Membrane reactors reaction equilibrium constants

Sousa et al [5.76, 5.77] modeled a CMR utilizing a dense catalytic polymeric membrane for an equilibrium limited elementary gas phase reaction of the type ttaA +abB acC +adD. The model considers well-stirred retentate and permeate sides, isothermal operation, Fickian transport across the membrane with constant diffusivities, and a linear sorption equilibrium between the bulk and membrane phases. The conversion enhancement over the thermodynamic equilibrium value corresponding to equimolar feed conditions is studied for three different cases An > 0, An = 0, and An < 0, where An = (ac + ad) -(aa + ab). Souza et al [5.76, 5.77] conclude that the conversion can be significantly enhanced, when the diffusion coefficients of the products are higher than those of the reactants and/or the sorption coefficients are lower, the degree of enhancement affected strongly by An and the Thiele modulus. They report that performance of a dense polymeric membrane CMR depends on both the sorption and diffusion coefficients but in a different way, so the study of such a reactor should not be based on overall component permeabilities. 

The mass polymerization is carried out at 40-70 C and 70-170 psi, and the monomer is in equilibrium with the vapor phase. The reaction temperature is kept constant by maintaining constant reactor pressure. It is necessary to have enough monomer to permit the heat transfer by vaporization and a free surface (reactor walls, agitators, condensers) for the recondensation of the monomer. The condensed monomer is readsorbed immediately by the PVC particles because, unlike the suspension process, there is no colloidal membrane ( skin ) around the particle. The residual monomer is degassed directly in the polymerization reactor until equilibrium between the reactor pressure and the pressure of the recovery condenser is achieved. Compressor degassing is then followed until a high vacuum is reached in the reactor (around 100 mm Hg). Finally, the vacuum is broken with nitrogen or water vapor. 

Some of these studies focused on the analysis of equilibrium-limited reactions, namely those in which the conditions of the respective conversion could be enhanced relatively to the value obtained in a conventional reactor, the so-called thermodynamic equilibrium conversion.i i The developed models considered generic equilibrium-limited reactions carried on in membrane reactors with perfectly mixed or plug-flow pattems. In all these studies, the main assumptions considered consisted in isothermal and steady-state operation, Fickian transport across a non-porous membrane with a homogeneously distributed nanosized catalyst with constant diffusion coefficients, Henry s law for describing the equilibrium condition at the interfaces membrane/gas, and equality of local concentrations at the interface polymer phase/catalyst surface. 

In the same suidy [Itoh et al., 1985], the molar flow rate of cyclohexane at the reactor outlet is calculated as a function of the membrane thickness which has the most effect on the permeation rate of gases. For a given constant inlet molar flow rate, the reaction does not proceed beyond the equilibrium conversion for a conventional reactor. With membrane permeation, however, the overall conversion (i.e., the combined conversions of cyclohexane on the tube and shell sides) reaches a maximum for a certain membrane... 

Keurentjes at al [3.27] carried out experiments to study the kinetics of this reaction, and fitted their data in terms of an activities dependent mass-action kinetic scheme. They utilized a simple model of a PVMR to study the effect of the ratio of membrane area (A) to reactor volume (V) on PVMR performance based on the measured rate constants and literature values for the water and ethanol permeances through a PVA membrane (PVMR models are further discussed in Chapter 5). Keurentjes Qt al [3.27] report that with the aid of the PV membrane the equilibrium can be significantly shifted towards the diethyltar-trate product. There is a certain optimum (A/V) ratio. This is because when the (A/V) ratio is too low, the water removal rate is too slow to have any influence, while for high values of this ratio too much ethanol is removed. 

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