Page 259 - Design and Operation of Heat Exchangers and their Networks

248 Design and operation of heat exchangers and their networks

in which the variables to be optimized is set to be
T
_
x ¼ Q E1 Q E2 Q E3 Q E4 C c,E4
According the network structure shown in Fig. 6.2, the equality
constraints can be expressed as

Heat load : Q E, j ¼ x j ð j ¼ 1, 2, 3, 4Þ
Hot stream : _ C E,h,1 ¼ _ C E,h,2 ¼ _ C E,h,3 ¼ _ C 1 , _ C E,h,4 ¼ _ C 2
0
Inlet : t 0 ¼ t , t 0 ¼ t 00 , t 0 ¼ t 00 , t 0 ¼ t 0
E,h,1 1 E,h,2 E,h,1 E,h,3 E,h,2 E,h,4 2
_
Outlet : t 00 ¼ t 0 Q E, j =C E,h, j ð j ¼ 1, 2, 3, 4Þ
E,h, j E,h, j
_
_
_
_
Cold stream : C E,c,1 ¼ C _ 00 M,2,1 , C E,c,2 ¼ C 4 , C E,c,3 ¼ C _ 00 M,1,1 ,
_
C E,c,4 ¼ C _ 00
M,1,2
00
0
0
0
Inlet : t E,c,1 ¼ t 00 M,2,1 , t 0 E,c,2 ¼ t , t 0 E,c,3 ¼ t M,1,1 , t E,c,4 ¼ t 00 M,1,2
4
_
Outlet : t 00 ¼ t 0 + Q E, j =C E,c, j ð j ¼ 1, 2, 3, 4Þ
E,c, j E,c, j
_
_
Mixer inlet : C _ 0 ¼ C 3 , C _ 0 ¼ C E,c,3 , C _ 0 _
M,1,1 M,2,1 M,2,2 ¼ C E,c,4
0
t 0 ¼ t , t 0 ¼ t 00 , t 0 ¼ t 00
M,1,1 3 M,2,1 E,c,3 M,2,2 E,c,4
Mixer outlet : C _ 00 ¼ C _ 0 C _ 00 , C _ 00 ¼ x 5 ,
M,1,1 M,1,1 M,1,2 M,1,2
C _ 00 ¼ C _ 0 + C _ 0 , t 00 ¼ t 00 ¼ t 0 ,
M,2,1 M,2,1 M,2,2 M,1,1 M,1,2 M,1,1

t 00 ¼ C _ 0 t 0 + C _ 0 t 0 = C _ 0 + C _ 0
M,2,1 M,2,1 M,2,1 M,2,2 M,2,2 M,2,1 M,2,2
00
00
00
00
00
00
Network exit : t ¼ t E,h,3 , t ¼ t E,h,4 , t ¼ t 00 E,c,1 , t ¼ t 00 E,c,2
2
3
1
4
Solving the earlier equality constraint system, we can obtain the outlet
temperatures of the process heat exchangers, mixers, and the exit
temperatures on the network. However, the guessed heat loads might
cause an unrealistic temperature cross

0
0
00
t t c 00 t t 0
c
h
h
Such cases can be avoided by the use of the unequality constraints (6.50)
or by the use of the penalty factor in Eqs. (6.41)–(6.46).
The optimization was carried out with the Excel solver. The upper and
lower bounds of the variables were set to be [1, 5000] for the heat transfer
areas and [1, 19] for the thermal capacity rates, and their lower bounds were
used as the initial values for the optimization. Besides the upper and lower
bounds of the variables, Eq. (6.50) was also set as the unequality constraints
in the solver. The penalty factor φ¼1000 was used for Eqs. (6.41)–(6.43).
By repeated use of the evolutionary solving method EA of the solver, we
obtained the best design for the H2C2_443K problem, of which the