Intraparticle Temperature Gradients

Hie Aris numbers Anx and An0 can be applied to nonisothermal catalyst pellets. Three items will be discussed  

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The Consequences of Intraparticle Temperature Gradients For Catalyst Effectiveness Factors... 

In summary, our analysis indicates that intraparticle temperature gradients and external concentration gradients are clearly negligible while intraparticle concentration gradients are clearly significant. External temperature gradients do exist, but they are small. 

If conversion levels are not too high, intraparticle temperature gradients are usually no problem. 

Another aspect concerns catalyst particles with intraparticle temperature gradients. In general the temperature inside a catalyst pellet will not be uniform, due to the heat effects of the reaction occurring inside the catalyst pellet. The temperature inside the catalyst can be related to the concentration with (see for example [4]) ... 

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 ... 

These formulae give the Aris numbers for arbitrary reaction kinetics and intraparticle temperature gradients. Thus the dependency of the conversion rate on the temperature can also be of any arbitrary form. 

The intraparticle temperature gradients result in an increase in the effectiveness factor. This is obvious since the reaction is strongly exothermic. The increase, however, is only 2 % relative. Thus in this case intraparticle temperature gradients can be neglected. 

Langmuir-Hinshelwood Kinetics and Intraparticle Temperature Gradients 223... 

The importance of the intraparticle heat transfer resistance is evident for particles with relatively short contact time in the bed or for particles with large Biot numbers. Thus, for a shallow spouted bed, the overall heat transfer rate and thermal efficiency are controlled by the intraparticle temperature gradient. This gradient effect is most likely to be important when particles enter the lowest part of the spout and come in contact with the gas at high temperature, while it is negligible when the particles are slowly flowing through the annulus. Thus, in the annulus, unlike the spout, thermal equilibrium between gas and particles can usually be achieved even in a shallow bed, where the particle contact time is relatively short. 

Direct experimental measurements of the temperature rise during sorption in a batch system have been reported by Eagan et al./ l Doelle and Riekert, and Ilavsky et al. The observed tcihpcraturc response curves were in all cases of the expected form, showing a rapid initial rise followed by a slow return to the ambient temperature. The absence of any. significant intraparticle temperature gradient was confirmed directly by Ilavsky et al. who... 

Catalyst particles in three-phase fixed-bed reactors are usually completely filled with liquid. Then intraparticle temperature gradients are negligible due to the low effective diffusivities in the liquid phase, as pointed out by Satterfield [13] and Baldi [92]. However, if the limiting reactant and the solvent are volatile, vapor-phase reaction may occur in the gas-filled pores, causing significant intraparticle temperature gradients [109, 110]. In these conditions, intraparticle heat transfer resistance is necessary to describe the heat transfer. 

It has been shown both experimentally and theoretically (Butt et al. 1977 Lee et al. 1978) for a pore-mouth poisoned pellet that the main intraparticle temperature gradient lies in the deactivated outer shell and that the fresh inner core is isothermal. This is the reason why the fresh inner core was treated as isothermal in writing Eq. 5.57. The intra- and interparticle temperature gradients (Lee 1980a) are related by ... 

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