Mass Balances for the Catalyst Particles

For the description of molecular and Knudsen diffusion inside the catalyst particles, the concept of the effective diffusion coefficient (Dei) combined with Pick s law is applied. Different catalyst geometries are accounted for by the shape factor (a = 1 for slabs, a = 2 for infinite cylinders, and a = 3 for spheres see Chapter 5). Catalytic and noncatalytic reactions are assumed to proceed simultaneously in completely wetted catalyst pores. 

Consequently, for the concentration profiles inside the catalyst particles, the component mass balance equation is written using dimensionless coordinates  

The flux into the particles (Np) is, in principle, obtained from the concentration gradients at the outer surface of the catalyst particle, but numerically a more robust way is to utilize the whole concentration profile, that is, the integrated generation rates  

The approach presented above in Equation 9.12 suppresses the effect of numerical errors originating from the solution of the differential equation. Equation 9.9. The effectiveness factors are obtained by dividing the flux in Equation 9.12 with the rate calculated with bulk-phase concentrations. 

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