Page 264 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchanger networks 253

The position where the heat input is zero is the pinch.
The problem table provides a simple framework for numerical analysis.
For simple problems, it can be quickly evaluated by hand. For larger prob-
lems, it is easily implemented on the computer. With the problem table
algorithm, the engineer has a powerful targeting technique at their finger-
tips. Data can be quickly extracted from flow sheets and analyzed to see
whether the process is nearing optimal or whether significant scope for
energy saving exists.

6.3.2 Composite curves
The composite curves were first used by Huang and Elshout (1976).
A similar concept is the composite line in the available energy diagram
applied by Umeda et al. (1978). To structure the composite curves, we draw
the hot and cold process streams on a temperature-heat content (enthalpy)
diagram. Starting from the individual streams, one composite curve is con-
structed for all hot streams in the process and another for all cold streams by
simple addition of heat contents over the temperature ranges in the problem.
The overlap between the two composite curves represents the maximum
amount of heat recovery possible within the process. The “overshoot” of
the hot composite curve represents the minimum amount of required exter-
nal cooling duty, and the “overshoot” of the cold composite curve repre-
sents the minimum amount of required external heating duty.
To draw the composite curves, let j 1 and j 2 indicate the maximum and
minimum temperature levels of the hot streams; k 1 and k 2 indicate those of
the cold streams, respectively, so that
n o n o
¼ max t 0 , t 0 , …, t 0 ¼ min t 00 , t 00 , …, t 00 (6.71)
h,1 h,2 h,N h h,1 h,2 h,N h
t j 1 , t j 2
n o n o
¼ max t 00 , t 00 , …, t 00 ¼ min t 0 , t 0 , …, t 0 (6.72)
c ∗,1 c ∗,2 c ∗,N c c ∗,1 c ∗,2 c ∗,N c
t k 1 , t k 2
Then, we can calculate the enthalpy flow rates of the hot and cold
streams at the temperature levels t j with Eq. (6.73):
j 2 1 k 2 1
X X
H h, j ¼ ΔH h,i , H c,k ¼ ΔH c,i + Q CU,min (6.73)
i¼j i¼k

to get the coordinates of the composite curve of the hot streams (t j , H h,j )
(j¼j 1 , j 1 +1, …, j 2 ) and those of the cold streams (t k – Δt m , H c,k )(k¼k 1 ,
k 1 +1, …, k 2 ), respectively, and draw the polyline composite curves.