Crystallization of active pharmaceutical ingredients (API) is one of the most important and complex multiphase engineering operations in pharmaceutical manufacturing industry. The desired physicochemical properties of solid crystalline product, such as crystal size distribution (CSD), are achieved by optimizing appropriate analyzed process operating conditions. In this application-derived study, an efficient straightforward mathematical modelling approach for the d value targeted CSD (characterized by 10^th, 50^th, and 90^th centiles d₁₀, d₅₀, and d₉₀) optimization of the API fesoterodine fumarate (FF) batches in different solvent mixtures on reactor dimension scales from 0.1 to 15 L is presented. The model is based on energy, mass, and population balance equations, the thermodynamic system equilibrium between solute/solution, and the kinetics of nucleation, crystal growth, and crystal agglomeration. In the first set of two experiments, the ability of the model to predict final CSD under chosen operating conditions was validated applying particular previously estimated kinetic parameters. An excellent statistical agreement between predicted and experimental CSD results was observed. Furthermore, the utility of the model to determine suitable operating conditions for the formation of FF crystals with d value defined CSD is presented. Two additional experiments were designed where stirring, cooling rate, and the amount of seed were optimally regressed. Good agreement between targeted and experimental CSD was shown and depending on the chosen vessel unit, mixing & cooling rates had the strongest relative impact on CSD. Algorithm may be beneficially utilized early during API industrial technological development, intensification, and scale-up, or transferred to continuous flow.

药物活性成分（API）的结晶是药物制造行业中最重要，最复杂的多阶段工程操作之一。通过优化适当的分析过程操作条件，可以实现固态晶体产品的所需理化特性，例如晶体尺寸分布（CSD）。在本申请中衍生的研究，对于一种有效的简单的数学建模方法d值靶向CSD（特征在于10^个，50^个和90^个百分位数ð ₁₀，d ₅₀，和d ₉₀）提出了在反应器尺寸范围为0.1至15 L的不同溶剂混合物中优化API非索罗定富马酸酯（FF）批次的方法。该模型基于能量，质量和总体平衡方程，溶质/溶液之间的热力学系统平衡以及成核，晶体生长和晶体团聚的动力学。在两个实验的第一组中，使用特定的先前估算的动力学参数验证了模型在选定的运行条件下预测最终CSD的能力。观察到的CSD预测结果与实验结果之间存在极好的统计一致性。此外，该模型可用于确定合适的操作条件以形成具有d的FF晶体提供了定义值的CSD。设计了另外两个实验，在这些实验中，搅拌，冷却速率和种子数量均得到了最佳回归。显示了目标CSD和实验CSD之间的良好一致性，并且取决于所选的容器单位，混合和冷却速率对CSD的影响最大。在API工业技术开发，增强和扩大规模的早期，可以有益地利用算法，或者将其转换为连续流。