Wednesday, July 2, 2014

Predicting effects of micro- and mesomixing on antisolvent crystallization

Careful measurements of fed batch process dynamics in antisolvent crystallization systems are quite few and far between.  A useful paper by the UCD Crystallization group from 2007 showed effects of agitator speed and antisolvent addition rate on the observed metastable zone width (MSZW) of benzoic acid crystallizing in ethanol/water. An FBRM probe was used to detect the onset of nucleation and MSZW was generally wider at higher addition rates.  MSZW was also a little wider at higher agitation speed when the feed point was not well located (above surface near the wall of the vessel).  It became narrower with higher agitation speed when the feed was more directly into the impeller suction, an effect that can be explained by the dependence of nucleation rate on agitator speed.

Higher than average supersaturation exists near the feed point and this can lead to premature nucleation, or a negative MSZW; this was observed in the UCD study at the less effective feed position.  CFD calculations of the flow patterns in the lab vessel were used to explain some of the mixing effects. A paper from the UCD group in 2011, based on research in the SSPC consortium, included analysis of relevant turbulent mixing time constants estimated from CFD calculations.  Other nice work in this field includes the PhD of Christian Lindenberg of ETH Zurich, the institution where Professor John Bourne completed much of his work on micromixing.

Integrated, predictive models for a system like this are useful to help practitioners to find conditions producing the right crystal number (and size) in this commonly used configuration, whether seeded or not. The scale-dependent equipment characteristics are one part and we can leverage insights from the micromixing and mesomixing research community; the DynoChem library contains tools to quantify and apply these time constants, as described in a previous post.  The system-specific crystal nucleation and growth kinetics are another part and these may be fitted to solute concentration and particle number data collected during lab experimentation.  Users may select from a range of rate expressions that may or may not include MSZW as a parameter; this carries some disadvantages in predictive mode as it is somewhat dependent on the conditions under which it was measured.

We have integrated these elements into detailed and fast-running models when supporting customers on projects in this area.  We typically use a feed-zone model, in which the zone size depends on the quality of mixing and its composition lies between that of the feed material (often pure antisolvent) and the bulk.  In this zone, if nucleation kinetics are rapid, significant nucleation can occur due to high local supersaturation.  Those nuclei appear before the system as a whole is supersaturated (negative MSZW) and will mostly redissolve in the bulk if the system is not yet supersaturated as a whole.  They continue to be produced throughout the feed addition process, for as long as a (local) superaturation driving force exists.

DynoChem simulation results using this integrated model for a system like the benzoic acid/ ethanol/ water system are shown below, using typical values for crystallization kinetics and driving forces based on supersaturation (not MSZW).

Figure 1:
 The model produces typical supersaturation curves for an unseeded system, with rising supersaturation reaching a peak that occurs at higher wt% antisolvent when the addition rate is higher.  (Note that with the kinetic parameters used, the peak occurs slightly sooner at higher agitator speed.)

Figure 2:
The number of particles formed in the system is higher when the addition rate is faster; this tallies with the higher level of supersaturation reached, with a greater driving force for nucleation.  The simulation includes a direct effect of impeller speed on nucleation, leading to more particles at higher agitation speed (and fast addition).

Figure 3: In this model, the number of particles in the feed zone is tracked separately from those in the bulk; this number depends primarily on the quality of meso- and micromixing and there are more particles formed in the feed zone at lower agitator speeds.  The number of particles in the feed zone is significantly higher with fast feeding.  Note that particles are formed from the start of the addition but many of the 'oldest' dissolve in the bulk while those formed later have a better chance of remaining out of solution.  

Figure 4: A plot of bulk particle number versus wt% antisolvent, with the scale reduced to highlight the first signs of particles in the bulk, indicates that a large number of particles may exist even when the system is undersaturated and the number of particles can be several times higher with fast feeding than with slow.

Such a particle number profile would make it more likely that a negative MSZW would be observed at higher addition rates when the FBRM (or other particle monitoring) probe may detect the larger particle number.

A potentially interesting parameter to complement MSZW is the observed induction time, which in the case of the present system reduces at higher addition rates and is often well under 1 second. This underlines the importance of rapid local mixing of the feed and induction time could be used to calculate a Damkoehler type number for the system.

The stochastic nature of both MSZW and induction time is well recognized and addressed again in a recent paper.

From a practical point of view, all of this makes it even clearer that relying on uncontrolled primary nucleation as a means to obtain a desired crystal size (or number) can be a risky approach.  The same models shown here can be used to investigate the impact of seeding and to find more robust, growth-dominated conditions in a specific system.

Whatever about the quantitative and specific interpretation of the simulation results shown, the power to quickly visualize these potential impacts before experiencing them in practise is of great educational value and assists with experimental design and planning.  Which reminds me of the poster I saw on the wall at a large chemical company several years ago, which read: "Don't speculate, Simulate!".

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