(23d) Modeling and Simulation of Coaxial Crystallizers by Dynamically Coupled Population Balance, Macromixing, and Micromixing Models

A leading method for the crystallization of pharmaceutical compounds is to rapidly mix an antisolvent with a solvent saturated with the desired drug. Many crystallizer designs have been explored to generate high supersaturation in such mixtures as an approach for generating consistent crystal nuclei that are subsequently grown to a desired size [1-5]. Compared to cross-flow mixers, coaxial jet mixers have negligible buildup of crystalline material on their surfaces and are less likely to plug. Coaxial mixers can be designed to deliver rapid turbulent mixing using short sections of pipe. As the energy required for mixing is provided by the inlet streams, with no moving metal parts and no bearings, these devices have simple maintenance and operation. Some experimental and modeling studies of coaxial crystallizers have been published to gain deeper understanding and to facilitate more efficient development and optimization of the coaxial mixer crystallization process [6-9]. Important design parameters for crystallization in coaxial mixers are the length of pipe downstream of the injection point, the velocity and temperature of the inlet streams, and the inner and outer pipe diameters.  

This presentation describes an effort whose goal is to speed up the design of the coaxial crystallizers to tailor the crystal size distribution according to the bioavailability and drug administration requirements. Dynamic simulations of a confirmed coaxial crystallizer were carried out that simultaneously solve partial differential equations for macromixing, micromixing, and a population balance for the crystals. The computational model [10-11] was used, which replaced a quadrature-method-of-moments model used to simulate the time evolution of the particle size distribution by Rodney Fox [12] with a full spatially varying population balance model implemented using a high resolution finite-volume method. This presentation employs an extension of the model [10-11] to include the temperature effects on the crystallization. Our simulations were used to perform a parameter sensitivity analysis (see [13] for background on such analyses) to identify the key model parameters and to simulate variations on their values on the full crystal size distribution (CSD) in the antisolvent crystallization of Lovastatin, using kinetics reported in the literature [14]. The effects of inlet concentrations and stream flow rates on CSD were numerically investigated and compared with CSDs obtained in a dual-impinging jet crystallizer [11]. As observed in simulations of dual impinging jets, the mean crystal size and the width of the distribution were found to decrease with an increase in inlet stream velocity. The simulation results showed different degrees of inhomogeneity in the supersaturation and the nucleation and growth rates for different inlet stream flow rates.

To the authors’ knowledge, this is the most detailed simulation study on coaxial crystallizers reported to date. The simulation results show the feasibility of tailoring a specific crystal size distribution by adjusting the operating conditions (such as inlet stream velocities) of the coaxial crystallizer. Such computational tools can provide a technological advancement for the process development in the pharmaceutical industry by providing a more in-depth understanding of the crystallization process, and by reducing the number of experiments required to determine the optimum operating conditions, to reduce the quantify of active pharmaceutical ingredient (API) needed for the experiments. Consequently, the crystallizer process design can be performed much earlier during the drug development process, where a limited quantity of API is available.

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