Computational fluid dynamics modelling of continuous crystallisation platforms

In manufacturing scale industrial crystallisers, it is crucial to maintain good mixing conditions, where the solution mixture is completely homogeneous, to achieve a crystal product with the desired critical quality attributes (CQAs) such as: narrow crystal size distribution (CSD), large mean crystal size and right polymorphic form. Moreover, operating at increased mixing intensity reduces concentration and temperature gradients, albeit, operating at extreme mixing conditions could also result in the broadening of the CSD due to increased crystal-crystal, crystal-impeller, crystal-wall collisions. Hence it is important to find the right conditions that provide adequate mixing without having detrimental effects on the crystal product. Some of the key parameters that have a significant effect on CQAs are mixing dependant e.g. heat and mass transfer, crystal suspension and residence time distribution (RTD). All these can be modelled using a numerical simulation via Computation Fluid Dynamics (CFD).

The research work reported here, a CFD based approach to assessing mixing and hydrodynamics in continuous crystallisation processes has been sought. This methodology is developed into a framework that can be applied to the assessment of flow and mixing in crystallisation platforms.

First in the framework development, flow variables: velocity, pressure, shear rate are assessed. Then the framework is extended to include determination of residence time distribution, axial dispersion and heat transfer. The framework is first applied on a meso-scale oscillatory baffled crystalliser (meso-OBC). Here, a full characterisation of flow in a 5 mm internal diameter meso-OBC is carried out. Conditions that give near plug flow performance are uncovered through the assessment of RTD and axial dispersion in the meso tube. It was found that, for good mixing, it was best to operate the meso-OBC at low values of x_0≤1 mm and medium values of f~6Hz. The magnitude of the shear strain rate was also investigated, and it was found to be highest near the walls of the baffle constriction and the region immediately after the constriction. The shear rate was evenly distributed for 〖Re〗_o>70 with its magnitude in the range 15-2000 s-1. It was concluded that with fine tuning of the oscillation conditions, low axial dispersion coefficient values and narrow RTD curves could be achieved which approximate to plug flow like behaviour. The axial dispersion coefficient showed more sensitivity towards oscillation amplitude than frequency. The axial dispersion coefficient showed an increase with net flow Reynolds number (〖Re〗_n). The lowest axial dispersion coefficient obtained in the meso-OBC for the conditions investigated was 7×〖10〗^(-5) m2 s-1 (0.5 mm amplitude and 6 Hz frequency at 〖Re〗_n=24), which would lead to plug flow (D/UL<0.01) in tube lengths of L≥1.6 meters. The heat transfer coefficient showed an increase with oscillatory Reynolds number with a maximum value being achieved at 〖Re〗_o~200 and further increase in 〖Re〗_o having an insignificant improvement in the heat transfer performance.

Furthermore, the framework is applied to assess the hydrodynamic performance of ten OBC tubes of mean internal diameter of 10 mm but different baffle geometry at their critical oscillation amplitude for particle suspension (x_o,crit). The geometries had varying geometric parameters i.e. baffle spacing (l), baffle spacing to diameter ratio (l/D), baffle free area (α) and baffle type (smooth or sharp edge baffles). The simulated conditions were frequency f=5 Hz, volumetric flow rate, q= 17.8 ml/min and the experimentally determined x_o,crit for each tube. At these conditions the tubes were assessed to ascertain which tube presented the best plug flow performance for both liquid and solid phase. For the liquid phase, tube E presented the best plug flow like behaviour while tube B exhibited the lowest D_a for the solid phase. In general, the liquid phase emerged first at the exit (output probe) ahead of the solids. The axial dispersion coefficients obtained for the liquid and solid differed greatly in all tubes apart from tube B which showed the closest similarity in magnitude of axial dispersion coefficient for the two phases.

Finally, the ability of the STAR-CCM+ inbuilt population balance model (S-Gamma) to simulate crystallisation was assessed using a paracetamol-water cooling crystallisation process in four different platforms namely: straight unbaffled tube, batch STC, MSMPR and meso-OBC. First the model was tested in simple laminar flow in a straight unbaffled tube. With successfully simulation of this test case, the paracetamol-water system was applied to slightly more complicated flow problems in the three platforms to further study its capabilities. The batch crystallisation process was initialised with very high supersaturation to obtain noticeable crystal growth in a short physical time span because of computational constraints. Mean size increased from 50 to 77 μm within 5 seconds of simulated physical time. The MSMPR simulation results showed low mean size in the tank and by extension at the outlet as well. The reason was not evident, it could be because of the steady state nature of the simulation and the lack of a time dependent temperature profile at the wall to control the process and keep it within the metastable zone width of the solubility-supersolubility diagram (favourable for growth). The meso-OBC was not solved to steady state due to computational constraints, however, even with the short simulated physical time of 132 s (equivalent to 2 residence times), it was observed that the inlet conditions were affected by the mixing of the downstream solution with the upstream due to the oscillatory nature of the flow. The S-Gamma model worked for the simple case of a straight unbaffled tube under laminar flow but gave inconsistent results for the other three crystallisation platforms studied.