Page 250 - Design and Operation of Heat Exchangers and their Networks

240 Design and operation of heat exchangers and their networks

00
upper and lower bounds of the target temperatures of N process streams
leaving the network
T T
00
T ¼ t 00 t 00 ⋯ t 00 , T ¼ t 00 t 00 ⋯ t 00
00
ub ub,1 ub,2 ub,N 00 lb lb,1 lb,2 lb,N 00
0
thermal capacity rates of process streams at N network entrances and N 00
network exits
_ 0 0 0 _ 00 00 00
C 0 ð i ¼ 1, 2, …, N Þ, C 00 ð i ¼ 1, 2, …, N Þ
i i
thermal capacity rates of hot and cold streams and overall heat transfer coef-
ficients of N E heat exchangers
_ _
C E,h, j , C E,c, j , k j ð j ¼ 1, 2, …, N E Þ
utility temperatures of N HU hot utilities and N CU cold utilities
t 0 , t 00 ð k ¼ 1, 2, …, N HU Þ, t 0 , t 00 ð l ¼ 1, 2, …, N CU Þ
HU,k HU,k CU,l CU,l
investment costs of process heat exchangers, heaters, and coolers

C E AðÞ, C E,HU,k AðÞ k ¼ 1, 2, …N HU Þand C E,CU,l AðÞ l ¼ 1, 2, …N CU Þ
ð
ð
hot and cold utility costs
ðÞ k ¼ 1, 2, …N HU Þ,
C U,HU,k Q ð C U,CU,l Q ð
ðÞ l ¼ 1, 2, …N CU Þ
And the network configuration (excluding the heaters and coolers),
together with a set of additional equality and inequality constraints g(x)
and h(x), determine the heat transfer areas and thermal capacity rates of
N E process heat exchangers, so that the objective function f (x) (usually
the total annual cost TAC) reaches the minimum.
This can be formulated as follows:

min f xðÞ (6.23)
00
00
s:b: T xðÞ T 0 (6.24)
ub
00
00
T T xðÞ 0 (6.25)
lb
hxðÞ 0 (6.26)
gxðÞ ¼ 0 (6.27)
The vector x is a set of variables to be optimized, mainly the heat transfer
areas and splitting factors of the thermal capacity rates.