Intraparticle temperature

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. 

Table 2 lists most of the available experimental criteria for intraparticle heat and mass transfer. These criteria apply to single reactions only, where it is additionally supposed that the kinetics may be described by a simple nth order power rate law. The most general of the criteria, 5 and 8 in Table 2, ensure the absence of any net effects (combined) of intraparticle temperature and concentration gradients on the observable reaction rate. However, these criteria do not guarantee that this may not be due to a compensation of heat and mass transfer effects (this point has been discussed in the previous section). In fact, this happens when y/J n [12]. 

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. 

Many complex situations have not been addressed, such as simultaneous intraparticle temperature and pressure gradients and nondiluted gases with anisotropic catalyst pellets. Calculations for these and other complex situations proceed along the same line as demonstrated for bimolecular reactions and nondiluted gases. A framework that can be used to investigate the effect of complex situations on the effectiveness factor is given. Also presented are criteria that can be used for a quick estimate as to whether or not certain phenomena are important. 

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... 

Cylindrical pellets arc made from the USDA samples expressly to remove consideration of native biomass morphology. We have shown biomass morphology alters pyrolysis slate (Chan et al 1988). If necessary, the sample is ground further in a Wile mill and reformed in a cylindrical die to the native density, approximately 1.0 g/cm, Three holes are made radially in the pellet with a small drill and thermocouples are inserted at distances of 2, 4 and 6 mm from the heated lace of the pellet. The pellet is then fitted tightly in a glass sleeve joined to the reactor via an O-ring seal. Real time intraparticle temperatures are displayed on the computer monitor and digitized at a rate of 1 Hz. The moisture content of the pellet is constant al a 5.0 wt %, equilibrium moisture except for some data in Chan et al (1988). 

C vs. the start at 100°C. Thus we have a significant effect of the level of activity upon the magnitude of intraparticle temperatures, but not upon the time response. None of this behavior shows up in the Prater Number. The key to understanding time response comes fi om a detailed solution of the transient heat transfer equation. The dimensionless time will take the form (Lee et al. [16]) ... 

The particle is isothermal, i.e. flat intraparticle temperature profile, with the temperature difference between the pellet surface and the bulk fluid concentrated across the external heat transfer resistance. 

Mathematically, the dynamic behaviour of the system is represented by ordinary differential equations in the state variables which are pellet temperature and concentration of reactants (and products in certain cases), with time as the independent variable. This is in contrast to the more realistic distributed models which account for intraparticle temperature and concentration gradients. 

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. 

Figure 7.38 Experimental intraparticle temperature profiles for benzene hydrogenation on Ni/kieselguhr. [After J.P. Kehoe and J.B. Butt, Amer. Inst. Chem. Eng. Jl., 18, 347, with permission of the American Institute of Chemical Engineers, (1972).]...

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