(491a) Transverse Pattern Formation Analysis with Cell Model

We utilize cell model to analyze the pattern formation in packed bed reactors. We predict the region of pattern formation utilizing linear stability analysis and provide a mechanism for pattern formation in the region of multiplicity. Region of the reactor that can be considered to have uniform conversion and temperature is considered as a cell and the single layer of catalyst particles are considered as a group of N_p cells. We utilize bifurcation analysis to obtain all possible steady state solutions and predict the region of possible patterned solutions using linear stability analysis. Bifurcation analysis with larger number of particles indicate that number of stable patterned states is determined by the communication between different cells. Increasing solid thermal conduction is more effective in removing patterned states compared to increasing fluid phase conduction. Onset of the stable patterned states for larger number of cells requires bifurcation point closer to ignition and extinction point. Patterned states may be observed for continuum model in the extreme limiting case of bifurcation points coinciding with ignition and extinction point where total number of stable patterned states is infinite. Continuum model well approximates the eigenfunction corresponding to patterned state and hence can be utilized for linear stability to predict the region where patterned states may exist.

Here we show that continuum model without considering variation in solid thermal conductivity as a function of location are unable to predict stable patterned states for finite solid thermal conduction. Cell models can predict stable patterned states resulting due to different particles being in different steady states, indicating that pattern formation may result from thermo-kinetic multiplicity. We also show that physical property variation results in shift in the location of bifurcation points and region of stable patterns and not creation of additional patterned states for flowrates in consideration.