The I D 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 sigma 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 < sigma < 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. (C) 2003 Elsevier Science B.V. All rights reserved.