本文旨在說明反算法應用於床式反應器中化學反應問題之研究。在許多傳統床式反應器之化學反應問題中，大部分都將系統中各種熱物理性質的參數、初始條件、邊界條件以及反應率假設為已知，進而求解出反應過程中的溫度或濃度分佈，此種求解方法可以稱為正算問題。相對於正算問題，本文中所介紹的反算問題則是利用較容易取得的溫度或濃度量測值，使用共軛梯度法來針對反算問題中未知的熱或質量產生速率進行預測。以下將分別針對兩種不同的床式反應器，分為兩個章節探討。
第一章主要探討利用反算法同時預測固定床反應器中熱與質量的產生速率，我們使用反算法中的共軛梯度法來進行反算分析工作。問題的物理模型是一固定床反應器中的化學反應過程，藉由溫度與濃度的量測，同時預測此反應進行時所伴隨的熱與質量產生速率。
在本章中，我們假設兩個未知的熱與質量產生速率，其隨溫度與濃度變化的函數型態並不知道，必須藉著量測的溫度與濃度資料來反求，所以我們將此類的反算問題歸類為函數預測法(function estimation)。在此利用反算法同時預測固定床反應器中熱與質量的產生速率的問題中，我們可以利用數值實驗來模擬正確之溫度與濃度量測值，且在考慮量測誤差的情況下，檢驗反算分析的正確性。結果顯示在初始值為未知任一猜值的情況下，我們可以成功的運用共軛梯度法進行反算分析，預測出準確的熱與質量產生速率。
第二章主要探討利用反算法預測環狀床反應器中一氧化碳甲烷化反應之質量產生速率，我們同樣利用反算法中的共軛梯度法來進行反算分析工作。此問題的物理模型為一環狀床反應器中的化學反應過程，藉由濃度的量測，預測此反應進行時所伴隨的質量產生速率。
在本章中，我們假設未知的質量產生速率，其隨濃度變化的函數型態並不知道，必須藉著量測的濃度資料來反求，所以本章節的反算問題同樣歸類為函數預測法(function estimation)。同樣地，在此利用反算法預測環狀床反應器中一氧化碳甲烷化反應之質量產生速率的問題中，我們利用數值實驗來模擬正確之濃度量測值，並且考慮量測誤差。結果顯示在初始值為未知任一猜值且量測誤差變大的情況下，我們同樣可以預測出準確的質量產生速率。

The purpose of this study is to estimate the chemical reaction rates for two different types of bed reactors based on the technique of inverse problems. The direct problem of many actual chemical reactions is concerned with the determination of concentration or temperature distributions when the thermophysical properties, initial conditions, boundary conditions and reaction rates are given. In contrast, the inverse problem involves the determination of the unknown reaction rates from the knowledge of concentration or temperature measurements taken within the domain. The following two chapters will demonstrate the estimation of two different chemical reaction rate functions for a fixed-bed reactor and an annular-bed reactor based on measured concentrations and temperatures.
In chapter one of this thesis, an inverse problem is investigated to estimate simultaneously the non-linear reaction rates for a fixed-bed reactor. The Conjugate Gradient Method (CGM) based inverse algorithm is utilized in this work to predict simultaneously the unknown conversions and temperature-dependent reaction rates for a fixed-bed reactor by using interior measurements of conversions and temperature distributions.
Since no prior information on the functional form of unknown reaction rates is available, it can be classified as function estimation for the inverse calculations. The validity and accuracy of this inverse fixed-bed reactor problem was examined using the simulated exact and inexact conversions and temperature measurements in the numerical experiments. Results show that the estimation of the conversions and temperature-dependent reaction rates can be obtained within a short CPU time on an Intel Xeon Core 2 2.00 GHz personal computer and the estimations are still reliable when measurement errors are included.
In chapter two of the present thesis, an inverse problem in estimating the non-linear reaction rate for an annular-bed reactor will be examined. The Conjugate Gradient Method (CGM) is also utilized in this chapter to predict the unknown concentration-dependent reaction rate for an annular-bed reactor by using interior measurements of concentration distributions.
As was mentioned previously, due to no prior information on the functional form of unknown reaction rate is available, it can be classified as function estimation for the inverse calculation. The validity and accuracy of this inverse annular-bed reactor problem is also examined using the simulated exact and inexact concentration measurements in the numerical experiments. Results show that the estimation of the concentration-dependent reaction rate can be obtained within a short CPU time and the estimations are still accurate, even though measurement error is included.

Chapter 1
1. G. F. Froment, Fixed Bed Catalytic Reactors, Industrial and Engineering Chemistry, Vol. 59, pp. 18-27, 1976.
2. D. Ferdous, A. K. Dalai, S. K. Bej and R. W. Thring, Production of Hydrogen and Medium BTU Gas via Pyrolysis of a Kraft Lignin in a Fixed-Bed Reactor, Energy Conversion Engineering Conference and Exhibit, Vol. 2, pp. 782-792, 2010.
3. Z. You, S. You, X. Li, Y. Luo and Y. Jiao, The Carbonization Characteristics Studies of Corn Stalk in a Fixed Bed Reactor, Bioinformatics and Biomedical Engineering, pp. 1-4, 2010.
4. D. Song , S. J. Ahn, W. Cho, D. K. Park and E. S. Yoon, Analysis of The Fixed Bed Reactor for DME Synthesis, SICE-ICASE, pp. 4072-4077, 2006.
5. O. M. Alifanov, Inverse Heat Transfer Problem, Springer-Verlag, Berlin, 1994.
6. H. R. B. Orlande and M. N. Ozisik, Determination of The Reaction Function in a Reaction-Diffusion Parabolic Problem, J. Heat Transfer, Vol. 116, pp.1041-1044, 1994.
7. C. H. Huang and J. Y. Yan, An Inverse Problem in Simultaneously Measuring Temperature Dependent Thermal Conductivity and Heat Capacity, Int. J. Heat and Mass Transfer, Vol. 38, pp. 3433-3441, 1995.
8. C. H. Huang and C. W. Chen, A Steady Inverse Problem of Estimating Boundary Condition in An Irregular Domain with Statistical Analysis, Numerical Heat Transfer, Vol. 33, pp. 251-268, 1998.
9. C. H. Huang and S. C. Chin, A Two-Dimensional Inverse Problem in Imaging the Thermal Conductivity of a Non-homogeneous Medium, Int. J. Heat and Mass Transfer, Vol. 43, pp. 4061-4071, 2000.
10. C. H. Huang, A Nonlinear Inverse Vibration Problem of Estimating the External Forces for A System with Displacement-Dependent Parameters, J. Sound and Vibration, Vol. 248, pp. 789-807, 2001.
11. C. H. Huang, C. Y. Yeh and Helcio R. B. Orlande, A Non-Linear Inverse Problem in Simultaneously Estimating the Heat and Mass Production Rates for A Chemically Reacting Fluid, Chemical Engineering Science, Vol. 58, pp. 3741-3752, 2003.
12. IMSL Library Edition 10.0. User's Manual: Math Library Version 1.0, IMSL, Houston, TX, 1987.

Chapter 2
1. M. E. Davis and J. Yamanis, Analysis of Annular Bed Reactor for Methanation of Carbon Monoxide, AlChE Journal, Vol. 28, pp. 266-273, 1982.
2. P. Cheng and C. T. Hsu, Fully-developed, forced convective flow through an annular packed-sphere bed with wall effects, Int. J. Heat and Mass Transfer, Vol. 29, pp. 1843-1853, 1986.
3. F. J. Doyle III, R. Jackson and J. C. Ginestra, The Phenomenon of Pinning in An Annular Moving Bed Reactor with Crossflow of Gas, Chemical Engineering Science, Vol. 41, pp. 1485-1495, 1986.
4. G. B. Raupp, J. A. Nico, S. Annangi, R. Changrani, and R. Annapragada, Two-Flux Radiation-Field Model for an Annular Packed-Bed Photocatalytic Oxidation Reactor, AIChE Journal, Vol. 43, pp. 792-801, 1997.
5. O. M. Alifanov, Inverse Heat Transfer Problem, Springer-Verlag, Berlin, 1994.
6. H. R. B. Orlande and M. N. Ozisik, Determination of the reaction function in a reaction-diffusion parabolic problem, J. Heat Transfer, Vol. 116, pp. 1041-1044, 1994.
7. C. H. Huang and J. Y. Yan, An Inverse Problem in Simultaneously Measuring Temperature Dependent Thermal Conductivity and Heat Capacity, Int. J. Heat and Mass Transfer, Vol. 38, pp. 3433-3441, 1995.
8. C. H. Huang and C. W. Chen, A Steady Inverse Problem of Estimating Boundary Condition in An Irregular Domain with Statistical Analysis, Numerical Heat Transfer, Vol. 33, pp. 251-268, 1998.
9. C. H. Huang and S. C. Chin, A Two-Dimensional Inverse Problem in Imaging the Thermal Conductivity of a Non-homogeneous Medium, Int. J. Heat and Mass Transfer, Vol. 43, pp. 4061-4071, 2000.
10. C. H. Huang, A Nonlinear Inverse Vibration Problem of Estimating the External Forces for A System with Displacement-Dependent Parameters, J. Sound and Vibration, Vol. 248, pp. 789-807, 2001.
11. C. H. Huang, C. Y. Yeh and Helcio R. B. Orlande, A Non-Linear Inverse Problem in Simultaneously Estimating the Heat and Mass Production Rates for A Chemically Reacting Fluid, Chemical Engineering Science, Vol. 58, pp. 3741-3752, 2003.
12. IMSL Library Edition 10.0. User's Manual: Math Library Version 1.0, IMSL, Houston, TX, 1987.