在批次結晶槽中濾餅的過濾阻力之最適化

Abstract

批次結晶廣泛應用於化學、製藥及相關產業中，用以將晶體產品從溶液中分離出來。相較於連續結晶，批次結晶具有更高的操作彈性，更適合用來獲得狹窄分布的產品晶體粒徑分布（CSD）。而產品的晶體粒徑分布對過濾性能及後續製程有顯著影響。為了有效優化批次結晶過程，必須理解晶體粒徑分布與濾餅可過濾性之間的關係。然而，這種估算具有挑戰性，目前針對優化批次結晶濾餅可過濾性的研究仍相當稀少。 Fang 等人 [1] 提出了一種根據特定晶體粒徑分布有效預測濾餅可過濾性的方法。該方法結合了由 Bourcier 等人 [3] 修改的 Kozeny-Carman 方程式 [2]，以及離散元法（DEM）[4]。在他們的方法中，首先利用結晶器模型根據結晶器的操作條件（如停留時間與晶體成長速率）預測產品的晶體粒徑分布；接著使用離散元法預測晶體濾餅的結構與孔隙率；然後，再使用經 Bourcier 等人修正、可應用於具有粒徑分布晶體濾餅的 Kozeny-Carman 方程式，來預測濾餅的過濾阻力；最後，根據濾餅過濾阻力進行過濾器設計，並估算整個結晶與過濾系統的總成本。此方法亦已被 Tan 等人 [5] 應用於包含細晶溶解與產品分級的連續結晶系統中。 在本研究中，該方法被用來評估不同操作條件下批次結晶器所產生晶體產品的濾餅可過濾性，目的是找出最佳的批次結晶操作條件。研究探討了三項對結晶操作影響重大的變數：晶種添加量、批次時間以及冷卻軌跡。結果顯示，濾餅過濾阻力對晶種添加量與冷卻軌跡的變化並不敏感。線性與二次冷卻曲線所產生的晶體產品，其粒徑分布相似。進一步結果指出，雖然晶種添加量主要影響大晶體的生成，但濾餅過濾阻力主要由小晶體的粒徑分布所決定，而該分布在不同晶種添加量下變化不大。在所有操作變數中，批次時間的影響最大。延長批次時間可降低過飽和度與成核速率，進而產生較大晶體並改善濾餅的可過濾性。此外，本研究也進行了參數分析，探討不同成核與成長速率對結果的影響。

Batch crystallization is widely used in the chemical, pharmaceutical and related industries to separate crystalline products from solution. Compared to continuous crystallization, batch crystallization offers greater flexibility and is better suited for achieving narrow product crystal size distributions (CSD). The product CSD significantly impacts filterability and downstream processes. In order to properly optimize batch crystallization processes it is necessary to understand the relationship between CSD and cake filterability. However, such estimation is challenging, and studies on optimizing cake filterability in batch crystallization are rare. Fang et al. [1] proposed an efficient method for estimating cake filterability based on a specified product CSD. Their method combines the Kozeny-Carman equation [2], as modified by Bourcier et al. [3] with the discrete element method (DEM) [4]. In their method a crystallizer model is used to predict a product crystal size distribution based on crystallizer properties such as residence time and crystal growth rate. Then the crystal cake structure and porosity are predicted using the discrete element method. Next, the Kozeny-Carman equation, modified by Bourcier et al. so that it can be applied to crystal cakes with size dispersity, is used to predict the filter cake resistance. Finally, the filter cake resistance is used to design the filter and the total cost of the combined system can be estimated. The method was further applied to continuous crystallizers with fines dissolution and product classification by Tan et al. [5]. In the present study, this method is applied to evaluate the filterability of crystalline products from a batch crystallizer under various operating conditions with the goal of determining the optimal recipe for batch crystallizer operation. The effect of three important crystallizer operating variables are studied: seed loading, batch time, and cooling trajectory. The results suggest that that cake resistance is relatively insensitive to seed loading and cooling trajectory. The linear cooling trajectory and quadratic cooling trajectory are found to produce crystalline product with a similar CSD. Results further suggest that while seed loading primarily affects the size of large crystals, cake resistance is predominantly determined by the CSD of small crystals, which remains nearly the same for different seed loadings. Among the three operating variables, the most significant factor is batch time. Extending the batch time reduces supersaturation and nucleation rates, leading to larger crystals and improved cake filterability. A parametric analysis was also conducted to study the effect of different nucleation and growth rates on the results.