Model pseudo-homogeneous plug-flow

In the previous section, it was recognized that for perfect fluid distribution flow direction has only a second order effect on conversion. In this section, the effects of maldistribution are investigated. In order to eliminate the influence of flow direction, a pseudo-homogeneous plug flow model is used with purely radial flow through the catalyst basket. The governing equation is thus Eqn. (14), which in more convenient form is... 

The first modeling attempts employed one dimensional pseudo- homogeneous plug flow models for the gas phase. For first order reactions the model can be written as ... 

One dimensional pseudo-homogeneous plug flow models for the species in the gas phase. 

The physical situation in a fluidized bed reactor is obviously too complicated to be modeled by an ideal plug flow reactor or an ideal stirred tank reactor although, under certain conditions, either of these ideal models may provide a fair representation of the behavior of a fluidized bed reactor. In other cases, the behavior of the system can be characterized as plug flow modified by longitudinal dispersion, and the unidimensional pseudo homogeneous model (Section 12.7.2.1) can be employed to describe the fluidized bed reactor. As an alternative, a cascade of CSTR s (Section 11.1.3.2) may be used to model the fluidized bed reactor. Unfortunately, none of these models provides an adequate representation of reaction behavior in fluidized beds, particularly when there is appreciable bubble formation within the bed. This situation arises mainly because a knowledge of the residence time distribution of the gas in the bed is insuf-... 

A simple model is the one-dimensional, plug-flow, pseudo-homogeneous model. In this model, we will consider the fluid and solid phases as a single phase. For this model to apply we must fulfill the following conditions ... 

One-Dimensional, Plug-Flow, Pseudo-Homogeneous, Model ... 

Table 7.15 Packed-Bed Reactor-Sizing Calculation Procedure - One-Dimensional, Plug-Flow, Pseudo-Homogeneous, Model ... 

The choice of a model to describe heat transfer in packed beds is one which has often been dictated by the requirement that the resulting model equations should be relatively easy to solve for the bed temperature profile. This consideration has led to the widespread use of the pseudo-homogeneous two-dimensional model, in which the tubular bed is modelled as though it consisted of one phase only. This phase is assumed to move in plug-flow, with superimposed axial and radial effective thermal conductivities, which are usually taken to be independent of the axial and radial spatial coordinates. In non-adiabatic beds, heat transfer from the wall is governed by an apparent wall heat transfer coefficient. ... 

Table III Pseudo-homogeneous 1-D plug flow model with pore-mouth poisoning...

Reactor Model A variation of the pseudo-homogeneous 1-D plug flow model with shell progressive mechanism of poisoning (SPM) is proposed. This model accounts for the intraparticle-diffusional resistance using a pore mouth poisoning mechanism. The... 

The model used here is a plug flow pseudo-homogeneous model (rj= 1.0). The mass balance equation for this single reaction can be written in the following dimensionless form,... 

The phenomenon of parametric sensitivity is not directly related to the multiplicity phenomenon, for parametric sensitivity is found using plug flow pseudo-homogeneous models which, by definition, do not show multiplicity of the steady states. A good review of the phenomenon is given by Rajadhyaksha and Palekar (1984). More recent research on this problem include the extensive work of Westerterp and co-workers (e.g. Westerterp and Ptasinky, 1984a,b Westerterp el al., 1984 Westerterp and Overtoom, 1985). 

The design of such gas-solid catalytic reactors can be approximated by a pseudo-homogeneous model with gas phase in plug flow. In the case of very exothermic reactions accounting for radial dispersion of heat and mass might be useful to prevent excessive particle overheating. The reaction time must find a compromise with the hydrodynamic design, namely the maximum gas velocity and pressure drop. 

The ID pseudo-homogeneous model is the most used model to describe packed bed membrane reactors, especially for laboratory-scale applications. In its simplest form, namely the plug flow steady state model, the model describes only axial profiles of radially averaged temperatures and concentrations. 

The prevailing heat and mass transfer processes in the periodically operated packed beds have been investigated with a pseudo-homogeneous, one-dimensional plug flow model with superimposed axial dispersion. 

---