Population balance modeling and digital design of degree of agglomeration in industrial crystallization

Abstract This study presents a coupled population balance model (PBM) for describing the degree‐of‐agglomeration (DoA) in crystallization by independently tracking total particle and agglomerate number densities. Applied to an industrial active pharmaceutical ingredient, the model outperformed bridge‐counting methods and accurately captured DoA trends using only inline concentration and crystal size distributions (CSDs). An optimization strategy minimizing agglomeration through temperature and cooling adjustments showed that thermal cycling reduced agglomeration and enhanced crystallinity. A multi‐objective optimization revealed improvements in dispersity and crystallinity, albeit with reduced particle size. Model‐based quality‐by‐control profiles surpassed the original quality‐by‐design recipe in agglomeration control and robustness, validated by image analysis and scanning electron microscopy. The optimized strategy also shortened batch times without compromising quality, demonstrating the benefits of digital design in crystallization optimization.