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flow, diffusion and heat transfer at the upper limit. Years later, in 1997, Boudart suggested membrane reactors should be classified analogously [91]. When an industrial reactor should have its STY around 10−6–10−5 mol·cm−3·s−1, a membrane reactor should be located in the same window—defined by its areal time yield (ATY). Boudart referred to a Pd/Al2O3 membrane and its ability to permeate hydrogen at a permeability P of at least 10−5 mol·cm−2·s−1 [92]. By assuming a cylindrical reactor of diameter d, ATY can be calculated from the STY by multiplying with the surface to volume ratio, d/4. As an example, a reactor tube of 40 cm in diameter would fit in a “window of reality” of a membrane reactor matching P, or ATY (40/4 × 10−6 mol·cm−2·s−1). By simply adjusting the diameter of the membrane tube, the “window of reality” can be reached in the case of high permeation rates. What about zeolite membranes? Van de Graaf et al. compared the volume ratio of the catalytic reactor derived from the productivity per unit volume (defined as STY) to the permeation per membrane area (defined as permeation flux), or in other words the ATY [93,94]. By dividing STY through ATY, the area to volume ratio (A/V) of the catalytic membrane reactor is obtained as a simple measure of the industrial feasibility of membrane reactors. However, the authors calculated A/V values between 20 and 5000 m−1 for porous inorganic membranes, whereas the example referred by Boudart (Pd/Al2O3 [92]) shows a much better performance of A/V = 10. It is clear, the smaller the A/V ratio the more realistic becomes an industrial transfer. Deeper insights between catalytic reaction and permeation can be obtained by comparison of catalytic performance and permeation rate—which are the two limiting factors of a membrane reactor. The catalytic performance can be understood as ratio between reaction rate and convective transport rate of the feed, given as Damkohler number (Da). The ratio of convective transport to permeation rate through the membrane is the so called Peclet number (Pe). The product of both numbers defines the efficiency of a given membrane reactor [95–97]. Hence, a catalytic membrane reactor can be optimized either by catalyst activity adjustment or by manipulating the permeability of the membrane. For industrial applications the focus should be on the latter: (i) diameters of membrane supports can be reduced up to a certain value (e.g., as hollow support fibres); and (ii) permeability can be increased. Recent developments in the fabrication of ultrathin membranes (see Section 2.1.) are promising enough to overcome barriers. Since permeation is inversely proportional to membrane thickness [98] a novel generation of fast permeating zeolite membranes can be directed towards industrial applications. Generally, the transport of molecules through zeolite membranes depends strongly on the membrane pore size and the interaction of the permeating species with the zeolite structure and can be modelled mainly as combined effect between adsorption and diffusion. This surface diffusion of adsorbed species from 8PDF Image | Zeolite Catalysis
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