Two- and Three-parameter Model

As mentioned in Chapter 6, for a reaction rate constant of the Arrhenius type we can write (Equation 6.18)  

the effectiveness factor is a function of three parameters a, e and a Thiele modulus. Therefore we speak of a three-parameter model. 

The number C, is the dimensionless ratio of the maximum increase in conversion rate due to intraparticle temperature gradients and the conversion rate at surface temperature. This can be seen as follows  

is the conversion rate for the surface temperature and Rm is the conversion rate that would have been obtained for the maximum temperature that can occur inside the catalyst pellet. 

the effectiveness factor is given by two parameters and a Thiele modulus. So, a two-parameter model is obtained if assumption 7.3 holds. The error we introduce by using a two- instead of three-parameter model is 

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It is possible to fit zero-, one-, two-, and three-parameter models to the data shown... 

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