Page 251 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchanger networks 241

We first guess the heat transfer areas of all process heat exchangers in the
given network. If the heaters and coolers are located at the exits of the net-
work, they will not be included in the matrix formulation. Otherwise, they
shall be treated as the process heat exchangers. According to the given net-
work, if there are stream splitting and rejoining, the corresponding splitting
factors shall be guessed, following the mass balance constraint:

n
X
c k ¼ 1 (6.28)
k¼1
where n is the number of splits of a splitting and c k is the splitting factor of the
kth split.
Luo et al. (2009) suggested that the constraints (6.24) and (6.25) can be
treated by adding additional heaters and coolers and taking the correspond-
ing costs as the penalty functions. Using the guessed heat transfer areas and
splitting factors, the coefficient matrix V and four matching matrices can be
determined, and the outlet temperatures of each exchanger in the network
and the exit temperatures of the streams before entering the heaters and
coolers can be obtained by the use of the general solution introduced in
Section 6.1. After the stream temperatures have been obtained, the con-
straints (6.24) and (6.25) will be checked. If the exit temperature of a stream
is higher than the upper bound of its target value, the stream will be cooled
by a cold utility. If it is lower than the lower bound of the target value, the
stream will be heated by a hot utility. With this method, the heat exchanger
network is always feasible.
As an example, we take the total annual cost as the objective function:

N E
X

TAC ¼ C E A E, j
j¼1
N 00
X
+ min C E,HU,k A HU,i k Þ + C U,HU,k Q HU,i k Þ; k ¼ 1, …, N HU g
ð
f
ð
00
00
i ¼1
00
N 00
X
+ ½min C E,CU,l A CU,i l Þ + C U,CU,l Q CU,i Þ; l ¼ 1, …, N CU g
ð
ð
f
00
00
00
i ¼1
(6.29)
in which
n o
_
00
00
Q HU,i ¼ max C 00 t 00 00 t 00 ,0 (6.30)
00
i lb,i i