One-dimensional Modeling of Packed-bed Membrane Reactors

In order to study general differences between FBR and PBMR, in the present work a simplified modeling approach has been followed, neglecting the diffusive transport in the membrane. Predefined component fluxes through the membrane were considered, making the application of a more sophisticated transport model 

The structure of this chapter is as follows. In the next section a comparison of the FBR and PBMR will be presented using a simplified ID modeL Advantages and drawbacks of the PBMR will be illustrated. Subsequently, a more detailed 2D model will be developed to study important aspects of radial mass and heat transfer, as well as scale-up problems that might occur in a PBMR. In the last section a short outlook to more sophisticated 3D membrane reactor models is given. Such models are still not suitable for extensive parametric studies. However, they enable a deeper investigation of local velocity and concentration profiles that develop in such reactors. 

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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. 

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. 

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