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Received August 8, 2012
Accepted November 3, 2012
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Applications of high-order approximate models for unsteady-state diffusion and reaction in a catalyst
enGibbs, A-503 Shin Young Gwell Estates, 93-10, Bansong-dong, Hwasung, Gyeonggi 445-160, Korea 1Department of Chemical Engineering, Kyungpook National University, Daegu 702-701, Korea
jtlee@knu.ac.kr
Korean Journal of Chemical Engineering, March 2013, 30(3), 580-586(7), 10.1007/s11814-012-0188-8
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Abstract
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.
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References
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