Continuous Supersaturation Control Results

The graphs for the continuous supersaturation control scenarios consist of 5 plots. The first row of plots are the feed flow rate and temperature trend and the phase diagram, followed by the supersaturation (output) trend, the temperature (input) profile and finally the crystal mean size. The results of the first scenario are shown in Figure 4-31. The feed conditions are constant in this scenario and the supersaturation target of 0.0006 g/g is reached quickly by the controller. The reason for this is because the feed temperature is at 305 K and during the first two minutes of open-loop simulation, the feed is reducing the temperature of the system and increasing the supersaturation. The system is initialised with the jacket temperature at 350 K for this reason, to prevent the supersaturation of the open-loop simulation overshooting the reference trajectory before the MPC is enabled. Then, the input profile shows a steady decrease for the first 100 minutes over which the system is in a transient phase where the MPC is cooling the MSMPR to maintain the supersaturation trajectory, thus changing the point of steady state operation that would be converged in open-loop. The controller settles on steady-state production after 100 minutes. The transient period also results in a change in the crystal mean size from the seed size of 10 µm to 20.6 µm, so at steady state there is a mean growth of 10.6 µm experienced. Furthermore, the phase diagram shows the trajectory of the operating profile and unlike the long batch trajectories which end at a low temperature and saturated, the MSMPR converges to a point of operation at a temperature above 306 K and operates in a supersaturated location in the phase diagram, thus the amount of recovered paracetamol in a single stage MSMPR is much smaller than that of batch.

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The next scenario shown in Figure 4-32 has a 50% larger seed loading than scenario 1. This again results in a higher depletion rate of supersaturation which requires a faster cooling rate to maintain the supersaturation target. As seen in the first 55 minutes of the simulation results, the output does not appear to converge onto the target immediately. This is caused by the SFL-Plant constraints which have an imposed move-limit on the inputs of 1 K/min, the system cannot cool fast enough to maintain the supersaturation rate. However, unlike the batch case, the continuous MSMPR production is at a steady-state position and the temperature limit of the system happens to be low enough that eventually steady state production will be reached and supersaturation control will be possible to the desired target. The feed flow rate is the same as the previous scenario so again the system reaches the steady state in a similar time after 100 minutes. The phase diagram also shows that this system’s steady state position is at a lower temperature but still supersaturated. This will result in a higher recovery of material. The crystal mean-size in the outlet of the MSMPR is also the same as the previous scenario, once steady state is reached.

The final scenario without disturbances is scenario 3 (Figure 4-33) where the seed loading is the same as scenario 1 (0.5 g/L) but the seed size is doubled from 10 µm to 20 µm. The resulting system shows a slight overshoot in the supersaturation trajectory which is related again to a smaller 2nd _{moment because the seed size is increased for the same seed loading.}

Thus the rate of supersaturation consumption is smaller than scenario 1. This results in immediate heating of the system from the initial jacket temperature of 350 K. Furthermore, the steady state operating point is reached in the same time as the previous scenarios but the operating point is at a higher temperature in the phase diagram, over 312 K, thus the recovery of material will be low at steady state in this single-stage MSMPR. The crystal mean-size grows from the 20 µm seed to 30.6 µm crystals though. Overall, these scenarios that are absent of disturbances demonstrate the ability of SFL-MPC to control continuous MSMPR crystallization with SFL-Plant constraints and the output trajectories are reasonable. The next stage is to consider the four scenarios where feed disturbances are applied.

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Scenario 4 with the feed temperature disturbances for the 10 µm seed size and 0.5 g/L seed loading is shown in Figure 4-34. The main difference between this trajectory and that of scenario 1 is that the temperature disturbances in the feed have a significant impact on the supersaturation profile. The SFL-MPC does indeed converge onto the setpoint, but the converged appears to require more time than prior cases. The input moves are mostly at their move limit between each implementation of the MPC, which suggests that the cooling rate limit imposed on the inputs is not sufficient enough to completely counteract the disturbances, but is sufficient to ensure the process still operates around the same target supersaturation. The resulting system also appears to operate at a lower temperature in the phase diagram, but this cannot be concluded through the operating profile because the system temperature is fluctuating throughout operation. The crystal mean-size in the outlet does appear to be similar to that of scenario 1 but the mean-size fluctuates in the range of 20 ± 3 µm.

Scenario 5 shown in Figure 4-35 aims to combine disturbances to both the feed temperature and feed flow rate to establish is the effects of multiple disturbances on the continuous process. The main conclusions from these results are that the process does not appear to require as long a time to settle near steady-state as scenario 4, but the effects of the combined disturbances do cause greater fluctuations in the supersaturation profile. However, the supersaturation remains centred on the setpoint, so given the limitations imposed by the SFL-Plant constraints on the inputs, the results in this scenario are also acceptable for the control problem. The outlet crystal mean size is also similar to that of scenario 4.

Finally, the CQA results for continuous MSMPR crystallization control are disclosed in Table 4-18. The results show that for the larger seed size, a larger mean size is obtained and a smaller COV is also achieved. For all scenarios with a 10 µm seed size, the outlet crystal number-weighted mean size appears to be similar and in the region of 20.6 µm. The yield also appeared to be larger for the 10 µm seeds size than for the scenario with a 20 µm seed size, and the recovery follows a similar trend too. This is expected though because the larger seed size will not consume as much supersaturation during the transient phase when at the supersaturation setpoint. This can be aided by adjusting the supersaturation setpoint based on the seed size and seed loading. To determine the best supersaturation setpoint to maximise the recovery and yield from given initial conditions, it is recommended to perform

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an offline optimization to maximise recovery and/or yield given the seed conditions using the setpoint as the decision variable. Alternatively, a multi-stage MSMPR approach can also be used to increase the paracetamol recovery.

Scenario

Mean Size

(µm) COV Recovery (%) Yield (%)

1 _{20.59 0.515 22.7 90.6}

2 _{20.59 0.515 34.1 93.6}

3 _{30.59 0.347 5.5 70.3}

4 _{20.15 ± 2.99 0.496 ± 0.17 20.7 90.3}

5 _{20.38 ± 2.72 0.501 ± 0.19 23.5 90.3}

Table 4-18 – Summary of KPIs for all Continuous Supersaturation Control Scenarios

Another approach is to select a different control problem and try to control one of the CQAs directly. This leads into the following section where instead of continuous MSMPR supersaturation control, the crystal mean-size will be used for control. The optimization of crystal mean-size in batch has been performed in chapter 3 of this research and by other authors too (Sarkar, Rohani and Jutan, 2006; Hemalatha et al., 2018). The crystal mean-size has also been used for control problems in various research, but the use of SFL-MPC to control mean-size has not been reported.

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