Page 248 - Design and Operation of Heat Exchangers and their Networks

238 Design and operation of heat exchangers and their networks

The supply temperature vector of the network is given by
0 T
T ¼ 500 480 460 380 380 290½ Š
The nonzero elements of the four matching matrices are calculated
according to the given thermal capacity rates in the channels:
g 2,13 ¼ g 4,13 ¼ g 6,13 ¼ g 10,12 ¼ g 11,1 ¼ 1, g 13,8 ¼ 0:500689,
g 13,10 ¼ 0:499311
g 0 ¼ g 0 ¼ g 0 ¼ g 0 ¼ g 0 ¼ g 0 ¼ g 0 ¼ 1
1,1 3,2 5,3 7,5 8,6 9,4 12,6
00
00
00
00
g 1,11 ¼ g 2,3 ¼ g 00 3,5 ¼ g 00 4,9 ¼ g 00 5,7 ¼ 1, g 6,2 ¼ 0:390306, g 6,4 ¼ 0:2421,
g 00 ¼ 0:367594
6,6
Because there is no bypass from entrances to exits of the network, the
000
bypass matrix G ¼0.
The inlet and outlet temperature vectors of the exchangers and the
mixer as well as the exit temperature vector of the network can then be
calculated with Eqs. (6.21), (6.13), (6.22),
0
T ¼ 500 370:63 480 370:63 460 370:63 380 290 380½
E
T
326:86 375:22 290 370:63Š
00
T ¼ 375:22 477:2 380 462:42 376:6 446:25 320 369:89 360
½
E
T
371:37 320 326:86 370:63Š
00 T
T ¼ 320 380 376:60 360 320 462:24Š
½
Since the exit temperatures of the hot stream H3 and cold stream C1
have not yet reached their target values, the hot utility and cold utility
shall be applied to them, respectively. The heating and cooling loads and
heat transfer areas of the heater HUC1 and cooler H3CU are calculated
as follows:
Heater HUC1:

_
Q HUC1 ¼ C C1 t 00 t 00 ¼ 18 660 462:24Þ ¼ 3559 kW
ð
C1 6

t 0 HU t 00 C1 t HU t 00 6
00
Δt m,HUC1 ¼
0 00 00 00
ð
ln t ð½ t Þ= t t ފ
HU C1 HU 6
ð 700 660Þ 700 462:24Þ
ð
¼ ¼ 110:95 K
½
ln 700 660Þ= 700 462:24ފ
ð
ð
ð
A HUC1 ¼ Q HUC1 = kΔt m,HUC1 Þ ¼ 3559= 1 110:95ð Þ ¼ 32:08 m 2
5
C U,HUC1 ¼ 140Q HUC1 ¼ 4:983 10 $=yr,
C E,HUC1 ¼ 1200A 0:6 ¼ 9615$=yr
HUC1