General Closed Solution by Combined Model Approximation

3 General Closed Solution by Combined Model (Approximation) 

A closed solution, which can be used as an approximation, is the so-called shrinking core model with the influence of the chemical reaction, subsequently denoted 

1) Diffusion of the gaseous reactant through an entirely converted shell (product layer) of the particle, ranging from the outer surface up to a defined reaction front at r= re. 

2) Chemical reaction without pore diffusion resistance in the remaining core (0 r r -) with a constant density of the solid reactant B, p  

According to this model, the influence of diffusion is restricted to a shell free of solid reactant, whereas in reality the solid reactant is still present to a certain extent in this outer zone. This leads to an underestimation of the (mean) reaction rate. Conversely, the assumption of a constant solid concentration in the core (equivalent to the initial value) overestimates the (mean) rate as in reality the concentration of the solid and of the gaseous reactant decrease in the core. As shown in Section 6.9.4 by the example of the regeneration of a coked catalyst, these effects compensate each other quite well. 

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