本文乃是對生物膜反應器之廢水處理進行模擬，以期能在廢水處理上得到較佳的數學模式。首先，為了使生物膜反應器得到最佳化管理之理論與實作經驗，對生物膜處理系統之生長膜的了解，並建立正確的模式，是相當重要的，而且正確的模式是個有用的工具去改善生物膜反應器廢水的操作程序。生長膜的模式建立主要是分別以Monod假設及Haldane假設進行處理，前者無基質抑制，而後者則為基質抑制之條件，結合基質的質傳擴散，建立不同形式的生物膜模式，模擬生物膜內微生物生長和基質消耗的動力機制，以提供生物膜反應器的設計與操作基礎。
其次，進行生物膜反應器廢水處理之模擬。垂直流動式 (vertical flow type) 及平行流動式 (parallel flow type) 兩種針對此生物膜反應器流動方式之假設亦予以比較，進流水流速與進流基質濃度之影響亦於文中進行討論，而由單一生物膜板以及多生物膜板構成之反應器所得到的處理結果亦予以比較。
另外，在進行生物膜反應器廢水處理系統分析時，針對生物膜活性厚度、基質消耗速率、生物膜反應器處理效能等，影響的參數非常繁多，而且各個參數之間也會互相影響，但是何種參數對結果產生的影響較大，迄今仍無一定論。灰關聯分析是一種針對一群離散的序列數據，找出其中一序列對其他序列的關聯性。因此，本文以灰關聯分析結合田口實驗設計法進行分析，首先藉由田口實驗設計法中的直交表，對實驗因子先行篩選而將範圍縮小，接著利用灰關聯理論分析參數對系統的影響並做一排序，決定何種因子對系統的影響最大，進而將分析的結果供做生物膜反應器的設計與操作基礎。

In this thesis, the theoretical analysis on the biofilm reactor was carried out. It is essential to understand the activated sludge growing discs of the biofilm reactor as well as to set up a proper model. A proper model is useful to improve the operation of wastewater treatment processes. The microbial kinetic model is established based on Monod kinetics and substrate inhibition kinetics (Haldane kinetics) respectively with the consideration of mass transfer. Deep and shallow types of biofilms are both examined and discussed. The relationships between substrate utilization rate, biofilm thickness, and liquid phase substrate concentration are discussed.
Simulation results of the biofilm reactor from both kinetic models were compared from the aspect of substrate removal efficiency. Vertical flow type and parallel flow type were also compared. Influence of flow rate as well as influent substrate concentration was discussed. The results from a single-biofilm reactor and biofilm reactors connected in series were also compared.
There are several major affecting parameters in the analysis of biofilm reactor. However, currently the influence priority was not yet studied. The influence order of the factors that affect the biofilm thickness, substrate removal efficiency and performance of the biofilm reactor is studied and discussed by combining Taguchi method and grey relational analysis.

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