Open Loop Transitions in a MTBE Column

The effects of various perturbations on the 17 stage MTBE column described in Table 8.1 were investigated via a series of dynamic simulations. The column was assumed to be operating in open-loop mode with the reflux rate and reboiler duty constant. Figure 8.9 indicates that there are three steady state solutions (i.e. high, low and medium conversions) with this set of input conditions, and the responses of the column were found separately from each steady state. The reboiler temperature was used to determine how the column responded to the various perturbations for each of the simulations.

8.5. J. 1 Transitions from the High Conversion (Stable) Steady State

Initially, the effects of perturbations in the feed composition were investigated. Starting with stable operation at the high conversion steady state, various increases and decreases in the methanol feed rate of 10% and 15% over 30, 60 and 120 minutes were considered. The column returned to the initial operating point without significant perturbation from the original condition in most cases. Numerical errors associated with rapid changes in state variables produced incomplete solutions in the other cases, possibly indicating an instability caused by a depletion of liquid in one part of the column. There was no evidence of a transition to another steady state for any of the perturbations considered. Figure 8.18 plots the column responses for a 10% increase in the methanol feed rate over 120 minutes (solid line) and a 10% decrease over 60 minutes (dashed line). Interestingly, a 10% decrease in the methanol feed rate for 60 minutes had almost no effect on the column while a 10% increase for 120 minutes substantially changed the bottoms temperature for a considerable period. These responses clearly show highly non-linear behaviour, which is a characteristic of many distillation processes.

Reboiler Duty Distillation Column
Figure 8.18 - 10% Methanol Feed Rate Changes from the High Comersion Sleadv Stale

Disturbances in the reboiler duty were also considered. In these simulations, the feed rate, feed composition and reflux rate were all fixed, while the reboiler duty was varied by ± 5% over 30 minutes and 120 minutes (four different cases). In three of the four cases, the column returned to the initial operating point quickly and smoothly, while a 5% increase over 120 minutes caused the column flows and temperature to oscillate divergently. The response to a 30 minute increase and decrease is shown in Figure 8.19. As would be expected, a much greater deviation from the initial conditions is observed for longer perturbations in the reboiler duty.

10 15

Time (Hours)

Figure 8.19 - 5% Rcboiler Duty Changes from the High Conversion Steady State

10 15

Time (Hours)

Figure 8.19 - 5% Rcboiler Duty Changes from the High Conversion Steady State

The results presented above suggest that the high conversion steady state is locally stable. Neither perturbations in the feed nor in a primary manipulated variable (i.e. reboiler duty) produced a steady state transition. This result is important as it implies that column operation should be stable once the high conversion steady state has been attained. This reduces the implications of steady state multiplicity for the operation of this MTBE column. However, it does not eliminate the possibility of a start-up sequence ending with the column in an undesirable steady state nor does it eliminate the possibility of an unstable high conversion steady state in other columns.

8.5.1.2 Transitions from the Low Conversion (Stable) Steady State

A similar series of tests was simulated starting from the low conversion steady state. The methanol feed rate was increased and decreased by 10% over 120 minutes. In both cases, the column settled to the original operating point. However, if the methanol feed rate was temporarily increased or decreased by 15% over the same period, the column jumped to the high conversion solution! The response to a 15% increase is shown in Figure 8.20. Steady state transitions were not detected for perturbations in the reboiler duty although relatively small increases (e.g. +3% over 30 minutes) caused the reboiler sump to dry up and destabilise the column. Similarly, relatively small decreases in the reboiler duty increased the internal column liquid rate significantly and induced flooding.

Transitions Extractive
Figure 8.20 - 10% and 15% Methanol Feed Increases from the Low Conversion Steady State

8.5.1.3 Transitions from the Medium Conversion (Unstable) Steady State Starting from the medium conversion steady state, several unusual results were found. Firstly, every perturbation that was considered produced a steady state transition. This is emphasised in Figure 8.21, which indicates that a steady state transition occurs after a short, temporary increase of only 1% in the reboiler duty. Secondly, the column could shift to either the high or low conversion steady state. Figure 8.22 indicates the effect of a 10% and a 15% increase in the methanol feed rate and shows that the column stabilised to the low conversion steady state in the first case (10% perturbation) and the high conversion steady state in the second case (15% perturbation). Thirdly, some transitions were very smooth and had been fully manifested within 120 minutes while some transitions took more than 15 hours. An example of this is given by Figure 8.23, which indicates the response to a perturbation of ± 5% in the methanol feed rate. The response to a 5% decrease was rapid while a 5% increase initiated a transient response that lasted for several hours.

Figure 8.21 - 1% Reboiler Duty Increase from the Medium Conversion Steady State
Figure 8.22 - Methanol Feed Rate Increases from the Medium Conversion Steady State
Reboiler Duty Distillation Column
Figure 8.23 - 5% Methanol Feed Rate Changes from the Medium Conversion Steady State

Fourthly, slight changes in the initial operating point sometimes resulted in completely different column responses. Figure 8.24 compares the response to a 10% increase in the methanol feed rate from two slightly different initial conditions. The solid line corresponds to the same base case as used for all the previous simulations (reboiler duty of 50.6 kW) while the dashed line shows the response for a reboiler duty of 50.0 kW with all other variables equal. Note that the initial bottoms temperature shifts from 144°C to 141°C due to the difference in the column energy balance. The column shifted from the medium conversion steady state to the high conversion steady state when the reboiler duty was 50.0 kW whereas it shifted to the low conversion steady state when the initial operating point equated to the original base case (50.6 kW).

Column Tray Design Definition

Timo (Hours)

Figure 8.24 - 10% Methanol Feed Increase from Similar Medium Conversion Steady States

Timo (Hours)

Figure 8.24 - 10% Methanol Feed Increase from Similar Medium Conversion Steady States

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