Membrane reactors calculation

In the isobutane dehydrogenation the catalytic membrane reactor allows a conversion which is twice the one observed in a conventional reactor operating under similar feed, catalyst and temperature conditions (and for which the performance corresponds to the one calculated from thermodynamics) [9]. 

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). 

Figure 16. Propylene conversion and product-selectivity results for the membrane-reactor measurements performed at 723 K with pure propylene as the feed. The results in panel a were for the SOFC with a Cu—ceria—YSZ anode, and the results in panel b were for the Cu-molybdena-YSZ anode. In panel a, the points are the rate of CO2 production, and the line was calculated from the current density and eq 8. In panel b, the points show the production of acrolein, and the line was calculated from eq 9. (Reprinted with permission from ref 165. Copyright 2002 Elsevier.)...

Fig. 2. Schematic presentation of a membrane reactor (left) and theoretical relative concentrations (Cfl of the dendritic species versus the substrate flow (in residence times Nfl calculated for various retention factors.

Furthermore, it can be shown that, in the limiting cases of first-order kinetics [Equation (11.35) also holds for this case] and zero-order kinetics, the equal and optimal sizes are exactly the same. As shown, the optimal holding times can be calculated very simply by means of Equation (11.40) and the sum of these can thus be used as a good approximation for the total holding time of equal-sized CSTRs. This makes Equation (11.31) an even more valuable tool for design equations. The restrictions are imposed by the assumption that the biocatalytic activity is constant in the reactors. Especially in the case of soluble enzymes, for which ordinary Michaelis-Menten kinetics in particular apply, special measures have to be taken. Continuous supply of relatively stable enzyme to the first tank in the series is a possibility, though in general expensive. A more attractive alternative is the application of a series of membrane reactors. 

Although these systems involve two variables, their steady-state solutions can be calculated in general and a more complete mathematical analysis of dissipative structures is possible. From a practical point of view it is interesting to note that systems obeying equations of the form (2) may be found in artificial membrane reactors.22 Examples are presented by D. Thomas in this volume. 

In the preceding section, we analyzed an immobilized enzyme process and calculated some important parameters such as productivity. In this section, we investigate another process configuration for retaining biocatalysts, the membrane reactor. The advantages and disadvantages of immobilization and membrane retention have already been discussed in Chapter 5. As in the case of immobilization, retention of catalyst by a membrane vastly improves biocatalyst productivity, a feature important on a processing scale but usually not on a laboratory scale. 

We will calculate the reactor performance itself as well as the productivity over time we will see that productivity is influenced by retention of the enzyme catalyst as much as by its deactivation behavior. In the schematic of an enzyme membrane reactor... 

The overall mass-transfer rates on both sides of the membrane can only be calculated when we know the convective velocity through the membrane layer. For this, Equation 14.2 should be solved. Its solution for constant parameters and for first-order and zero-order reaction have been given by Nagy [68]. The differential equation 14.26 with the boundary conditions (14.28a) to (14.28c) can only be solved numerically. The boundary condition (14.28c) can cause strong nonlinearity because of the space coordinate and/or concentration-dependent diffusion coefficient [40, 57, 58] and transverse convective velocity [11]. In the case of an enzyme membrane reactor, the radial convective velocity can often be neglected. Qin and Cabral [58] and Nagy and Hadik [57] discussed the concentration distribution in the lumen at different mass-transport parameters and at different Dm(c) functions in the case of nL = 0, that is, without transverse convective velocity (not discussed here in detail). 

Fig. 12.12. Calculated dependence of cyclohexane conversion (Eq. (37)) as a function of the Damkohler number (Eq. (41)) for a) the conventional fixed-bed reactor b) the diluted fixed-bed reactor and c) the membrane reactor with an optimized thickness ofVycor glass membrane (the dashed line corresponds to a hypothetically higher membrane selectivity, Sm). The range in which the membrane reactor experiments were performed is also indicated. Parameters T = 473 K, x r H =...

Cost calculations for a membrane reactor are very cumbersome. Numerous uncertainties and assumptions have to be made for a large number of parameters. Tube length and sealing costs are very important and up to now it is not even sure whether a sealing material can be developed that is able to withstand the severe operation conditions. This makes a proper... 

Combustion reactions often cause extensive exergy loss. Exeigy calculations show that the entropy production can cause the loss of considerable potential work due to a reaction. An electrochemical membrane reactor or a fuel cell could reduce exergy loss considerably. 

Figure 9.2 Calculated total conversion profile of cyclohexane to benzene in a porous shell-and-tube Vycor glass membrane reactor with membrane thickness as a parameter [ltohetal.,1985]...

In addition to the Navier-Stokes equations, the convective diffusion or mass balance equations need to be considered. Filtration is included in the simulation by preventing convection or diffusion of the retained species. The porosity of the membrane is assumed to decrease exponentially with time as a result of fouling. Wai and Fumeaux [1990] modeled the filtration of a 0.2 pm membrane with a central transverse filtrate outlet across the membrane support. They performed transient calculations to predict the flux reduction as a function of time due to fouling. Different membrane or membrane reactor designs can be evaluated by CFD with an ever decreasing amount of computational time. 

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. 

There are a number of instances when it is much more convenient to work in terms of the number of moles (iV, N-g) or molar flow rates (Fj, Fg, etc.) rather than conversion. Membrane reactors and multiple reactions taking place in the gas phase are two such cases where molar flow rates rather than conversion are preferred. In Section 3.4 we de.scribed how we can express concentrations in terms of the molar flow rates of the reacting species rather than conversion, We will develop our algorithm using concentrations (liquids) and molar flow rates (gas) as our dependent variables. The main difference is that when conversion is used as our variable to relate one species concentration to that of another species concentration, we needed to write a mole balance on only one species, our basis of calculation. When molar flow rates and concentrations are used as our variables, we must write a mole balance on each species and then relate the mole balances to one another through the relative rates of reaction for... 

Takeuchi et al. 7 reported a membrane reactor as a reaction system that provides higher productivity and lower separation cost in chemical reaction processes. In this paper, packed bed catalytic membrane reactor with palladium membrane for SMR reaction has been discussed. The numerical model consists of a full set of partial differential equations derived from conservation of mass, momentum, heat, and chemical species, respectively, with chemical kinetics and appropriate boundary conditions for the problem. The solution of this system was obtained by computational fluid dynamics (CFD). To perform CFD calculations, a commercial solver FLUENT has been used, and the selective permeation through the membrane has been modeled by user-defined functions. The CFD simulation results exhibited the flow distribution in the reactor by inserting a membrane protection tube, in addition to the temperature and concentration distribution in the axial and radial directions in the reactor, as reported in the membrane reactor numerical simulation. On the basis of the simulation results, effects of the flow distribution, concentration polarization, and mass transfer in the packed bed have been evaluated to design a membrane reactor system. 

Figure 9.12 depicts the profiles of feed-side H2 concentrations on the dry and wet bases. As depicted in this figure, the membrane reactor could enhance H2 concentration from 45.30% to 54.95% (on dry basis), that is, from 41% to 49.32% (on wet basis). In this case, the H2 recovery calculated from the model was 97.38%. With the advancement of the high-temperature proton exchange membrane fuel cell (120-160 °C), it is expected that the constraint of CO concentration can be relaxed to about 50 ppm in the near future. Then, the required hollow-fiber number could be reduced significantly to 39,000 based on the modeling results. 

The membrane areas required for the exit feed CO concentration of <10 ppm in the H2 product were calculated with seven different inlet sweep temperatures ranging from 80 to 200 °C, while the other parameters for the reference case were kept constant. As demonstrated in Figure 9.19, the required membrane area or hollow-fiber number dropped rapidly as the inlet sweep temperature increased from 80 to 160 °C. Beyond 160 °C, it increased slightly. Figure 9.20 depicts the feed-side temperature profiles along the membrane reactor with different inlet sweep temperatures. Increasing the inlet sweep temperature increased the feed-side temperature... 

Figure 9.24. The calculated GHSV results for the data shown in Figure 9.23 at various flow rates from the rectangular WGS membrane reactor.

Fig. 11.4. Top figure shows the effect of pressure on the reaction side of the membrane cm methane conversion in the Pd membrane reactor bottom figure shows the effect of temperature. The solid line and the sjmtibols (o) are for the Pd membrane reactor. The dotted line is the calculated equilibrium conversion and the symbols ( ) are for a membrane reactor using a porous Vycor glass membrane. Reproduced from Uemiya et al. [29] with permission.

Fig. 11.8. The use of membrane reactors in partial oxidation reactions. Upper figure represents a schematic of the concept. Lower figure gives the calculated )deld as a function of the Thiele modulus.

In the various feasibility studies presented in this chapter, models of membrane separation and membrane reactor systems play an important role. Models are being used for various reasons not only because there is a lack of experimental data, or the calculations concern non-existing, fictive membranes, they are also used to conveniently represent available data. In the various studies, different types of models have been used. However, the basis of all the models used is the same and will be discussed here. 

Permeation characteristics of Knudsen diffusion membranes, consisting of a support and two consecutive layers, have been used to calculate the performance of the ceramic membrane reactor, see also Section 14.2.1 [17,31]. The pore size of the separation layer of these membranes is 4 nm in diameter [31,38]. Ideal membranes which remove all the hydrogen formed do not exist (possible Pd-based membranes will come close to the required characteristics), but are used as a basis for calculating the maximum possible increase in conversion and selectivity. 

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