廢水處理在現代社會一直是個相當重要的議題，傳統的方法包括化學沉澱法，其缺點為產生大量含水之泥漿，處理成本居高不下。顆粒流體化床用於長晶程序最大的優點在於產物不含水，且可做進一步的回收應用。另外流體化之顆粒提供了大量表面積，使反應速率及效率提高。蕭立鼎教授於2001年提出了一數學模型，用來模擬流體化床中溶液濃度變化及晶體顆粒大小之分布。在此論文中，我們首先引用蕭教授之文獻來描述顆粒流體化床中的長晶程序，接著我們利用MATLAB建構出一個數學模型，應用在不同的化學系統中去模擬及檢視各個實驗變數對於時間以及位置的變化性。接著我們根據此模型之模擬結果，提出一個可能的流體化床設計程序。我們可以決定一些基本的實驗參數，匯入模型模擬並且觀察在給定的初始條件下是否能夠達到我們所想要的目標。這個數學模型及設計程序提供了我們相當多有用的資訊，讓我們能夠了解長晶程序於顆粒流體化床中的許多面貌，也能夠進一步的應用在實際的工業製程上。

Wastewater treatment has been a significant issue in modern society, typical process including chemical precipitation, which generates large amounts of water-rich sludge that has to be disposed of with increasing costs. The major advantage of using a fluidized pellet bed for crystallization process is the production of small amount of water-free and reusable pellets without extra sludge. Another characteristic of the FBPR is that fluidization of pellets provides large crystallization surface, so that the process operates at high rate and high efficiency. Shiau et al, 2001[1] proposed a mathematical model to simulate concentration and crystal size profile inside a fluidized pellet bed reactor. In this thesis, we first introduce Shiau’s model to describe the crystallization process in a fluidized pellet bed reactor. Then we apply this model with MATLAB to examine several chemical systems to see how the experimental variables change with time and positions. Next, a general reactor design procedure is built according to the simulation results of the model. We can determine some basic parameters and run the model to see if the outlet consequences meet our goal under certain initial conditions. It provides us many useful information in reactor design and gives general features about a FPBR. It’s also applicable to practical industrial processes.

口試委員會審定書 I
Acknowledgement II
摘要 III
Abstract IV
List of figures VII
List of tables XII
1 Introduction
1.1 Overview 1
1.2 Literature survey 2
1.3 Review of crystallization kinetics 5
2 Modeling of a fluidized pellet bed reactor for crystallization process
2.1 Introduction 6
2.2 Modeling 8
3 Simulation
3.1 Introduction 14
3.2 Case study 14
3.3 Simulation results 15
3.4 Variable verification 20
3.5 Conclusions and discussions 29
4 Application to other chemical systems
4.1 Introduction 31
4.2 Calcium fluoride system 31
4.3 Struvite system 48
5 Reactor design procedure
5.1 Introduction 63
5.2 Reactor design procedure 63
5.3 Case study 65
6 Conclusion 75
7 Notations 76
8 Reference 80

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