Pseudo-homogeneous models

Temperature and concentration differences between gas and catalyst can be neglected to give a pseudo-homogeneous model,... 

The units of rv are moles converted/(volume-time), and rv is identical with the rates employed in homogeneous reactor design. Consequently, the design equations developed earlier for homogeneous reactors can be employed in these terms to obtain estimates of fixed bed reactor performance. Two-dimensional, pseudo homogeneous models can also be developed to allow for radial dispersion of mass and energy. 

This equation may be used as an appropriate form of the law of energy conservation in various pseudo homogeneous models of fixed bed reactors. Radial transport by effective thermal conduction is an essential element of two-dimensional reactor models but, for one-dimensional models, the last term must be replaced by one involving heat losses to the walls. 

Pseudo homogeneous models of fixed bed reactors are widely employed in reactor design calculations. Such models assume that the fluid within the volume element associated with a single catalyst pellet or group of pellets can be characterized by a given bulk temperature, pressure, and composition and that these quantities vary continuously with position in the reactor. In most industrial scale equipment, the reactor volume is so large compared to the volume of an individual pellet and the fraction of the void volume associated therewith that the assumption of continuity is reasonable. 

Pseudo homogeneous models require global rate expressions of the type discussed in Section... 

The term pseudo homogeneous model has been popularized by Froment (94, 95). 

Equations 12.7.28 and 12.7.29 provide a two-dimensional pseudo homogeneous model of a fixed bed reactor. The one-dimensional model is obtained by omitting the radial dispersion terms in the mass balance equation and replacing the radial heat transfer term by one that accounts for thermal losses through the tube wall. Thus the material balance becomes... 

The One-Dimensional Pseudo Homogeneous Model of Fixed Bed Reactors. The design of tubular fixed bed catalytic reactors has generally been based on a one-dimensional model that assumes that species concentrations and fluid temperature vary only in the axial direction. Heat transfer between the reacting fluid and the reactor walls is considered by presuming that all of the resistance is contained within a very thin boundary layer next to the wall and by using a heat transfer coefficient based on the temperature difference between the fluid and the wall. Per unit area of the tube... 

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-... 

In the pseudo-homogeneous model equn. (7) is written in characteristic normal form... 

When integrating, the increments in x and x are related as above so as to follow the development of 0 along the characteristics. Though the pseudo-homogeneous model gives shorter solution times we shall see that it Introduces significant error in 0 in certain circumstances. 

This would give a tube diameter dt = 0.14 m, whereas our selectivity requirement asks for a tube diameter < 0.06 m. Although the one-dimensional pseudo-homogeneous model is no more valid for dt = 0.14 m, this proves that maintaining the selectivity asks for much smaller tube diameters than the runaway prevention. 

Metha, P. S., Sams, W. N., and Luss D. Wrong-Way Behavior of Packed-Bed Reactors 1. The Pseudo-Homogeneous Model. AIChE J., 27, 234-246 (1981). 

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 fluid-phase temperatures predicted from a two-phase pseudo-homogeneous model were shown to give reasonable agreement with experimental measurements, without explicitly adjusting the model parameters. It was demonstrated that more refined experimental measurements will be needed to determine the parameters of the model in particular, the solid and fluid phase wall Biot numbers were mutually adjustable. 

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