Pseudohomogeneous one-dimensional

Assume steady-state, adiabatic operation, and use the pseudohomogeneous, one-dimensional plug-flow model. 

Reactor models accounting for radial porosity profile were compared with models using the averaged bed-porosity value. Isothermal conditions were applied in order to rule out thermal effects on the concentration profiles. To check the need for two-dimensional models the results were compared with that obtained by using the pseudohomogeneous one-dimensional reactor model (Eqs. (5.1)-(5.4)). 

The reactor is fed with an inflow of lOOkmol/h of CO2 and a stoichiometric feed of H2. A conversion level of 20% for CO2 is desired. Calculate the catalyst mass required in the catalytic bed so that the required conversion is obtained. Assume that the bed can be described with a pseudohomogeneous, one-dimensional model. 

The experimental setup has been modeled as pseudohomogeneous one-dimensional reactor. The classical continuous kinetic model (Laxminarasimhan et al., 1996) was used for hydrocracking reactions thus, the mass balance into the reactor can be represented by an integrodifferential equation as in Equation 11.55. This equation and the following equations are similar to Equations 11.8 through 11.15 in which k has been replaced by 1 hdc (Elizalde and Ancheyta, 2012) ... 

In this chapter, we first cite examples of catalyzed two-phase reactions. We then consider types of reactors from the point of view of modes of operation and general design considerations. Following introduction of general aspects of reactor models, we focus on the simplest of these for pseudohomogeneous and heterogeneous reactor models, and conclude with a brief discussion of one-dimensional and two-dimensional models. 

Wei [107] in 1982 was the first to come up with a continuous pseudohomogeneous model which allowed to simulate shape-selective effects observed during the alkylation of toluene using methanol to yield xylene isomers on a HZSM-5 catalyst. He treated diffusion and reaction of the xylene isomers inside the pores in a one-dimensional model. The isomer concentration at the pore mouth was set to zero, as a boundary condition. This allowed the model equations to be solved analytically, but it also limited the application of the results to small conversions. 

The development of mathematical models for the simulation of non-adiabatic fixed-bed catalytic reactors has received considerable attention. In previous work, we have analyzed the two-dimensional and one-dimensional versions of the models (1, 2) which, in turn, were classified as (I) pseudohomogeneous, (II) heterogeneous, but conceptually wrong, and (III) heterogeneous, written in the correct way (Table I). Model equations are in the Appendix. 

Transfer parameters of the simplified models. The pseudohomogeneous two-dimensional parameters Xer and aw have been extensively studied. Although several analytical expressions in terms of the basic parameters have been proposed (6, 1), we consider that there is no general criteria on the relations that have to be established between the models to obtain those parameters. One alternative is to assume equal heat fluxes, and for models I-T and III-T it follows that ... 

For the coefficient of the one-dimensional models 1-0 and II-O we have used the well known expression in terms of the two-dimensional pseudohomogeneous parameters 9) ... 

A one-dimensional pseudohomogeneous plug flow reactor model assuming isothermality was used to simulate experimental results. The continuity and kinetic expressions used were as follows ... 

The process is described by an one-dimensional, pseudohomogeneous, non-steady state dispersion model for an adiabatic fixed bed reactor. The kinetics are modelled by a re-versibll reaction system where each reaction step follows a power law with a reaction order of one in the gas and in the solid component. The temperature dependency of the reaction rate constant follows the Arrhenius law. The equilibrium constant is set to be independent of temperature. 

A broad classification of the various quasi-continuum models is presented in Table 12.1. The simplest is clearly the one-dimensional pseudohomogeneous plug-flow model (Al-a) in which the radial gradients of heat and mass within a tube are neglected. Then complicating factors can be added, one at a time, to allow for increasing reality,... 

One-dimensional pseudohomogeneous nonisothermal nonadiabatic plug flow (model A1-a)... 

The one-dimensional pseudohomogeneous model is the most used model to describe PB MRs, 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. 

In the following section, a two-dimensional model will be described that is used for the computation of temperature and concentration profiles inside a PB MR for hydrogen production. For simplicity, only a pseudohomogeneous model will be described. The extension of the heterogeneous model is analogous to the one-dimensional model. 

Figure 3.8 Cross-sectional average concentration (a) and temperature (b) profiles according to a pseudohomogeneous model (full lines two-dimensional dashed lines one-dimensional). After Ref [133] with tj = 160 C and Tw = 100 C.

Design of a Eixed Bed Reactor According to the One-Dimensional Pseudohomogeneous Model... 

These are not a priori criteria, but the gradients can be approximated from a simulation based upon the one-dimensional basic pseudohomogeneous model. It takes very steep gradients not to satisfy (11.6-4). 

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