Establishing a multi-vial design space for the freeze-drying process by means of mathematical modeling of the primary drying stage

Primary drying is the most critical stage of the freeze-drying process. This work aimed to establish a design space for this process by means of mathematical modeling of the primary drying stage, capable of addressing the thermal characteristics of distinct vial suppliers. Modeling of primary drying was implemented on Microsoft Excel using steady-state heat and mass transfer equations at two extreme conditions as assessed by risk analysis, to predict product temperature and primary-drying time. The heat transfer coefficients (Kv) of four different vial suppliers were experimentally determined, both, at the center and edge of the freeze-dryer’s shelf. Statistically significant differences (ANOVA p<0.05) were observed between suppliers throughout the assessed pressure range. Overall, the average Kve/Kvc (edge/center) ratio was higher than 1.6 for all suppliers due to the radiation effect. A design space for the drying process was established using mathematical modeling taking into account the Kv of the worst-case supplier, in the shelf edge. A primary drying cycle was carried out at a shelf temperature of -25°C and a chamber pressure of 45 mTorr for 8% sucrose and at -10°C and 75 mTorr for 5% NaCl. Freeze-dried products with good cosmetic appearance were obtained for the four vial suppliers both, in the shelf center and edge. The results show that it is possible to predict and establish the critical parameters for the primary drying stage, under a design space concept, considering the differences in the Kv of vial suppliers without adverse consequences on the quality of the finished freeze-dried product.

初级干燥是冷冻干燥工艺中最关键的一环。本研究旨在通过建立初级干燥阶段的数学模型，对该过程进行设计空间构建，模型能够解决不同瓶供应商的热特性问题。初级干燥的建模工作采用Microsoft Excel完成，运用稳态热质传递方程，在风险评估确定的两个极端条件下进行，以预测产品温度和初级干燥时间。通过对四个不同瓶供应商的热传递系数（Kv）进行实验测定，发现其在冻干机的搁架中心及边缘均有显著差异（ANOVA p<0.05）。总体而言，由于辐射效应，所有供应商的平均Kve/Kvc（边缘/中心）比率均高于1.6。基于最坏情况供应商的Kv，在搁架边缘建立了干燥过程的设计空间。在-25°C的搁架温度和45 mTorr的腔室压力下，对8%蔗糖进行初级干燥，在-10°C和75 mTorr下对5%氯化钠进行干燥。对于四个瓶供应商，无论是在搁架中心还是边缘，均获得了外观良好的冻干产品。结果表明，在考虑瓶供应商Kv差异的设计空间概念下，可以预测并建立初级干燥阶段的临界参数，而对最终冻干产品的质量不产生不利影响。