First-Order Reactions. The Concept of Effectiveness

1 First-Order Reactions. The Concept of Effectiveness Factor 

When reaction occurs on the pore walls simultaneously with diffusion, the process is not a strictly consecutive one and both phenomena must be considered together. For a first-order reaction, equimolar counterdiffusion and isothermal conditions the steady-state continuity equation for A can be written when the / coordinate is oriented from the center line to the surface of the slab  

Distribution and average value of reactant concentration within a catalyst slab as a function of the parameter (f). Adapted from Levenspiel [1962). 

The concentration profiles are as shown in Fig. 3.6.1-1. The diffusion resistance causes a concentration profile in the pellet because reactants cannot diffuse in from the bulk at a sufficient rate. A small diffusion resistance (say, large De gives a rather flat profile, whereas a steep curve is obtained for a large diffusion resistance. As the rate of reaction at any point in the slab equals kpsCs( ), this profile causes an average rate which is lower than that obtained at the surface concentration C. The ratio of available area between a porous and an impervious catalyst is so large that this penalty is minimal when compared to the gain in productivity associated with the porosity. 

The curves in Fig. 3.6.1-1 could be used to directly characterize the diffusion limitations, but it is more convenient to have a rating factor for the effect. This was provided by Thiele [1939] and Zeldowich [1939], who defined the effectiveness factor  

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