(150a) Modeling and Analysis of Instabilities in Autothermal Packed-Bed Catalytic Reactors

Meet Shah, Vemuri Balakotaiah

University of Houston

Houston TX,77004

Keywords:

Linear stability, Bifurcation, Pattern formation

Abstract:

Packed bed reactors are among the most common reactors used in the chemical and petrochemical industries. It is a well-known fact that when one or more exothermic reactions occur in a packed bed catalytic reactor, multiple steady-states may exist, and the steady-state attained in a specific case depends on the start-up conditions. The terms “autothermal reactor” or “autothermal operation” refers to intentional operation of a reactor in the region of multiple steady-states. The optimum point of operation of most autothermal reactors falls on the ignited branch close to the extinction point. Further, the largest region of autothermal operation is attained for shallow beds for which the bed thickness is much smaller than the diameter. While such beds lead to high productivity and low pressure drop, the main disadvantage is that there may be non-uniform flow, temperature and concentration profiles in the transverse direction, which can lead to hot spot formation and other operational problems. The main objective of this work is to develop models of shallow packed bed catalytic reactors, analyze and determine the conditions under which transverse patterns and other instabilities could occur.

A 3-D two-phase model incorporating heat conduction in both phases and mass dispersion in fluid phase. Model utilizes local heat and mass transfer coefficients based on local fluid velocity. Boussinesq approximation for density variation and linear variation of viscosity with temperature is considered. Bifurcation diagram for steady state 1-D (transversely uniform) solutions obtained indicate that fluid phase dispersion marginally reduces the conversion as a result of back mixing. Increasing the adiabatic temperature rise widens the region of multiplicity. Ignited branch solutions for high values of activation energy and adiabatic temperature rise exist for very small residence time (Damköhler number < 10^-7) maintaining high solid phase temperatures close to adiabatic temperature rise. Fluid phase mass dispersion and heat conduction change the steady state behavior of the system marginally for single reaction system but alter the stability of the steady states.

Stability of steady states to transverse perturbations increases with increasing fluid phase dispersion. Neutral stability curves for different solution at same non-dimensional residence time show us that middle branch solutions are only stable to very small wavelength perturbations. Stability of middle and ignited branch are same at extinction point which is unstable with respect to long scale perturbation. Similarly the case for ignition point where middle and extinguished branches share the neutral stability curve and ignited branch is more stable compared to others. This implies that catalyst particle located at same bed length might be operating at different steady state temperature close to the ignition and extinction points. Further work will be done on 2-dimensional steady state bifurcation analysis of the model on rectangular packed bed.