Analysis of temperature patterns in shallow-bed autothermal catalytic reactors

Abstract

Stationary transverse temperature patterns have been observed in packed-bed catalytic reactors used to carry out exothermic reactions in the autothermal mode of operation. In the literature, pattern formation was explained using physical property variations and different rates of heat and mass transport by utilizing continuum models but with less emphasis on the impact of thermokinetic multiplicity at the catalyst particle length scale. In this work, we show that continuum models with uniform averaged bed properties (e.g. effective radial conductivity) are unable to predict stable patterns whenever multiplicity exists at the cell or particle length scale. In such cases, we reason that cell models that incorporate and properly represent the appropriate physical phenomena can predict stable patterns that arise due to multiplicity at the particle or cell length scale. We analyze the bounds for stable pattern formation in shallow-bed reactors operated in the region of multiple steady-states and present a procedure for determining the bed conductivity needed for eliminating the patterned states. The general cell models analyzed incorporate physical property variations and approach the continuum limit for vanishingly small cell size. Our analysis shows that the inclusion of physical property variation compounds the impact of multiple mechanisms on pattern formation.