Sergio D. Keegan

A One-Dimensional Equivalent Model to Evaluate Overall Reaction Rates in Catalytic Pellets

The problem of finding a one-dimensional (ID) model to approximate the behaviour of actual three-dimensional (3D) catalyst pellets is undertaken. It is shown that the ID model proposed by Burghardt and Kubaczka (Chem Eng Proc 35: 65–74, 1996), called here the generalized cylinder (GC) model, is most suitable for this purpose, provided that its main parameter (the shape power σ) is fitted to the behaviour of the actual pellet at low reaction rates. Calculations from the GC model are expected to be precise at around 1% for most geometrical cases of practical interest. The evaluation of σ for a given pellet geometry involves the solution of a Poisson equation. An approximate method that greatly simplifies this task for finite cylinders of any cross-section shape is developed. The procedure assumes knowledge of σ just for the cross-section (at most, a 2D problem). This is readily available for some practical cases, but if not, a suitable numerical procedure based on the boundary element method (BEM) is proposed. BEM is also suitable for the general 3D case.

Approximation of the effectiveness factor in catalytic pellets

The 1D model proposed by Burghardt and Kubaczka [Chem. Eng. Proc. 35 (1996) 65] to approximate the behavior of 3D catalytic pellets has been recently found able to provide accurate results for evaluating effective reaction rates when its parameter σ is suitable adjusted [Chem. Eng. Res. Des., submitted for publication]. This parameter represents the contraction of the cross-section available for diffusion. A formulation coupling a first-order Galerkin approximation with a truncated asymptotic expansion is proposed here to evaluate the effectiveness factor of single reactions in the range of interest −1/5 <σ< 5 [Chem. Eng. Res. Des., submitted for publication]. The formulation provides a 3% level of precision for essentially all normal kinetics of practical interest and a large range of abnormal kinetics. In particular, this conclusion includes reaction rates approaching a zero-order reaction, for which large deviations arise from the use of previous approximations proposed in the literature. On the other hand, the extent of abnormal kinetics being accurately approximated is significantly enlarged.