Ind. Eng. Chem. Res. 2008, 47, 3213-3224
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Modeling Pervaporation of Ethanol/Water Mixtures within ‘Real’ Zeolite NaA Membranes Marc Pera-Titus,*,† Carles Fite´ ,† Victor Sebastia´ n,‡ Esther Lorente,‡ Joan Llorens,† and Fidel Cunill† Chemical Engineering Department, UniVersity of Barcelona, 08028-Barcelona, Spain, and Department of Chemical and EnVironmental Engineering, UniVersity of Zaragoza, 50009-Zaragoza, Spain
A modified version of the adsorption-diffusion model derived form the Maxwell-Stefan theory developed in a previous study (Pera-Titus, et al. Catal. Today 2006, 118, 73) is presented in this paper to describe the dehydration behavior of zeolite NaA membranes for pervaporation of ethanol/water mixtures. Compared to the former version, two additional contributions are included in the model: (1) the adsorbed solution theory of Myers and Prausnitz is used instead of the extended Langmuir isotherm to account for binary adsorption equilibria of water and ethanol on zeolite A, and (2) the explicit role of pressure-driven mechanisms in large intercrystalline defects (macrodefects) to permeation is considered. These refinements in the Maxwell-Stefan equations provide a superior description of solvent dehydration using zeolite NaA membranes. The fitted surface diffusivities at 323 K and at zero loading of water and ethanol for weak confinement show values in the order of 10-12 and 10-13 m2‚s-1, respectively. The former values are 3-4 orders of magnitude higher than those that have been measured from water adsorption kinetics experiments. This difference might be ascribed to a certain role of nanosized grain boundaries between adjacent zeolite A crystals. Grain boundaries might behave as fast diffusion paths or nanoscopic shortcuts due to anisotropy of zeolite layers, resulting in higher apparent water surface diffusivities and lower apparent activation energies for surface diffusion. 1. Introduction Over the past years, there has been an increasing interest in the use of polycrystalline zeolite membranes for separation of species relying on molecular size, adsorption affinity, and/or surface diffusion differences.1,2 In the special case of liquid mixture separation by pervaporation (PV), separation occurs on the basis of adsorption differences.3 This is especially true for solvent dehydration by hydrophilic zeolite membranes (e.g., zeolite NaA), characterized by their low Si/Al ratios, where water adsorbs preferentially on the zeolite material. Most studies reported in the literature have focused on zeolite NaA membrane synthesis and PV performance.4-10 However, only a few works can be found dealing with the modeling of the process. This issue is essential not only for a proper understanding of the process itself but also for design purposes. The so-called solution-diffusion model of Wijmans and Baker11 constitutes the simplest approach to describe the PV process within a membrane. This model, originally conceived for polymeric films, assumes that the liquid mixture dissolves in the polymer matrix at the feed/membrane interface, diffuses through the membrane thickness, and finally desorbs at the membrane/permeate interface. The driving force of the process is often regarded as a fugacity difference (or partial pressure difference) over the selective layer.12 Note that the fugacity of a target species i, fi, in the liquid feed is independent of feed pressure below 10 bar, but depends on the saturation vapor pressure, i.e., fi ) xiγiP*. Moreover, the diffusion step is described using Fick’s first law with constant or concentrationdependent diffusivities. The permeability constant of a mem* To whom correspondence should be addressed. Present address: Institut de Recherches sur la Catalyse et l’Environnement de Lyon (IRCELYON), UMR5256-CNRS/Universite´ Claude Bernard-Lyon 1. E-mail:
[email protected]. † University of Barcelona. ‡ University of Zaragoza.
brane includes the information related to the affinity and diffusivity of the permeating species. This implies that no aprioristic information dealing with the membrane material properties and sorbate affinity to the material is required. Recently, the solution-diffusion model has been successfully applied to describe pure component PV, solvent dehydration, and organic-organic separations using amorphous silica,13-15 Ge-modified ZSM-5,16 and zeolite NaA membranes at low water concentrations (8 wt %),6,19,20 adsorption is usually described using Langmuir-type nonlinear isotherms. In its simplest form, the single-site Langmuir isotherm is characterized by a linear trend between the surface loading and the partial pressure at low loadings, while it approaches to saturation at higher values. The mathematical form of this isotherm limits the use of fugacity differences as driving force to describe PV in zeolite membranes, as we have recently pointed out in a recent paper.19 In contrast, the use of chemical potential gradients in the Maxwell-Stefan (MS) formalism, as usually applied to describe gas permeation within MFI-type zeolite membranes,21-27 allows circumventing the above stated shortcomings. De Bruijn et al.13 have recently derived simplified expressions from these equations that represent successfully PV data of methanol within
10.1021/ie071645b CCC: $40.75 © 2008 American Chemical Society Published on Web 04/10/2008
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Ind. Eng. Chem. Res., Vol. 47, No. 9, 2008
amorphous methylated silica membranes in the temperature range 333-428 K for different feed and permeate pressures. In the case of solvent dehydration, the MS equations are usually implemented with the extended Langmuir isotherm (single-site) to account for mixture adsorption at the feed/ membrane and permeate/membrane surfaces, as well as for deriving analytical expressions for the Γij thermodynamic factors. Such an isotherm has been used by some of us in a previous study19 to obtain an analytical solution of the MS equations that predicts the dehydration performance of zeolite NaA membranes. Nevertheless, the extended Langmuir isotherm is not thermodynamically consistent for describing competitive adsorption of water and organic solvents, since the requirement of equal molar saturation loading for each adsorbing species is not actually fulfilled (compare for instance the values 15 and 4.5 mol‚kg-1 for water and ethanol, respectively6). According to Krishna,28 when two species in a mixture have significantly different molecular sizes, size entropy effects tend to favor the adsorption of smaller species (in this case water in front of ethanol) at higher loadings. This is the case, for instance, of methane and n-butane adsorption in silicalite-1.29 Various approaches have been proposed in the literature to account for thermodynamically consistent models to describe mixture adsorption. Among them, the ideal adsorbed solution theory (IAST) of Myers and Prausnitz30 reveals useful for predicting mixture adsorption from pure Langmuir isotherms without the need to include additional parameters in the thermodynamic treatment. Kapteijn et al.31 have shown that the combination of this IAS theory with the MS equations provides a superior description of the gas separation performance of silicalite-1 membranes towards separation of hydrocarbons with different molar saturation loadings. Further modifications of the original IAST model, such as the real adsorbed solution theory (RAST)32 and the predictive adsorbed solution theory (PRAST) of Sakuth et al.33 to account for nonideality of the sorbate mixture have been proposed as well. Another problem dealing with the modeling PV within ‘real’ zeolite membranes is ascribed to the presence of intercrystalline defects. Mass transfer within large pores (preferentially macropores) should in principle depend on pressure-driven mechanisms (viscous + Knudsen) with a relevant contribution of capillary forces, as we have recently underlined in a previous work.34 In practice, this involves a linear trend of the PV flux through defects with the feed pressure. Despite the presence of a certain amount of defects in a zeolite NaA layer, high compressive tensions due to negative capillary forces might allow discrimination between water and organic species in smallsized mesopores (i.e.,
