Gas Permeation Model Research Articles

Modeling of dual-skin asymmetric hollow fiber microporous membranes for predicting the skins parameters separately using gas permeation test

This study presented a comprehensive gas permeation model to predict the skin parameters of a complex system, specifically a hollow fiber membrane with an asymmetric structure consisting of two external and internal skin layers. According to the work of Haefer for n segments of pores connected in series as in hollow fiber membranes, applying the Wakao et al. model, a comprehensive model for the transition regime was derived. The model was examined against the various fabricated PES and PEI hollow fiber membranes. Unlike conventional models, the proposed method predicted the mean pore size and mean pore length independent of surface porosity for each skin layer. The study revealed valuable insights into i) the middle pressure, ii) the difference between the skin parameters of the two membrane skins, and iii) the impact of the feeding direction on gas permeation behavior. It was shown that the dependency of permeation behavior on the feeding direction is linked to the influence of middle pressure on viscous flow, which is closely related to surface porosities of each side. It is evident that even the slightest variations in the fabrication parameters can result in different structures. Furthermore, it is evident that the assumption of neglecting slip flow was reasonable within the experienced Knudsen number range. The model also highlighted that the skin parameters of the two skin layers may not be identical, a distinction not captured by the current models. The traditional approach of setting the middle pressure as the average of the upstream and downstream pressures has been improved by expressing it as a linear function of both pressures. In the feed side, higher pressures led to dominant viscous flow, whilst the permeate side was more influenced by the free molecular regime due to lower pressures. There existed a competition between the Knudsen flow and the viscous flow at a specific Knudsen number for the feeding side pores, whether it was the inner or outer surface. The finding emphasized the significance of porosity values on each side in determining the proximity of middle pressure to feed and permeate side pressures, underscoring the importance of accurate knowledge of surface porosities, mean pore sizes, and pore lengths for both skin layers in understanding processes involving porous dual-skin hollow fiber membranes.

The interpretation of diverging hydrogen and carbon dioxide permeations with temperature across silica-based membranes

Hydrogen (H2) permeance across silica-based membranes increases with temperature, but carbon dioxide (CO2) permeance decreases. Because of the opposite signs of activation energies for H2 and CO2 permeation, silica-based membranes are widely used in separating H2 and CO2 at high temperatures due to the elevated difference between H2 and CO2 permeabilities. However, there has not been an explanation of the diverging permeance between H2 and CO2 with temperature. This study developed a gas permeation model encompassing gas penetration through silica matrix, Knudsen diffusion, and viscous flow. An Oscillator model with an effective medium approach was used to screen all possible pore size distributions and calculate the gas penetration through the silica matrix. However, no pore size distribution could allow positive activation energy for hydrogen and negative activation energy for carbon dioxide at the same time. After including Knudsen diffusion and viscous flow, the diverging permeance between H2 and CO2 with temperature was successfully interpreted. The pore size distribution and the fractional contribution from Knudsen diffusion and viscous flow, which could best fit experimental activation energies for H2 and CO2 permeation, were identified. In the silica matrix that formed the membranes, 5-membered rings were the dominant structures in pores, which was responsible for the positive apparent activation energy for H2. The negative CO2 apparent activation energy indicated that it was inevitable to have some Knudsen diffusion and viscous flow through some imperfections of the membrane. Our model demonstrated the importance of high-temperature gas separation, as high temperature could minimize the undesirable gas flow through imperfections. This study also implied that further improvement of H2/CO2 separation by silica-based membranes could be achieved by reducing imperfections.

Improved predictions of permeability properties in cement-based materials: A comparative study of pore size distribution-based models

Permeability is a fundamental physical property of a cement-based material and is closely related to its pore structure. This study developed an improved model for permeability prediction of cementitious materials with a function of the pore size distribution (PSD), in which PSD is simulated from single and compound lognormal distribution functions, respectively. The efficiency of the improved model is demonstrated by calculating permeability for mortars and pastes available in the literature. It is found that, first, for cementitious materials with unimodal PSD, the single lognormal distribution function is adequate to describe the pore structures. In contrast, for cementing mixtures presenting multimodal PSD, the compounded lognormal distribution function is highly recommended to cover a wide range of pore components. Second, the permeability model based on the compound PSD can predict well permeability to gas intrusion, whereas the single PSD-based model is applicable for calculating permeability via water intrusion. Furthermore, slippage effect and water saturation degree are introduced in the PSD-based model. Results prove that the corrected gas permeability model from the compound PSD performs well in estimating the gas permeability in unsaturated states. Finally, the compound PSD-based model is extended by considering varying porosities and relative humidities, which can be used to quantitively describe permeability when cementitious materials undergoing pore structure degradation induced by durability issues.

Gas permeability and emission in unsaturated vegetated landfill cover with biochar addition

Plant–biochar interaction has been recognized to affect the hydraulic properties of landfill cover soils, while its influence on landfill gas emission is rarely studied. This study investigated the coupled effects of biochar and vegetation on gas permeability and emission in unsaturated landfill cover through an integrated theoretical modelling and laboratory investigation. First, a gas permeability model was developed for vegetated coarse-grained soils with biochar addition. Then, a well-instrumented laboratory column test and two tests from the literature, considering bare, grass, biochar and grass + biochar conditions, were used for model validation. Finally, a numerical parametric study was conducted to investigate the influence of root growth and drought conditions on the gas emission rate. Results showed that the developed model can satisfactorily capture the gas permeability of unsaturated soils at various degrees of saturation. The lowest water retention capacity, the highest gas permeability and gas emission rate after 24 months of growth were observed in the grassed column. However, adding biochar in vegetated soils can maximize the water retention capacity and decrease the gas permeability, resulting in the lowest gas emission rate. The measured gas emission rates for the four cases meet the recommended value by the design guideline. The parametric study showed that the increased root depth from 0.2 m to 0.4 m improved the gas emission rate by 170% in the grass case but decreased by 97% in the grass + biochar case. Under the severe drought condition with soil suction around 500 kPa, the gas emission rate in the grassed case exceeded the design value by 18%, while those in the biochar cases were far below the allowable value. Therefore, peanut shell biochar should be considered to amend the grassed landfill cover using coarse-grained soils as it can significantly improve engineering performance in reducing gas emissions under extreme drought conditions.Graphical abstract

Gas permeation model for mixed matrix membranes: the new renovated Maxwell model

ABSTRACT The accurate prediction of gas separation properties of mixed matrix membranes (MMMs) is essential to eliminate the tedious experimental work. In this work, a new model is proposed to predict the gas permeability of MMMs, considering the role of interface voids between the polymer matrix and inorganic fillers. The new model is developed based on an analogy with a model derived for thermal conduction through the particulate composites using effective medium theory. The new model is validated using the gas permeability data of four sets of MMMs containing spherical micro- or nano-fillers reported in the literature. The results show an excellent agreement between new model predictions and gas permeability experimental data with deviations lower than 10% in comparison with the other models (29–43%). In addition, the value of the thickness of the interface voids layer for MMMs, which is difficult to directly determine by experimental methods, is correctly predicted using the new model. Therefore, a new theoretical model named as renovated Maxwell model considering the effect of filler/polymer interface voids is developed to accurately predict the gas permeability of MMMs.

GAS PERMEABILITY IN POROUS MEDIA WITH ROUGH SURFACES BY FRACTAL-MONTE CARLO SIMULATIONS

Gas permeability is an important parameter for gas transport in microporous and nanoporous media. A probability model of gas permeability of fractal porous media with rough surfaces is proposed and numerically simulated by the Monte Carlo technique. This model consists of two gas flow mechanisms: the Poiseuille flow and the Knudsen flow, and can be expressed by structural parameters, such as the pore fractal dimension, the tortuosity fractal dimension, the relative roughness and porosity. The validity of the proposed model is investigated through the available experimental data, and a good agreement is obtained. The predicted results indicate that gas permeability of microporous and nanoporous media with rough surfaces decreases with the increase of the relative roughness and the tortuosity fractal dimension, and increases with the increase of porosity and the pore fractal dimension. Our gas permeability model could reveal the physical mechanisms of gas transport in porous media with rough surfaces.

Implementation and validation of pressure-dependent gas permeability model for bentonite in FEM code Thebes

In an Engineered Barrier System of a nuclear waste repository, gas migrates through: a) diffusion/advection of dissolved gases, b) two-phase continuum flow, c) dilatant pathway flow and d) single-phase gas flow through macro-fractures in the soil. The gas production rate and the corresponding gas pressure accumulation affect the clay material behaviour and its properties such as air entry value. For the safe design of the EBS system, computational models need to account for the identified transport mechanisms. This study presents an enhancement in the finite element code Thebes [1, 2] that replicates the observed increase in permeability at higher gas pressures, e.g. due to pore dilatancy and gas fracture as proposed by Xu et al. [3]. The formulation links permeability to gas pressure and threshold/critical pressure. For model validation, the study utilizes a gas injection experiment carried out in IfG (Institute for Rock Mechanics, Germany) on Opalinus Clay [4]. The results show a good fit against the measurements while giving insight into gas flow through clays.

Design of a Gas Permeation and Pervaporation Membrane Model for an Open Source Process Simulation Tool.

Gas permeation and pervaporation are technologies that emerged several decades ago. Even though they have discovered increasing popularity for industrial separation processes, they are not represented equally within process simulation tools except for commercial systems. The availability of such a numerical solution shall be extended due to the design of a membrane model with Visual Basic based on the solution-diffusion model. Although this works approach is presented for a specific process simulator application, the algorithm can generally be transferred to any other programming language and process simulation solver, which allows custom implementations or modeling. Furthermore, the modular design of the model enables its further development by operators through the integration of physical effects. A comparison with experimental data of gas permeation and pervaporation applications as well as other published simulation data delivers either good accordance with the results or negligible deviations of less than 1% from other data.

CO2 separation of fluorinated 6FDA-based polyimides, performance-improved ZIF-incorporated mixed matrix membranes and gas permeability model evaluations

In this study, we compare a newly introduced high free volume fluorinated 6FDA-polyimide, namely 6FDA-bisP, with excellent gas separation properties (CO2 permeability, PCO2 of 35.3 Barrer; CO2/CH4 selectivity, αCO2/CH4 of 25.5) to the well-investigated, lower free volume 6FDA-ODA (PCO2 = 25.9 Barrer; αCO2/CH4 = 20.6). Their gas separation performances were improved in the form of mixed matrix membranes (MMMs) with size sieving zeolitic imidazolate framework (ZIF-8, particle range of <160 nm) addition between 5 and 20 wt% loadings. XRD, BET, FTIR, TGA, DSC, SEM, and TEM were used to characterize the nanoparticles and MMMs. Solid density was obtained from He pycnometry analysis (pressurized cycle test between 2 and 20 bar at 20 °C) to calculate the free fractional volume (FFV). Using an equimolar CO2 and CH4 mixture, gas separation performance was evaluated at a constant 5 bar, at 25 °C. The optimum loading was achieved at 15 wt% for 6FDA-bisP with MMM performance of PCO2 = 81.2 Barrer and αCO2/CH4 = 35.0, whereas 10 wt% for 6FDA-ODA (PCO2 = 42.2 Barrer; αCO2/CH4 = 44.8). The MMMs showed superior performances than the currently relevant polymers in industrial separation processes. Four different gas permeability models: Maxwell, Maxwell-Wagner-Sillar, Higuchi and Lewis Nielsen, were utilized to analyze the obtained data.

Functionalized organic filler based integrated membranes for environmental remediation.

Mixed matrix membranes (MMMs) are synthesized for efficient CO2 separation released from various anthropogenic sources, which are due to global environmental concerns. The synergetic effect of porous nitrogen-rich, CO2-philic filler and polymer in mixed matrix-based membranes (MMMs) can separate CO2 competent. The development of various loadings of porphyrin poly(N-isopropyl Acryl Amide) (P-NIPAM)as functionalized organic fillers (5-20%) in polysulfone (PSU) through solution casting is carried out followed by the various characterizations including field emission scanning electron microscopy (FESEM), X-ray diffraction analysis (XRD), Fourier Transform Infrared Spectrometer(FT-IR) analysis and pure and mixed gas permeations ranging from 2 to 10bar feed pressure. Due to both organic species interactions in the matrix, well-distributed fillers and homogenous surfaces, and cross-sectional structures were observed due to π-π interactions and Lewis's basic functionalities. The strong affinity of porous nitrogen-rich and CO2-philic fillers through gas permeation analysis showed high CO2/CH4 and CO2/N2 gas performance that surpassed Robeson's upper bound limit. Comparatively, MMMs showed improved CO2/CH4 permeabilities from 87.5±0.5 Barrer to 88.2±0.9 Barrer than pure polymer matrix. For CO2/N2, CO2 permeabilities improved to 75±0.8 Barrer than pure polymer matrix. For both gas pairs (CO2/CH4, CO2/N2), respective pureselectivities (84%; 86%) and binary selectivities (85% and 85%)were improved. Various theoretical gas permeation models were used to predict CO2 permeabilities for MMMs from which the modified Maxwell-Wagner-Sillar model showed the least AARE% of 0.87. The results showed promising results for efficient CO2 separation due to exceptional functionalized P-PNIPAM affinitive properties. Finally, cost analysis reflected the inflated cost of membranes production for industrial setup using indigenous resources.

Influences of gas permeation with adsorption effect on the transient thermal insulation performance of silica aerogel at pressure and temperature differences

Silica aerogel is a thermal protective material for an outer space launch under aerodynamic heating, significant temperature difference, and pressure gradient conditions. This paper proposes a gas permeation model by considering the gas adsorption effect for silica aerogel under pressure differences. The gas (N2) adsorption behavior of silica aerogel is simulated by the grand canonical Monte Carlo method. This simulation provides the concentration of the adsorbate gas layer and the average thickness of adsorbate gas in the nanopore. An unsteady-state heat transfer model within silica aerogel, coupling with the acquired gas diffusion effect, heat conduction, and thermal radiation, is developed to study the thermal insulation performance. The gas permeation with the gas adsorption inside silica aerogel exerts a prominent influence on the dynamic temperature response of the hot surface. At the temperature of 77–90 K, the gas adsorption has a remarkable impact on the gas permeation within silica aerogel, which would finally affect the energy migration. The order of the coefficient changes from 10−14 to 10−10 m2. In contrast, the adsorption effect is negligible at the temperature of 298–1300 K. When the gas diffusion and heat transfer directions are opposite, gas diffusion will impede heat transfer, and thus the thermal insulation performance will be improved up to 88.94% and 25.65% at unsteady- and steady-state, respectively.

Interfacial layer thickness is a key parameter in determining the gas separation properties of spherical nanoparticles-mixed matrix membranes: A modeling perspective

The existing traditional models cannot accurately predict the gas permeability of spherical nanoparticle-mixed matrix membranes (SP-MMMs) due to ignoring the physical and chemical characteristics of the SP/matrix interface. In this paper, first, a new model is derived for the prediction of thermal conductivity of SP-polymer composites according to multiple scattering theory. Then, a new theoretical model for gas permeability of SP-MMMs is developed based on the analogy with the derived model for the prediction of thermal conductivity. The significant feature of the new model is its ability to quantify the crucial role of SPs/matrix interface in gas permeability by introducing a new dense interfacial layer thickness (aint) parameter, which increases with increasing the strength of interfacial interactions. It is demonstrated that the value of aint is independent of the nature of gas molecules and mathematically correlated to the strength of SPs/matrix interfacial interactions. Finally, the gas permeability of SP-MMMs is accurately predicted by inserting the values of non-adjustable aint parameter, obtained from the correlation, diameter of SPs as well as the gas permeability of matrix into the new model, without using any adjustable parameter. Moreover, this technique can be utilized to determine the dense interfacial layer thickness in SP-polymer composites using gas permeation data.

Gas Permeability Model for Porous Materials from Underground Coal Gasification Technology

Underground coal gasification (UCG) technology converts deep coal resources into synthesis gas for use in the production of electricity, fuels and chemicals. This study provides an overview of the systematic methods of the in situ coal gasification process. Furthermore, the model of the porous structure of coal has been presented and the gas movement taking place in the carbon matrix—which is part of the bed—has been described. The experimental tests were carried out with the use of air forced through the nozzle in the form of a gas stream spreading in many directions in a porous bed under bubbling conditions. The gas flow resistance coefficient was determined as a function of the Reynolds number in relation to the diameter of the gas flow nozzle. The proprietary calculation model was compared to the models of many researchers, indicating a characteristic trend of a decrease in the gas flow resistance coefficient with an increase in Reynolds number. The novelty of the study is the determination of the permeability characteristics of char (carbonizate) in situ in relation to melted waste rock in situ, taking into account the tortuosity and gas permeability factors for an irregularly shaped solid.

Cyclic olefin copolymer (COC)-metal organic framework (MOF) mixed matrix membranes (MMMs) for H2/CO2 separation

In this study, thermoplastic based mixed matrix membranes (MMMs) were prepared by using cyclic olefin copolymer (COC) and two different metal organic frameworks (MOFs), HKUST-1 and MIL-53(Al) via solution mixing (SM) and melt processing (MP) methods. Structural and physical properties of COC, MOFs, and MMMs were characterized by SEM, XRD, TGA, and DMA methods. H2 and CO2 permeability values of MMMs were measured and ideal selectivity values (α) for H2/CO2 were determined. Characterization studies confirmed that the both preparation methods yielded a strong interfacial adhesion between MOF particles and COC. Different semi-empirical gas permeation models including the Maxwell, Maxwell‐Wagner‐Sillar, Bruggeman, Pal, Lewis‐Nielson, and Higuchi equations were used to fit relative increase in the gas permeation values of H2 as a function of volume fraction of HKUST-1. It was found that the Higuchi model was successfully fit the increase in H2 permeability. Loadings of 40 wt% of HKUST-1 and MIL-53 (Al) increased the H2 permeability by 85 % and 59 %, respectively and significantly improved the ideal selectivity (α) of H2/CO2, compared to COC. The gas separation performances of MMMs implied that the both series of COC/MOF membranes surpassed the Robeson's 2008 upper bound for H2/CO2 separation.

An Apparent Gas Permeability Model for Real Gas Flow in Fractured Porous Media with Roughened Surfaces.

The investigation of gas transport in fractured porous media is essential in most petroleum and chemical engineering. In this paper, an apparent gas permeability model for real gas flow in fractured porous media is derived with adequate consideration of real gas effect, the roughness of fracture surface, and Knudsen diffusion based on the fractal theory. The fractal apparent gas permeability model is obtained to be a function of micro-structural parameters of fractured porous media, relative roughness, the pressure, the temperature, and the properties of gas. The predictions from the apparent gas permeability model based on the fractal theory match well with the published permeability model and experimental data, which verifies the rationality of the present fractal apparent gas permeability model.

Towards a systematic determination of multicomponent gas separation with membranes: the case of CO2/CH4 in cellulose acetates

This work aims at obtaining a systematic description and prediction of the multicomponent gas separation behavior of membranes, using the Non-Equilibrium Lattice Fluid (NELF) model for gas sorption and the Standard Transport (ST) model for gas permeation. The scheme is applied to a comprehensive analysis of CO2/CH4 separation with cellulose acetate membranes. A dedicated experimental campaign (pressure-volume-temperature (PVT), differential scanning calorimetry (DSC) and pure gas sorption tests) was performed to obtain reliable model parameters, accounting also for crystallinity. The approach was validated against a complete set of literature data, including mixed gas sorption and permeation.The parameters obtained were used to perform predictive simulations of mixed CO2/CH4 sorption and permeation in a wide mixture composition range. The NELF model accurately predicts the effect of temperature on sorption, as well as the strong competitive exclusion of CH4 when CO2 is present, that enhances the solubility-selectivity. The ST model correctly estimates the experimentally observed lower-than-ideal CO2/CH4 perm-selectivity. The model shows that low perm-selectivity is due to mixed gas diffusivity-selectivity (which is not available experimentally): even though solubility-selectivity increases in the mixed gas case, diffusivity-selectivity suffers a larger departure from pure gas conditions, ultimately leading to a lower perm-selectivity under multicomponent conditions.

Effect of silica nanoparticles on carbon dioxide separation performances of PVA/PEG cross-linked membranes

Novel PVA/PEG cross-linked membranes were prepared with (0–20 wt. %) of silica nanoparticles. The presence of both the polymers and additive was confirmed by FTIR analysis. The thermal properties of the membranes were analyzed by TGA and DSC analysis. The morphological and mechanical properties of the membranes were studied by SEM analysis and tensile testing, respectively. The gas permeation performances of the membranes were examined using state-of-the-art gas permeability cell. It was found that permeability of all the gases increased with the increase of silica loading, whereas ideal selectivity of carbon dioxide with respect to nitrogen and methane increased up to 10 wt. % loading and then became nearly constant on further loading. 20 wt. % silica loaded membrane was found to be the best performance membrane. The gas permeability of CO2 was also compared with different gas permeation models and was found to be in close agreement with Maxwell Model. The effect of temperature and pressure of feed gas pressure was also studied on permeation performances and optimum performances were achieved around 65 °C. The gas permeation performances were observed to decrease slightly with the increase in feed gas pressure up to 20 bar which confirms the absence of plasticization phenomenon up to 20 bar. Finally, gas permeation performances were compared with 2008 Robeson trade-off lines and it was found that at 20 wt. % loading, gas permeation performances surpassed the trade-off line for CO2/N2, and for CO2/CH4, the gas permeation performances approached the trade-off line.

A model to predict the solubility and permeability of gaseous penetrant in the glassy polymeric membrane at high pressure

AbstractIn this work, the transport properties of gaseous penetrant through several dense glassy polymeric membranes are studied. The nonequilibrium lattice fluid (NELF) in conjunction with the modified Fick's law and dual mode sorption model was used to simulate the gas transport in glassy polymeric membranes. The approach is based on the sorption, diffusion, in which solubility is calculated based on the NELF model, and diffusion coefficient is obtained from the product thermodynamic coefficient and molecular mobility. The governing equation is solved by the finite element method using COMSOL multi‐physics software. The developed model for gas permeability of glassy polymeric membrane can be applied in a wide range of pressure and temperature. The comparison of the calculated permeability and solubility of gasses with the experimental data represented the ability of the developed model. Increasing feed gas temperature increases the gas permeability, while this variation leads to lower gas solubility in the glassy polymeric membranes. The effect of feed temperature and pressure on permeability and solubility is investigated, and the experimental data from literature are described by the developed model. A good prediction of the experimental data can be observed over the considered condition.

Gas Permeation Model of Mixed-Matrix Membranes with Embedded Impermeable Cuboid Nanoparticles.

In the packaging industry, the barrier property of packaging materials is of paramount importance. The enhancement of barrier properties of materials can be achieved by adding impermeable nanoparticles into thin polymeric films, known as mixed-matrix membranes (MMMs). Three-dimensional numerical simulations were performed to study the barrier property of these MMMs and to estimate the effective membrane gas permeability. Results show that horizontally-aligned thin cuboid nanoparticles offer far superior barrier properties than spherical nanoparticles for an identical solid volume fraction. Maxwell’s model predicts very well the relative permeability of spherical and cubic nanoparticles over a wide range of the solid volume fraction. However, Maxwell’s model shows an increasingly poor prediction of the relative permeability of MMM as the aspect ratio of cuboid nanoparticles tends to zero or infinity. An artificial neural network (ANN) model was developed successfully to predict the relative permeability of MMMs as a function of the relative thickness and the relative projected area of the embedded nanoparticles. However, since an ANN model does not provide an explicit form of the relation of the relative permeability with the physical characteristics of the MMM, a new model based on multivariable regression analysis is introduced to represent the relative permeability in a MMM with impermeable cuboid nanoparticles. The new model possesses a simple explicit form and can predict, very well, the relative permeability over an extensive range of the solid volume fraction and aspect ratio, compared with many existing models.

Plasticization Modeling in Cellulose Acetate/NaY Mixed Matrix Membranes

The plasticization of mixed matrix membranes (MMMs) in the presence of solid particles differs from pure glassy polymeric membranes. This study aims to develop a mathematical model for gas permeability in the glassy polymer/nano-porous filler MMMs, considering the plasticization phenomenon in the presence of the solid particles. The diffusivity of each component is assumed to be a function of the plasticization in the presence of nano-porous fillers. The partial immobilization model with the insertion of filler contributions in gas solubility of MMMs is also applied to determine the fraction of sorbed mobile gases. In this case, the model parameters were determined by fitting the experimental data of cellulose acetate/sodium Y zeolite (CA/NaY) MMMs for CO2 /N2 separation. The results showed that the plasticization parameter (β) is reduced by increasing the zeolite content in the MMMs, both for CO2 and N2 gases. The MMM plasticization declined by a shift in the plasticization pressure towards larger values. Except for the MMM with 20 wt.% NaY content, CO2 - induced plasticization fugacities of all the MMMs were best modeled with a relative error of less than 8%. Moreover, an acceptable mean relative error of 7.57% was obtained for all the MMMs containing 0-20 wt. % NaY. Statistical analysis with calculating the Pearson correlation’s parameters showed a direct and strong relationship between the two coefficients C′HA and b. Furthermore, it revealed a close relationship between all other coefficients, while no relationships were observed between D0 and β, and also, F and D0 for both the CO2 and N2 gases, maybe because of the small sizes of these coefficients. The zeolite particles play a role of anti-plasticizer. Additionally, by increasing the zeolite loading, the gas diffusivity variations in the membranes decreased. This reduction is another sign of the plasticization reduction in the MMMs as compared to the pure glassy membranes.