https://scholars.lib.ntu.edu.tw/handle/123456789/64194
標題: | 晶種式批次結晶程序之最適化─考慮晶種成長與粒徑相關之情況 The optimization of seeded batch crystallization when growth rate is size-dependent |
作者: | 丁偉倫 Ting, Wei-Lun |
關鍵字: | 晶種式批次結晶;最適化;晶種成長;粒徑相關;無因次;過飽合度;seeded batch crystallization;optimization;size-dependent;crystal growth;non-dimensional system;supersaturation | 公開日期: | 2012 | 摘要: | 本篇論文探討當晶種成長與粒徑相關時,晶種式批次結晶程序的最適化。晶種成長與粒徑相關時的程序模型是根據Qamar et al. 提出的 Quadrature Method of Moment, Method of Characteristics 和 Duhamel’s Principle 所解出。此論文討論了四種系統,分別是Ward at el. 提出的無因次模型和三個文獻中使用的真實系統。 當使用「最小化新成核晶體的質量」為目標函數而探討無因次系統時,晶種成長的粒徑相依性對於最適化過飽和度成長曲線的形狀影響很小;換句話說,一個簡化的無粒徑相依性的晶種成長模型可以得到誤差很小的最適化成長曲線。此處理方式具有優勢,因為考慮晶種成長與粒徑無關時,最適化所需的計算時間較短。真實系統的結果也支持此結論。 此研究還針對Qamar提出的程序做了改良,即直接求出所需變數而不是用Qamar所建議的近似法。改良後的近似法,不但大量提升了準確度,還不會增加計算時間。在有大量新晶體的質量時其誤差由60%降到低於1%。最後,研究結果還顯示經由過飽合度最適化較經由溫度最適化還來的更好。 In this work, the optimization of seeded batch crystallization processes is investigated when crystal growth rate is size-dependent. The process model with size-dependent growth was solved using the Quadrature Method of Moment (QMOM), Method of Characteristics (MOCH) and Duhamel’s Principle as proposed by Qamar et al. [Chem. Eng. Sci., 2009; 64: 3659-3667]. Four systems were studied: a dimensionless model based on previous work by Ward et al. [AIChE J., 2011; 54 (3) 606-617], and three case studies based on real crystallization kinetics reported in the literature. Investigation of the dimensionless model using the objective of minimizing the nucleus-grown crystal mass shows that the size-dependency of the growth rate has only a small effect on the shape of the optimal supersaturation trajectory, i.e. an approximate, size-independent model can be used for the optimization with little error. This is advantageous because optimizing the size-independent model requires much less computational effort. Results from the real case studies also support this conclusion. A modification to the procedure of Qamar is also proposed: By calculating a parameter exactly instead of using an approximation recommended by Qamar, the accuracy of the approximation can be significantly improved without a significant increase in computational effort. The error is reduced from more than 60% to less than 1% in the case where the nucleated crystal mass is large. Finally, it is also shown that optimization over the supersaturation trajectory is preferable to optimization over the temperature trajectory. |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/252179 |
顯示於: | 化學工程學系 |
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ntu-101-R99524053-1.pdf | 23.54 kB | Adobe PDF | 檢視/開啟 |
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