Internal Prater number

P, is the internal Prater number, which represents the maximum relative temperature difference across the particle, or the ratio of the heat production rate and the heat conduction rate in the particle. 

Figure 13. Internal effectiveness factor as a function of the Thiele modulus for nonisothermal reactions at different values for the Prater number and y, = 10 (numerical solutions for a first order reaction).

Since the Prater numbers of RD processes were found to have values p < 10, the internal heat-transport effects can be neglected. The same is true for external heat transport effects [33]. 

A steady-state one-dimensional heterogeneous plug-flow model has been used to represent the behavior of the laboratory reactor. The internal and external mass transfer resistances are taken into account. For different operating conditions, very small Prater numbers were calculated. For this reason, the thermal gradients inside the washcoat were not included in the reactor model (Froment and Bischoff, 1990). The axial solid temperature profiles were measured for each experiment, therefore only the mass balances for gas and solid phases are needed to model the reactor. The equations that represent the system are the following ... 

Combination of this condition with Eq. (4.5.90) for CA,center = 0 leads to the criterion for exclusion of internal heat effects based on the Prater number and... 

To ensure the system is probing reactions in a kinetically controlled regime, the reaction conditions must be calculated to determine the value of the Wiesz-Prater criterion. This criterion uses measured values of the rate of reaction to determine if internal dififusion has an influence. Internal mass transfer effects can be neglected for values of the dimensionless number lower than 0.1. For example, taking a measured CPOX rate of 5.9 x 10 molcH4 s g results... 

The Weisz-Prater criterion can be used for detecting drop in effectiveness due to internal diffusion. This is a number representing the ratio of actual reaction rate to a diffusion rate, and is given by ... 

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