Mathematical modelling of catalytic converters
Byrne H., Norbury J.
Two models of catalytic converters are developed. First a three space-dimensional time-dependent model is presented. This is subsequently simplified to a transient one-dimensional model. Both models are considered sufficiently general to provide reasonable qualitative descriptions of different types of catalytic converters, such as monolithic and packed-bed converters. The two models derive from conservation of thermal energy and mass imposed separately in the solid and gas phases whilst Darcy's Law and the perfect gas law determine the velocity and pressure fields. Lawson and Norbury (1983) and Norbury and Stuart (1989) adopted a similar approach in their derivations of models of porous medium combustion. However, here the modelling of the chemical processes occurring in the converter as three-stage is new, as is the presence of a catalyst in the solid medium. The active constituents of the gas phase must diffuse to the solid boundary, move along the solid surface to the reaction site and combine exothermically, and finally the reaction products must return to the gas mainstream. A new form of the reaction rate is suggested to describe these processes.