Single particle unreacted core models

Most of the gas-solid reactions that have been studied appear to proceed by the shrinking core reaction mode. In the simplest type of unreacted core model it is assumed that there is a non-porous unreacted solid with the reaction taking place in an infinitely thin zone separating the core from a completely reacted product as shown in Fig. 3.36 for a spherical particle. Considering a reaction between a gaseous reactant A and a solid B and assuming that a coherent porous solid product is formed, five consecutive steps may be distinguished in the overall process  

If no gaseous products are formed, steps (4) and (5) cannot contribute to the resistance of the overall process. Similarly, when gaseous products are formed, their counterdiffusion away from the reaction zone may influence the effective diffusivity 

The shrinking core reaction mode is not necessarily limited to non-porous unreacted solids. With a fast reaction in a porous solid, diffusion into the core and chemical reaction occur in parallel. The mechanism of the process is very similar to the mechanism of the catalysed gas-solid reactions where the Thiele modulus is large, the effectiveness factor is small and the reaction is confined to a thin zone (Section 3.3.1). This combination of reaction with core diffusion gives rise to a reaction zone which, although not infinitely thin but diffuse, nevertheless advances into the core at a steady rate. 

Before a simple mathematical analysis is possible a further restriction needs to be applied it is assumed that the rate of advance of the reaction zone is small compared with the diffusional velocity of A through the product layer, i.e. that a pseudo steady-state exists. 

Unreacted Core Model—Fast Chemical Reaction 

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The reaction system studied includes reactions R1 and R2 only. Gaseous reduction of a single iron ore particle proceeds following the shrink unreacted core model. Gas film resistance on mass transfer around the particle could be ignored since ore fines are under bubbling state. The shrink unreacted core model is used for expressing the reaction rates of R1 and R2 and they are expressed as Eqs.( 3-4). 

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