Effective dispersion model for flow-through catalytic membrane reactors combining axial dispersion and pore size distribution
Introduction
The term “flow-through catalytic membrane reactor” describes a reactor concept for heterogeneous reactions, where the catalyst is immobilized in the pores of a mostly ceramic membrane, which are convectively passed by the reaction mixture. The porous membrane does not perform any separative tasks and is solely used as microstructured catalyst support. This type of reactor allows for high catalytic activity due to intensive contact between reactants and catalyst and potentially for a narrow residence time distribution (Zaspalis et al., 1991, Julbe et al., 2001, Sanchez Marcano and Tsotsis, 2002, Dixon, 2003, Dittmeyer et al., 2004, Schomäcker et al., 2005, Westermann and Melin, 2009).
The residence time distribution of the reactants inside the catalytic pores is of major interest, if for example a sequential reaction with a desired intermediate product is performed. In this case the highest selectivity can be achieved in an ideal plug flow reactor. The flat membrane geometry with rather large lateral dimensions in the order of centimeters compared to the extremely short reactor length of a membrane pore prevents the direct measurement of a meaningful residence time distribution, because the time a tracer spends for spreading radially across the membrane without contact to catalyst is at least in the same order of magnitude as the time it spends inside the catalytically active pores.
In order to at least qualitatively assess the hydrodynamic behavior inside the catalytic pores, this work introduces a residence time distribution model for flow-through membrane reactors, which accounts for the main deviations from ideal plug flow. Non-ideal reactor behavior results from maldistribution of the flow due to a pore size distribution (Fig. 1) on the one hand and from axial dispersion inside the pores induced by molecular diffusion on the other hand. The model is based on the straight microchannel structure of anodized membranes. It might be applied for sintered membranes as well, but would require implementation of suitable correction factors such as tortuosity.
Section snippets
Anodized alumina membranes
Anodized alumina membranes consist of uniform cylindrical pores with a narrow size distribution (Masuda et al., 1997, Jessensky et al., 1998). They are commercially available for microfiltration applications with a nominal pore diameter of and a thickness of (Whatman Anodisc). Their regular structure provokes a closer investigation of their hydrodynamic behavior if applied as catalytic flow-through membrane reactor.
Commercially available anodized alumina membranes do not show exactly
Combined pore size distribution and axial dispersion
In reality, the two considered effects do not occur separately. The resulting RTD is influenced by both pore size distribution (PSD) and axial dispersion. As a combined model, the multi-tube model composed of PFTRs with different diameters as introduced in Section 2.3 can be extended by allowing axial dispersion according to Section 2.4 in each pore size class. The analytical solution for the dispersion model with open–open boundary conditions (Eq. (18)) is applied to each pore size class.
Conclusions
The residence time distribution provides important information about the hydrodynamic behavior of a reactor. A direct measurement of the RTD inside the catalytic pores can hardly be realized for the investigated reactor concept. Thus, a reactor model is created, which allows for calculation of the RTD taking into account deviations from an ideal plug flow reactor caused by pore size distribution and axial dispersion.
The influence of the pore size distribution is demonstrated by treating a
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