Page 271 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchanger networks 259

Now, the two rules for the matching of streams will be checked. In the
_
part below the pinch, N h ¼N c ¼3, and since C h,E2 ¼ 10 kW/K and
_
C c,E4 ¼ 15 kW/K, all the three matchings fulfills with Eq. (6.77).
For Δt min ¼5K, the pinch is located at t h ¼125°C and
TAC¼109,768$/yr. As has been mentioned earlier, for given
investment and utility cost functions, there is an optimal value of
Δt min ¼4.055K, yielding the minimum TAC of 109,535$/yr. The
calculation results are provided in Table 6.5. Analyzing the heat transfer
among the streams without the restricts of isothermal mixing and the
third principle of the pinch technology, “Do not transfer heat across the
pinch,” we find that the network has four independent variables, two for
_
_
stream splits (e.g., C h,E4 and C c,E3 ) and two for heat loads of the process
heat exchangers (e.g., Q E1 and Q E2 ). Optimizing these four variables, we
finally obtain the best network for this design problem with
TAC¼108,072$/yr, in which
_
_
C h,E4 ¼ 20:723533 kW=K, C c,E3 ¼ 13:032104 kW=K
Q E1 ¼ 483:13886kW, Q E2 ¼ 712:508733kW

Example 6.5 Pinch method for H2C2_150.
This example is taken from Zhu (1997). The problem data are listed in
Table 6.6. It deals with two hot streams (N h ¼2) and two cold streams
(N c ¼2). For Δt min ¼10K, we obtain that the pinch position is located
at t h ¼90°C, with Q HU,min ¼5500kW and Q CU,min ¼2500kW. The
problem table is given in Table 6.7. The composite curves are shown in
Fig. 6.6. It is interesting to notice that the zero heat input I happens at
t h ¼60°C and 90°C, and the hot and cold composite curves are parallel
in the cold stream temperature range of 60–90°C, because in this range,
the sum of the thermal capacity rates of hot streams H1 and H2 is the
same as that of the cold stream C1.
To design the network, we divide the problem into two parts at the
pinch. In the part above the pinch, there are two hot streams and two
_
_
_
_
cold streams, that is, N h ¼N c with C H2 < C H1 < C C1 < C C2 ; therefore,
no splitting is necessary. According to the temperature levels of hot and
cold streams, Zhu (1997) adopted the matches as H1C2 and H2C1.
In the part below the pinch, there are two hot streams but only one cold
_
_
_
stream, N h >N c ,but C H2 < C H1 < C C1 , so a splitting in C1 is required.