indicate that somewhat tighter control can be achieved in the 32-stage column because of the larger controller gain and smaller integral time.
These predictions are not borne out by dynamic simulations. Figure 7.43a gives results for the two columns with a 20% step increase in feedflow. For this disturbance, the biggest difference between the two columns is in the bottoms impurity. The 44-stage column displays a much smaller transient peak departure from the desired value of 1 mol% propane. Although the response of the 32-stage column is faster, the dynamic deviation is larger.
The explanation for this difference is that there are more trays between the feedpoint and the base (feed stage is 19 and base is 44, giving 25 trays) in the 44-stage column. In the 32-stage column the feed stage is 14 and the base is 32, giving only 18 trays. Therefore the disturbance takes longer to reach the base and the temperature controller has more time to take corrective action.
We could try to advance the general conclusion that having more trays in the column helps the dynamic response. This certainly is the conventional wisdom in distillation control.
However, the response of the system to other disturbances brings this conclusion into question. Figure 7.43b gives results for the two columns with a 20% step decrease in feed-flow. Now the deviation in bottoms composition is larger in the 44-stage column and the response is quite slow.
It should be remembered that a reflux to feed ratio is adjusting the reflux flow to the top of the column as soon as the feed flowrate changes. The change in reflux affects the control tray quickly because it is only eight stages down in both columns. For an increase in feed flowrate, the increase in reflux starts to reduce the temperature on the control tray, and the temperature controller increases the heat input, which affects the bottoms composition quickly. So the bottoms composition is being affected by three
inputs: the feed flowrate, the reflux flowrate, and the reboiler heat input. These inputs all have different timescales in terms of the time when they affect the bottoms composition. The net effect is difficult to predict. This demonstrates the usefulness of a rigorous dynamic simulation.
Figure 7.44 gives results for a feed composition change. The difference between the two columns is quite small. There are no changes in reflux or feed flowrates. So the variables affecting bottoms composition are the feed composition and the vapor boilup changes that result from the feed composition affecting the control tray temperature. Note that the energy consumption in the 32-stage column is higher than that in the 44-stage column.
These results demonstrate that distillation column dynamics are not as simple as one might expect, even in this ideal VLE system. The dynamic interplay between the effects of disturbances, measurements, and manipulated variables can lead to some unexpected and counterintuitive results.
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