Effective models for packed-bed catalytic reactors

An approach based on the theory of dynamical systems is used to derive rigo rously effective or pseudohomogeneous type models for catalytic reactors. I n the absence of a reaction, it is shown that the two-phase model for descr ibing heat/mass transfer in a packed-bed reduces to the pseudohomogeneous m odel only if the ratio of the interphase transfer time to the convection ti me is smaller than a critical value, which is of order unity. The length sc ale used to define the convection time, is generally not equal to the lengt h of the bed but depends on the initial conditions. When a chemical reactio n 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 tim e and the characteristic reaction time. More importantly, our results indic ate that the mathematical form of the effective model is substantially diff erent from the standard pseudohomogeneous models used in the literature. Fo r example, in addition to the usual dispersion terms, the effective model i ncludes corrections to the convection and source terms as well as additiona l: cross-coupling convection terms between the species and energy balances. It is also shown that the effective dispersion coefficients of the pseudoh omogeneous models depend on the reaction parameters and formulas are derive d for this dependence. (C) 1999 Elsevier Science Ltd. All rights reserved.