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On the solution of the one-dimensional variable-diffusivity model to predict effectiveness factor
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DOI：10.1016/j.ces.2026.123785.png)
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Abstract
En 中文
The one-dimensional variable-diffusivity model (1D-VD), proposed by Mocciaro et al. (2011) to approximate the shape-effect of 3D catalytic pellets on effective reaction rates, was found to provide accurate results. The shape-effect is introduced by a diffusion coefficient depending on the spatial coordinate. As the purpose of the 1D-VD model is to strongly reduce computational demand, the search for an efficient numerical procedure to solve the governing equation is undertaken here for single reactions. A global procedure is proposed combining a weighted residuals method (WRM) for low values of Thiele modulus I with an analytical solution for the high range of I. Well established WRMs were tried for a representative set of commercial 3D-pellets, finding that the performance was poorer than expected for some of the pellets. The regular perturbation analysis on I2 was helpful to disclose that such behaviour is caused by the nature of the diffusivity coefficient of the model. Moreover, the analysis allowed identifying that, when integrated to the global procedure, the Finite Element Method with at most 4 elements of suitable sizes leads to predictions of the effectiveness factor at any I with an accuracy higher than 2%, for a wide range of kinetic expressions.
Keywords:
Diffusion-reaction phenomena
Catalyst pellet shapes
Effectiveness factor
One-dimensional model
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