Investigating the influence of diffusional coupling on mixture permeation across porous membranes
Graphical abstract
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 layerwhere 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 fluxesand
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 membrane
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 , and , and (b) the degree of correlations .
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.
A further useful metric is the diffusion selectivity of the membrane, Sdiffwhere 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 yield
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 and, as a consequence, Eqs. (2), (3) simplify to yield
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 , and 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 , and 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
M–S 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
References (97)
Are MOF membranes better in gas separation than those made of zeolites?
Curr. Opin. Chem. Eng.
(2011)Membrane processes and postcombustion carbon dioxide capture: challenges and prospects
Chem. Eng. J.
(2011)- et al.
In silico screening of zeolite membranes for CO2 capture
J. Membr. Sci.
(2010) - et al.
Insights into diffusion of gases in zeolites gained from molecular dynamics simulations
Micropor. Mesopor. Mater.
(2008) - et al.
Onsager coefficients for binary mixture diffusion in nanopores
Chem. Eng. Sci.
(2008) - et al.
Investigating the potential of MgMOF-74 membranes for CO2 capture
J. Membr. Sci
(2011) - et al.
Maxwell–Stefan modeling of slowing-down effects in mixed gas permeation across porous membranes
J. Membr. Sci.
(2011) - et al.
Unified Maxwell–Stefan description of binary mixture diffusion in micro- and meso- porous materials
Chem. Eng. Sci
(2009) - et al.
Investigation of slowing-down and speeding-up effects in binary mixture permeation across SAPO-34 and MFI membranes
Sep. Purif. Technol.
(2008) - et al.
Segregation effects in adsorption of CO2 containing mixtures and their consequences for separation selectivities in cage-type zeolites
Sep. Purif. Technol.
(2008)
Separation and permeation characteristics of a DD3R zeolite membrane
J. Membr. Sci
Natural gas purification with a DDR zeolite membrane; permeation modelling with Maxwell–Stefan equations
Stud. Surf. Sci. Catal.
Hindering effects in diffusion of CO2/CH4 mixtures in ZIF-8 crystals
J. Membr. Sci.
A molecular dynamics investigation of the diffusion characteristics of cavity-type zeolites with 8-ring windows
Micropor. Mesopor. Mater
Effective separation of propylene/propane binary mixtures by ZIF-8 membranes
J. Membr. Sci.
Ethene/ethane separation by the MOF membrane ZIF-8: molecular correlation of permeation, adsorption, diffusion
J. Membr. Sci.
Adsorptive separation of light olefins from paraffins
Micropor. Mesopor. Mater.
Very high flux MFI membrane for CO2 separation
J. Membr. Sci.
Mixed gas separation study for the hydrogen recovery from H2/CO/N2/CO2 post combustion mixtures using a Matrimid membrane
J. Membr. Sci.
Transport properties of alkanes through ceramic thin zeolife MFI membranes
J. Membr. Sci.
Diffusion of hydrocarbon mixtures in MFI zeolite: influence of intersection blocking
Chem. Eng. J.
Preparation of Ni-MOF-74 membrane for CO2 separation by layer-by-layer seeding technique
Micropor. Mesopor. Mater.
Dehydrating performance of commercial LTA zeolite membranes and application to fuel grade bio-ethanol production by hybrid distillation/vapor permeation process
Micropor. Mesopor. Mater.
Development of practically available up-scaled high-silica CHA-type zeolite membranes for industrial purpose in dehydration of N-methyl pyrrolidone solution
J. Membr. Sci.
Simulation of adsorption and separation of ethanol–water mixture with zeolite and carbon nanotube
Fluid Phase Equilib.
Analyzing diffusion behaviors of methanol/water through MFI membranes by molecular simulation
J. Membr. Sci.
A novel model based on cluster formation for pervaporation separation of polar components from aqueous solutions
Sep. Purif. Technol.
Molecular dynamics simulation study of the concentration dependence of the self-diffusivity of methanol in NaX zeolite
Micropor. Mesopor. Mater.
Electrokinetic transport of water and methanol in Nafion membranes as observed by NMR spectroscopy
Electrochim. Acta
Application of hydroxy sodalite films as novel water selective membranes
J. Membr. Sci.
Formation of high flux CHA-type zeolite membranes and their application to the dehydration of alcohol solutions
J. Membr. Sci.
Monte Carlo Simulation of methanol diffusion in critical media
Chinese J. Chem. Eng.
Modeling transient permeation of polar organic mixtures through a MFI zeolite membrane using the Maxwell–Stefan equations
J. Membr. Sci.
Pervaporation of binary water-alcohol and methanol-alcohol mixtures through microporous methylated silica membranes: Maxwell–Stefan modeling
Comput. Chem. Eng.
Rigorous dynamic model of a direct methanol fuel cell based on Maxwell–Stefan mass transport equations and a Flory–Huggins activity model: formulation and experimental validation
J. Power Sources
Mass, charge and energy transport phenomena in a polymer electrolyte membrane (PEM) used in a direct methanol fuel cell (DMFC): modelling and experimental validation of fluxes
J. Membr. Sci.
Adsorptive separation of CO2/CH4/CO gas mixtures at high pressures
Micropor. Mesopor. Mater.
Diffusion of alkane mixtures in MFI zeolite
Micropor. Mesopor. Mater.
Investigating the validity of the Bosanquet formula for estimation of diffusivities in mesopores
Chem. Eng. Sci.
Highlighting pitfalls in the Maxwell–Stefan modeling of water–alcohol mixture permeation across pervaporation membranes
J. Membr. Sci.
A rationalization of the Type IV loading dependence in the Kärger–Pfeifer classification of self-diffusivities
Micropor. Mesopor. Mater.
Inorganic membranes for carbon dioxide and nitrogen separation
Rev. Chem. Eng.
Metal-organic framework membranes—high potential, bright future?
Angew. Chem. Int. Ed.
Diffusion in Nanoporous Materials
In silico screening of metal-organic frameworks in separation applications
Phys. Chem. Chem. Phys.
Zeolite membranes: microstructure characterization and permeation mechanisms
Acc. Chem. Res.
Modeling permeation of binary mixtures through zeolite membranes
AIChE J.
Role of adsorption in the permeation of CH4 and CO2 through a silicalite-1 membrane
Ind. Eng. Chem. Res.
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