Page 262 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchanger networks 251

If this match is not satisfied, the utility usage increases, and additional pen-
alties may result during the remaining design. The identification of the
essential and other matches at the pinch is achieved by applying feasibility
criteria to the stream data at the pinch. Also, the feasibility criteria can indi-
cate whether it is necessary for a stream splitting. After leaving away from the
pinch, the design task is no longer so constraint. The main synthesis steps of
the pinch design method are as follows: (1) assume the minimum temper-
ature difference Δt m and build the problem table, (2) draw the composite
curves, (3) match the hot and cold process streams following the pinch
design principles and rules, and (4) optimize Δt m and repeat the earlier steps
until the pinch position does not change.
The key established principles of the pinch technology are demonstrated
in detail in Linnhoff et al. (1982).

6.3.1 Problem table

The problem table algorithm proposed by Linnhoff and Flower (1978a) is
used to determine the pinch location and was formulated by Luo and
Roetzel (2010, 2013). For a given synthesis task dealing with N h hot streams
and N c cold streams and for a specified value of the minimum temperature
difference Δt min , we define the following temperature vectors:
2 0 3 2 00 3 2 0 3 2 0 3
t t t t
h,1 h,1 c ∗,1 c,1 + Δt min
t t t t
6 0 7 6 00 7 6 0 7 6 0 7
0 6 h,2 7 00 6 h,2 7 0 6 c ∗,2 7 6 c,2 + Δt min 7
7,
h h c∗ ⋮
T ¼ 6 7, T ¼ 6 7, T ¼ 6 7 ¼ 6
4 ⋮ 5 4 ⋮ 5 4 ⋮ 5 4 5
t 0 t 00 t 0 t 0 + Δt min
h,N h h,N h c ∗,N c c,N c
2 00 3 2 00 3
t t
c ∗,1 c,1 + Δt min
t t
6 00 7 6 00 7
00 6 c ∗,2 7 6 c,2 + Δt min 7
c∗ ⋮
T ¼ 6 7 ¼ 6 7
4 ⋮ 5 4 5
t 00 t 00 + Δt min
c ∗,N c c,N c
(6.60)
Let the set
n o n o n o
S T ¼ t 0 , t 0 , …, t 0 [ t 00 , t 00 , …, t 00 [ t 0 , t 0 , …, t 0
h,1 h,2 h,N h h,1 h,2 h,N h c ∗,1 c ∗,2 c ∗,N c
n o
[ t 00 , t 00 , …, t 00
c ∗,1 c ∗,2 c ∗,N c
(6.61)