Reaction and diffusion in the catalytic washcoat

Catalytic monoliths are structured heterogeneous reactors. These two features require the consideration of the reaction-diffusion problem in the catalytic washcoat (the internal region), which can be designed with much more independence from the external domain, when compared to nonstructured reactors. In general, the operating conditions will be such that 

It is curious that despite the levels of complexity involved (with different sources), the bottom line of the existing studies is still the computation of the classical effectiveness factor or of the average reaction rate. Whenever possible, simple 

In a simplified reaction-diffusion model for a pseudo-homogeneous catalytic coating (the assumptions involved can be found, e.g., in Ref. [95]), the mass balance is given by 

Axial diffusion is ignored based on the previous considerations regarding the typical geometric ranges for monolith reactors (see following text), and the dependence of concentration on this coordinate is only introduced by the boundary condition at the surface (concentration continuity). The dimensionless variables are defined as follows (see Nomenclature section at the end of this chapter)  

It is possible to observe that a ID model to describe diffusion in the directions normal to the axial one was adopted (similarly to that described for channel flow and mass transfer in Sections 8.2.1 and 8.2.2). Hence, a shape factor a appears in order to translate the deviation between the actual geometry and the one modeled with reduced dimensionality. The behavior of an isothermal catalytic coating (and consequently its effectiveness) is mainly governed by two parameters (a is the previously defined aspect ratio)  

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