批次結晶程序之最適化及晶種策略

Abstract

本論文主要探討晶種批次結晶程序的設計方法。論文中主要針對兩大因素作探討：程序中之長晶速率(與過飽和度有關)以及晶種方針。論文第一部份探討晶種方針。對於某些結晶系統，使用足量的晶種(又稱為臨界晶種負載率)，可以幾乎完全壓制成核現象。本論文中提出基於成核動力式以解析的方式推導出的捷徑方程式來計算臨界晶種負載率。用捷徑方程式計算之結果與模擬詳細的程序模型所得到之結果十分符合。因此進一步使用捷徑方程式去計算約三十個不同的結晶系統之臨界晶種負載率。本論文中也應用類似的分析來計算當給定結晶產品之大小時，晶種的合適尺寸大小以及對應的晶種負載率。此類似分析方法也可應用於在批次操作中連續地加入晶種之程序。 本論文第二部份探討長晶速率之最適化。在此主要應用龐特里亞金(Pontryagin)的最小化原理來求解最適化問題。論文中考慮基於產物結晶分布之矩(moments)的九個不同的目標函數。本研究中亦探討多目標函數之最適化，並將結果與標準的捷徑途徑例如線性或立方的溫度分布比較。本研究亦表明在只知道成核動力式(與論文第一部份同樣之結晶系統)時仍可解出最適化問題，得到最適化之長晶途徑。

This thesis is concerned with the development of recipes for seeded batch crystallization processes. Two major components of such recipes are considered: the growth rate profile (which is related to the superaturation profile) during the batch and the seeding policy. The effect of seeding policy is investigated first. For some crystallization systems, it is possible to almost completely suppress nucleation by using a sufficient quantity of seeds, called the critical seed loading ratio. An analytical short-cut equation is proposed to determine critical seed loading ratio in terms of the nucleation kinetics. Results from the short-cut equation show high consistency with results from simulation using detailed process models. The shortcut equation is further applied to determine the critical seed loading ratio for a set of about thirty crystallization systems. A similar analysis is also applied to determine the feasible range of seed crystal sizes and corresponding seed loading given a desired product crystal size, and the method is also applied to the case of continuous seeding during the batch. In the second part of this thesis, the optimization of the growth rate is investigated. Pontryagin’s Minimum Principle (PMP) is applied to solve the optimization problem. Nine different objective functions based on the moments of the product crystal size distribution are considered. Multi-objective optimization problems are also solved and discussed in this work. Results are compared with standard shortcut trajectories such as the linear and cubic temperature profiles. It is shown that the optimization problem can also be solved knowing only the nucleation kinetics and the optimal growth rate trajectory is determined for the same set of crystallization systems considered in the first part of the thesis.