With the aim of simulating the product crystal size, which is one of the important physical properties for active pharmaceutical ingredients, an antisolvent crystallization model is proposed, including only six experimentally determined kinetic parameters to develop a concise model. As a first step, the methodology to assess the growth rate parameters, which are some of the six kinetic parameters, is discussed. An approach for appropriately treating the size distribution data obtained by means of the laser diffraction/scattering method is suggested. The determined growth rate parameters could be used to simulate the crystal size indicating that the simulation by crystallization modeling is a practical application for the pharmaceutical industry.

Methodologies for the estimation of nucleation rate parameters, which are rate constants and orders in antisolvent crystallization, are proposed with the aim of applying to the pharmaceutical industry. Primary and secondary nucleations are clearly distinguished and these rates are defined as power laws of the supersaturation in our antisolvent crystallization model. Primary nucleation rate parameters were experimentally determined using the theoretical equation about the modified induction time in antisolvent crystallization based on the past study reported by KubotaN. Kubota, N. J. Cryst. Growth], in which the induction time is defined as the time when the number density of the crystal reaches a fixed value. It is difficult to estimate the number density at the detection point using an experimental approach. Therefore, a numerical approach was used to determine the number density. The estimated number density at the detection point can determine the secondary nucleation rate parameters. These determined nucleation rate parameters become effective factors for simulating the number mean diameter in antisolvent crystallization and can be applied to the pharmaceutical industry.

A previously proposed method for estimating antisolvent crystallization kinetics has been successfully applied to cooling crystallization to yield kinetic parameters for simulating the crystallization process. In particular, the primary nucleation kinetics were analyzed using the modi ed induction time data, essentially as proposed by Kubota. The number density at the detection point, (N/M) det , is an important value in the kinetic analysis but is di cult to estimate experimentally. Therefore, the numerical optimization was used to estimate the value of (N/M) det in the same manner as for antisolvent crystallization. Primary nucleation was detected for both antisolvent and cooling crystallization with a sensitive detection method, visual detection, to reduce the e ects of secondary nucleation. As a result, the (N/M) det values for each method are small and almost identical (approximately 200 #/kg-solvent). The secondary nucleation and growth rate parameters for cooling crystallization were also successfully determined by numerical optimization. All the kinetic parameters determined for cooling crystallization were evaluated with experimental data. Consequently, it is con rmed that these rate parameters can simulate trends in concentration as well as the nal number mean diameter of the product crystals with acceptable accuracy. Moreover, the crystallization rate parameters determined for both antisolvent and cooling crystallization were validated with simulations and experimental data from combined crystallization, where antisolvent crystallization is followed by cooling crystallization. The simulation and experimental results for the concentration trend and number mean diameter of the produced crystal were in good agreement. The applicability of our estimation method to both antisolvent and cooling crystallization indicates the broad utility of this method for various crystallization process in the pharmaceutical industry.