Korean Journal of Chemical Engineering, Vol.30, No.3, 580-586, March, 2013
Applications of high-order approximate models for unsteady-state diffusion and reaction in a catalyst
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The partial differential equation for unsteady-state diffusion, adsorption and a first-order reaction in a catalyst is often approximated to ordinary differential equations for reduced computational loads. Very high-order models obtained by the continued fraction expansion method are accurate for a wide range of the Thiele modulus and the changing frequency of surface concentration. In addition, they are numerically well-conditioned. However, due to their high dimensionalities, they will not have merits over other low-order models. Here, high-order models based on the continued fraction expansion method are shown to be used to obtain various practical models. With the Taylor series obtained from high-order models, Pade approximations are easily obtained regardless of the Thiele modulus and the shape of catalyst. Low-order models by applying the balanced truncation method to a high-order model can also be obtained, providing better approximations than the well-known Pade models.
Keywords:Adsorption Dynamics;Pore Diffusion Model;Fractional Order System;Linear Driving Force Model;Convolution
- Kim DH, AIChE J., 54(9), 2423 (2008)
- Dantas TLP, Luna FMT, Silva IJ, de Azevedo DCS, Grande CA, Rodrigues AE, Moreira RFPM, Chem. Eng. J., 169(1-3), 11 (2011)
- Glueckauf E, Trans. Faraday Soc., 51, 1540 (1998)
- Lee JT, Kim DH, Chem. Eng. Sci., 53(6), 1209 (1998)
- Cruz P, Magalhaes FD, Mendes A, Chem. Eng. Sci., 61(11), 3519 (2006)
- Patton A, Crittenden BD, Perera SP, Chem. Eng. Res. Des., 82(8), 999 (2004)
- Kim DH, AIChE J., 55(3), 834 (2009)
- Lee J, Kim DH, Chem. Eng. J., 173(2), 644 (2011)
- Kim DH, Lee J, Korean J. Chem. Eng., 29(1), 42 (2012)
- Kreyszig E, Advanced engineering mathematics, Wiley, New York (1999)
- Abramowitz M, Stegun IA, Handbook of mathematical functions, Dover Pub., New York (1972)
- Chen CF, Shieh LS, IEEE Trans. Circuit Theory., 16, 197 (1969)
- Lee JT, Edgar TF, Comput. Chem. Eng., 28(4), 479 (2004)
- Green M, Limebeer DJN, Linear robust control, Prentice-Hall, New Jersey (1995)
- MATLAB, The MathWorks, Inc.
- Kailath T, Linear Systems, Prentice-Hall, New Jersey (1980)