Page 256 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchanger networks 245

hot and cold utility costs
C U,HU,k QðÞ k ¼ 1, 2, …N HU Þ, C U,CU,l QðÞ l ¼ 1, 2, …N CU Þ
ð
ð
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 loads and thermal capacity rates of process heat
exchangers
_ _
Q E, j , C E,h, j , C E,c, j ð j ¼ 1, 2, …N E Þ
so that the objective function f (x) (usually the total annual cost) reaches the
minimum.
As an example, we take the total annual cost as the objective function

N E
X

minf xðÞ ¼ TAC ¼ C E A E, j
j¼1
N
X
+ min C E,HU,k A HU,ik Þ + C U,HU,k Q HU,i Þ; k ¼ 1, 2, …, N HU g
ð
f
ð
i¼1
N
X
+ min C E,CU,l A CU,il Þ + C U,CU,l Q CU,i Þ; l ¼ 1, 2, …, N CU g
ð
ð
f
i¼1
(6.38)
in which

_
00
Q HU,i ¼ max C i t 00 t ,0 (6.39)
lb,i i
_

Q CU,i ¼ max C i t t 00 ,0 (6.40)
00
i ub,i
f
max Q E,k , φQ E,k g
A E,k ¼ (6.41)
f
F E,k k E,k max Δt m,E,k , Δt m,E,k =φg
f
max Q HU,i , φQ HU,i g
A HU,ik ¼ (6.42)
F HU,ik k HU,ik max Δt m,HU,ik , Δt m,HU,ik =φg
f
f
max Q CU,i , φQ CU,i g
A CU,il ¼ (6.43)
F CU,il k CU,il max Δt m,CU,il , Δt m,CU,il =φg
f

8
t 0 t 00 t 00 t 0
>
> h,E,k c,E,k h,E,k c,E,k
> 0 00 00 0
< i, t t t t > 0
h h,E,k c,E,k h,E,k c,E,k
Δt m,E,k ¼ ln t 0 t 00 = t 00 t 0
> h,E,k c,E,k h,E,k c,E,k
>
>
: 0 00 00 0
1, t t t t 0
h,E,k c,E,k h,E,k c,E,k
(6.44)