Non-isothermal reactions in porous catalyst pellets

So far the effect of temperature gradients within the particle has been ignored. Strongly exothermic reactions generate a considerable amount of heat which, if conditions are to remain stable, must be transported through the particle to the exterior surface where it may then be dissipated. Similarly an endothermic reaction requires a source of heat and in this case the heat must permeate the particle from the exterior to the interior. In any event a temperature gradient within the particle is established and the chemical reaction rate will vary with position. 

We may consider the problem by writing a material and heat balance for the slab of catalyst depicted in Fig. 3.2 For an irreversible first-order exothermic reaction the material balance on reactant A is  

Because of the non-linearity of the equations the problem can only be solved in this form by numerical techniques l9 . However, an approximation may be made which gives an asymptotically exact solution 20, or, alternatively, the exponen- 

The parameter 0 represents the maximum temperature difference that could exist in the particle relative to the temperature at the exterior surface, for if we recognise that in the steady state the heat flux within an elementary thickness of the particle is balanced by the heat generated by chemical reaction then  

If equation 3.30 is then integrated from the exterior surface where T=Tm and Ca = CAm to the centre of the particle where (say) T=TM and CA - CAM we obtain  

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