Chemical Engineering November 2011 - 38

Cover Story
Unshifted composite curve
300
275
250
200
225
175
150
100
125
25
50
75
100
100 100 400 500
Heat duty, MBtu/h
600 700 800 900 1,000
FIGURE 9. Optimizing the pinch temperature can sometimes
eliminate the need for a utility
temperature is the following heat
transfer equation:
Q = U0  A  LMTD
Cold utility duty =
72 MBtu/h
Pinch = 10°F
No hot utility
Unoptimized utilitiesgr and composite curve
300
275
250
200
225
175
125
150
100
75
50
25
Shifted temperature = 85°F
Actual temperature = 80°F
Cold utility = 72 MBtu/h
10
20
30 40 50 60 70 80 90
Heat duty, MBtu/h
100 110 120 140100
150160
FIGURE 10. Optimizing the pinch temperature can sometimes
even change the type of utility required
(1)
Where:
Q = the duty of the heat exchanger
U0 = the overall heat transfer coefficient
A
= the heat-exchanger heat-transfer
surface area
LMTD = the log mean temperature
difference
In this equation, minimizing the
pinch temperature increases the heat
recovery (Q) from the process. Minimizing
the pinch temperature will
decrease the LMTD, so in order to
increase the duty (Q) we need to provide
additional surface area (A). In
this example, it is assumed that the
overall heat-transfer coefficient stays
relatively constant, because trying to
increase the overall heat-transfer coefficient
usually requires increasing
the fluid velocities, which increases
the pressure drop. Often this pressure
drop is not available due to compressor
or pump limitations. It is the overall
heat transfer coefficient that is used
to determine whether to use a small
or large pinch temperature. Therefore,
it is necessary to have a good knowledge
of the process. If the process heat
exchangers have small overall heat
transfer coefficients near the pinch
point (such as for vapor-vapor heat
exchangers), then it will require a lot
of extra surface area per extra Btu desired,
thereby increasing the capital
requirements significantly.
However, if the overall heat transfer
coefficients are large near the pinch
point, then a smaller pinch temperature
can be used, requiring less surface
area per Btu than in the case of
the low overall heat transfer coefficient.
The above overall heat-transfercoefficient
relationship must be used
in conjunction with the size of the potential
utility-duty savings. If the potential
utility savings are small, there
typically isn't enough savings to justify
much capital expenditure for heat
exchangers and piping.
Returning to the example, someone
not familiar with pinch analysis would
be tempted to add the utilities at the
end of the hot and cold curves in order
to match the end point temperatures.
Their solution might look similar to
Figure 4. A novice at pinch analysis
would know that the utilities could
be added at a lower temperature, but
might not know how to determine the
optimum temperatures.
Shifted composite curve. In order to
find the optimum solution, you need
to re-plot the composite curve as a
" shifted composite curve. " This is accomplished
by subtracting one half of
the pinch temperature from the hot
composite curve temperatures and
adding one half of the pinch temperature
to the cold composite curve temperatures.
The resulting plot is shown
in Figure 5. This plot shows that the
hot and cold utility requirements have
not changed, but at the pinch point,
the curves now touch. This is mainly
done to allow the curves to be replotted
in a different form, to create a
" grand composite curve. "
Grand composite curve. The grand
composite curve is created by subtracting
the hot curve duties from the
cold curve duties at each temperature.
38 CHEMICAL ENGINEERING WWW.CHE.COM NOVEMBER 2011
Where there is no cold line to subtract
the hot duty from, use the duty at the
end point of the cold curve. Re-plotting
the curve in this manner produces a
plot as shown in Figure 6. As pointed
out earlier, the hot stream inlet is hotter
than the required cold-stream outlet
temperature and the cold stream
inlet is colder than the required hot
stream outlet. These traits produce a
grand composite curve that doubles
back toward the y-axis. This allows
us to use the graph to easily find the
optimum temperature needed for
the utilities. This is accomplished by
drawing a line from the endpoint of
each branch of the curve back up or
down to the adjacent leg of the curve
and then over to the y-axis.
Utility temperatures. This gives
the " shifted " temperature of the utility
required to achieve the desired
process-outlet temperature. The actual
temperature required would be
the shifted temperature plus one half
of the pinch temperature for the hot
utility, and minus one half of the pinch
temperature for the cold utility. This
shows that the heat source for this example
only needs to be ~159°F versus
275°F. The cold utility should be ~65°F
versus 4°F. A utility at 65°F is usually
much cheaper to obtain than one at
4°F, which requires a refrigeration
system. If you choose a colder hot utility
or a warmer cold utility, you would
find that the process would pinch
before enough heat or cold could be
added to obtain the desired temperatures
at the stream outlets.
Inserting the utilities into the shifted
composite curve yields the curve
shown in Figure 7. Shown on the curve
Temperature, °F
Temperature, °F
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Chemical Engineering November 2011

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