Theoretical analysis of the propagation of a reaction front in a packed bed

Abstract

The propagation of a reaction front through a packed bed is analyzed theoretically. The chemical reaction rate is represented by Arrhenius temperature kinetics with external transfer limitation and general power law dependency on both gaseous and solid reactant concentrations. Analogous to so-called "Activation Energy Asymptotics" developed for premixed laminar flames, the largeness of the activation energy of the chemical reaction is exploited to derive asymptotic solutions from the three governing differential equations pertaining to transport of heat, of solid reactant, and of gaseous reactant, making use of the method of matched asymptotic expansions. Two regions are distinguished, i.e., an outer region or preheat zone and an inner region or reaction zone. In the preheat zone, the reaction terms can be neglected as compared to the convective and diffusive terms. In the reaction zone, the diffusion of heat is dominating over the convective heat transport mechanism and balances the heat of reaction. In accordance with the magnitudes taken for the Lewis numbers, for solid and gaseous reactants convective transports are dominating and submitting diffusive transports in the reaction zone, respectively. Solutions in closed form are presented for governing variables including reaction front velocity whereby previously published results appear as special cases. The solutions provide direct insight into underlying physical processes and enable the effects of important parameters to be quantified analytically. © 2001 by The Combustion Institute

Grate Furnace Combustion: A Submodel for the Solid Fuel Layer

“…[10] is given. The model consists of a set of three equations for the porosity of the fuel bed , the temperature T and the oxygen mass fraction Y as a function of the spatial coordinate x.…”

“…The model consists of a set of three equations for the porosity of the fuel bed , the temperature T and the oxygen mass fraction Y as a function of the spatial coordinate x. In order to obtain this set, the original timedependent model equations have been transformed to a reference frame traveling at the same velocity as the combustion front [9]. This results in:…”

“…Therefore, a limited set of equations based on a model from the literature [9] is used. The predictions of the model are at the length scale of the bed, while in the model chemistry and transport processes at the level of a single particle are accounted for.…”

“…Firstly, it is shown that this model can be solved also numerically, while in the past it has been solved analytically only [10]. This opens the possibility to extend the model for increased accuracy and flexibility if necessary.…”

“…Suffice it to remark that the model currently predicts conversion rates that have the correct order of magnitude compared to experimental results (eg. [14]) which is good, considering that i) the model is not highly detailed, while fixed bed conversion is a complex process, ii) no adaption of the model constants was performed to fit the model to the measurements, iii) there are large uncertainties in some of the model constants and iv) there are large uncertainties in experimental results reported (compare [10] with [14])…”