Programmed Transitions Motivation

A column that exhibits multiple steady states could reach an undesirable steady state during a period of open-loop operation or as a result of an inappropriate start-up procedure. Open-loop operation is necessary to tune controllers, calibrate transmitters, etc. and makes the column vulnerable to an unwanted transition that might result from a transient disturbance (perturbation). A poorly managed start-up could also allow a column to stabilise at an undesirable steady state. Although the implementation of a device (e.g. a monitoring system for the product yield or temperature which is connected to an alarm or warning) to detect an unwanted steady state should be straight forward, a method for returning the column to the coveted conditions must be established.

The mechanism for completing the return transition should use only the available manipulated variables and avoid any risk of destabilising the column, for example, rapid changes in the internal flow rates or detrimental interactions with the inventory controllers. Ideally, the transition would also be achieved quickly and smoothly with minimal operator intervention. Possible means of achieving this objective include:

a) pertuTbating the column in a controlled manner in order to promote a transition to the desirable steady state;

b) confining the column operation to a single steady state by initiating closed-loop control of a suitable temperature;

c) forcing a change in the column material balance by manipulating a product draw rate;

d) adjusting the primary manipulated variable until a catastrophic shift occurs.

These alternatives are evaluated below for implementation on the MTBE column described in Chapter 8. This column was selected because it has already been shown to exhibit multiple steady states in the significant operating range. Controlled Perturbation

A suitable perturbation in the feed rate, feed composition or either of the manipulated variables being used for composition control (the other manipulated variables should be retained in closed-loop control of the column inventory) might be effective in producing the desired steady state transition. However, the feed rate and composition are normally determined by external factors (e.g. product demand and upstream processes) so that it would be preferable to use one of the manipulated variables to force the transition.

The simulation results included in Chapter 8 did not include a case where a reboiler duty perturbation produced a steady state transition from the low conversion steady state so that a solution is not immediately evident. However, the simulation results can be used to calculate the net amount of heat contained within the column to determine whether ditterences between the steady states might be offset by an energy impulse (i.e. reboiler dut> perturbation). The required relationship is shown in equation (10.9), where H is the total energy contained within the column, M is the hold-up on each stage, H is the specific enthalpy on each stage and n is the number of stages (including the condenser and reflux accumulator, and the reboiler sump).

Evaluation of equation (10.9) for parallel steady states of this MTBE column indicates that the low conversion solution contains the most energy while the high conversion solution contains the least energy. This suggests that a temporary decrease in the energy input to the column might initiate a transition to the high conversion steady state. The difference in heat content is approximately 110 MJ, which is equivalent to a perturbation of 5 kW (approximately 10%) for 360 minutes at the base case feed rate of 2.75 kmol/hr. Unfortunately, such a large perturbation produced very rapid changes in column properties and prevented a complete solution during simulation. This perturbation might also result in process instability in practice. Even comparatively small perturbations (e.g. 2.8 kW over 60

minutes, equivalent to an energy impulse of -10 MJ) prevented the simulation from converging. This testifies to the sensitivity of the column operation and suggests that manual control of this column would be difficult.

The observed sensitivity is a result of a domino effect that is initiated by an energy impulse, llie reactive section is affected most significantly: the initial change in the heat input produces a change in the composition profile which then affects the reaction and changes the heat balance (via a change in the net heat of reaction) which has a further effect on the composition profile. Simulations indicated that, generally, imparting a small perturbation allows the column to return to the original operating conditions while a larger perturbation produced instability caused by the formation of a dry stage(s) within the column. Although a suitable perturbation might exist, this method of forcing a transition was considered impractical due to the degree of precision required and the risk of destabilising the column operation.

Reflux rate perturbations were also found to be ineffective in forcing a steady state transition. As with the reboiler duty, small perturbations resulted in the column returning to the original steady state after the transient response or produced sufficiently rapid changes in the column properties to prevent a complete dynamic solution. The simulation results suggest that a controlled perturbation in a manipulated variable is not a practical method of forcing a steady state transition. Closed-Loop Control

The possibility of using closed-loop operation to manage a transition between parallel steady states appears to have some potential. Theoretically, the column inputs could be manipulated in order to achieve a specified output condition that was only found in the desirable steady state. For example, a high reboiler temperature and moderate stripping section temperature are characteristics of the high conversion solution so that either of these variables could potentially be controlled to force a transition.

However, as described above, the relationships between potential manipulated and controlled variables place restrictions on the performance of linear controllers. Robust control of the reboiler temperature is not possible as the process gain changes sign in the interval around the normal operating point. Although an effective controller for T[2 is easier to develop, global stability is not possible for the medium conversion solution unless the controller gain changes sign at the singular points. Thus, a finely tuned adaptive controller is required. Finally, the controller must be capable of both increasing and decreasing the manipulated variable in the course of a single set-point update in order to return the column inputs to the original values after the steady state transition has been completed. An adaptive controller is a technically feasible method of programming a steady state transition but is unlikely to be a practical solution due to the required accuracy of the model and the complexity of the continuation path (via an unstable, medium conversion steady state) which must be followed. Material Balance Manipulation

The manipulation of the column material balance via a product draw rate was also considered as a method of programming a transition. A temporary reassignment of manipulated variables is required if the LV configuration (the preferred control structure) is in use as neither the reflux rate nor the reboiler duty can affect the material balance directly. If the material balance change is to be affected using the bottoms draw rate, the reboiler sump level must be temporarily controlled via the reboiler duty. Tight level control is also required to ensure that the changes in the bottoms rate are transmitted directly to the column and are not absorbed by inventory changes.

Whereas previously a perturbation in a manipulated variable was required, here the shift must be permanent as the bottoms rate is different for each steady state. This was tested using dynamic simulations of the MTBE column. The bottoms rate was ramped over a period of 60 minutes from the low conversion steady state value (0.0935 m3/hr) to the high conversion steady state value (0.1181 m3/hr). The column responded in the desired manner and a transition to the high conversion steady state was completed after about eight hours, as shown in Figure 10.10. The reboiler duty (for perfect level control of the reboiler sump) varied both above and below the steady state value during the transition, as shown in Figure 10.12.

Draw Rate

Bottoms Temperature

Bottoms Temperature

Time (Hours)



Figure 10.11 - Steady State Transition bv Matena I Balance Manipulation

Figure 10.11 - Steady State Transition bv Matena I Balance Manipulation

Perfect level control is not always practically possible. Does the steady state transition still occur if the level control is imperfect? Steady state simulations can be used to generate the continuation curve for the reboiler duty as the bottoms rate is varied from 0.0935 to 0.1181 m3/hr. This was done and is shown in Figure 10.13. The continuation path moving from the low conversion steady state (point A) through the medium conversion steady state (point B)

to the high conversion steady state (point C). The shape of the path resembles the reboiler duty responses shown in Figure 10.12.

Figure 10.13 - Reboiler Duty Continuation Path

Time (Hours)

Figure 10.14 - Programmed Transition Using Reboilei Duty

Time (Hours)

Figure 10.14 - Programmed Transition Using Reboilei Duty

A fourth order polynomial regression was found to produce a good fit for the continuation path (R2 > 0.99). If the reboiler duty is programmed to respond according to the regression function over a period of 240 minutes, the bottoms temperature (Tb) responds as shown in Figure 10.14. The column resiabilises to the low conversion steady state. Therefore, while a planned manipulation of the column material balance can be used to transfer the operating point between parallel steady states, perfect level control is a prerequisite for a successful transition. Thus, manipulation of the bottoms rate is also not a practical method of promoting a steady state transition.

Material balance manipulation via the distillate product draw is also unviable due to the difficulties in maintaining perfect level control of the reflux accumulator. Once again, a linear controller is incapable of providing perfect level control as the manipulated variable (the reflux rate) must be both increased and decreased during the steady state transition. Catastrophic Shift

Multiple steady states only exist for this column for finite ranges of the column inputs: there are three steady states for reboiler duties between 49.6 kW and 5 1 8 kW but only one steady state for reboiler duties outside this interval. Therefore, if the column is operating at the low conversion steady state with a reboiler duty of, say, 50.6 kW, decreasing the duty to a value below 49.6 kW without changing any other input will force a catastrophic shift in the column operating point. Increasing the reboiler duty again should move the operating point along the continuation path to the high conversion steady state, regardless of the starting point. Note that the reboiler temperature will only change slightly during the catastrophic shift but that other temperatures, the internal flow rates and the stage-to-stage compositions will all change dramatically.

Other column inputs can also be manipulated in this manner to affect catastrophic shifts. For example, from the low conversion initial state described above, increasing the reflux rate to 1.25 m3/hr would have a similar affect to decreasing the reboiler duty. Reversing this change should complete a steady state transition to the high conversion steady state. Similarly, a transition in the opposite direction could be enforced by increasing the reboiler duty to affect a catastrophic shift and then reversing the change to allow the column to move along the continuation path and restabilise at the low conversion steady state.

Unfortunately, as the name suggests, the catastrophic shift might temporarily destabilise the column due to the rapid changes in the internal flow rates. However, this appears to be the only effective method of guaranteeing a transition between parallel steady states.

10.3 Integrated Control Schemes

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