Bed-to-wall mass

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 When these limitations prevail, the hypotheses behind the ID model are no longer valid and more sophisticated 2D models need to be used.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. 

For multi-tubular MR configurations, the catalyst-in-tube configuration can be preferred especially for construction reason and for the extent of bed-to-wall mass and heat transfer limitations, which can be very detrimental in the catalyst in shell configuration. 

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. 

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... 

For mass transfer outside particles, the transfer coefficient can be calculated by using Equation (7). Inside the particles, the diffusion coefficient can be modified by means of the effective porosity (see Section I.B., or determined by another method such as that of Lou et al., 1991). For bed-to-wall heat transfer, the transfer coefficient can be computed by using relevant correlations presented in Chapter 5. 

However, each configuration, PBMR and FBMR, presents benefits and drawbacks. In particular, PBMR is characterized by a very simple configumtion in which catalyst particles can be packed. The particles dimension plays an important role for the performance of this kind of reactor. Indeed, very small particles can increase pressure drop and, on the contrary, big particles can limit the internal mass transfer. Moreover, other drawbacks can occur by using PBMR, such as the mass transfer limitafion from bed to wall, which negatively influences the hydrogen permeation and remarkable temperature profile along the reactor, with a consequent detrimental effect on catalyst and membrane (Roses et al., 2013). 

A sequel to this study was presented later by the same group (Freund et al., 2003), this time for the simple first-order reaction A->B in a cylindrical bed of spheres with N — 5. The reaction was again taken to be mass-transfer limited and to occur on the surfaces of the catalyst particles, but at a very low flow rate at Re — 6.5. It was found that concentration peaks occurred near the wall at values close to the inlet value of species A, indicating that channeling was taking place. There were also local peaks of product concentration that indicated areas of high reactivity that could give rise to hotspots in practice. 

Figure 16 shows the normalized mass distribution inside the filter wall vs. the normalized wall thickness as a function of the utilized capacity of the filter wall, for the low porous and the high porous material (small wall thickness) at a filtration velocity of 4cm/s. The line of the highest utilized capacity gives the state of loading inside the filter wall when the transition from the deep-bed to cake filtration has occurred and there is no more mass entering inside the filter wall. This final state of the mass distribution along the filter wall thickness was calculated for all the cases listed in Table I and the results are shown in Fig. 17. 

Fig. 19. Simulation of soot deposition on a filter wall, (a) Evolution of soot deposits (gray) in the wall (black is solid, white is pore space) and incipient cake formation (b) pressure drop as function of challenge soot mass demonstrating the deep-bed to cake filtration transition (c) visualization of soot deposition in an extruded ceramic (granular) filter wall and (d) development of soot deposits (black) and soot mass fraction in the wall (solid material is gray) to the onset of cake formation. Soot mass fraction scale is from 0 (violet) to the inflow value (red). In (d) the velocity on a section through the filter wall is shown, with overlay of the soot deposit shapes (see Plate 9 in Color Plate Section at the end of this book).

In the fixed-bed type, the cake of solids remains on the walls of the bowl until removed manually, or automatically by means of a knife mechanism. It is essentially cyclic in operation. In the moving-bed type, the mass of solids is moved along the bowl by the action of a scroll (similar to the solid-bowl sedimentation type), or by a ram (pusher type), or by a vibration mechanism, or by the bowl angle. Washing and drying zones can be incorporated into the moving-bed type. 

Fig. 8. Heat and mass transfer processes in a rotating drum bioreactor [146]. (1) Entry of sensible energy in inlet air (2) Release of waste metabolic heat by the microorganism (3) Convective heat transfer from the substrate bed to the headspace (4) Evaporation of water from the bed to the headspace, carrying with it the heat of vaporization (5) Conduction from the bed to the drum wall (6) Convective cooling of the drum wall by the headspace gases (7) Convection to the surrounding air (8) Exit of sensible energy in the outlet air (9) The substrate bed is assumed to be well mixed (10) The headspace gases are assumed to be well mixed (11) The high thermal conductivity of the drum wall is assumed to lead to thermal homogeneity...

Gas plus catalyst soUd Usually BFB. For fast reactions, gas film diffusion may control and catalyst pore diffusion mass transfer may control if catalyst diameter >1.5 mm. Heat transfer heat transfer coefficient wall to fluidized bed is 20-40 X gas-wall at the same superficial velocity, h = 0.15-0.3 kW/m K. Nu = 0.5-2. Heat transfer from the bed to the walls U = 0.45 to 1.1 kW/m °C. from bed to immersed tubes U = 0.2 to 0.4 kW/m °C from solids to gas in the bed U = 0.017 to 0.055 kW/m °C. Fluidized bed usually expands 10-25 %. Backmix type reactor which increases the volume of the reactor and usually gives a loss in selectivity. Usually characterized as backmix operation or more realistically as a series of CSTR if the height/diameter > 2 Usually 1 CSTR for each H/D= 1. If the reactor operates in the bubble region, then much of the gas short circuits the catalyst so the overall apparent rate constant is lower by a factor of 10. 

---