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 本研究室推導出一個在球型載體上製備非均勻觸媒之含浸及乾燥過程的數學模式。含浸模式（硝酸鎳及檸檬酸之共含浸），包含了四個偏微分方程式；而乾燥模式，則包含了五個偏微分方程式和一個常微分方程式。我們藉著變數變換的方法將移動邊界的含浸過程轉換成固定邊界，並且將數學模式中之偏微分方程式藉由正交配置法(Orthogonal Collocation)轉換成常微分方程式，再用Gear Method 解之。為了製備理想金屬分佈之觸媒，我們發展了一個最佳化的程式去找尋出最佳的含浸條件（含浸濃度、共含浸物濃度、含浸時間），而此程式則使用GRG2(Generalized reduced gradient method)找最佳化條件。 在電腦模擬中所使用的參數皆為本研究室早期研究的實驗數據。由模擬結果得到下列結論：當含浸時間或含浸物濃度增加時，載體觸媒內的金屬分佈會向球體中心移動。同時，琪最大值亦會增加。再者，硝酸鎳在載體上之覆蓋率及最大值會隨著檸檬酸濃度的增加而變大。最佳化問題結果顯示我們可以求出整體最大值，而且，此為一多極大值之問題，然而，整體最大值落在一個極小的長方體中。
 A mathematical model of dry-impregnation and drying for preparing non-uniform catalyst in a spherical support has been developed. The model for dry-impregnation, which was used for co-impregnation of nickel nitrate and citric acid, consists four simultaneous PDE’s, while the model for drying consists five PDE’s and one ODE. The dry-impregnation model is a moving-boundary problem which has been transformed to a fixed-boundary one by change of variables. The simultaneous PDE’s in the mathematical model have been transformed to a series of ODE’s by orthogonal collocation. Gear’s method was used to solve the ODE’s. To prepare a catalyst with desired metal distribution, an optimization problem was set up to search for the best impregnation conditions including impregnation time and bulk concentrations of nickel nitrate and citric acid. Generalized reduced gradient method was used to find the optimal. The parameters used in computer simulation are experimental data obtained previously in this research group. Simulation results show that, as impregnation time or Ni concentration increases, the metal distribution moves toward the center of the pellet. In the meantime, the value of the maximum increases. Both the maximum value and the average amount of the nickel nitrate become larger with increasing acid concentration. Results of the optimization problem show that a global maximum can be obtained, and the problem is a multi-optimum one, however, the global optimum is located in a small cuboid.
 ACKNOWLEDGEMENTS ABSTRACT CHINESE ABSTRACT TABLE OF CONTENTES LIST OF TABLES LIST OF FIGURES NOTATION CHAPTER 1 INTRODUCTION 1.1 Previous Study 1.2 Objective of This Study CHAPTER 2 MATHEMATICAL MODEL 2.1 Co-impregnation Model in Spherical Support 2.2 Drying Model in Spherical Support 2.3 Dimensionless Transform for Co-impregnation Model 2.4 Dimensionless Transform for Drying Model 2.5 Change of Variable for Co-Impregnation Model 2.6 Penetration Velocity Model 2.7 Determination of Temperature — Dependent Parameters in Drying Model CHAPTER 3 NUMERICAL METHODS 3.1 Orthogonal Collocation Method for Co-impregnation in Spherical Support 3.2 Orthogonal Collocation Method for Drying in Spherical Support CHAPTER 4 MODEL PARAMETERS AND OPTIMIZATION PROBLEM 4.1 Model Parameters 4.2 Optimization Problem CHAPTER 5 RESULTS AND DISCUSSION 5.1 Results of Computer Simulation CHAPTER 6 CONCLUSIONS REFERENCES
 1. Satterfield, C. N., “Heterogeneous Catalysis in Practice”, 2nd ed. McGraw-Hill, New York (1991).2. Lee, S. Y. and R. Aris, “The Dirtribution of Active Ingredients in Supported Catalyst Prepared by Impregnation,” Catal. Rev. Sci. Eng., 27, 207 (1985).3. Ann, B. J., “Simulation of Dynamic Behaviors of Catalyst Co Impregnantion by Orthogonal Collocation,” Master Thesis, Tatung Institute of Technology, Taipei, Taiwan (1998).4. Huang, K. C., “Simulation of Dynamic Behaviors of Catalyst Drying by Orthogonal Collocation,” Master Thesis, Tatung University, Taipei, Taiwan (2001).5. Lin, H.C., “Preparation of Nonuniform Catalyst：Simulation of Dry Impregnation by Orthogonal Collocation,” Master Thesis, Tatung University, Taipei, Taiwan (2001).6. Houng, J.A., “Simulation of Catalyst Impregnation by Orthogonal Collocation: A Two dimensional Model,” Master Thesis, Tatung University, Taipei, Taiwan (2002).7. Shen, C.H., “Study on Orthogonal Collocation Method Used in Transferring Partial Differential Equations to Ordinary Differential Equations,” Master Thesis, Tatung University, Taipei, Taiwan (2002).8. Peng, C. H., “Preparation of Multilayered Catalyst: A Successive Impregnation Model and Independently-Determined Parameters,” Master Thesis, Tatung Institute of Technology, Taipei, Taiwan (1996).9. Ferguson, N. B. and B. A. Finlayson, “Transient Chemical Reaction Analysis by Orthogonal Collocation,” Chem. Eng. J., 1, 327 (1970).10. Richard, G. R. and D. D. Duong, “Applied Mathematics and Modeling for Chemical Engineers,” Jonh Wiley & Sons, Inc., (1995).11. Tsai, Y. T., “A Non-Isothermal Mathematical Model for Catalyst Drying,” Master Thesis, Tatung Institute of Technology, Taipei, Taiwan (1995)12. Stewart, W. E. and J. Villadsen, AIChE., 15, 28 (1953).13. Chiou, Y. J., “Preparation of Nonuniform Catalyst by Impregnantion,” Master Thesis, Tatung Institute of Technology, Taipei, Taiwan (1992).14. Finlayson, B. A., “Packed Bed Reactor Analysis by Orthogonal Collocation,” Chem. Eng. Sci., 26, 1081 (1971).15. Leon, S. L. and A. D. Waren, “GRG2 User Guide,” University of Texas at Austin, Texas (1989).16.“IMSL Computational Technology Toolkit,” 593, Visual Numerics, Inc (1997).
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