(174ar) Effectiveness Factor for Multi-Step Reactions

Ernest Thiele’s 1939 presentation of a dimensionless diffusion-reaction number and its application using the effectiveness factor paved the way for phenomenal advancements in the design and operation of commercial chemical reactors. However, despite its usefulness, it has been challenging to apply the effectiveness factor to multi-step chemical reactions that occur in series within catalyst particles. The authors herein present a generalized analytical solution to diffusion-reaction using the quasi-steady state approximation which is valid for first-order reactions in series which was derived using Eigenanalysis. Thus, a new corollary effectiveness factor was developed for each reaction which is a combination of all the effectiveness factors. The solution is applied to a fluid catalytic cracking (FCC) reaction scheme and compared with direct numerical simulation (DNS) of a single catalyst particle for comparison. Comparison is then made with the classical effectiveness factor approach to illustrate its superiority over existing methods available in the field. We can implement this multistep effectiveness factor into reactor scale models (e.g. DEM, two-fluid models) to accurately predict chemistry using coarse-graining with dramatically less computational cost than DNS.