Two-dimensional Modeling of Packed-bed Membrane Reactors

In the previous section a one-dimensional model was developed and used to demonstrate the possible benefits of packed-bed membrane reactors as compared to the established fixed-bed reactors. Basic phenomena can be described with sufficient accuracy even with this simple model. However, when the goal is to predict reactor behavior in more detail the one-dimensional model may reach its limits due to radial mass- and heat-transfer limitations. Additionally, flow-maldistribution effects can also not be captured. Taking advantage of improvements in computation speed, it is nowadays possible to predict the influence of these phenomena with two- or even three-dimensional models and use this knowledge to optimize reactor performance. However, detailed modeling of membrane reactors is not as straightforward as in the case of fixed-bed reactors. There are still a couple of open questions e.g. whether semiempirical correlations obtained under nonreactive conditions in fixed beds are applicable also to membrane reactors or not. Until these questions have been completely clarified one has to rely on the available database and correlations as the best possible estimate. 

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. 

Neglecting the third (angular) coordinate can distinctly speed up the calculations compared to the solution of a. ID model (see Section 5.4). Further reduction 

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Two-dimensional Modeling of Packed-bed Membrane Reactors 1121 Table 5.4 Standard simulation parameters for the 2D PBMR model. 

Two-dimensional simulations enable analysis of the complex and coupled physicochemical processes that occur in packed-bed membrane reactors more deeply and comprehensively than is possible with a simple one-dimensional model. Special attention was given above to the analysis of hydrodynamic effects caused by local variation in bed porosity and to the definition of appropriate boundary conditions depending on the particular membrane properties. It was demonstrated that larger-scale applications require a precise treatment of, especially, radial heat transfer, which possesses a large effect on the integral reactor performance. 

In the following section a two-dimensional model will be described that is used for the computation of temperature and concentration profiles inside a packed bed membrane reactor for hydrogen production. For simplicity, only a pseudo-homogeneous model will be described. The extension of the heterogeneous model is analogous to the ID model. 

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