The Pseudohomogeneous Model

Wei el al. (1984) show that the average temperature difference between the solid and gas phase is yXAA/fi for fixed bed reactors. This then defines one possible criterion for the applicability of the pseudohomogeneous model as given in Table V. Another possible criterion is that given by Vortmeyer and Schaefer (1974), discussed later in this section. 

Simulation of an Industrial Reactor Using the Pseudohomogeneous Model... 

Note that the results of our simulation via the pseudohomogeneous model tracks the actual plant very closely. However, since the effectiveness factors r]i were included in a lumped empirical fashion in the kinetic parameters, this model is not suitable for other reactors. A heterogeneous model, using intrinsic kinetics and a rigorous description of the diffusion and conduction, as well as the reactions in the catalyst pellet will be more reliable in general and can be used to extract intrinsic kinetic parameters from the industrial data. 

The industrial rates obtained earlier from the pseudohomogeneous model actually include diffusional limits and are suitable for the specific reactor with the specific catalyst particle size for which the data was extracted. Such pseudohomogeneous models do not account explicitly for the catalyst packing of the reactor. On the other hand, heterogeneous models account for the catalyst explicitly by considering the diffusion of reactants and of products through the pores of the catalyst pellet. 

The rate constants of the pseudohomogeneous model are used as starting values or the initial guess in the heterogeneous model. The results obtained from the heterogeneous model with these settings will show lower conversion (as is to be expected) when compared with the results of the actual industrial plant and of the... 

The remaining two rate constants are multiplied by suitable factors to give the best match between the heterogeneous model and the industrial data, or equivalently, the data obtained from the pseudohomogeneous model. 

The experimental values of the effective diffusivities are clearly lower than the values deduced from the theoretical models, even taking into consideration the internal convective flow. Of course, the experimental values depend on the pseudohomogeneous model chosen to represent the alumina particle, but even if the spherical model were used, the values obtained (1,8 times those obtained with the slab model by identification of the variance) would be less than the theoretical values. Thus, the theoretical models based on the porous structure of the particles cannot be used for... 

Using the pseudohomogeneous model (surprisingly upheld by a number of experiments) as the fundamental basis, we list here some commonly used... 

Because the holdup of the microphase in the continuous phase is very low, a requirement for the pseudohomogeneous model, the macrointerface—or the interface between the two major phases—is assumed to be physically undisturbed by the presence of the microphase. 

From the above simple discussion, it is clear that the pseudohomogeneous model is simply a heterogeneous model but with t = 1.0 [or at least r] = constant (i.e., it is not changing along the length of the reactor)]. Therefore, when rj approaches 1.0, the pseudohomogeneous models are valid for design, operation, and optimization of catalytic... 

This is a case with negligible mass transfer resistances, as described by the pseudohomogeneous model. For a full heterogeneous system, see Chapter 6. This situation is a bit more complicated compared to the lumped system. We will consider a two-phase system with no mass transfer resistance between the phases and the voidage is equal to s (see Fig. 4.9). The mass balance design equation over the element A/ is ... 

The relationships that were derived in an earlier chapter between concentrations and the volume flow, as well as the stoichiometric measures (n t> flp for homogeneous flow reactors (Chapter 3), are also valid for the pseudohomogeneous model for a packed bed discussed here. 

In Figures 13a and 13b we show axial concentration (partial pressure of o-xylene) and temperature profiles.For conditions similar to those used in the pseudohomogeneous model it can be seen that the runaway limit is higher.Now we are observing a runaway condition at an initial o-xylene partial pressure of 0.0458 atm instead of 0.019 atm (Figure 12a). 

This diagram has been constructed from all the three models described above.The diagram is shown in Figure 15. For the situation under study the pseudohomogeneous model appears to be the most conservative model.Model sophistication can justify work in more severe conditions without danger of runaway.Moreover runaway limits predicted by the model with convection (HT, ) are intermediate between pseudohomogeneous and heterogeneous (diffusion ) models. 

In the pseudohomogeneous models described in the first section of this paper and by de Lasa et alo [6] the diffusional limitations in the macropore structure of the pellet was neglected. In fact, the rate expression proposed by Liederman et al. [ ] was obtained in a fluid bed where the dimensions of the zeolite particles were in the range of 50 ymo... 

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