Environmental Engineering Reference
parallel branches. Thus in addition to the CP(FCp) criterion, there is a stream number
criterion above the pinch such that
Sh is less than or equal to Sc (above the pinch)
Sh = number of hot streams at the pinch
Sc = number of cold streams at the pinch
If there had been more cold streams than hot streams in the design above the pinch, this
would not have created a problem, since hot utility can be used above the pinch.
Let us now consider the sub-problem below the pinch. Here hot utility must not be used
below the pinch. That' means that all cold streams must be heated to pinch temperature by
heat recovery. Again, for below the pinch, if we have the number of cold streams greater than
the number of hot streams (3 cold streams and two hot streams, for instance) regardless of the
CP(FCp) values, one of the cold streams can not be heated to pinch temperature without some
violation of the ∆Tmin constraint.
The problem can be solved by splitting a hot stream into two parallel branches. In such a
case, each cold stream at the pinch will have a partner with which to match and be capable of
heating it to pinch temperature. Thus there is also a stream number criterion below the pinch
Sh is greater than or equal to Sc (below pinch)
If we have more hot streams than cold streams below the pinch, this would not be a
problem, since cold utility can be used below the pinch.
It is instructive to mention here that it is not only the stream number that creates the need
to split streams at the pinch but also the streams CP(FCp) inequality.
Sometimes the CP(FCp) inequality criteria for the streams above the pinch “at the pinch”
and below the pinch “at the pinch” can not be met at the pinch without a stream split. It is
important to emphasize here the need to satisfy both criteria; the stream population and the
The number of hot streams above the pinch at the pinch needs to be less than or equal to
the number of cold streams above the pinch at the pinch. If this is not the case then we need to
split a cold stream to achieve this guideline. At the same time, the CP(FCp) of the hot stream
above the pinch at the pinch shall be less than or equal to the CP(FCp) of the cold stream
above the pinch at the pinch in order to be able to match them in a heat exchanger. If this is
not the case the cold stream needs to be split into two.