Thiele modulus effectiveness factors modeled with

Comparison of the Effectiveness Factors Modeled with Presto Kinetics and Calculated by Means of the Thiele Modulus Lpore = 6.75-10-4 m -%... 

The calculated time-dependent effectiveness factor as a function of Thiele modulus along with experimental observation is shown in Fig, 2. The solid lines represent the computed effectiveness factor using Eq, 4 and the broken line represents experimental values. When compared with experimental data, we sec that the mathematical model represents the actual behaviour quite well. 

If the catalyst is dispersed throughout the pellet, then internal diffusion of the species within the pores of the pellet, along with simultaneous reaction(s) must be accounted for if the prevailing Thiele modulus > 1. This aspect gives rise to the effectiveness factor" problem, to which a significant amount of effort, summarized by Aris ( ), has been devoted in the literature. It is important to realize that if the catalyst pellet effectiveness factor is different from unity, then the packed-bed reactor model must be a heterogeneous model it cannot be a pseudohomogeneous model. 

Solve the model exactly and compare the numerical solution to the solution obtained with the approximate Thiele modulus and effectiveness factor approaches shown in Figure 7.26. 

The molecular weight differences between lignin and its model compounds also complicate the use of model compound kinetics in a predictive simulation. The mobility of a high-molecular weight polymer would be much less than that of smaller model substrates (14). As for catalyst decay, a simple model was used to probe transport issues. For a first order, irreversible reaction in an isothermal, spherical catalyst pellet with equimolar counterdiffusion, the catalyst effectiveness factor and Thiele modulus provide the relevant information as... 

Assume that the reaction and diffusion model is applicable, as presented in section 5,4,3.1, When the Thiele modulus cp > 3, only a fraction of l/(p of the porous particle, close to the outer surface, will take part in the reaction. As the solid is converted to a solid product with a larger volume, the pore diameter will decrease. The effective diffusivity is thereby reduced, so that the thickness of the reaction zone is also reduc. The higher the reaction rate constant, the higher the Thiele modulus was at the beginning, and the sooner the pore mouth will be plugged. A rough estimate indicates that the maximum degree of conversion of the solid reactant will be smaller than the effectiveness factor, which is tank (p/(p. 

A commercial cumene cracking catalyst is in the form of pellets with a diameter of 0.35 cm which have a surface area. Am, of 420 m g and a void volume, Vm, of 0.42cm g. The pellet density is 1.14g cm. The measured l -order rate constant for this reaction at 685K was 1.49cm s g . Assume that Knudsen diffusion dominates and the path length is determined by the pore diameter, dp. An average pore radius can be estimated from the relationship fp = 2Vm/Am if the pores are modeled as noninterconnected cylinders (see equation 4.94). Assuming isothermal operation, calculate the Thiele modulus and determine the effectiveness factor, tti, vmder these conditions. 

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