Modeling and optimization of spherical agglomeration in suspension through a coupled population balance model

- A coupled population balance model for spherical agglomeration systems is proposed.
- The model enables simulation of crystals and agglomerate particles independently.
- First principles based process parameters (i.e. agglomeration efficiency, porosity).
- Optimization framework for both bioavailability and manufacturability targeting.
- The proposed model can lead to improved parameter estimation and kinetic studies.

The population balance model is the common approach to simulation and prediction of the size distribution and other properties of particulate systems. Population balance models include any nucleation, growth, breakage and agglomeration mechanisms that are relevant to all industrial particulate processes. However, there are some limitations to many of the previous population balance model formulations for systems with agglomeration. Limitations include physically irrelevant and/or empirically based agglomeration kernels, difficulties in assessing the influence of process conditions (e.g. hydrodynamics, particulate physical properties), solution method efficiency for optimization and control applications, and loss of information on constituent particles. These limitations have prevented the use of population balance models to accurately predict and simulate agglomeration in suspension techniques such as spherical crystallization. To overcome these limitations, an extension of the concept of a coupled population balance model is presented for application in the simulation and optimization of a spherical crystallization system. A coupled population balance model formulation has been developed for a semi-batch, reverse addition, anti-solvent crystallization system with agglomeration. The system includes nucleation and growth of the primary crystals and subsequent agglomeration. The advantages presented by a coupled population balance model formulation include the ability to optimize for specific primary and agglomerate sizes. This presents an opportunity to find optimal operating conditions that meet both bioavailability and manufacturability demands.