Elsevier

Journal of Membrane Science

Volume 430, 1 March 2013, Pages 113-128
Journal of Membrane Science

Investigating the influence of diffusional coupling on mixture permeation across porous membranes

https://doi.org/10.1016/j.memsci.2012.12.004Get rights and content

Abstract

A careful analysis of published experimental data on permeation of a variety of binary mixtures reveals that there are fundamentally two types of diffusional coupling effects that need to be recognized. The first type of coupling occurs when the less-mobile species slows down its more mobile partner by not vacating an adsorption site quick enough for its more mobile partner to occupy that position. Such slowing-down effects, also termed correlation effects, are quantified by the exchange coefficient Ð12 in the Maxwell–Stefan (M–S) formulation. The parameter Ð1/Ð12, quantifying the degree of correlations, is strongly dependent on the pore size, topology and connectivity and reasonable estimates are provided by molecular dynamics (MD) simulations. In cage-type structures (e.g. CHA, DDR, LTA, and ZIF-8) in which adjacent cages are separated by narrow windows correlations are weak, and Ð1/Ð12≈0 is a good approximation. On the other hand correlations are particularly strong in structures consisting of one-dimensional channels (e.g. NiMOF-74), or intersecting channels (e.g. MFI) structures; in these cases the values of Ð1/Ð12 are in the range 1–5. A wide variety of experimental data on binary mixture permeation can be quantitatively modeled with the Maxwell–Stefan equations using data inputs based on unary permeation experiments, along with Ð1/Ð12 values suggested by MD. The second type of coupling occurs as a consequence of molecular clustering due to hydrogen bonding. Such clustering effects, commonly prevalent in alcohol/water pervaporation, can cause mutual slowing-down of partner molecules in the mixture. When molecular clustering occurs the Maxwell–Stefan diffusivity of a species in the mixture, Ði, cannot be identified with that obtained from unary permeation.

Highlights

► Correlation effects in mixture permeation are modeled using the Maxwell–Stefan equations. ► Correlations cause slowing-down of the more mobile partners. ► Slowing-down effects increase permeation selectivity in CO2 capture applications in some cases. ► Mutual slowing-down effects prevail in membrane pervaporation.

Introduction

The proper description of permeation of mixtures across porous membranes consisting of thin layers of ordered crystalline materials such as zeolites (crystalline aluminosilicates), metal-organic frameworks (MOFs), and zeolitic imidazolate frameworks (ZIFs) is important in development and design of a variety of industrially important separation processes, such as CO2 capture, natural gas purification, fuel gas purification and pervaporation [1], [2], [3], [4], [5], [6], [7], [8]. For separation of a binary mixture, the permeation selectivity, Sperm, is commonly defined as the ratio of the component permeances across the porous layerSperm=Π1Π2=N1/Δp1N2/Δp2where the fluxes Ni, are defined in terms of the cross-sectional area of the membrane (see schematic in Fig. 1). The Maxwell–Stefan (M–S) formulation for mixture diffusion is most commonly used for modeling membrane permeation [5], [9], [10], [11], [12], [13], [14]. Solution of the M–S equations for steady-state binary mixture permeation results in the following set of equations for the permeation fluxesN1=ρÐ1δ[(1+x1Ð2/Ð12)Δq1+x1Ð2/Ð12Δq21+x1Ð2/Ð12+x2Ð1/Ð12]andN2=ρÐ2δ[x2Ð1/Ð12Δq1+(1+x2Ð1/Ð12)Δq21+x1Ð2/Ð12+x2Ð1/Ð12]

In the derivations of the Eqs. (2), (3), details of which are provided in the Supplementary Material accompanying this publication, the resistance of the support layer is ignored. Furthermore, the micro-porous crystalline layer is considered to be defect-free, and inter-grain boundary resistances have not been accounted for.

The molar loadings, qi, in the adsorbed phase at either face of the membrane are obtained from adsorption equilibrium. In all the calculations presented is this study, the adsorption equilibrium is determined using the Ideal Adsorbed Solution Theory of Myers and Prausnitz [15], on the basis of pure component isotherm fits. The xi are the component mole fractions in the adsorbed phase within the membranex1=q1/(q1+q2);x2=q2/(q1+q2)

The calculation of xi using the upstream loadings is sufficiently accurate for the estimation of the permeation fluxes.

There are basically two different types of M–S diffusivities. The Ð1 and Ð2 characterize the interactions, in the broadest sense, with the pore walls. The Ð12 is the exchange coefficient which quantify diffusional coupling between the two components. At the molecular level, the Ð12 reflect how the facility for transport of species 1 correlates with that of species 2. In subsequent discussions, it is convenient to define the ratio (Ð1/Ð12) as a reflection of the degree of correlations. The diffusional characteristics of the porous crystalline layer is therefore described by three separate independent parameters: (a) the two membrane transport coefficients ρÐ1/δ, and ρÐ2/δ, and (b) the degree of correlations Ð1/Ð12.

In assessing the separation capability of any membrane for a given separation task it is useful to also define the adsorption selectivity, Sads, in terms of the component loadings and partial pressures in the upstream compartment.Sads=q10/q20p10/p20

A further useful metric is the diffusion selectivity of the membrane, SdiffSdiff=SpermSads=Ð1Ð2(1+Ð2/Ð12)(1+Ð1/Ð12)where the second right member in Eq. (6) is derived for the commonly valid assumption that the downstream partial pressures, and component loadings are negligible in comparison with the corresponding upstream values (detailed derivations are provided in the Supplementary Material). For the special limiting case for which the degree of correlations is negligible small, Eq. (6) simplifies to yieldSdiff=Ð1Ð2;negligiblecorrelations

A special distinguishing feature of membrane separations, in contrast to other competitive technologies such as pressure swing adsorption (PSA) devices, is that the permeation selectivity Sperm is governed not only by Sads but also by the diffusional characteristics. PSA units are largely, though not exclusively, governed by Sads but membrane-based separations offer the possibility of also exploiting Sdiff to significantly enhance the obtained value of Sperm.

There are three major objectives of the investigations reported here.

The first objective is to identify conditions and systems for which the diffusional coupling effects can be assumed to be of negligible significance. This scenario corresponds to the limiting case in which (Ð1/Ð12)0 and, as a consequence, Eqs. (2), (3) simplify to yieldN1=ρÐ1δΔq1;N2=ρÐ2δΔq2;negligiblecorrelations

The second objective is to identify and examine systems for which the correlation effects are significant. In such cases we seek to establish the applicability of M–S Eqs. (2), (3) in describing mixture permeation characteristics by estimating the membrane transport coefficients ρÐ1/δ, and ρÐ2/δ from unary permeation data. We aim to show that a clever choice of the membrane material, with the appropriate degree of correlations, will serve to significantly enhance the permeation selectivity.

The third objective is to identify systems for which the ρÐ1/δ, and ρÐ2/δ characterizing mixture permeation cannot be identified with those obtained from unary permeation.

Section snippets

Comparing the degree of correlations in different host materials

There is no experimental technique for direct determination of the exchange coefficients Ð12, that quantify molecule–molecule interactions. For this reason we use molecular dynamics (MD) simulation data from the literature [13], [14], [16], [17], [18], [19] to obtain the necessary insights and inputs. For convenience, a summary of available MD simulation data, and the interpretation thereof, is provided as Supplementary Material.

For mesoporous materials, such as BTP-COF, the values of the

Systems with negligible degree of correlations

We first examine mixture permeation across structures such as CHA, DDR, LTA, ITQ-29, SAPO-34, and ZIF-8 that consist of cages separated by narrow windows in the 3.2–4.2 Å range. We shall analyze experimental mixture permeation data to examine whether the uncoupled Eq. (8) is of sufficient accuracy for use in practice.

Consider permeation of CO2/CH4 separation using a membrane made up of thin layers of SAPO-34 that consists of 316 Å3 sized cages separated by 3.8 Å×4.2 Å sized windows. Experimental

Systems with significant degree of correlations

We now investigate membranes made up of thin layers of materials such as MFI, FAU, NaX, IRMOF-1, and Matrimid for which correlation effects exert a strong influence causing the mixture permeation characteristics to be significantly different from unary permeation. Such effects are best illustrated by considering the experimental data of Sandström et al. [41] for permeances of H2 and CO2 in a MFI membrane, determined both from unary and binary mixture permeation data; see Fig. 8a. We note that

Systems exhibiting molecular clustering

Pervaporation of water/alcohol mixtures is an important process in the processing industry, and a wide variety of membrane materials has been used, including polymeric (e.g. PERVAP, Chitosan, PDMS), zeolites (e.g. CHA, LTA, MFI, FAU, DDR), zeolitic imidazolate frameworks (e.g. ZIF-8) and mixed matrix membranes [49], [50], [51]. There is considerable evidence in the literature to indicate that hydrogen bonding, and consequent cluster formation manifests in LTA-4A [52], [53], MFI [54], [55], [56]

Conclusions

By analyzing experimental data on permeation of a variety of mixtures across membrane materials with different characteristics we have discerned two types of coupling effects.

The first type of coupling occurs when the less-mobile species slows down its more mobile partner by not vacating an adsorption site quick for its more mobile partner to occupy that position. The Maxwell–Stefan formulation for mixture permeation, expressed in Eqs. (2), (3), allows a quantitative prediction of mixture

Notation

    ci

    pore concentration of species i, ci=qi/Vp, mol m−3

    ct

    total pore concentration in mixture, ct=qt/Vp, mol m−3

    Ði

    MS diffusivity of species i, m2 s−1

    Di,self

    Self-diffusivity of species i, m2 s−1

    Ð12

    M–S exchange coefficient, m2 s−1

    F

    factor defined by Eq. (9), dimensionless

    pi

    partial pressure of species i in upstream compartment, Pa

    pt

    total pressure in upstream compartment, Pa

    qi

    molar loading of species i, mol kg−1

    qt

    total molar loading of mixture, mol kg−1

    Ni

    molar flux of species i defined in terms of the

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