Effective models for packed-bed catalytic reactors

An approach based on the theory of dynamical systems is used to derive rigorously effective or pseudohomogeneous type models for catalytic reactors. In the absence of a reaction, it is shown that the two-phase model for describing heat/mass transfer in a packed-bed reduces to the pseudohomogeneous model only if the ratio of the interphase transfer time to the convection time is smaller than a critical value, which is of order unity. The length scale used to define the convection time, is generally not equal to the length of the bed but depends on the initial conditions. When a chemical reaction occurs in the solid phase, it is shown that an effective model may exist only if the interphase transfer time is smaller than both the residence time and the characteristic reaction time. More importantly, our results indicate that the mathematical form of the effective model is substantially different from the standard pseudohomogeneous models used in the literature. For example, in addition to the usual dispersion terms, the effective model includes corrections to the convection and source terms as well as additional: cross-coupling convection terms between the species and energy balances. It is also shown that the effective dispersion coefficients of the pseudohomogeneous models depend on the reaction parameters and formulas are derived for this dependence. (C) 1999 Elsevier Science Ltd. All rights reserved.