Bifurcation and Stability Analysis of Temperature Patterns in Shallow-bed Catalytic Reactors



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Packed-bed catalytic reactors are widely used in industry to carry out many exothermic reactions. Reaction induced flow instabilities can lead to temperature patterns and localized hot spots through multiple mechanisms in these reactors. This work examines two of these mechanisms that lead to the formation of complex temperature patterns that bifurcate from the uniform state using continuum and discrete models.

In the first part of the work, a two-phase finite dispersion continuum model is utilized to analyze the instabilities arising due to coupling between momentum, species and energy balances and variation of fluid physical properties with temperature. It is found that multiple flow rates through the reactor are possible for the same pressure drop. Linear stability analysis is used to determine the impact of catalyst particle size (bed permeability), reactor aspect ratio and reaction parameters on the stability boundary under different boundary conditions.

The second part of the work examines temperature patterns due the existence of multiple steady states at the catalyst particle scale. Generalized cell models are developed to understand the impact of multiple length scales in the reactor and their impact on stable temperature patterns. Transverse arrangement of cells is used to examine pattern formation due to thermokinetic multiplicity occurring at smaller length scales of the reactor. Linear stability and bifurcation analysis are utilized to compute various stable and unstable patterned branches, and the impact of various parameters. Transient analysis is performed to determine the basins of attraction of various patterned states in the phase space.

The third part of the work examines transverse 2D arrangement of cells to understand the pattern formation behavior in shallow bed reactors. The boundaries of stable patterns for different reactor geometries and scaling of the bed conductivity at which stable patterns are eliminated with reactor size are determined. Models with 2D arrangement of cells with axial variation in temperature and concentrations and multiple reactions are analyzed to further explain the experimentally observed patterns.



Particle ignition, Cell model, Bifurcation, Thermoflow multiplicity, Thermokinetic multiplicity


Portions of this document appear in: M.Shah, D. West, V. Balakotaiah, Analysis of temperature patterns in shallow-bed autothermal catalytic reactors, Chemical Engineering Journal 437 (2022), 135027,; and in: M.Shah, D. West, V. Balakotaiah, Bifurcation and stability analysis of temperature patterns in shallow-bed catalytic reactors, Chemical Engineering Journal 446 (2022), 137146,