Page 261 - Design and Operation of Heat Exchangers and their Networks

250 Design and operation of heat exchangers and their networks

00
00
s:b: t t 00 0, t 00 t 0 i ¼ 1, 2, …, N H Þ (6.54)
ð
h,i ub,h,i lb,h,i h,i
00
t t 00 0, t 00 t 00 0 ð j ¼ 1, 2, …, N C Þ (6.55)
c, j ub,c, j lb,c, j c, j
and additional inequality and equality constraints:
hxðÞ 0 (6.56)
gxðÞ ¼ 0 (6.57)
The annual investment costs can be calculated in two ways. The one is
for using available invested capital, for which the annuity factor is calcu-
lated based on the capital appreciation in financial markets during the plan
lifetime n:

n
C a ¼ 1+ rð Þ =n (6.58)
The other is for using loan, for which it is calculated based on the fixed
annual repayment of the loan during the plan lifetime:
r 0
0
C ¼ n (6.59)
a
0
1 1+ r Þ
ð
In the synthesis problem, the possible structures of a heat exchanger net-
work could be astronomical figures, and the traditional optimization solvers
cannot be directly applied to Eqs. (6.53)–(6.57). Therefore, lots of synthesis
methodologies have been developed, and the most practical procedure is the
pinch technology.
The pinch technology is the first complete practical method for the syn-
thesis of heat exchanger networks. In the late 1970s, the pinch design
method was developed by Linnhoff and his coworkers (Linnhoff and
Flower, 1978a,b; Linnhoff et al., 1979, 1982; Flower and Linnhoff, 1980;
Linnhoff and Hindmarsh, 1983). In the pinch technology, the minimization
of the energy usage is addressed from a thermodynamic point of view. At
first, the minimum requirement of heating and cooling of the process
streams through a heat cascading calculation is determined. This calculation
is executed before the design of the equipment. Then, the method identifies
a location of the minimum temperature difference in the process called
“pinch point.” The pinch represents the most constrained location of a
design. It divides the overall problem into two independent problems that
are further treated separately. This means that the design starts at the pinch
and is carried out from it toward two opposite directions, like two separates
problems. At the pinch, quite often, there is a crucial or essential match.