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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Cho, W., Lee, J. Applications of high-order approximate models for unsteady-state diffusion and reaction in a catalyst. Korean J. Chem. Eng. 30, 580–586 (2013). https://doi.org/10.1007/s11814-012-0188-8
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DOI: https://doi.org/10.1007/s11814-012-0188-8