Supersaturation Or the Crystal Size Distribution

Supersaturation or the Crystal Size DistributionWhich Measurement Is More Important?

In an ideal world, you may want to directly measure the crystal population within the crystallizer (a critical product quality attribute) and measure the supersaturation which is driving the process (a critical process parameter).  Today’s advanced Process Analytical Technology (PAT) allows you to measure both of these critical parameters in real time. But where should you begin – especially if budget constraints limit you to implementing only one advanced measurement.

The crystal population, as discussed previously, is often the product itself. An online measurement of the crystals gives you the possibility of control and the possibility of assurance that the crystals meet final product specifications before actually being discharged from the crystallizer.

Supersaturation monitoring and control
can provide an optimal path to your final product. However, without actual crystal population information, this only makes sense if you have tight control of the crystallizer vessel, a precise supersaturation measurement, and a very reliable model of the system (i.e. where you can predict nucleation and growth as a function of supersaturation with reasonable accuracy throughout the operating range).

In laboratory-scale R&D this is certainly achievable.   However, in a larger scale crystallizer there are limitations and complications that make the control of the crystallizer based solely on supersaturation very difficult. As discussed previously, gradients in temperature (and therefore supersaturation) and solids concentration throughout the vessel can have a dramatic impact on the crystal population. Therefore, to compensate for these potential gradients – without measuring the crystals themselves – the controlled level of supersaturation has to be tuned down to limit the maximum level of supersaturation that might occur.

And that’s not really control, just avoidance.

If you manage to control the crystal product using only supersaturation, chances are you are over-tuned to stay far away from conditions that might promote nucleation. This likely means the production rate is not optimized.  From the viewpoint of process control, you can think of the two measurements as examples of feedforward and feedback control. Supersaturation gives you the ability to predict what is going to happen (feedforward), but you need a near-perfect model and a high level of measurement precision for this to work. In some batch crystallization applications, this has been shown to be successful using mid-IR as the measurement of supersaturation.

Measuring the crystals in process with FBRM® real-time measurement (allowing feedback control) is much more reliable for dealing with disturbances. However, as with any feedback control, you actually depend on a slight disturbance before you can respond and correct the system.

An analogy of supersaturation control is simply trying to get from one location to another using a map (your model of the process) and a compass (your supersaturation measurement). To get to the desired endpoint, you need to know your starting point (clear liquor concentration) and you need to know what effect each step will have along your path. If your map is correct and your measurement has sufficient accuracy, you should reach your destination. But if there are changes to the terrain (such as the presence of impurities), or if your measurement is less than perfect, you can drift off course.

Measurement of the crystal population, following the same analogy, is the addition of a global positioning system (GPS). It tells you exactly where you are throughout the course of the batch (within the accuracy of the measurement of course.) The GPS (crystal population measurement), used along with the map (process model), will guide you more effectively than the map (model) and compass (supersaturation). The best results would be achieved with all three components (and one can note that all GPS navigation systems actually do combine GPS location with a map and a compass).

And in a similar way, many of the best examples of batch crystallizer control actually use both FBRM® crystal population measurement and supersaturation measurement in their models and control algorithms (see academic research from the research groups of Prof. Richard Braatz (UIUC, USA)2,3,4, Prof. Sohrab Rohani (Western Ontario, Canada)5, Prof. Marco Mazzotti (ETH, Switzerland)6, and Prof. Brian Glennon (UCD, Ireland)7 ). These advanced model-based controllers using neural networks and fuzzy logic rely on measurements of both supersaturation and the crystal population for optimum results.

If you have to choose one method of advanced Process Analytical Technology (PAT), measuring the crystals themselves is the best option for control AND assurance that the product will meet specifications. Supersaturation is very valuable in understanding and modeling the system, but it provides limited monitoring and control capability without real-time confirmation of the crystal size distribution.

This is an excerpt from the white paper – A Guide to Scale-up of Batch Crystallization from Lab to Plant.

Authors
Terry Redman, MSc, MBA
Benjamin Smith, BSC
Mark Barrett BE, PhD

References
2. X. Y. Woo, Z. K. Nagy, R. B. H. Tan, R. D. Braatz, Adaptive Concentration Control of Cooling and Antisolvent Crystallization with Laser Backscattering Measurement, Crystal Growth & Design, 9 (1): 182-191 (2009).
3. Z. K. Nagy, M. Fujiwara, J. W. Chew, and R. D. Braatz. Comparative performance of concentration and temperature controlled batch crystallizations. Special Issue in Honor of Dale Seborg, J. of Process Control, 18 (3-4): 399-407 (2008).
4. T. Togkalidou, H.-H. Tung, Y. Sun, A. Andrews, and R. D. Braatz. Parameter estimation and optimization of a loosely-bound aggregating pharmaceutical crystallization using in-situ infrared and laser backscattering measurements. Ind. Eng. Chem. Res., 43 (19):6168-6181, (2004).
5. M. Trifkovic, M. Sheikhzadeh, and S. Rohani, Multivariable real-time optimal control of a cooling and antisolvent semibatch crystallization process, AIChE J., 55 (10): 2591-2602 (2009).
6. C. Lindenberg, M. Krättli, J. Cornel, J. Brozio, and M. Mazzotti, Design and Optimization of a Combined Cooling/antisolvent Crystallization Process, Crystal Growth & Design, 9(2): 1124-1136 (2009).
7. D. O’Grady, M. Barrett, E. Casey, B. Glennon, The effect of mixing on the metastable zone width and nucleation kinetics in the anti-solvent crystallization of benzoic acid. Chemical Engineering Research and Design, Transactions, 85 (A7):945-952 (2007).

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