Page 249 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchanger networks 239

Cooler H3CU:

00
Q H3CU ¼ _ C H3 t t H3 ¼ 6 376:60 360Þ ¼ 99:6kW
00
ð
3

t t 00 CU t 00 H3 t CU
0
00
3
Δt m,H3CU ¼
00 00 00 0
ð
ln t tð½ Þ t t ފ
3 CU H3 CU
ð 376:60 320Þ 360 300Þ
ð
¼ ¼ 58:28 K
ln 376:60 320Þ= 360 300ފ
ð
½
ð
A H3CU ¼ Q H3CU = kΔt m,H3CU Þ ¼ 99:6= 1 58:28Þ ¼ 1:709 m 2
ð
ð
C U,H3CU ¼ 10Q H3CU ¼ 996$=yr,
C E,H3CU ¼ 1200A 0:6 ¼ 1655$=yr
H3CU
Total annual cost:
6
X 0:6
TAC ¼ 1200A + C E,H3CU + C U,H3CU + C E,HUC1 + C U,HUC1
i
i¼1
¼ 570,764$=yr
6.2 Mathematical model and calculation methods for
sizing heat exchanger networks
Design of heat exchanger networks refers to two aspects: parameter
design (sizing of a heat exchanger network) and structure design (synthe-
sis of a heat exchanger network). Unlike the rating problem, no general
explicit solutions are available for sizing heat exchanger networks. For a
given network configuration, there might be infinitely many solutions if
there is no restriction on the use of the hot and cold utilities. As a result,
sizing a heat exchanger network becomes a constrained optimization
problem.

6.2.1 Matrix formulation
In the matrix formulation, we express the task of sizing a heat exchanger
network as follows:
0
For given supply temperatures of N process streams entering the
network
T
0 0 0 0
½
T ¼ t t ⋯ t Š
N
1
2
0