To be able to determine the reaction temperature at a certain position along a channel in a converter’s monolith at a certain time, energy balances should be made on the solid and the gaseous phase. The following schematic of the reactor and the reactor channel should help to visualize the situation.
The authors need to define many material constants in order to perform this analysis. These important parameters are listed below.
In general, energy balances obey the energy conservation law which can be expressed in terms of temperature and reactor parameters as shown below for the case of the energy balance on the solid phase. As explained before, the energy balance on a solid depends on conduction and convection heat transfer mechanisms as well as on the heat generated by the reactions occurring.
In the gas phase the balance is somewhat different because the accumulation of heat in the gas in considered to be negligible, thus there is no accumulation term.
The mass balance is another important element in the mathematical description of our reaction system. In this study, the authors presumed that the reactants entering the channels, diffuse into the solid surface, and react such that no reactant loss is taken into account. The resulting expression:
These three mass balances mathematically describe the reactor’s behavior under a set of conditions and allow the modeling of the reactions taking place within it.