Combined Composition and Conversion Control

The operation of reactive distillation processes requires careful optimisation: increasing the product purity too far (by manipulating the reboiler duty or by some other means) can significantly inhibit the reaction. Satisfactory operation is certainly possible with a one-point (composition only) control scheme but satisfying the primary operating objective (e.g. the bottoms purity specification) does not necessarily guarantee adequate process performance. A very low reactant conversion can still result from operating conditions that satisfy the purity requirement, and effective control of the reaction should be considered vital.

A combined composition and conversion control scheme which automatically ensures that satisfactory reaction conditions are maintained was implemented on the ETBE column using the inferential conversion model described in Section 10.1.2 and the LV control configuration. The five degrees of freedom that are available are utilised according to the variable pairings given in Table 10.4. The reboiler duty and reflux rate were assigned for composition and conversion control, respectively. The distillate draw rate and bottoms draw rate were assigned to level control according to dynamic responsiveness considerations and the condenser duty was used for pressure control as is the popular convention. This arrangement is also shown diagrammatically, Figure 10.1, to indicate where the inferential model was applied. An alternative control structure could have been developed using the bottoms draw rate for composition control and the reflux rate for conversion control: similar results would have been achieved. However, transposed couplings (reflux rate to control composition and reboiler duty or bottoms rate to control conversion) would yield poor dynamic responsiveness and is not recommended.

Table 10.4 - Variable Pairings for Two-Point Reactive Distillation Control.

Controlled Variable

Manipulated Variable

Pressure (overhead)

Condenser duty

Reflux accumulator level

Distillate draw rate

Reboiler sump level

Bottoms draw rate

Bottoms composition (ether purity)

Reboiler duty

Isobutene conversion

Reflux rate

Distillation Control Degrees Freedom
Figure 10.1 - Two-Point Control Configuration for ETBE Reactive Distillation Column

The considerations of linearity, sensitivity and responsiveness apply to the implementation of the inferential conversion model equally as they did to the composition controller. Figure 10.2 shows the relationship between the actual isobutene conversion (as determined from the lull simulation model) and the predicted conversion (determined from the inferential model), and the reflux rate. When the composition control is operated in open-loop (constant reboiler duty), both the actual conversion and the inferential model are highly non-

linear and non-monotonic with respect to the reflux rate, making it unsuitable for use in a closed-loop control system. However, if the composition controller is operated in closed-loop, both the actual conversion and the inferential model are monotonic increasing and close to linear over the entire operating range. Therefore, as part of a two-point control scheme, the inferential model has good characteristics.

Figure 10.2 - Linearity of the Inferential Conversion Model

Sensitivity was considered in the development of the inferential model and in the selection of the preferred model but Figure 10.2 indicates only a low sensitivity between the reflux rate and the predicted conversion (in closed-loop mode). This is primarily a result of the implicit conversion control produced by the composition controller. An uncertainty of only 0.2°C in both of the temperature measurements equates to a maximum error of 0.7 mol% in the predicted conversion. While this is significant (it could result in a 20% change in the reflux rate), high sensitivity is inherent in the process (as with other high-purity distillation processes), and several techniques, including time series averaging or variable filtering, could be used to overcome any erratic tendency in the model output. The greatest contribution to the conversion prediction is from the temperature at the top of the reactive section (stage 3) so that dynamic responsiveness should be good. Overall, the inferential model appears to be suitable for closed-loop operation.

Controller performance is always a strong function of the tuning parameters and it is difficult to compare alternative control schemes on an even basis. Two options exist: tune both (all) schemes using a single criteria (e.g. singular value decomposition, SVD) or a particular set of tuning rules (e.g. the Ziegler-Nichols constants); or compare perfect controller performance (i.e. controlled variables always at set-point) for both configurations. The reactive distillation process is inherently complex and cannot be adequately represented with simple linear models. Bode plots can be produced using a dynamic simulation model but the results are inconclusive due to the presence of higher-order lags and dead-times. Other tuning rules, including the SVD approach, are equally difficult to apply to such a complex process.

The parametric sensitivity with respect to the tuning constants was investigated by comparing the process responses to a 10% increase in feed rate under three scenarios: open-loop control (no control action so that the reboiler duty and the reflux rate remain at their initial values); combined composition and conversion control using the inferential conversion model with a set of conservative empirically defined tuning constants; and perfect control with the combination of controller and conversion model. Figures 10.3 and 10.4 show that the control performance was close to perfect with the empirically defined tuning constants. This suggests that the alternative control schemes can be effectively compared using dynamic responses that assume perfect controller performance.

The combined composition and conversion control scheme uses the stage 7 temperature to infer the ether product composition which is controlled via the reboiler duty, and an inferential model to predict the isobutene conversion which is controlled via the reflux rate. This system was benchmarked against a one-point control scheme that used the stage 7 temperature to control the product composition by manipulating the reboiler duty with a constant reflux rate. Both control schemes were assumed to operate perfectly so that the controlled variables never deviated from their set-points. Two tests were considered: a 20% increase in feed rate made over 10 minutes (Figures 10.5 and 10.6); and a 2% increase in the overall ethanol to isobutene ratio (ethanol excess) made smoothly over 60 minutes (Figures 10.7 and 10.8). In each case, composition control is achieved via the stage 7 temperature without cascading the set-point from a process analyser measurement. Therefore, the actual ether purity vanes somewhat from the initial conditions.

The combined composition and conversion controller provides effective disturbance rejection for the increase in feed rate and significantly reduces the deviation in ether purity and isobutene conversion that would result from a one-point control scheme. Although the composition offset could have been eliminated using a cascade loop to manipulate the temperature controller set-point according to a process analyser measurement, this process enhancement could add significant dead-time to the control loop which might worsen the overall control performance. Furthermore, the isobutene conversion would still deviate from its initial value since no adjustment would be made to the reflux rate if one-point control was used.

Two-point control was less successful in rejecting feed composition disturbances. Figure 10.7 indicates that the ether purity deviates less than with one-point control but the offset is still significant and the advantage is only incremental. Figure 10.8 shows that the inferential conversion model is unable to effectively control the isobutene conversion to a set-point. This is a result of model mismatch and an inability of the inferential model to predict the conversion for feed compositions that are significantly different to the base case. The performance of the inferential model could be enhanced in this area by collecting more data with different feed compositions but an intrinsic problem remains. This is not necessarily surprising given the difficulty of inferring composition from VLE temperature measurements in a multi-component mixture (Marlin, 1995).

perfect control

•c-—

realisable control

:

;

open-loop response

s

N

Time (mins)

0 60 120 180 240

Time (mins)

Figure 10.3 - Effect of Tuning on the Ether Purity Response to a Feed Rate Disturbance with a Combined Composition and Conversion Controller

J

?

\ h 1 ' i 1 1

f """" ~

- — ^ \ realisable control

V / I

open-loop response ^ — ^

perfect control ^

120 Time (mins)

Figure 10.4 - Effect of Tuning on the Actual Conversion Response to a Feed Rate Disturbance with a Combined Composition and Conversion Controller

98.0

97.5

95.5

95.0

0 60 120 180 240

Time (mins)

Figure 10.5 - Ether Purity Responses to a Feed Rate Disturbance with and without Combined Composition and Conversion Control

97.5

95.5

' " two-point control

composition control only

/ :

1 feed rate

Time (mins)

Figure 10.6 - Conversion Responses to a Feed Rale Disturbance with and without Combined Composition and Conversion Control
Duty Controller Reboiler

0 60 120 180 240

Time (mins)

0 60 120 180 240

Time (mins)

Figure

'uritv Responses to a Feed Composition Disturba Combined Composition and Conversion Control

Reboiler Duty Distillation Column
Figure 10.8 - Conversion Responses to a feed Composition Disturbance with and without Combined Composition and Conversion Control

Although the inferential conversion model is not sufficiently accurate to allow the isobutene conversion to be controlled to a set-point, the model bias can be updated periodically (daily, if necessary) to provide adequate set-point control. The two-point control scheme can also be used to manipulate the conversion (by changing the set-point) to return the column operating conditions to the desired level. For example, if a laboratory result indicated a low isobutene conversion, the conversion set-point could be increased accordingly (by an amount equal to the difference between the measured value and the desired result) to optimise the process. Similarly, a very high conversion generally indicates that the ether purity is low or that the energy input is higher than required to meet the product quality specifications. The actual isobutene conversion could then be decreased by adjusting the controller set-point. Therefore, although set-point control is not directly realisable, techniques are available to overcome this limitation. Figure 10.9 shows that the actual conversion increases by a similar amount to the change in the set-point (0.5%). Note that the set-point is changed slowly as perfect inventory control was again assumed and a rapid change has the potential to destabilise the column operation. Note also the inverse response that potentially increases the complexity of the control problem.

actual conversion

c o set-point

120 Time (mins)

Figure 10.9 - Response to a 0.5% Increase in the Inferential Conversion Controller Set-Point

A less obvious advantage of the two-point control scheme is implicit decoupling of the composition control loop. The one-point (composition only) control scheme suffers from the disadvantage of a low process gain between the temperature controller set-point and the ether purity so that a large change is required in the stage 7 temperature to effect a relatively small change to the ether purity. Figure 10.10 shows the effect of a 10°C increase in the temperature controller set-point with and without inferential conversion control. Reactive distillation (like conventional distillation) is an ill-conditioned process which implies that the open-loop and closed-loop gains differ significantly (often by an order of magnitude). Effectively, the process is bidirectional as there is a low-gain and a high-gain relationship for each of the manipulated variables. Inferential conversion control effectively allows the column to be operated as if the secondary manipulated variable (in this case, the reflux rate) is closed-loop. Thus, the process objective (i.e. the ether purity) is much more sensitive to changes in the primary controlled variable (i.e. the stage 7 temperature).

Variable Compensation Process
Figure 10.10 - Effect of a Composition Controller Set-Point Change on the Ether Purity with Combined Composition and Conversion Control

Dynamic compensation could ha\e been added to the closed-loop inferential controller but was not essential given the effectiveness of the control system without dynamic compensation and the location of the temperature sensors relatively close to the column extremities. Furthermore, the usefulness of dynamic compensation deteriorates if the process time constants vary due to regular and/or large changes in the feed rate. Here, a packed column is advantageous as the volumetric hold-up increases to some extent with increases in the feed rate so that the changes in time constants are diminished.

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