Page 263 - Design and Operation of Heat Exchangers and their Networks

252 Design and operation of heat exchangers and their networks

then we can further define a temperature level vector
T
½
T ¼ t 1 t 2 …t N SN +1 Š (6.62)
in which the temperature levels t i 2S T (i¼1, 2, …, N SN +1) and
t 1 >t 2 >…>t N SN +1 . The streams in each temperature interval [t i , t i+1 ] con-
sists a subnetwork SN i (i¼1, 2, …, N SN ). The heat transport difference
between the heat input I i and heat output O i in SN i can be calculated by
means of Eq. (6.63):

D i ¼ I i O i ¼ ΔH c,i ΔH h,i (6.63)
in which ΔH h,i and ΔH c,i are the total enthalpy change of hot streams and
that of the cold streams in the subnetwork SN i
N h
X
_
ΔH h,i ¼ t i t i +1 Þ C h, ij (6.64)
ð
j¼1
N c
X
_
ΔH c,i ¼ t i t i +1 Þ C c, ij (6.65)
ð
j¼1
_
0
_ C h, j , t 00 h, j t i +1 and t i t h, j
C h, ij ¼ (6.66)
0, others
_
_ C c, j , t 0 c ∗, j t i +1 andt i t 00 c ∗, j
C c, ij ¼ (6.67)
0, others
According to the energy balance, if there is no heat utility connecting to
SN i+1 , the heat input of SN i+1 should be equal to the heat output of SN i :
I i +1 ¼ O i (6.68)
We begin the calculation of heat input I i from SN 1 , assuming I 1 ¼0, to
. The assumption of I 1 ¼0 might yield neg-
that of the last subnetwork I N SN
ative values of heat inputs and heat outputs of the subnetworks. This is not
allowed because the heat cannot flow from a lower temperature region to a
higher temperature region. Therefore, a modification should be performed
by adding the minimum hot utility duty

Q HU,min ¼ min I i , O i ; i ¼ 1, 2, …, N SN g (6.69)
f
to all heat inputs and outputs. After the modification, we also obtain the
minimum cold utility duty

Q CU,min ¼ O N SN (6.70)