Page 134 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

5.4 Pinch design analysis 131

Based on the above discussion, the pinch point is estimated by the following methodology
1) The shifted temperature intervals ðDT Þ are set up from stream supply and target temperatures by

subtracting ðDT min =2Þ from the hot stream and adding ðDT min =2Þ to the cold stream
Thus for the hot streams

DT min
(5.15a)

T h ¼ T h
2
and for the cold streams

DT min
(5.15b)

T c ¼ T c þ
2
2) In each shifted temperature interval, the heat deficit/surplus is calculated from energy balance
over the streams present in the interval
X
h P i
CP c CP h
DT k
(5.16)
DH k ¼ i
i k

where DT ¼ T T is the temperature difference across the shifted interval, k numbered

k ðk 1Þ k
according to decreasing temperature level. As per Eq. (5.16), the intervals with positive DH k
signify net heat deficit while a negative value denotes energy surplus.
3) The heat from each interval is then cascaded down the temperature scale such that the output from
each interval serves as the input to the next lower interval. The heat output from any interval is the

input to the interval minus the heat deficit DH k in that interval. Thus for the first interval, since

there is no heat input, the output is DH 1 and so on. While the deficit heat (positive DH k )
in any interval can be supplied by heat flow from the higher interval, this is infeasible for negative
DH k . Accordingly, negative heat flows need to be eliminated.

4) Provided there is only one hot utility and that is available above the highest temperature of the
streams, this is achieved by addition of the highest negative DH k at the top. It increases all the

heat flows down the temperature intervals without changing the heat balance within them and
results in zero heat flow at one T . This corresponds to the pinch point (T pinch ). The actual hot

DT min DT min
,
and cold pinch temperatures are then obtained as T pinch þ and T pinch
2 2
respectively.
A typical cascade diagram depicting how heat cascades through the temperature intervals is shown
in the Example problems. While the first cascade with no hot utility is consistent with the first law
requirement, the minimum heating and cooling loads have been fixed to satisfy the second law.
5) The highest negative DH k thus gives the minimum amount of hot utility to be added to the

cascade and the minimum cold utility usage is given by the heat flow out of the lowest (coldest)
shifted temperature interval.