Permeation to reaction rate ratio

The situation is somewhat different with porous membranes, where the permselectivities for all components do not equal zero but exhibit certain values determined in most cases by the Knudsen law of molecular masses. In general, when porous membranes are used as separators in a membrane reactor next to the catalyst or the reaction zone (Figure 7.2a), it has been shown experimentally (Yamada et al. 1988) and theoretically (Mohan and Govind 1986, 1988a, b, Itoh et al. 1984, 1985) that there is a maximum equilibrium shift that can be achieved. On the basis of simple mass balances one can calculate that this maximum depends on, besides the reaction mechanism, the membrane permselectivities (the difference in molecular weights of the components to be separated) and it corresponds to an optimum permeation to reaction-rate ratio for the faster permeating component (which is a reaction product). 

Below the optimum value of this permeation to reaction-rate ratio the effect of separation of this product is stronger than the permeation of... 

Figure 10.9 Effect of permeation to reaction rate ratio on reaction conversion in a porous membrane reactor [Mohan and Govind 1988c]...

Figure 11.21. Conversion of endothermic and exothermic reaction A = B im plug How membrane reactor with permeation to reaction rate ratio as parameter [Mohan and Govind, 1988b]...

For those cases where the permeability of reactant A is in between those of the two products, B and C, both the conversion and extent of separation increase with increasing permeation rate or permeation to reaction rate ratio (Table 11.9). The corresponding optimal compressor load (recycle flow rate to feed flow rate) also increases with the rate ratio. The top (permeate) stream is enriched with the most permeable product (i.e., B) while the bottom (retentate) stream is enriched with the least permeable product (i.e., C). It is noted from Table 11.9 that the optimal compressor loads for achieving the highest conversion and extents of separation can be quite different and a decision needs to be made for the overall objective. 

Figure 11.29 Conversion and separation index of a membrane reactor as a function of permeation to reaction rate ratio when reactant permeability is smaller than product permeabilities [Mohand and Govind, 1988a]...

Idealized membrane reactors. Mohand and Govind [1986] have suggested that, to achieve a maximum conversion due to equilibrium displacement, an idealized simple co-current or counter-current membrane reactor should have the following attributes infinitely long reactor to consume all rcactant(s), essentially zero pressure on the permeate side, an infinitesimally small (but not zero) ratio of permeation to reaction rate to reduce reactant loss. For a membrane reactor with finite values of the reactor length... 

The conversions in a PMMR for an endothermic and an exothermic reaction as a function of the reactor temperature are given in Figure 11.24 and Figure 11.25, respectively. The intersection of a material balance curve with a given ratio of the permeation to reaction rate and an energy balance line with a known heat generation index provides the conversion under the operating conditions. 

To measure the separation efficiency of a membrane reactor involving multiple reaction components, the extent of separation, briefly introduced in Chapter 7, was used to replace the more commonly used separation factor by Mohan and Govind [1988a]. This alternative index of separation performance is based on the flow quantities of the process streams involved while the separation factor is calculated from the compositions instead. The goals of a high conversion and a high separation sometimes contradict each other. The choice or, more often than not, compromise of the two goals depends, on one hand, on the downstream separation costs and, on the other, on the process parameters such as the ratio of the reactant permeation to reaction rate and the relative permeabilities of the reaction components. 

The effect of reactant loss on membrane reactor performance was explained nicely in a study by Harold et al [5.25], who compared conversion during the cyclohexane dehydrogenation reaction in a PBMR equipped with different types of membranes. The results are shown in Fig. 5.4, which shows the cyclohexane conversion in the reactor as a function of the ratio of permeation to reaction rates (proportional to the ratio of a characteristic time for reaction in the packed bed to a characteristic time for transport through the membrane). Curves 1 and 2 correspond to mesoporous membranes with a Knudsen (H2/cyclohexane) separation factor. Curves 3 and 4 are for microporous membranes with a separation factor of 100, and curves 5 and 6 correspond to dense metal membranes with an infinite separation factor. The odd numbered curves correspond to using an inert sweep gas flow rate equal to the cyclohexane flow, whereas for the even numbered curves the sweep to cyclohexane flow ratio is 10. 

In the case of dense membranes where only one component (usually a reaction product) can permeate through the membrane, the permselectivities for all the other components are zero, and the extent of the equilibrium shift is determined only by the ratio of the permeation rate to reaction rate for the permeating component. For values of this ratio approximately equal to unity (e.g. for a dehydrogenation reaction this means that the production rate of... 

Figure 11.33, Reaction conversion as a function of the ratio of total permeation rate to reaction rate for a packed bcd microporous membrane reactor with the permeate side under vacuum [Mohan and Govind, 1988a]...

Fig. 11.13. Cyclohexane conversion vs. the (permeation/reaction rate) ratio. Curves 1 and 2 for mesoporous membranes with Knudsen separation factors. Curves 3 and 4 for microporous membranes with a separation factor of 100. Curves 5 and 6 for membranes permeable only to hydrogen. Odd (even) numbered curves correspond to an inert sweep gas rate of 1 (10) times the cyclohexane flow. The temperature is 477 K, Pfeed= 100 kPa. From Flarold et al. [130] with permission.

In the present concept of styrene dehydrogenation implementation of inorganic membranes is not feasible. Application of Knudsen diffusion membranes with a low permselectivity to hydrogen leads to a considerable permeation of ethylbenzene and thus, to lower yields. Microporous and palladium membranes give better results, but worse than a conventional case, because the conversion is limited by reaction kinetics. The ratio of permeation rate to reaction rate is very important in selecting membranes in a membrane reactor process in which equilibrium shift is foreseen. 

When the membrane performs only a separation function and has no catalytic activity, two membrane properties arc of importance, the permeability and the selectivity which is given by the separation factor. In combination with a given reaction, two process parameters are of importance, the ratio of the permeation rate to the reaction rate for the faster permeating component (c.g. a reaction product such as hydrogen in a dehydrogenation reaction) and the separation factors (permselectivities) of all the other components (in particular those of the reactants) relative to the faster permeating gas. These permselectivities can be expressed as the ratios of the permeation rates of... 

Using a developed plug-flow membrane reactor model with the catalyst packed on the tube side, Mohan and Govind [1986] studied cyclohexane dehydrogenation. They concluded that, for a fixed length of the membrane reactor, the maximum conversion occurs at an optimum ratio of the permeation rate to the reaction rate. This effect will be discussed in more detail in Chapter 11. They also found that, as expected, a membrane with a highly permselective membrane for the product(s) over the reactant(s) results in a high conversion. 

Mohan and Govind [1988c] applied their isothermal packed-bed porous membrane reactor model to the same equilibrium-limited reaction and found that the reactor conversion easily exceeds the equilibrium value. The HI conversion ratio (reactor conversion to equilibrium conversion) exhibits a maximum as a function of the ratio of the permeation rate to the reaction rate. This trend, which also occurs with other reactions such as cyclohexane dehydrogenation and propylene disproportionation, is the result of significant loss of reactant due to increased permeation rate. This loss of reactant eventually negates the equilibrium displacement and consequently the conversion enhancement effects. 

Figure 11.38 Comparison of single- and two-membrane reactors as a function of the ratio of the reactant permeation rale to the reaction rate [Tekid et al., 1994]...

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