Two-Dimensional Pseudohomogeneous Models

The heat transfer coefficient h was calculated according to Hand-ley and Heggs (24) with the Reynolds number based upon an equivalent diameter, namely that of a sphere with the same volume as the actual particle. The overall heat transfer coefficient U was calculated from the heat transfer parameters of the two dimensional pseudohomogeneous model (since the interfacial At was found to be negligible), to allow for a consistent comparison with two dimensional predictions and to try to predict as closely as possible radially averaged temperatures in the bed (25). Therefore ... 

TWO-DIMENSIONAL PSEUDOHOMOGENEOUS MODELS 11.7.1 The Effective Transport Concept... 

Calculate the heat transfer parameters of the two-dimensional pseudohomogeneous models for the design of the reactor for hydrocarbon oxidation of Section 11.7.3, using the correlations given in Section 11.7.1. Compare the value calculated from the expressions given by (a) Kunii and Smith, (b) Zehner and Schundler. Determine their sensitivity with respect to the solid conductivity. Additional data ... 

The objective of the present study is to show that the agreement between one and two dimensional pseudohomogeneous models is satisfactory in the PO regime, and that this agreement is still valid when the intrapartiele diffusional effects are considered. 

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) ... 

Assuming a pseudohomogeneous two-dimensional reactor model with plug flow of fluid and constant properties, calculate the axial concentration and temperature profiles at several radial positions along the axis of a single tube. Use the following property/parameter values (Doraiswamy, 2001) ... 

The basic model (model A2-a) two-dimensional pseudohomogeneous nonisothermal nonadiabatic with no axial diffusion... 

In this section, a two-dimensional, pseudohomogeneous reactor model will be developed neglecting heat- and mass-transfer limitations between the bulk phase and catalyst particles, as well as inside the catalyst pellets. The two-dimensional formulation presented takes advantage of the cylindrical reactor geometry shown in Fig. 5.11. 

A pseudohomogeneous, two-dimensional reactor model for MRs consists of the total gas—phase continuity and Navier—Stokes equations, augmented with gas—phase component mass balances and the overall energy balance. 

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. 

The following example illustrates the derivation of the continuity and energy equations for model 1.2.2 in Figure 21.5, a pseudohomogeneous, two-dimensional model... 

Derive the continuity and energy equations for an FBCR model based on pseudohomogeneous, two-dimensional, DPF considerations. State any assumptions made, and include the boundary conditions for the equations. 

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 ... 

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)). 

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.

The pseudohomogeneous two-dimensional model is truly homogeneous if the reaction rates, Rj, remain constant inside the catalyst particles, in other words, when diffusion in the porous catalyst particles does not affect the reaction rate. In case diffusion effects are notable, the terms r, and SR,(-AJTrj) should be replaced with the terms qin and as was described in Equations 5.55 and 5.164. 

The results shown in Figure 3 were obtained for one dimensional models using the pseudohomogeneous and heterogeneous approaches. Here again we present two examples (p = 4 atm and 5 atm) where MFARP conditions with a pseudohomogeneous model become PO with the heterogeneous representation. Moreover, Table 2 compares the... 

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