Controlling Crystallization through Modeling

CFD modeling and particle population control are key to improving processes and product quality at the crystallizer, and further downstream.

By Kumar Dhanasekharan, Ph.D., Consulting Team Leader, Fluent, Inc., and Terry Ring, Ph.D., Professor, Dept. of Chemical Engineering, University of Utah

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Controlling a product’s crystal size distribution (CSD) is one of the key challenges in drug manufacturing. CSD control is critical to successful crystallizer operation and to product quality and purity, as CSD often impacts downstream processing such as filtration, centrifugation and milling. Size distribution also affects the rate at which a powdered material dissolves in the body. Thus, greater control of CSD leads to better control of the release rate of active ingredients.

In spite of its importance, CSD control is not well understood. Part of the complexity is that size distribution varies in space and time in a crystallizer due to non-ideal flow patterns and heat transfer. Furthermore, it is dependent upon solution thermodynamics and crystallization phenomena such as nucleation, growth, aggregation and breakage.

A better understanding of CSD can be gained through detailed modeling such as computational fluid dynamics, or CFD, which studies the effect of fluid mechanics and non-ideal mixing on processes (see A CFD Primer, below). CFD is an established technology that can predict the fluid flow and mixing characteristics in a wide range of applications. It can also facilitate product scale-up through better understanding of the interactive effects of mixing, fluid mechanics, solid and liquid chemical-physical properties, and the overall supersaturation profile. Such a science-based approach falls directly in line with FDA’s process analytical technology (PAT) initiative.

Despite their importance, detailed models have not been used to their full potential in pharmaceutical crystallization. Simple models such as Mixed-Suspension Mixed-Product Removal (MSMPR) models have been more popular but have limited usefulness. For instance, they assume the crystallizer is well-mixed and neglect hydrodynamic effects. Nevertheless, these simple models have been used extensively in designing crystallizers and, as a result, current designs are extremely conservative and are not optimized for operation or yield.

The problem is made worse by the fact that, in pharmaceutical crystallization, new drugs are typically made in existing stirred tanks that allow for limited changes to operation profiles and no design modifications. The lack of understanding of the flow characteristics and crystallization kinetics within these tanks makes process development and scale-up difficult and time consuming.

Mixing analyses defined

Mixing analyses based on CFD can provide significant insight into the crystallization process. For example, in antisolvent addition, key decisions about the feed location, feed pipe diameter and feed rates can be made by understanding the local flow field and local mixing characteristics. The mixing analyses can include macromixing, mesomixing and micromixing effects.

Macromixing effects include prediction of blend times, power numbers, turbulence quantities and shear quantities. During scale-up or a scale-down analysis, using these predictions can help in deciding impeller speeds (in rpm), locations and types. Since most manufacturers do not have the flexibility to change impellers or purchase new equipment, it is important to choose the right reactor vessel from those available within the production facility. An example of a mixing time analysis is shown in Figure 1, below.

Figure 1. Left: Dimensionless tracer concentration monitored at different locations as a function of time. Right: Velocity contours in tank showing regions of high velocity (red) and regions of low velocity (blue).

Figure 2. Velocity contours in a glass-lined crystallizer vessel. Antisolvent addition through a dip-tube and the feed path is shown through fluid-packets represented by spheres and colored by residence time.

Mesomixing helps in understanding local turbulence due to the addition of antisolvent or reactant. This is typically important for fast additions. Figure 2 (at right) shows an example of antisolvent addition and its path through a semi-batch crystallization process.

For slow additions, micromixing effects become important. Micromixing is mixing at a molecular scale and affects the course of the crystallization and most definitely affects particle size and morphology. The effects of micromixing can be incorporated into CFD through additional transport equations and help predict supersaturation history more accurately.

Particle population control

Population balance can be incorporated into CFD models to predict crystal size distribution. Fluid flow occurs in conjunction with evolutionary processes such as nucleation and growth, producing the crystalline phase. The population balance equation accounts for various ways in which particles of a specific state can form, migrate to another state or disappear from the system. Typically, these ways are nucleation, growth, dissolution, aggregation and breakage. Together, these processes are called crystallization phenomena.

The population balance equation is coupled with flow, energy and species (mass balance) equations through convective terms and local values such as velocity, turbulence and temperature in different parts of the crystallizer. The population is usually described by the number density of particles, and the usual conservation law can be written for the number density, which includes birth and death terms due to the above processes.

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