy of the fluid
properties and specific heats. Examples
shown in the online version of
this article illustrate this procedure for
evaluating
off-design
performance
of superheater, economizer, fluid
heater, such as glycol heated by exhaust
gases from a gas turbine.
Evaporator performance
Fire-tube boiler or water-tube evaporator
performance may be obtained
in a far easier manner compared to
superheaters or economizers. Since
the cold-side fluid temperature is
constant at saturation temperature,
this evaluation is rather simple. T1
and T2 refer to hot gas inlet and exit
temperatures, respectively, and ts
is
the saturation temperature. Neglecting
casing heat losses, the following
equation can be written:
WgCpg (T1 - T2) = Q = UA∆T =
UA [(T1 - ts) - (T2 - ts)] / ln[(T1 - ts) /
(T2 - ts)]
(13)
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Chemical Engineering June 2018

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