Methods for estimating supersaturation in antisolvent crystallization systems

Abstract

The mole fraction and activity coefficient-dependent (MFAD) supersaturation expression is the least-assumptive, practical choice for calculating supersaturation in solvent mixtures. This paper reviews the basic thermodynamic derivation of the supersaturation expression, revisits common simplifying assumptions, and discusses the shortcomings of those assumptions for the design of industrial crystallization processes. A step-by-step methodology for estimating the activity-dependent supersaturation is provided with focus on ternary systems. This method requires only solubility data and thermal property data from a single differential scanning calorimetry (DSC) experiment. Two case studies are presented, where common simplifications to the MFAD supersaturation expression are evaluated: (1) for various levels of supersaturation of L-asparagine monohydrate in water–isopropanol mixtures and (2) for the dynamic and steady-state mixed-suspension, mixed-product removal (MSMPR) crystallization of a proprietary API in water–ethanol–tetrahydrofuran solvent mixtures. When compared to the MFAD supersaturation estimation, it becomes clear that errors in excess of 190% may be introduced in the estimation of the crystallization driving force by making unnecessary simplifications to the supersaturation expression. These errors can result in additional parameter regression errors – sometimes by nearly an order of magnitude – for nucleation and growth kinetic parameters, limiting the accurate simulation of dynamic and steady-state crystallization systems.