Population Balance Model Development Verification and Validation of Cooling Crystallization of Carbamazepine

Abstract

Using process modeling to understand process dynamics and potentially explore the design space of a crystallization process is difficult because of its complex nature with many factors at play, such as initial concentration, supersaturation, seeding strategy, and flow pattern. In this work, a systematic approach is applied to sequentially estimate the growth and nucleation rate of the cooling crystallization of carbamazepine at various conditions in batch operation. Different formulations of the kinetic expressions are tested as a model discrimination exercise to obtain the best fit with the most confidence form. Then, based on the risk, determined by the purpose of the obtained model, verification and validation activities are applied. The model is verified and validated to predict concentration and D50 for a specific seeding strategy for crystallization mechanisms, including both nucleation and growth, are highly dependent on the seed PSD. A brief discussion is also given on the transferring of the batch-developed model to continuous operations in response to the growing interest in continuous crystallization development. It is found that the model can be transferred to continuous operations where the supersaturation and solid concentration are similar to those tested during batch experimentation. Because of the complex and interactive effects of supersaturation and solid conditions on crystallization kinetics, it is reasonable to conclude that in order to infer transferable crystallization kinetics, batch experimental conditions must be wide and similar enough to cover the potential continuous operating space.

Comparison of One-Dimensional and Two-Dimensional Population Balance Models for Optimization of a Crystallization Process for a Needle-Shaped Active Pharmaceutical Ingredient

“…When completely unconstrained, the growth rate and nucleation rate supersaturation dependencies would reach values as high as 5. Growth rate supersaturation dependencies above 2 have precedent in the literature, , and nucleation orders as high as 3 have been reported. , Hence, a value of 3 was selected as a high, yet feasible, upper bound for the supersaturation dependencies for both growth and secondary nucleation. It likely that the high dependence of the crystallization kinetics on supersaturation for this API is responsible for the observed enhanced desupersaturation rate upon an increase of supersaturation at the seed point, whereas the other process parameters (seed PSD, seed load, agitation rate) had minimal or no impact.…”

“…Classical two-step growth and the Evans secondary nucleation were evaluated to describe the crystallization mechanisms. The mass transfer step of growth is described by where G is the linear growth rate of the crystal, k d is a mass transfer coefficient, and C bulk and C int are the concentration of the solute in the bulk liquid phase and the concentration at the crystal surface, respectively.…”

“…Therefore, the crystallization process is well-suited for the population balance model (PBM), which utilizes a set of differential algebraic equations to describe the temporal evolution of the distribution of a given particle property, such as particle size distribution (PSD) . Advances in both analytical equipment and computational methods have allowed the PBM to become more increasingly accessible to the crystallization community . Typically, the PBM of the crystallization process has been conducted by utilizing a single dimension to describe the particle size and a shape factor to account for particle morphology .…”

Nanoplastic State and Fate in Aquatic Environments: Multiscale Modeling

“…Population balance models have been implemented in studies of nanoparticle precipitation, 65 polymer flocculation, 66 aerosol dynamics, 67,68 and cooling crystallization. 69 These models are extendable, that is, to integrate processes such as sedimentation, resuspension, and hydrological effects, and thus better reflect the local environment in rivers, lakes, and oceans, but few studies 47,48 have attempted to implement these for evaluating the environmental fate of nanoparticles and nanoplastics in particular.…”

Rapid, Automated Measurement of Dynamic Size Distributions and Size-Dependent Growth Rates of Crystal Ensembles within Microfluidic Flow Cells

“…Furthermore, the growth kinetics data obtained are average values obtained from crystals in constant motion and therefore do not shed detailed quantitative insights into crystal growth phenomena such as the presence of size-dependent growth. 8,26 Single, multicrystal and microfluidic growth cells have been designed to facilitate microscopic observation at the singlecrystal level and extraction of crystal growth kinetics under stagnant or flow conditions. In particular, single-crystal growth cells have been designed to facilitate sustained microscopic observations and extraction of face-specific crystal growth kinetics under stagnant conditions.…”