Isothermal reactions in porous catalyst pellets

Thiele(I4 , who predicted how in-pore diffusion would influence chemical reaction rates, employed a geometric model with isotropic properties. Both the effective diffusivity and the effective thermal conductivity are independent of position for such a model. Although idealised geometric shapes are used to depict the situation within a particle such models, as we shall see later, are quite good approximations to practical catalyst pellets. 

An analogous equation may be written for component B. By reference to Fig. 3.2, it will be seen that, because the product B diffuses outward, its flux is positive. Reaction produces B within the slab of material and hence makes the term depicting the rate of formation of B in the material balance equation positive, resulting in an equation similar in form to equation 3.10. 

The boundary conditions for the problem may be written by referring to Fig. 3.2. At the exterior surface of the slab the concentration will be that corresponding to the conditions in the bulk gas phase, provided there is no resistance to mass transfer in the gas phase. Hence  

At the centre of the slab considerations of symmetry demand that  

If the whole of the catalyst surface area were available to the exterior concentration CA there would be no diffusional resistance and the rate would then be - 2AcLkCAa . The ratio of these two rates is the effectiveness factor  

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