Crystallization process simulation for pharmaceuticals

Scale-up of batch cooling crystallization of an Active Pharmaceutical Ingredient

Fig. 1 – The crystals were needle-shaped, with length up to 350mm

The hybrid multizonal approach – click to enlarge

Fig. 2 – The hybrid multizonal concept

Power law growth kinetics fit to data – click to enlarge

Fig. 3a – Traditional power law growth kinetics equation (above), showing poor fit to the measured solute concentration

Mass transfer and surface integration growth kinetics

Mass transfer and surface integration growth kinetics fit to data – click to enlarge

Fig. 3b – Mass transfer and surface integration growth kinetics equations (above), showing a much better fit to the measured solute concentration. Note that these equations are implicit in temperatures, T, and length, L.

Fig.4a

Chord length distribution – click to enlarge

Fig.4b

Fig.4c

NaNO3 formation before process changes – click to enlarge

Figs. 5a and 5b – Growth rates for original (upper) and optimised (lower) batch procedures

Figs. 6a and 6b – Supersaturation profiles for original (upper) and optimised (lower) batch procedures

This case involved PSE working in conjunction with a pharmaceutical company and Mettler-Toledo AutoChem to scale-up a crystalliser for an active pharmaceutical ingredient (API) from 1 litre lab scale to a 1.6 m³ production vessel.

Because of the tight schedules in pharmaceutical discovery, preclinical testing and clinical trials, only six calendar weeks are typically allowed for scale-up of the manufacturing process. This meant that there were severe time constraints on the project.

The challenge was the usual one in scale-up: to ensure that a process that worked at lab scale would continue to produce crystals of the correct size under the different hydrodynamic conditions encountered at a larger scale.

The process

The stirred-tank batch cooling process was seeded using crystals of 60 mm median size produced by milling and sieving. The crystals formed were needle-shaped, with length of up to 350mm (Fig. 1).

Initially the temperature was held constant for 30-60 minutes. It then followed a linear cooling profile to a final temperature that was held for several hours.

Solute concentration (UV) and chord length distribution (FBRM) were measured throughout.

Requirements

The objective was to scale-up the process to run in a 1.6 m³ vessel while:

retaining the same particle size distribution (PSD) as produced on 1-litre scale
achieving the same or higher purity.

In addition, the customer wished to determine the optimal batch recipe, representing the minimum batch time that could be achieved while maintaining the growth rate at less than 10^-2 µm/s, thus decreasing any incorporation of solvent and/or impurities.

The model

The model used to describe the crystallisation of an API was taken from PSE's Advanced Model Library for Solution Crystallisation (AML:SC). This library combines a population balance approach with kinetic models of crystal growth, agglomeration and attrition.

The key to the project was to ensure that the model accurately represented the observed crystal growth and attrition, by validating them against laboratory data.

Agglomeration was not observed during experimentation. It was thus assumed to be a result of sampling techniques, and not included in the model. A constant aspect ratio was assumed for the needles.

Model validation

The model was validated extensively against laboratory data, mainly to determine accurate kinetic constants for the growth kinetics.

Using traditional power law growth kinetics, there was a poor fit against observed data in certain areas for solute concentration (Fig. 3a).

However, the approach was changed to use a combined description of mass transfer and surface integration. This gave a much better fit (Fig. 3b).

Hybrid multizonal modelling

Hybrid multizonal modelling is used for predicting effects of scale-up and other changes in hydrodynamics by:

taking into account the effect of spatial non-uniformity on crystallisation phenomena caused by different hydrodynamic regimes in different parts of the vessel
at the same time using the most detailed crystallisation models possible – including, for example, fully-discretised partial differential equations (PDEs).

while keeping the overall amount of calculation required to a manageable timescale.

The approach combines crystallisation models built in gPROMS with CFD models of the zone hydrodynamics, using the gPROMS–CFD Hybrid Multizonal interface (schematically depicted in Fig. 2).

Based on experience, 10 to 100 zones is usually sufficient, with the actual number determined by engineering judgement.

By decoupling the hydrodynamics and crystallisation phenomenological model, it is possible to:

perform model validation, including detailed model-based data analysis using parameter estimation techniques. Parameter estimation typically requires 10–100 function evaluations (simulations), which would not be feasible on a full-scale hydrodynamic model.
model important dynamic effects (essential when considering batch processes) and perform dynamic optimisation.

Results

Chord lengths

Fig. 4a shows chord length distribution at three stages in the batch The disappearance of the shoulder around 100 mm seems to denote deagglomeration/breakage.

Fig. 4b shows the total count and unweighted mean chord length as a function of time. The increase in total chord count is most probably due to needle growth and attrition/breakage.

An area where further investigation is warranted is the chord length profile over time, where discrepancies between observed and predicted values were seen in the early stages of the batch (Fig. 4c).

A likely causes for the observed discrepancies is the fact that the PSD – Chord length distribution (CLD) convolution matrix assumes a constant aspect ratio, which may not be strictly true.

Optimisation

Following initial simulation runs for the batch, the problem was formulated as a dynamic optimisation with the following characteristics:

Objective function	Minimise batch time
Constraint 1 (path)	Growth rate < 0.01 µm/s
Constraint 2 (end-point)	Growth rate < 1E-5 µm/s
Constraint 3 (end-point)	Amount of seeds
Variable 1	Initial temperature
Variable 2	Cooling profile

Optimisation results

The key results are shown in Figs. 5 and 6. In Fig. 5b the optimised temperature profile can be seen (green line): a gradual cooling by 2 – 3 ° over 6 hours, followed by a similar period of more rapid cooling.

Fig. 5a shows the growth rate for the original batch procedure, which peaks dramatically about an hour after the start of the batch, then drops to nearly zero after about 4 hours.
Fig. 5b shows the growth rate for the optimised batch procedure. Growth rate is kept at less than 0.01 µm/s over the entire duration of the batch, with an end-point growth rate of 10^-5µm/s. This helps to produce much more uniform crystals.

The different growth rates are a consequence of the altered supersaturation profiles, shown in Fig. 6. for the original and optimised batch procedure respectively

Conclusions

Experience shows that the key to obtaining well-validated models is to use more rigorous rate expressions for crystallisation phenomena where possible.

This can often be done at little extra computational cost, and yields a model that is not only more accurate in the area that it is fitted, but because of the better representation of the system fundamentals, in areas outside the area that it is fitted as well.

The hybrid modelling approach allowed scale-up to the new size based with design decisions based on detailed understanding of the growth in various zones of the crystalliser.

Having created a well-validated model that gave good agreement with experimental results, it was very easy to add dynamic optimisation criteria and execute an optimisation run that came up with a completely different (and much better) operating policy.

This was also made possible because the hydrodynamics and crystallisation models could be decoupled – by using the hydrodynamic information as an input to the Crystallisation model – thus allowing the crystallisation model to run in dynamic mode to simulated behaviour over the batch cycle.

One conclusion from the model validation confidence analysis was that measurements for validation of batch systems indicate that solute concentration as a function of time plus final PSD typically contains more information than PSD as a function of time. [EXPLAIN]