(472e) Model-Driven Controller Design for Continuous Crystallisation of ?-Lactose Monohydrate

The focus of this work is to improve the method of designing controllers for continuous crystallisation platforms. The current method of designing a controller for such a platform is iterative and requires significant data collection of process outputs across an array of process conditions[1][2]. The obvious issue with this method is the waste of precious material. This work focusses on bypassing this issue by designing a controller based upon a mechanistic model that accurately depicts the crystallisation process of the chosen material.

The focus of this research is to build a model that accurately depicts the crystallisation of alpha-lactose monohydrate (ALM) from water via cooling that can then be used instead of copious large scale experiments. The building of a mechanistic model requires the individual mechanisms of crystallisation to be defined accurately in order to build a full kinetic description of the system. As such, the experiments were designed to include conditions that would highlight individual mechanisms within the crystallisation process as well as minimising the remaining competing mechanisms[3][4].

Theory

This research was based on work previously done by Perez-Calvo, Kadam and Kramer[3]. The structure of the experiments is designed to allow for individual mechanisms to be assessed by altering process conditions to minimize competing mechanisms and maximize those of current interest. The mechanisms studied in previous work were: growth (volume diffusion and surface integration), nucleation (primary and secondary) and agglomeration[3].

Methods and Materials

The ALM used for bulk material was purchased from Sigma Aldrich, UK. The seeding material for these experiments was recrystallized from the bulk material excepting the 5 µm seeds as these were purchased directly from DFE Pharma. Finally, all water used within these experiments was deionised and laboratory grade.

A chosen mass of ALM was weighed out and supplied to a corresponding mass of water within the 100 ml EasyMax vessel to achieve precise concentrations. The vessel and its content were then heated to a temperature at least 5°C above the saturation temperature. The contents were then held at this temperature for an hour to ensure complete dissolution. The temperature was then lowered to obtain the chosen supersaturation ratio. At this point the experiments were split between seeded and unseeded dependent on the crystallisation mechanism of interest.

The different crystallisation mechanisms were assessed under an array of supersaturation ratios and concentrations varying from 1.1-1.4 and 19.18-35.13 wt% respectively. This allowed for a larger workspace to be covered in the data collection stage and will ultimately allow for a more robust model to be developed.

Seeded Desupersaturation Experiments

Growth and secondary nucleation kinetics were assessed under seeded conditions with 400 rpm and 900 rpm stirring rate, respectively. The seed was added to the vessel either dry or as a slurry depending on the mechanism being studied. The system was then held at this temperature for a minimum of 5 hours to allow time for the mechanism being investigated to have a significant effect on the system and resulting particle size.

Unseeded Desupersaturation Experiments

To investigate the primary nucleation kinetics of this system, induction experiments were carried out. The system was held at the chosen temperature until nucleation is detected by an increase in particle count read by the FBRM probe. The vessel was then heated above saturation temperature to dissolve particles present. The system was cycled in this manner to obtain a distribution of induction times.

Experimental Analysis

The experiments were monitored in-situ with two process analytical tool (PAT) probes: FTIR (ReactIR, Mettler 333 Toledo) and FBRM (G400, Mettler-Toledo.) The FTIR probe allowed for continual monitoring of lactose concentration in solution, while the FBRM probe monitored particle count. The particles produced and recovered experimentally were analysed using a laser diffractometer (Mastersizer 3000, Malvern Instruments) for size analysis as well as DSC and x-ray to assess form and degree of crystallinity.

Modelling Platform

The modelling software used in this research is gPROMS FormulatedProduct 1.6.1 (Process Systems Enterprise Ltd.). This software utilises population balance modelling to describe and simulate the crystallisation process. The basis of the models themselves, incorporate the mutarotation kinetics of lactose when in solution. This inclusion allows for the accurate concentrations of the beta and alpha anomers to be calculated and defined throughout the processes. As such, the supersaturation ratios are based on alpha-lactose specifically rather than the combination of alpha and beta. In order to improve the representation of the system, a few of the physical properties have also been custom modelled including density and viscosity based on literature[5].

Within gPROMS, the raw concentration results from the experiments can be inputted to allow iteration of the unknown constants defining the individual crystallisation mechanisms models. The individual mechanistic model equations can then be defined and collated to allow for a complete working model that represents the crystallisation of ALM. In the case of the growth kinetics, the process is being modelled on the basis of a two-step Mersmann model. The choice of the two-step model allows both crystallisation and dissolution can be simulated from the resulting growth model.

Results and Discussion

The investigation of primary nucleation was found to have exceedingly long induction times at the highest supersaturation ratios and concentrations of interest in this work. With the minimum induction time recorded above 16 hours this suggested the industrial importance of this mechanism was minimal and no further investigation or modelling was completed. Similarly, the investigation of secondary nucleation from an attrition point of view was gauged via FBRM probe and no significant increase in particle count was found under the conditions of interest. As such, the presence of secondary nucleation in terms of attrition have not been continued on for the modelling aspect of this work.

Therefore, the current focus of this work is to use the outputs from the completed growth experiments as a basis for designing a corresponding growth-only model. The recorded concentration profiles and the size predictions of the produced crystalline material are compared with those predicted from the model to assess its accuracy. The current model is focused on growth and predictions lie well within the RMSE of the IR predictions, however; the predicted trends are close to linear as opposed to the exponential decay of the recorded data.

In terms of the size of particles produced there is quite a large discrepancy when comparing the experimental results to the gPROMS model predictions as can be seen in Figure 1. The mastersizer measurements were done with the introduction of ultrasound to minimize the effects of weak agglomeration. However, the recorded sizes are still larger than those predicted via the model. The continual under-sizing of PSD predictions from the model suggested the presence of agglomeration. Subsequently, samples from all growth experiments were examined using a scanning electron microscope (SEM). The SEM images show heavy agglomeration across all tested conditions and can be seen in Figure 2. As such, the presence of agglomeration could be the cause of the discrepancy between the PSD comparisons which has not currently been considered within the development of the model.

Conclusion

From the mechanisms investigated in this work, primary and secondary nucleation were not found to be present under the investigated conditions and as such have not been carried on for the modelling stage of this work. The resulting growth-only model predicts concentration profiles within an acceptable error margin with slight deviations from the true trends. However, the size predictions are consistently under-predicting across all tested conditions. From the SEM images, the necessity of incorporating the agglomeration term within the model has been highlighted to improve size prediction. This will ultimately improve the prediction capability of the model and make it a valid basis for controller design.

References

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[2] M. G. Safonov and T.-C. Tsao, “The unfalsified control concept and learning,” IEEE Trans. Automat. Contr., vol. 42, no. 6, pp. 843–847, 1997, doi: 10.1109/9.587340.

[3] J.-F. Pérez-Calvo, S. S. Kadam, and H. J. M. Kramer, “Determination of kinetics in batch cooling crystallization processes-A sequential parameter estimation approach,” AIChE J., vol. 62, no. 11, pp. 3992–4012, Nov. 2016, doi: 10.1002/aic.15295.

[4] A. H. Bari and A. B. Pandit, “Sequential Crystallization Parameter Estimation Method for Determination of Nucleation, Growth, Breakage, and Agglomeration Kinetics,” Ind. Eng. Chem. Res., vol. 57, no. 5, pp. 1370–1379, 2018, doi: 10.1021/acs.iecr.7b03995.

[5] K. R. Morison and F. M. Mackay, “Viscosity of Lactose and Whey Protein Solutions” Int. J. Food Prop., vol. 4, no. 3, pp. 441–454, Nov. 2001, doi: 10.1081/JFP-100108647.