Control Objective

The controlled variable should always be selected in order to reflect the process objectives as reliably as possible. Before this can be done, it is necessary to determine the priority of the process objectives since there is only one available degree of freedom in a one-point control scheme. It is also necessary to find a means of determining whether the process objectives are being met.

The most important process objective is likely to be the control of the bottoms product composition as the process will normally be constrained by external quality specifications (e.g. minimum ETBE content, maximum Reid vapour pressure, etc.). This makes the bottoms product composition the most likely control objective. There are essentially three methods for monitoring product composition: (a) directly, with one or more online analysers; (b) indirectly, using a temperature or pressure corrected temperature to infer composition; and, (c) externally, using process samples taken at regular intervals and appropriate laboratory equipment. Analysers have many advantages but are costly, require regular maintenance and usually introduce a significant time delay into the process. Inferential control is cheaper and, often, more reliable but can also be less accurate. The use of external measuring equipment (e.g. laboratory techniques) limits the measurement frequency and is unsuitable for closed loop control.

If some form of inferential control is to be used (either in a closed-loop or open-loop system) to monitor product composition, the temperature sensor must be located carefully to ensure that changes in the composition are accurately reflected and good sensitivity to set point changes is provided. The reboiler sump is commonly used as a sensing location as it minimises process dead time and sensitivity is usually high (except with very high product purities). It might be expected that variations in the reboiler temperature (at constant pressure) would directly relate to changes in the product composition whereas other locations would be susceptible to interference from changes in the stage-to-stage composition profile. However, in an ETBE reactive distillation column, the relationship between reboiler temperature and bottoms composition is neither linear nor even monotonie, as indicated by Figure 9.1, which was produced from simulation data of the 10 stage ETBE column described previously. The absence of a one-to-one relationship prevents the reboiler temperature from being used to infer composition. The convex dependence will also lead to controller instability as it is not clear from the measured temperature whether the reboiler duty (or bottoms rate) should be increased or decreased to change the ETBE purity towards its desired value.

Reboiler Still Column
Figure 9.1 - Non-linear Relationship Between Bottoms Temperature and Composition

The best location for the temperature sensor in this column appears to be approximately midway between the feed point and the reboiler as that location provides adequate sensitivity and avoids any convex relationship with potential manipulated variables. Figure 9.2 shows how the liquid temperature on stage 7 (middle of the stripping section) relates to the bottoms composition and, although the relationship is still strongly non-linear, and a bottoms composition of, say 90 mol%, is obtained at two temperatures (approximately 99°C and 132°C), every temperature corresponds to one, and only one, composition. Therefore, the stripping section temperature uniquely defines the operating point of the column and is suitable for inferential control of the bottoms composition. The sensitivity is also high with a change of 5°C representing only a small change in ether purity near the optimum operating point. Shifting the sensing point away from the reboiler increases the dead time in the control loop but this cannot be avoided if a stable inferential controller is to be implemented.

Operation Reboiler Duty
Figure 9 2 - Relationship Between Stripping Section Temperature and Bottoms Composition

Alternatively, the isobutene conversion could be selected as the control objective. Direct measurement of the conversion would require complex, synchronised analysers on the feed, distillate and bottoms products plus a calculation module. This combination would clearly be difficult to implement successfully and prone to instrument uncertainty. It might also result in the production of unsaleable product since there would be no guarantee that the quality specifications would be observed. Fortunately, the coincidence of phase and chemical equilibrium is usually sufficiently large so that the reaction proceeds satisfactorily under most conditions. This is indicated in Figure 9.3, which predicts the isobutene conversion for a given ETBE purity in the bottoms product. Provided that a high purity is maintained, the conversion should remain acceptable too. Thus, it is better to control the bottoms composition directly rather than the isobutene conversion. Similar arguments apply to the other process objectives: provided that an appropriate purity target is selected and then maintained, the other process objectives will be mostly satisfied.

Isobutene Process

ETBE Purity (mol%)

Figure 9.3 - Relationship Between ETBE Purity and Isobulene Conversion

ETBE Purity (mol%)

Figure 9.3 - Relationship Between ETBE Purity and Isobulene Conversion

The purity and conversion curves in Figure 9.3 do not correspond exactly and the maximum conversion is achieved at an ether purity just less than the maximum. The optimal operating point would probably be between the two maxima but would need to be determined for the specific column installation with respect to raw material costs and product values. Regular laboratory tests could be used to monitor the isobutene conversion and adjust the closed-loop control of the bottoms composition, as required, in a one-point control scheme.

Overall, it appears that a satisfactory one-point control scheme could be implemented using a temperature from the stripping section to infer the bottoms composition. This arrangement should allow the bottoms composition to be controlled between specification limits and the process to be managed around equipment constraints in order to maximise throughput. The secondary process objectives cannot be met directly as there are insufficient available degrees of freedom but the careful selection of operating point will allow satisfactory performance to be maintained.

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