Wall mass transfer

It is often convenient to represent the mass transfer at the wall in terms of a mass-transfer coefficient that relates the wall mass transfer to the local mean mass fraction Y across the channel,... 

On the other hand, with ultra-thin (high permeation flux) membranes, which have recently become available, it has been experimentally shown that the extent of bed-to-wall mass transfer limitations in case of hydrogen purification/ production become prominent, which greatly influences the reactor performance. When these limitations prevail, the hypotheses behind the ID model are no longer valid and more sophisticated 2D models need to be used. 

Let us compute the radial H2 concentration profiles at different axial positions at isothermal conditions. As can be seen in Figure 10.4, radial concentration profiles are present but not very pronounced. It can be concluded that for the membranes used and for small membrane diameters (1 cm in the simulation shown in the figure), the bed-to-wall mass transfer limitations have a negligible influence on the required membrane area. 

With this reactor, the bed-to-wall mass transfer limitations can be circumvented, while the heat required for the reforming reactions (often endothermic equilibrium reaction) is supplied through heat exchange surfaces inserted in the reactor system. In fact, fluidized bed reactors present higher heat exchange coefficients compared to fixed-bed reactors. 

For predicting mass transfer in Taylor flow, gas-liquid and liquid-wall mass transfer coefficients are required. Mass transfer coefficients from gas to liquid were found experimentally to be in the range 0.1-0.8 s and correlations have been... 

J.M. van Baten, R. Krishna, CFD simulations of wall mass transfer for Taylor flow in circular capillaries, Chem. Eng. Sci., 2005, 60, 1117-1126. 

Van Eaten and Krishna [91] simulated liquid-to-wall mass transfer for Taylor flow in circular capillaries of 1.5, 2.0, and 3.0 mm diameter. In their analysis, the wall mass transfer process consisted of two separate contributions (i) wall-slug contribution of the regions in contact with the liquid slug and (ii) wall-film contribution of the region in contact with the liquid film surrounding the bubble. A correlation for total liquid-to-wall mass transfer coefficient was proposed ... 

This correlation is valid for Gzt < 0.01 and it is in reasonably good agreement with earlier findings by Berac and Pintar [92]. However, further research on liquid-to-wall mass transfer would be desirable. 

FIGURE 5.15. Values of local wall mass transfer coefficients due to sudden expansion from a circular entry into a square channel, (a) Variation with downstream distance. Re=5000, expansion O 1 10, 1 6, A 1 4, 1 3, Al 2 (b) spanwise variation. Re=15670, 1 3 expansion parameters xjd. 

King DH, Smith JW. Wall mass transfer in liquid-fluidized beds. Can J Chem Eng 45 329-333, 1967. 

Packed bed membrane reactors have two main limitations (i) the difficult heat management that can be very detrimental for highly exothermic reactions like in perovskite membrane reactors and (ii) the extent of bed-to-wall mass transfer limitations that are more important for extractor-type reactors like Pd-based membrane reactors (due to the high permeation fluxes of membranes). In fact, the bed-to-wall mass transfer limitations would decrease the partial pressure of hydrogen close to the membrane surface and thus decrease the membrane flux. 

A typical fluidized membrane reactor (or membrane-assisted fluidized bed reactor - MAFBR) consists in a bundle of permselective membranes immersed in a catalytic bed operated in a bubbling or turbulent fluidization regime. The use of fluidized bed membrane reactors not only makes possible the reduction of bed-to-wall mass transfer limitations, but also allows operating the reactor under virtually isothermal conditions (due to the movement of catalyst). This possibility can be used for operating the autothermal reforming of hydrocarbons inside the membrane reactor. In fact, as indicated by Tiemersma et al. [13], the autothermal reforming of methane in a packed bed membrane reactor is quite... 

Sh Sherwood number for wall mass transfer, k. dp/D. t solid phase temperature (two-phase model). 

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